Practice exam - Apartment applicants

www.PredictiveInsightsAI.com

#NO CHANGES NEEDED
set.seed(1)
library(knitr)
library(broom)
library(ggplot2)
library(plyr)
library(corrplot)
library(caret)
library(gridExtra)
library(scales)
library(Rmisc)
library(randomForest)
library(psych)
library(xgboost)
library(rpart)
library(rpart.plot)
library(randomForest)
library(tidyverse)
theme_set(theme_minimal())

# 1. Disable the broken uv temp stuff
Sys.setenv(RETICULATE_UV_ENABLED = "0")
# 2. Tell reticulate the full path to your real Python 3.13.2
reticulate::use_python("C:/Users/casti/AppData/Local/Programs/Python/Python313/python.exe", required = TRUE)
# 3. Restart R session inside RStudio
#.rs.restartR()

library(reticulate)
datasets <- import("datasets")
# Load the dataset
ds <- datasets$load_dataset("supersam7/apartment_apps")
df <- ds["train"]$to_pandas()    # or ds$train$to_pandas() also works
df <- df[-1]
head(df)

  applicants sale_price num_units year_sold month_sold overall_qual
1          3     208500         4      2008          2            7
2          5     181500         5      2007          5            6
3          3     223500         1      2008          9            7
4          4     140000         3      2011          2            7
5          5     250000         5      2008         12            8
6          5     143000         3      2009         10            5
  total_sq_feet gr_liv_area tot_bathrooms lot_area exter_qual full_bath
1      3586.886    2785.060             5 3898.256          4         4
2      3560.348    2315.267             3 4149.410          3         4
3      3672.314    2852.313             5 4461.603          4         4
4      3527.523    2791.378             3 4139.131          3         2
5      4012.276    3173.357             5 4928.292          4         4
6      3308.431    2433.181             3 4908.174          3         2
  central_air garage_type_attchd garage_type_basment garage_type_builtIn
1         yes                  1                   0                   0
2         yes                  1                   0                   0
3         yes                  1                   0                   0
4         yes                  0                   0                   0
5         yes                  1                   0                   0
6         yes                  1                   0                   0
  garage_type_detchd garage_type_no_garage NeighborhoodBrDale
1                  0                     0                  0
2                  0                     0                  0
3                  0                     0                  0
4                  1                     0                  0
5                  0                     0                  0
6                  0                     0                  0
  neighborhood_brk_side neighborhood_clear_cr neighborhood_collg_cr
1                     0                     0                     1
2                     0                     0                     0
3                     0                     0                     1
4                     0                     0                     0
5                     0                     0                     0
6                     0                     0                     0
  neighborhood_crawfor neighborhood_edwards neighborhood_gilbert
1                    0                    0                    0
2                    0                    0                    0
3                    0                    0                    0
4                    1                    0                    0
5                    0                    0                    0
6                    0                    0                    0
  neighborhood_idottrr neighborhood_meadowv neighborhood_mitchel
1                    0                    0                    0
2                    0                    0                    0
3                    0                    0                    0
4                    0                    0                    0
5                    0                    0                    0
6                    0                    0                    1
  neighborhood_n_ames neighborhood_n_ridge neighborhood_n_ridge_hghts
1                   0                    0                          0
2                   0                    0                          0
3                   0                    0                          0
4                   0                    0                          0
5                   0                    1                          0
6                   0                    0                          0
  neighborhood_n_w_ames neighborhood_old_town neighborhood_sawyer
1                     0                     0                   0
2                     0                     0                   0
3                     0                     0                   0
4                     0                     0                   0
5                     0                     0                   0
6                     0                     0                   0
  neighborhood_sawyer_w neighborhood_somerst neighborhood_stone_br
1                     0                    0                     0
2                     0                    0                     0
3                     0                    0                     0
4                     0                    0                     0
5                     0                    0                     0
6                     0                    0                     0
  neighborhood_swisu neighborhood_timber neighborhood_veenker
1                  0                   0                    0
2                  0                   0                    1
3                  0                   0                    0
4                  0                   0                    0
5                  0                   0                    0
6                  0                   0                    0
  neighborhood_saleprice
1               198517.7
2               245890.6
3               198517.7
4               213681.7
5               331835.3
6               157755.8

Set up

Your assistant has provided you with these code templates.

#This function will calculate the log-liklihood based on a Poisson model for the number of applicants
LLfunction <- function(targets, predicted_values){
  p_v_zero <- ifelse(predicted_values <= 0, 0, predicted_values)
  p_v_pos <- ifelse(predicted_values <= 0, 0.000001 ,predicted_values)
  return(sum(targets*log(p_v_pos)) - sum(p_v_zero))
}
print("loglikelihood")
LLfunction(test$applicants,predictions)

This code creates a scatter plot, a box plot, and a histogram.

#create a boxplot
ggplot(df, aes(as.factor(applicants),VARIABLE)) + 
  geom_boxplot()

#create a scatterplot
ggplot(df,aes(applicants,VARIABLE)) + 
  geom_point()

#create a histogram
ggplot(df,aes(VARIABLE)) + 
  geom_histogram()

#create a bar plot
ggplot(df, aes(VARIABLE)) + 
  geom_bar(stat = "count")

Shows the average number of applicants across factor levels.

#Average number of health applicants per unit
df %>% 
  group_by(VARIABLE) %>% 
  summarise(
    average_num_applicants = sum(applicants*num_units)/sum(num_units)
  )

Converts variables to numeric or factor while also setting the base reference level to the value which has the most observations.

##Convert to factor and set factor levels
df <- df %>% mutate(VARIABLE = fct_infreq(as.character(VARIABLE))

#Using Base R
df$VARIABLE = fct_infreq(as.character(df$VARIABLE))

#Convert to numeric
df <- df %>% mutate(VARIABLE = fct_infreq(as.characterVARIABLE))

#Using Base R
df$VARIABLE = as.numeric(df$VARIABLE)

Task 1 - Examine the target variable and number of units

glimpse(df)

Rows: 1,430
Columns: 41
$ applicants                 <dbl> 3, 5, 3, 4, 5, 5, 5, 5, 2, 3, 1, 6, 1, 5, 3…
$ sale_price                 <dbl> 208500, 181500, 223500, 140000, 250000, 143…
$ num_units                  <dbl> 4, 5, 1, 3, 5, 3, 1, 3, 5, 4, 3, 1, 5, 2, 5…
$ year_sold                  <dbl> 2008, 2007, 2008, 2011, 2008, 2009, 2007, 2…
$ month_sold                 <dbl> 2, 5, 9, 2, 12, 10, 8, 11, 4, 1, 2, 7, 9, 8…
$ overall_qual               <dbl> 7, 6, 7, 7, 8, 5, 8, 7, 7, 5, 5, 9, 5, 7, 6…
$ total_sq_feet              <dbl> 3586.886, 3560.348, 3672.314, 3527.523, 401…
$ gr_liv_area                <dbl> 2785.060, 2315.267, 2852.313, 2791.378, 317…
$ tot_bathrooms              <dbl> 5, 3, 5, 3, 5, 3, 4, 5, 3, 3, 3, 5, 3, 3, 3…
$ lot_area                   <dbl> 3898.256, 4149.410, 4461.603, 4139.131, 492…
$ exter_qual                 <dbl> 4, 3, 4, 3, 4, 3, 4, 3, 3, 3, 3, 5, 3, 4, 3…
$ full_bath                  <dbl> 4, 4, 4, 2, 4, 2, 4, 4, 4, 2, 2, 6, 2, 4, 2…
$ central_air                <chr> "yes", "yes", "yes", "yes", "yes", "yes", "…
$ garage_type_attchd         <dbl> 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 0, 0, 0, 1, 1…
$ garage_type_basment        <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$ garage_type_builtIn        <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0…
$ garage_type_detchd         <dbl> 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0…
$ garage_type_no_garage      <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$ NeighborhoodBrDale         <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$ neighborhood_brk_side      <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0…
$ neighborhood_clear_cr      <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$ neighborhood_collg_cr      <dbl> 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0…
$ neighborhood_crawfor       <dbl> 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$ neighborhood_edwards       <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$ neighborhood_gilbert       <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$ neighborhood_idottrr       <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$ neighborhood_meadowv       <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$ neighborhood_mitchel       <dbl> 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$ neighborhood_n_ames        <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1…
$ neighborhood_n_ridge       <dbl> 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$ neighborhood_n_ridge_hghts <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0…
$ neighborhood_n_w_ames      <dbl> 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0…
$ neighborhood_old_town      <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0…
$ neighborhood_sawyer        <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0…
$ neighborhood_sawyer_w      <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$ neighborhood_somerst       <dbl> 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0…
$ neighborhood_stone_br      <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$ neighborhood_swisu         <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$ neighborhood_timber        <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$ neighborhood_veenker       <dbl> 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$ neighborhood_saleprice     <dbl> 198517.7, 245890.6, 198517.7, 213681.7, 331…

summary(df)

   applicants      sale_price       num_units       year_sold   
 Min.   :0.000   Min.   : 34900   Min.   :1.000   Min.   :2007  
 1st Qu.:2.000   1st Qu.:129600   1st Qu.:1.000   1st Qu.:2008  
 Median :4.000   Median :163000   Median :2.000   Median :2009  
 Mean   :3.633   Mean   :181069   Mean   :2.685   Mean   :2009  
 3rd Qu.:5.000   3rd Qu.:214375   3rd Qu.:4.000   3rd Qu.:2010  
 Max.   :7.000   Max.   :755000   Max.   :5.000   Max.   :2011  
   month_sold      overall_qual    total_sq_feet   gr_liv_area    
 Min.   : 1.000   Min.   : 1.000   Min.   : 311   Min.   : 261.6  
 1st Qu.: 5.000   1st Qu.: 5.000   1st Qu.:3193   1st Qu.:2139.6  
 Median : 6.000   Median : 6.000   Median :3528   Median :2547.0  
 Mean   : 6.329   Mean   : 6.082   Mean   :3510   Mean   :2511.2  
 3rd Qu.: 8.000   3rd Qu.: 7.000   3rd Qu.:3852   3rd Qu.:2852.3  
 Max.   :12.000   Max.   :10.000   Max.   :5171   Max.   :4273.5  
 tot_bathrooms      lot_area         exter_qual     full_bath    
 Min.   :1.000   Min.   :  465.9   Min.   :2.00   Min.   :0.000  
 1st Qu.:3.000   1st Qu.: 3725.6   1st Qu.:3.00   1st Qu.:2.000  
 Median :3.000   Median : 4138.8   Median :3.00   Median :4.000  
 Mean   :2.952   Mean   : 4070.4   Mean   :3.39   Mean   :3.115  
 3rd Qu.:3.000   3rd Qu.: 4529.0   3rd Qu.:4.00   3rd Qu.:4.000  
 Max.   :8.000   Max.   :10271.5   Max.   :5.00   Max.   :6.000  
 central_air        garage_type_attchd garage_type_basment garage_type_builtIn
 Length:1430        Min.   :0.0000     Min.   :0.00000     Min.   :0.00000    
 Class :character   1st Qu.:0.0000     1st Qu.:0.00000     1st Qu.:0.00000    
 Mode  :character   Median :1.0000     Median :0.00000     Median :0.00000    
                    Mean   :0.5888     Mean   :0.01329     Mean   :0.06084    
                    3rd Qu.:1.0000     3rd Qu.:0.00000     3rd Qu.:0.00000    
                    Max.   :1.0000     Max.   :1.00000     Max.   :1.00000    
 garage_type_detchd garage_type_no_garage NeighborhoodBrDale
 Min.   :0.0000     Min.   :0.00000       Min.   :0.00000   
 1st Qu.:0.0000     1st Qu.:0.00000       1st Qu.:0.00000   
 Median :0.0000     Median :0.00000       Median :0.00000   
 Mean   :0.2699     Mean   :0.05664       Mean   :0.01119   
 3rd Qu.:1.0000     3rd Qu.:0.00000       3rd Qu.:0.00000   
 Max.   :1.0000     Max.   :1.00000       Max.   :1.00000   
 neighborhood_brk_side neighborhood_clear_cr neighborhood_collg_cr
 Min.   :0.00000       Min.   :0.00000       Min.   :0.0000       
 1st Qu.:0.00000       1st Qu.:0.00000       1st Qu.:0.0000       
 Median :0.00000       Median :0.00000       Median :0.0000       
 Mean   :0.04056       Mean   :0.01958       Mean   :0.1049       
 3rd Qu.:0.00000       3rd Qu.:0.00000       3rd Qu.:0.0000       
 Max.   :1.00000       Max.   :1.00000       Max.   :1.0000       
 neighborhood_crawfor neighborhood_edwards neighborhood_gilbert
 Min.   :0.00000      Min.   :0.00000      Min.   :0.00000     
 1st Qu.:0.00000      1st Qu.:0.00000      1st Qu.:0.00000     
 Median :0.00000      Median :0.00000      Median :0.00000     
 Mean   :0.03566      Mean   :0.06853      Mean   :0.05524     
 3rd Qu.:0.00000      3rd Qu.:0.00000      3rd Qu.:0.00000     
 Max.   :1.00000      Max.   :1.00000      Max.   :1.00000     
 neighborhood_idottrr neighborhood_meadowv neighborhood_mitchel
 Min.   :0.00000      Min.   :0.00000      Min.   :0.00000     
 1st Qu.:0.00000      1st Qu.:0.00000      1st Qu.:0.00000     
 Median :0.00000      Median :0.00000      Median :0.00000     
 Mean   :0.02587      Mean   :0.01189      Mean   :0.03427     
 3rd Qu.:0.00000      3rd Qu.:0.00000      3rd Qu.:0.00000     
 Max.   :1.00000      Max.   :1.00000      Max.   :1.00000     
 neighborhood_n_ames neighborhood_n_ridge neighborhood_n_ridge_hghts
 Min.   :0.0000      Min.   :0.00000      Min.   :0.00000           
 1st Qu.:0.0000      1st Qu.:0.00000      1st Qu.:0.00000           
 Median :0.0000      Median :0.00000      Median :0.00000           
 Mean   :0.1573      Mean   :0.02867      Mean   :0.05385           
 3rd Qu.:0.0000      3rd Qu.:0.00000      3rd Qu.:0.00000           
 Max.   :1.0000      Max.   :1.00000      Max.   :1.00000           
 neighborhood_n_w_ames neighborhood_old_town neighborhood_sawyer
 Min.   :0.00000       Min.   :0.00000       Min.   :0.00000    
 1st Qu.:0.00000       1st Qu.:0.00000       1st Qu.:0.00000    
 Median :0.00000       Median :0.00000       Median :0.00000    
 Mean   :0.05105       Mean   :0.07902       Mean   :0.05175    
 3rd Qu.:0.00000       3rd Qu.:0.00000       3rd Qu.:0.00000    
 Max.   :1.00000       Max.   :1.00000       Max.   :1.00000    
 neighborhood_sawyer_w neighborhood_somerst neighborhood_stone_br
 Min.   :0.00000       Min.   :0.00000      Min.   :0.00000      
 1st Qu.:0.00000       1st Qu.:0.00000      1st Qu.:0.00000      
 Median :0.00000       Median :0.00000      Median :0.00000      
 Mean   :0.04126       Mean   :0.06014      Mean   :0.01748      
 3rd Qu.:0.00000       3rd Qu.:0.00000      3rd Qu.:0.00000      
 Max.   :1.00000       Max.   :1.00000      Max.   :1.00000      
 neighborhood_swisu neighborhood_timber neighborhood_veenker
 Min.   :0.00000    Min.   :0.00000     Min.   :0.000000    
 1st Qu.:0.00000    1st Qu.:0.00000     1st Qu.:0.000000    
 Median :0.00000    Median :0.00000     Median :0.000000    
 Mean   :0.01748    Mean   :0.02657     Mean   :0.007692    
 3rd Qu.:0.00000    3rd Qu.:0.00000     3rd Qu.:0.000000    
 Max.   :1.00000    Max.   :1.00000     Max.   :1.000000    
 neighborhood_saleprice
 Min.   :101389        
 1st Qu.:136902        
 Median :181841        
 Mean   :180909        
 3rd Qu.:198518        
 Max.   :331835        

sum(df$num_units)

[1] 3839

sum(df$num_units*df$applicants)/sum(df$num_units)

[1] 3.588695

df %>% summarise(avg_applicants = sum(applicants*num_units)/sum(num_units))

  avg_applicants
1       3.588695

#NO CODE CHANGES NEEDED
df %>% 
  group_by(applicants) %>% 
  summarise(total_units = sum(num_units))

# A tibble: 8 × 2
  applicants total_units
       <dbl>       <dbl>
1          0         152
2          1         360
3          2         532
4          3         898
5          4         487
6          5        1028
7          6         103
8          7         279

#Graph A: Histogram
ggplot(data=df, aes(applicants)) +
        geom_histogram()

`stat_bin()` using `bins = 30`. Pick better value `binwidth`.

#Graph B: Bar plot
df %>% 
  mutate(applicants = as.factor(applicants)) %>% 
  group_by(applicants) %>% 
  summarise(
    total_units = sum(num_units)
  ) %>% 
  ungroup() %>% 
  ggplot(aes(x=applicants, y=total_units)) + 
  geom_bar(stat="identity") 

Task 2 - Explore the predictor variables

# Task 2 - Explore the predictor variables – FIXED VERSION
summary(df)

   applicants      sale_price       num_units       year_sold   
 Min.   :0.000   Min.   : 34900   Min.   :1.000   Min.   :2007  
 1st Qu.:2.000   1st Qu.:129600   1st Qu.:1.000   1st Qu.:2008  
 Median :4.000   Median :163000   Median :2.000   Median :2009  
 Mean   :3.633   Mean   :181069   Mean   :2.685   Mean   :2009  
 3rd Qu.:5.000   3rd Qu.:214375   3rd Qu.:4.000   3rd Qu.:2010  
 Max.   :7.000   Max.   :755000   Max.   :5.000   Max.   :2011  
   month_sold      overall_qual    total_sq_feet   gr_liv_area    
 Min.   : 1.000   Min.   : 1.000   Min.   : 311   Min.   : 261.6  
 1st Qu.: 5.000   1st Qu.: 5.000   1st Qu.:3193   1st Qu.:2139.6  
 Median : 6.000   Median : 6.000   Median :3528   Median :2547.0  
 Mean   : 6.329   Mean   : 6.082   Mean   :3510   Mean   :2511.2  
 3rd Qu.: 8.000   3rd Qu.: 7.000   3rd Qu.:3852   3rd Qu.:2852.3  
 Max.   :12.000   Max.   :10.000   Max.   :5171   Max.   :4273.5  
 tot_bathrooms      lot_area         exter_qual     full_bath    
 Min.   :1.000   Min.   :  465.9   Min.   :2.00   Min.   :0.000  
 1st Qu.:3.000   1st Qu.: 3725.6   1st Qu.:3.00   1st Qu.:2.000  
 Median :3.000   Median : 4138.8   Median :3.00   Median :4.000  
 Mean   :2.952   Mean   : 4070.4   Mean   :3.39   Mean   :3.115  
 3rd Qu.:3.000   3rd Qu.: 4529.0   3rd Qu.:4.00   3rd Qu.:4.000  
 Max.   :8.000   Max.   :10271.5   Max.   :5.00   Max.   :6.000  
 central_air        garage_type_attchd garage_type_basment garage_type_builtIn
 Length:1430        Min.   :0.0000     Min.   :0.00000     Min.   :0.00000    
 Class :character   1st Qu.:0.0000     1st Qu.:0.00000     1st Qu.:0.00000    
 Mode  :character   Median :1.0000     Median :0.00000     Median :0.00000    
                    Mean   :0.5888     Mean   :0.01329     Mean   :0.06084    
                    3rd Qu.:1.0000     3rd Qu.:0.00000     3rd Qu.:0.00000    
                    Max.   :1.0000     Max.   :1.00000     Max.   :1.00000    
 garage_type_detchd garage_type_no_garage NeighborhoodBrDale
 Min.   :0.0000     Min.   :0.00000       Min.   :0.00000   
 1st Qu.:0.0000     1st Qu.:0.00000       1st Qu.:0.00000   
 Median :0.0000     Median :0.00000       Median :0.00000   
 Mean   :0.2699     Mean   :0.05664       Mean   :0.01119   
 3rd Qu.:1.0000     3rd Qu.:0.00000       3rd Qu.:0.00000   
 Max.   :1.0000     Max.   :1.00000       Max.   :1.00000   
 neighborhood_brk_side neighborhood_clear_cr neighborhood_collg_cr
 Min.   :0.00000       Min.   :0.00000       Min.   :0.0000       
 1st Qu.:0.00000       1st Qu.:0.00000       1st Qu.:0.0000       
 Median :0.00000       Median :0.00000       Median :0.0000       
 Mean   :0.04056       Mean   :0.01958       Mean   :0.1049       
 3rd Qu.:0.00000       3rd Qu.:0.00000       3rd Qu.:0.0000       
 Max.   :1.00000       Max.   :1.00000       Max.   :1.0000       
 neighborhood_crawfor neighborhood_edwards neighborhood_gilbert
 Min.   :0.00000      Min.   :0.00000      Min.   :0.00000     
 1st Qu.:0.00000      1st Qu.:0.00000      1st Qu.:0.00000     
 Median :0.00000      Median :0.00000      Median :0.00000     
 Mean   :0.03566      Mean   :0.06853      Mean   :0.05524     
 3rd Qu.:0.00000      3rd Qu.:0.00000      3rd Qu.:0.00000     
 Max.   :1.00000      Max.   :1.00000      Max.   :1.00000     
 neighborhood_idottrr neighborhood_meadowv neighborhood_mitchel
 Min.   :0.00000      Min.   :0.00000      Min.   :0.00000     
 1st Qu.:0.00000      1st Qu.:0.00000      1st Qu.:0.00000     
 Median :0.00000      Median :0.00000      Median :0.00000     
 Mean   :0.02587      Mean   :0.01189      Mean   :0.03427     
 3rd Qu.:0.00000      3rd Qu.:0.00000      3rd Qu.:0.00000     
 Max.   :1.00000      Max.   :1.00000      Max.   :1.00000     
 neighborhood_n_ames neighborhood_n_ridge neighborhood_n_ridge_hghts
 Min.   :0.0000      Min.   :0.00000      Min.   :0.00000           
 1st Qu.:0.0000      1st Qu.:0.00000      1st Qu.:0.00000           
 Median :0.0000      Median :0.00000      Median :0.00000           
 Mean   :0.1573      Mean   :0.02867      Mean   :0.05385           
 3rd Qu.:0.0000      3rd Qu.:0.00000      3rd Qu.:0.00000           
 Max.   :1.0000      Max.   :1.00000      Max.   :1.00000           
 neighborhood_n_w_ames neighborhood_old_town neighborhood_sawyer
 Min.   :0.00000       Min.   :0.00000       Min.   :0.00000    
 1st Qu.:0.00000       1st Qu.:0.00000       1st Qu.:0.00000    
 Median :0.00000       Median :0.00000       Median :0.00000    
 Mean   :0.05105       Mean   :0.07902       Mean   :0.05175    
 3rd Qu.:0.00000       3rd Qu.:0.00000       3rd Qu.:0.00000    
 Max.   :1.00000       Max.   :1.00000       Max.   :1.00000    
 neighborhood_sawyer_w neighborhood_somerst neighborhood_stone_br
 Min.   :0.00000       Min.   :0.00000      Min.   :0.00000      
 1st Qu.:0.00000       1st Qu.:0.00000      1st Qu.:0.00000      
 Median :0.00000       Median :0.00000      Median :0.00000      
 Mean   :0.04126       Mean   :0.06014      Mean   :0.01748      
 3rd Qu.:0.00000       3rd Qu.:0.00000      3rd Qu.:0.00000      
 Max.   :1.00000       Max.   :1.00000      Max.   :1.00000      
 neighborhood_swisu neighborhood_timber neighborhood_veenker
 Min.   :0.00000    Min.   :0.00000     Min.   :0.000000    
 1st Qu.:0.00000    1st Qu.:0.00000     1st Qu.:0.000000    
 Median :0.00000    Median :0.00000     Median :0.000000    
 Mean   :0.01748    Mean   :0.02657     Mean   :0.007692    
 3rd Qu.:0.00000    3rd Qu.:0.00000     3rd Qu.:0.000000    
 Max.   :1.00000    Max.   :1.00000     Max.   :1.000000    
 neighborhood_saleprice
 Min.   :101389        
 1st Qu.:136902        
 Median :181841        
 Mean   :180909        
 3rd Qu.:198518        
 Max.   :331835        

#NO CHANGES NEEDED – weighted averages
df %>%
  summarise(
    mean_number_of_units = sum(num_units),
    mean_sale_price = dollar(sum(num_units*sale_price)/sum(num_units)),
    mean_overall_qual = sum(num_units*overall_qual)/sum(num_units)
  )

  mean_number_of_units mean_sale_price mean_overall_qual
1                 3839        $180,146          6.060172

# ... your plots ...

# FIXED: Keep the original columns, just ADD the logged versions
df <- df %>% 
  mutate(
    log_rel_price   = log(sale_price / neighborhood_saleprice),
    log_sale_price  = log(sale_price)
    # DO NOT drop sale_price or neighborhood_saleprice here!
  )

#overall qual
ggplot(df,aes(overall_qual)) + 
  geom_bar(stat = "count")

df %>% 
  summarise(
    avg = sum(num_units*overall_qual)/sum(num_units)
  ) 

       avg
1 6.060172

df %>% 
  group_by(overall_qual) %>% 
  summarise(
    total_units = sum(num_units)
  ) %>% 
  ggplot(aes(x=overall_qual, y=total_units)) + 
  geom_bar(stat="identity") 

#central air

df %>% 
  group_by(central_air) %>% 
  summarise(
    total_units = sum(num_units)
  ) %>% 
  ggplot(aes(x=central_air, y=total_units)) + 
  geom_bar(stat="identity") 

df %>% 
  group_by(central_air) %>% 
  summarise(
    total_units = sum(num_units)
  ) 

# A tibble: 2 × 2
  central_air total_units
  <chr>             <dbl>
1 no                  269
2 yes                3570

df %>% count(overall_qual)

   overall_qual   n
1             1   2
2             2   3
3             3  20
4             4 116
5             5 397
6             6 363
7             7 305
8             8 165
9             9  43
10           10  16

#check that bae level (the one that appears first) is the one with the most observations
summary(df$central_air)

   Length     Class      Mode 
     1430 character character 

df %>% group_by(central_air) %>% 
  summarise(applicants=sum(applicants),
            total_units = sum(num_units))

# A tibble: 2 × 3
  central_air applicants total_units
  <chr>            <dbl>       <dbl>
1 no                  54         269
2 yes               5141        3570

ggplot(df,aes(as.factor(central_air),applicants)) + 
  geom_boxplot()

df$central_air <- fct_infreq(df$central_air)
summary(df$central_air)

 yes   no 
1335   95 

Task 3 - Engineer three additional features

Code is provided to calculate the average and create box plots of sale_price by year and month.

df <- df %>% 
  mutate(
    sale_price_per_sqft = exp(log_rel_price) / total_sq_feet,
    bath_pr_sqft = tot_bathrooms/total_sq_feet,
    student_apt = ifelse(month_sold %in% c(7,8),1,0)
  )
df %>% count(student_apt)

  student_apt    n
1           0 1079
2           1  351

df %>% summary()

   applicants      sale_price       num_units       year_sold   
 Min.   :0.000   Min.   : 34900   Min.   :1.000   Min.   :2007  
 1st Qu.:2.000   1st Qu.:129600   1st Qu.:1.000   1st Qu.:2008  
 Median :4.000   Median :163000   Median :2.000   Median :2009  
 Mean   :3.633   Mean   :181069   Mean   :2.685   Mean   :2009  
 3rd Qu.:5.000   3rd Qu.:214375   3rd Qu.:4.000   3rd Qu.:2010  
 Max.   :7.000   Max.   :755000   Max.   :5.000   Max.   :2011  
   month_sold      overall_qual    total_sq_feet   gr_liv_area    
 Min.   : 1.000   Min.   : 1.000   Min.   : 311   Min.   : 261.6  
 1st Qu.: 5.000   1st Qu.: 5.000   1st Qu.:3193   1st Qu.:2139.6  
 Median : 6.000   Median : 6.000   Median :3528   Median :2547.0  
 Mean   : 6.329   Mean   : 6.082   Mean   :3510   Mean   :2511.2  
 3rd Qu.: 8.000   3rd Qu.: 7.000   3rd Qu.:3852   3rd Qu.:2852.3  
 Max.   :12.000   Max.   :10.000   Max.   :5171   Max.   :4273.5  
 tot_bathrooms      lot_area         exter_qual     full_bath     central_air
 Min.   :1.000   Min.   :  465.9   Min.   :2.00   Min.   :0.000   yes:1335   
 1st Qu.:3.000   1st Qu.: 3725.6   1st Qu.:3.00   1st Qu.:2.000   no :  95   
 Median :3.000   Median : 4138.8   Median :3.00   Median :4.000              
 Mean   :2.952   Mean   : 4070.4   Mean   :3.39   Mean   :3.115              
 3rd Qu.:3.000   3rd Qu.: 4529.0   3rd Qu.:4.00   3rd Qu.:4.000              
 Max.   :8.000   Max.   :10271.5   Max.   :5.00   Max.   :6.000              
 garage_type_attchd garage_type_basment garage_type_builtIn garage_type_detchd
 Min.   :0.0000     Min.   :0.00000     Min.   :0.00000     Min.   :0.0000    
 1st Qu.:0.0000     1st Qu.:0.00000     1st Qu.:0.00000     1st Qu.:0.0000    
 Median :1.0000     Median :0.00000     Median :0.00000     Median :0.0000    
 Mean   :0.5888     Mean   :0.01329     Mean   :0.06084     Mean   :0.2699    
 3rd Qu.:1.0000     3rd Qu.:0.00000     3rd Qu.:0.00000     3rd Qu.:1.0000    
 Max.   :1.0000     Max.   :1.00000     Max.   :1.00000     Max.   :1.0000    
 garage_type_no_garage NeighborhoodBrDale neighborhood_brk_side
 Min.   :0.00000       Min.   :0.00000    Min.   :0.00000      
 1st Qu.:0.00000       1st Qu.:0.00000    1st Qu.:0.00000      
 Median :0.00000       Median :0.00000    Median :0.00000      
 Mean   :0.05664       Mean   :0.01119    Mean   :0.04056      
 3rd Qu.:0.00000       3rd Qu.:0.00000    3rd Qu.:0.00000      
 Max.   :1.00000       Max.   :1.00000    Max.   :1.00000      
 neighborhood_clear_cr neighborhood_collg_cr neighborhood_crawfor
 Min.   :0.00000       Min.   :0.0000        Min.   :0.00000     
 1st Qu.:0.00000       1st Qu.:0.0000        1st Qu.:0.00000     
 Median :0.00000       Median :0.0000        Median :0.00000     
 Mean   :0.01958       Mean   :0.1049        Mean   :0.03566     
 3rd Qu.:0.00000       3rd Qu.:0.0000        3rd Qu.:0.00000     
 Max.   :1.00000       Max.   :1.0000        Max.   :1.00000     
 neighborhood_edwards neighborhood_gilbert neighborhood_idottrr
 Min.   :0.00000      Min.   :0.00000      Min.   :0.00000     
 1st Qu.:0.00000      1st Qu.:0.00000      1st Qu.:0.00000     
 Median :0.00000      Median :0.00000      Median :0.00000     
 Mean   :0.06853      Mean   :0.05524      Mean   :0.02587     
 3rd Qu.:0.00000      3rd Qu.:0.00000      3rd Qu.:0.00000     
 Max.   :1.00000      Max.   :1.00000      Max.   :1.00000     
 neighborhood_meadowv neighborhood_mitchel neighborhood_n_ames
 Min.   :0.00000      Min.   :0.00000      Min.   :0.0000     
 1st Qu.:0.00000      1st Qu.:0.00000      1st Qu.:0.0000     
 Median :0.00000      Median :0.00000      Median :0.0000     
 Mean   :0.01189      Mean   :0.03427      Mean   :0.1573     
 3rd Qu.:0.00000      3rd Qu.:0.00000      3rd Qu.:0.0000     
 Max.   :1.00000      Max.   :1.00000      Max.   :1.0000     
 neighborhood_n_ridge neighborhood_n_ridge_hghts neighborhood_n_w_ames
 Min.   :0.00000      Min.   :0.00000            Min.   :0.00000      
 1st Qu.:0.00000      1st Qu.:0.00000            1st Qu.:0.00000      
 Median :0.00000      Median :0.00000            Median :0.00000      
 Mean   :0.02867      Mean   :0.05385            Mean   :0.05105      
 3rd Qu.:0.00000      3rd Qu.:0.00000            3rd Qu.:0.00000      
 Max.   :1.00000      Max.   :1.00000            Max.   :1.00000      
 neighborhood_old_town neighborhood_sawyer neighborhood_sawyer_w
 Min.   :0.00000       Min.   :0.00000     Min.   :0.00000      
 1st Qu.:0.00000       1st Qu.:0.00000     1st Qu.:0.00000      
 Median :0.00000       Median :0.00000     Median :0.00000      
 Mean   :0.07902       Mean   :0.05175     Mean   :0.04126      
 3rd Qu.:0.00000       3rd Qu.:0.00000     3rd Qu.:0.00000      
 Max.   :1.00000       Max.   :1.00000     Max.   :1.00000      
 neighborhood_somerst neighborhood_stone_br neighborhood_swisu
 Min.   :0.00000      Min.   :0.00000       Min.   :0.00000   
 1st Qu.:0.00000      1st Qu.:0.00000       1st Qu.:0.00000   
 Median :0.00000      Median :0.00000       Median :0.00000   
 Mean   :0.06014      Mean   :0.01748       Mean   :0.01748   
 3rd Qu.:0.00000      3rd Qu.:0.00000       3rd Qu.:0.00000   
 Max.   :1.00000      Max.   :1.00000       Max.   :1.00000   
 neighborhood_timber neighborhood_veenker neighborhood_saleprice
 Min.   :0.00000     Min.   :0.000000     Min.   :101389        
 1st Qu.:0.00000     1st Qu.:0.000000     1st Qu.:136902        
 Median :0.00000     Median :0.000000     Median :181841        
 Mean   :0.02657     Mean   :0.007692     Mean   :180909        
 3rd Qu.:0.00000     3rd Qu.:0.000000     3rd Qu.:198518        
 Max.   :1.00000     Max.   :1.000000     Max.   :331835        
 log_rel_price      log_sale_price  sale_price_per_sqft  bath_pr_sqft      
 Min.   :-1.19109   Min.   :10.46   Min.   :0.0001087   Min.   :0.0002562  
 1st Qu.:-0.18330   1st Qu.:11.77   1st Qu.:0.0002471   1st Qu.:0.0006980  
 Median :-0.03704   Median :12.00   Median :0.0002804   Median :0.0008476  
 Mean   :-0.03482   Mean   :12.02   Mean   :0.0002850   Mean   :0.0008319  
 3rd Qu.: 0.11353   3rd Qu.:12.28   3rd Qu.:0.0003160   3rd Qu.:0.0010070  
 Max.   : 1.33727   Max.   :13.53   Max.   :0.0009952   Max.   :0.0032157  
  student_apt    
 Min.   :0.0000  
 1st Qu.:0.0000  
 Median :0.0000  
 Mean   :0.2455  
 3rd Qu.:0.0000  
 Max.   :1.0000  

Task 4 - Inspect the garage_type variables

No code is provided.

df %>% filter(
  (garage_type_attchd + garage_type_basment + garage_type_detchd + garage_type_builtIn + garage_type_no_garage) > 0)

     applicants sale_price num_units year_sold month_sold overall_qual
1             3     208500         4      2008          2            7
2             5     181500         5      2007          5            6
3             3     223500         1      2008          9            7
4             4     140000         3      2011          2            7
5             5     250000         5      2008         12            8
6             5     143000         3      2009         10            5
7             5     307000         1      2007          8            8
8             5     200000         3      2009         11            7
9             2     129900         5      2008          4            7
10            3     118000         4      2008          1            5
11            1     129500         3      2008          2            5
12            6     345000         1      2011          7            9
13            1     144000         5      2008          9            5
14            5     279500         2      2007          8            7
15            3     157000         5      2008          5            6
16            3     132000         4      2007          7            7
17            3     149000         2      2010          3            6
18            4     159000         1      2008          6            5
19            4     139000         1      2009          5            5
20            4     325300         2      2011         11            8
21            1     139400         5      2007          6            7
22            3     230000         2      2008          9            8
23            2     129900         5      2007          6            5
24            2     154000         5      2010          5            5
25            7     256300         4      2009          7            8
26            2     134800         2      2010          5            5
27            5     306000         4      2010          5            8
28            3     207500         5      2011         12            5
29            0      68500         3      2008          5            4
30            0      40000         3      2008          7            4
31            2     149350         2      2008          6            5
32            5     179900         4      2008          1            8
33            3     165500         1      2010          4            5
34            7     277500         4      2007          8            9
35            4     309000         2      2011          9            8
36            5     145000         1      2009          6            5
37            2     153000         5      2009         10            5
38            4     109000         2      2010          1            5
39            1      82000         4      2008          6            4
40            3     160000         3      2011         12            6
41            7     170000         1      2007          7            5
42            5     144000         3      2007         12            5
43            6     130250         4      2008          7            5
44            5     141000         4      2011          5            5
45            5     319900         4      2010          2            9
46            5     239686         2      2009          8            7
47            7     249700         2      2007          7            8
48            4     113000         5      2009          6            4
49            2     127000         4      2007          1            5
50            7     177000         1      2007          7            6
51            1     114500         4      2011          9            6
52            3     385000         5      2011         11            9
53            1     130000         1      2007          2            5
54            5     180500         5      2008          7            6
55            7     172500         3      2009          8            8
56            7     196500         5      2011          8            7
57            2     438780         5      2011         10           10
58            3     124900         1      2008          1            5
59            4     158000         1      2011          5            6
60            0     101000         4      2007          3            5
61            5     202500         4      2007         10            8
62            2     140000         4      2010          4            7
63            3     219500         2      2009          2            7
64            4     317000         1      2007         10            8
65            7     180000         5      2010          7            7
66            3     226000         3      2007          6            7
67            4      80000         4      2010          6            4
68            7     225000         1      2011          7            7
69            3     244000         4      2007          2            7
70            2     129500         2      2007          6            4
71            5     185000         1      2009         12            7
72            3     144900         3      2010          5            5
73            1     107400         2      2010          5            3
74            1      91000         1      2009         11            4
75            1     135750         3      2008          4            4
76            2     127000         2      2008          1            5
77            1     136500         5      2010          4            4
78            2     110000         1      2009          5            5
79            3     193500         5      2009          6            6
80            5     153500         1      2011          3            6
81            5     245000         1      2008         10            8
82            6     126500         1      2007          7            5
83            2     168500         4      2009          5            7
84            5     260000         1      2011          4            8
85            4     174000         1      2009          3            6
86            4     164500         1      2009          6            6
87            0      85000         1      2009         10            3
88            6     123600         3      2007          8            4
89            3     109900         4      2011          7            4
90            4      98600         5      2011         12            5
91            6     163500         4      2009          8            5
92            1     133900         5      2007         11            6
93            3     204750         4      2007          5            6
94            2     185000         1      2009          4            6
95            7     214000         1      2011          8            7
96            5      94750         1      2007          5            4
97            0      83000         5      2010          5            5
98            4     128950         1      2010          1            4
99            5     205000         2      2010          2            6
100           5     178000         2      2010          6            6
101           5     118964         5      2009          6            5
102           3     198900         4      2010          5            7
103           0     169500         4      2007          6            7
104           7     250000         1      2008          8            8
105           5     100000         1      2007          8            4
106           1     115000         4      2008          4            5
107           1     115000         3      2007          8            5
108           5     190000         3      2010          1            6
109           3     136900         3      2011         10            6
110           2     180000         1      2010          4            7
111           2     383970         2      2007         10            7
112           4     217000         2      2007         10            6
113           4     259500         1      2007          7            6
114           4     176000         5      2007          6            6
115           2     139000         2      2009          9            5
116           3     155000         5      2007          4            5
117           3     320000         1      2010          5            7
118           7     163990         1      2011          7            6
119           5     180000         3      2011         10            6
120           0     100000         4      2007          6            4
121           4     136000         4      2008          6            6
122           5     153900         3      2008          3            6
123           5     181000         5      2009          1            6
124           1      84500         4      2011          6            6
125           3      87000         1      2007          6            5
126           5     155000         2      2011          7            6
127           3     226000         5      2011          5            7
128           4     244000         5      2009          7            6
129           4     150750         3      2007          7            5
130           5     220000         2      2009          6            8
131           4     180000         1      2011          7            5
132           5     174000         4      2008          5            7
133           7     143000         2      2007          7            5
134           3     230000         3      2008         12            8
135           5     231500         1      2009          8            6
136           3     115000         3      2010          4            4
137           3     260000         3      2011          1            7
138           2     166000         1      2010          6            5
139           5     204000         1      2009          6            7
140           3     125000         4      2011         11            5
141           2     130000         1      2011          4            6
142           2     105000         1      2009         11            5
143           2     222500         1      2010          5            7
144           4     141000         2      2008          4            7
145           3     115000         2      2011          4            5
146           5     122000         4      2007          1            5
147           3     372402         3      2008          1            8
148           5     190000         1      2011          6            6
149           3     235000         1      2008          3            6
150           1     125000         3      2011          3            6
151           0      79000         2      2008          4            6
152           1     109500         3      2011          6            5
153           2     269500         5      2010          5            8
154           3     254900         1      2010          5            7
155           3     320000         4      2011          3            7
156           5     162500         5      2008          6            6
157           2     412500         2      2008          3            9
158           5     220000         5      2010          5            7
159           3     103200         4      2007          4            4
160           2     152000         5      2007         10            6
161           2     127500         1      2008          9            5
162           5     190000         1      2009         11            5
163           5     325624         2      2007         11            8
164           5     183500         1      2007          5            7
165           5     228000         3      2011          1            8
166           2     128500         1      2007          5            5
167           3     215000         4      2010          5            6
168           5     239000         2      2011          6            7
169           3     163000         1      2008          6            6
170           5     184000         3      2008         11            6
171           3     243000         2      2007          6            6
172           5     211000         2      2007          9            6
173           4     172500         5      2011          7            5
174           5     501837         1      2009          7            9
175           5     100000         5      2007          7            5
176           4     177000         4      2007          6            6
177           5     200100         4      2011          7            7
178           2     120000         4      2007          6            5
179           2     200000         5      2008          6            7
180           2     127000         2      2011          6            5
181           2     475000         2      2011          6           10
182           3     173000         1      2009          6            7
183           4     135000         2      2009          8            5
184           4     153337         5      2009          6            5
185           7     286000         4      2008          8            8
186           2     315000         5      2007         12            8
187           3     184000         3      2007          6            7
188           5     192000         2      2009          9            7
189           2     130000         5      2011          5            7
190           3     127000         3      2008          5            5
191           3     311872         3      2007          9            7
192           2     235000         1      2011          3            8
193           5     104000         1      2009          7            6
194           5     274900         4      2009          1            8
195           3     140000         1      2010          3            4
196           2     171500         2      2008          2            6
197           3     112000         1      2011          5            6
198           5     149000         2      2008          1            6
199           4     110000         2      2009          4            5
200           5     180500         1      2009          5            7
201           1     143900         2      2007          3            5
202           3     141000         2      2008          4            4
203           3     277000         4      2007          4            7
204           5     145000         5      2008          7            6
205           1      98000         5      2008          4            5
206           3     186000         3      2010          3            6
207           5     252678         5      2009          7            7
208           7     156000         2      2011          7            5
209           5     161750         4      2010          3            6
210           5     134450         2      2011          5            5
211           3     210000         5      2008          4            7
212           0     107000         5      2011          9            4
213           3     311500         3      2008          5            7
214           5     204900         3      2011          4            7
215           4     200000         3      2009         12            6
216           5     179900         4      2011          2            6
217           3      97000         1      2009          3            4
218           5     386250         1      2009          6           10
219           1     112000         1      2009          5            5
220           5     290000         5      2007          6            7
221           1     106000         3      2008          9            6
222           0     125000         1      2010          5            5
223           3     148000         4      2010          4            6
224           7     403000         5      2009          7            8
225           2      94500         4      2011          6            6
226           5     128200         1      2010          2            5
227           2     216500         5      2010          5            6
228           3      89500         1      2008          8            6
229           5     185500         2      2010          5            7
230           3     194500         1      2010          2            7
231           5     318000         5      2007         12            8
232           4     113000         2      2010          4            6
233           3     262500         1      2010          4            8
234           3     110500         3      2007          8            5
235           0      79000         5      2011          4            5
236           5     120000         1      2009          4            6
237           3     205000         1      2010          5            7
238           3     241500         2      2011          6            7
239           1     137000         2      2011          4            6
240           4     140000         3      2011          6            6
241           5     180000         5      2007          9            7
242           3     277000         2      2007          6            6
243           3      76500         3      2010          5            3
244           5     235000         1      2007         12            8
245           5     173000         4      2008         12            6
246           3     158000         1      2007         10            6
247           5     145000         1      2010          6            5
248           2     230000         5      2011          2            7
249           5     207500         2      2008          5            6
250           3     220000         5      2009          3            7
251           3     231500         1      2008          5            7
252           1      97000         2      2008         12            5
253           3     176000         1      2009          5            6
254           2     276000         4      2007         11            8
255           4     151000         1      2011          7            6
256           2     130000         5      2010          4            5
257           0      73000         1      2008          6            5
258           5     175500         1      2008          6            6
259           5     185000         1      2011          6            6
260           4     179500         2      2008          7            5
261           0     120500         5      2008          2            5
262           3     148000         1      2007          5            6
263           5     266000         5      2011          8            8
264           3     241500         2      2008          4            7
265           5     290000         1      2010          4            8
266           5     139000         2      2009          4            6
267           4     124500         1      2007          6            5
268           1     205000         5      2009         10            7
269           3     201000         5      2010          4            7
270           3     141000         2      2010          6            4
271           3     415298         5      2007          5            9
272           5     192000         5      2008          3            7
273           3     228500         2      2007          1            7
274           5     185000         1      2011          5            6
275           5     207500         3      2009          4            7
276           5     244600         1      2009         12            8
277           7     179200         1      2007          7            6
278           4     164700         2      2007          6            7
279           2     159000         1      2011          6            6
280           3      88000         5      2011          6            4
281           0     122000         2      2010          2            5
282           3     153575         3      2007          7            6
283           5     233230         1      2011          7            8
284           1     135900         1      2008          3            5
285           2     131000         2      2009          1            5
286           3     235000         3      2011          3            7
287           3     167000         4      2009         10            6
288           2     142500         5      2011          3            6
289           2     152000         1      2007          6            5
290           4     239000         4      2007          6            7
291           5     175000         5      2007          6            6
292           7     158500         5      2009          8            6
293           5     157000         1      2011          6            5
294           2     267000         1      2007          5            8
295           5     205000         2      2011          1            7
296           7     149900         2      2011          7            5
297           3     295000         1      2008          5            7
298           5     305900         5      2007          7            8
299           3     225000         1      2007          6            7
300           0      89500         3      2008          3            6
301           3      82500         4      2009          3            4
302           5     360000         3      2011         11            9
303           5     165600         4      2011          5            6
304           2     132000         2      2009          5            6
305           2     119900         2      2011          5            5
306           3     375000         3      2009          6            7
307           4     178000         1      2011          8            7
308           5     188500         4      2009          7            7
309           5     260000         3      2009          8            7
310           3     270000         3      2007         12            8
311           5     260000         5      2009          4            7
312           5     187500         4      2009          6            7
313           5     342643         3      2011          9            9
314           4     354000         1      2007          6            8
315           5     301000         4      2007          8            7
316           5     126175         2      2011          7            3
317           2     242000         4      2010          6            7
318           0      87000         1      2007         12            5
319           3     324000         3      2008          5            8
320           4     145250         4      2011          4            6
321           1     214500         3      2009          7            6
322           0      78000         3      2009          7            5
323           4     119000         1      2007         11            5
324           5     139000         3      2007          8            5
325           5     284000         4      2009         10            8
326           7     207000         1      2008          7            7
327           7     192000         5      2008          7            6
328           7     228950         1      2008          8            5
329           5     377426         1      2007          7            9
330           5     214000         5      2008         12            7
331           3     202500         1      2011          5            7
332           2     155000         3      2009          6            6
333           5     202900         2      2010          4            8
334           1      87500         2      2011          5            3
335           7     266000         3      2008          7            9
336           2      85000         1      2010          4            5
337           1     140200         1      2011         10            6
338           2     151500         2      2007          4            6
339           5     157500         1      2009         12            6
340           4     154000         3      2008         10            7
341           3     437154         1      2011          4            9
342           5     318061         1      2007         12            9
343           5     190000         3      2011         12            7
344           1      95000         4      2008          3            5
345           1     105900         1      2010          5            6
346           4     140000         4      2011          6            6
347           7     177500         2      2007          8            6
348           7     173000         2      2009          7            6
349           4     134000         1      2007          8            5
350           6     130000         1      2011          7            5
351           5     280000         5      2011          6            8
352           3     156000         1      2007          6            6
353           4     145000         4      2008          7            5
354           4     198500         3      2009          7            7
355           1     118000         1      2009          5            6
356           5     190000         3      2011          7            6
357           2     147000         3      2009          7            5
358           5     159000         4      2009          7            6
359           1     165000         3      2008         12            6
360           4     132000         3      2010          3            5
361           2     162000         1      2010          3            5
362           5     172400         1      2011          1            6
363           6     134432         2      2008          7            4
364           5     125000         5      2010          2            6
365           5     123000         5      2009         11            5
366           4     219500         4      2007          7            7
367           1      61000         1      2009          3            1
368           5     148000         1      2011          7            5
369           3     340000         5      2007         12            8
370           3     394432         4      2010          6            9
371           5     179000         1      2009          6            6
372           4     127000         2      2010          5            5
373           7     187750         4      2011          8            7
374           3     213500         2      2007          4            7
375           0      76000         3      2009         10            6
376           3     240000         1      2007          6            6
377           3      81000         1      2011          5            5
378           2     125000         1      2009         10            6
379           7     191000         2      2008          7            7
380           4     426000         1      2008          8           10
381           2     119000         1      2008          4            5
382           2     215000         3      2009          6            6
383           4     106500         1      2007          7            5
384           1     100000         1      2011          4            4
385           3     109000         2      2007          7            5
386           3     129000         4      2010          6            5
387           3     123000         3      2009          9            5
388           5     169500         2      2007          7            5
389           2      67000         5      2007         11            5
390           3     241000         4      2009         10            7
391           5     245500         3      2008         12            8
392           7     164990         3      2011          7            7
393           2     108000         3      2008          8            5
394           6     258000         1      2011          7            8
395           4     168000         1      2007          5            6
396           2     150000         5      2009          6            4
397           3     115000         4      2008          3            6
398           5     177000         1      2008          3            6
399           7     280000         4      2007          8            7
400           3     339750         2      2008          4            8
401           6      60000         1      2009          6            5
402           1     145000         1      2011          1            5
403           5     222000         1      2010          6            7
404           1     115000         4      2010          3            5
405           3     228000         5      2008         12            7
406           7     181134         4      2007          8            7
407           2     149500         5      2011          3            6
408           1     239000         2      2007         11            6
409           1     126000         3      2007          4            5
410           5     142000         1      2010          7            5
411           3     206300         1      2008         11            7
412           3     215000         1      2009          6            6
413           4     113000         3      2008          2            5
414           5     315000         1      2008          6            8
415           5     139000         2      2008          5            6
416           2     135000         1      2009          9            7
417           5     275000         3      2009          8            7
418           5     109008         4      2008          7            4
419           3     195400         2      2007          9            7
420           5     175000         2      2009          3            6
421           3      85400         5      2008          7            6
422           3      79900         2      2008          9            6
423           3     122500         5      2007          8            5
424           7     181000         1      2008          7            6
425           1      81000         5      2008          6            4
426           3     212000         1      2009          4            7
427           1     116000         1      2011         10            6
428           1     119000         2      2009          1            6
429           0      90350         5      2007          3            5
430           3     110000         3      2009          8            6
431           3     555000         1      2009          4           10
432           1     118000         4      2008          9            4
433           2     162900         2      2008          6            5
434           5     210000         3      2008          7            7
435           4     127500         1      2009         11            6
436           3     190000         5      2010          6            6
437           7     199900         1      2011          7            7
438           1     119500         1      2011          6            6
439           2     120000         3      2007          6            3
440           1     110000         4      2011          6            6
441           3     280000         2      2011         12            7
442           7     204000         1      2007          7            6
443           5     210000         1      2009          6            8
444           4     188000         5      2011          7            5
445           4     175500         1      2007          9            7
446           0      98000         5      2008          5            5
447           3     256000         3      2008          3            4
448           1     161000         1      2008          6            8
449           6     110000         1      2009          7            5
450           2     263435         1      2009         12            8
451           2     155000         3      2009          4            7
452           4      62383         3      2009         12            5
453           6     188700         2      2008          8            6
454           6     124000         1      2009          8            5
455           3     167000         1      2007          4            7
456           3     146500         1      2007          6            5
457           5     250000         5      2007          5            8
458           3     187000         3      2008          6            6
459           5     212000         1      2010          6            8
460           5     190000         4      2007         11            7
461           2     148000         1      2008          6            6
462           5     440000         5      2007          7            8
463           7     251000         2      2007          8            8
464           3     132500         2      2007          7            5
465           5     208900         2      2008          4            6
466           4     380000         1      2007          3            9
467           3     297000         1      2009          9            8
468           3      89471         1      2007          3            4
469           5     326000         3      2011          3            9
470           5     374000         4      2011          8            9
471           3     155000         5      2009          6            7
472           3     164000         1      2011          5            6
473           1     132500         5      2007          3            5
474           4     147000         1      2009          7            5
475           3     156000         4      2007          6            5
476           5     175000         4      2007          2            5
477           1     160000         2      2011          5            5
478           2      86000         2      2009          5            4
479           1     115000         2      2008          6            5
480           7     133000         2      2011          8            6
481           5     172785         5      2011          5            6
482           1     155000         2      2008          6            5
483           2      91300         3      2009         12            5
484           0      34900         1      2009         11            4
485           5     430000         1      2007          5            8
486           2     184000         5      2008          6            7
487           1     130000         1      2009          6            5
488           5     120000         5      2007          6            5
489           1     113000         1      2007          5            6
490           5     226700         1      2008          2            7
491           2     140000         1      2007          4            5
492           3     289000         5      2010          3            7
493           6     124500         1      2009          7            5
494           3     215000         3      2011          9            8
495           5     208300         3      2009          9            6
496           2     161000         3      2008         10            7
497           7     124500         2      2009          7            5
498           5     202665         5      2011          3            7
499           4     129900         1      2011          7            5
500           5     134000         4      2007          6            6
501           0      96500         1      2007          6            5
502           3     402861         1      2009          9           10
503           7     158000         4      2009          8            6
504           7     265000         4      2009          7            7
505           3     211000         4      2007          5            6
506           3     234000         3      2009          6            7
507           1     106250         1      2008          8            4
508           2     150000         1      2007          5            6
509           2     159000         3      2011         10            6
510           7     315750         1      2007          8            7
511           5     176000         1      2011          4            7
512           2     132000         4      2007          6            5
513           3     446261         4      2008         11            9
514           4      86000         5      2007          7            4
515           5     200624         1      2007          3            6
516           7     175000         3      2008          8            6
517           2     128000         3      2008          6            6
518           1     107500         1      2010          4            5
519           1      39300         3      2007          1            1
520           5     178000         4      2011         10            8
521           4     107500         3      2008          1            5
522           7     188000         5      2008          7            7
523           3     111250         5      2008          4            4
524           4     158000         1      2011          7            5
525           3     272000         5      2010          5            8
526           3     315000         5      2009          3            9
527           4     248000         1      2007          6            8
528           5     213250         2      2009          6            7
529           3     133000         1      2007          6            7
530           3     179665         3      2011          9            7
531           3     229000         3      2011          2            7
532           1     210000         2      2007          5            6
533           2     129500         1      2007          4            5
534           2     125000         5      2008          6            5
535           2     263000         5      2009         11            7
536           2     112500         5      2008          6            5
537           7     255500         1      2009          7            8
538           2     108000         2      2009          5            4
539           6     284000         1      2008          8            7
540           5     113000         5      2011          8            5
541           3     141000         1      2011          5            5
542           7     175000         4      2008          8            7
543           3     121500         3      2010          5            5
544           3     170000         2      2011          4            5
545           6     108000         1      2008          7            5
546           4     185000         1      2008          7            6
547           7     268000         5      2011          7            7
548           1     128000         1      2010          5            6
549           4     325000         1      2008          6            9
550           5     214000         2      2010          3            7
551           2     316600         5      2009          9            8
552           2     135960         4      2011         12            5
553           4     142600         1      2008         11            5
554           5     120000         5      2011         10            6
555           7     224500         5      2009          7            7
556           2     170000         1      2007         12            7
557           2     139000         3      2007         12            5
558           3     118500         1      2008         10            5
559           4     145000         5      2009          8            7
560           2     164500         3      2011          5            5
561           4     146000         1      2008          2            7
562           1     131500         2      2008         11            5
563           2     181900         2      2007          6            6
564           7     253293         4      2009          8            8
565           2     118500         5      2007          5            6
566           4     325000         1      2008          7           10
567           3     133000         4      2009          7            4
568           3     369900         1      2011          3            8
569           2     130000         2      2008          5            6
570           3     137000         3      2009          7            5
571           5     143000         1      2009          6            5
572           5      79500         3      2008          8            5
573           5     185900         4      2008          9            7
574           2     451950         1      2009          6           10
575           2     138000         3      2008          6            5
576           5     140000         2      2009          5            6
577           3     110000         4      2008          4            5
578           7     319000         4      2011          8            8
579           0     114504         2      2011         10            6
580           5     217500         3      2011          3            5
581           4     275000         2      2011          6            8
582           1     141000         2      2007         12            6
583           3     220000         1      2011          2            8
584           4     151000         2      2010          6            7
585           3     221000         1      2008          9            7
586           3     205000         2      2009         10            7
587           4     152000         2      2009         11            5
588           5     225000         1      2011          8            5
589           2     359100         4      2007          9            8
590           4     118500         2      2007          4            4
591           3     313000         1      2009          5            9
592           7     148000         1      2007          7            6
593           2     261500         4      2009         11            8
594           3     147000         1      2007         12            5
595           1      75500         2      2010          5            4
596           3     137500         1      2010          5            6
597           5     183200         1      2011          6            6
598           3     105500         2      2008          6            6
599           7     314813         1      2007          7            9
600           5     305000         3      2008          8            8
601           1      67000         4      2008          9            3
602           3     240000         5      2008          6            6
603           2     135000         2      2009          7            5
604           4     168500         3      2007          6            6
605           5     165150         5      2011         11            6
606           3     160000         2      2010          2            6
607           6     139900         1      2007          8            5
608           2     153000         1      2010          3            6
609           5     135000         4      2007          9            5
610           3     168500         3      2008          6            6
611           1     124000         3      2011          6            5
612           7     209500         3      2007          8            8
613           7      82500         1      2009          4            7
614           5     139400         1      2007          7            5
615           2     144000         1      2010          6            6
616           2     200000         4      2007          3            6
617           0      60000         4      2009          1            2
618           4      93000         1      2009         11            5
619           3      85000         5      2008          5            5
620           4     274000         1      2008          4            8
621           5     226000         3      2007          5            7
622           5     345000         4      2009          7            8
623           5     152000         1      2007          4            5
624           3     370878         1      2009         10            9
625           2     143250         1      2007          3            6
626           3      98300         4      2008          7            5
627           2     155000         2      2008          6            6
628           2     155000         1      2010          6            6
629           1      84500         1      2007         12            4
630           5     205950         2      2008          5            7
631           4     108000         2      2009         10            4
632           7     191000         1      2009          7            7
633           0     135000         1      2008          6            6
634           7     350000         2      2008          8            8
635           1      88000         2      2010          3            6
636           5     145500         2      2008          8            5
637           5     149000         5      2008          2            7
638           5      97500         4      2010          1            6
639           2     167000         1      2009          3            5
640           5     197900         4      2007         11            7
641           7     402000         3      2009          7            8
642           7     110000         1      2009          7            6
643           2     137500         5      2008          4            4
644           3     423000         5      2011          1            8
645           3     230500         3      2011         11            8
646           5     193500         2      2008         10            6
647           1     168000         5      2011         11            5
648           5     137500         5      2011          7            4
649           5     173500         1      2009          2            6
650           1     103600         4      2009          7            6
651           5     165000         1      2011          6            6
652           3     257500         2      2007          6            6
653           7     140000         1      2008          7            6
654           1     109500         4      2009          5            5
655           7     372500         1      2009          7            8
656           1     128500         4      2007         10            5
657           5     143000         1      2010          5            6
658           3     159434         1      2009          7            5
659           5     173000         5      2008         11            6
660           5     285000         2      2007          7            9
661           5     221000         4      2010          6            7
662           5     207500         1      2007          9            7
663           7     227875         2      2007          8            7
664           4     148800         1      2007          3            7
665           3     392000         5      2007         10            8
666           5     194700         1      2007          6            6
667           5     141000         5      2008          5            6
668           3     755000         1      2007          1           10
669           3     335000         4      2011          4            7
670           3     108480         2      2011         12            5
671           2     141500         1      2009          4            5
672           7     176000         3      2011          7            6
673           1      89000         4      2011          6            5
674           2     123500         2      2011          9            5
675           1     138500         3      2010          4            5
676           7     196000         1      2008          7            7
677           3     312500         1      2011          5            8
678           7     140000         4      2011          7            7
679           6     361919         1      2011          7            8
680           2     140000         1      2010          5            5
681           3     213000         1      2010          5            7
682           1      55000         5      2010          7            4
683           3     302000         5      2007          6            7
684           5     254000         5      2009         12            8
685           7     179540         1      2007          7            7
686           3     109900         3      2008         12            5
687           7      52000         1      2008          7            3
688           0     102776         3      2010          1            4
689           5     189000         4      2008         10            8
690           1     129000         5      2011          5            4
691           2     130500         2      2010          3            6
692           7     165000         2      2009          8            6
693           3     159500         3      2007          7            7
694           5     157000         1      2008         11            5
695           7     341000         4      2008          8            7
696           5     128500         2      2011          5            5
697           5     275000         2      2011         12            8
698           5     143000         1      2010          5            6
699           3     124500         4      2009          7            4
700           2     135000         2      2008          5            4
701           3     320000         1      2009          2            9
702           3     120500         3      2009         11            4
703           3     222000         1      2009         12            6
704           5     194500         2      2009          2            7
705           6     110000         4      2009          7            5
706           0     103000         3      2009          1            4
707           5     236500         1      2010          3            8
708           5     187500         3      2007          5            7
709           5     222500         1      2008          7            7
710           2     131400         2      2009          3            5
711           3     108000         3      2007          5            5
712           0     163000         4      2011         10            7
713           1      93500         2      2011          7            3
714           3     239900         3      2011          6            8
715           2     179000         1      2009          3            5
716           5     190000         2      2009          4            7
717           2     132000         5      2007          5            5
718           1     142000         5      2008          5            6
719           5     179000         5      2007         12            7
720           2     175000         1      2009         10            5
721           5     180000         4      2008         10            8
722           4     299800         2      2008          7            8
723           2     236000         2      2009          4            7
724           0     265979         1      2009          5            7
725           5     260400         2      2010          3            7
726           1      98000         1      2009          4            4
727           3      96500         2      2010          6            4
728           7     162000         4      2007          8            7
729           5     217000         2      2011          7            6
730           5     275500         3      2011          3            8
731           4     156000         1      2009          7            6
732           4     172500         1      2009          3            6
733           3     212000         3      2009          4            8
734           2     158900         5      2010          4            6
735           6     179400         3      2008          8            7
736           5     290000         3      2007         11            8
737           1     127500         4      2009         10            6
738           3     100000         1      2009         10            5
739           5     215200         1      2010          6            7
740           7     337000         2      2009          7            8
741           3     270000         1      2011          4            8
742           5     264132         5      2008          8            9
743           5     196500         5      2010          3            7
744           7     160000         3      2008          7            6
745           5     216837         3      2011         10            7
746           2     538000         3      2010          6            8
747           1     134900         1      2009          4            5
748           3     102000         1      2011          4            4
749           4     107000         3      2010          3            6
750           6     114500         1      2007          7            5
751           5     395000         1      2007          7            8
752           3     162000         5      2009          6            6
753           5     221500         3      2011          7            7
754           2     142500         4      2011          6            5
755           4     144000         5      2007         10            5
756           5     135000         2      2011          5            6
757           5     176000         2      2007          6            7
758           7     175900         4      2011          7            6
759           5     187100         4      2009          6            7
760           5     165500         2      2009          7            5
761           2     128000         4      2008          6            6
762           5     161500         4      2009          9            6
763           2     139000         2      2010          6            5
764           2     233000         1      2010          1            7
765           3     107900         5      2008          8            4
766           7     187500         5      2007          7            6
767           3     146800         5      2007          5            6
768           5     269790         4      2007          6            7
769           5     225000         4      2007          6            8
770           5     194500         1      2008         10            7
771           3     171000         4      2010          4            6
772           2     143500         1      2007          4            6
773           4     110000         5      2008          4            5
774           4     485000         3      2009          7            9
775           2     175000         5      2007          6            5
776           3     200000         1      2008          5            6
777           3     109900         4      2007          7            4
778           3     189000         2      2008         10            7
779           2     582933         3      2009          1            9
780           4     118000         1      2011          6            5
781           7     227680         1      2008          7            7
782           3     135500         3      2011         10            5
783           3     223500         5      2009          5            5
784           3     159950         2      2011          6            5
785           1     106000         2      2009         11            5
786           5     181000         4      2011          1            6
787           5     144500         1      2008          6            6
788           0      55993         1      2010          6            5
789           2     157900         2      2007          4            6
790           4     116000         2      2011          7            5
791           3     224900         4      2010          5            7
792           4     137000         4      2011          7            5
793           5     271000         5      2008          7            8
794           5     155000         5      2010          6            6
795           5     224000         1      2010          6            7
796           5     183000         5      2008          6            7
797           0      93000         3      2009          2            4
798           2     225000         5      2007         10            7
799           4     139500         4      2009          7            6
800           5     232600         5      2011          6            8
801           3     385000         1      2008          6           10
802           2     109500         2      2008          5            5
803           5     189000         4      2009          4            7
804           5     185000         5      2009          6            5
805           6     147400         5      2011          7            7
806           3     166000         1      2008          6            6
807           4     151000         1      2011          6            7
808           3     237000         4      2010          1            7
809           2     167000         2      2009          2            6
810           5     139950         2      2008          9            5
811           2     128000         1      2010          2            4
812           2     153500         5      2007          6            5
813           1     100000         1      2008         11            6
814           5     144000         5      2008          6            5
815           1     130500         4      2008          5            5
816           1     140000         1      2008          3            6
817           2     157500         4      2008          6            5
818           3     174900         2      2008          5            6
819           1     141000         3      2007          7            5
820           2     153900         1      2008          6            5
821           1     171000         4      2007          1            5
822           5     213000         3      2009          7            7
823           7     133500         1      2009          8            5
824           2     240000         1      2008          9            6
825           7     187000         2      2007          8            6
826           5     131500         4      2007         11            6
827           6     164000         1      2007          8            7
828           4     158000         2      2009          8            6
829           4     170000         2      2011          7            5
830           1     127000         1      2010          4            5
831           4     147000         3      2008         10            6
832           5     174000         5      2009          3            6
833           5     152000         1      2009          6            7
834           5     250000         3      2011          8            6
835           4     189950         2      2007          6            7
836           2     131500         5      2010          4            5
837           5     152000         4      2010          5            6
838           7     132500         3      2009          7            5
839           3     250580         2      2008          5            7
840           4     148500         5      2009          8            5
841           5     248900         5      2007         11            8
842           2     129000         2      2007          5            4
843           5     169000         1      2011          5            5
844           3     236000         3      2010          6            7
845           0     109500         2      2009          8            5
846           3     200500         1      2010          6            6
847           2     116000         2      2008         10            5
848           4     133000         4      2009          9            5
849           6      66500         4      2009          8            5
850           4     303477         1      2007          8            8
851           5     132250         4      2007          1            4
852           5     350000         1      2009          6            9
853           1     148000         2      2010          6            5
854           7     136500         1      2009          7            5
855           3     157000         3      2007          6            5
856           5     187500         3      2007          4            7
857           4     178000         5      2009         12            6
858           1     118500         2      2011          3            4
859           6     100000         4      2009          7            5
860           3     328900         4      2008          1            9
861           5     145000         1      2011          6            5
862           3     135500         5      2008          4            5
863           3     268000         2      2007         10            8
864           5     149500         2      2009          2            6
865           3     122900         4      2007          7            5
866           4     172500         1      2009          7            6
867           2     154500         2      2011          2            6
868           2     165000         1      2008          6            5
869           5     118858         1      2009          6            5
870           5     140000         4      2008         10            6
871           0     106500         3      2011          4            4
872           4     142953         5      2009          6            5
873           3     611657         2      2010          3            9
874           1     135000         1      2011          6            5
875           3     110000         4      2007          6            4
876           2     153000         5      2009          5            5
877           7     180000         1      2011          7            7
878           5     240000         1      2011          8            7
879           3     125500         3      2007          8            5
880           5     128000         2      2010          2            5
881           5     255000         4      2007          6            8
882           2     250000         1      2011          6            7
883           5     131000         4      2011          6            5
884           5     174000         2      2009          6            6
885           4     154300         1      2010          1            5
886           3     143500         3      2009         10            5
887           0      88000         4      2011          7            5
888           4     173733         2      2009          6            6
889           4      75000         1      2007          1            4
890           0      35311         1      2011         10            2
891           2     135000         3      2009          4            4
892           3     238000         1      2007         11            7
893           3     176500         1      2008          5            6
894           5     201000         4      2007          7            6
895           2     145900         5      2008          9            5
896           5     169990         5      2011         10            6
897           7     193000         1      2008          7            6
898           5     207500         5      2011          5            6
899           5     175000         2      2008          3            5
900           4     285000         4      2007          5            8
901           5     176000         4      2008          4            7
902           3     236500         5      2009          6            8
903           2     222000         3      2011         11            7
904           7     201000         4      2009          7            8
905           6     117500         1      2009          7            5
906           3     320000         1      2007          3            9
907           7     190000         2      2009          8            7
908           3     242000         5      2008         11            7
909           3      79900         1      2011          6            4
910           5     184900         1      2009          8            7
911           3     253000         5      2009          2            7
912           5     239799         3      2011          8            7
913           3     244400         1      2010          6            7
914           7     150900         4      2011          7            6
915           2     214000         4      2009          6            7
916           4     150000         1      2007          8            4
917           5     143000         3      2007          6            5
918           4     137500         5      2009          1            6
919           3     124900         1      2009          9            5
920           3     143000         4      2011          3            5
921           5     270000         1      2007         11            8
922           5     192500         4      2011          2            7
923           3     197500         5      2010          3            6
924           4     129000         1      2007          7            5
925           6     119900         2      2011          7            5
926           4     133900         1      2009          4            5
927           3     172000         1      2008          9            5
928           2     127500         4      2011         10            6
929           1     145000         1      2007          8            6
930           0     132000         5      2007          4            5
931           5     185000         1      2007         10            7
932           4     155000         1      2010          5            7
933           2     116500         1      2010          2            5
934           5     272000         1      2008          7            6
935           3     239000         3      2009          5            9
936           4     214900         4      2010          2            7
937           7     178900         5      2007          7            6
938           4     160000         2      2009          6            5
939           7     135000         1      2008          7            5
940           0      37900         4      2009          5            3
941           3     140000         2      2011          3            6
942           1     135000         1      2011         12            4
943           6     173000         4      2009          7            7
944           5      99500         3      2010          4            6
945           5     182000         1      2008         12            7
946           0     167500         1      2009         10            7
947           4     165000         5      2011          4            7
948           5      85500         5      2011          8            4
949           5     199900         1      2007         11            7
950           1     110000         1      2007          5            4
951           1     139000         1      2009          6            5
952           5     178400         1      2008          7            7
953           7     336000         2      2009          7            8
954           3     255900         1      2008          5            8
955           7     126000         3      2009          8            5
956           1     125000         1      2008          8            5
957           2     117000         2      2011          6            6
958           3     395192         3      2010          4            9
959           5     195000         3      2007          6            6
960           7     197000         3      2011          8            7
961           5     348000         1      2011          6            8
962           2     168000         1      2009         11            8
963           5     187000         4      2007          7            6
964           7     173900         3      2011          8            6
965           7     337500         2      2009          7           10
966           4     121600         5      2011          8            4
967           3     136500         5      2011          1            5
968           5     185000         1      2009          2            6
969           0      91000         1      2011          5            3
970           3     206000         1      2010          2            7
971           0      82000         2      2009          7            3
972           3      86000         3      2007          1            5
973           7     232000         1      2008          7            8
974           4     136905         5      2007          6            5
975           5     149900         1      2008         11            5
976           5     163500         1      2007          3            6
977           4      88000         1      2009          8            4
978           3     240000         4      2009          4            7
979           4     102000         2      2011          6            5
980           4     135000         3      2008          8            5
981           1     100000         4      2010          5            5
982           6     165000         5      2007          8            6
983           1      85000         2      2009          6            5
984           3     119200         3      2007         11            6
985           3     227000         4      2009         11            8
986           5     203000         1      2009          6            7
987           7     187500         2      2009          8            8
988           5     160000         4      2007          5            7
989           3     176000         5      2008          6            4
990           7     194000         4      2011          7            7
991           3      87000         4      2007          3            5
992           5     287000         1      2008          5            8
993           4     112500         3      2007          3            5
994           3     167500         2      2010          4            5
995           3     293077         1      2008          4            8
996           5     105000         2      2007          4            5
997           1     118000         5      2011          5            6
998           4     160000         1      2011          7            5
999           4     197000         5      2009          8            7
1000          5     310000         4      2011         11            8
1001          3     230000         2      2011          2            7
1002          3     119750         3      2007          6            5
1003          0      84000         4      2009          1            4
1004          3     315500         3      2009          9            9
1005          2     287000         5      2008          9            8
1006          1      97000         5      2009          5            4
1007          2      80000         4      2009          4            4
1008          2     155000         1      2011          1            5
1009          7     173000         3      2008          7            6
1010          7     196000         4      2009          8            6
1011          3     262280         2      2008          5            7
1012          5     278000         5      2009          7            8
1013          3     139600         2      2009          6            3
1014          4     556581         2      2011          7            9
1015          4     145000         1      2008          2            5
1016          4     115000         1      2009         11            5
1017          1      84900         3      2010          4            4
1018          7     176485         1      2007          8            7
1019          5     200141         1      2007         10            7
1020          3     165000         2      2007          6            6
1021          1     144500         2      2010          5            5
1022          3     255000         1      2011         11            8
1023          5     180000         3      2008          5            6
1024          5     185850         1      2011          6            7
1025          4     248000         5      2009          1            7
1026          7     335000         1      2009          7            9
1027          3     220000         3      2007          3            6
1028          5     213500         1      2010          4            8
1029          4      81000         5      2008          8            3
1030          1      90000         3      2007          9            5
1031          5     110500         3      2011          7            6
1032          3     154000         2      2009         11            5
1033          3     328000         1      2010          4            7
1034          5     178000         1      2009          5            6
1035          3     167900         2      2008          6            6
1036          2     151400         5      2011          6            6
1037          2     135000         4      2007          5            5
1038          5     135000         2      2007          6            5
1039          5     154000         3      2009          5            6
1040          6      91500         2      2011          8            5
1041          5     159500         5      2009          7            6
1042          5     194000         1      2007          5            7
1043          4     219500         5      2007          7            7
1044          3     170000         3      2011          4            5
1045          3     138800         5      2011          3            5
1046          5     155900         3      2011          5            6
1047          4     126000         4      2007          4            5
1048          5     145000         2      2008         10            6
1049          2     133000         3      2010          6            5
1050          5     192000         1      2007          9            7
1051          3     160000         3      2011          3            6
1052          5     187500         3      2011          7            6
1053          5     147000         3      2010          4            6
1054          2      83500         5      2010          5            4
1055          3     252000         1      2009          5            8
1056          2     137500         2      2011          4            7
1057          5     197000         1      2011          4            8
1058          1      92900         4      2009          6            3
1059          4     160000         5      2008          3            7
1060          4     136500         1      2008          6            6
1061          2     146000         2      2011         10            5
1062          3     129000         4      2010          5            5
1063          5     176432         1      2007          3            6
1064          1     127000         4      2007          3            6
1065          5     170000         5      2007         10            8
1066          3     128000         4      2009          7            4
1067          5     157000         1      2009          4            7
1068          1      60000         4      2009          1            2
1069          5     119500         3      2007          7            5
1070          4     135000         1      2007          4            5
1071          4     159500         2      2011          7            6
1072          1     106000         5      2007          4            5
1073          5     325000         2      2010          4            8
1074          3     179900         1      2007          5            7
1075          2     274725         3      2011          9            7
1076          5     181000         3      2007         11            6
1077          5     280000         5      2009          3            8
1078          5     188000         1      2008          6            6
1079          3     205000         2      2008          9            7
1080          4     129900         3      2011          7            5
1081          3     134500         1      2007          5            5
1082          3     117000         3      2011          8            5
1083          5     318000         1      2007         11            8
1084          2     184100         1      2009          3            8
1085          2     130000         1      2008          5            5
1086          1     140000         2      2008         12            5
1087          6     133700         5      2011          7            5
1088          0     118400         1      2007          5            6
1089          7     212900         1      2011          7            7
1090          1     112000         1      2009         10            4
1091          2     118000         4      2009          6            5
1092          7     163900         3      2007          7            7
1093          3     115000         2      2009         11            4
1094          3     259000         4      2007         11            7
1095          4     215000         2      2007          7            7
1096          4     140000         3      2007          8            5
1097          4     135000         1      2009         12            4
1098          3      93500         5      2007          9            5
1099          4     117500         5      2007          5            6
1100          3     239500         1      2009          6            8
1101          7     169000         2      2007          8            6
1102          0     102000         4      2007          5            6
1103          4     119000         2      2008          4            6
1104          0      94000         1      2010          5            5
1105          3     196000         4      2009          5            6
1106          1     144000         4      2007          5            5
1107          2     139000         5      2008          6            5
1108          3     197500         5      2009         10            5
1109          2     424870         4      2007          4            8
1110          4      80000         1      2008          7            5
1111          1      80000         4      2010          7            4
1112          3     149000         3      2011          8            5
1113          5     180000         1      2011          5            6
1114          7     174500         1      2009          7            7
1115          3     116900         2      2008          8            7
1116          4     143000         1      2009          7            7
1117          4     124000         1      2007         11            6
1118          2     149900         1      2011         11            5
1119          4     230000         4      2011          7            6
1120          0     120500         2      2008          6            6
1121          3     201800         5      2008          5            7
1122          7     218000         2      2007          7            5
1123          3     179900         2      2008         10            5
1124          7     230000         4      2009          7            7
1125          5     235128         5      2008          6            8
1126          7     185000         3      2008          7            6
1127          4     224000         4      2008         11            6
1128          1     129000         5      2007          5            5
1129          5     194000         2      2007          6            5
1130          5     233170         5      2009          9            7
1131          3     245350         1      2010          2            8
1132          5     173000         4      2011          2            6
1133          4     235000         3      2008          7            6
1134          5     625000         5      2011          7           10
1135          5     171000         5      2008          7            6
1136          3     163000         5      2008         11            6
1137          4     171900         1      2008          3            7
1138          4     200500         2      2007          3            5
1139          6     239000         3      2011          7            6
1140          5     285000         2      2007          4            8
1141          5     119500         4      2008         10            5
1142          1     115000         5      2009         12            6
1143          6     154900         1      2009          7            5
1144          1      93000         2      2011          4            5
1145          5     250000         2      2011          4            7
1146          3     392500         3      2008         11            8
1147          5     745000         3      2007          7           10
1148          2     120000         2      2011          6            5
1149          5     104900         5      2011          3            5
1150          7     262000         1      2011          7            8
1151          7     195000         1      2009          7            7
1152          5     189000         2      2010          6            7
1153          4     174000         1      2007         11            8
1154          3     125000         1      2007          7            5
1155          3     165000         1      2009          6            6
1156          2     158000         3      2010          3            6
1157          7     176000         5      2008          7            6
1158          2     219210         1      2011         11            7
1159          3     144000         3      2011          7            7
1160          5     178000         1      2009          6            7
1161          2     148000         2      2011         10            4
1162          6     116050         1      2011          7            4
1163          5     197900         5      2009          3            7
1164          4     117000         3      2009          5            5
1165          5     213000         2      2009         10            7
1166          7     153500         2      2011          7            5
1167          3     271900         2      2009          6            7
1168          4     107000         3      2011         11            4
1169          5     200000         4      2011          5            6
1170          2     140000         5      2008         10            5
1171          3     290000         5      2011          5            8
1172          5     189000         4      2010          5            6
1173          4     164000         5      2010          6            8
1174          5     113000         4      2009          8            4
1175          2     145000         1      2011          5            4
1176          3     134500         2      2011          5            5
1177          0     125000         3      2007          5            5
1178          4     112000         5      2010          4            6
1179          5     229456         1      2009          9            8
1180          0      80500         4      2011          7            4
1181          1      91500         2      2011          4            6
1182          4     115000         5      2011         11            5
1183          3     134000         1      2008          8            5
1184          5     143000         2      2007          1            6
1185          1     137900         5      2011         10            5
1186          5     184000         4      2008          2            7
1187          3     145000         2      2007          6            6
1188          4     214000         3      2008          1            6
1189          2     147000         5      2008         12            5
1190          3     367294         1      2008         10            9
1191          6     127000         1      2008          8            5
1192          3     190000         3      2007          8            5
1193          5     132500         4      2011          5            5
1194          5     142000         3      2010          5            5
1195          0     130000         4      2008         11            5
1196          5     138887         2      2011          7            5
1197          4     175500         3      2010          6            7
1198          4     195000         4      2011          9            7
1199          4     142500         3      2011          3            6
1200          3     265900         4      2007         12            8
1201          5     224900         4      2008          7            7
1202          5     248328         5      2007          6            7
1203          5     170000         1      2010          1            7
1204          3     465000         5      2011          9           10
1205          1     230000         1      2011          6            8
1206          4     178000         3      2007          1            6
1207          5     186500         5      2011          3            7
1208          3     169900         1      2010          5            6
1209          0     129500         3      2008          4            6
1210          4     119000         2      2007          5            5
1211          3     244000         2      2010          4            7
1212          5     171750         5      2011          3            7
1213          5     130000         3      2009         11            5
1214          5     294000         3      2007          7            7
1215          4     165400         2      2008          7            7
1216          1     127500         1      2007         11            6
1217          7     301500         5      2008          8            8
1218          5      99900         5      2009          7            5
1219          5     190000         2      2008          7            7
1220          5     151000         2      2008          7            6
1221          4     181000         5      2009          6            6
1222          4     128900         4      2009          6            5
1223          5     161500         4      2009         11            4
1224          3     180500         5      2007          7            6
1225          5     181000         1      2008          8            6
1226          4     183900         2      2011          3            7
1227          0     122000         3      2007          1            7
1228          3     378500         4      2010          5            9
1229          2     381000         5      2008          5            8
1230          7     144000         2      2007          7            5
1231          3     260000         2      2010          4            7
1232          7     185750         1      2009          8            6
1233          2     137000         3      2011         11            5
1234          2     177000         4      2008          5            6
1235          4     139000         4      2007         11            5
1236          6     137000         3      2007          7            5
1237          5     162000         5      2009         12            6
1238          5     197900         1      2009          6            6
1239          3     237000         4      2008          3            8
1240          2      68400         5      2010          4            4
1241          3     227000         2      2009          3            7
1242          7     180000         1      2011          7            7
1243          4     150500         2      2009          9            5
1244          4     139000         4      2010          4            6
1245          2     169000         1      2010          3            6
1246          1     132500         4      2009          5            6
1247          5     143000         2      2010          6            6
1248          5     190000         5      2011          6            5
1249          5     278000         2      2009         10            8
1250          4     281000         4      2011         10            8
1251          3     180500         3      2010          4            5
1252          1     119500         1      2009          2            5
1253          1     107500         4      2009         12            5
1254          5     162900         1      2011          3            7
1255          2     115000         1      2011          4            5
1256          3     138500         1      2011         11            5
1257          3     155000         1      2008         12            5
1258          2     140000         2      2011          6            6
1259          3     154000         2      2010          5            5
1260          3     225000         1      2009          5            7
1261          4     177500         4      2009         11            6
1262          5     290000         3      2011         12            8
1263          5     232000         1      2011          4            7
1264          2     130000         1      2011          4            7
1265          5     325000         1      2009         11            9
1266          5     202500         1      2011          9            7
1267          4     138000         3      2009          5            5
1268          3     147000         4      2008          5            5
1269          5     179200         5      2008          6            6
1270          3     335000         2      2010          5            7
1271          3     203000         5      2007          1            7
1272          5     302000         1      2007          6            8
1273          4     333168         2      2010          5            9
1274          2     119000         2      2007         10            4
1275          3     206900         5      2008          6            6
1276          3     295493         1      2009          1            8
1277          5     208900         1      2007          4            7
1278          5     275000         3      2011          8            8
1279          2     111000         1      2007          2            4
1280          5     156500         2      2009          6            6
1281          1      72500         4      2008          7            3
1282          5     190000         1      2010          6            7
1283          1      82500         1      2009         12            4
1284          5     147000         1      2007          2            8
1285          0      55000         3      2008          1            4
1286          3      79000         2      2007          5            3
1287          3     130500         5      2008         10            5
1288          2     256000         4      2008          6            6
1289          5     176500         1      2011          6            7
1290          5     227000         3      2007         12            8
1291          5     132500         4      2011          7            5
1292          2     100000         3      2009          5            4
1293          3     125500         5      2011          7            5
1294          2     125000         4      2009          5            5
1295          5     167900         5      2009          4            6
1296          4     135000         1      2008         11            5
1297          0      52500         2      2011          3            4
1298          4     200000         1      2011          6            7
1299          4     128500         3      2011          6            5
1300          1     123000         2      2007          6            4
1301          6     155000         5      2008          7            6
1302          5     228500         2      2007          8            8
1303          3     177000         1      2009          3            6
1304          7     155835         4      2007          7            7
1305          5     108500         1      2007          7            4
1306          3     262500         3      2011          6            7
1307          3     283463         2      2007          5            8
1308          5     215000         1      2007          8            7
1309          1     122000         1      2008         12            8
1310          4     200000         5      2009          8            5
1311          2     171000         1      2008          3            6
1312          3     134900         1      2009          7            6
1313          5     410000         3      2010          3            8
1314          3     235000         5      2008          6            7
1315          5     170000         4      2011          9            7
1316          4     110000         4      2008         10            5
1317          3     149900         1      2010          4            5
1318          4     177500         1      2010          6            6
1319          5     315000         2      2011          9            9
1320          2     189000         3      2008          5            5
1321          5     260000         4      2009          6            7
1322          5     104900         2      2009          6            4
1323          4     156932         2      2007          3            6
1324          4     144152         5      2011          4            7
1325          5     216000         1      2010          1            7
1326          5     193000         1      2008          6            7
1327          4     127000         3      2011          7            5
1328          5     144000         1      2009          6            6
1329          3     232000         3      2010          5            8
1330          3     105000         5      2009         10            4
1331          2     165500         5      2008         10            6
1332          2     274300         2      2011          6            7
1333          3     466500         1      2007          3           10
1334          5     250000         1      2008          7            7
1335          5     239000         1      2007         12            8
1336          0      91000         5      2008          4            6
1337          6     117000         2      2009          7            5
1338          1      83000         3      2011          6            6
1339          4     167500         1      2008          5            5
1340          1      58500         1      2010          6            3
1341          3     237500         4      2008          5            6
1342          2     157000         3      2011         10            7
1343          6     112000         2      2007          8            5
1344          3     105000         5      2009         10            6
1345          1     125500         3      2010          5            4
1346          5     250000         5      2011          7            7
1347          1     136000         1      2007          8            6
1348          3     377500         1      2009         10            9
1349          2     131000         3      2007          3            6
1350          3     235000         4      2011          9            7
1351          4     124000         3      2009          4            5
1352          5     123000         1      2011         12            5
1353          1     163000         3      2008          4            6
1354          2     281213         5      2007          2            8
1355          4     160000         5      2010          6            5
1356          2     137500         5      2007          5            5
1357          5     138000         2      2009          5            5
1358          4     137450         1      2009         10            6
1359          3     120000         5      2008          7            6
1360          3     193000         4      2008          4            6
1361          7     193879         3      2011          7            7
1362          5     282922         1      2007          8            8
1363          3     105000         1      2011          1            3
1364          3     275000         1      2008          1            8
1365          4     133000         5      2009          3            5
1366          4     112000         4      2009          3            5
1367          1     125500         1      2010          6            4
1368          3     215000         3      2008         11            7
1369          3     230000         1      2009          6            7
1370          4     140000         1      2009          9            6
1371          1      90000         2      2009          6            4
1372          3     257000         1      2009          9            8
1373          1     207000         1      2008          6            6
1374          4     122500         1      2010          4            4
1375          5     340000         1      2009          5            8
1376          6     124000         1      2008          8            5
1377          5     223000         4      2011         12            6
1378          3     179900         5      2011          5            6
1379          5     136500         2      2008          3            6
1380          5     274970         1      2011          8            6
1381          2     144000         2      2007          6            5
1382          3     142000         2      2008         10            6
1383          7     271000         1      2008          8            7
1384          5     140000         5      2008          4            5
1385          3     119000         1      2010          2            5
1386          5     182900         1      2007          4            6
1387          6     192140         4      2011          7            5
1388          6      64500         4      2007          8            4
1389          5     186500         1      2008          5            6
1390          3     160000         5      2011          5            5
1391          5     174000         2      2008          7            6
1392          3     120500         1      2007          5            4
1393          3     394617         5      2008         11            8
1394          3     149700         1      2010          4            6
1395          3     197000         4      2007         11            7
1396          4     191000         1      2008          9            6
1397          5     149300         5      2008          5            6
1398          3     310000         5      2009          4           10
1399          0     121000         1      2009          5            6
1400          5     179600         5      2007         11            7
1401          1     129000         4      2007          5            6
1402          2     157900         1      2010          4            5
1403          3     240000         2      2007         12            8
1404          1     112000         4      2007          5            4
1405          3      92000         4      2011          8            5
1406          4     136000         4      2009          9            5
1407          3     287090         4      2009          5            8
1408          2     145000         3      2011          5            5
1409          5      84500         1      2011          7            5
1410          5     185000         1      2009         10            7
1411          7     175000         1      2007          8            6
1412          5     210000         5      2010          2            6
1413          3     266500         1      2010          5            7
1414          3     142125         2      2010          4            5
1415          3     147500         4      2008          6            5
     total_sq_feet gr_liv_area tot_bathrooms   lot_area exter_qual full_bath
1        3586.8865   2785.0597             5  3898.2563          4         4
2        3560.3479   2315.2671             3  4149.4097          3         4
3        3672.3138   2852.3129             5  4461.6028          4         4
4        3527.5226   2791.3777             3  4139.1311          3         2
5        4012.2765   3173.3573             5  4928.2918          4         4
6        3308.4310   2433.1814             3  4908.1739          3         2
7        4029.9784   2770.5208             4  4246.2272          4         4
8        3940.4604   3095.4265             5  4303.5529          3         4
9        3684.1556   2841.8864             3  3263.2797          3         4
10       3239.9327   2070.1756             3  3642.4009          3         2
11       3249.2361   2016.1292             3  4452.8350          3         2
12       4085.6259   3259.5781             5  4576.1336          5         6
13       3038.0634   1813.0998             3  4741.3445          3         2
14       3831.7332   2576.2262             3  4354.0891          4         4
15       3548.8388   2304.2005             3  4402.9999          3         2
16       2911.5738   1711.5327             1  3263.2797          3         2
17       3192.5911   1961.6673             3  4460.0275          3         2
18       3359.7615   2122.3978             3  4848.7134          3         2
19       3457.7556   2406.8458             1  3679.1926          3         2
20       4101.6330   3293.8067             5  4922.0703          4         6
21       2966.8741   2114.0482             1  3650.0787          3         2
22       4118.8338   2860.0870             3  4178.3117          4         4
23       3264.6231   2045.5776             3  2533.5231          3         2
24       3279.8644   2045.5776             3  3850.1540          3         2
25       3924.7903   2682.2312             3  4924.1463          4         4
26       3016.7675   1792.6258             2  3583.1593          3         2
27       4043.2462   2779.6236             4  4501.0965          4         4
28       3882.5889   2682.2312             3  5194.0182          3         2
29       2134.9384    944.9928             1  3327.8180          3         2
30       3158.6031   2381.2287             1  3909.8688          3         2
31       3516.4303   2273.0382             2  3920.0315          3         2
32       3524.2681   2280.5746             3  4426.1164          4         4
33       3889.8728   2775.9889             3  4335.5229          3         2
34       3902.2834   2644.0685             4  3613.8106          5         4
35       4117.4825   3342.5095             5  4808.4914          4         6
36       3335.0340   2098.6225             2  4391.9736          3         2
37       3604.3387   2357.5667             2  3917.2651          3         2
38       3275.3072   2041.1960             3  3771.2550          3         2
39       2299.3248   2174.2578             3  3237.3815          3         4
40       3487.3604   2389.4257             3  3946.1207          3         4
41       3655.5874   2394.0903             3  5263.2223          3         2
42       2947.4081   1764.8989             3  4061.3539          3         2
43       3083.2597   1856.5520             3  4065.6376          3         2
44       3410.9035   2171.5713             3  3776.9614          3         2
45       4087.9224   2822.5867             4  3704.5436          5         4
46       4123.7788   3138.4854             3  4719.0575          4         2
47       3997.2937   2735.4335             3  4434.4717          4         4
48       3330.6306   2532.1299             3  2638.7556          3         4
49       3112.1390   1884.3173             3  3726.0162          3         2
50       3385.5357   2551.1824             3  4873.5653          3         4
51       3179.7279   2206.1381             1  3301.4991          3         2
52       4168.4864   2900.0623             3  7408.5165          4         0
53       2965.9525   2430.9091             1  3565.0335          3         2
54       3755.6911   2503.1040             3  4263.9104          3         4
55       3674.0956   2811.0681             5  1612.2968          4         4
56       3595.6363   2794.0776             3  4529.5294          4         4
57       4437.5968   3625.9072             5  4846.8440          5         6
58       2786.6976   1571.4462             1  3583.1593          3         2
59       3422.0509   2182.2897             3  4757.0676          3         2
60       2868.0795   2118.2286             1  3583.1593          3         2
61       3692.3934   2442.2376             3  3364.2052          4         4
62       3401.0857   2785.0597             3  4287.9445          3         4
63       3886.2350   3053.4180             5  4102.7273          3         4
64       4138.5234   3355.7009             3  4147.5635          4         4
65       4361.5986   3179.6778             4  5584.2968          3         4
66       3801.3076   2560.6214             4  4356.4899          4         4
67       2717.2008   1504.6387             1  2704.7712          3         2
68       4127.3657   3234.7537             3  5104.1976          4         4
69       4470.8576   3190.8509             4  4842.3790          3         4
70       2915.3836   1695.1572             3  3689.3204          3         2
71       3576.8281   2792.2782             3  4257.3221          3         4
72       3318.8290   2083.0414             3  4268.7407          3         2
73       3509.2119   2687.0564             3  3154.1812          4         4
74       2669.1435   1936.8328             3   618.3283          3         2
75       3107.0802   1879.4536             1  3904.0711          3         2
76       3151.2256   2343.1938             3  3940.8849          3         2
77       4102.5429   2836.6467             3  4377.2359          3         4
78       2896.2435   2275.5544             2  4314.5188          3         2
79       3858.4211   3133.4389             3  4746.1958          3         4
80       3591.8922   2404.5344             4  2658.0941          3         4
81       3904.3425   2646.0486             3  4269.8983          3         4
82       3287.4313   2052.8530             2  3998.6127          3         2
83       3067.7581   2555.3846             3  3916.8036          3         4
84       4177.6281   3320.2708             3  5162.1627          4         4
85       3371.2677   2643.0775             3  4573.9864          4         4
86       3048.6066   2267.9935             3  2402.0284          4         4
87       3569.8763   2608.9998             1  3902.9095          2         2
88       3170.0124   1939.9590             3  3807.6881          3         2
89       2134.9384   2016.1292             1  3583.1593          3         2
90       3525.5707   2281.8271             1  3909.8688          3         2
91       3052.1057   1898.8174             3  4799.9644          3         2
92       4088.3813   3237.4567             3  3583.1593          3         4
93       3614.2271   2852.3129             5  4094.7327          3         4
94       3302.4590   2551.1824             3  4182.9534          5         4
95       3929.8619   2670.5887             3  4281.0527          4         4
96       3120.5352   1892.3897             3  4403.1801          3         2
97       2484.9228   1676.7567             1  4349.0935          3         2
98       3321.0484   2269.2562             3  4091.1457          3         2
99       3951.9888   2691.8667             4  4345.0136          3         4
100      3527.5226   2804.8301             3  4066.9209          4         4
101      2760.7251   2618.0936             3  3532.7659          3         4
102      3513.8091   2270.5179             3  4307.3412          3         4
103      3760.1989   2879.7784             2  3730.0798          3         2
104      3862.1223   3021.1459             3  4102.7273          4         4
105      2913.4798   2026.5001             1  4381.2497          3         2
106      2805.1416   1589.1768             1  3224.3035          3         2
107      3417.8797   2599.8521             3  3909.8688          3         4
108      4170.2317   2901.7406             3  4547.3658          3         4
109      3755.1268   2910.9393             3  4133.9716          3         4
110      3029.2244   2508.5204             3  3728.0490          3         4
111      4284.6769   3489.2531             5  4222.8606          4         4
112      4327.9523   3215.6993             4  5690.2054          3         4
113      4014.6800   3256.9135             5  3599.2226          3         4
114      3329.8955   2538.5068             3  2005.5016          3         4
115      3327.6883   2091.5596             2  4524.6213          3         2
116      3375.5614   2137.5895             2  3918.1877          3         2
117      4625.5973   3764.9692             5  4649.3696          3         6
118      3327.6883   2536.3841             3  3900.8169          4         4
119      3125.5520   1936.8328             3  5732.2164          3         2
120      3065.1599   2134.8385             1  3243.8880          3         2
121      3309.9205   2074.4761             1  4121.3254          3         2
122      3477.9997   2236.0858             3  3763.7871          4         4
123      3810.0595   2668.6398             3  5279.2260          3         4
124      2461.1268   1519.0530             3  3464.8582          3         2
125      2736.4542   1685.9843             1  2608.4900          3         2
126      3192.5911   2417.2045             2  3686.9878          3         2
127      3881.0238   3144.2327             3  4919.9921          3         4
128      3862.6503   3068.5523             5  4625.0443          4         4
129      3472.6261   2392.9255             3  3633.8940          3         2
130      3585.0053   2356.3741             4  3485.9372          4         4
131      3932.8972   2794.9765             3  4294.6218          3         4
132      3830.6564   2759.5263             3  4306.9627          3         4
133      3497.9922   2255.3093             3  4298.4272          3         4
134      3759.0731   2908.4360             3  4036.7574          4         4
135      3663.9723   2833.1436             5  5083.0021          3         4
136      2951.1341   1729.5267             1  4325.7989          3         2
137      4071.3139   2806.6150             4  4529.5294          4         4
138      3407.4040   2459.0763             3  3914.4948          3         4
139      3833.3470   2583.4550             4  4294.6218          4         4
140      4065.7394   2801.2542             4  4044.1254          3         4
141      3656.1878   2784.1550             3  1518.5926          4         4
142      2817.3212   1749.0814             3  3263.2797          3         2
143      3794.1614   3054.1782             3  4129.8342          4         4
144      3309.9205   2074.4761             3  3663.5088          3         2
145      3368.3988   2412.6092             1  3301.4991          3         2
146      3135.5388   1906.8146             2  4298.6173          3         2
147      4048.8990   2785.0597             4  4876.6853          4         4
148      3737.5327   3021.9222             3  5001.8546          3         4
149      3757.9466   2302.9660             3  4820.4842          3         2
150      3479.3403   2237.3748             1  4477.2872          3         2
151      2894.3169   2097.2125             1  4149.4097          3         2
152      2134.9384   2016.1292             1  3583.1593          3         2
153      3693.5667   3002.3980             3  4589.1317          4         4
154      3804.5951   2985.8051             3  4677.1651          4         4
155      4241.0399   3348.8051             5  5531.9726          4         4
156      3521.6597   2278.0665             3  4438.7246          3         4
157      4394.5557   3473.1035             5  4847.7070          4         4
158      3881.5456   2624.1266             3  4618.2695          4         4
159      2984.2855   1761.3978             1  3053.0464          3         2
160      3706.9995   2697.6194             3  3016.9317          3         4
161      3185.3682   2425.2136             4  4250.5168          3         4
162      4078.7166   2920.9123             3  4364.4102          4         2
163      4194.0392   3147.0984             3  4337.3874          4         2
164      3583.1219   2794.0776             3  3849.6765          4         4
165      4036.1520   2782.3440             3  5235.5485          4         4
166      3266.1538   2455.7232             2  4646.5046          3         2
167      3690.0440   2735.4335             3  6505.1565          3         2
168      3744.9343   2835.7716             4  2982.3689          4         4
169      3682.9754   2433.1814             3  4268.1617          3         2
170      3970.3629   2730.7570             4  4655.7213          3         4
171      4020.4340   3144.9496             4  4687.0201          3         4
172      3947.4876   3073.0638             4  4235.4620          4         4
173      3823.0987   2964.2066             4  4842.2348          4         4
174      4472.3040   3198.4859             4  5322.6333          5         4
175      3133.8787   1905.2185             1  3914.4948          4         2
176      3397.5648   2607.9860             3  1174.1415          4         4
177      3604.9585   2866.1066             2  3686.4691          3         2
178      2542.3173   2408.0002             1  4035.4543          3         2
179      4060.1455   3089.4946             3  4492.1587          3         4
180      2976.9773   2302.9660             1  3647.1700          3         2
181      4565.3390   3940.0158             3  5864.9964          4         4
182      3482.6869   2259.1255             4  4219.3019          3         4
183      3422.0509   2735.4335             3  4308.8544          3         4
184      3417.8797   2267.9935             4  3532.7659          3         0
185      3934.9175   2675.4504             3  2834.9131          4         2
186      4122.4317   3506.9386             3  4338.8778          4         4
187      3342.3463   2560.6214             3  3656.1468          3         2
188      3762.4481   2509.6014             4  4026.0901          4         4
189      3656.1878   2784.1550             3  1518.5926          4         4
190      2951.1341   1729.5267             1  3577.6843          3         2
191      4063.8769   2799.4632             4  4111.3168          5         4
192      4480.2358   3711.2323             5  6066.1334          4         4
193      3829.5789   3195.0201             1  3060.1905          3         2
194      4051.7180   2787.7705             4  4147.5635          4         4
195      3369.8339   2132.0825             3  3920.4922          3         4
196      3528.8225   2335.9570             3  4254.2140          3         4
197      3126.3866   2372.9881             3  3527.7111          3         4
198      2921.0815   1700.6350             3  2630.7893          4         2
199      3189.3850   2341.9901             2  2163.4921          3         2
200      3764.6941   2521.4429             3  4564.0458          3         4
201      3747.7720   2772.3457             2  4845.5487          3         2
202      3339.4254   2102.8447             3  4667.8910          3         2
203      3951.4893   3074.5648             5  4942.5956          4         4
204      3327.6883   2091.5596             3  3851.1086          3         2
205      2951.1341   1729.5267             3  3089.9158          3         2
206      3495.3408   2252.7599             3  4310.7443          3         4
207      3699.4209   2908.4360             5  3942.0243          3         4
208      3170.0124   1939.9590             2  4830.3742          3         2
209      3250.0089   2466.8722             2  4399.3915          3         2
210      3415.0928   2283.0786             2  4231.9260          3         2
211      3768.0572   2514.9951             4  3898.2563          4         4
212      3197.3885   2394.0903             1  4211.1719          3         2
213      3699.4209   2991.3559             3  5112.6374          4         2
214      3836.0331   2580.3611             3  4020.1873          4         4
215      3980.2082   3221.1674             3  3807.2002          4         4
216      3386.2458   2635.1264             5  4500.5820          3         4
217      2951.1341   1729.5267             1  4325.7989          3         2
218      4588.7056   3304.1881             3  4816.3973          5         4
219      3130.5532   2363.5162             3   719.2405          3         4
220      4185.4226   3384.8232             3  4219.8955          4         4
221      2691.1659   1935.2673             2   928.9895          3         2
222      3038.0634   1813.0998             1  3914.7258          3         2
223      3471.2799   2229.6246             3  3969.1741          3         2
224      4400.6134   3544.4854             5  5045.9046          4         4
225      2691.1659   1935.2673             2   719.2405          3         2
226      3006.0129   1782.2863             3  4353.7195          3         2
227      3738.6736   2996.0979             5  3753.5348          4         4
228      2691.1659   1935.2673             2   719.2405          3         2
229      3743.2293   2491.1207             3  3972.0930          4         4
230      3692.3934   2815.5085             3  4119.0362          4         4
231      4033.7804   2770.5208             3  4593.5545          5         4
232      3355.4253   2568.9636             2  3964.9002          3         2
233      3907.4263   2649.0141             4  4022.3756          4         4
234      2778.4319   1733.1005             1  2366.3406          3         2
235      3170.0124   2519.2966             1  2865.4586          3         2
236      3054.7250   2259.1255             2  4374.3117          3         2
237      3868.9735   3110.1573             5  3995.9546          4         4
238      4182.8286   2925.0488             3  4306.9627          3         4
239      3810.0595   2970.6377             3  4053.1892          3         4
240      3693.5667   2447.8709             1  4472.0730          3         2
241      3550.1217   2746.5999             3  4473.2909          4         4
242      4126.0215   3134.8824             3  9675.2363          4         4
243      3213.2771   2368.2594             1  2998.6228          3         2
244      3940.9634   2706.2085             5  2764.5055          4         4
245      3504.6015   2720.4186             3  3878.5916          4         4
246      3610.5261   2363.5162             3  4097.4714          3         4
247      3625.2793   2377.7024             3  3886.5748          3         2
248      3974.8007   3237.4567             3  3964.2246          4         4
249      3603.0984   2801.2542             3  3976.1274          4         4
250      3945.9843   2686.0926             5  3981.2704          4         4
251      3701.1729   2857.5000             3  4658.7312          4         4
252      1870.1262   1761.3978             1  4700.5487          3         2
253      3694.7393   2455.7232             3  5523.6252          3         2
254      4323.2010   3417.6201             3  4146.9478          4         4
255      2941.8028   2252.7599             3  3903.1419          3         2
256      3369.8339   2380.0542             3  3053.0464          3         2
257      2662.4776   1539.4147             1  2954.7265          3         2
258      3752.3020   2499.8450             3  4603.3476          3         4
259      3419.9666   2593.7236             5  4454.0648          3         4
260      3790.3003   3169.1293             3  3886.5748          3         4
261      2742.8211   1567.4783             1  3499.3902          3         2
262      3379.8437   2121.0094             3  3770.0123          3         2
263      3856.3023   2979.4369             3  4368.0832          4         4
264      3697.0818   2434.3163             3  6914.0189          3         2
265      4049.8392   3223.2129             3  4549.5422          4         4
266      3768.0572   2712.8561             4  4149.4097          3         4
267      2859.2377   1641.1812             1  3866.3190          3         2
268      3544.9841   2631.1356             3  3600.5779          4         4
269      3901.2528   2643.0775             3  4064.7816          4         4
270      2951.1341   1729.5267             1  5507.4407          3         2
271      4395.3141   3118.1999             3  4954.3458          5         4
272      3932.8972   3044.2659             3  4230.7459          3         4
273      3720.8977   3013.3619             3  4468.0660          4         4
274      3560.3479   2315.2671             3  3583.1593          4         4
275      3625.2793   2377.7024             4  2890.1026          4         4
276      3803.5000   2549.0770             3  4151.8686          4         4
277      3916.6423   2657.8764             4  3793.4905          4         4
278      3082.4024   2300.4940             3  2546.0632          4         4
279      3636.2561   2806.6150             2  4187.1819          3         2
280      2939.9301   1718.7554             1  3821.0573          3         2
281      3000.6085   1792.6258             1  4193.8083          3         2
282      3260.0224   2471.3093             1  3962.4217          3         2
283      3837.1063   2963.4009             3  5106.4685          4         4
284      3542.4091   2790.4767             4  3118.8529          3         4
285      3534.6594   2790.4767             2  4489.2279          3         2
286      3868.9735   3218.4357             5  5234.3673          3         4
287      3870.0249   2724.1860             3  4149.4097          3         2
288      3190.9888   1960.1268             3  3774.9784          3         2
289      3524.2681   2641.0935             2  4850.8682          3         2
290      3797.4636   2988.1865             3  3636.8224          4         4
291      3509.2119   2814.6214             3  4538.8043          4         2
292      3371.2677   2174.2578             2  4892.0708          3         2
293      3545.6272   2403.3774             3  5123.9178          3         2
294      4076.8691   3342.5095             3  5182.5270          4         4
295      3881.5456   2624.1266             3  4850.0066          4         4
296      3006.0129   1782.2863             3  4189.9958          3         2
297      4647.7867   3889.9034             4  5428.5325          3         6
298      4300.8409   3027.3451             4  4304.3111          4         4
299      3807.3296   3204.7048             5  4816.6895          4         4
300      2948.3404   2482.3469             1  3770.7581          3         2
301      2945.5418   1724.1504             1  4643.9544          3         2
302      4235.1870   2983.4201             4  4649.6876          4         4
303      3337.9629   2583.4550             3  3711.4711          3         4
304      3140.5091   1911.5932             3  3790.5402          3         2
305      3112.9806   2127.9394             3  3740.7070          3         2
306      4368.5527   3054.9381             5 10271.4555          3         4
307      3458.4345   2721.3613             3  4149.4097          3         2
308      3300.9625   2510.6816             5  3739.4448          4         4
309      3940.9634   3278.7604             5  4746.9527          4         4
310      3863.1782   2995.3085             3  4022.3756          4         4
311      4298.0239   3460.2952             5  4209.9793          4         4
312      3752.3020   2553.2849             4  4908.1739          3         4
313      4237.2798   3430.7850             5  5186.5263          3         6
314      4133.1773   3352.5703             5  4604.8123          4         4
315      4391.5182   3508.6395             5  4303.1737          4         4
316      3428.2875   2188.9512             3  3164.3529          3         2
317      4170.2317   3643.1450             3  4465.9722          4         4
318      2748.1077   1616.3601             1  2865.4586          3         2
319      4057.3412   2793.1781             5  4389.6157          4         2
320      3707.5810   2456.8417             2  4521.9082          3         2
321      3826.3421   3127.6513             3  4570.1817          3         4
322      3006.0129   2227.0325             1  3351.9458          3         2
323      4065.7394   2801.2542             3  4348.9082          3         4
324      3273.7852   2039.7326             3  3833.3737          3         2
325      4605.7609   2710.0106             4  4354.6434          4         4
326      3678.2456   2428.6334             4  3838.6629          4         4
327      3596.2594   2718.5314             5  4031.5398          3         4
328      3984.1294   2852.3129             5  9744.0931          3         4
329      4236.8614   2965.8169             4  4914.0223          4         4
330      3876.3192   2619.1008             4  4051.6815          4         4
331      3743.7978   2702.3970             4  4912.3531          4         4
332      3499.3162   2256.5824             1  4653.1831          3         2
333      3769.7362   2954.5097             3  4918.7441          4         4
334      2134.9384   2016.1292             3  3920.0315          3         4
335      4024.2585   2761.3642             3  3989.0711          5         4
336      2874.9230   2119.6196             2  1572.4658          3         2
337      3576.1974   2659.8390             1  3362.0653          3         2
338      3117.1820   1889.1658             1  4711.3666          3         2
339      3814.4177   2559.5755             4  5342.5298          3         4
340      3472.6261   2707.1599             5  1459.9909          4         4
341      4517.2110   3507.5058             5  5636.1335          5         4
342      4191.8894   2922.5682             3  3745.7475          5         4
343      3786.9834   2533.1945             3  2969.3431          3         2
344      2950.2034   2118.2286             2  4040.6616          3         2
345      2547.1087   1447.7479             1  3914.4948          3         2
346      3567.3409   2677.3908             1  3886.5748          3         2
347      3479.3403   2237.3748             4  4461.4278          4         4
348      3428.2875   2194.2598             4  4075.8805          3         4
349      3399.6783   2160.7781             3  2533.5231          3         2
350      3488.6932   2421.7862             2  3507.9293          3         2
351      3843.5305   2967.4255             5  4590.4432          4         4
352      3016.7675   1813.0998             3  3673.9785          3         2
353      3471.2799   2587.5706             3  4053.6198          3         2
354      3122.2092   2965.8169             4  3610.5781          4         6
355      2691.1659   1935.2673             2   719.2405          3         2
356      3459.1132   2656.8942             5  5472.3648          3         4
357      3198.9844   2412.6092             1  4361.0986          3         2
358      3720.3210   2469.0923             3  4128.7985          3         2
359      3564.1660   2509.6014             2  4054.9109          3         2
360      3567.9751   2322.6010             1  3740.7070          3         2
361      3445.4858   2345.5986             3  4196.0122          3         2
362      3618.5342   2742.8867             3  3820.0881          3         4
363      2815.2976   2670.5887             3  5288.0993          3         4
364      2719.3515   1514.9483             3  3576.3131          3         2
365      3126.3866   2383.5752             3  4350.7601          3         2
366      3712.8050   2970.6377             3  3839.1431          4         4
367      2814.2849   1799.4806             2  4233.6948          2         0
368      3002.4120   1816.4859             1  3988.4037          4         2
369      4319.2308   3351.3162             4  4442.7917          4         6
370      4180.6638   2911.7729             3  4486.6382          4         2
371      3716.8564   2864.3891             3  3820.5728          3         4
372      3678.8376   2767.7795             3  2865.4586          3         4
373      3604.3387   2362.3282             4  3583.1593          4         4
374      3690.0440   2861.8093             3  4075.2419          4         4
375      2794.9211   1579.3515             1  4022.3756          3         2
376      4101.1779   2990.5641             5  7516.5496          4         4
377      3053.8524   2216.6206             1  3888.9166          3         2
378      3314.3809   2137.5895             3  3583.1593          3         2
379      3809.5139   2560.6214             3  4104.1965          4         4
380      4306.4601   3264.8935             5  4664.8950          5         4
381      3359.7615   2438.8477             3  3887.7461          3         2
382      3706.9995   2996.8868             5  4622.6274          3         4
383      1870.1262   1761.3978             1  3872.2289          3         2
384      2803.1027   1587.2167             1  3649.2859          3         2
385      2988.8363   2007.1843             1  4255.9629          3         2
386      3402.4919   2163.4834             3  4143.4547          3         2
387      3006.0129   1782.2863             1  3583.1593          3         2
388      3654.3860   2874.6656             3  3686.9878          3         4
389      3216.4360   2070.1756             1  4015.1451          3         2
390      3633.8233   2633.1323             4  3821.0573          4         4
391      3575.5664   2346.7996             3  5023.0164          4         2
392      3620.3766   2372.9881             3  3970.7463          4         4
393      2547.1087   1341.1370             1  4268.7407          3         2
394      4041.3574   3218.4357             3  4603.3476          4         4
395      3464.5320   2654.9280             3  4300.1373          3         4
396      3784.2141   2701.4427             4  4227.9897          3         4
397      3670.5300   2719.4753             1  4322.0460          3         2
398      3557.7974   2757.6863             3  5102.0503          3         4
399      3959.4631   3154.9518             3  4913.6051          4         4
400      3897.1239   3086.5202             5  4381.2497          4         4
401      3578.0888   2332.3259             1  4143.4547          3         2
402      3273.7852   2039.7326             3  6675.9735          3         2
403      3810.0595   2559.5755             5  2615.2063          5         4
404      3214.8573   1998.1874             1  4013.6079          3         2
405      3930.3681   3100.5982             4  4457.7498          4         4
406      3656.7879   2408.0002             3  4000.1616          4         4
407      3243.0398   2475.7338             2  3751.7791          3         2
408      4298.4266   3447.3800             5  5819.0041          3         4
409      3095.2140   2149.9091             3  3829.5180          3         2
410      3273.7852   2039.7326             3  3898.2563          3         2
411      3661.5811   2412.6092             5  3544.5102          3         4
412      3943.9778   2684.1631             3  5231.5294          4         4
413      3166.7609   1936.8328             1  5759.2814          3         2
414      4340.5542   3450.9130             5  4065.6376          4         4
415      3473.9712   2232.2123             3  4022.3756          3         2
416      3218.0132   2463.5359             2  2093.6696          3         2
417      3922.7572   2724.1860             5  4715.6772          4         4
418      3029.2244   1804.6018             1  3931.2877          3         2
419      3490.0250   2247.6485             4  3459.6258          4         4
420      3729.5235   2488.9319             4  4497.4919          3         4
421      2691.1659   1935.2673             2   719.2405          3         2
422      3263.8573   2234.7957             1  3083.5838          3         2
423      3287.4313   2436.5837             3   981.9583          3         2
424      3564.1660   2686.0926             3  4388.3449          3         4
425      2443.3649   1241.4190             3   950.9730          3         2
426      3519.0471   2740.0960             5  4356.8590          4         4
427      2986.1074   2127.9394             1  2613.8649          3         2
428      3006.0129   1799.4806             1  3224.3035          4         2
429      2274.0125   1390.9136             1  2559.4438          3         2
430      3086.6843   2232.2123             1  4645.8674          3         2
431      4811.8597   3310.6412             4  5083.6400          5         4
432      3772.5305   2519.2966             3  4606.2760          3         4
433      3639.2920   2655.9114             3  3301.4991          3         4
434      3740.3835   2954.5097             5  3966.9259          4         4
435      3903.8280   2765.9493             1  4201.0118          3         2
436      4041.8298   2938.2118             3  5214.5349          4         4
437      3736.3910   2936.5726             3  4455.2939          4         4
438      3306.9401   2448.9951             3  3932.8905          3         4
439      3045.0999   2215.3141             2  3224.3035          3         2
440      2853.3161   1635.4884             1  3117.8144          3         2
441      3873.1751   2616.0774             4  8081.5149          3         4
442      3625.2793   2826.1137             5  4087.5521          4         4
443      3450.9506   2672.5352             3  4022.3756          4         4
444      4065.7394   2801.2542             5  4086.2822          3         4
445      3534.6594   2290.5663             2  4149.4097          3         2
446      3160.2380   2412.6092             1  2688.9043          3         2
447      3852.5876   2741.9571             3  7520.9926          3         2
448      3378.4175   2744.7444             1  2904.4335          3         2
449      3113.8218   2241.2355             3  3531.9244          3         2
450      3708.1623   2976.2430             5  3791.5242          4         4
451      2920.1333   2151.2719             3  3583.1593          4         2
452      2951.1341   1729.5267             1  3858.4908          3         2
453      3462.5021   2739.1646             2  4586.6703          3         2
454      3249.2361   2016.1292             3  3893.5920          3         4
455      3579.3486   2333.5372             3  4349.6492          3         2
456      3460.4696   2724.1860             2  4124.6503          3         2
457      3971.8435   2714.7502             3  4492.5032          4         4
458      3571.7752   2785.0597             3  4085.0114          4         4
459      3832.8093   2584.4849             3  3476.4363          4         2
460      3713.9636   3003.1837             3  4580.7503          3         4
461      2846.3799   2062.9814             3  2259.5116          3         2
462      4281.4245   3008.6726             4  5024.8573          4         4
463      3914.5989   2731.6934             4  2991.2513          4         4
464      3137.1973   1908.4091             3  3905.2320          3         2
465      3822.5575   2575.1908             4  4765.0323          3         4
466      4592.7349   3458.5403             3  4848.4259          5         4
467      4050.3091   2792.2782             4  4351.3153          4         4
468      3216.4360   2145.8135             1  3199.5456          3         2
469      4168.0498   2906.7649             4  5158.9732          4         4
470      4124.2276   2857.5000             4  4563.2152          4         4
471      3690.0440   2886.5693             3  1501.3520          4         2
472      3500.6391   2257.8544             4  2658.0941          3         4
473      3184.5636   1953.9493             3  3730.0798          3         2
474      3358.3174   2121.0094             1  4149.4097          4         2
475      3299.4647   2064.4229             3  4285.8412          3         2
476      3820.9329   2565.8405             3  4628.1015          3         4
477      4024.2585   3318.3497             3  4381.2497          3         4
478      2443.3649   1241.4190             3   530.0939          3         2
479      2794.9211   2365.8896             2  1627.1203          3         2
480      3468.5841   2660.8193             3  4126.7255          3         2
481      3327.6883   2536.3841             3  5102.3031          4         4
482      3569.2428   2323.8200             2  3773.4899          3         2
483      2189.6306   1768.3920             1  3152.1406          3         2
484      2658.0183   1447.7479             1  3760.5421          3         2
485      5063.8097   3767.8474             5  4698.9984          4         6
486      3753.4325   2881.4789             4  4048.4467          3         4
487      2983.3738   1790.9073             1  3740.7070          3         2
488      3038.0634   1813.0998             2  3672.6729          3         2
489      3095.2140   2260.3954             2   950.9730          3         2
490      3628.9466   2836.6467             3  4190.5983          4         4
491      3497.9922   2255.3093             3  4059.2086          3         2
492      3992.4306   2865.2481             4  5105.3334          3         4
493      3794.7123   2996.0979             3  3688.5432          3         4
494      3661.5811   2956.9396             3  4139.9554          4         4
495      3503.2818   2260.3954             3  3756.2906          4         4
496      3239.1550   2451.2410             3  4149.4097          3         4
497      3250.7814   2017.6150             3  4149.4097          3         2
498      3690.0440   2439.9785             3  3468.3388          4         4
499      2951.1341   1729.5267             3  4044.1254          3         2
500      3312.8955   2074.4761             2  4062.8543          3         2
501      2783.6030   1589.1768             1  4343.3421          3         2
502      4311.2610   3042.7352             5  4624.4001          5         4
503      3731.8159   3116.7408             3  4316.0265          3         4
504      4134.9613   3272.8327             3  4270.2840          4         4
505      3601.8571   2860.9484             5  4135.2111          3         4
506      4018.5183   3088.0081             2  4402.6394          4         2
507      2486.1656   2353.9860             3  4381.2497          3         4
508      3537.2468   2293.0542             2  4586.6703          3         2
509      3649.5713   2742.8867             3  2865.4586          3         4
510      4208.5822   3308.0632             5  4553.3869          4         4
511      3559.7107   2320.1602             3  3663.5088          4         4
512      3066.0265   1839.9837             1  4791.1044          3         2
513      4365.8519   3498.9766             5  5021.0421          5         4
514      2272.5945   1178.8613             3  4043.6928          3         2
515      4508.0466   3381.7510             5  6560.0255          4         6
516      3822.0162   2591.6753             4  4268.7407          4         4
517      3164.3179   2433.1814             3  3274.5039          3         4
518      1766.6670   1661.8771             1  3583.1593          3         2
519       310.9762    261.6012             1  2865.4586          2         2
520      3280.6227   2491.1207             3  4034.5851          4         4
521      3521.6597   2416.0569             3  3527.7111          3         2
522      3610.5261   2797.6701             3  4005.6835          3         4
523      2951.1341   1729.5267             1  4705.6560          3         2
524      3346.7178   2183.6243             2  4513.9166          3         2
525      3932.8972   2683.1974             4  4491.6418          4         4
526      4164.9902   2896.7000             4  4974.8087          5         4
527      3968.8809   3233.4004             3  4417.3677          4         4
528      4006.0103   2757.6863             4  4257.1279          4         4
529      2712.8908   1545.4713             3  2454.6181          3         2
530      3302.4590   2578.2950             5  5286.2588          4         4
531      4033.3056   3162.7655             3  4869.0183          4         4
532      3668.7442   2715.6964             2  3963.9993          3         2
533      2761.7721   1547.4849             3  3595.1511          3         2
534      2876.8729   1658.1347             3  3847.5266          3         2
535      3841.3919   3098.3839             3  4102.7273          4         4
536      3066.0265   1839.9837             1  3224.3035          3         2
537      4051.7180   2791.3777             3  4443.3216          4         4
538      2262.6334   2138.9632             3  3972.9902          3         4
539      3861.5941   3062.5163             5  4349.0935          4         4
540      3218.8012   2027.9759             1  3345.1704          3         2
541      3327.6883   2091.5596             3  5008.0945          3         2
542      3321.0484   2525.7266             4  5770.2921          3         4
543      3718.0121   2466.8722             3  4477.4608          3         2
544      3714.5426   2463.5359             3  4231.7294          3         2
545      3179.7279   1949.2999             3  4878.9512          3         2
546      3748.3390   2752.1530             3  5761.9947          3         4
547      4034.7294   3240.1549             5  4797.9006          4         4
548      3514.4648   2727.0056             3  3487.3728          3         2
549      4142.9648   3374.9706             3  4452.4834          4         4
550      3865.8150   2618.0936             3  4263.1364          4         4
551      4143.8517   3126.2010             3  4641.5607          4         2
552      3091.8076   1864.7701             3  3536.6885          3         2
553      4065.7394   2801.2542             3  4761.4297          3         4
554      2951.1341   1729.5267             3  3618.9178          3         2
555      3569.2428   2768.6938             3  4770.1249          3         4
556      3029.2244   2508.5204             3  4223.2557          3         4
557      2703.1509   2115.4429             2  4325.7989          3         2
558      3224.3064   2257.8544             1  3905.2320          3         2
559      3437.2536   2558.5288             3  3317.8332          3         4
560      3534.6594   2384.7470             3  4551.7162          3         2
561      3250.0089   2466.8722             3  2221.1179          4         4
562      3752.8674   2860.0870             3  4613.0921          3         4
563      3591.2673   2507.4386             2  4972.6505          3         2
564      4334.2656   3059.4895             3  4700.8586          5         4
565      2859.2377   1641.1812             3  4562.3842          3         2
566      4305.6585   3533.9300             5  4820.4842          5         6
567      3517.0849   2655.9114             1  3263.2797          3         2
568      4258.4719   3048.8487             4  4495.0852          4         4
569      2880.7657   1682.2998             3  4281.6279          3         2
570      2924.8689   1722.3542             3  3964.6750          3         2
571      3789.1954   2554.3351             4  6040.8811          3         2
572      2902.9685   1851.6001             1  4044.1254          3         2
573      3446.8537   2664.7345             3  3867.7390          4         4
574      4308.0620   3240.8288             5  4817.2738          5         4
575      2859.2377   1641.1812             3  3411.8973          3         2
576      2921.0815   1700.6350             3  2629.4584          4         2
577      3059.0811   1833.3064             1  3788.0783          3         2
578      4149.1624   2886.5693             4  4470.6802          4         4
579      3227.4439   2439.9785             1  2218.9325          3         2
580      3878.9345   2727.0056             4  4743.7716          3         4
581      3817.6786   2951.2638             5  4404.2613          4         4
582      3306.1941   2447.8709             2  4022.3756          3         2
583      3740.3835   2960.1736             5  4237.8158          4         4
584      3016.7675   2237.3748             3  1976.0372          4         4
585      3831.7332   2576.2262             4  4716.1385          4         4
586      3700.5891   3016.4802             3  4835.0113          3         4
587      3249.2361   2016.1292             3  4663.3164          3         2
588      3785.8762   3033.5195             5  3740.7070          3         6
589      4363.5334   3751.4668             3  4616.0061          3         4
590      3232.1385   1999.6905             3  3776.4658          3         2
591      4128.2611   3141.3617             5  4426.2946          4         4
592      3236.8195   2004.1912             3  4306.0161          3         4
593      3927.3281   2925.0488             5  4569.6850          4         4
594      3368.3988   2130.7027             1  3887.0434          3         2
595      2443.3649   1241.4190             3   484.4479          3         2
596      3178.1127   2036.8018             3  3978.1415          3         2
597      3405.3006   2591.6753             5  3756.0403          4         4
598      2890.4568   1671.1936             1  3590.5266          3         2
599      4153.5747   2888.2624             3  4537.7946          5         4
600      4194.4688   3217.7521             5  4628.2622          4         4
601      2951.1341   1729.5267             3  3850.6313          3         2
602      4354.6144   3441.4736             3  4381.2497          3         4
603      3153.6885   1924.2645             1  3545.6251          3         2
604      3388.3742   2594.7467             3  1174.1415          4         4
605      3559.0732   2855.7729             4  4306.9627          3         2
606      3362.6457   2125.1711             2  4229.7620          3         2
607      3479.3403   2499.8450             1  4643.9544          3         2
608      3654.3860   2602.9074             3  4149.4097          3         2
609      3901.2528   3088.0081             3  4522.9261          3         2
610      3606.8165   2419.4970             3  4026.7448          3         2
611      3469.9326   2820.8202             1  4022.3756          3         2
612      3895.0555   2637.1180             3  2697.0681          4         4
613      3725.5039   2487.8364             3  4572.1677          3         4
614      3273.7852   2039.7326             2  4076.3062          3         2
615      3273.7852   2039.7326             3  3521.7974          3         0
616      4605.7609   3845.8796             3  4398.6690          2         4
617      2171.6057   1610.5751             1  3263.2797          2         2
618      3337.9629   2461.3077             3  3224.3035          3         4
619      2819.3421   1602.8281             1  3972.9902          3         2
620      3857.3620   2600.8712             2  4696.6706          5         2
621      3830.6564   2971.4397             5  3541.7203          4         4
622      4545.0862   3493.8365             5  4872.2875          4         4
623      3479.3403   2701.4427             3  4379.9734          3         4
624      4100.7226   2834.8961             5  4062.8543          5         4
625      3155.3284   1925.8411             3  4331.4148          3         2
626      2147.2539   2027.9759             1  3583.1593          3         2
627      3330.6306   2094.3886             1  4316.7800          3         2
628      3604.9585   2897.5413             2  3715.3092          3         2
629      2443.3649   1241.4190             3   998.2865          3         2
630      3530.7705   2743.8159             3  3821.0573          4         4
631      3386.2458   2592.6998             3  4040.6616          3         2
632      3605.5781   2790.4767             3  3966.9259          4         4
633      3357.5949   2550.1301             1  4291.7628          3         2
634      4387.7133   3112.3549             5  4313.9531          4         4
635      2844.3926   2091.5596             2   719.2405          3         2
636      3269.2107   2035.3343             3  4231.1394          4         2
637      3395.4485   2584.4849             2  3583.1593          3         2
638      3459.1132   2538.5068             2  5331.6510          3         2
639      3823.0987   2567.9232             3  4217.3221          3         2
640      3685.3350   2976.2430             3  4650.6415          3         4
641      4331.5066   3339.9840             5  7258.7834          4         4
642      3718.0121   2466.8722             3  4829.2133          3         2
643      3424.1325   2212.6980             4  4232.1226          3         4
644      4369.3235   3100.5982             3  5680.4325          4         2
645      4011.7953   2977.0421             3  4451.7802          4         4
646      3884.1525   2756.7655             4  3821.0573          3         4
647      3623.4425   2516.0716             3  4916.5235          3         2
648      3086.6843   2211.3882             1  4521.9082          3         2
649      3349.6256   2557.4815             5  3940.4289          4         4
650      3218.8012   2441.1084             4  3420.5267          3         4
651      3490.0250   2247.6485             3  4461.6028          4         2
652      3999.2348   2897.5413             4  4953.2557          3         4
653      3391.2076   2152.6335             3  4065.6376          3         2
654      2786.6976   1595.0421             1  4027.1812          4         2
655      4337.4130   3062.5163             3  4562.8828          4         4
656      3166.7609   1936.8328             3  4218.9061          3         2
657      3057.3401   1831.6325             3  3793.4905          3         4
658      3419.9666   2602.9074             1  2658.0941          3         2
659      3596.8824   2350.3970             3  1784.5754          3         2
660      3988.5295   2746.5999             4  4461.2529          4         4
661      3856.3023   2897.5413             3  5247.4396          4         4
662      3981.6798   3095.4265             4  2889.7138          4         4
663      3629.5570   2830.5111             4  4270.0911          4         6
664      2879.7934   2105.6532             3  2906.3621          4         4
665      3748.9057   2496.5791             4  3812.3168          4         4
666      3682.9754   2433.1814             3  3683.6137          4         4
667      2921.0815   1700.6350             3  2625.4604          4         2
668      5144.8110   4217.2135             5  5739.7262          5         6
669      4188.0124   3384.2093             5  6124.0509          4         4
670      3299.4647   2064.4229             1  3016.9317          3         2
671      3522.9644   2622.1182             2  3263.2797          3         2
672      3374.8466   2153.9939             4  4865.3161          3         4
673      2407.2417   1206.6988             1  3224.3035          3         2
674      3285.9207   2168.8800             2  3357.4720          3         2
675      3006.0129   1782.2863             3  3898.2563          3         2
676      3716.8564   2465.7609             3  2560.3633          4         4
677      4131.3914   2864.3891             4  4938.0682          4         4
678      3430.3611   2190.2801             2  4149.4097          3         2
679      4222.5729   3418.8215             3  4659.2060          5         4
680      3318.8290   2874.6656             3  3697.3337          3         4
681      3814.9616   2565.8405             4  3886.5748          4         4
682      2213.3539   2091.5596             3  3088.5105          2         4
683      4070.8501   2884.8744             4  9040.0322          3         4
684      3637.4711   2389.4257             4  3301.4991          4         4
685      3327.6883   2536.3841             3  4026.3084          4         4
686      2998.8030   1799.4806             1  3572.7437          3         2
687      2070.2977   1466.9448             1  2489.2310          4         2
688      3215.6469   2208.7654             1  3958.3591          3         2
689      3516.4303   2273.0382             4  2731.4970          4         4
690      3120.5352   1892.3897             3  4204.6037          3         2
691      3342.3463   2560.6214             3  4822.9613          4         4
692      3488.6932   2419.4970             3  4257.1279          3         4
693      3977.7525   3405.5540             2  4381.2497          3         2
694      3448.2205   2208.7654             3  4229.7620          3         2
695      4188.0124   3320.9107             5  4333.6566          4         4
696      3138.8540   1910.0020             2  4213.9518          3         2
697      4078.7166   2813.7339             4  3400.8320          4         4
698      2921.0815   1700.6350             3  2625.4604          4         2
699      2951.1341   1729.5267             1  3819.8457          3         2
700      3486.6936   2551.1824             3  3832.4105          3         4
701      4037.5734   2774.1684             4  4789.0312          5         4
702      2951.1341   1729.5267             1  3516.4316          3         2
703      3583.1219   2757.6863             4  5754.2974          4         4
704      3521.6597   2278.0665             4  3614.0797          4         4
705      4020.4340   2843.6290             4  4500.5820          3         4
706      3176.4959   2247.6485             1  3301.4991          3         2
707      3947.4876   2697.6194             4  3012.9183          4         4
708      3197.3885   2166.1841             4  4147.3583          4         4
709      3933.9077   3051.1350             3  4488.3651          4         4
710      3192.5911   2163.4834             3  4229.7620          3         2
711      3100.3103   1872.9448             1  4017.5582          3         2
712      3637.4711   2836.6467             2  4381.2497          3         2
713      2134.9384   2016.1292             3  3920.0315          3         4
714      3665.1666   2865.2481             3  4318.8505          4         4
715      3479.3403   2237.3748             8  4381.2497          3         6
716      3603.0984   2801.2542             3  4089.6667          4         4
717      2921.0815   2510.6816             3  4149.4097          3         4
718      3038.0634   1813.0998             3  3461.3715          3         2
719      3667.5525   2418.3512             3  3898.2563          3         4
720      3173.2574   2544.8576             3  4728.8582          3         4
721      3653.1837   2404.5344             4  3015.1084          4         4
722      4242.2913   3500.1166             5  4014.2669          5         6
723      3945.9843   3213.6438             3  3977.0228          4         4
724      4251.8534   3456.7835             2  4538.8043          4         2
725      4058.2765   2794.0776             4  4343.1563          4         4
726      2754.4287   2612.0370             3  3887.7461          3         4
727      2939.9301   2158.0680             1  3978.1415          3         2
728      3170.0124   2384.7470             3  3728.0490          4         4
729      3823.6398   2576.2262             4  4073.3248          3         4
730      3905.3711   3101.3357             3  4276.4447          4         4
731      3227.4439   1995.1768             3  3773.2417          3         2
732      3339.4254   2552.2340             3  2005.5016          3         4
733      3628.9466   2836.6467             3  4375.5916          4         4
734      3232.1385   2460.1924             3  4524.6213          3         4
735      3371.9841   2583.4550             3  1320.0937          3         4
736      4238.9520   3391.5607             3  4630.3511          4         4
737      2951.1341   1729.5267             1  4044.1254          3         2
738      3509.8695   2362.3282             1  3502.5255          3         2
739      3412.9995   2630.1362             3  3942.0243          3         4
740      4138.9681   3286.6289             5  4114.2412          4         4
741      3831.7332   2576.2262             3  4138.9250          4         2
742      3840.3216   2588.5978             3  4972.9204          4         4
743      3665.1666   2788.6731             3  4310.9332          3         4
744      3688.2798   2820.8202             4  4670.2529          3         4
745      4173.7166   2895.0162             3  4044.1254          4         4
746      4636.7302   3792.0976             6  7531.2105          5         6
747      2939.9301   1718.7554             3  3597.3236          3         2
748      3230.5752   2262.9323             1  3995.2895          3         2
749      3299.4647   2126.5558             3  3745.4957          3         2
750      3038.0634   1813.0998             1  4259.0682          3         2
751      4263.4179   3006.3226             3  4923.5929          4         4
752      3484.6915   2242.5202             4  2658.0941          3         4
753      3955.9794   2695.7042             3  4454.5917          4         4
754      2978.8075   1782.2863             3  4798.4905          3         2
755      3202.1716   3042.7352             3  3886.5748          3         4
756      3169.2002   1961.6673             3  4331.4148          3         2
757      3538.5389   2304.2005             3  3759.5426          3         4
758      3455.0371   2685.1281             3  3570.2687          4         4
759      3751.7365   2508.5204             3  5189.6716          4         4
760      3344.5336   2116.8364             3  4044.3417          3         2
761      3358.3174   2565.8405             3  3320.3341          3         4
762      3677.0610   2410.3064             3  4187.9863          3         4
763      3437.2536   2731.6934             4  4381.2497          3         4
764      3859.4794   3090.9797             5  4257.5161          4         4
765      3018.5530   1794.3423             1  3224.3035          3         2
766      3794.1614   3093.2047             3  4621.9824          3         4
767      3257.7172   2048.4919             3  4476.0718          3         2
768      3906.3990   3037.3661             5  4213.9518          4         4
769      3833.8846   2578.2950             3  4056.6311          4         4
770      3612.3776   2943.9356             3  4387.0733          4         4
771      3349.6256   2647.0377             3  3886.5748          3         4
772      3141.3360   2343.1938             2  3838.4228          3         2
773      2772.2047   1557.5139             1  3709.4210          3         2
774      4680.8248   3725.0889             5  4823.1070          5         6
775      3544.3407   2836.6467             3  3583.1593          3         2
776      3413.6976   2765.0333             5  4715.3696          3         4
777      3473.9712   2232.2123             3  2785.1145          3         2
778      3327.6883   2536.3841             5  3838.9030          4         4
779      4510.1661   3559.9106             5  4876.6853          5         6
780      3236.8195   2141.7069             1  4022.3756          3         2
781      3752.8674   2506.3561             3  4633.0793          4         4
782      3153.6885   1924.2645             3  4179.9275          3         4
783      3783.6596   2658.8580             5  5725.8750          3         2
784      3272.2618   2083.0414             3  4805.8491          3         2
785      3831.1949   3130.5478             3  3814.9917          3         4
786      3444.8014   2371.8073             3  4257.1279          3         2
787      2921.0815   1700.6350             3  2630.7893          4         2
788      2811.2429   2022.0639             1  3958.3591          2         2
789      3774.7625   2521.4429             2  4179.9275          3         2
790      3133.8787   2300.4940             3  3850.6313          3         2
791      3996.3222   2740.0960             3  4610.9849          3         4
792      3198.9844   1967.8142             1  4491.9864          3         2
793      3970.3629   2765.9493             4  4785.9175          4         4
794      3235.2607   2033.8654             3  3981.7170          3         2
795      3678.2456   2428.6334             4  3342.3919          4         4
796      3504.6015   2720.4186             3  3590.2542          4         4
797      3079.8278   1853.2525             1  3224.3035          2         2
798      3595.6363   2805.7228             3  4652.2304          4         4
799      3387.6650   2571.0421             3  4209.9793          3         4
800      3826.3421   2571.0421             3  4455.6449          4         4
801      4364.6931   3090.9797             4  5001.8546          5         4
802      2794.9211   1579.3515             3  3266.4931          3         2
803      3776.9914   2512.8399             3  3916.5729          4         4
804      3911.0166   3121.8419             4  6304.9706          3         4
805      3037.1817   2266.7297             3  1535.6836          4         4
806      3718.0121   2466.8722             3  4572.1677          3         2
807      3016.7675   2237.3748             3  1974.7999          3         4
808      3709.9049   2889.1082             5  4138.7189          4         4
809      3855.2418   2598.8324             2  4230.5492          3         2
810      3402.4919   2163.4834             3  3759.5426          3         2
811      3290.4481   2055.7536             3  4149.4097          3         4
812      3900.2216   2642.0858             3  3814.9917          3         2
813      2691.1659   1935.2673             3   719.2405          3         2
814      3337.9629   2101.4386             2  4133.9716          3         2
815      3160.2380   2237.3748             1  4550.0442          3         2
816      3305.4478   2563.7550             3  4613.9020          3         4
817      3331.3654   2622.1182             3  4314.5188          3         4
818      3405.3006   2191.6078             3  4026.7448          3         2
819      4131.3914   2864.3891             3  3790.5402          3         4
820      3405.3006   2493.3064             2  4694.8065          3         2
821      3886.2350   2776.8984             4  5232.9488          3         4
822      3554.6036   2842.7580             5  4090.5120          4         4
823      2951.1341   1729.5267             3  5095.3410          3         2
824      3974.3082   3282.0438             4  7216.5454          3         6
825      3467.9095   2910.9393             3  4149.4097          4         4
826      2921.0815   1700.6350             3  2629.4584          4         2
827      3585.6326   2726.0663             3  3563.3774          3         4
828      3590.6422   2524.6568             2  4604.1614          3         2
829      4105.2696   2846.2393             3  5377.9983          3         2
830      3249.2361   2016.1292             3  3498.5342          3         2
831      3158.6031   1995.1768             3  4411.9920          3         2
832      3326.9519   2562.7112             3  3821.0573          3         4
833      3519.0471   2442.2376             3  4306.9627          3         4
834      4178.9298   3464.9650             5  4422.5502          3         4
835      3437.2536   2504.1888             2  3700.4269          4         2
836      3247.6892   2014.6420             3  4526.1458          3         2
837      3292.7070   2098.6225             3  4164.1173          3         4
838      3408.1045   2168.8800             3  3773.4899          3         2
839      3694.7393   2444.4934             3  3942.0243          4         4
840      3189.3850   1958.5847             3  3966.9259          3         2
841      3983.6398   2726.0663             3  4354.8281          4         4
842      3309.9205   2130.7027             3  3519.2575          3         2
843      3424.8257   3256.9135             3  4996.3951          3         4
844      3837.6426   2987.3931             5  4217.5202          4         4
845      3006.0129   1782.2863             1  3411.8973          3         2
846      3535.9536   2759.5263             3  3966.9259          3         4
847      2095.8332   1809.7062             1  3998.6127          4         2
848      3264.6231   2322.6010             1  4612.1198          4         2
849      3023.0080   2145.8135             2  3130.2409          3         2
850      4215.8047   3439.1047             3  4022.3756          4         4
851      3267.6830   2016.1292             3  6055.8066          3         2
852      4169.3593   3191.5466             5  3985.7317          4         4
853      3385.5357   2178.2790             3  4552.5518          3         2
854      2951.1341   1729.5267             3  3527.7111          4         2
855      3324.7406   2088.7254             3  3534.4480          3         2
856      3768.6171   2791.3777             3  4857.7478          4         4
857      3480.0101   2675.4504             3  4156.7773          3         4
858      3851.5247   3195.7139             3  3290.1110          4         2
859      3002.4120   1778.8244             1  3569.4430          3         2
860      4042.7742   2784.1550             4  2911.7523          4         4
861      4009.8693   2786.8674             3  3884.9338          3         4
862      3345.9901   2467.9826             2  5211.4291          3         2
863      4466.5108   3186.6705             4  5138.2383          4         4
864      3843.5305   2587.5706             3  4614.7115          3         2
865      2823.3765   1833.3064             1  3806.2241          3         2
866      3608.6723   2760.4455             3  4450.0210          3         4
867      3285.1650   2057.2019             2  3889.8526          3         2
868      3707.5810   2456.8417             3  4788.7349          3         2
869      2760.7251   2618.0936             3  3532.7659          3         4
870      3593.1412   2860.9484             3  3543.3947          3         2
871      3105.3904   1877.8290             1  3970.2973          3         2
872      3368.3988   3202.6346             3  3532.7659          3         4
873      4558.1596   3285.9747             5  4733.8927          5         4
874      3300.9625   2283.0786             1  3525.7419          3         2
875      2939.9301   1718.7554             1  3621.0642          3         2
876      3409.5046   2368.2594             3  3958.3591          3         2
877      3405.3006   2591.6753             3  3759.5426          4         4
878      4010.8326   2748.4532             3  5009.2871          4         4
879      2996.9954   1796.0570             1  3280.2515          3         2
880      3279.1058   2049.9470             3  4213.9518          3         2
881      3971.3502   2716.6420             4  4820.6300          4         4
882      3877.3658   3070.8097             2  4504.8658          4         2
883      2986.1074   1796.0570             3  3997.0626          3         2
884      3358.3174   2565.8405             3  4682.9589          4         4
885      4029.5025   3225.9362             3  4521.9082          3         4
886      3567.9751   2322.6010             2  4083.9519          3         2
887      3001.5105   1978.5127             1  3263.2797          3         2
888      3048.6066   2267.9935             3  1860.1313          4         4
889      2865.1376   2091.5596             2  1063.2613          3         2
890      2006.3019    821.3768             1  4022.3756          3         0
891      3454.3567   2274.2968             1  5290.3976          3         2
892      3957.4734   3122.5693             5  4765.0323          4         4
893      3606.8165   2491.1207             3  4422.5502          5         2
894      3638.0783   2794.9765             4  3901.0495          4         4
895      4073.1677   3174.7641             6  3972.9902          3         4
896      3627.7251   2380.0542             3  4275.8680          4         4
897      3952.4882   2698.5761             4  3793.4905          4         4
898      4026.1674   2763.1998             4  4276.4447          3         4
899      3376.9901   2138.9632             3  5106.4685          3         4
900      4111.1614   3292.5041             3  4588.4756          4         4
901      3732.9609   3010.2372             3  4209.9793          3         4
902      4104.8155   2854.0439             3  4561.8854          4         4
903      3941.9688   3199.8700             3  4747.1040          3         4
904      3801.3076   2546.9687             3  4005.9041          4         4
905      3060.8203   1834.9784             2  4044.1254          3         2
906      4222.5729   2952.0759             3  4533.7507          5         4
907      3838.1788   2582.4244             3  3906.8562          4         4
908      3641.1108   3079.8066             4  6231.7395          3         4
909      2550.6929   1504.6387             1  3166.0431          3         2
910      3463.1790   2237.3748             4  4246.0320          4         4
911      3882.5889   3004.7539             3  4164.7277          4         4
912      4017.0800   2997.6753             3  3969.1741          4         4
913      4055.9373   3311.2851             3  5960.4259          3         4
914      4065.7394   2801.2542             3  4690.9171          3         4
915      3865.8150   3073.0638             5  3968.0503          4         4
916      3772.5305   2519.2966             5  3718.1190          3         4
917      3973.8156   2712.8561             3  6033.4151          3         4
918      3312.1523   2412.6092             2  4944.1025          3         2
919      3814.9616   2922.5682             1  3982.6099          3         2
920      3402.4919   2163.4834             3  3830.2415          3         2
921      3964.4267   2710.0106             4  4966.0263          4         4
922      3675.8755   2843.6290             3  4892.9142          4         4
923      3571.7752   2454.6039             3  4099.5754          3         2
924      2951.1341   1729.5267             3  3583.1593          3         2
925      3010.5027   1900.4201             3  3740.7070          3         2
926      2761.7721   1547.4849             2  3583.1593          3         2
927      3699.4209   3002.3980             4  4430.7429          3         4
928      3124.7170   1924.2645             4  4107.9693          3         4
929      3804.0477   2994.5188             3  3565.5853          3         4
930      3275.3072   2041.1960             1  3642.4009          3         2
931      3653.1837   2404.5344             4  3898.2563          4         4
932      3273.7852   2493.3064             5  1557.2233          4         4
933      2939.9301   1718.7554             3  3585.0720          3         2
934      4380.0765   3587.0789             5  4625.5274          3         4
935      4131.3914   2864.3891             3  4575.9685          4         4
936      3675.2824   2943.1192             5  4473.1169          4         4
937      3387.6650   2565.8405             3  4275.8680          4         4
938      3214.8573   2370.6256             3  4149.4097          4         2
939      3336.4991   2100.0312             3  3634.4267          3         2
940      2794.9211   1905.2185             1  3199.5456          3         2
941      2908.7104   2095.8012             3  4303.5529          3         2
942      3113.8218   2227.0325             2  4381.2497          3         2
943      3472.6261   2707.1599             3  1309.7100          4         4
944      3048.6066   1823.2360             3  3763.7871          3         4
945      3759.0731   2506.3561             3  4528.5149          4         4
946      3696.4965   3041.9694             1  4490.0903          3         2
947      3229.7929   2455.7232             5  1616.7556          4         4
948      2504.6921   1738.4458             1  3191.2233          3         2
949      3533.3642   2289.3209             3  2556.6829          4         2
950      3006.0129   1782.2863             1  4118.4114          3         2
951      3369.8339   2132.0825             3  3981.7170          3         2
952      3139.6818   1953.9493             3  4608.5507          5         2
953      4233.9300   3440.2896             5  4621.6599          4         4
954      4047.9582   3236.7813             3  4461.6028          4         4
955      2956.7070   2806.6150             3  4254.2140          3         4
956      3430.3611   2190.2801             3  4395.7765          3         2
957      3279.8644   2715.6964             1  2983.8521          3         2
958      4247.7029   2980.2344             5  4260.8127          5         4
959      3771.4134   3050.3733             3  4596.1708          3         4
960      3442.7464   2658.8580             3  3821.0573          4         4
961      4213.2593   3304.1881             5  4118.8280          4         4
962      3643.5326   2813.7339             2  5350.4548          4         2
963      3652.5822   2907.6007             3  4181.9453          3         4
964      3375.5614   2582.4244             3  3988.4037          3         4
965      4047.9582   2792.2782             4  4662.0526          5         4
966      3167.5744   2275.5544             3  2748.6971          3         2
967      3264.6231   2030.9235             3  4355.3822          3         2
968      3774.7625   2521.4429             3  4541.6623          3         4
969      3252.3253   2070.1756             1  4187.1819          3         2
970      3475.9867   2247.6485             4  3459.6258          4         4
971      1979.2926   1866.4085             1  4269.8983          3         2
972      2591.9290   1384.2194             1  3016.9317          3         2
973      3915.6209   2656.8942             3  4581.5736          4         4
974      4020.4340   2757.6863             3  4504.8658          3         4
975      3161.8712   1932.1316             3  3883.0568          4         4
976      3998.2645   2736.3672             3  4613.9020          3         4
977      2865.1376   2091.5596             2  1264.9582          3         2
978      4048.8990   2785.0597             3  4607.9010          4         4
979      3564.1660   2604.9408             3  3224.3035          3         4
980      3178.9205   2326.2550             3  5716.8331          3         4
981      2890.4568   2742.8867             3  4195.0107          3         4
982      3267.6830   2584.4849             2  4342.9704          3         2
983      3221.1629   1989.1379             3  3583.1593          3         2
984      3312.8955   2077.3365             1  4532.7384          3         2
985      3528.8225   2743.8159             5  3886.5748          4         4
986      3842.4615   2586.5427             4  4569.3537          4         4
987      3595.6363   2430.9091             3  3162.3228          4         2
988      3066.0265   2553.2849             3  4378.3314          4         4
989      3385.5357   2147.1799             3  3534.4480          3         2
990      3492.0205   2262.9323             4  3638.6837          4         4
991      3309.9205   2298.0180             1  4116.1189          3         2
992      4476.9957   3601.0201             4  5092.1683          4         4
993      2984.2855   1761.3978             3  3715.3092          3         2
994      3565.4367   2317.7156             3  4086.9172          3         2
995      3983.6398   2726.0663             4  4132.9381          4         4
996      3297.9654   2448.9951             3  4127.1403          3         2
997      3095.2140   2260.3954             3   719.2405          3         2
998      3616.6897   2970.6377             3  3550.6341          3         4
999      4262.5946   3696.2471             5  5137.9901          3         4
1000     4242.7082   3384.8232             5  4966.7032          4         4
1001     3995.3502   2733.5646             4  3821.0573          4         4
1002     3081.5447   1882.6978             1  3321.8956          3         2
1003     1801.2641   1695.1572             1  4504.8658          3         2
1004     3961.9468   2701.4427             4  4730.6904          4         4
1005     4000.2045   3218.4357             3  4074.1771          4         4
1006     3095.2140   2412.6092             2   539.0975          3         2
1007     2443.3649   1241.4190             3   465.8890          3         2
1008     3804.0477   2866.9646             4  4765.0323          3         4
1009     3500.6391   2712.8561             3  4050.6038          3         2
1010     3615.4588   2368.2594             4  3009.9944          4         4
1011     4220.0382   3262.9024             5  4562.0517          3         4
1012     4675.0998   3387.2766             5  4149.4097          4         4
1013     2955.7795   2805.7228             3  4846.5562          3         4
1014     4614.0558   3584.9229             5  5161.7949          4         6
1015     3170.0124   1939.9590             2  4075.2419          3         2
1016     2990.6530   2839.2687             1  5759.2814          3         2
1017     1955.2816   1843.3116             1  4435.1812          3         2
1018     3610.5261   2363.5162             3  4020.8441          4         4
1019     3627.7251   2380.0542             3  4448.4363          4         4
1020     3723.2024   3009.4551             3  4128.7985          3         2
1021     3693.5667   2608.9998             1  3924.1739          3         2
1022     3866.8685   3018.8148             5  4481.9683          4         4
1023     3678.2456   2605.9566             3  4480.9290          3         4
1024     3685.3350   2435.4504             4  3542.2786          4         4
1025     3740.3835   2906.7649             3  6389.6203          4         4
1026     3985.5975   3163.4739             5  4471.7249          5         4
1027     3752.8674   3020.3693             2  4465.9722          3         2
1028     3654.3860   2405.6905             4  2833.7134          4         4
1029     3006.0129   1782.2863             1  5386.7665          2         2
1030     3837.6426   3268.2065             3  4835.0113          3         4
1031     3343.8048   2107.0555             1  3224.3035          3         2
1032     3416.4868   2176.9398             2  4417.3677          3         2
1033     4116.1301   3216.3839             5  4892.0708          4         4
1034     3459.1132   2653.9439             3  3750.0217          4         4
1035     3473.2988   2692.8270             3  4181.9453          3         2
1036     4068.9935   3385.4369             5  2408.4933          3         4
1037     2960.4116   1780.5564             2  4149.4097          3         2
1038     3261.5575   2027.9759             3  4259.4560          3         2
1039     3398.9741   2639.1071             2  4538.8043          3         2
1040     3386.9555   2536.3841             3  3685.6907          3         2
1041     3276.8277   2504.1888             2  3778.1997          3         2
1042     3532.0679   2288.0744             3  3922.7941          4         4
1043     3570.5095   2811.9572             2  4765.0323          3         2
1044     3384.1146   2546.9687             3  4381.2497          3         4
1045     3333.5676   2097.2125             3  5138.8586          3         2
1046     2921.0815   1700.6350             3  2629.4584          4         2
1047     3170.0124   1939.9590             1  3972.5416          3         2
1048     3555.2429   2310.3583             3  4424.5124          4         4
1049     3249.2361   2016.1292             3  3663.5088          3         2
1050     3793.6104   2539.5671             3  3966.7009          4         4
1051     3546.2700   2301.7305             3  3978.1415          3         2
1052     3331.3654   2580.3611             3  4750.8841          3         4
1053     3130.5532   1949.2999             3  4037.4087          3         2
1054     2865.1376   2091.5596             2  1036.5317          3         2
1055     3856.8322   2990.5641             3  4339.6225          4         4
1056     3656.1878   2784.1550             3  1518.5926          4         4
1057     3541.1201   2296.7786             3  2057.2138          4         2
1058     2134.9384   2016.1292             3  3920.0315          3         4
1059     3062.5575   2302.9660             5  1213.7072          4         4
1060     3769.7362   2770.5208             3  3886.5748          3         4
1061     3236.8195   2237.3748             3  4072.0457          3         2
1062     3079.8278   1853.2525             3  3180.5191          3         2
1063     3625.2793   2377.7024             3  4090.5120          4         4
1064     3217.2248   2425.2136             2  3494.2488          3         2
1065     3311.4087   2085.8860             2  2270.7254          4         2
1066     3182.9533   2389.4257             1  3224.3035          3         2
1067     3768.0572   2683.1974             3  4568.8567          3         4
1068     1561.8152    679.9881             1  3886.5748          3         2
1069     3103.6988   1876.2026             1  4181.5419          3         2
1070     3297.9654   2149.9091             1  3527.7111          3         2
1071     3059.9509   2229.6246             2  4002.5931          3         2
1072     3130.5532   2363.5162             3  1077.9558          3         4
1073     4334.6594   3446.2005             5  4630.1905          4         4
1074     3446.8537   2521.4429             4  4298.8073          4         4
1075     3777.5481   3043.5007             3  5891.1540          4         4
1076     3616.6897   2766.8647             3  3805.9800          3         4
1077     4163.2392   2895.0162             4  4481.1023          4         4
1078     3499.9778   2737.3002             5  3790.5402          3         4
1079     3708.1623   2999.2511             3  4322.0460          3         4
1080     2859.2377   1641.1812             3  3555.6305          3         2
1081     3198.9844   1967.8142             3  4005.4629          3         2
1082     2892.3880   1673.0502             1  3016.9317          3         2
1083     4071.3139   2806.6150             4  4602.5333          4         4
1084     3040.7057   2496.5791             5  3728.0490          4         4
1085     3006.0129   1782.2863             3  4182.7518          3         2
1086     3290.4481   2683.1974             2  4867.3105          3         2
1087     3249.2361   2016.1292             1  3679.1926          3         2
1088     3205.3524   1973.9367             1  3854.2077          3         2
1089     3892.9845   2635.1264             3  4246.2272          4         4
1090     2859.2377   1892.3897             1  4006.1246          3         2
1091     2608.1319   1399.7943             2  4109.0160          3         2
1092     3074.6662   2563.7550             3  4049.5256          3         4
1093     3194.1918   1963.2063             1  4313.3872          3         2
1094     3870.0249   2613.0481             4  4970.8952          4         4
1095     3730.6701   2995.3085             3  4554.8893          4         4
1096     3079.8278   1853.2525             3  3583.1593          3         2
1097     3892.4663   3012.5813             4  3741.7161          3         4
1098     3143.8141   1914.7708             1  4365.1454          3         2
1099     3950.9897   3181.7790             3  4209.9793          3         4
1100     3915.6209   3042.7352             3  4195.6117          4         4
1101     3555.2429   2682.2312             3  3972.0930          3         4
1102     3142.1624   1933.7003             1  3282.4821          3         2
1103     3399.6783   2302.9660             1  4149.4097          3         2
1104     3016.7675   1986.1095             1  3333.4122          3         2
1105     3908.4529   2650.0013             4  4193.8083          3         4
1106     3250.7814   2194.2598             1  3962.6471          3         2
1107     3107.0802   1879.4536             3  3623.7440          3         2
1108     3637.4711   2921.7405             5  4288.7087          3         4
1109     4414.9098   3563.1961             5  4222.8606          4         6
1110     3195.7910   1964.7438             1  4022.3756          3         2
1111     2823.3765   1833.3064             3  4617.9464          3         2
1112     3619.1485   2658.8580             1  3301.4991          3         2
1113     3605.5781   2358.7584             4  4452.8350          4         4
1114     3388.3742   2647.0377             2  4588.6397          3         2
1115     2908.7104   2118.2286             1  3123.3470          3         2
1116     3288.9404   2563.7550             2  4022.3756          3         2
1117     3072.9419   1846.6323             1  3858.2531          3         2
1118     3801.3076   2546.9687             2  5359.7897          3         2
1119     3774.7625   2873.8119             1  4908.1739          3         2
1120     2859.2377   1641.1812             1  3187.8845          4         2
1121     3659.1863   2881.4789             3  4849.4319          3         2
1122     3769.1767   2516.0716             4  4375.4088          4         4
1123     3534.6594   2318.9384             3  4097.4714          3         4
1124     3625.2793   2377.7024             4  2865.8522          4         4
1125     3921.7396   2662.7782             3  4577.4537          4         4
1126     3713.9636   2928.3501             3  4048.4467          4         4
1127     3803.5000   2720.4186             3  4998.5274          4         2
1128     3006.0129   1782.2863             1  3961.0684          3         2
1129     3722.6265   2510.6816             3  5174.1386          3         2
1130     3840.3216   2584.4849             3  4137.2752          4         4
1131     4033.7804   2770.5208             3  4321.1067          4         4
1132     3626.5026   2749.3790             5  4390.7043          3         4
1133     3959.4631   3108.6905             3  4853.4509          3         4
1134     4829.6131   3948.1412             6  6738.0447          4         6
1135     3349.6256   2127.9394             3  4205.9988          3         2
1136     3559.0732   2314.0413             3  4048.4467          3         2
1137     3082.4024   2300.4940             3  2434.6326          4         4
1138     4554.7295   3698.2535             4  5390.0445          3         6
1139     3989.9935   3273.4924             3  5222.6345          3         4
1140     4509.8130   3587.0789             3  4358.8878          4         4
1141     3015.8740   1831.6325             3  3513.8848          3         2
1142     3219.5888   2267.9935             1  2401.5302          3         2
1143     3244.5911   2411.4582             2  3710.4463          3         2
1144     2259.7760   2136.2146             1  3871.2845          3         2
1145     4188.4437   3381.1359             3  4447.5554          3         4
1146     3967.8922   2731.6934             5  3083.9361          5         4
1147     5171.2419   4273.5296             6  5107.9811          4         6
1148     3375.5614   2144.4458             3  4381.2497          3         2
1149     3190.1871   2264.1991             3  4177.5034          3         2
1150     3965.9128   2705.2565             4  4662.8426          4         4
1151     3539.1846   2739.1646             3  4008.1082          4         4
1152     3726.0787   2867.8222             3  3663.5088          3         4
1153     3351.8029   2520.3702             3  1612.2968          4         4
1154     3320.3089   2553.2849             1  4149.4097          3         2
1155     3511.1838   2267.9935             4  2658.0941          3         4
1156     3198.1867   2421.7862             2  4100.4164          3         2
1157     3327.6883   2536.3841             3  3797.6625          3         4
1158     3693.5667   2917.5951             3  4899.6486          4         4
1159     3548.1970   2766.8647             1  3989.2935          3         2
1160     3495.3408   2252.7599             3  4044.1254          4         4
1161     3501.3002   2455.7232             2  4458.9766          3         2
1162     2951.1341   1729.5267             1  4098.1028          3         2
1163     3635.6482   2846.2393             3  4306.9627          3         4
1164     3362.6457   2417.2045             3  3224.3035          3         2
1165     3971.8435   2710.9597             3  4179.9275          4         4
1166     3287.4313   2065.8631             3  4257.1279          3         2
1167     4437.2275   3171.9493             3  4985.9666          4         4
1168     3273.7852   2039.7326             3  4000.3828          3         2
1169     4030.9297   2775.9889             4  4051.6815          4         4
1170     3349.6256   2340.7853             3  3731.3479          3         2
1171     4001.1736   2739.1646             4  4265.2641          4         4
1172     3783.6596   2902.5792             3  4455.9959          4         4
1173     3418.5756   2822.5867             3  4610.4983          4         4
1174     2547.1087   1341.1370             3  4095.3651          3         2
1175     2835.4193   1892.3897             2  4277.5977          3         0
1176     3123.8815   1953.9493             3  4269.7054          3         2
1177     3006.0129   1782.2863             1  3553.9664          3         2
1178     3105.3904   2949.6383             3  4007.0065          3         4
1179     3616.6897   2377.7024             4  3942.0243          4         4
1180     1923.8742   1813.0998             1  3301.4991          3         2
1181     3095.2140   2260.3954             2   719.2405          3         2
1182     3038.0634   1813.0998             1  3740.7070          3         2
1183     3312.1523   2251.4836             1  3851.1086          3         2
1184     3775.8773   2903.4172             3  4325.0489          3         4
1185     4406.6484   3129.1002             3  4359.2564          3         4
1186     3395.4485   2572.0803             5  5077.6354          4         4
1187     2949.2722   2155.3531             2  4322.4216          3         2
1188     3742.6605   2974.6435             3  4974.4043          4         4
1189     3038.0634   1813.0998             3  3994.1805          3         2
1190     4041.3574   2777.8073             3  3971.1953          5         2
1191     3596.8824   2589.6243             3  3768.2713          3         4
1192     4293.1832   3445.0201             4  5481.7657          3         4
1193     3408.1045   2224.4361             3  3722.4536          3         2
1194     3463.1790   2221.8353             3  4614.7115          3         2
1195     3785.8762   2999.2511             2  3915.6495          3         2
1196     3564.8015   2850.5801             2  4766.0819          3         2
1197     3472.6261   2707.1599             3  1599.6084          4         4
1198     3724.3536   2986.5993             3  4652.0715          4         4
1199     3398.2696   2159.4236             2  4757.0676          4         2
1200     3816.5923   2565.8405             3  4030.4511          4         4
1201     3639.8985   2836.6467             5  3829.0355          4         4
1202     4029.0265   2765.9493             3  4199.8131          4         4
1203     3358.3174   2202.1888             4  4349.0935          3         4
1204     4360.8241   3085.0308             5  4876.6853          5         4
1205     3417.1834   2599.8521             1  4493.7085          3         2
1206     3514.4648   2921.7405             5  4603.3476          3         6
1207     3417.1834   2636.1226             3  3821.0573          4         4
1208     3222.7354   2007.1843             3  4641.7203          3         2
1209     3723.2024   3071.5614             2  4149.4097          3         2
1210     3072.9419   1936.8328             1  3583.1593          3         2
1211     4386.9513   3110.1573             5  4445.7924          4         4
1212     3732.9609   2481.2467             3  1947.3805          4         4
1213     2960.4116   1747.3138             3  4201.6109          3         2
1214     4019.9553   3151.3870             5  5336.0322          4         4
1215     3480.6797   2735.4335             3  3508.2133          4         4
1216     3376.2759   2438.8477             1  3301.4991          3         2
1217     4289.9480   3017.2588             4  4934.2185          4         4
1218     2951.1341   1729.5267             1  2455.5879          3         2
1219     3203.7628   2192.9344             4  4146.7425          4         4
1220     3270.7370   2036.8018             3  4179.9275          3         2
1221     3555.2429   2753.0766             3  6008.2154          3         4
1222     3264.6231   2030.9235             1  4149.4097          3         2
1223     3779.2172   2854.0439             3  4461.6028          3         2
1224     3600.6149   2884.8744             1  4822.6701          3         2
1225     3693.5667   2404.5344             4  2455.5879          4         4
1226     3297.2152   2532.1299             5  2291.3831          4         4
1227     3735.2484   2939.0308             2  4253.2417          2         2
1228     4308.8623   3041.2031             3  4778.3350          5         4
1229     4369.7088   3869.3950             5  4906.0809          3         6
1230     3477.9997   2606.9716             2  4477.9814          3         2
1231     3759.0731   2606.9716             3  5919.5564          4         0
1232     3826.3421   2571.0421             3  4056.2012          3         4
1233     3078.1091   1851.6001             3  4824.2715          3         2
1234     3463.1790   2427.4943             3  4506.9187          3         2
1235     3112.9806   2300.4940             3  3003.0325          3         4
1236     3754.5622   2964.2066             3  4478.1549          3         4
1237     3278.3468   2470.2012             3  4736.4812          3         2
1238     4041.3574   2797.6701             3  5372.6085          3         2
1239     3921.2306   3051.1350             5  4123.1963          4         4
1240     3039.8254   2141.7069             1  3663.5088          3         2
1241     3914.5989   2655.9114             4  4191.6020          4         4
1242     3637.4711   2406.8458             4  3802.5594          3         4
1243     3249.2361   2016.1292             3  3978.1415          3         4
1244     3690.0440   2884.8744             4  4107.9693          3         4
1245     3967.3976   3339.3520             3  4157.1858          3         4
1246     3333.5676   2488.9319             1  3224.3035          3         2
1247     3642.3221   2394.0903             3  4187.9863          3         2
1248     3944.9814   2664.7345             3  6778.3642          3         4
1249     3921.7396   2738.2327             4  3110.8767          4         4
1250     3867.3950   3003.9690             3  4428.9648          4         4
1251     3413.6976   2174.2578             3  4907.7554          3         2
1252     3130.5532   2363.5162             3   719.2405          3         4
1253     4023.3032   3291.2005             3  3411.8973          3         4
1254     3542.4091   2742.8867             3  4257.1279          3         4
1255     2951.1341   1729.5267             3  3832.4105          3         2
1256     3267.6830   2033.8654             3  3886.5748          3         2
1257     3374.1314   2141.7069             4  3955.6460          3         4
1258     2846.3799   2062.9814             4  2259.5116          3         4
1259     3539.8300   2295.5381             3  3663.5088          3         2
1260     3817.1355   3014.1420             3  4374.3117          4         4
1261     3386.2458   2576.2262             1  3663.5088          3         2
1262     4171.5394   3388.5018             5  4253.2417          4         4
1263     3957.9710   2697.6194             3  3952.9292          4         4
1264     3659.1863   2783.2498             3  2084.9114          4         4
1265     3993.4044   2731.6934             4  4772.2179          4         4
1266     3690.0440   2439.9785             3  3515.0171          4         4
1267     3170.0124   1939.9590             3  3808.1758          3         2
1268     3222.7354   2133.4611             3  4588.6397          3         2
1269     3590.6422   2353.9860             4  3570.2687          3         4
1270     4220.0382   2949.6383             4  5331.3136          4         4
1271     3575.5664   2329.9004             4  3981.2704          4         4
1272     4403.2565   3553.3186             3  4143.6603          4         4
1273     4297.6210   3432.5716             3  4997.9945          4         4
1274     3100.3103   1872.9448             3  3836.7412          3         2
1275     3872.1257   3111.6227             3  4430.7429          3         4
1276     3967.8922   2710.9597             4  4273.7518          4         4
1277     3671.1248   2421.7862             3  2536.3167          4         4
1278     4104.3612   2853.1787             3  4998.9270          4         4
1279     3027.4507   1872.9448             1  4271.6333          3         2
1280     3814.4177   2559.5755             3  3886.5748          3         2
1281     1544.0637   1447.7479             1  3419.9328          3         2
1282     3652.5822   2966.6214             5  4266.0372          4         4
1283     2265.4857   1421.7758             1  2991.2513          2         2
1284     4126.9178   2860.0870             3  4227.0044          4         4
1285     2819.3421   1602.8281             1  2238.5149          3         2
1286     2515.7065   1559.5119             1  2554.8401          3         2
1287     2859.2377   1641.1812             2  3411.8973          4         2
1288     4417.9034   3543.3777             3  4314.5188          4         4
1289     3587.5130   2712.8561             3  4040.6616          3         4
1290     3929.8619   2670.5887             3  4229.7620          4         4
1291     3073.8043   1882.6978             1  4377.6011          3         2
1292     2859.2377   1641.1812             3  3995.2895          3         2
1293     3312.1523   2430.9091             2  3583.1593          3         2
1294     3287.4313   2436.5837             2  1394.6114          3         2
1295     3659.1863   2401.0609             3  4159.6350          3         4
1296     3997.2937   2735.4335             3  4075.4548          3         4
1297     2596.5750   1388.6854             1  2483.5043          3         2
1298     3713.9636   2915.9339             5  4813.1802          4         4
1299     2951.1341   1729.5267             1  4141.1911          3         2
1300     2952.9939   1743.7727             1  3861.5784          3         2
1301     3359.7615   2122.3978             3  4848.7134          3         2
1302     4064.3427   3152.8139             3  4102.7273          4         4
1303     3732.3885   2958.5575             2  3678.6718          3         2
1304     3327.6883   2536.3841             3  4435.7131          4         4
1305     3120.5352   1892.3897             1  3224.3035          3         2
1306     4185.8546   3143.5155             3  5669.5693          3         4
1307     4089.7572   2843.6290             4  5067.6297          4         4
1308     3825.2617   2576.2262             4  5178.8843          4         4
1309     3860.5371   3282.0438             3  2961.4861          3         4
1310     4252.6822   3453.2639             6  4529.1913          3         4
1311     3591.8922   2790.4767             2  4075.6677          3         2
1312     3081.5447   2206.1381             1  3224.3035          4         2
1313     4744.6275   3772.6323             5  4990.7866          4         4
1314     3759.6361   2919.2546             5  4290.9997          4         4
1315     3538.5389   2964.2066             4  4267.1963          3         6
1316     2976.9773   1778.8244             1  4124.0273          3         2
1317     3306.9401   2071.6104             3  4674.8114          3         2
1318     3431.0516   2655.9114             3  1174.1415          4         4
1319     4284.6769   3011.8003             4  5243.5623          4         4
1320     3948.4889   3433.7615             5  4198.4136          3         6
1321     3870.0249   2613.0481             4  5174.2604          4         4
1322     3514.4648   2810.1785             3  4671.0396          3         4
1323     3208.5270   2488.9319             3  3909.6373          3         4
1324     3016.7675   2237.3748             3  1974.7999          4         4
1325     3537.2468   2752.1530             5  3663.5088          4         4
1326     3646.5548   2855.7729             5  4061.1395          4         4
1327     3362.6457   2556.4334             3  1627.1203          3         4
1328     2921.0815   1700.6350             3  2629.4584          4         2
1329     4003.5938   2746.5999             4  4350.9452          4         4
1330     3349.6256   2446.7459             1  3016.9317          2         2
1331     3640.5047   2740.0960             3  4149.4097          3         2
1332     3944.4797   3100.5982             5  4179.9275          3         4
1333     4743.1011   3452.6765             5  4487.6745          5         4
1334     3829.5789   2994.5188             3  4349.0935          4         4
1335     3912.5528   2653.9439             3  4415.7565          4         4
1336     2784.6352   1591.1343             1  3317.8332          3         2
1337     3600.6149   2686.0926             3  4417.0098          3         4
1338     2691.1659   1935.2673             2  1015.4881          3         2
1339     2996.9954   2469.0923             3  4176.8969          3         4
1340     2951.1341   1729.5267             3  3842.0214          3         2
1341     4002.1421   3115.2802             3  4734.8067          3         4
1342     3450.9506   2831.3891             3  3583.1593          3         2
1343     3362.6457   2493.3064             3  6059.9283          3         4
1344     3032.7658   2310.3583             1  4035.4543          3         2
1345     3145.4640   2176.9398             3  3030.0094          3         2
1346     4370.0940   3538.9389             6  5238.2627          3         6
1347     3961.9468   3388.5018             3  3914.4948          3         4
1348     4082.4052   2817.2811             4  5013.6539          5         4
1349     3147.9358   2260.3954             2  3224.3035          3         2
1350     3864.7608   2607.9860             4  4044.1254          4         4
1351     3925.8059   2666.6884             3  4010.0899          3         4
1352     2984.2855   1792.6258             3  3750.2729          3         2
1353     3475.3151   2957.7488             3  4381.2497          3         4
1354     4120.6337   3361.3201             3  4694.8065          4         4
1355     3501.9610   2764.1169             3  7662.7028          3         2
1356     3513.8091   2595.7691             2  3263.2797          3         2
1357     3897.1239   2951.2638             3  3583.1593          3         2
1358     3598.1275   2689.9444             3  3279.6137          3         4
1359     3202.1716   2182.2897             1  3224.3035          3         2
1360     3500.6391   2675.4504             5  3641.0741          3         4
1361     3595.6363   2353.9860             3  3459.6258          4         4
1362     3810.6049   2544.8576             4  5061.1889          4         4
1363     3091.8076   2255.3093             1  4308.8544          3         2
1364     3961.9468   2726.0663             5  2346.9709          4         4
1365     2761.7721   1547.4849             3  3897.0912          3         2
1366     2892.3880   1673.0502             3  3973.6629          3         2
1367     3174.0677   2434.3163             1  3725.5076          3         2
1368     3774.7625   3097.6451             3  5646.9907          3         4
1369     3718.0121   2898.3821             5  4656.3553          4         4
1370     3560.3479   2746.5999             2  4149.4097          3         2
1371     2134.9384   2016.1292             3  3583.1593          3         4
1372     4170.2317   2901.7406             4  4416.2937          4         4
1373     3657.3879   2905.0920             2  4754.2045          3         2
1374     3873.6995   3236.7813             3  4477.2872          3         4
1375     4190.1674   3341.2473             5  5220.8507          4         4
1376     3402.4919   2163.4834             3  4066.4932          3         2
1377     4170.2317   2901.7406             4  5201.2414          4         4
1378     3282.8954   2493.3064             3  4538.8043          3         4
1379     2921.0815   1700.6350             3  2629.4584          4         2
1380     3782.5502   3175.4670             3  5563.4137          4         4
1381     3457.7556   2412.6092             3  4129.4200          3         2
1382     3547.5549   2302.9660             1  4366.7984          4         2
1383     4015.6404   3122.5693             5  4407.3213          4         4
1384     3526.2216   2641.0935             3  4404.8016          3         2
1385     2819.3421   1618.2836             3  3583.1593          3         2
1386     3772.5305   2519.2966             3  4676.2240          4         4
1387     3589.3913   2896.7000             3  5775.5051          4         4
1388     2851.3374   1905.2185             3  4381.2497          3         4
1389     3685.3350   2857.5000             5  4280.4773          3         4
1390     3376.9901   2138.9632             4  5320.0331          3         4
1391     3759.0731   2620.1072             3  3886.5748          4         2
1392     2951.1341   1729.5267             1  4022.3756          3         2
1393     4245.2075   2973.8432             4  4660.1553          5         4
1394     3300.9625   2283.0786             3  3638.9494          3         2
1395     3385.5357   2798.5669             3  4519.1913          3         4
1396     3913.0646   3406.1595             3  4509.3110          3         4
1397     2921.0815   1700.6350             3  2625.4604          4         2
1398     3850.9930   3032.7491             5  4417.9044          5         4
1399     3107.0802   1879.4536             1  3990.1830          3         2
1400     3752.3020   2499.8450             3  3909.8688          4         4
1401     2950.2034   1814.7937             3  3886.5748          3         2
1402     3463.1790   2221.8353             1  6121.3420          3         2
1403     3996.3222   3095.4265             5  4229.7620          4         4
1404     3108.7683   2414.9085             2  4550.0442          3         2
1405     2443.3649   1241.4190             3   539.0975          3         2
1406     3661.5811   2857.5000             4  4022.3756          3         4
1407     3917.1528   2660.8193             3  4078.8580          4         4
1408     2846.3799   2062.9814             3  2259.5116          3         2
1409     3396.8597   2158.0680             1  5299.2208          3         2
1410     3507.2376   2264.1991             4  3663.5088          4         4
1411     3608.0540   2727.0056             3  3770.0123          3         4
1412     4138.0785   3082.7940             4  4772.5168          3         4
1413     4082.4052   3270.1908             3  4031.5398          5         4
1414     3306.9401   2071.6104             3  4173.2540          3         2
1415     3552.6843   2307.8981             3  4217.3221          4         2
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1338         yes                  0                   0                   0
1339         yes                  0                   0                   1
1340          no                  0                   0                   0
1341         yes                  1                   0                   0
1342         yes                  0                   0                   0
1343         yes                  1                   0                   0
1344         yes                  0                   0                   0
1345         yes                  0                   0                   0
1346         yes                  1                   0                   0
1347          no                  0                   0                   0
1348         yes                  1                   0                   0
1349         yes                  0                   0                   0
1350         yes                  1                   0                   0
1351         yes                  0                   0                   0
1352         yes                  1                   0                   0
1353          no                  0                   0                   0
1354         yes                  0                   0                   1
1355         yes                  0                   0                   0
1356         yes                  0                   0                   0
1357         yes                  1                   0                   0
1358         yes                  0                   0                   0
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1360         yes                  1                   0                   0
1361         yes                  1                   0                   0
1362         yes                  1                   0                   0
1363         yes                  0                   0                   0
1364         yes                  1                   0                   0
1365         yes                  0                   0                   0
1366         yes                  0                   0                   0
1367         yes                  0                   0                   0
1368         yes                  1                   0                   0
1369         yes                  1                   0                   0
1370         yes                  1                   0                   0
1371          no                  0                   0                   0
1372         yes                  1                   0                   0
1373         yes                  0                   0                   0
1374         yes                  0                   0                   0
1375         yes                  1                   0                   0
1376         yes                  0                   0                   0
1377         yes                  1                   0                   0
1378         yes                  1                   0                   0
1379         yes                  1                   0                   0
1380         yes                  1                   0                   0
1381         yes                  0                   0                   0
1382         yes                  0                   0                   0
1383         yes                  1                   0                   0
1384         yes                  1                   0                   0
1385         yes                  1                   0                   0
1386         yes                  1                   0                   0
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1388         yes                  0                   0                   0
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1390         yes                  1                   0                   0
1391         yes                  1                   0                   0
1392         yes                  0                   0                   0
1393         yes                  1                   0                   0
1394         yes                  1                   0                   0
1395         yes                  1                   0                   0
1396         yes                  0                   0                   0
1397         yes                  1                   0                   0
1398         yes                  1                   0                   0
1399          no                  0                   0                   0
1400         yes                  1                   0                   0
1401         yes                  0                   0                   0
1402         yes                  1                   0                   0
1403         yes                  1                   0                   0
1404          no                  0                   0                   0
1405         yes                  0                   0                   0
1406         yes                  0                   0                   0
1407         yes                  1                   0                   0
1408         yes                  0                   1                   0
1409         yes                  0                   0                   0
1410         yes                  1                   0                   0
1411         yes                  1                   0                   0
1412         yes                  1                   0                   0
1413         yes                  1                   0                   0
1414         yes                  1                   0                   0
1415         yes                  1                   0                   0
     garage_type_detchd garage_type_no_garage NeighborhoodBrDale
1                     0                     0                  0
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1195                  1                   0                    0
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1198                  0                   0                    0
1199                  0                   0                    0
1200                  0                   1                    0
1201                  0                   0                    0
1202                  0                   0                    0
1203                  0                   0                    0
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1214                  0                   0                    1
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     neighborhood_saleprice log_rel_price log_sale_price sale_price_per_sqft
1                  198517.7  4.906067e-02       12.24769        0.0002928122
2                  245890.6 -3.036312e-01       12.10901        0.0002073205
3                  198517.7  1.185330e-01       12.31717        0.0003065762
4                  213681.7 -4.228453e-01       11.84940        0.0001857338
5                  331835.3 -2.831778e-01       12.42922        0.0001877702
6                  157755.8 -9.820383e-02       11.87060        0.0002739861
7                  231775.4  2.810788e-01       12.63460        0.0003286762
8                  191923.4  4.122118e-02       12.20607        0.0002644571
9                  124716.1  4.072477e-02       11.77452        0.0002827148
10                 126987.8 -7.340635e-02       11.67844        0.0002868032
11                 136902.4 -5.558748e-02       11.77144        0.0002911236
12                 306152.5  1.194611e-01       12.75130        0.0002758180
13                 136902.4  5.054494e-02       11.87757        0.0003462219
14                 198517.7  3.421239e-01       12.54076        0.0003674407
15                 147744.3  6.076265e-02       11.96400        0.0002994350
16                 126987.8  3.871095e-02       11.79056        0.0003570131
17                 147744.3  8.463154e-03       11.91170        0.0003158873
18                 181841.2 -1.342294e-01       11.97666        0.0002602534
19                 147744.3 -6.100922e-02       11.84223        0.0002720882
20                 306152.5  6.066447e-02       12.69250        0.0002590535
21                 101388.7  3.183861e-01       11.84510        0.0004634194
22                 198517.7  1.472009e-01       12.34583        0.0002812900
23                 101947.9  2.423029e-01       11.77452        0.0003902993
24                 136902.4  1.176842e-01       11.94471        0.0003429681
25                 306152.5 -1.777347e-01       12.45410        0.0002133017
26                 147744.3 -9.169095e-02       11.81155        0.0003024386
27                 306152.5 -4.982576e-04       12.63134        0.0002472028
28                 147744.3  3.396482e-01       12.24289        0.0003617312
29                 126987.8 -6.172572e-01       11.13459        0.0002526639
30                 101388.7 -9.300820e-01       10.59663        0.0001249037
31                 136902.4  8.702419e-02       11.91405        0.0003102359
32                 198517.7 -9.847723e-02       12.10016        0.0002571360
33                 147744.3  1.134880e-01       12.01673        0.0002879730
34                 306152.5 -9.826243e-02       12.53358        0.0002322771
35                 306152.5  9.257917e-03       12.64110        0.0002451257
36                 198517.7 -3.141446e-01       11.88449        0.0002190123
37                 147744.3  3.495477e-02       11.93819        0.0002873129
38                 147744.3 -3.041353e-01       11.59910        0.0002252494
39                 123526.7 -4.097382e-01       11.31447        0.0002887039
40                 147744.3  7.969066e-02       11.98293        0.0003105363
41                 243074.5 -3.575694e-01       12.04355        0.0001913165
42                 181841.2 -2.333203e-01       11.87757        0.0002686767
43                 198517.7 -4.214227e-01       11.77721        0.0002127984
44                 147744.3 -4.672326e-02       11.85652        0.0002797943
45                 306152.5  4.392509e-02       12.67576        0.0002556076
46                 157755.8  4.182813e-01       12.38709        0.0003684359
47                 231775.4  7.449129e-02       12.42802        0.0002695163
48                 124716.1 -9.865233e-02       11.63514        0.0002720379
49                 136902.4 -7.508127e-02       11.75194        0.0002980805
50                 193941.9 -9.140871e-02       12.08391        0.0002695717
51                 126987.8 -1.035161e-01       11.64833        0.0002835656
52                 245890.6  4.483565e-01       12.86100        0.0003756128
53                 147744.3 -1.279487e-01       11.77529        0.0002966664
54                 147744.3  2.002476e-01       12.10349        0.0003252944
55                 231775.4 -2.953717e-01       12.05815        0.0002025682
56                 198517.7 -1.021594e-02       12.18842        0.0002752882
57                 309745.6  3.482469e-01       12.99175        0.0003192228
58                 198517.7 -4.633650e-01       11.73527        0.0002257737
59                 181841.2 -1.405386e-01       11.97035        0.0002539092
60                 101388.7 -3.840917e-03       11.52288        0.0003473287
61                 306152.5 -4.133435e-01       12.21850        0.0001791345
62                 124716.1  1.156023e-01       11.84940        0.0003300562
63                 198517.7  1.004739e-01       12.29911        0.0002845157
64                 306152.5  3.481841e-02       12.66666        0.0002501935
65                 147744.3  1.974737e-01       12.10071        0.0002793290
66                 198517.7  1.296566e-01       12.32829        0.0002994857
67                 124716.1 -4.440135e-01       11.28978        0.0002360726
68                 205982.8  8.830757e-02       12.32386        0.0002646540
69                 147744.3  5.016851e-01       12.40492        0.0003693926
70                 157755.8 -1.973676e-01       11.77144        0.0002815715
71                 193941.9 -4.720261e-02       12.12811        0.0002666872
72                 147744.3 -1.943930e-02       11.88380        0.0002955104
73                 124716.1 -1.494800e-01       11.58432        0.0002453986
74                 101947.9 -1.136026e-01       11.41861        0.0003344191
75                 147744.3 -8.466819e-02       11.81857        0.0002957172
76                 126987.8  9.611393e-05       11.75194        0.0003173674
77                 136902.4 -2.943743e-03       11.82408        0.0002430348
78                 124716.1 -1.255598e-01       11.60824        0.0003045335
79                 147744.3  2.697944e-01       12.17303        0.0003394381
80                 157755.8 -2.734789e-02       11.94146        0.0002708942
81                 231775.4  5.548931e-02       12.40901        0.0002707390
82                 147744.3 -1.552408e-01       11.74800        0.0002604492
83                 193941.9 -1.406227e-01       12.03469        0.0002832091
84                 331835.3 -2.439571e-01       12.46844        0.0001875517
85                 193941.9 -1.085031e-01       12.06681        0.0002661242
86                 231775.4 -3.428583e-01       12.01067        0.0002328076
87                 101388.7 -1.763102e-01       11.35041        0.0002348423
88                 198517.7 -4.738278e-01       11.72481        0.0001964076
89                 147744.3 -2.959123e-01       11.60733        0.0003484188
90                 147744.3 -4.044119e-01       11.49883        0.0001892939
91                 213681.7 -2.676747e-01       12.00457        0.0002506979
92                 124716.1  7.105310e-02       11.80485        0.0002626072
93                 198517.7  3.091135e-02       12.22955        0.0002853706
94                 193941.9 -4.720261e-02       12.12811        0.0002888436
95                 198517.7  7.509765e-02       12.27373        0.0002743072
96                 123526.7 -2.652156e-01       11.45900        0.0002458042
97                 123526.7 -3.976169e-01       11.32660        0.0002703985
98                 147744.3 -1.360584e-01       11.76718        0.0002628061
99                 191923.4  6.591379e-02       12.23077        0.0002702777
100                181841.2 -2.135009e-02       12.08954        0.0002774968
101                181841.2 -4.243127e-01       11.68658        0.0002369737
102                198517.7  1.923818e-03       12.20056        0.0002851395
103                101388.7  5.138915e-01       12.04061        0.0004446000
104                231775.4  7.569201e-02       12.42922        0.0002792844
105                124716.1 -2.208700e-01       11.51293        0.0002752107
106                124716.1 -8.110802e-02       11.65269        0.0003287157
107                101388.7  1.259707e-01       11.65269        0.0003318575
108                191923.4 -1.007212e-02       12.15478        0.0002373917
109                123526.7  1.027933e-01       11.82701        0.0002951331
110                193941.9 -7.460159e-02       12.10071        0.0003063864
111                198517.7  6.596861e-01       12.85832        0.0004514191
112                213681.7  1.540965e-02       12.28765        0.0002346442
113                213681.7  1.942690e-01       12.46651        0.0003024956
114                231775.4 -2.752849e-01       12.07824        0.0002280419
115                136902.4  1.520558e-02       11.84223        0.0003051132
116                123526.7  2.269676e-01       11.95118        0.0003717276
117                181841.2  5.651874e-01       12.67608        0.0003804433
118                198517.7 -1.910729e-01       12.00756        0.0002482421
119                205982.8 -1.348360e-01       12.10071        0.0002795856
120                101388.7 -1.379125e-02       11.51293        0.0003217788
121                147744.3 -8.282827e-02       11.82041        0.0002781061
122                181841.2 -1.668306e-01       11.94406        0.0002433419
123                191923.4 -5.859916e-02       12.10625        0.0002475249
124                101388.7 -1.822099e-01       11.34451        0.0003386361
125                124716.1 -3.601320e-01       11.37366        0.0002549227
126                147744.3  4.794196e-02       11.95118        0.0003286076
127                147744.3  4.250518e-01       12.32829        0.0003941408
128                193941.9  2.296098e-01       12.40492        0.0003257113
129                147744.3  2.013968e-02       11.92338        0.0002938249
130                243074.5 -9.974026e-02       12.30138        0.0002524606
131                136902.4  2.736885e-01       12.10071        0.0003343096
132                191923.4 -9.804089e-02       12.06681        0.0002366727
133                147744.3 -3.263852e-02       11.87060        0.0002766983
134                198517.7  1.472009e-01       12.34583        0.0003082107
135                198517.7  1.537015e-01       12.35234        0.0003182728
136                147744.3 -2.505510e-01       11.65269        0.0002637534
137                198517.7  2.698033e-01       12.46844        0.0003216914
138                147744.3  1.165046e-01       12.01974        0.0003297416
139                198517.7  2.724163e-02       12.22588        0.0002680728
140                136902.4 -9.095462e-02       11.73607        0.0002245739
141                123526.7  5.107698e-02       11.77529        0.0002878419
142                126987.8 -1.901306e-01       11.56172        0.0002934884
143                193941.9  1.373687e-01       12.31268        0.0003023727
144                181841.2 -2.543738e-01       11.85652        0.0002342660
145                126987.8 -9.915884e-02       11.65269        0.0002688514
146                198517.7 -4.868573e-01       11.71178        0.0001959965
147                306152.5  1.958906e-01       12.82773        0.0003004258
148                191923.4 -1.007212e-02       12.15478        0.0002648749
149                205982.8  1.317927e-01       12.36734        0.0003035891
150                124716.1  2.273586e-03       11.73607        0.0002880650
151                123526.7 -4.470096e-01       11.27720        0.0002209633
152                147744.3 -2.995586e-01       11.60368        0.0003471507
153                243074.5  1.032006e-01       12.50432        0.0003001743
154                231775.4  9.510241e-02       12.44863        0.0002890640
155                193941.9  5.007626e-01       12.67608        0.0003890506
156                245890.6 -4.142088e-01       11.99843        0.0001876567
157                306152.5  2.981528e-01       12.92999        0.0003065993
158                306152.5 -3.304558e-01       12.30138        0.0001851314
159                124716.1 -1.893713e-01       11.54442        0.0002772788
160                124716.1  1.978404e-01       11.93164        0.0003287747
161                123526.7  3.165889e-02       11.75587        0.0003240333
162                205982.8 -8.076876e-02       12.15478        0.0002261513
163                306152.5  6.165998e-02       12.69350        0.0002535982
164                193941.9 -5.534377e-02       12.11997        0.0002640602
165                243074.5 -6.402218e-02       12.33710        0.0002323957
166                124716.1  2.988875e-02       11.76368        0.0003154597
167                147744.3  3.751549e-01       12.27839        0.0003943630
168                309745.6 -2.592877e-01       12.38422        0.0002060386
169                147744.3  9.826705e-02       12.00151        0.0002995560
170                243074.5 -2.784320e-01       12.12269        0.0001906550
171                123526.7  6.766040e-01       12.40082        0.0004892969
172                205982.8  2.406530e-02       12.25961        0.0002594960
173                136902.4  2.311289e-01       12.05815        0.0003295812
174                309745.6  4.825241e-01       13.12603        0.0003622649
175                124716.1 -2.208700e-01       11.51293        0.0002558558
176                231775.4 -2.696192e-01       12.08391        0.0002247699
177                213681.7 -6.567046e-02       12.20657        0.0002597643
178                123526.7 -2.896573e-02       11.69525        0.0003821119
179                124716.1  4.722772e-01       12.20607        0.0003949715
180                126987.8  9.611393e-05       11.75194        0.0003359435
181                124716.1  1.337275e+00       13.07107        0.0008342534
182                157755.8  9.224314e-02       12.06105        0.0003148809
183                124716.1  7.923463e-02       11.81303        0.0003163186
184                181841.2 -1.704955e-01       11.94039        0.0002467164
185                309745.6 -7.975946e-02       12.56375        0.0002346525
186                213681.7  3.880849e-01       12.66033        0.0003575936
187                147744.3  2.194526e-01       12.12269        0.0003726109
188                198517.7 -3.338300e-02       12.16525        0.0002570582
189                123526.7  5.107698e-02       11.77529        0.0002878419
190                198517.7 -4.466913e-01       11.75194        0.0002167781
191                231775.4  2.968239e-01       12.65035        0.0003311071
192                147744.3  4.641024e-01       12.36734        0.0003550228
193                124716.1 -1.816493e-01       11.55215        0.0002177508
194                306152.5 -1.076760e-01       12.52416        0.0002216143
195                123526.7  1.251849e-01       11.84940        0.0003363246
196                157755.8  8.353481e-02       12.05234        0.0003080696
197                124716.1 -1.075413e-01       11.62625        0.0002872452
198                198517.7 -2.869321e-01       11.91170        0.0002569469
199                124716.1 -1.255598e-01       11.60824        0.0002765433
200                193941.9 -7.182766e-02       12.10349        0.0002472156
201                136902.4  4.985026e-02       11.87687        0.0002804636
202                147744.3 -4.672326e-02       11.85652        0.0002857831
203                181841.2  4.208839e-01       12.53177        0.0003855021
204                147744.3 -1.874941e-02       11.88449        0.0002949270
205                123526.7 -2.314900e-01       11.49272        0.0002688291
206                123526.7  4.092892e-01       12.13350        0.0004307869
207                231775.4  8.634705e-02       12.43987        0.0002946906
208                198517.7 -2.410224e-01       11.95761        0.0002478931
209                198517.7 -2.048264e-01       11.99381        0.0002507035
210                147744.3 -9.429077e-02       11.80895        0.0002664695
211                198517.7  5.622916e-02       12.25486        0.0002807389
212                124716.1 -1.532113e-01       11.58058        0.0002683279
213                213681.7  3.769116e-01       12.64915        0.0003940551
214                198517.7  3.164369e-02       12.23028        0.0002690669
215                193941.9  3.075893e-02       12.20607        0.0002590912
216                191923.4 -6.469505e-02       12.10016        0.0002768119
217                147744.3 -4.207722e-01       11.48247        0.0002224703
218                306152.5  2.324015e-01       12.86424        0.0002749416
219                104897.7  6.551302e-02       11.62625        0.0003410601
220                331835.3 -1.347578e-01       12.57764        0.0002088027
221                104897.7  1.045324e-02       11.57119        0.0003754908
222                136902.4 -9.095462e-02       11.73607        0.0003005399
223                147744.3  1.729122e-03       11.90497        0.0002885767
224                331835.3  1.942978e-01       12.90669        0.0002759747
225                104897.7 -1.043860e-01       11.45636        0.0003347536
226                198517.7 -4.372868e-01       11.76135        0.0002148315
227                193941.9  1.100321e-01       12.28535        0.0002985855
228                104897.7 -1.587472e-01       11.40199        0.0003170418
229                198517.7 -6.782349e-02       12.13081        0.0002496308
230                181841.2  6.729852e-02       12.17819        0.0002896806
231                306152.5  3.796802e-02       12.66981        0.0002574999
232                123526.7 -8.906966e-02       11.63514        0.0002726277
233                231775.4  1.244822e-01       12.47801        0.0002898485
234                124716.1 -1.210246e-01       11.61277        0.0003188893
235                124716.1 -4.565923e-01       11.27720        0.0001998221
236                181841.2 -4.156419e-01       11.69525        0.0002160314
237                181841.2  1.198763e-01       12.23077        0.0002913841
238                191923.4  2.297733e-01       12.39462        0.0003008287
239                124716.1  9.394077e-02       11.82774        0.0002883143
240                147744.3 -5.384073e-02       11.84940        0.0002565496
241                198517.7 -9.792152e-02       12.10071        0.0002554053
242                205982.8  2.962247e-01       12.53177        0.0003259247
243                126987.8 -5.068002e-01       11.24505        0.0001874784
244                213681.7  9.509782e-02       12.36734        0.0002790603
245                181841.2 -4.984205e-02       12.06105        0.0002714659
246                147744.3  6.711188e-02       11.97035        0.0002961937
247                147744.3 -1.874941e-02       11.88449        0.0002707171
248                193941.9  1.705209e-01       12.34583        0.0002983602
249                231775.4 -1.106376e-01       12.24289        0.0002484704
250                198517.7  1.027492e-01       12.30138        0.0002808459
251                198517.7  1.537015e-01       12.35234        0.0003150738
252                124716.1 -2.513292e-01       11.48247        0.0004158898
253                147744.3  1.750008e-01       12.07824        0.0003224171
254                198517.7  3.295225e-01       12.52816        0.0003215914
255                136902.4  9.801148e-02       11.92504        0.0003749318
256                124716.1  4.149430e-02       11.77529        0.0003093230
257                124716.1 -5.355807e-01       11.19821        0.0002198438
258                191923.4 -8.945715e-02       12.07539        0.0002436977
259                193941.9 -4.720261e-02       12.12811        0.0002789191
260                142765.4  2.289723e-01       12.09793        0.0003317170
261                101388.7  1.726883e-01       11.69941        0.0004333114
262                123526.7  1.807548e-01       11.90497        0.0003544902
263                231775.4  1.377274e-01       12.49125        0.0002976070
264                205982.8  1.590766e-01       12.39462        0.0003171225
265                331835.3 -1.347578e-01       12.57764        0.0002157931
266                147744.3 -6.100922e-02       11.84223        0.0002496816
267                157755.8 -2.367427e-01       11.73206        0.0002760156
268                126987.8  4.789190e-01       12.23077        0.0004553838
269                157755.8  2.422565e-01       12.21106        0.0003265928
270                193941.9 -3.187985e-01       11.85652        0.0002463534
271                306152.5  3.049130e-01       12.93675        0.0003086257
272                205982.8 -7.029746e-02       12.16525        0.0002370051
273                181841.2  2.284026e-01       12.33929        0.0003377118
274                231775.4 -2.254131e-01       12.12811        0.0002241878
275                306152.5 -3.889520e-01       12.24289        0.0001869557
276                231775.4  5.385532e-02       12.40738        0.0002774634
277                181841.2 -1.463114e-02       12.09626        0.0002516123
278                231775.4 -3.416433e-01       12.01188        0.0002305350
279                147744.3  7.342105e-02       11.97666        0.0002959592
280                147744.3 -5.181463e-01       11.38509        0.0002025979
281                136902.4 -1.152473e-01       11.71178        0.0002969883
282                126987.8  1.900981e-01       11.94194        0.0003709693
283                198517.7  1.611467e-01       12.35978        0.0003061832
284                142765.4 -4.928363e-02       11.81967        0.0002687186
285                123526.7  5.873985e-02       11.78295        0.0003000287
286                191923.4  2.024893e-01       12.36734        0.0003164785
287                147744.3  1.225107e-01       12.02575        0.0002920734
288                157755.8 -1.017065e-01       11.86710        0.0002830767
289                101388.7  4.049191e-01       11.93164        0.0004253880
290                231775.4  3.069465e-02       12.38422        0.0002715419
291                191923.4 -9.231021e-02       12.07254        0.0002598368
292                213681.7 -2.987331e-01       11.97351        0.0002200233
293                213681.7 -3.082419e-01       11.96400        0.0002072236
294                198517.7  2.963703e-01       12.49500        0.0003299022
295                198517.7  3.213161e-02       12.23077        0.0002660418
296                198517.7 -2.809100e-01       11.91772        0.0002511953
297                124716.1  8.609352e-01       12.59473        0.0005089243
298                198517.7  4.323799e-01       12.63101        0.0003582835
299                181841.2  2.129668e-01       12.32386        0.0003249899
300                101388.7 -1.247228e-01       11.40199        0.0002994029
301                123526.7 -4.036592e-01       11.32055        0.0002267398
302                306152.5  1.620207e-01       12.79386        0.0002776464
303                193941.9 -1.579832e-01       12.01733        0.0002558040
304                147744.3 -1.126812e-01       11.79056        0.0002844874
305                124716.1 -3.938209e-02       11.69441        0.0003088305
306                243074.5  4.335582e-01       12.83468        0.0003531461
307                124716.1  3.557434e-01       12.08954        0.0004126842
308                193941.9 -2.846043e-02       12.14685        0.0002944416
309                191923.4  3.035854e-01       12.46844        0.0003437503
310                231775.4  1.526531e-01       12.50618        0.0003015447
311                331835.3 -2.439571e-01       12.46844        0.0001822980
312                191923.4 -2.331734e-02       12.14153        0.0002603608
313                306152.5  1.126057e-01       12.74444        0.0002641295
314                306152.5  1.452136e-01       12.77705        0.0002797573
315                181841.2  5.039766e-01       12.61487        0.0003769290
316                124716.1  1.162968e-02       11.74543        0.0002951029
317                147744.3  4.934546e-01       12.39669        0.0003927755
318                101388.7 -1.530533e-01       11.37366        0.0003122454
319                245890.6  2.758567e-01       12.68850        0.0003247592
320                147744.3 -1.702676e-02       11.88621        0.0002651641
321                126987.8  5.242188e-01       12.27607        0.0004414500
322                101388.7 -2.622526e-01       11.26446        0.0002559259
323                147744.3 -2.163597e-01       11.68688        0.0001981056
324                147744.3 -6.100922e-02       11.84223        0.0002873782
325                306152.5 -7.510912e-02       12.55673        0.0002014091
326                306152.5 -3.913646e-01       12.24047        0.0001838196
327                193941.9 -1.006307e-02       12.16525        0.0002752825
328                243074.5 -5.986417e-02       12.34126        0.0002364111
329                309745.6  1.976232e-01       12.84113        0.0002875957
330                198517.7  7.509765e-02       12.27373        0.0002780961
331                191923.4  5.364370e-02       12.21850        0.0002818284
332                147744.3  4.794196e-02       11.95118        0.0002998042
333                243074.5 -1.806546e-01       12.22047        0.0002214276
334                147744.3 -5.238444e-01       11.37939        0.0002774035
335                306152.5 -1.405871e-01       12.49125        0.0002159026
336                101947.9 -1.818108e-01       11.35041        0.0002900109
337                126987.8  9.897900e-02       11.85083        0.0003087199
338                147744.3  2.510247e-02       11.92834        0.0003289574
339                147744.3  6.394231e-02       11.96718        0.0002794741
340                306152.5 -6.871308e-01       11.94471        0.0001448521
341                306152.5  3.562022e-01       12.98804        0.0003161013
342                306152.5  3.815983e-02       12.67000        0.0002478351
343                205982.8 -8.076876e-02       12.15478        0.0002435730
344                123526.7 -2.625806e-01       11.46163        0.0002606818
345                124716.1 -1.635449e-01       11.57025        0.0003333695
346                142765.4 -1.956053e-02       11.84940        0.0002748909
347                198517.7 -1.119078e-01       12.08673        0.0002569817
348                193941.9 -1.142668e-01       12.06105        0.0002601940
349                101947.9  2.733777e-01       11.80560        0.0003866238
350                205982.8 -4.602584e-01       11.77529        0.0001809046
351                331835.3 -1.698491e-01       12.54254        0.0002195357
352                157755.8 -1.119245e-02       11.95761        0.0003277912
353                126987.8  1.326428e-01       11.88449        0.0003289398
354                123526.7  4.743316e-01       12.19854        0.0005146804
355                104897.7  1.176988e-01       11.67844        0.0004179992
356                191923.4 -1.007212e-02       12.15478        0.0002861943
357                101388.7  3.714712e-01       11.89819        0.0004532270
358                147744.3  7.342105e-02       11.97666        0.0002892717
359                147744.3  1.104623e-01       12.01370        0.0003133396
360                147744.3 -1.126812e-01       11.79056        0.0002504040
361                147744.3  9.211318e-02       11.99535        0.0003182393
362                193941.9 -1.177411e-01       12.05757        0.0002456592
363                205982.8 -4.267343e-01       11.80881        0.0002318181
364                181841.2 -3.748199e-01       11.73607        0.0002527857
365                147744.3 -1.832988e-01       11.71994        0.0002662880
366                198517.7  1.004739e-01       12.29911        0.0002978058
367                123526.7 -7.055836e-01       11.01863        0.0001754692
368                198517.7 -2.936661e-01       11.90497        0.0002483088
369                231775.4  3.831767e-01       12.73670        0.0003396293
370                309745.6  2.416955e-01       12.88520        0.0003045943
371                193941.9 -8.017263e-02       12.09514        0.0002483166
372                142765.4 -1.170159e-01       11.75194        0.0002418077
373                231775.4 -2.106576e-01       12.14287        0.0002247434
374                198517.7  7.275846e-02       12.27139        0.0002914520
375                181841.2 -8.724003e-01       11.23849        0.0001495381
376                205982.8  1.528461e-01       12.38839        0.0002841002
377                123526.7 -4.220083e-01       11.30220        0.0002147218
378                123526.7  1.185626e-02       11.73607        0.0003053140
379                198517.7 -3.860494e-02       12.16003        0.0002525600
380                306152.5  3.303560e-01       12.96219        0.0003231107
381                123526.7 -3.733398e-02       11.68688        0.0002867330
382                157755.8  3.095896e-01       12.27839        0.0003676466
383                147744.3 -3.273382e-01       11.57590        0.0003854499
384                126987.8 -2.389208e-01       11.51293        0.0002809306
385                124716.1 -1.346923e-01       11.59910        0.0002924164
386                123526.7  4.335493e-02       11.76757        0.0003069246
387                198517.7 -4.786940e-01       11.71994        0.0002061176
388                147744.3  1.373698e-01       12.04061        0.0003139385
389                101388.7 -4.142688e-01       11.11245        0.0002054520
390                231775.4  3.902803e-02       12.39255        0.0002861448
391                245890.6 -1.589876e-03       12.41105        0.0002792317
392                198517.7 -1.849935e-01       12.01364        0.0002295644
393                136902.4 -2.371371e-01       11.58989        0.0003097171
394                331835.3 -2.516791e-01       12.46071        0.0001923844
395                193941.9 -1.435945e-01       12.03172        0.0002500306
396                136902.4  9.136694e-02       11.91839        0.0002895373
397                142765.4 -2.162708e-01       11.65269        0.0002194553
398                213681.7 -1.883380e-01       12.08391        0.0002328223
399                306152.5 -8.929376e-02       12.54254        0.0002309851
400                231775.4  3.824411e-01       12.73597        0.0003761386
401                123526.7 -7.221129e-01       11.00210        0.0001357498
402                193941.9 -2.908247e-01       11.88449        0.0002283738
403                231775.4 -4.309152e-02       12.31043        0.0002513934
404                124716.1 -8.110802e-02       11.65269        0.0002868227
405                181841.2  2.262120e-01       12.33710        0.0003190137
406                193941.9 -6.832135e-02       12.10699        0.0002554046
407                136902.4  8.802804e-02       11.91505        0.0003367269
408                213681.7  1.119759e-01       12.38422        0.0002602082
409                123526.7  1.982443e-02       11.74404        0.0003295482
410                147744.3 -3.965609e-02       11.86358        0.0002935806
411                157755.8  2.682830e-01       12.23709        0.0003571455
412                191923.4  1.135418e-01       12.27839        0.0002840378
413                157755.8 -3.336606e-01       11.63514        0.0002261923
414                331835.3 -5.206608e-02       12.66033        0.0002186970
415                147744.3 -6.100922e-02       11.84223        0.0002708182
416                124716.1  7.923463e-02       11.81303        0.0003363747
417                181841.2  4.136375e-01       12.52453        0.0003855219
418                147744.3 -3.040619e-01       11.59918        0.0002435657
419                198517.7 -1.582963e-02       12.18280        0.0002820309
420                243074.5 -3.285818e-01       12.07254        0.0001930391
421                104897.7 -2.056397e-01       11.35510        0.0003025181
422                124716.1 -4.452643e-01       11.28853        0.0001962877
423                104897.7  1.551252e-01       11.71587        0.0003552330
424                193941.9 -6.906141e-02       12.10625        0.0002618479
425                101947.9 -2.300129e-01       11.30220        0.0003251759
426                198517.7  6.570791e-02       12.26434        0.0003034670
427                124716.1 -7.244996e-02       11.66135        0.0003114799
428                126987.8 -6.496748e-02       11.68688        0.0003117412
429                213681.7 -8.607967e-01       11.41145        0.0001859379
430                123526.7 -1.159771e-01       11.60824        0.0002884958
431                306152.5  5.948848e-01       13.22672        0.0003767404
432                123526.7 -4.577285e-02       11.67844        0.0002532144
433                126987.8  2.490455e-01       12.00089        0.0003524863
434                198517.7  5.622916e-02       12.25486        0.0002828159
435                123526.7  3.165889e-02       11.75587        0.0002643983
436                147744.3  2.515409e-01       12.15478        0.0003181741
437                193941.9  3.025880e-02       12.20557        0.0002758601
438                101388.7  1.643549e-01       11.69107        0.0003564118
439                124716.1 -3.854841e-02       11.69525        0.0003159782
440                124716.1 -1.255598e-01       11.60824        0.0003091151
441                205982.8  3.069968e-01       12.54254        0.0003509618
442                243074.5 -1.752478e-01       12.22588        0.0002314991
443                231775.4 -9.866137e-02       12.25486        0.0002625507
444                157755.8  1.753935e-01       12.14420        0.0002931115
445                191923.4 -8.945715e-02       12.07539        0.0002587031
446                124716.1 -2.410727e-01       11.49272        0.0002486473
447                205982.8  2.173846e-01       12.45293        0.0003225941
448                124716.1  2.553642e-01       11.98916        0.0003821114
449                126987.8 -1.436106e-01       11.60824        0.0002781871
450                231775.4  1.280378e-01       12.48156        0.0003065119
451                142765.4  8.222216e-02       11.95118        0.0003717971
452                136902.4 -7.859756e-01       11.04105        0.0001544067
453                213681.7 -1.243292e-01       12.14791        0.0002550436
454                198517.7 -4.705968e-01       11.72804        0.0001922388
455                147744.3  1.225107e-01       12.02575        0.0003157924
456                147744.3 -8.457724e-03       11.89478        0.0002865443
457                306152.5 -2.026224e-01       12.42922        0.0002055938
458                181841.2  2.797498e-02       12.13886        0.0002879156
459                309745.6 -3.791650e-01       12.26434        0.0001785721
460                191923.4 -1.007212e-02       12.15478        0.0002665558
461                123526.7  1.807548e-01       11.90497        0.0004209281
462                306152.5  3.626914e-01       12.99453        0.0003356809
463                309745.6 -2.102983e-01       12.43321        0.0002070052
464                136902.4 -3.268571e-02       11.79434        0.0003085055
465                198517.7  5.097730e-02       12.24961        0.0002752866
466                306152.5  2.160879e-01       12.84793        0.0002702554
467                198517.7  4.028538e-01       12.60149        0.0003693763
468                124716.1 -3.321256e-01       11.40167        0.0002230410
469                306152.5  6.281402e-02       12.69465        0.0002554741
470                306152.5  2.001724e-01       12.83201        0.0002962042
471                124716.1  2.173850e-01       11.95118        0.0003368042
472                157755.8  3.881797e-02       12.00762        0.0002969690
473                136902.4 -3.268571e-02       11.79434        0.0003039169
474                147744.3 -5.050565e-03       11.89819        0.0002962681
475                147744.3  5.437286e-02       11.95761        0.0003200150
476                191923.4 -9.231021e-02       12.07254        0.0002386386
477                124716.1  2.491337e-01       11.98293        0.0003187950
478                101947.9 -1.701148e-01       11.36210        0.0003452485
479                101947.9  1.204701e-01       11.65269        0.0004035989
480                147744.3 -1.051340e-01       11.79810        0.0002595306
481                193941.9 -1.155104e-01       12.05980        0.0002677268
482                147744.3  4.794196e-02       11.95118        0.0002939306
483                124716.1 -3.118894e-01       11.42191        0.0003343315
484                101388.7 -1.066475e+00       10.46024        0.0001295025
485                331835.3  2.591465e-01       12.97154        0.0002558990
486                126987.8  3.708448e-01       12.12269        0.0003860355
487                136902.4 -5.173391e-02       11.77529        0.0003182912
488                147744.3 -2.079914e-01       11.69525        0.0002673460
489                104897.7  7.440197e-02       11.63514        0.0003480340
490                231775.4 -2.214135e-02       12.33138        0.0002695278
491                123526.7  1.251849e-01       11.84940        0.0003240025
492                213681.7  3.019390e-01       12.57418        0.0003387607
493                124716.1 -1.734435e-03       11.73206        0.0002630679
494                181841.2  1.675044e-01       12.27839        0.0003229071
495                231775.4 -1.067896e-01       12.24673        0.0002565351
496                124716.1  2.553642e-01       11.98916        0.0003985397
497                147744.3 -1.711774e-01       11.73206        0.0002592214
498                306152.5 -4.125290e-01       12.21931        0.0001793946
499                147744.3 -1.287182e-01       11.77452        0.0002979267
500                157755.8 -1.632087e-01       11.80560        0.0002563962
501                213681.7 -7.949447e-01       11.47730        0.0001622380
502                306152.5  2.745082e-01       12.90635        0.0003052201
503                191923.4 -1.945012e-01       11.97035        0.0002206018
504                331835.3 -2.249089e-01       12.48749        0.0001931309
505                198517.7  6.097977e-02       12.25961        0.0002950915
506                213681.7  9.083342e-02       12.36308        0.0002725100
507                124716.1 -1.602453e-01       11.57355        0.0003426702
508                147744.3  1.515214e-02       11.91839        0.0002870220
509                126987.8  2.248132e-01       11.97666        0.0003430783
510                331835.3 -4.968795e-02       12.66271        0.0002260919
511                231775.4 -2.752849e-01       12.07824        0.0002133195
512                147744.3 -1.126812e-01       11.79056        0.0002913985
513                306152.5  3.768206e-01       13.00866        0.0003338736
514                123526.7 -3.621102e-01       11.36210        0.0003063484
515                213681.7 -6.305519e-02       12.20919        0.0002082702
516                243074.5 -3.285818e-01       12.07254        0.0001883676
517                126987.8  7.939291e-03       11.75979        0.0003185429
518                147744.3 -3.179923e-01       11.58525        0.0004118537
519                126987.8 -1.172866e+00       10.57898        0.0009951841
520                193941.9 -8.577489e-02       12.08954        0.0002797642
521                123526.7 -1.389666e-01       11.58525        0.0002471156
522                198517.7 -5.443641e-02       12.14420        0.0002622938
523                147744.3 -2.837032e-01       11.61954        0.0002551528
524                136902.4  1.433267e-01       11.97035        0.0003448473
525                198517.7  3.149237e-01       12.51356        0.0003483831
526                243074.5  2.592048e-01       12.66033        0.0003111410
527                331835.3 -2.912100e-01       12.42118        0.0001883047
528                191923.4  1.053690e-01       12.27022        0.0002773634
529                147744.3 -1.051340e-01       11.79810        0.0003318246
530                193941.9 -7.646443e-02       12.09885        0.0002805140
531                191923.4  1.766258e-01       12.34148        0.0002958329
532                126987.8  5.030166e-01       12.25486        0.0004507543
533                157755.8 -1.973676e-01       11.77144        0.0002972327
534                124716.1  2.273586e-03       11.73607        0.0003483908
535                231775.4  1.263851e-01       12.47991        0.0002953927
536                124716.1 -1.030869e-01       11.63071        0.0002942077
537                306152.5 -1.808609e-01       12.45098        0.0002059747
538                123526.7 -1.343262e-01       11.58989        0.0003864103
539                306152.5 -7.510912e-02       12.55673        0.0002402226
540                126987.8 -1.167032e-01       11.63514        0.0002764536
541                147744.3 -4.672326e-02       11.85652        0.0002867911
542                193941.9 -1.027725e-01       12.07254        0.0002717010
543                136902.4 -1.193541e-01       11.70767        0.0002387011
544                157755.8  7.474998e-02       12.04355        0.0002901070
545                123526.7 -1.343262e-01       11.58989        0.0002749621
546                123526.7  4.038984e-01       12.12811        0.0003995508
547                331835.3 -2.136517e-01       12.49874        0.0002001695
548                142765.4 -1.091727e-01       11.75979        0.0002551101
549                309745.6  4.807391e-02       12.69158        0.0002532602
550                306152.5 -3.581073e-01       12.27373        0.0001808152
551                181841.2  5.545055e-01       12.66539        0.0004201598
552                147744.3 -8.312243e-02       11.82012        0.0002976377
553                147744.3 -3.543964e-02       11.86780        0.0002373937
554                147744.3 -2.079914e-01       11.69525        0.0002752210
555                243074.5 -7.949210e-02       12.32163        0.0002587623
556                193941.9 -1.317600e-01       12.04355        0.0002893649
557                147744.3 -6.100922e-02       11.84223        0.0003480437
558                147744.3 -2.205702e-01       11.68267        0.0002487547
559                142765.4  1.553079e-02       11.88449        0.0002954836
560                136902.4  1.836422e-01       12.01067        0.0003399439
561                231775.4 -4.621623e-01       11.89136        0.0001938210
562                124716.1  5.296670e-02       11.78676        0.0002809570
563                147744.3  2.079739e-01       12.11121        0.0003428264
564                306152.5 -1.895364e-01       12.44230        0.0001908841
565                123526.7 -4.154451e-02       11.68267        0.0003355113
566                124716.1  9.577850e-01       12.69158        0.0006052310
567                126987.8  4.625816e-02       11.79810        0.0002977877
568                243074.5  4.198649e-01       12.82099        0.0003573479
569                126987.8  2.344348e-02       11.77529        0.0003553640
570                136902.4  7.125682e-04       11.82774        0.0003421394
571                205982.8 -3.649482e-01       11.87060        0.0001832137
572                126987.8 -4.683340e-01       11.28351        0.0002156566
573                198517.7 -6.566947e-02       12.13296        0.0002716797
574                306152.5  3.894882e-01       13.02133        0.0003426657
575                157755.8 -1.337948e-01       11.83501        0.0003059450
576                198517.7 -3.492359e-01       11.84940        0.0002414266
577                198517.7 -5.903980e-01       11.60824        0.0001811350
578                309745.6  2.943983e-02       12.67295        0.0002482133
579                124716.1 -8.543039e-02       11.64837        0.0002844719
580                213681.7  1.771115e-02       12.28995        0.0002624094
581                306152.5 -1.073123e-01       12.52453        0.0002352857
582                101388.7  3.297985e-01       11.85652        0.0004206310
583                181841.2  1.904939e-01       12.30138        0.0003234553
584                231775.4 -4.284891e-01       11.92504        0.0002159572
585                198517.7  1.072843e-01       12.30592        0.0002905345
586                147744.3  3.275268e-01       12.23077        0.0003749490
587                198517.7 -2.669978e-01       11.93164        0.0002356476
588                123526.7  5.996429e-01       12.32386        0.0004811220
589                213681.7  5.191132e-01       12.79136        0.0003851321
590                136902.4 -1.443554e-01       11.68267        0.0002678041
591                198517.7  4.553248e-01       12.65396        0.0003819248
592                191923.4 -2.598839e-01       11.90497        0.0002382404
593                198517.7  2.755559e-01       12.47419        0.0003354094
594                157755.8 -7.061587e-02       11.89819        0.0002766358
595                101947.9 -3.003294e-01       11.23189        0.0003030960
596                147744.3 -7.185923e-02       11.83138        0.0002928348
597                193941.9 -5.697999e-02       12.11833        0.0002773949
598                147744.3 -3.367722e-01       11.56647        0.0002470445
599                306152.5  2.789545e-02       12.65973        0.0002475670
600                243074.5  2.269440e-01       12.62807        0.0002991462
601                123526.7 -6.117649e-01       11.11245        0.0001837913
602                191923.4  2.235427e-01       12.38839        0.0002871664
603                136902.4 -1.399358e-02       11.81303        0.0003126827
604                231775.4 -3.188332e-01       12.03469        0.0002145562
605                191923.4 -1.502420e-01       12.01461        0.0002417763
606                147744.3  7.969066e-02       11.98293        0.0003220536
607                147744.3 -5.455527e-02       11.84868        0.0002721511
608                147744.3  3.495477e-02       11.93819        0.0002833781
609                147744.3 -9.020837e-02       11.81303        0.0002342173
610                147744.3  1.314526e-01       12.03469        0.0003162023
611                124716.1 -5.758586e-03       11.72804        0.0002865352
612                306152.5 -3.793596e-01       12.25248        0.0001756841
613                191923.4 -8.442979e-01       11.32055        0.0001153828
614                147744.3 -5.813565e-02       11.84510        0.0002882052
615                124716.1  1.437731e-01       11.87757        0.0003526872
616                142765.4  3.371144e-01       12.20607        0.0003041624
617                126987.8 -7.497464e-01       11.00210        0.0002175747
618                124716.1 -2.934407e-01       11.44035        0.0002233978
619                123526.7 -3.738062e-01       11.35041        0.0002440677
620                306152.5 -1.109553e-01       12.52088        0.0002320184
621                231775.4 -2.523391e-02       12.32829        0.0002545469
622                147744.3  8.480613e-01       12.75130        0.0005137670
623                191923.4 -2.332157e-01       11.93164        0.0002276244
624                231775.4  4.701043e-01       12.82363        0.0003902144
625                147744.3 -3.089180e-02       11.87235        0.0003072835
626                147744.3 -4.074591e-01       11.49578        0.0003098556
627                123526.7  2.269676e-01       11.95118        0.0003767422
628                147744.3  4.794196e-02       11.95118        0.0002910185
629                101947.9 -1.877105e-01       11.34451        0.0003392267
630                231775.4 -1.181355e-01       12.23539        0.0002516662
631                123526.7 -1.343262e-01       11.58989        0.0002581929
632                198517.7 -3.860494e-02       12.16003        0.0002668451
633                101388.7  2.863133e-01       11.81303        0.0003965665
634                331835.3  5.329444e-02       12.76569        0.0002403849
635                104897.7 -1.756490e-01       11.38509        0.0002949355
636                147744.3 -1.530707e-02       11.88793        0.0003012377
637                213681.7 -3.605414e-01       11.91170        0.0002053628
638                147744.3 -4.156308e-01       11.48761        0.0001907783
639                123526.7  3.015363e-01       12.02575        0.0003536226
640                191923.4  3.066566e-02       12.19552        0.0002797956
641                331835.3  1.918134e-01       12.90421        0.0002796820
642                147744.3 -2.950028e-01       11.60824        0.0002002494
643                123526.7  1.071664e-01       11.83138        0.0003250807
644                231775.4  6.016033e-01       12.95513        0.0004176945
645                193941.9  1.726924e-01       12.34801        0.0002962515
646                181841.2  6.214387e-02       12.17303        0.0002739633
647                136902.4  2.046956e-01       12.03172        0.0003386701
648                213681.7 -4.408638e-01       11.83138        0.0002084698
649                198517.7 -1.347008e-01       12.06393        0.0002609179
650                123526.7 -1.759201e-01       11.54829        0.0002605582
651                245890.6 -3.989413e-01       12.01370        0.0001922708
652                213681.7  1.865320e-01       12.45877        0.0003013234
653                147744.3 -5.384073e-02       11.84940        0.0002794235
654                124716.1 -1.301156e-01       11.60368        0.0003150661
655                309745.6  1.844858e-01       12.82799        0.0002772620
656                136902.4 -6.333945e-02       11.76368        0.0002963990
657                181841.2 -2.402890e-01       11.87060        0.0002572172
658                142765.4  1.104271e-01       11.97939        0.0003265397
659                205982.8 -1.745012e-01       12.06105        0.0002335011
660                198517.7  3.616108e-01       12.56024        0.0003599422
661                331835.3 -4.064760e-01       12.30592        0.0001727025
662                309745.6 -4.006199e-01       12.24289        0.0001682467
663                231775.4 -1.697167e-02       12.33655        0.0002708792
664                231775.4 -4.431658e-01       11.91036        0.0002229329
665                309745.6  2.355106e-01       12.87902        0.0003375798
666                306152.5 -4.526234e-01       12.17922        0.0001726749
667                198517.7 -3.421185e-01       11.85652        0.0002431511
668                331835.3  8.220790e-01       13.53447        0.0004422369
669                243074.5  3.207627e-01       12.72189        0.0003290770
670                124716.1 -1.394743e-01       11.59432        0.0002636232
671                126987.8  1.082087e-01       11.86005        0.0003162905
672                243074.5 -3.228838e-01       12.07824        0.0002145455
673                126987.8 -3.554546e-01       11.39639        0.0002911443
674                123526.7 -2.163179e-04       11.72400        0.0003042629
675                136902.4  1.160197e-02       11.83863        0.0003365486
676                231775.4 -1.676542e-01       12.18587        0.0002275165
677                243074.5  2.512367e-01       12.65236        0.0003111819
678                191923.4 -3.154538e-01       11.84940        0.0002126475
679                309745.6  1.556692e-01       12.79918        0.0002767127
680                124716.1  1.156023e-01       11.84940        0.0003382366
681                198517.7  7.041380e-02       12.26905        0.0002812485
682                101388.7 -6.116282e-01       10.91509        0.0002450882
683                205982.8  3.826342e-01       12.61818        0.0003601561
684                306152.5 -1.867491e-01       12.44509        0.0002280848
685                193941.9 -7.716041e-02       12.09815        0.0002781935
686                136902.4 -2.196975e-01       11.60733        0.0002676940
687                126987.8 -8.928473e-01       10.85900        0.0001977919
688                101388.7  1.359043e-02       11.54031        0.0003152346
689                309745.6 -4.940043e-01       12.14950        0.0001735220
690                126987.8  1.572143e-02       11.76757        0.0003255357
691                136902.4 -4.789513e-02       11.77913        0.0002851990
692                191923.4 -1.511507e-01       12.01370        0.0002464298
693                124716.1  2.460038e-01       11.97980        0.0003215143
694                191923.4 -2.008504e-01       11.96400        0.0002372339
695                331835.3  2.724376e-02       12.73964        0.0002453713
696                198517.7 -4.349495e-01       11.76368        0.0002062209
697                309745.6 -1.189802e-01       12.52453        0.0002176727
698                198517.7 -3.280337e-01       11.87060        0.0002466000
699                147744.3 -1.711774e-01       11.73206        0.0002855418
700                123526.7  8.881730e-02       11.81303        0.0003134434
701                123526.7  9.518635e-01       12.67608        0.0006416063
702                147744.3 -2.038334e-01       11.69941        0.0002763677
703                213681.7  3.818968e-02       12.31043        0.0002899506
704                198517.7 -2.044621e-02       12.17819        0.0002782101
705                147744.3 -2.950028e-01       11.60824        0.0001851864
706                101388.7  1.576755e-02       11.54248        0.0003198155
707                309745.6 -2.698031e-01       12.37370        0.0001934217
708                243074.5 -2.595890e-01       12.14153        0.0002412496
709                198517.7  1.140487e-01       12.31268        0.0002849093
710                136902.4 -4.102225e-02       11.78600        0.0003006360
711                136902.4 -2.371371e-01       11.58989        0.0002544530
712                124716.1  2.677100e-01       12.00151        0.0003593068
713                147744.3 -4.575217e-01       11.44572        0.0002964255
714                193941.9  2.126637e-01       12.38798        0.0003374931
715                123526.7  3.709283e-01       12.09514        0.0004164810
716                198517.7 -4.385430e-02       12.15478        0.0002656307
717                124716.1  5.676177e-02       11.79056        0.0003623328
718                136902.4  3.655870e-02       11.86358        0.0003414133
719                181841.2 -1.574784e-02       12.09514        0.0002684012
720                136902.4  2.455176e-01       12.07254        0.0004028298
721                309745.6 -5.427944e-01       12.10071        0.0001590728
722                191923.4  4.460194e-01       12.61087        0.0003682165
723                193941.9  1.962734e-01       12.37159        0.0003083792
724                124716.1  7.573772e-01       12.49117        0.0005015872
725                331835.3 -2.424198e-01       12.46997        0.0001933645
726                123526.7 -2.314900e-01       11.49272        0.0002880273
727                124716.1 -2.564971e-01       11.47730        0.0002631890
728                193941.9 -1.799621e-01       11.99535        0.0002635011
729                198517.7  8.901899e-02       12.28765        0.0002858798
730                306152.5 -1.054957e-01       12.52634        0.0002304207
731                147744.3  5.437286e-02       11.95761        0.0003271562
732                231775.4 -2.953717e-01       12.05815        0.0002228692
733                198517.7  6.570791e-02       12.26434        0.0002942768
734                136902.4  1.490067e-01       11.97603        0.0003591061
735                231775.4 -2.561510e-01       12.09737        0.0002295459
736                331835.3 -1.347578e-01       12.57764        0.0002061659
737                147744.3 -1.473668e-01       11.75587        0.0002924223
738                126987.8 -2.389208e-01       11.51293        0.0002243608
739                231775.4 -7.420108e-02       12.27932        0.0002720437
740                331835.3  1.544422e-02       12.72784        0.0002453665
741                245890.6  9.353514e-02       12.50618        0.0002865672
742                231775.4  1.306801e-01       12.48420        0.0002967468
743                191923.4  2.356624e-02       12.18842        0.0002793450
744                157755.8  1.412536e-02       11.98293        0.0002749861
745                198517.7  8.826755e-02       12.28690        0.0002617045
746                309745.6  5.521073e-01       13.19561        0.0003745979
747                136902.4 -1.473459e-02       11.81229        0.0003351690
748                123526.7 -1.914847e-01       11.53273        0.0002555992
749                123526.7 -1.436286e-01       11.58058        0.0002625303
750                147744.3 -2.549083e-01       11.64833        0.0002550926
751                306152.5  2.548024e-01       12.88664        0.0003026226
752                157755.8  2.654788e-02       11.99535        0.0002946899
753                198517.7  1.095442e-01       12.30818        0.0002820463
754                136902.4  4.007364e-02       11.86710        0.0003494309
755                181841.2 -2.333203e-01       11.87757        0.0002473009
756                157755.8 -1.557737e-01       11.81303        0.0002700217
757                193941.9 -9.707444e-02       12.07824        0.0002564585
758                181841.2 -3.321799e-02       12.07767        0.0002799761
759                198517.7 -5.923513e-02       12.13940        0.0002512130
760                157755.8  4.792274e-02       12.01673        0.0003136729
761                124716.1  2.599011e-02       11.75979        0.0003056086
762                191923.4 -1.725910e-01       11.99226        0.0002288463
763                124716.1  1.084338e-01       11.84223        0.0003242505
764                181841.2  2.479048e-01       12.35879        0.0003319976
765                124716.1 -1.448353e-01       11.58896        0.0002866157
766                205982.8 -9.401399e-02       12.14153        0.0002399134
767                157755.8 -7.197734e-02       11.89683        0.0002856454
768                331835.3 -2.069948e-01       12.50540        0.0002081262
769                231775.4 -2.966850e-02       12.32386        0.0002532072
770                193941.9  2.873725e-03       12.17819        0.0002776227
771                181841.2 -6.147008e-02       12.04942        0.0002807421
772                136902.4  4.706668e-02       11.87409        0.0003336771
773                147744.3 -2.950028e-01       11.60824        0.0002685695
774                306152.5  4.600655e-01       13.09190        0.0003384399
775                142765.4  2.035830e-01       12.07254        0.0003458434
776                205982.8 -2.947547e-02       12.20607        0.0002844290
777                101388.7  8.060943e-02       11.60733        0.0003120197
778                198517.7 -4.913135e-02       12.14950        0.0002861013
779                306152.5  6.439889e-01       13.27583        0.0004221709
780                147744.3 -2.247985e-01       11.67844        0.0002467475
781                231775.4 -1.782777e-02       12.33570        0.0002617546
782                147744.3 -8.651151e-02       11.81673        0.0002908103
783                126987.8  5.653204e-01       12.31717        0.0004651612
784                147744.3  7.937811e-02       11.98262        0.0003308457
785                124716.1 -1.626011e-01       11.57119        0.0002218447
786                191923.4 -5.859916e-02       12.10625        0.0002737704
787                198517.7 -3.175989e-01       11.88103        0.0002491867
788                101388.7 -5.937348e-01       10.93298        0.0001964472
789                147744.3  6.647877e-02       11.96972        0.0002831273
790                123526.7 -6.286728e-02       11.66135        0.0002996504
791                198517.7  1.247775e-01       12.32341        0.0002834847
792                147744.3 -7.550223e-02       11.82774        0.0002898663
793                157755.8  5.410704e-01       12.50987        0.0004326669
794                205982.8 -2.843677e-01       11.95118        0.0002325902
795                306152.5 -3.124373e-01       12.31940        0.0001989159
796                198517.7 -8.139222e-02       12.11724        0.0002630348
797                124716.1 -2.934407e-01       11.44035        0.0002421218
798                193941.9  1.485420e-01       12.32386        0.0003226526
799                142765.4 -2.313835e-02       11.84582        0.0002884368
800                231775.4  3.551335e-03       12.35708        0.0002622760
801                306152.5  2.291600e-01       12.86100        0.0002881172
802                126987.8 -1.481664e-01       11.60368        0.0003085195
803                181841.2  3.861337e-02       12.14950        0.0002751843
804                205982.8 -1.074370e-01       12.12811        0.0002296419
805                231775.4 -4.526189e-01       11.90091        0.0002093916
806                147744.3  1.165046e-01       12.01974        0.0003021945
807                231775.4 -4.284891e-01       11.92504        0.0002159572
808                198517.7  1.771818e-01       12.37582        0.0003218002
809                147744.3  1.225107e-01       12.02575        0.0002931933
810                147744.3 -5.419794e-02       11.84904        0.0002783973
811                136902.4 -6.723809e-02       11.75979        0.0002841475
812                124716.1  2.076604e-01       11.94146        0.0003155706
813                104897.7 -4.781566e-02       11.51293        0.0003542366
814                198517.7 -3.210651e-01       11.87757        0.0002173110
815                123526.7  5.491575e-02       11.77913        0.0003342950
816                142765.4 -1.956053e-02       11.84940        0.0002966707
817                124716.1  2.333853e-01       11.96718        0.0003790842
818                147744.3  1.687312e-01       12.07197        0.0003476351
819                147744.3 -4.672326e-02       11.85652        0.0002310000
820                124716.1  2.102629e-01       11.94406        0.0003623769
821                136902.4  2.223952e-01       12.04942        0.0003214075
822                181841.2  1.581585e-01       12.26905        0.0003295309
823                198517.7 -3.967769e-01       11.80186        0.0002278731
824                205982.8  1.528461e-01       12.38839        0.0002931694
825                245890.6 -2.737782e-01       12.13886        0.0002192966
826                198517.7 -4.118715e-01       11.78676        0.0002267685
827                213681.7 -2.646213e-01       12.00762        0.0002140477
828                147744.3  6.711188e-02       11.97035        0.0002978339
829                136902.4  2.165301e-01       12.04355        0.0003024796
830                136902.4 -7.508127e-02       11.75194        0.0002855034
831                198517.7 -3.004458e-01       11.89819        0.0002344353
832                193941.9 -1.085031e-01       12.06681        0.0002696691
833                191923.4 -2.332157e-01       11.93164        0.0002250560
834                191923.4  2.643647e-01       12.42922        0.0003117074
835                213681.7 -1.177268e-01       12.15452        0.0002586189
836                136902.4 -4.026151e-02       11.78676        0.0002957605
837                181841.2 -1.792531e-01       11.93164        0.0002538623
838                147744.3 -1.089005e-01       11.79434        0.0002631432
839                231775.4  7.800933e-02       12.43153        0.0002926141
840                147744.3  5.101806e-03       11.90834        0.0003151438
841                243074.5  2.368340e-02       12.42481        0.0002570428
842                136902.4 -5.945595e-02       11.76757        0.0002846827
843                193941.9 -1.376597e-01       12.03765        0.0002544349
844                181841.2  2.606982e-01       12.37159        0.0003381857
845                147744.3 -2.995586e-01       11.60368        0.0002465543
846                198517.7  9.935878e-03       12.20857        0.0002856331
847                147744.3 -2.418930e-01       11.66135        0.0003746196
848                147744.3 -1.051340e-01       11.79810        0.0002757451
849                124716.1 -6.288382e-01       11.10496        0.0001763842
850                231775.4  2.695369e-01       12.62306        0.0003105832
851                157755.8 -1.763544e-01       11.79245        0.0002565490
852                306152.5  1.338498e-01       12.76569        0.0002741959
853                136902.4  7.794392e-02       11.90497        0.0003193179
854                198517.7 -3.745538e-01       11.82408        0.0002329938
855                123526.7  2.397883e-01       11.96400        0.0003822795
856                243074.5 -2.595890e-01       12.14153        0.0002046821
857                193941.9 -8.577489e-02       12.08954        0.0002637351
858                142765.4 -1.862900e-01       11.68267        0.0002155076
859                147744.3 -3.903130e-01       11.51293        0.0002254338
860                231775.4  3.499848e-01       12.70351        0.0003510080
861                147744.3 -1.874941e-02       11.88449        0.0002447524
862                123526.7  9.251417e-02       11.81673        0.0003278338
863                147744.3  5.955038e-01       12.49874        0.0004061212
864                147744.3  1.181324e-02       11.91505        0.0002632692
865                147744.3 -1.841121e-01       11.71913        0.0002946268
866                136902.4  2.311289e-01       12.05815        0.0003491649
867                136902.4  1.209257e-01       11.94795        0.0003435265
868                136902.4  1.866771e-01       12.01370        0.0003250740
869                181841.2 -4.252041e-01       11.68568        0.0002367626
870                147744.3 -5.384073e-02       11.84940        0.0002637200
871                101388.7  4.918355e-02       11.57590        0.0003382548
872                181841.2 -2.406177e-01       11.87027        0.0002333875
873                306152.5  6.920883e-01       13.32393        0.0004383092
874                136902.4 -1.399358e-02       11.81303        0.0002987322
875                147744.3 -2.950028e-01       11.60824        0.0002532474
876                147744.3  3.495477e-02       11.93819        0.0003037312
877                193941.9 -7.460159e-02       12.10071        0.0002725496
878                193941.9  2.130805e-01       12.38839        0.0003085355
879                136902.4 -8.696260e-02       11.74006        0.0003058768
880                147744.3 -1.434529e-01       11.75979        0.0002642067
881                231775.4  9.549464e-02       12.44902        0.0002770350
882                213681.7  1.569732e-01       12.42922        0.0003017420
883                157755.8 -1.858511e-01       11.78295        0.0002780869
884                193941.9 -1.085031e-01       12.06681        0.0002671505
885                147744.3  4.341561e-02       11.94665        0.0002591813
886                198517.7 -3.245433e-01       11.87409        0.0002025960
887                126987.8 -3.667542e-01       11.38509        0.0002308771
888                231775.4 -2.882493e-01       12.06527        0.0002458745
889                101947.9 -3.069739e-01       11.22524        0.0002567659
890                101388.7 -1.054767e+00       10.47195        0.0001735898
891                123526.7  8.881730e-02       11.81303        0.0003163776
892                181841.2  2.691370e-01       12.38003        0.0003307248
893                147744.3  1.778377e-01       12.08108        0.0003312149
894                181841.2  1.001713e-01       12.21106        0.0003038308
895                123526.7  1.664640e-01       11.89068        0.0002899760
896                193941.9 -1.318188e-01       12.04349        0.0002416114
897                181841.2  5.955655e-02       12.17045        0.0002685310
898                191923.4  7.803515e-02       12.24289        0.0002685335
899                191923.4 -9.231021e-02       12.07254        0.0002700103
900                306152.5 -7.159418e-02       12.56024        0.0002264345
901                191923.4 -8.661219e-02       12.07824        0.0002456583
902                198517.7  1.750698e-01       12.37370        0.0002902273
903                193941.9  1.351189e-01       12.31043        0.0002903810
904                243074.5 -1.900629e-01       12.21106        0.0002175323
905                147744.3 -2.290448e-01       11.67419        0.0002598300
906                231775.4  3.225521e-01       12.67608        0.0003269681
907                198517.7 -4.385430e-02       12.15478        0.0002493613
908                147744.3  4.934546e-01       12.39669        0.0004498531
909                126987.8 -4.633151e-01       11.28853        0.0002466758
910                181841.2  1.668150e-02       12.12757        0.0002936093
911                231775.4  8.762058e-02       12.44114        0.0002811459
912                198517.7  1.889227e-01       12.38756        0.0003007029
913                205982.8  1.710134e-01       12.40656        0.0002925357
914                157755.8 -4.443109e-02       11.92437        0.0002352688
915                193941.9  9.841758e-02       12.27373        0.0002854310
916                123526.7  1.941778e-01       11.91839        0.0003218827
917                157755.8 -9.820383e-02       11.87060        0.0002281093
918                243074.5 -5.697439e-01       11.83138        0.0001707863
919                124716.1  1.473266e-03       11.73527        0.0002625123
920                147744.3 -3.263852e-02       11.87060        0.0002844646
921                243074.5  1.050542e-01       12.50618        0.0002801845
922                198517.7 -3.078221e-02       12.16785        0.0002637975
923                191923.4  2.864240e-02       12.19349        0.0002881079
924                147744.3 -1.356707e-01       11.76757        0.0002958626
925                181841.2 -4.164756e-01       11.69441        0.0002190221
926                198517.7 -3.937851e-01       11.80485        0.0002442269
927                157755.8  8.644602e-02       12.05525        0.0002947198
928                123526.7  3.165889e-02       11.75587        0.0003303228
929                213681.7 -3.877540e-01       11.88449        0.0001783835
930                136902.4 -3.646644e-02       11.79056        0.0002943817
931                198517.7 -7.052254e-02       12.12811        0.0002550944
932                231775.4 -4.023438e-01       11.95118        0.0002042745
933                126987.8 -8.619970e-02       11.66565        0.0003120520
934                191923.4  3.487059e-01       12.51356        0.0003235634
935                198517.7  1.855852e-01       12.38422        0.0002914085
936                243074.5 -1.231950e-01       12.27793        0.0002405506
937                193941.9 -8.073145e-02       12.09458        0.0002722942
938                213681.7 -2.893139e-01       11.98293        0.0002329115
939                147744.3 -9.020837e-02       11.81303        0.0002738621
940                124716.1 -1.191089e+00       10.54271        0.0001087294
941                147744.3 -5.384073e-02       11.84940        0.0003257743
942                147744.3 -9.020837e-02       11.81303        0.0002934467
943                306152.5 -5.707918e-01       12.06105        0.0001627235
944                181841.2 -6.029760e-01       11.50791        0.0001794855
945                231775.4 -2.417622e-01       12.11176        0.0002088927
946                126987.8  2.768924e-01       12.02874        0.0003568310
947                231775.4 -3.398234e-01       12.01370        0.0002204154
948                126987.8 -3.955746e-01       11.35627        0.0002688127
949                231775.4 -1.479517e-01       12.20557        0.0002440939
950                123526.7 -1.159771e-01       11.60824        0.0002962381
951                136902.4  1.520558e-02       11.84223        0.0003012973
952                147744.3  1.885451e-01       12.09178        0.0003845904
953                331835.3  1.247245e-02       12.72487        0.0002391515
954                198517.7  2.539084e-01       12.45254        0.0003184454
955                157755.8 -2.247665e-01       11.74404        0.0002701325
956                123526.7  1.185626e-02       11.73607        0.0002949913
957                124716.1 -6.386622e-02       11.66993        0.0002860272
958                306152.5  2.552884e-01       12.88713        0.0003038898
959                191923.4  1.590337e-02       12.18075        0.0002694031
960                231775.4 -1.625652e-01       12.19096        0.0002468845
961                331835.3  4.756377e-02       12.75996        0.0002489078
962                124716.1  2.979238e-01       12.03172        0.0003697124
963                147744.3  2.356255e-01       12.13886        0.0003465220
964                198517.7 -1.323979e-01       12.06624        0.0002595101
965                306152.5  9.748215e-02       12.72932        0.0002723328
966                126987.8 -4.335400e-02       11.70849        0.0003023046
967                147744.3 -7.915854e-02       11.82408        0.0002830016
968                191923.4 -3.674036e-02       12.12811        0.0002553608
969                101388.7 -1.081019e-01       11.41861        0.0002759675
970                198517.7  3.699780e-02       12.23563        0.0002985313
971                123526.7 -4.097382e-01       11.31447        0.0003353845
972                124716.1 -3.716929e-01       11.36210        0.0002660436
973                231775.4  9.684665e-04       12.35449        0.0002556348
974                191923.4 -3.378089e-01       11.82704        0.0001774265
975                198517.7 -2.809100e-01       11.91772        0.0002388131
976                147744.3  1.013298e-01       12.00457        0.0002767805
977                101947.9 -1.471252e-01       11.38509        0.0003012720
978                157755.8  4.195905e-01       12.38839        0.0003757413
979                142765.4 -3.362301e-01       11.53273        0.0002004561
980                136902.4 -1.399358e-02       11.81303        0.0003102009
981                123526.7 -2.112873e-01       11.51293        0.0002800739
982                213681.7 -2.585422e-01       12.01370        0.0002363070
983                124716.1 -3.833889e-01       11.35041        0.0002115844
984                147744.3 -2.146804e-01       11.68856        0.0002435330
985                191923.4  1.678538e-01       12.33271        0.0003351723
986                198517.7  2.232761e-02       12.22096        0.0002661260
987                309745.6 -5.019724e-01       12.14153        0.0001683528
988                193941.9 -1.923846e-01       11.98293        0.0002690745
989                123526.7  3.540265e-01       12.07824        0.0004208471
990                198517.7 -2.302021e-02       12.17561        0.0002798502
991                124716.1 -3.601320e-01       11.37366        0.0002107556
992                243074.5  1.661144e-01       12.56724        0.0002637278
993                198517.7 -5.679251e-01       11.63071        0.0001898947
994                147744.3  1.255002e-01       12.02874        0.0003179738
995                243074.5  1.870676e-01       12.58819        0.0003026651
996                147744.3 -3.415228e-01       11.56172        0.0002154926
997                104897.7  1.176988e-01       11.67844        0.0003634337
998                142765.4  1.139709e-01       11.98293        0.0003098744
999                142765.4  3.220008e-01       12.19096        0.0003237197
1000               331835.3 -6.806642e-02       12.64433        0.0002201892
1001               198517.7  1.472009e-01       12.34583        0.0002899838
1002               213681.7 -5.790815e-01       11.69316        0.0001818610
1003               123526.7 -3.856407e-01       11.33857        0.0003775209
1004               243074.5  2.607909e-01       12.66191        0.0003276057
1005               198517.7  3.686038e-01       12.56724        0.0003614102
1006               101947.9 -4.975108e-02       11.48247        0.0003073992
1007               101947.9 -2.424354e-01       11.28978        0.0003211614
1008               136902.4  1.241568e-01       11.95118        0.0002976286
1009               191923.4 -1.038046e-01       12.06105        0.0002574962
1010               306152.5 -4.459687e-01       12.18587        0.0001770740
1011               181841.2  3.662790e-01       12.47717        0.0003417878
1012               191923.4  3.705249e-01       12.53538        0.0003098318
1013               123526.7  1.223237e-01       11.84654        0.0003823424
1014               309745.6  5.860614e-01       13.22957        0.0003894399
1015               198517.7 -3.141446e-01       11.88449        0.0002304134
1016               157755.8 -3.161163e-01       11.65269        0.0002437510
1017               123526.7 -3.749834e-01       11.34923        0.0003515098
1018               193941.9 -9.432255e-02       12.08099        0.0002520378
1019               198517.7  8.143750e-03       12.20678        0.0002779089
1020               147744.3  1.104623e-01       12.01370        0.0002999553
1021               123526.7  1.568220e-01       11.88103        0.0003167094
1022               198517.7  2.503852e-01       12.44902        0.0003321861
1023               191923.4 -6.413934e-02       12.10071        0.0002549787
1024               306152.5 -4.991435e-01       12.13270        0.0001647205
1025               331835.3 -2.912100e-01       12.42118        0.0001998081
1026               306152.5  9.004717e-02       12.72189        0.0002745450
1027               213681.7  2.913985e-02       12.30138        0.0002743418
1028               309745.6 -3.721144e-01       12.27139        0.0001886159
1029               101388.7 -2.245123e-01       11.30220        0.0002657692
1030               124716.1 -3.262305e-01       11.40756        0.0001880422
1031               124716.1 -1.210246e-01       11.61277        0.0002649712
1032               147744.3  4.146945e-02       11.94471        0.0003050916
1033               205982.8  4.652208e-01       12.70077        0.0003868599
1034               193941.9 -8.577489e-02       12.08954        0.0002653284
1035               147744.3  1.278854e-01       12.03112        0.0003271883
1036               101947.9  3.954633e-01       11.92768        0.0003649728
1037               147744.3 -9.020837e-02       11.81303        0.0003086533
1038               147744.3 -9.020837e-02       11.81303        0.0002801547
1039               191923.4 -2.201436e-01       11.94471        0.0002360723
1040               123526.7 -3.001185e-01       11.42409        0.0002187010
1041               123526.7  2.555864e-01       11.97980        0.0003940453
1042               198517.7 -2.302021e-02       12.17561        0.0002766772
1043               213681.7  2.686453e-02       12.29911        0.0002876981
1044               124716.1  3.097583e-01       12.04355        0.0004027924
1045               147744.3 -6.244910e-02       11.84079        0.0002818185
1046               198517.7 -2.416636e-01       11.95697        0.0002688457
1047               198517.7 -4.545965e-01       11.74404        0.0002002213
1048               191923.4 -2.803624e-01       11.88449        0.0002125058
1049               136902.4 -2.891923e-02       11.79810        0.0002989918
1050               198517.7 -3.338300e-02       12.16525        0.0002549466
1051               147744.3  7.969066e-02       11.98293        0.0003053778
1052               193941.9 -3.377959e-02       12.14153        0.0002902067
1053               181841.2 -2.127011e-01       11.89819        0.0002582284
1054               101947.9 -1.996154e-01       11.33260        0.0002858661
1055               231775.4  8.366018e-02       12.43718        0.0002819048
1056               123526.7  1.071664e-01       11.83138        0.0003044481
1057               231775.4 -1.625652e-01       12.19096        0.0002400259
1058               147744.3 -4.639595e-01       11.43928        0.0002945233
1059               231775.4 -3.705951e-01       11.98293        0.0002254075
1060               142765.4 -4.487834e-02       11.82408        0.0002536288
1061               147744.3 -1.187653e-02       11.89136        0.0003052977
1062               147744.3 -1.356707e-01       11.76757        0.0002834996
1063               198517.7 -1.179428e-01       12.08069        0.0002451527
1064               101388.7  2.252257e-01       11.75194        0.0003893434
1065               309745.6 -5.999528e-01       12.04355        0.0001657414
1066               126987.8  7.939291e-03       11.75979        0.0003166779
1067               191923.4 -2.008504e-01       11.96400        0.0002170972
1068               142765.4 -8.668584e-01       11.00210        0.0002690906
1069               147744.3 -2.121668e-01       11.69107        0.0002606019
1070               147744.3 -9.020837e-02       11.81303        0.0002770620
1071               147744.3  7.656077e-02       11.97980        0.0003528056
1072               104897.7  1.045324e-02       11.57119        0.0003227890
1073               331835.3 -2.081353e-02       12.69158        0.0002259466
1074               181841.2 -1.073250e-02       12.10016        0.0002870226
1075               193941.9  3.482122e-01       12.52353        0.0003749873
1076               193941.9 -6.906141e-02       12.10625        0.0002580452
1077               306152.5 -8.929376e-02       12.54254        0.0002196792
1078               193941.9 -3.111647e-02       12.14420        0.0002769625
1079               191923.4  6.591379e-02       12.23077        0.0002880496
1080               147744.3 -1.287182e-01       11.77452        0.0003075021
1081               147744.3 -9.391895e-02       11.80932        0.0002845767
1082               124716.1 -6.386622e-02       11.66993        0.0003243446
1083               306152.5  3.796802e-02       12.66981        0.0002551260
1084               193941.9 -5.207935e-02       12.12323        0.0003121820
1085               136902.4 -5.173391e-02       11.77529        0.0003158940
1086               136902.4  2.237406e-02       11.84940        0.0003107863
1087               147744.3 -9.988467e-02       11.80335        0.0002785091
1088               101388.7  1.551073e-01       11.68182        0.0003643229
1089               198517.7  6.994420e-02       12.26858        0.0002754823
1090               123526.7 -9.795860e-02       11.62625        0.0003171077
1091               123526.7 -4.577285e-02       11.67844        0.0003662617
1092               193941.9 -1.683020e-01       12.00701        0.0002748587
1093               147744.3 -2.505510e-01       11.65269        0.0002436835
1094               193941.9  2.892696e-01       12.46458        0.0003450758
1095               193941.9  1.030796e-01       12.27839        0.0002971530
1096               124716.1  1.156023e-01       11.84940        0.0003644844
1097               142765.4 -5.592818e-02       11.81303        0.0002429326
1098               157755.8 -5.230870e-01       11.44572        0.0001885252
1099               124716.1 -5.960182e-02       11.67419        0.0002384566
1100               181841.2  2.754198e-01       12.38631        0.0003363664
1101               193941.9 -1.376597e-01       12.03765        0.0002451014
1102               126987.8 -2.191182e-01       11.53273        0.0002556287
1103               147744.3 -2.163597e-01       11.68688        0.0002369182
1104               136902.4 -3.759736e-01       11.45105        0.0002276014
1105               157755.8  2.170662e-01       12.18587        0.0003178819
1106               126987.8  1.257223e-01       11.87757        0.0003488291
1107               147744.3 -6.100922e-02       11.84223        0.0003027970
1108               191923.4  2.864240e-02       12.19349        0.0002829044
1109               198517.7  7.609049e-01       12.95954        0.0004847691
1110               136902.4 -5.372417e-01       11.28978        0.0001828523
1111               123526.7 -4.344308e-01       11.28978        0.0002293825
1112               126987.8  1.598553e-01       11.91170        0.0003242036
1113               181841.2 -1.017679e-02       12.10071        0.0002745398
1114               213681.7 -2.025630e-01       12.06968        0.0002410109
1115               124716.1 -6.472128e-02       11.66907        0.0003222489
1116               124716.1  1.368045e-01       11.87060        0.0003486241
1117               147744.3 -1.752016e-01       11.72804        0.0002731219
1118               123526.7  1.935109e-01       11.91772        0.0003192330
1119               213681.7  7.359161e-02       12.34583        0.0002851483
1120               101388.7  1.726883e-01       11.69941        0.0004156687
1121               147744.3  3.117940e-01       12.21503        0.0003732724
1122               245890.6 -1.203918e-01       12.29225        0.0002352166
1123               147744.3  1.969180e-01       12.10016        0.0003444870
1124               306152.5 -2.860041e-01       12.34583        0.0002072281
1125               231775.4  1.436114e-02       12.36789        0.0002586772
1126               191923.4 -3.674036e-02       12.12811        0.0002595411
1127               213681.7  4.715835e-02       12.31940        0.0002756114
1128               136902.4 -5.945595e-02       11.76757        0.0003134641
1129               245890.6 -2.370287e-01       12.17561        0.0002119387
1130               306152.5 -2.723156e-01       12.35952        0.0001983203
1131               198517.7  2.118074e-01       12.41044        0.0003063900
1132               193941.9 -1.142668e-01       12.06105        0.0002459725
1133               123526.7  6.431280e-01       12.36734        0.0004804748
1134               331835.3  6.331129e-01       13.34551        0.0003899825
1135               157755.8  8.061510e-02       12.04942        0.0003236044
1136               147744.3  9.826705e-02       12.00151        0.0003099845
1137               231775.4 -2.988560e-01       12.05467        0.0002406130
1138               205982.8 -2.697859e-02       12.20857        0.0002137080
1139               213681.7  1.119759e-01       12.38422        0.0002803227
1140               331835.3 -1.521495e-01       12.56024        0.0001904425
1141               157755.8 -2.777321e-01       11.69107        0.0002511709
1142               124716.1 -8.110802e-02       11.65269        0.0002864012
1143               213681.7 -3.217080e-01       11.95054        0.0002234210
1144               123526.7 -2.838580e-01       11.44035        0.0003331629
1145               243074.5  2.809311e-02       12.42922        0.0002455546
1146               213681.7  6.080488e-01       12.88029        0.0004629269
1147               331835.3  8.087455e-01       13.52114        0.0004341491
1148               124716.1 -3.854841e-02       11.69525        0.0002850445
1149               123526.7 -1.634500e-01       11.56076        0.0002661941
1150               331835.3 -2.362942e-01       12.47610        0.0001990836
1151               198517.7 -1.787881e-02       12.18075        0.0002775442
1152               193941.9 -2.581142e-02       12.14950        0.0002615401
1153               231775.4 -2.867136e-01       12.06681        0.0002239770
1154               124716.1  2.273586e-03       11.73607        0.0003018623
1155               157755.8  4.489702e-02       12.01370        0.0002978825
1156               136902.4  1.433267e-01       11.97035        0.0003608629
1157               193941.9 -9.707444e-02       12.07824        0.0002727084
1158               193941.9  1.224717e-01       12.29779        0.0003060151
1159               124716.1  1.437731e-01       11.87757        0.0003254109
1160               198517.7 -1.090948e-01       12.08954        0.0002565259
1161               136902.4  7.794392e-02       11.90497        0.0003087602
1162               147744.3 -2.414620e-01       11.66178        0.0002661616
1163               198517.7 -3.116516e-03       12.19552        0.0002741982
1164               126987.8 -8.191704e-02       11.66993        0.0002739951
1165               198517.7  7.041380e-02       12.26905        0.0002701396
1166               191923.4 -2.233956e-01       11.94146        0.0002432898
1167               181841.2  4.023007e-01       12.51319        0.0003369809
1168               181841.2 -5.303048e-01       11.58058        0.0001797386
1169               198517.7  7.438998e-03       12.20607        0.0002499341
1170               147744.3 -5.384073e-02       11.84940        0.0002828922
1171               231775.4  2.241120e-01       12.57764        0.0003127110
1172               181841.2  3.861337e-02       12.14950        0.0002746993
1173               193941.9 -1.676920e-01       12.00762        0.0002473586
1174               123526.7 -8.906966e-02       11.63514        0.0003591452
1175               136902.4  5.746538e-02       11.88449        0.0003735421
1176               147744.3 -9.391895e-02       11.80932        0.0002914184
1177               136902.4 -9.095462e-02       11.73607        0.0003037443
1178               136902.4 -2.007695e-01       11.62625        0.0002634455
1179               231775.4 -1.005762e-02       12.34347        0.0002737290
1180               126987.8 -4.558338e-01       11.29601        0.0003295014
1181               104897.7 -1.366469e-01       11.42409        0.0002818151
1182               147744.3 -2.505510e-01       11.65269        0.0002562066
1183               136902.4 -2.142856e-02       11.80560        0.0002955176
1184               147744.3 -3.263852e-02       11.87060        0.0002563347
1185               147744.3 -6.895437e-02       11.83428        0.0002118093
1186               193941.9 -5.262268e-02       12.12269        0.0002794146
1187               147744.3 -1.874941e-02       11.88449        0.0003327686
1188               231775.4 -7.979289e-02       12.27373        0.0002466982
1189               147744.3 -5.050565e-03       11.89819        0.0003274988
1190               306152.5  1.820793e-01       12.81392        0.0002968580
1191               147744.3 -1.512961e-01       11.75194        0.0002389828
1192               136902.4  3.277557e-01       12.15478        0.0003232683
1193               147744.3 -1.089005e-01       11.79434        0.0002631432
1194               147744.3 -3.965609e-02       11.86358        0.0002775253
1195               142765.4 -9.366850e-02       11.77529        0.0002405215
1196               213681.7 -4.308270e-01       11.84142        0.0001823303
1197               306152.5 -5.564443e-01       12.07539        0.0001650750
1198               198517.7 -1.787881e-02       12.18075        0.0002637451
1199               181841.2 -2.437916e-01       11.86710        0.0002306029
1200               243074.5  8.975249e-02       12.49088        0.0002866179
1201               198517.7  1.247775e-01       12.32341        0.0003112439
1202               231775.4  6.898155e-02       12.42251        0.0002659244
1203               191923.4 -1.212978e-01       12.04355        0.0002637542
1204               306152.5  4.179540e-01       13.04979        0.0003482945
1205               213681.7  7.359161e-02       12.34583        0.0003149866
1206               191923.4 -7.531264e-02       12.08954        0.0002638961
1207               231775.4 -2.173377e-01       12.13619        0.0002354741
1208               157755.8  7.416157e-02       12.04297        0.0003341822
1209               124716.1  3.764073e-02       11.77144        0.0002788884
1210               147744.3 -2.163597e-01       11.68688        0.0002621089
1211               147744.3  5.016851e-01       12.40492        0.0003764578
1212               306152.5 -5.780434e-01       12.05380        0.0001502815
1213               157755.8 -1.935140e-01       11.77529        0.0002783594
1214               245890.6  1.786929e-01       12.59134        0.0002974296
1215               123526.7  2.919093e-01       12.01612        0.0003846897
1216               126987.8  4.025392e-03       11.75587        0.0002973790
1217               331835.3 -9.586870e-02       12.61653        0.0002117935
1218               123526.7 -2.122878e-01       11.51192        0.0002740411
1219               193941.9 -2.053437e-02       12.15478        0.0003057889
1220               147744.3  2.179668e-02       11.92504        0.0003124788
1221               193941.9 -6.906141e-02       12.10625        0.0002625051
1222               147744.3 -1.364462e-01       11.76679        0.0002672447
1223               205982.8 -2.432877e-01       11.99226        0.0002074625
1224               126987.8  3.516398e-01       12.10349        0.0003947649
1225               147744.3  2.030139e-01       12.10625        0.0003316820
1226               231775.4 -2.313768e-01       12.12215        0.0002406396
1227               124716.1 -2.201911e-02       11.71178        0.0002618893
1228               243074.5  4.428483e-01       12.84397        0.0003613799
1229               213681.7  5.783117e-01       12.85055        0.0004080422
1230               147744.3 -2.566985e-02       11.87757        0.0002802349
1231               205982.8  2.328888e-01       12.46844        0.0003357852
1232               191923.4 -3.269451e-02       12.13216        0.0002529398
1233               136902.4  7.125682e-04       11.82774        0.0003251064
1234               123526.7  3.596923e-01       12.08391        0.0004137494
1235               213681.7 -4.300138e-01       11.84223        0.0002089638
1236               147744.3 -7.550223e-02       11.82774        0.0002469736
1237               191923.4 -1.694999e-01       11.99535        0.0002574733
1238               191923.4  3.066566e-02       12.19552        0.0002551471
1239               198517.7  1.771818e-01       12.37582        0.0003044575
1240               101388.7 -3.935886e-01       11.13313        0.0002219310
1241               198517.7  1.340716e-01       12.33271        0.0002921052
1242               243074.5 -3.004110e-01       12.10071        0.0002035793
1243               198517.7 -2.769153e-01       11.92172        0.0002333221
1244               157755.8 -1.265745e-01       11.84223        0.0002387799
1245               142765.4  1.686958e-01       12.03765        0.0002983719
1246               126987.8  4.249167e-02       11.79434        0.0003130002
1247               191923.4 -2.942516e-01       11.87060        0.0002045643
1248               205982.8 -8.076876e-02       12.15478        0.0002338178
1249               309745.6 -1.081302e-01       12.53538        0.0002288553
1250               306152.5 -8.572869e-02       12.54611        0.0002373285
1251               147744.3  2.002476e-01       12.10349        0.0003578833
1252               104897.7  1.303305e-01       11.69107        0.0003638989
1253               124716.1 -1.485493e-01       11.58525        0.0002142412
1254               191923.4 -1.639597e-01       12.00089        0.0002396042
1255               123526.7 -7.152535e-02       11.65269        0.0003154627
1256               147744.3 -6.461283e-02       11.83863        0.0002868792
1257               147744.3  4.794196e-02       11.95118        0.0003109274
1258               123526.7  1.251849e-01       11.84940        0.0003981753
1259               147744.3  4.146945e-02       11.94471        0.0002944608
1260               193941.9  1.485420e-01       12.32386        0.0003039299
1261               213681.7 -1.855171e-01       12.08673        0.0002453084
1262               331835.3 -1.347578e-01       12.57764        0.0002094976
1263               231775.4  9.684665e-04       12.35449        0.0002528995
1264               123526.7  5.107698e-02       11.77529        0.0002876060
1265               306152.5  5.974182e-02       12.69158        0.0002658289
1266               306152.5 -4.133435e-01       12.21850        0.0001792486
1267               198517.7 -3.636247e-01       11.83501        0.0002192900
1268               124716.1  1.643924e-01       11.89819        0.0003657380
1269               181841.2 -1.463114e-02       12.09626        0.0002744566
1270               213681.7  4.496428e-01       12.72189        0.0003715019
1271               198517.7  2.232761e-02       12.22096        0.0002859907
1272               331835.3 -9.421170e-02       12.61818        0.0002066857
1273               331835.3  4.008153e-03       12.71640        0.0002336214
1274               123526.7 -3.733398e-02       11.68688        0.0003107284
1275               147744.3  3.367524e-01       12.23999        0.0003616598
1276               198517.7  3.977668e-01       12.59640        0.0003751354
1277               231775.4 -1.039132e-01       12.24961        0.0002455115
1278               198517.7  3.258927e-01       12.52453        0.0003375109
1279               123526.7 -1.069273e-01       11.61729        0.0002968144
1280               147744.3  5.757286e-02       11.96081        0.0002776996
1281               126987.8 -5.605044e-01       11.19134        0.0003697522
1282               331835.3 -5.576146e-01       12.15478        0.0001567585
1283               126987.8 -4.312927e-01       11.32055        0.0002867680
1284               231775.4 -4.553363e-01       11.89819        0.0001536824
1285               101388.7 -6.116282e-01       10.91509        0.0001924090
1286               123526.7 -4.470096e-01       11.27720        0.0002542179
1287               157755.8 -1.896752e-01       11.77913        0.0002893176
1288               124716.1  7.191373e-01       12.45293        0.0004646235
1289               193941.9 -9.423756e-02       12.08108        0.0002536762
1290               231775.4 -2.081889e-02       12.33271        0.0002492190
1291               198517.7 -4.042957e-01       11.79434        0.0002171403
1292               123526.7 -2.112873e-01       11.51293        0.0002831319
1293               101388.7  2.133443e-01       11.74006        0.0003737180
1294               104897.7  1.753279e-01       11.73607        0.0003624827
1295               191923.4 -1.337276e-01       12.03112        0.0002390773
1296               191923.4 -3.518214e-01       11.81303        0.0001759705
1297               124716.1 -8.652270e-01       10.86857        0.0001621197
1298               198517.7  7.438998e-03       12.20607        0.0002712646
1299               198517.7 -4.349495e-01       11.76368        0.0002193385
1300               147744.3 -1.832988e-01       11.71994        0.0002819238
1301               181841.2 -1.597085e-01       11.95118        0.0002537062
1302               198517.7  1.406578e-01       12.33929        0.0002832022
1303               213681.7 -1.883380e-01       12.08391        0.0002219315
1304               198517.7 -2.420806e-01       11.95655        0.0002358974
1305               124716.1 -1.392900e-01       11.59451        0.0002787905
1306               191923.4  3.131549e-01       12.47801        0.0003267513
1307               243074.5  1.537138e-01       12.55484        0.0002851409
1308               181841.2  1.675044e-01       12.27839        0.0003090901
1309               124716.1 -2.201911e-02       11.71178        0.0002533900
1310               147744.3  3.028342e-01       12.20607        0.0003183144
1311               147744.3  1.461804e-01       12.04942        0.0003222271
1312               126987.8  6.044279e-02       11.81229        0.0003447319
1313               331835.3  2.115184e-01       12.92391        0.0002604109
1314               198517.7  1.687071e-01       12.36734        0.0003148638
1315               191923.4 -1.212978e-01       12.04355        0.0002503209
1316               147744.3 -2.950028e-01       11.60824        0.0002500958
1317               147744.3  1.448525e-02       11.91772        0.0003068065
1318               231775.4 -2.667983e-01       12.08673        0.0002232049
1319               306152.5  2.848928e-02       12.66033        0.0002401346
1320               142765.4  2.805441e-01       12.14950        0.0003352801
1321               309745.6 -1.750696e-01       12.46844        0.0002168975
1322               147744.3 -3.424756e-01       11.56076        0.0002020252
1323               193941.9 -2.117458e-01       11.96357        0.0002521937
1324               231775.4 -4.749006e-01       11.87862        0.0002061633
1325               231775.4 -7.049050e-02       12.28303        0.0002634638
1326               198517.7 -2.818818e-02       12.17045        0.0002666093
1327               101947.9  2.197250e-01       11.75194        0.0003704625
1328               198517.7 -3.210651e-01       11.87757        0.0002483245
1329               198517.7  1.558590e-01       12.35449        0.0002919031
1330               124716.1 -1.720798e-01       11.56172        0.0002513451
1331               147744.3  1.134880e-01       12.01673        0.0003076987
1332               198517.7  3.233440e-01       12.52198        0.0003502973
1333               331835.3  3.406193e-01       13.05301        0.0002963922
1334               231775.4  7.569201e-02       12.42922        0.0002816577
1335               243074.5 -1.690425e-02       12.38422        0.0002513034
1336               142765.4 -4.503434e-01       11.41861        0.0002289022
1337               123526.7 -5.428354e-02       11.66993        0.0002630560
1338               104897.7 -2.341452e-01       11.32660        0.0002940164
1339               243074.5 -3.723845e-01       12.02874        0.0002299267
1340               123526.7 -7.474307e-01       10.97678        0.0001604745
1341               147744.3  4.746845e-01       12.37792        0.0004016616
1342               124716.1  2.302057e-01       11.96400        0.0003647861
1343               136902.4 -2.007695e-01       11.62625        0.0002432909
1344               123526.7 -1.624971e-01       11.56172        0.0002802783
1345               101388.7  2.133443e-01       11.74006        0.0003935225
1346               191923.4  2.643647e-01       12.42922        0.0002980721
1347               124716.1  8.661473e-02       11.82041        0.0002752375
1348               193941.9  6.660121e-01       12.84133        0.0004767924
1349               126987.8  3.110635e-02       11.78295        0.0003277053
1350               198517.7  1.687071e-01       12.36734        0.0003062993
1351               147744.3 -1.752016e-01       11.72804        0.0002137874
1352               147744.3 -1.832988e-01       11.71994        0.0002789677
1353               124716.1  2.677100e-01       12.00151        0.0003760718
1354               243074.5  1.457446e-01       12.54687        0.0002807579
1355               243074.5 -4.181940e-01       11.98293        0.0001879617
1356               126987.8  7.953294e-02       11.83138        0.0003081503
1357               147744.3 -6.822947e-02       11.83501        0.0002396758
1358               142765.4 -3.794274e-02       11.83102        0.0002675748
1359               126987.8 -5.659923e-02       11.69525        0.0002951037
1360               193941.9 -4.868249e-03       12.17045        0.0002842748
1361               198517.7 -2.364412e-02       12.17499        0.0002716162
1362               231775.4  1.994023e-01       12.55293        0.0003203358
1363               124716.1 -1.720798e-01       11.56172        0.0002723041
1364               213681.7  2.522834e-01       12.52453        0.0003248304
1365               198517.7 -4.005292e-01       11.79810        0.0002425853
1366               157755.8 -3.425496e-01       11.62625        0.0002454574
1367               124716.1  6.265607e-03       11.74006        0.0003170333
1368               191923.4  1.135418e-01       12.27839        0.0002967707
1369               198517.7  1.472009e-01       12.34583        0.0003116146
1370               147744.3 -5.384073e-02       11.84940        0.0002661490
1371               147744.3 -4.956735e-01       11.40756        0.0002853293
1372               181841.2  3.459424e-01       12.45683        0.0003389071
1373               126987.8  4.886278e-01       12.24047        0.0004456946
1374               124716.1 -1.792912e-02       11.71587        0.0002535640
1375               331835.3  2.430690e-02       12.73670        0.0002445260
1376               147744.3 -1.752016e-01       11.72804        0.0002466686
1377               213681.7  4.268407e-02       12.31493        0.0002502518
1378               191923.4 -6.469505e-02       12.10016        0.0002855264
1379               198517.7 -3.745538e-01       11.82408        0.0002353909
1380               123526.7  8.002045e-01       12.52442        0.0005884908
1381               147744.3 -2.566985e-02       11.87757        0.0002818756
1382               147744.3 -3.965609e-02       11.86358        0.0002709246
1383               331835.3 -2.025199e-01       12.50987        0.0002033724
1384               147744.3 -5.384073e-02       11.84940        0.0002687248
1385               124716.1 -4.691666e-02       11.68688        0.0003384360
1386               191923.4 -4.815663e-02       12.11669        0.0002526115
1387               193941.9 -9.334165e-03       12.16598        0.0002760104
1388               124716.1 -6.593749e-01       11.07442        0.0001813796
1389               193941.9 -3.912720e-02       12.13619        0.0002609338
1390               157755.8  1.412536e-02       11.98293        0.0003003342
1391               147744.3  1.635721e-01       12.06681        0.0003132981
1392               147744.3 -2.038334e-01       11.69941        0.0002763677
1393               306152.5  2.538323e-01       12.88567        0.0003036261
1394               124716.1  1.825931e-01       11.91639        0.0003636291
1395               191923.4  2.610754e-02       12.19096        0.0003031873
1396               213681.7 -1.122143e-01       12.16003        0.0002284278
1397               198517.7 -2.849207e-01       11.91371        0.0002574642
1398               231775.4  2.908034e-01       12.64433        0.0003473134
1399               126987.8 -4.830043e-02       11.70355        0.0003066697
1400               198517.7 -1.001462e-01       12.09849        0.0002411067
1401               136902.4 -5.945595e-02       11.76757        0.0003193939
1402               157755.8  9.134647e-04       11.96972        0.0002890159
1403               198517.7  1.897606e-01       12.38839        0.0003025182
1404               123526.7 -9.795860e-02       11.62625        0.0002916546
1405               101947.9 -1.026735e-01       11.42954        0.0003693356
1406               147744.3 -8.282827e-02       11.82041        0.0002513966
1407               231775.4  2.140269e-01       12.56755        0.0003162133
1408               123526.7  1.602763e-01       11.88449        0.0004123958
1409               157755.8 -6.242969e-01       11.34451        0.0001576862
1410               231775.4 -2.254131e-01       12.12811        0.0002275827
1411               193941.9 -1.027725e-01       12.07254        0.0002500883
1412               191923.4  9.001134e-02       12.25486        0.0002644190
1413               213681.7  2.208865e-01       12.49313        0.0003055017
1414               147744.3 -3.877620e-02       11.86446        0.0002908931
1415               123526.7  1.773707e-01       11.90158        0.0003361046
     bath_pr_sqft student_apt
1    0.0013939666           0
2    0.0008426143           0
3    0.0013615394           0
4    0.0008504552           0
5    0.0012461753           0
6    0.0009067742           0
7    0.0009925612           1
8    0.0012688872           0
9    0.0008142978           0
10   0.0009259452           0
11   0.0009232940           0
12   0.0012238027           1
13   0.0009874711           0
14   0.0007829355           1
15   0.0008453469           0
16   0.0003434569           1
17   0.0009396756           0
18   0.0008929205           0
19   0.0002892049           0
20   0.0012190267           0
21   0.0003370551           0
22   0.0007283615           0
23   0.0009189422           0
24   0.0009146720           0
25   0.0007643721           1
26   0.0006629613           0
27   0.0009893041           0
28   0.0007726803           0
29   0.0004683976           0
30   0.0003165956           1
31   0.0005687586           0
32   0.0008512406           0
33   0.0007712334           0
34   0.0010250409           1
35   0.0012143342           0
36   0.0005996940           0
37   0.0005548868           0
38   0.0009159446           0
39   0.0013047308           0
40   0.0008602495           0
41   0.0008206615           1
42   0.0010178434           0
43   0.0009729962           1
44   0.0008795324           0
45   0.0009784922           0
46   0.0007274881           1
47   0.0007505078           1
48   0.0009007303           0
49   0.0009639672           0
50   0.0008861227           1
51   0.0003144923           0
52   0.0007196857           0
53   0.0003371598           0
54   0.0007987877           1
55   0.0013608791           1
56   0.0008343447           1
57   0.0011267360           0
58   0.0003588477           0
59   0.0008766673           0
60   0.0003486654           0
61   0.0008124811           0
62   0.0008820713           0
63   0.0012865923           0
64   0.0007248962           0
65   0.0009170949           1
66   0.0010522695           0
67   0.0003680258           0
68   0.0007268559           1
69   0.0008946829           0
70   0.0010290241           0
71   0.0008387319           0
72   0.0009039333           0
73   0.0008548928           0
74   0.0011239560           0
75   0.0003218456           0
76   0.0009520105           0
77   0.0007312538           0
78   0.0006905497           0
79   0.0007775201           0
80   0.0011136192           0
81   0.0007683752           0
82   0.0006083777           1
83   0.0009779128           0
84   0.0007181108           0
85   0.0008898730           0
86   0.0009840561           0
87   0.0002801218           0
88   0.0009463685           1
89   0.0004683976           1
90   0.0002836420           0
91   0.0009829279           1
92   0.0007337867           0
93   0.0013834217           0
94   0.0009084140           0
95   0.0007633856           1
96   0.0009613735           0
97   0.0004024270           0
98   0.0009033292           0
99   0.0010121486           0
100  0.0008504552           0
101  0.0010866711           0
102  0.0008537743           0
103  0.0005318868           0
104  0.0007767750           1
105  0.0003432322           1
106  0.0003564882           0
107  0.0008777372           1
108  0.0007193845           0
109  0.0007989078           0
110  0.0009903525           0
111  0.0011669491           0
112  0.0009242246           0
113  0.0012454293           1
114  0.0009009292           0
115  0.0006010178           0
116  0.0005924940           0
117  0.0010809415           0
118  0.0009015267           1
119  0.0009598305           0
120  0.0003262473           0
121  0.0003021221           0
122  0.0008625648           0
123  0.0007873893           0
124  0.0012189538           0
125  0.0003654364           0
126  0.0006264504           1
127  0.0007729919           0
128  0.0012944480           1
129  0.0008638995           1
130  0.0011157585           0
131  0.0007627965           1
132  0.0007831556           0
133  0.0008576349           1
134  0.0007980691           0
135  0.0013646391           1
136  0.0003388528           0
137  0.0009824838           0
138  0.0008804357           0
139  0.0010434745           0
140  0.0009838309           0
141  0.0008205268           0
142  0.0010648413           0
143  0.0007906885           0
144  0.0009063662           0
145  0.0002968770           0
146  0.0006378489           0
147  0.0009879229           0
148  0.0008026686           0
149  0.0007983083           0
150  0.0002874108           0
151  0.0003455047           0
152  0.0004683976           0
153  0.0008122230           0
154  0.0007885202           0
155  0.0011789561           0
156  0.0008518711           0
157  0.0011377715           0
158  0.0007728880           0
159  0.0003350886           0
160  0.0008092799           0
161  0.0012557418           0
162  0.0007355255           0
163  0.0007153009           0
164  0.0008372587           0
165  0.0007432822           0
166  0.0006123410           0
167  0.0008129984           0
168  0.0010681095           0
169  0.0008145588           0
170  0.0010074646           0
171  0.0009949175           0
172  0.0010133027           0
173  0.0010462717           1
174  0.0008943936           1
175  0.0003190934           1
176  0.0008829854           0
177  0.0005547914           1
178  0.0003933419           0
179  0.0007388898           0
180  0.0003359112           0
181  0.0006571253           0
182  0.0011485385           0
183  0.0008766673           1
184  0.0011703162           0
185  0.0007624048           1
186  0.0007277258           0
187  0.0008975731           0
188  0.0010631376           0
189  0.0008205268           0
190  0.0003388528           0
191  0.0009842818           0
192  0.0011160127           0
193  0.0002611253           1
194  0.0009872355           0
195  0.0008902516           0
196  0.0008501419           0
197  0.0009595742           0
198  0.0010270169           0
199  0.0006270802           0
200  0.0007968775           0
201  0.0005336504           0
202  0.0008983581           0
203  0.0012653457           0
204  0.0009015267           1
205  0.0010165583           0
206  0.0008582854           0
207  0.0013515629           1
208  0.0006309124           1
209  0.0006153829           0
210  0.0005856356           0
211  0.0010615550           0
212  0.0003127552           0
213  0.0008109377           0
214  0.0007820579           0
215  0.0007537294           0
216  0.0014765615           0
217  0.0003388528           0
218  0.0006537791           0
219  0.0009582971           0
220  0.0007167735           0
221  0.0007431723           0
222  0.0003291570           0
223  0.0008642345           0
224  0.0011362052           1
225  0.0007431723           0
226  0.0009979997           0
227  0.0013373727           0
228  0.0007431723           1
229  0.0008014470           0
230  0.0008124811           0
231  0.0007437192           0
232  0.0005960496           0
233  0.0010236917           0
234  0.0003599152           1
235  0.0003154562           0
236  0.0006547234           0
237  0.0012923325           0
238  0.0007172180           0
239  0.0007873893           0
240  0.0002707410           0
241  0.0008450415           0
242  0.0007270927           0
243  0.0003112088           0
244  0.0012687253           0
245  0.0008560174           0
246  0.0008309039           0
247  0.0008275224           0
248  0.0007547548           0
249  0.0008326167           0
250  0.0012671110           0
251  0.0008105539           0
252  0.0005347233           0
253  0.0008119653           0
254  0.0006939303           0
255  0.0010197828           1
256  0.0008902516           0
257  0.0003755900           0
258  0.0007995092           0
259  0.0014620026           0
260  0.0007914940           1
261  0.0003645881           0
262  0.0008876150           0
263  0.0007779473           1
264  0.0008114508           0
265  0.0007407701           0
266  0.0010615550           0
267  0.0003497436           0
268  0.0008462661           0
269  0.0007689837           0
270  0.0003388528           0
271  0.0006825451           0
272  0.0007627965           0
273  0.0008062571           0
274  0.0008426143           0
275  0.0011033633           0
276  0.0007887472           0
277  0.0010212829           1
278  0.0009732668           0
279  0.0005500163           0
280  0.0003401441           0
281  0.0003332657           0
282  0.0003067464           1
283  0.0007818392           1
284  0.0011291750           0
285  0.0005658254           0
286  0.0012923325           0
287  0.0007751888           0
288  0.0009401474           0
289  0.0005674937           0
290  0.0007900010           0
291  0.0008548928           0
292  0.0005932486           1
293  0.0008461126           0
294  0.0007358588           0
295  0.0007728880           0
296  0.0009979997           1
297  0.0008606247           0
298  0.0009300507           1
299  0.0013132564           0
300  0.0003391739           0
301  0.0003394961           0
302  0.0009444683           0
303  0.0008987517           0
304  0.0009552591           0
305  0.0009637066           0
306  0.0011445438           0
307  0.0008674445           1
308  0.0015147097           1
309  0.0012687253           1
310  0.0007765627           0
311  0.0011633253           0
312  0.0010660123           0
313  0.0011800023           0
314  0.0012097231           0
315  0.0011385584           1
316  0.0008750725           1
317  0.0007193845           0
318  0.0003638868           0
319  0.0012323341           0
320  0.0005394353           0
321  0.0007840386           1
322  0.0003326666           1
323  0.0007378732           0
324  0.0009163704           1
325  0.0008684776           0
326  0.0010874750           1
327  0.0013903335           1
328  0.0012549793           1
329  0.0009440951           1
330  0.0010319068           0
331  0.0010684338           0
332  0.0002857701           0
333  0.0007958117           0
334  0.0014051928           0
335  0.0007454789           1
336  0.0006956708           0
337  0.0002796266           0
338  0.0003208026           0
339  0.0010486529           0
340  0.0014398325           0
341  0.0011068777           0
342  0.0007156677           0
343  0.0007921873           0
344  0.0006779194           0
345  0.0003926020           0
346  0.0002803208           0
347  0.0011496432           1
348  0.0011667633           1
349  0.0008824364           1
350  0.0005732806           1
351  0.0013008873           0
352  0.0009944419           0
353  0.0008642345           1
354  0.0012811441           1
355  0.0007431723           0
356  0.0014454572           1
357  0.0003125992           1
358  0.0008063820           1
359  0.0005611411           0
360  0.0002802710           0
361  0.0008707045           0
362  0.0008290650           0
363  0.0010656067           1
364  0.0011032042           0
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1047 0.0003154562           0
1048 0.0008438242           0
1049 0.0009232940           0
1050 0.0007908034           0
1051 0.0008459593           0
1052 0.0009005317           1
1053 0.0009582971           0
1054 0.0006980467           0
1055 0.0007778404           0
1056 0.0008205268           0
1057 0.0008471896           0
1058 0.0014051928           0
1059 0.0016326224           0
1060 0.0007958117           0
1061 0.0009268357           0
1062 0.0009740804           0
1063 0.0008275224           0
1064 0.0006216538           0
1065 0.0006039726           0
1066 0.0003141736           1
1067 0.0007961663           0
1068 0.0006402806           0
1069 0.0003221962           1
1070 0.0003032173           0
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1074 0.0011604786           0
1075 0.0007941659           0
1076 0.0008294878           0
1077 0.0009607903           0
1078 0.0014285805           0
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1080 0.0010492307           1
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1086 0.0006078200           0
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1100 0.0007661620           0
1101 0.0008438242           1
1102 0.0003182522           0
1103 0.0002941455           0
1104 0.0003314806           0
1105 0.0010234228           0
1106 0.0003076183           0
1107 0.0009655367           0
1108 0.0013745814           0
1109 0.0011325260           0
1110 0.0003129116           1
1111 0.0010625575           1
1112 0.0002763081           1
1113 0.0011093921           0
1114 0.0005902536           1
1115 0.0003437950           1
1116 0.0006080986           1
1117 0.0003254211           0
1118 0.0005261347           0
1119 0.0002649173           1
1120 0.0003497436           0
1121 0.0008198544           0
1122 0.0010612397           1
1123 0.0008487381           0
1124 0.0011033633           1
1125 0.0007649666           0
1126 0.0008077624           1
1127 0.0007887472           0
1128 0.0003326666           0
1129 0.0008058826           0
1130 0.0007811846           0
1131 0.0007437192           0
1132 0.0013787388           0
1133 0.0007576785           1
1134 0.0012423355           1
1135 0.0008956225           1
1136 0.0008429161           0
1137 0.0009732668           0
1138 0.0008782080           0
1139 0.0007518809           1
1140 0.0006652161           0
1141 0.0009947365           0
1142 0.0003105987           0
1143 0.0006164105           1
1144 0.0004425217           0
1145 0.0007162565           0
1146 0.0012601149           0
1147 0.0011602629           1
1148 0.0008887411           0
1149 0.0009403837           0
1150 0.0010085950           1
1151 0.0008476529           1
1152 0.0008051360           0
1153 0.0008950407           0
1154 0.0003011768           1
1155 0.0011392169           0
1156 0.0006253544           0
1157 0.0009015267           1
1158 0.0008122230           0
1159 0.0002818333           1
1160 0.0008582854           0
1161 0.0005712164           0
1162 0.0003388528           1
1163 0.0008251623           0
1164 0.0008921546           0
1165 0.0007553168           0
1166 0.0009125666           1
1167 0.0006760979           0
1168 0.0009163704           0
1169 0.0009923269           0
1170 0.0008956225           0
1171 0.0009997067           0
1172 0.0007928832           0
1173 0.0008775585           0
1174 0.0011778060           1
1175 0.0007053630           0
1176 0.0009603437           0
1177 0.0003326666           0
1178 0.0009660621           0
1179 0.0011059837           0
1180 0.0005197845           1
1181 0.0006461589           0
1182 0.0003291570           0
1183 0.0003019185           1
1184 0.0007945173           0
1185 0.0006807895           0
1186 0.0014725595           0
1187 0.0006781334           0
1188 0.0008015688           0
1189 0.0009874711           0
1190 0.0007423248           0
1191 0.0008340556           1
1192 0.0009317096           1
1193 0.0008802547           0
1194 0.0008662561           0
1195 0.0005282793           0
1196 0.0005610411           1
1197 0.0008638995           0
1198 0.0008055089           0
1199 0.0005885348           0
1200 0.0007860415           0
1201 0.0013736647           1
1202 0.0007445967           0
1203 0.0011910727           0
1204 0.0011465723           0
1205 0.0002926387           0
1206 0.0014226917           0
1207 0.0008779160           0
1208 0.0009308862           0
1209 0.0005371720           0
1210 0.0003254211           0
1211 0.0011397437           0
1212 0.0008036516           0
1213 0.0010133726           0
1214 0.0012437949           1
1215 0.0008619006           1
1216 0.0002961843           0
1217 0.0009324122           1
1218 0.0003388528           1
1219 0.0012485319           1
1220 0.0009172245           1
1221 0.0008438242           0
1222 0.0003063141           0
1223 0.0007938152           0
1224 0.0002777303           1
1225 0.0010829640           1
1226 0.0015164312           0
1227 0.0005354396           0
1228 0.0006962395           0
1229 0.0011442410           0
1230 0.0005750432           1
1231 0.0007980691           0
1232 0.0007840386           1
1233 0.0009746243           0
1234 0.0008662561           0
1235 0.0009637066           0
1236 0.0007990279           1
1237 0.0009150954           0
1238 0.0007423248           0
1239 0.0012751099           0
1240 0.0003289663           0
1241 0.0010218161           0
1242 0.0010996651           1
1243 0.0009232940           0
1244 0.0010839979           0
1245 0.0007561632           0
1246 0.0002999789           0
1247 0.0008236504           0
1248 0.0007604599           0
1249 0.0010199555           0
1250 0.0007757160           0
1251 0.0008788125           0
1252 0.0009582971           0
1253 0.0007456559           0
1254 0.0008468813           0
1255 0.0010165583           0
1256 0.0009180817           0
1257 0.0011854903           0
1258 0.0014052938           0
1259 0.0008474983           0
1260 0.0007859297           0
1261 0.0002953123           0
1262 0.0011985983           0
1263 0.0007579641           0
1264 0.0008198544           0
1265 0.0010016516           0
1266 0.0008129984           0
1267 0.0009463685           0
1268 0.0009308862           0
1269 0.0011140068           0
1270 0.0009478587           0
1271 0.0011187039           0
1272 0.0006813139           0
1273 0.0006980606           0
1274 0.0009676451           0
1275 0.0007747682           0
1276 0.0010080919           0
1277 0.0008171882           0
1278 0.0007309298           1
1279 0.0003303109           0
1280 0.0007864896           0
1281 0.0006476417           1
1282 0.0013688946           0
1283 0.0004414064           0
1284 0.0007269348           0
1285 0.0003546927           0
1286 0.0003975026           0
1287 0.0006994871           0
1288 0.0006790551           0
1289 0.0008362339           0
1290 0.0007633856           0
1291 0.0003253298           1
1292 0.0010492307           0
1293 0.0006038370           1
1294 0.0006083777           0
1295 0.0008198544           0
1296 0.0007505078           0
1297 0.0003851227           0
1298 0.0013462706           0
1299 0.0003388528           0
1300 0.0003386394           0
1301 0.0008929205           1
1302 0.0007381267           1
1303 0.0005358499           0
1304 0.0009015267           1
1305 0.0003204578           1
1306 0.0007166995           0
1307 0.0009780532           0
1308 0.0010456801           1
1309 0.0007770939           0
1310 0.0014108743           1
1311 0.0005568096           0
1312 0.0003245126           1
1313 0.0010538235           0
1314 0.0013299159           0
1315 0.0011304101           0
1316 0.0003359112           0
1317 0.0009071831           0
1318 0.0008743675           0
1319 0.0009335593           0
1320 0.0012663072           0
1321 0.0010335851           0
1322 0.0008536150           0
1323 0.0009350085           0
1324 0.0009944419           0
1325 0.0014135287           0
1326 0.0013711572           0
1327 0.0008921546           1
1328 0.0010270169           0
1329 0.0009991024           0
1330 0.0002985408           0
1331 0.0008240616           0
1332 0.0012675943           0
1333 0.0010541627           0
1334 0.0007833759           1
1335 0.0007667628           0
1336 0.0003591135           0
1337 0.0008331910           1
1338 0.0007431723           0
1339 0.0010010025           0
1340 0.0010165583           0
1341 0.0007495986           0
1342 0.0008693257           0
1343 0.0008921546           1
1344 0.0003297320           0
1345 0.0009537543           0
1346 0.0013729682           1
1347 0.0007572035           1
1348 0.0009798145           0
1349 0.0006353370           0
1350 0.0010349929           0
1351 0.0007641743           0
1352 0.0010052657           0
1353 0.0008632311           0
1354 0.0007280434           0
1355 0.0008566629           0
1356 0.0005691829           0
1357 0.0007697985           0
1358 0.0008337670           0
1359 0.0003122881           1
1360 0.0014283106           0
1361 0.0008343447           1
1362 0.0010497021           1
1363 0.0003234354           0
1364 0.0012620058           0
1365 0.0010862591           0
1366 0.0010372052           0
1367 0.0003150531           0
1368 0.0007947520           0
1369 0.0013448047           0
1370 0.0005617429           0
1371 0.0014051928           0
1372 0.0009591793           0
1373 0.0005468384           0
1374 0.0007744535           0
1375 0.0011932697           0
1376 0.0008817067           1
1377 0.0009591793           0
1378 0.0009138275           0
1379 0.0010270169           0
1380 0.0007931157           1
1381 0.0008676148           0
1382 0.0002818843           0
1383 0.0012451314           1
1384 0.0008507690           0
1385 0.0010640780           0
1386 0.0007952222           0
1387 0.0008357963           1
1388 0.0010521379           1
1389 0.0013567287           0
1390 0.0011844867           0
1391 0.0007980691           1
1392 0.0003388528           0
1393 0.0009422390           0
1394 0.0009088258           0
1395 0.0008861227           0
1396 0.0007666625           0
1397 0.0010270169           0
1398 0.0012983664           0
1399 0.0003218456           0
1400 0.0007995092           0
1401 0.0010168790           0
1402 0.0002887520           0
1403 0.0012511504           0
1404 0.0006433416           0
1405 0.0012278150           1
1406 0.0010924243           0
1407 0.0007658624           0
1408 0.0010539704           0
1409 0.0002943896           1
1410 0.0011404987           0
1411 0.0008314731           1
1412 0.0009666322           0
1413 0.0007348609           0
1414 0.0009071831           0
1415 0.0008444319           0

#rows_with_errors <- (df$garage_type_attchd==0) + (df$garage_type_detchd==0) + (df$garage_type_builtIn==0) + (df$garage_type_no_garage==0)

#df <- df[-rows_with_errors]

No changes are needed to the below code. It is included because the results may be helpful for subsequent tasks.

#NO CHANGES NEEDED
#Example: the 18th property has 0's for all garage type variables
df %>% dplyr::select(contains("garage")) %>%  dplyr::slice(18)

  garage_type_attchd garage_type_basment garage_type_builtIn garage_type_detchd
1                  0                   0                   0                  0
  garage_type_no_garage
1                     0

#NO CHANGES NEEDED
#Calculate the Number of Units for each garage type
df %>% dplyr::select(num_units,contains("garage")) %>% gather(feature,value,-num_units) %>% group_by(feature) %>%  summarise(total_units=sum(num_units*value))

# A tibble: 5 × 2
  feature               total_units
  <chr>                       <dbl>
1 garage_type_attchd           2227
2 garage_type_basment            55
3 garage_type_builtIn           235
4 garage_type_detchd           1052
5 garage_type_no_garage         226

#NO CHANGES NEEDED
#Calculate the Number of Units for each neighborhood
df %>% dplyr::select(num_units,contains("neighborhood")) %>% gather(feature,value,-num_units) %>% group_by(feature) %>%  summarise(total_units=sum(num_units*value))

# A tibble: 23 × 2
   feature               total_units
   <chr>                       <dbl>
 1 NeighborhoodBrDale             44
 2 neighborhood_brk_side         170
 3 neighborhood_clear_cr          72
 4 neighborhood_collg_cr         390
 5 neighborhood_crawfor          137
 6 neighborhood_edwards          259
 7 neighborhood_gilbert          204
 8 neighborhood_idottrr          112
 9 neighborhood_meadowv           48
10 neighborhood_mitchel          141
# ℹ 13 more rows

You do not need to check the neighborhood columns as your assistent has already verified that these are correct for all properties.

Task 5 - Select GLM parameters

No code is provided

Task 6 - Fit a GLM

#NO CHANGES NEEDED
#Create training and test sets
index <- createDataPartition(y = df$applicants, p = 0.8, list = F)

train <- df %>% dplyr::slice(index)

Warning: Slicing with a 1-column matrix was deprecated in dplyr 1.1.0.

test <- df %>% dplyr::slice(-index)

train_x <- train[,-1]
train_y <- train$applicants

#standardize to be between 0 and 1
train_number_of_units <- train$num_units/sum(train$num_units)

test_x <- test[,-1]
test_y <- test$applicants

#standardize to be between 0 and 1
test_number_of_units <- test$num_units/sum(test$num_units)

#the base (reference) level for neighborhood is the one with the most observations
#the base (reference) level for garage is the one with the most observations

# Create the log_sale_price variable
train <- train %>% 
  mutate(log_sale_price = log(sale_price))

test <- test %>% 
  mutate(log_sale_price = log(sale_price))

#Fit a GLM
#Do not use the offset or weight variables as predictors.  Remove them from the formula (as the below is doing)
#Type ?family into the R console to see options for FAMILY
glm <- glm(
  applicants ~ . + offset(log(num_units)) - neighborhood_n_ames - garage_type_attchd - num_units - log_sale_price, 
  data = train,
  family = poisson(link = "log")
)
AIC(glm)

[1] 5228.818

summary(glm)

Call:
glm(formula = applicants ~ . + offset(log(num_units)) - neighborhood_n_ames - 
    garage_type_attchd - num_units - log_sale_price, family = poisson(link = "log"), 
    data = train)

Coefficients: (1 not defined because of singularities)
                             Estimate Std. Error z value Pr(>|z|)    
(Intercept)                 4.612e+00  2.188e+01   0.211 0.833062    
sale_price                  6.177e-07  8.633e-07   0.716 0.474284    
year_sold                  -3.159e-03  1.088e-02  -0.290 0.771571    
month_sold                 -7.745e-03  6.154e-03  -1.258 0.208227    
overall_qual               -4.370e-02  2.487e-02  -1.758 0.078831 .  
total_sq_feet               6.023e-04  1.234e-04   4.879 1.07e-06 ***
gr_liv_area                -1.777e-05  7.970e-05  -0.223 0.823556    
tot_bathrooms              -3.178e-01  1.119e-01  -2.841 0.004502 ** 
lot_area                    3.411e-06  2.402e-05   0.142 0.887072    
exter_qual                  1.621e-01  4.573e-02   3.544 0.000394 ***
full_bath                   1.128e-02  2.489e-02   0.453 0.650537    
central_airno              -1.780e+00  1.625e-01 -10.950  < 2e-16 ***
garage_type_basment        -6.379e-01  1.790e-01  -3.563 0.000366 ***
garage_type_builtIn        -2.797e-01  7.508e-02  -3.725 0.000195 ***
garage_type_detchd         -3.346e-01  5.183e-02  -6.455 1.08e-10 ***
garage_type_no_garage      -3.939e-01  9.798e-02  -4.021 5.80e-05 ***
NeighborhoodBrDale         -4.755e-01  2.562e-01  -1.856 0.063429 .  
neighborhood_brk_side      -1.957e-01  1.163e-01  -1.684 0.092249 .  
neighborhood_clear_cr      -4.917e-02  1.275e-01  -0.386 0.699756    
neighborhood_collg_cr      -8.473e-02  8.668e-02  -0.977 0.328356    
neighborhood_crawfor       -1.207e-01  1.202e-01  -1.004 0.315313    
neighborhood_edwards        7.295e-02  8.902e-02   0.819 0.412545    
neighborhood_gilbert        1.496e-02  9.569e-02   0.156 0.875738    
neighborhood_idottrr       -8.539e-01  2.115e-01  -4.037 5.41e-05 ***
neighborhood_meadowv       -3.208e-01  2.008e-01  -1.597 0.110193    
neighborhood_mitchel       -1.280e-01  9.581e-02  -1.337 0.181385    
neighborhood_n_ridge       -3.254e-01  1.969e-01  -1.653 0.098379 .  
neighborhood_n_ridge_hghts -3.719e-01  1.735e-01  -2.143 0.032097 *  
neighborhood_n_w_ames      -8.980e-02  9.123e-02  -0.984 0.324963    
neighborhood_old_town      -4.565e-02  8.864e-02  -0.515 0.606522    
neighborhood_sawyer        -4.130e-01  9.983e-02  -4.137 3.52e-05 ***
neighborhood_sawyer_w      -5.371e-02  9.290e-02  -0.578 0.563154    
neighborhood_somerst       -3.092e-02  1.227e-01  -0.252 0.801017    
neighborhood_stone_br      -1.747e-01  1.993e-01  -0.877 0.380701    
neighborhood_swisu          2.543e-01  1.504e-01   1.691 0.090895 .  
neighborhood_timber        -1.799e-01  1.442e-01  -1.248 0.212172    
neighborhood_veenker       -3.291e-01  2.109e-01  -1.560 0.118722    
neighborhood_saleprice             NA         NA      NA       NA    
log_rel_price              -7.583e-01  3.327e-01  -2.280 0.022635 *  
sale_price_per_sqft        -1.534e+03  1.210e+03  -1.268 0.204712    
bath_pr_sqft                1.234e+03  3.836e+02   3.217 0.001294 ** 
student_apt                 4.999e-01  3.452e-02  14.482  < 2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

(Dispersion parameter for poisson family taken to be 1)

    Null deviance: 2784.1  on 1144  degrees of freedom
Residual deviance: 1722.6  on 1104  degrees of freedom
AIC: 5228.8

Number of Fisher Scoring iterations: 5

#Alternative answer
#Models claim frequency (average applicants per unit)
glm2 <- glm(
  applicants/num_units ~ . + - neighborhood_n_ames - garage_type_attchd  - log_sale_price - num_units, 
  data = train,
  weights = num_units,
  family = poisson(link = "log")
)

Warning in terms.formula(formula, data = data): 'varlist' has changed (from
nvar=45) to new 46 after EncodeVars() -- should no longer happen!

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.750000

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.333333

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.666667
Warning in dpois(y, mu, log = TRUE): non-integer x = 1.666667

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.400000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.750000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.333333

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.200000

Warning in dpois(y, mu, log = TRUE): non-integer x = 2.500000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.600000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.750000

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.500000
Warning in dpois(y, mu, log = TRUE): non-integer x = 1.500000

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.250000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.600000

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.250000

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.750000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.400000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.250000

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.500000

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.250000
Warning in dpois(y, mu, log = TRUE): non-integer x = 1.250000

Warning in dpois(y, mu, log = TRUE): non-integer x = 2.500000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.800000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.500000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.250000
Warning in dpois(y, mu, log = TRUE): non-integer x = 0.250000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.600000

Warning in dpois(y, mu, log = TRUE): non-integer x = 2.333333

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.400000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.400000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.500000

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.500000

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.400000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.750000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.333333

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.200000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.500000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.750000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.800000

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.500000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.200000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.750000

Warning in dpois(y, mu, log = TRUE): non-integer x = 2.500000
Warning in dpois(y, mu, log = TRUE): non-integer x = 2.500000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.750000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.250000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.333333

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.666667

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.800000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.600000

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.666667
Warning in dpois(y, mu, log = TRUE): non-integer x = 1.666667

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.250000

Warning in dpois(y, mu, log = TRUE): non-integer x = 2.500000

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.333333

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.600000

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.333333

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.250000

Warning in dpois(y, mu, log = TRUE): non-integer x = 3.500000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.750000

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.500000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.333333

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.750000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.400000

Warning in dpois(y, mu, log = TRUE): non-integer x = 2.500000

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.666667

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.750000

Warning in dpois(y, mu, log = TRUE): non-integer x = 2.500000

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.500000

Warning in dpois(y, mu, log = TRUE): non-integer x = 2.500000

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.250000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.500000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.400000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.800000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.400000

Warning in dpois(y, mu, log = TRUE): non-integer x = 2.500000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.400000

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.250000

Warning in dpois(y, mu, log = TRUE): non-integer x = 2.500000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.500000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.200000

Warning in dpois(y, mu, log = TRUE): non-integer x = 3.500000

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.250000

Warning in dpois(y, mu, log = TRUE): non-integer x = 2.500000

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.666667

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.333333

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.250000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.333333

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.750000

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.400000

Warning in dpois(y, mu, log = TRUE): non-integer x = 2.500000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.500000

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.333333

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.400000

Warning in dpois(y, mu, log = TRUE): non-integer x = 2.500000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.600000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.500000
Warning in dpois(y, mu, log = TRUE): non-integer x = 0.500000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.400000

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.500000

Warning in dpois(y, mu, log = TRUE): non-integer x = 2.500000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.600000

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.500000
Warning in dpois(y, mu, log = TRUE): non-integer x = 1.500000

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.666667

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.600000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.750000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.400000

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.400000

Warning in dpois(y, mu, log = TRUE): non-integer x = 2.500000

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.666667

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.250000

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.666667

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.250000

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.666667

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.250000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.500000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.333333

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.666667

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.250000

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.400000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.666667

Warning in dpois(y, mu, log = TRUE): non-integer x = 2.500000

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.250000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.500000

Warning in dpois(y, mu, log = TRUE): non-integer x = 2.333333

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.333333

Warning in dpois(y, mu, log = TRUE): non-integer x = 3.500000

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.333333

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.666667

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.250000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.333333

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.333333

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.600000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.750000

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.750000

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.500000

Warning in dpois(y, mu, log = TRUE): non-integer x = 3.500000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.666667

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.500000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.750000

Warning in dpois(y, mu, log = TRUE): non-integer x = 2.500000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.400000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.750000

Warning in dpois(y, mu, log = TRUE): non-integer x = 2.333333

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.666667

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.400000

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.750000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.600000

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.750000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.400000

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.250000

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.500000

Warning in dpois(y, mu, log = TRUE): non-integer x = 2.500000

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.500000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.600000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.200000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.250000

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.666667

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.600000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.666667

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.250000

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.500000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.666667

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.333333

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.250000

Warning in dpois(y, mu, log = TRUE): non-integer x = 3.500000

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.500000

Warning in dpois(y, mu, log = TRUE): non-integer x = 2.500000

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.666667

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.250000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.600000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.200000

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.250000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.500000
Warning in dpois(y, mu, log = TRUE): non-integer x = 0.500000

Warning in dpois(y, mu, log = TRUE): non-integer x = 3.500000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.500000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.400000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.600000

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.666667

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.666667

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.250000

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.750000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.750000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.666667

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.500000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.750000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.800000

Warning in dpois(y, mu, log = TRUE): non-integer x = 2.333333

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.666667

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.333333

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.333333

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.400000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.600000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.500000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.400000
Warning in dpois(y, mu, log = TRUE): non-integer x = 0.400000

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.750000

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.500000

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.400000

Warning in dpois(y, mu, log = TRUE): non-integer x = 2.500000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.400000

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.400000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.666667
Warning in dpois(y, mu, log = TRUE): non-integer x = 0.666667

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.500000

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.750000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.400000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.750000

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.250000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.666667

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.750000

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.666667

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.500000
Warning in dpois(y, mu, log = TRUE): non-integer x = 0.500000
Warning in dpois(y, mu, log = TRUE): non-integer x = 0.500000
Warning in dpois(y, mu, log = TRUE): non-integer x = 0.500000

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.500000

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.666667

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.250000

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.333333

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.500000

Warning in dpois(y, mu, log = TRUE): non-integer x = 2.333333

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.500000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.600000

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.666667

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.250000

Warning in dpois(y, mu, log = TRUE): non-integer x = 3.500000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.500000

Warning in dpois(y, mu, log = TRUE): non-integer x = 2.500000

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.250000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.400000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.600000

Warning in dpois(y, mu, log = TRUE): non-integer x = 2.500000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.250000

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.500000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.250000
Warning in dpois(y, mu, log = TRUE): non-integer x = 0.250000
Warning in dpois(y, mu, log = TRUE): non-integer x = 0.250000

Warning in dpois(y, mu, log = TRUE): non-integer x = 2.500000

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.250000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.600000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.750000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.250000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.333333

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.750000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.200000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.600000

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.250000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.200000

Warning in dpois(y, mu, log = TRUE): non-integer x = 3.500000

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.750000

Warning in dpois(y, mu, log = TRUE): non-integer x = 2.500000
Warning in dpois(y, mu, log = TRUE): non-integer x = 2.500000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.750000

Warning in dpois(y, mu, log = TRUE): non-integer x = 2.500000

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.500000

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.666667

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.500000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.400000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.200000

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.250000

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.500000

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.750000

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.666667

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.400000

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.666667

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.250000

Warning in dpois(y, mu, log = TRUE): non-integer x = 3.500000

Warning in dpois(y, mu, log = TRUE): non-integer x = 2.333333

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.666667

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.666667

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.333333

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.600000

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.666667

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.500000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.800000

Warning in dpois(y, mu, log = TRUE): non-integer x = 2.500000
Warning in dpois(y, mu, log = TRUE): non-integer x = 2.500000

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.750000

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.250000

Warning in dpois(y, mu, log = TRUE): non-integer x = 2.500000

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.250000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.600000

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.400000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.600000

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.250000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.750000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.800000

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.333333

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.750000

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.500000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.666667

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.600000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.500000

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.250000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.750000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.400000

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.250000

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.200000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.750000

Warning in dpois(y, mu, log = TRUE): non-integer x = 2.500000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.250000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.500000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.250000

Warning in dpois(y, mu, log = TRUE): non-integer x = 3.500000

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.250000

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.333333

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.400000

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.250000

Warning in dpois(y, mu, log = TRUE): non-integer x = 2.333333

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.500000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.800000

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.500000

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.250000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.500000

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.666667

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.500000

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.500000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.750000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.600000

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.500000

Warning in dpois(y, mu, log = TRUE): non-integer x = 2.500000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.750000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.800000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.400000

Warning in dpois(y, mu, log = TRUE): non-integer x = 2.500000

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.250000
Warning in dpois(y, mu, log = TRUE): non-integer x = 1.250000

Warning in dpois(y, mu, log = TRUE): non-integer x = 2.500000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.333333

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.666667

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.250000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.400000

Warning in dpois(y, mu, log = TRUE): non-integer x = 2.500000

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.250000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.600000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.666667

Warning in dpois(y, mu, log = TRUE): non-integer x = 3.500000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.600000
Warning in dpois(y, mu, log = TRUE): non-integer x = 0.600000

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.666667

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.500000

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.666667

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.800000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.750000

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.250000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.600000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.500000

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.400000

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.500000
Warning in dpois(y, mu, log = TRUE): non-integer x = 1.500000

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.666667

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.800000

Warning in dpois(y, mu, log = TRUE): non-integer x = 3.500000

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.666667

Warning in dpois(y, mu, log = TRUE): non-integer x = 2.333333

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.250000

Warning in dpois(y, mu, log = TRUE): non-integer x = 2.333333

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.800000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.600000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.800000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.250000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.500000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.750000

Warning in dpois(y, mu, log = TRUE): non-integer x = 3.500000

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.250000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.600000

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.750000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.750000

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.500000

Warning in dpois(y, mu, log = TRUE): non-integer x = 2.500000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.200000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.800000

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.250000

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.500000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.400000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.200000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.500000

Warning in dpois(y, mu, log = TRUE): non-integer x = 2.333333

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.500000
Warning in dpois(y, mu, log = TRUE): non-integer x = 1.500000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.333333

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.500000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.500000

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.666667

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.800000
Warning in dpois(y, mu, log = TRUE): non-integer x = 0.800000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.333333

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.666667

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.500000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.400000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.500000

Warning in dpois(y, mu, log = TRUE): non-integer x = 2.500000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.800000

Warning in dpois(y, mu, log = TRUE): non-integer x = 2.500000

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.666667
Warning in dpois(y, mu, log = TRUE): non-integer x = 1.666667

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.400000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.800000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.750000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.250000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.750000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.250000

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.666667

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.200000

Warning in dpois(y, mu, log = TRUE): non-integer x = 2.500000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.666667

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.666667

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.333333

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.500000

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.200000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.500000

Warning in dpois(y, mu, log = TRUE): non-integer x = 2.333333

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.500000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.750000

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.333333

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.600000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.800000

Warning in dpois(y, mu, log = TRUE): non-integer x = 3.500000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.750000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.250000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.400000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.600000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.500000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.250000

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.500000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.600000

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.500000

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.750000

Warning in dpois(y, mu, log = TRUE): non-integer x = 2.333333

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.200000

Warning in dpois(y, mu, log = TRUE): non-integer x = 2.500000

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.250000

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.333333

Warning in dpois(y, mu, log = TRUE): non-integer x = 2.500000

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.250000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.200000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.500000

Warning in dpois(y, mu, log = TRUE): non-integer x = 2.500000

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.666667

Warning in dpois(y, mu, log = TRUE): non-integer x = 2.500000

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.400000

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.333333

Warning in dpois(y, mu, log = TRUE): non-integer x = 2.500000

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.500000

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.333333

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.250000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.400000

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.250000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.800000

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.250000

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.500000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.800000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.500000

Warning in dpois(y, mu, log = TRUE): non-integer x = 2.500000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.200000

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.250000

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.500000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.400000

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.333333
Warning in dpois(y, mu, log = TRUE): non-integer x = 1.333333

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.750000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.600000

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.333333

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.500000

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.666667

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.400000

Warning in dpois(y, mu, log = TRUE): non-integer x = 2.500000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.600000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.750000

Warning in dpois(y, mu, log = TRUE): non-integer x = 3.500000

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.500000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.666667

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.500000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.750000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.400000

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.500000

Warning in dpois(y, mu, log = TRUE): non-integer x = 2.500000
Warning in dpois(y, mu, log = TRUE): non-integer x = 2.500000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.250000

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.500000

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.666667

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.333333

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.750000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.600000

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.666667

Warning in dpois(y, mu, log = TRUE): non-integer x = 2.500000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.250000

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.500000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.600000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.500000

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.666667

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.666667

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.600000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.500000

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.333333

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.500000

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.200000

Warning in dpois(y, mu, log = TRUE): non-integer x = 2.500000

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.750000

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.500000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.800000

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.666667

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.600000

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.250000

Warning in dpois(y, mu, log = TRUE): non-integer x = 2.500000

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.250000

Warning in dpois(y, mu, log = TRUE): non-integer x = 2.500000

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.333333

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.600000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.333333

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.750000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.666667

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.600000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.333333

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.666667

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.333333

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.333333

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.400000
Warning in dpois(y, mu, log = TRUE): non-integer x = 0.400000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.600000

Warning in dpois(y, mu, log = TRUE): non-integer x = 2.333333

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.800000

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.250000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.600000

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.500000
Warning in dpois(y, mu, log = TRUE): non-integer x = 1.500000
Warning in dpois(y, mu, log = TRUE): non-integer x = 1.500000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.600000

Warning in dpois(y, mu, log = TRUE): non-integer x = 2.500000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.600000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.750000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.600000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.250000

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.500000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.250000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.750000

Warning in dpois(y, mu, log = TRUE): non-integer x = 0.666667

Warning in dpois(y, mu, log = TRUE): non-integer x = 1.500000

AIC(glm2)

[1] Inf

summary(glm2)

Call:
glm(formula = applicants/num_units ~ . + -neighborhood_n_ames - 
    garage_type_attchd - log_sale_price - num_units, family = poisson(link = "log"), 
    data = train, weights = num_units)

Coefficients: (2 not defined because of singularities)
                             Estimate Std. Error z value Pr(>|z|)    
(Intercept)                 4.283e+00  2.187e+01   0.196 0.844719    
sale_price                  6.177e-07  8.633e-07   0.716 0.474284    
year_sold                  -3.159e-03  1.088e-02  -0.290 0.771571    
month_sold                 -7.745e-03  6.154e-03  -1.258 0.208227    
overall_qual               -4.370e-02  2.487e-02  -1.758 0.078831 .  
total_sq_feet               6.023e-04  1.234e-04   4.879 1.07e-06 ***
gr_liv_area                -1.777e-05  7.970e-05  -0.223 0.823556    
tot_bathrooms              -3.178e-01  1.119e-01  -2.841 0.004502 ** 
lot_area                    3.411e-06  2.402e-05   0.142 0.887072    
exter_qual                  1.621e-01  4.573e-02   3.544 0.000394 ***
full_bath                   1.128e-02  2.489e-02   0.453 0.650538    
central_airno              -1.780e+00  1.625e-01 -10.950  < 2e-16 ***
garage_type_basment        -6.379e-01  1.790e-01  -3.563 0.000366 ***
garage_type_builtIn        -2.797e-01  7.508e-02  -3.725 0.000195 ***
garage_type_detchd         -3.346e-01  5.183e-02  -6.455 1.08e-10 ***
garage_type_no_garage      -3.939e-01  9.798e-02  -4.021 5.80e-05 ***
NeighborhoodBrDale         -1.464e-01  3.439e-01  -0.426 0.670320    
neighborhood_brk_side       1.333e-01  2.485e-01   0.537 0.591566    
neighborhood_clear_cr       2.799e-01  2.124e-01   1.318 0.187653    
neighborhood_collg_cr       2.443e-01  1.925e-01   1.269 0.204319    
neighborhood_crawfor        2.084e-01  2.065e-01   1.009 0.313056    
neighborhood_edwards        4.020e-01  2.354e-01   1.708 0.087652 .  
neighborhood_gilbert        3.440e-01  1.990e-01   1.729 0.083767 .  
neighborhood_idottrr       -5.248e-01  3.120e-01  -1.682 0.092607 .  
neighborhood_meadowv        8.288e-03  3.029e-01   0.027 0.978168    
neighborhood_mitchel        2.010e-01  2.183e-01   0.921 0.357056    
neighborhood_n_ames         3.291e-01  2.109e-01   1.560 0.118722    
neighborhood_n_ridge        3.637e-03  2.102e-01   0.017 0.986197    
neighborhood_n_ridge_hghts -4.286e-02  2.010e-01  -0.213 0.831107    
neighborhood_n_w_ames       2.393e-01  1.982e-01   1.207 0.227450    
neighborhood_old_town       2.834e-01  2.310e-01   1.227 0.219763    
neighborhood_sawyer        -8.389e-02  2.315e-01  -0.362 0.717115    
neighborhood_sawyer_w       2.754e-01  2.029e-01   1.357 0.174676    
neighborhood_somerst        2.981e-01  1.954e-01   1.526 0.127104    
neighborhood_stone_br       1.544e-01  2.213e-01   0.698 0.485302    
neighborhood_swisu          5.834e-01  2.565e-01   2.274 0.022956 *  
neighborhood_timber         1.492e-01  2.034e-01   0.734 0.463238    
neighborhood_veenker               NA         NA      NA       NA    
neighborhood_saleprice             NA         NA      NA       NA    
log_rel_price              -7.583e-01  3.327e-01  -2.280 0.022635 *  
sale_price_per_sqft        -1.534e+03  1.210e+03  -1.268 0.204713    
bath_pr_sqft                1.234e+03  3.836e+02   3.217 0.001294 ** 
student_apt                 4.999e-01  3.452e-02  14.482  < 2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

(Dispersion parameter for poisson family taken to be 1)

    Null deviance: 2784.1  on 1144  degrees of freedom
Residual deviance: 1722.6  on 1104  degrees of freedom
AIC: Inf

Number of Fisher Scoring iterations: 5

#You can verify that both models return the same predictions

app_count <- predict(glm, type="response", newdata = test)

app_frequency <- predict(glm2, type="response", newdata = test)*test$num_units

head(app_count)

        1         2         3         4         5         6 
 7.466909  1.381043  1.193778  3.390522  3.733967 10.568552 

head(app_frequency)

        1         2         3         4         5         6 
 7.466909  1.381043  1.193778  3.390522  3.733967 10.568552 

Task 7 - Use AIC to select features

#NO CODE CHANGES NEEDED
#The following code will use the same formula and family from the `glm` object to perform stepwise selection

library(MASS)

Attaching package: 'MASS'

The following object is masked from 'package:dplyr':

    select

stepwise_result <- stepAIC(glm)

Start:  AIC=5228.82
applicants ~ sale_price + num_units + year_sold + month_sold + 
    overall_qual + total_sq_feet + gr_liv_area + tot_bathrooms + 
    lot_area + exter_qual + full_bath + central_air + garage_type_attchd + 
    garage_type_basment + garage_type_builtIn + garage_type_detchd + 
    garage_type_no_garage + NeighborhoodBrDale + neighborhood_brk_side + 
    neighborhood_clear_cr + neighborhood_collg_cr + neighborhood_crawfor + 
    neighborhood_edwards + neighborhood_gilbert + neighborhood_idottrr + 
    neighborhood_meadowv + neighborhood_mitchel + neighborhood_n_ames + 
    neighborhood_n_ridge + neighborhood_n_ridge_hghts + neighborhood_n_w_ames + 
    neighborhood_old_town + neighborhood_sawyer + neighborhood_sawyer_w + 
    neighborhood_somerst + neighborhood_stone_br + neighborhood_swisu + 
    neighborhood_timber + neighborhood_veenker + neighborhood_saleprice + 
    log_rel_price + log_sale_price + sale_price_per_sqft + bath_pr_sqft + 
    student_apt + offset(log(num_units)) - neighborhood_n_ames - 
    garage_type_attchd - num_units - log_sale_price


Step:  AIC=5228.82
applicants ~ sale_price + year_sold + month_sold + overall_qual + 
    total_sq_feet + gr_liv_area + tot_bathrooms + lot_area + 
    exter_qual + full_bath + central_air + garage_type_basment + 
    garage_type_builtIn + garage_type_detchd + garage_type_no_garage + 
    NeighborhoodBrDale + neighborhood_brk_side + neighborhood_clear_cr + 
    neighborhood_collg_cr + neighborhood_crawfor + neighborhood_edwards + 
    neighborhood_gilbert + neighborhood_idottrr + neighborhood_meadowv + 
    neighborhood_mitchel + neighborhood_n_ridge + neighborhood_n_ridge_hghts + 
    neighborhood_n_w_ames + neighborhood_old_town + neighborhood_sawyer + 
    neighborhood_sawyer_w + neighborhood_somerst + neighborhood_stone_br + 
    neighborhood_swisu + neighborhood_timber + neighborhood_veenker + 
    log_rel_price + sale_price_per_sqft + bath_pr_sqft + student_apt + 
    offset(log(num_units))

                             Df Deviance    AIC
- lot_area                    1   1722.6 5226.8
- neighborhood_gilbert        1   1722.6 5226.8
- gr_liv_area                 1   1722.7 5226.9
- neighborhood_somerst        1   1722.7 5226.9
- year_sold                   1   1722.7 5226.9
- neighborhood_clear_cr       1   1722.8 5227.0
- full_bath                   1   1722.8 5227.0
- neighborhood_old_town       1   1722.9 5227.1
- neighborhood_sawyer_w       1   1722.9 5227.2
- sale_price                  1   1723.1 5227.3
- neighborhood_edwards        1   1723.3 5227.5
- neighborhood_stone_br       1   1723.4 5227.6
- neighborhood_collg_cr       1   1723.6 5227.8
- neighborhood_n_w_ames       1   1723.6 5227.8
- neighborhood_crawfor        1   1723.6 5227.8
- neighborhood_timber         1   1724.2 5228.4
- month_sold                  1   1724.2 5228.4
- sale_price_per_sqft         1   1724.3 5228.5
- neighborhood_mitchel        1   1724.4 5228.6
<none>                            1722.6 5228.8
- neighborhood_veenker        1   1725.2 5229.4
- neighborhood_swisu          1   1725.3 5229.5
- neighborhood_n_ridge        1   1725.3 5229.5
- neighborhood_meadowv        1   1725.3 5229.5
- neighborhood_brk_side       1   1725.5 5229.7
- overall_qual                1   1725.7 5229.9
- NeighborhoodBrDale          1   1726.5 5230.7
- neighborhood_n_ridge_hghts  1   1727.1 5231.3
- log_rel_price               1   1727.5 5231.7
- tot_bathrooms               1   1730.6 5234.8
- bath_pr_sqft                1   1732.8 5237.0
- exter_qual                  1   1735.1 5239.3
- garage_type_builtIn         1   1737.3 5241.5
- garage_type_basment         1   1737.9 5242.1
- garage_type_no_garage       1   1739.8 5244.0
- neighborhood_sawyer         1   1741.2 5245.4
- total_sq_feet               1   1741.5 5245.7
- neighborhood_idottrr        1   1742.7 5246.9
- garage_type_detchd          1   1765.4 5269.6
- central_air                 1   1916.0 5420.2
- student_apt                 1   1923.6 5427.8

Step:  AIC=5226.84
applicants ~ sale_price + year_sold + month_sold + overall_qual + 
    total_sq_feet + gr_liv_area + tot_bathrooms + exter_qual + 
    full_bath + central_air + garage_type_basment + garage_type_builtIn + 
    garage_type_detchd + garage_type_no_garage + NeighborhoodBrDale + 
    neighborhood_brk_side + neighborhood_clear_cr + neighborhood_collg_cr + 
    neighborhood_crawfor + neighborhood_edwards + neighborhood_gilbert + 
    neighborhood_idottrr + neighborhood_meadowv + neighborhood_mitchel + 
    neighborhood_n_ridge + neighborhood_n_ridge_hghts + neighborhood_n_w_ames + 
    neighborhood_old_town + neighborhood_sawyer + neighborhood_sawyer_w + 
    neighborhood_somerst + neighborhood_stone_br + neighborhood_swisu + 
    neighborhood_timber + neighborhood_veenker + log_rel_price + 
    sale_price_per_sqft + bath_pr_sqft + student_apt + offset(log(num_units))

                             Df Deviance    AIC
- neighborhood_gilbert        1   1722.7 5224.9
- gr_liv_area                 1   1722.7 5224.9
- neighborhood_somerst        1   1722.7 5224.9
- year_sold                   1   1722.7 5224.9
- neighborhood_clear_cr       1   1722.8 5225.0
- full_bath                   1   1722.8 5225.0
- neighborhood_old_town       1   1722.9 5225.1
- neighborhood_sawyer_w       1   1723.0 5225.2
- sale_price                  1   1723.2 5225.4
- neighborhood_edwards        1   1723.3 5225.5
- neighborhood_stone_br       1   1723.4 5225.6
- neighborhood_n_w_ames       1   1723.6 5225.8
- neighborhood_collg_cr       1   1723.6 5225.8
- neighborhood_crawfor        1   1723.6 5225.9
- neighborhood_timber         1   1724.2 5226.4
- month_sold                  1   1724.2 5226.4
- sale_price_per_sqft         1   1724.3 5226.5
- neighborhood_mitchel        1   1724.4 5226.7
<none>                            1722.6 5226.8
- neighborhood_veenker        1   1725.2 5227.4
- neighborhood_swisu          1   1725.3 5227.5
- neighborhood_n_ridge        1   1725.3 5227.6
- neighborhood_brk_side       1   1725.6 5227.8
- overall_qual                1   1725.9 5228.1
- neighborhood_meadowv        1   1725.9 5228.1
- NeighborhoodBrDale          1   1727.0 5229.2
- neighborhood_n_ridge_hghts  1   1727.2 5229.5
- log_rel_price               1   1727.5 5229.7
- tot_bathrooms               1   1730.7 5232.9
- bath_pr_sqft                1   1732.9 5235.1
- exter_qual                  1   1735.1 5237.3
- garage_type_builtIn         1   1737.4 5239.6
- garage_type_basment         1   1737.9 5240.1
- garage_type_no_garage       1   1740.0 5242.2
- neighborhood_sawyer         1   1741.2 5243.4
- total_sq_feet               1   1741.7 5243.9
- neighborhood_idottrr        1   1742.7 5244.9
- garage_type_detchd          1   1766.2 5268.5
- central_air                 1   1916.1 5418.3
- student_apt                 1   1923.7 5425.9

Step:  AIC=5224.86
applicants ~ sale_price + year_sold + month_sold + overall_qual + 
    total_sq_feet + gr_liv_area + tot_bathrooms + exter_qual + 
    full_bath + central_air + garage_type_basment + garage_type_builtIn + 
    garage_type_detchd + garage_type_no_garage + NeighborhoodBrDale + 
    neighborhood_brk_side + neighborhood_clear_cr + neighborhood_collg_cr + 
    neighborhood_crawfor + neighborhood_edwards + neighborhood_idottrr + 
    neighborhood_meadowv + neighborhood_mitchel + neighborhood_n_ridge + 
    neighborhood_n_ridge_hghts + neighborhood_n_w_ames + neighborhood_old_town + 
    neighborhood_sawyer + neighborhood_sawyer_w + neighborhood_somerst + 
    neighborhood_stone_br + neighborhood_swisu + neighborhood_timber + 
    neighborhood_veenker + log_rel_price + sale_price_per_sqft + 
    bath_pr_sqft + student_apt + offset(log(num_units))

                             Df Deviance    AIC
- gr_liv_area                 1   1722.7 5222.9
- year_sold                   1   1722.7 5223.0
- neighborhood_clear_cr       1   1722.9 5223.1
- full_bath                   1   1722.9 5223.1
- neighborhood_somerst        1   1722.9 5223.1
- neighborhood_old_town       1   1723.0 5223.2
- neighborhood_sawyer_w       1   1723.3 5223.5
- neighborhood_edwards        1   1723.3 5223.5
- sale_price                  1   1723.5 5223.7
- neighborhood_stone_br       1   1724.1 5224.3
- neighborhood_crawfor        1   1724.1 5224.3
- month_sold                  1   1724.3 5224.5
- neighborhood_n_w_ames       1   1724.3 5224.5
- sale_price_per_sqft         1   1724.6 5224.8
<none>                            1722.7 5224.9
- neighborhood_collg_cr       1   1724.8 5225.0
- neighborhood_mitchel        1   1724.8 5225.0
- neighborhood_timber         1   1725.2 5225.5
- neighborhood_swisu          1   1725.3 5225.5
- neighborhood_brk_side       1   1725.7 5225.9
- neighborhood_veenker        1   1725.8 5226.1
- neighborhood_meadowv        1   1725.9 5226.1
- overall_qual                1   1725.9 5226.1
- NeighborhoodBrDale          1   1727.0 5227.2
- neighborhood_n_ridge        1   1727.3 5227.5
- log_rel_price               1   1727.5 5227.8
- neighborhood_n_ridge_hghts  1   1731.1 5231.3
- tot_bathrooms               1   1731.3 5231.5
- bath_pr_sqft                1   1733.8 5234.0
- exter_qual                  1   1735.6 5235.8
- garage_type_builtIn         1   1737.4 5237.6
- garage_type_basment         1   1737.9 5238.1
- garage_type_no_garage       1   1740.4 5240.7
- total_sq_feet               1   1741.8 5242.0
- neighborhood_sawyer         1   1741.8 5242.0
- neighborhood_idottrr        1   1742.8 5243.0
- garage_type_detchd          1   1767.4 5267.7
- central_air                 1   1919.3 5419.6
- student_apt                 1   1923.8 5424.0

Step:  AIC=5222.91
applicants ~ sale_price + year_sold + month_sold + overall_qual + 
    total_sq_feet + tot_bathrooms + exter_qual + full_bath + 
    central_air + garage_type_basment + garage_type_builtIn + 
    garage_type_detchd + garage_type_no_garage + NeighborhoodBrDale + 
    neighborhood_brk_side + neighborhood_clear_cr + neighborhood_collg_cr + 
    neighborhood_crawfor + neighborhood_edwards + neighborhood_idottrr + 
    neighborhood_meadowv + neighborhood_mitchel + neighborhood_n_ridge + 
    neighborhood_n_ridge_hghts + neighborhood_n_w_ames + neighborhood_old_town + 
    neighborhood_sawyer + neighborhood_sawyer_w + neighborhood_somerst + 
    neighborhood_stone_br + neighborhood_swisu + neighborhood_timber + 
    neighborhood_veenker + log_rel_price + sale_price_per_sqft + 
    bath_pr_sqft + student_apt + offset(log(num_units))

                             Df Deviance    AIC
- year_sold                   1   1722.8 5221.0
- full_bath                   1   1722.9 5221.1
- neighborhood_somerst        1   1722.9 5221.2
- neighborhood_clear_cr       1   1722.9 5221.2
- neighborhood_old_town       1   1723.0 5221.2
- neighborhood_sawyer_w       1   1723.3 5221.5
- neighborhood_edwards        1   1723.3 5221.6
- sale_price                  1   1723.6 5221.8
- neighborhood_stone_br       1   1724.1 5222.3
- neighborhood_crawfor        1   1724.2 5222.5
- month_sold                  1   1724.3 5222.5
- neighborhood_n_w_ames       1   1724.4 5222.6
- sale_price_per_sqft         1   1724.7 5222.9
<none>                            1722.7 5222.9
- neighborhood_collg_cr       1   1724.8 5223.0
- neighborhood_mitchel        1   1724.8 5223.0
- neighborhood_timber         1   1725.3 5223.5
- neighborhood_swisu          1   1725.3 5223.5
- neighborhood_brk_side       1   1725.7 5224.0
- neighborhood_veenker        1   1725.9 5224.1
- neighborhood_meadowv        1   1726.0 5224.2
- overall_qual                1   1726.0 5224.2
- NeighborhoodBrDale          1   1727.1 5225.3
- neighborhood_n_ridge        1   1727.5 5225.7
- log_rel_price               1   1727.6 5225.8
- neighborhood_n_ridge_hghts  1   1731.1 5229.3
- tot_bathrooms               1   1731.3 5229.6
- bath_pr_sqft                1   1733.8 5232.0
- exter_qual                  1   1735.8 5234.0
- garage_type_basment         1   1738.2 5236.4
- garage_type_builtIn         1   1739.3 5237.5
- garage_type_no_garage       1   1740.5 5238.7
- neighborhood_sawyer         1   1741.8 5240.1
- neighborhood_idottrr        1   1742.9 5241.1
- total_sq_feet               1   1743.7 5241.9
- garage_type_detchd          1   1767.7 5265.9
- central_air                 1   1921.7 5419.9
- student_apt                 1   1923.9 5422.1

Step:  AIC=5221
applicants ~ sale_price + month_sold + overall_qual + total_sq_feet + 
    tot_bathrooms + exter_qual + full_bath + central_air + garage_type_basment + 
    garage_type_builtIn + garage_type_detchd + garage_type_no_garage + 
    NeighborhoodBrDale + neighborhood_brk_side + neighborhood_clear_cr + 
    neighborhood_collg_cr + neighborhood_crawfor + neighborhood_edwards + 
    neighborhood_idottrr + neighborhood_meadowv + neighborhood_mitchel + 
    neighborhood_n_ridge + neighborhood_n_ridge_hghts + neighborhood_n_w_ames + 
    neighborhood_old_town + neighborhood_sawyer + neighborhood_sawyer_w + 
    neighborhood_somerst + neighborhood_stone_br + neighborhood_swisu + 
    neighborhood_timber + neighborhood_veenker + log_rel_price + 
    sale_price_per_sqft + bath_pr_sqft + student_apt + offset(log(num_units))

                             Df Deviance    AIC
- full_bath                   1   1723.0 5219.2
- neighborhood_clear_cr       1   1723.0 5219.2
- neighborhood_somerst        1   1723.0 5219.2
- neighborhood_old_town       1   1723.1 5219.3
- neighborhood_sawyer_w       1   1723.4 5219.6
- neighborhood_edwards        1   1723.4 5219.6
- sale_price                  1   1723.7 5219.9
- neighborhood_stone_br       1   1724.2 5220.4
- month_sold                  1   1724.3 5220.5
- neighborhood_crawfor        1   1724.3 5220.6
- neighborhood_n_w_ames       1   1724.5 5220.7
- sale_price_per_sqft         1   1724.8 5221.0
<none>                            1722.8 5221.0
- neighborhood_collg_cr       1   1724.8 5221.1
- neighborhood_mitchel        1   1724.9 5221.1
- neighborhood_timber         1   1725.3 5221.5
- neighborhood_swisu          1   1725.4 5221.6
- neighborhood_brk_side       1   1725.9 5222.1
- neighborhood_veenker        1   1726.0 5222.2
- neighborhood_meadowv        1   1726.1 5222.3
- overall_qual                1   1726.2 5222.4
- NeighborhoodBrDale          1   1727.2 5223.4
- neighborhood_n_ridge        1   1727.6 5223.8
- log_rel_price               1   1727.7 5223.9
- neighborhood_n_ridge_hghts  1   1731.1 5227.4
- tot_bathrooms               1   1731.5 5227.7
- bath_pr_sqft                1   1734.0 5230.2
- exter_qual                  1   1735.9 5232.1
- garage_type_basment         1   1738.2 5234.5
- garage_type_builtIn         1   1739.5 5235.7
- garage_type_no_garage       1   1740.5 5236.7
- neighborhood_sawyer         1   1741.9 5238.1
- neighborhood_idottrr        1   1742.9 5239.1
- total_sq_feet               1   1743.8 5240.0
- garage_type_detchd          1   1767.7 5263.9
- central_air                 1   1922.6 5418.8
- student_apt                 1   1924.5 5420.7

Step:  AIC=5219.22
applicants ~ sale_price + month_sold + overall_qual + total_sq_feet + 
    tot_bathrooms + exter_qual + central_air + garage_type_basment + 
    garage_type_builtIn + garage_type_detchd + garage_type_no_garage + 
    NeighborhoodBrDale + neighborhood_brk_side + neighborhood_clear_cr + 
    neighborhood_collg_cr + neighborhood_crawfor + neighborhood_edwards + 
    neighborhood_idottrr + neighborhood_meadowv + neighborhood_mitchel + 
    neighborhood_n_ridge + neighborhood_n_ridge_hghts + neighborhood_n_w_ames + 
    neighborhood_old_town + neighborhood_sawyer + neighborhood_sawyer_w + 
    neighborhood_somerst + neighborhood_stone_br + neighborhood_swisu + 
    neighborhood_timber + neighborhood_veenker + log_rel_price + 
    sale_price_per_sqft + bath_pr_sqft + student_apt + offset(log(num_units))

                             Df Deviance    AIC
- neighborhood_somerst        1   1723.2 5217.5
- neighborhood_clear_cr       1   1723.3 5217.5
- neighborhood_old_town       1   1723.3 5217.5
- neighborhood_sawyer_w       1   1723.6 5217.8
- neighborhood_edwards        1   1723.7 5217.9
- sale_price                  1   1724.0 5218.2
- month_sold                  1   1724.5 5218.7
- neighborhood_stone_br       1   1724.6 5218.8
- neighborhood_n_w_ames       1   1724.7 5218.9
- neighborhood_crawfor        1   1724.7 5218.9
- sale_price_per_sqft         1   1725.0 5219.2
<none>                            1723.0 5219.2
- neighborhood_collg_cr       1   1725.1 5219.3
- neighborhood_mitchel        1   1725.1 5219.3
- neighborhood_timber         1   1725.7 5219.9
- neighborhood_swisu          1   1725.7 5219.9
- neighborhood_brk_side       1   1726.1 5220.3
- overall_qual                1   1726.2 5220.4
- neighborhood_meadowv        1   1726.3 5220.5
- neighborhood_veenker        1   1726.5 5220.7
- NeighborhoodBrDale          1   1727.3 5221.6
- log_rel_price               1   1728.2 5222.4
- neighborhood_n_ridge        1   1728.3 5222.5
- tot_bathrooms               1   1731.6 5225.8
- neighborhood_n_ridge_hghts  1   1731.8 5226.0
- bath_pr_sqft                1   1734.3 5228.5
- exter_qual                  1   1736.4 5230.6
- garage_type_basment         1   1738.5 5232.7
- garage_type_builtIn         1   1739.5 5233.7
- garage_type_no_garage       1   1740.7 5234.9
- neighborhood_sawyer         1   1742.0 5236.3
- neighborhood_idottrr        1   1743.0 5237.2
- total_sq_feet               1   1745.2 5239.4
- garage_type_detchd          1   1768.5 5262.7
- central_air                 1   1922.6 5416.8
- student_apt                 1   1926.9 5421.1

Step:  AIC=5217.45
applicants ~ sale_price + month_sold + overall_qual + total_sq_feet + 
    tot_bathrooms + exter_qual + central_air + garage_type_basment + 
    garage_type_builtIn + garage_type_detchd + garage_type_no_garage + 
    NeighborhoodBrDale + neighborhood_brk_side + neighborhood_clear_cr + 
    neighborhood_collg_cr + neighborhood_crawfor + neighborhood_edwards + 
    neighborhood_idottrr + neighborhood_meadowv + neighborhood_mitchel + 
    neighborhood_n_ridge + neighborhood_n_ridge_hghts + neighborhood_n_w_ames + 
    neighborhood_old_town + neighborhood_sawyer + neighborhood_sawyer_w + 
    neighborhood_stone_br + neighborhood_swisu + neighborhood_timber + 
    neighborhood_veenker + log_rel_price + sale_price_per_sqft + 
    bath_pr_sqft + student_apt + offset(log(num_units))

                             Df Deviance    AIC
- neighborhood_clear_cr       1   1723.4 5215.6
- neighborhood_old_town       1   1723.5 5215.7
- neighborhood_sawyer_w       1   1723.7 5215.9
- neighborhood_edwards        1   1723.8 5216.1
- sale_price                  1   1724.0 5216.2
- neighborhood_stone_br       1   1724.6 5216.8
- neighborhood_n_w_ames       1   1724.7 5216.9
- neighborhood_crawfor        1   1724.7 5216.9
- month_sold                  1   1724.7 5216.9
- sale_price_per_sqft         1   1725.0 5217.2
- neighborhood_mitchel        1   1725.2 5217.4
<none>                            1723.2 5217.5
- neighborhood_collg_cr       1   1725.2 5217.5
- neighborhood_timber         1   1725.8 5218.0
- neighborhood_swisu          1   1726.0 5218.2
- neighborhood_veenker        1   1726.5 5218.7
- neighborhood_brk_side       1   1726.5 5218.7
- neighborhood_meadowv        1   1726.8 5219.0
- overall_qual                1   1727.0 5219.3
- NeighborhoodBrDale          1   1727.8 5220.0
- log_rel_price               1   1728.2 5220.4
- neighborhood_n_ridge        1   1729.7 5221.9
- tot_bathrooms               1   1731.6 5223.8
- bath_pr_sqft                1   1734.3 5226.5
- neighborhood_n_ridge_hghts  1   1735.9 5228.2
- exter_qual                  1   1736.5 5228.7
- garage_type_basment         1   1738.7 5230.9
- garage_type_builtIn         1   1739.5 5231.7
- garage_type_no_garage       1   1740.8 5233.0
- neighborhood_sawyer         1   1742.4 5234.6
- neighborhood_idottrr        1   1744.0 5236.2
- total_sq_feet               1   1745.2 5237.5
- garage_type_detchd          1   1769.8 5262.0
- central_air                 1   1923.6 5415.8
- student_apt                 1   1929.5 5421.7

Step:  AIC=5215.6
applicants ~ sale_price + month_sold + overall_qual + total_sq_feet + 
    tot_bathrooms + exter_qual + central_air + garage_type_basment + 
    garage_type_builtIn + garage_type_detchd + garage_type_no_garage + 
    NeighborhoodBrDale + neighborhood_brk_side + neighborhood_collg_cr + 
    neighborhood_crawfor + neighborhood_edwards + neighborhood_idottrr + 
    neighborhood_meadowv + neighborhood_mitchel + neighborhood_n_ridge + 
    neighborhood_n_ridge_hghts + neighborhood_n_w_ames + neighborhood_old_town + 
    neighborhood_sawyer + neighborhood_sawyer_w + neighborhood_stone_br + 
    neighborhood_swisu + neighborhood_timber + neighborhood_veenker + 
    log_rel_price + sale_price_per_sqft + bath_pr_sqft + student_apt + 
    offset(log(num_units))

                             Df Deviance    AIC
- neighborhood_old_town       1   1723.7 5213.9
- neighborhood_sawyer_w       1   1723.8 5214.0
- neighborhood_edwards        1   1724.0 5214.2
- sale_price                  1   1724.0 5214.2
- neighborhood_n_w_ames       1   1724.7 5214.9
- neighborhood_stone_br       1   1724.7 5214.9
- neighborhood_crawfor        1   1724.7 5215.0
- month_sold                  1   1724.9 5215.1
- sale_price_per_sqft         1   1725.1 5215.3
- neighborhood_collg_cr       1   1725.3 5215.5
- neighborhood_mitchel        1   1725.3 5215.5
<none>                            1723.4 5215.6
- neighborhood_timber         1   1725.8 5216.0
- neighborhood_swisu          1   1726.2 5216.4
- neighborhood_veenker        1   1726.5 5216.7
- neighborhood_brk_side       1   1726.6 5216.8
- neighborhood_meadowv        1   1726.9 5217.1
- overall_qual                1   1727.1 5217.3
- NeighborhoodBrDale          1   1728.0 5218.2
- log_rel_price               1   1728.3 5218.5
- neighborhood_n_ridge        1   1729.7 5219.9
- tot_bathrooms               1   1731.7 5221.9
- bath_pr_sqft                1   1734.3 5224.5
- neighborhood_n_ridge_hghts  1   1736.1 5226.3
- exter_qual                  1   1737.2 5227.5
- garage_type_basment         1   1738.8 5229.0
- garage_type_builtIn         1   1739.6 5229.8
- garage_type_no_garage       1   1740.8 5231.0
- neighborhood_sawyer         1   1742.5 5232.7
- neighborhood_idottrr        1   1744.3 5234.5
- total_sq_feet               1   1745.2 5235.5
- garage_type_detchd          1   1769.9 5260.1
- central_air                 1   1923.8 5414.0
- student_apt                 1   1930.2 5420.4

Step:  AIC=5213.87
applicants ~ sale_price + month_sold + overall_qual + total_sq_feet + 
    tot_bathrooms + exter_qual + central_air + garage_type_basment + 
    garage_type_builtIn + garage_type_detchd + garage_type_no_garage + 
    NeighborhoodBrDale + neighborhood_brk_side + neighborhood_collg_cr + 
    neighborhood_crawfor + neighborhood_edwards + neighborhood_idottrr + 
    neighborhood_meadowv + neighborhood_mitchel + neighborhood_n_ridge + 
    neighborhood_n_ridge_hghts + neighborhood_n_w_ames + neighborhood_sawyer + 
    neighborhood_sawyer_w + neighborhood_stone_br + neighborhood_swisu + 
    neighborhood_timber + neighborhood_veenker + log_rel_price + 
    sale_price_per_sqft + bath_pr_sqft + student_apt + offset(log(num_units))

                             Df Deviance    AIC
- neighborhood_sawyer_w       1   1724.0 5212.2
- neighborhood_edwards        1   1724.7 5212.9
- sale_price                  1   1724.7 5212.9
- neighborhood_n_w_ames       1   1724.9 5213.1
- neighborhood_crawfor        1   1725.0 5213.2
- month_sold                  1   1725.1 5213.4
- neighborhood_stone_br       1   1725.2 5213.4
- neighborhood_mitchel        1   1725.4 5213.6
- neighborhood_collg_cr       1   1725.5 5213.7
<none>                            1723.7 5213.9
- sale_price_per_sqft         1   1725.7 5213.9
- neighborhood_timber         1   1726.2 5214.4
- neighborhood_brk_side       1   1726.6 5214.8
- neighborhood_swisu          1   1726.8 5215.1
- neighborhood_veenker        1   1726.9 5215.1
- neighborhood_meadowv        1   1727.0 5215.2
- overall_qual                1   1727.4 5215.6
- NeighborhoodBrDale          1   1728.0 5216.2
- log_rel_price               1   1728.5 5216.8
- neighborhood_n_ridge        1   1730.8 5219.0
- tot_bathrooms               1   1732.4 5220.6
- bath_pr_sqft                1   1735.2 5223.4
- exter_qual                  1   1737.4 5225.6
- neighborhood_n_ridge_hghts  1   1737.6 5225.8
- garage_type_basment         1   1739.1 5227.3
- garage_type_builtIn         1   1739.8 5228.0
- garage_type_no_garage       1   1742.4 5230.6
- neighborhood_sawyer         1   1742.7 5230.9
- neighborhood_idottrr        1   1744.8 5233.0
- total_sq_feet               1   1745.4 5233.7
- garage_type_detchd          1   1778.8 5267.0
- student_apt                 1   1930.5 5418.7
- central_air                 1   1936.7 5424.9

Step:  AIC=5212.18
applicants ~ sale_price + month_sold + overall_qual + total_sq_feet + 
    tot_bathrooms + exter_qual + central_air + garage_type_basment + 
    garage_type_builtIn + garage_type_detchd + garage_type_no_garage + 
    NeighborhoodBrDale + neighborhood_brk_side + neighborhood_collg_cr + 
    neighborhood_crawfor + neighborhood_edwards + neighborhood_idottrr + 
    neighborhood_meadowv + neighborhood_mitchel + neighborhood_n_ridge + 
    neighborhood_n_ridge_hghts + neighborhood_n_w_ames + neighborhood_sawyer + 
    neighborhood_stone_br + neighborhood_swisu + neighborhood_timber + 
    neighborhood_veenker + log_rel_price + sale_price_per_sqft + 
    bath_pr_sqft + student_apt + offset(log(num_units))

                             Df Deviance    AIC
- sale_price                  1   1724.9 5211.1
- neighborhood_n_w_ames       1   1725.0 5211.3
- neighborhood_edwards        1   1725.0 5211.3
- neighborhood_crawfor        1   1725.2 5211.4
- neighborhood_stone_br       1   1725.3 5211.5
- month_sold                  1   1725.5 5211.7
- neighborhood_collg_cr       1   1725.5 5211.7
- neighborhood_mitchel        1   1725.6 5211.8
<none>                            1724.0 5212.2
- sale_price_per_sqft         1   1726.0 5212.2
- neighborhood_timber         1   1726.3 5212.6
- neighborhood_brk_side       1   1726.9 5213.1
- neighborhood_veenker        1   1727.0 5213.3
- neighborhood_swisu          1   1727.2 5213.4
- neighborhood_meadowv        1   1727.2 5213.4
- overall_qual                1   1727.7 5213.9
- NeighborhoodBrDale          1   1728.3 5214.5
- log_rel_price               1   1728.8 5215.0
- neighborhood_n_ridge        1   1730.8 5217.0
- tot_bathrooms               1   1732.8 5219.0
- bath_pr_sqft                1   1735.6 5221.8
- neighborhood_n_ridge_hghts  1   1737.6 5223.8
- exter_qual                  1   1737.6 5223.8
- garage_type_basment         1   1739.4 5225.6
- garage_type_builtIn         1   1740.0 5226.2
- garage_type_no_garage       1   1742.5 5228.7
- neighborhood_sawyer         1   1742.8 5229.0
- neighborhood_idottrr        1   1745.0 5231.2
- total_sq_feet               1   1745.7 5231.9
- garage_type_detchd          1   1778.9 5265.1
- student_apt                 1   1932.2 5418.4
- central_air                 1   1936.7 5422.9

Step:  AIC=5211.14
applicants ~ month_sold + overall_qual + total_sq_feet + tot_bathrooms + 
    exter_qual + central_air + garage_type_basment + garage_type_builtIn + 
    garage_type_detchd + garage_type_no_garage + NeighborhoodBrDale + 
    neighborhood_brk_side + neighborhood_collg_cr + neighborhood_crawfor + 
    neighborhood_edwards + neighborhood_idottrr + neighborhood_meadowv + 
    neighborhood_mitchel + neighborhood_n_ridge + neighborhood_n_ridge_hghts + 
    neighborhood_n_w_ames + neighborhood_sawyer + neighborhood_stone_br + 
    neighborhood_swisu + neighborhood_timber + neighborhood_veenker + 
    log_rel_price + sale_price_per_sqft + bath_pr_sqft + student_apt + 
    offset(log(num_units))

                             Df Deviance    AIC
- neighborhood_edwards        1   1725.6 5209.8
- neighborhood_stone_br       1   1725.6 5209.9
- neighborhood_crawfor        1   1725.7 5209.9
- neighborhood_n_w_ames       1   1725.8 5210.0
- neighborhood_collg_cr       1   1726.2 5210.5
- sale_price_per_sqft         1   1726.5 5210.7
- month_sold                  1   1726.5 5210.7
- neighborhood_timber         1   1726.7 5210.9
- neighborhood_mitchel        1   1726.7 5210.9
<none>                            1724.9 5211.1
- neighborhood_veenker        1   1727.5 5211.7
- overall_qual                1   1727.8 5212.0
- neighborhood_swisu          1   1727.9 5212.1
- neighborhood_brk_side       1   1728.5 5212.7
- neighborhood_meadowv        1   1729.0 5213.2
- log_rel_price               1   1729.5 5213.7
- NeighborhoodBrDale          1   1730.1 5214.3
- neighborhood_n_ridge        1   1731.2 5215.4
- tot_bathrooms               1   1733.0 5217.2
- bath_pr_sqft                1   1735.8 5220.0
- neighborhood_n_ridge_hghts  1   1738.9 5223.1
- exter_qual                  1   1740.5 5224.7
- garage_type_builtIn         1   1740.7 5224.9
- garage_type_basment         1   1740.7 5224.9
- garage_type_no_garage       1   1742.9 5227.1
- neighborhood_sawyer         1   1745.4 5229.6
- total_sq_feet               1   1747.2 5231.4
- neighborhood_idottrr        1   1748.0 5232.2
- garage_type_detchd          1   1780.5 5264.7
- student_apt                 1   1932.8 5417.0
- central_air                 1   1937.1 5421.3

Step:  AIC=5209.79
applicants ~ month_sold + overall_qual + total_sq_feet + tot_bathrooms + 
    exter_qual + central_air + garage_type_basment + garage_type_builtIn + 
    garage_type_detchd + garage_type_no_garage + NeighborhoodBrDale + 
    neighborhood_brk_side + neighborhood_collg_cr + neighborhood_crawfor + 
    neighborhood_idottrr + neighborhood_meadowv + neighborhood_mitchel + 
    neighborhood_n_ridge + neighborhood_n_ridge_hghts + neighborhood_n_w_ames + 
    neighborhood_sawyer + neighborhood_stone_br + neighborhood_swisu + 
    neighborhood_timber + neighborhood_veenker + log_rel_price + 
    sale_price_per_sqft + bath_pr_sqft + student_apt + offset(log(num_units))

                             Df Deviance    AIC
- neighborhood_stone_br       1   1726.2 5208.4
- neighborhood_crawfor        1   1726.4 5208.6
- neighborhood_n_w_ames       1   1726.5 5208.7
- neighborhood_collg_cr       1   1727.0 5209.2
- sale_price_per_sqft         1   1727.1 5209.3
- month_sold                  1   1727.2 5209.4
- neighborhood_timber         1   1727.3 5209.5
<none>                            1725.6 5209.8
- neighborhood_mitchel        1   1727.7 5209.9
- neighborhood_veenker        1   1728.1 5210.3
- neighborhood_swisu          1   1728.3 5210.5
- overall_qual                1   1728.9 5211.1
- neighborhood_brk_side       1   1729.9 5212.1
- log_rel_price               1   1729.9 5212.1
- neighborhood_meadowv        1   1730.2 5212.4
- NeighborhoodBrDale          1   1731.2 5213.4
- neighborhood_n_ridge        1   1731.5 5213.7
- tot_bathrooms               1   1733.7 5215.9
- bath_pr_sqft                1   1736.5 5218.7
- neighborhood_n_ridge_hghts  1   1739.0 5221.3
- garage_type_basment         1   1740.8 5223.0
- exter_qual                  1   1741.1 5223.3
- garage_type_builtIn         1   1741.3 5223.6
- garage_type_no_garage       1   1743.1 5225.3
- neighborhood_sawyer         1   1747.7 5229.9
- total_sq_feet               1   1747.7 5229.9
- neighborhood_idottrr        1   1750.2 5232.4
- garage_type_detchd          1   1780.6 5262.8
- student_apt                 1   1933.2 5415.4
- central_air                 1   1937.5 5419.7

Step:  AIC=5208.41
applicants ~ month_sold + overall_qual + total_sq_feet + tot_bathrooms + 
    exter_qual + central_air + garage_type_basment + garage_type_builtIn + 
    garage_type_detchd + garage_type_no_garage + NeighborhoodBrDale + 
    neighborhood_brk_side + neighborhood_collg_cr + neighborhood_crawfor + 
    neighborhood_idottrr + neighborhood_meadowv + neighborhood_mitchel + 
    neighborhood_n_ridge + neighborhood_n_ridge_hghts + neighborhood_n_w_ames + 
    neighborhood_sawyer + neighborhood_swisu + neighborhood_timber + 
    neighborhood_veenker + log_rel_price + sale_price_per_sqft + 
    bath_pr_sqft + student_apt + offset(log(num_units))

                             Df Deviance    AIC
- neighborhood_crawfor        1   1726.9 5207.1
- neighborhood_n_w_ames       1   1727.0 5207.2
- neighborhood_collg_cr       1   1727.3 5207.5
- neighborhood_timber         1   1727.6 5207.8
- month_sold                  1   1728.0 5208.2
- sale_price_per_sqft         1   1728.1 5208.3
<none>                            1726.2 5208.4
- neighborhood_mitchel        1   1728.3 5208.5
- neighborhood_veenker        1   1728.5 5208.7
- neighborhood_swisu          1   1728.9 5209.1
- log_rel_price               1   1730.0 5210.2
- overall_qual                1   1730.3 5210.5
- neighborhood_brk_side       1   1730.7 5210.9
- neighborhood_meadowv        1   1731.0 5211.2
- neighborhood_n_ridge        1   1731.5 5211.7
- NeighborhoodBrDale          1   1731.9 5212.1
- tot_bathrooms               1   1735.1 5215.3
- bath_pr_sqft                1   1738.0 5218.2
- neighborhood_n_ridge_hghts  1   1739.3 5219.5
- garage_type_basment         1   1741.3 5221.5
- exter_qual                  1   1741.4 5221.6
- garage_type_builtIn         1   1742.3 5222.5
- garage_type_no_garage       1   1743.6 5223.8
- total_sq_feet               1   1747.8 5228.0
- neighborhood_sawyer         1   1748.6 5228.8
- neighborhood_idottrr        1   1751.2 5231.4
- garage_type_detchd          1   1780.8 5261.0
- student_apt                 1   1935.2 5415.4
- central_air                 1   1937.5 5417.7

Step:  AIC=5207.14
applicants ~ month_sold + overall_qual + total_sq_feet + tot_bathrooms + 
    exter_qual + central_air + garage_type_basment + garage_type_builtIn + 
    garage_type_detchd + garage_type_no_garage + NeighborhoodBrDale + 
    neighborhood_brk_side + neighborhood_collg_cr + neighborhood_idottrr + 
    neighborhood_meadowv + neighborhood_mitchel + neighborhood_n_ridge + 
    neighborhood_n_ridge_hghts + neighborhood_n_w_ames + neighborhood_sawyer + 
    neighborhood_swisu + neighborhood_timber + neighborhood_veenker + 
    log_rel_price + sale_price_per_sqft + bath_pr_sqft + student_apt + 
    offset(log(num_units))

                             Df Deviance    AIC
- neighborhood_n_w_ames       1   1727.5 5205.8
- neighborhood_collg_cr       1   1727.9 5206.1
- neighborhood_timber         1   1728.2 5206.4
- month_sold                  1   1728.8 5207.0
- sale_price_per_sqft         1   1728.8 5207.0
- neighborhood_mitchel        1   1728.9 5207.1
<none>                            1726.9 5207.1
- neighborhood_veenker        1   1729.2 5207.4
- neighborhood_swisu          1   1729.8 5208.0
- log_rel_price               1   1730.7 5208.9
- neighborhood_brk_side       1   1731.2 5209.4
- overall_qual                1   1731.4 5209.6
- neighborhood_meadowv        1   1731.7 5209.9
- neighborhood_n_ridge        1   1731.9 5210.1
- NeighborhoodBrDale          1   1732.5 5210.8
- tot_bathrooms               1   1735.6 5213.8
- bath_pr_sqft                1   1738.5 5216.7
- neighborhood_n_ridge_hghts  1   1739.5 5217.7
- garage_type_basment         1   1742.4 5220.6
- garage_type_builtIn         1   1742.9 5221.1
- exter_qual                  1   1743.0 5221.2
- garage_type_no_garage       1   1744.2 5222.5
- total_sq_feet               1   1748.2 5226.4
- neighborhood_sawyer         1   1749.0 5227.2
- neighborhood_idottrr        1   1751.7 5229.9
- garage_type_detchd          1   1782.6 5260.8
- student_apt                 1   1935.2 5413.5
- central_air                 1   1938.9 5417.1

Step:  AIC=5205.75
applicants ~ month_sold + overall_qual + total_sq_feet + tot_bathrooms + 
    exter_qual + central_air + garage_type_basment + garage_type_builtIn + 
    garage_type_detchd + garage_type_no_garage + NeighborhoodBrDale + 
    neighborhood_brk_side + neighborhood_collg_cr + neighborhood_idottrr + 
    neighborhood_meadowv + neighborhood_mitchel + neighborhood_n_ridge + 
    neighborhood_n_ridge_hghts + neighborhood_sawyer + neighborhood_swisu + 
    neighborhood_timber + neighborhood_veenker + log_rel_price + 
    sale_price_per_sqft + bath_pr_sqft + student_apt + offset(log(num_units))

                             Df Deviance    AIC
- neighborhood_collg_cr       1   1728.3 5204.5
- neighborhood_timber         1   1728.6 5204.8
- neighborhood_mitchel        1   1729.3 5205.5
- month_sold                  1   1729.3 5205.5
- sale_price_per_sqft         1   1729.4 5205.6
<none>                            1727.5 5205.8
- neighborhood_veenker        1   1729.6 5205.8
- neighborhood_swisu          1   1730.5 5206.7
- log_rel_price               1   1731.2 5207.4
- neighborhood_brk_side       1   1731.9 5208.1
- neighborhood_n_ridge        1   1732.1 5208.3
- neighborhood_meadowv        1   1732.3 5208.5
- overall_qual                1   1732.3 5208.5
- NeighborhoodBrDale          1   1733.2 5209.4
- tot_bathrooms               1   1736.4 5212.6
- bath_pr_sqft                1   1739.2 5215.4
- neighborhood_n_ridge_hghts  1   1739.6 5215.8
- garage_type_basment         1   1742.7 5218.9
- garage_type_builtIn         1   1743.4 5219.6
- garage_type_no_garage       1   1744.5 5220.7
- exter_qual                  1   1745.8 5222.0
- total_sq_feet               1   1748.6 5224.8
- neighborhood_sawyer         1   1749.2 5225.4
- neighborhood_idottrr        1   1752.3 5228.5
- garage_type_detchd          1   1782.7 5258.9
- student_apt                 1   1936.7 5412.9
- central_air                 1   1938.9 5415.1

Step:  AIC=5204.5
applicants ~ month_sold + overall_qual + total_sq_feet + tot_bathrooms + 
    exter_qual + central_air + garage_type_basment + garage_type_builtIn + 
    garage_type_detchd + garage_type_no_garage + NeighborhoodBrDale + 
    neighborhood_brk_side + neighborhood_idottrr + neighborhood_meadowv + 
    neighborhood_mitchel + neighborhood_n_ridge + neighborhood_n_ridge_hghts + 
    neighborhood_sawyer + neighborhood_swisu + neighborhood_timber + 
    neighborhood_veenker + log_rel_price + sale_price_per_sqft + 
    bath_pr_sqft + student_apt + offset(log(num_units))

                             Df Deviance    AIC
- neighborhood_timber         1   1729.2 5203.4
- neighborhood_mitchel        1   1729.9 5204.1
- month_sold                  1   1730.0 5204.2
- sale_price_per_sqft         1   1730.1 5204.3
- neighborhood_veenker        1   1730.2 5204.4
<none>                            1728.3 5204.5
- neighborhood_swisu          1   1731.3 5205.5
- log_rel_price               1   1732.0 5206.3
- neighborhood_n_ridge        1   1732.3 5206.5
- neighborhood_brk_side       1   1732.6 5206.8
- neighborhood_meadowv        1   1732.9 5207.1
- overall_qual                1   1733.3 5207.5
- NeighborhoodBrDale          1   1733.8 5208.1
- tot_bathrooms               1   1737.1 5211.3
- neighborhood_n_ridge_hghts  1   1739.6 5213.8
- bath_pr_sqft                1   1739.8 5214.1
- garage_type_basment         1   1743.3 5217.5
- garage_type_builtIn         1   1744.0 5218.2
- garage_type_no_garage       1   1745.1 5219.3
- exter_qual                  1   1745.8 5220.0
- neighborhood_sawyer         1   1749.6 5223.8
- total_sq_feet               1   1749.7 5223.9
- neighborhood_idottrr        1   1753.1 5227.3
- garage_type_detchd          1   1782.7 5256.9
- student_apt                 1   1937.0 5411.2
- central_air                 1   1939.1 5413.3

Step:  AIC=5203.37
applicants ~ month_sold + overall_qual + total_sq_feet + tot_bathrooms + 
    exter_qual + central_air + garage_type_basment + garage_type_builtIn + 
    garage_type_detchd + garage_type_no_garage + NeighborhoodBrDale + 
    neighborhood_brk_side + neighborhood_idottrr + neighborhood_meadowv + 
    neighborhood_mitchel + neighborhood_n_ridge + neighborhood_n_ridge_hghts + 
    neighborhood_sawyer + neighborhood_swisu + neighborhood_veenker + 
    log_rel_price + sale_price_per_sqft + bath_pr_sqft + student_apt + 
    offset(log(num_units))

                             Df Deviance    AIC
- neighborhood_mitchel        1   1730.7 5202.9
- month_sold                  1   1730.7 5202.9
- neighborhood_veenker        1   1731.0 5203.2
- sale_price_per_sqft         1   1731.0 5203.2
<none>                            1729.2 5203.4
- neighborhood_swisu          1   1732.3 5204.5
- log_rel_price               1   1732.7 5204.9
- neighborhood_n_ridge        1   1732.7 5204.9
- neighborhood_brk_side       1   1733.5 5205.7
- neighborhood_meadowv        1   1733.9 5206.1
- overall_qual                1   1734.6 5206.8
- NeighborhoodBrDale          1   1734.8 5207.0
- tot_bathrooms               1   1738.1 5210.3
- neighborhood_n_ridge_hghts  1   1739.7 5211.9
- bath_pr_sqft                1   1740.9 5213.1
- garage_type_basment         1   1744.9 5217.1
- garage_type_builtIn         1   1745.0 5217.2
- garage_type_no_garage       1   1745.9 5218.1
- exter_qual                  1   1746.5 5218.7
- total_sq_feet               1   1750.2 5222.4
- neighborhood_sawyer         1   1750.5 5222.8
- neighborhood_idottrr        1   1754.2 5226.4
- garage_type_detchd          1   1783.2 5255.4
- student_apt                 1   1937.8 5410.0
- central_air                 1   1939.6 5411.9

Step:  AIC=5202.89
applicants ~ month_sold + overall_qual + total_sq_feet + tot_bathrooms + 
    exter_qual + central_air + garage_type_basment + garage_type_builtIn + 
    garage_type_detchd + garage_type_no_garage + NeighborhoodBrDale + 
    neighborhood_brk_side + neighborhood_idottrr + neighborhood_meadowv + 
    neighborhood_n_ridge + neighborhood_n_ridge_hghts + neighborhood_sawyer + 
    neighborhood_swisu + neighborhood_veenker + log_rel_price + 
    sale_price_per_sqft + bath_pr_sqft + student_apt + offset(log(num_units))

                             Df Deviance    AIC
- month_sold                  1   1732.2 5202.4
- sale_price_per_sqft         1   1732.4 5202.6
- neighborhood_veenker        1   1732.4 5202.7
<none>                            1730.7 5202.9
- neighborhood_swisu          1   1733.9 5204.1
- neighborhood_n_ridge        1   1734.3 5204.5
- log_rel_price               1   1734.4 5204.7
- neighborhood_brk_side       1   1734.8 5205.0
- neighborhood_meadowv        1   1735.1 5205.3
- overall_qual                1   1735.8 5206.0
- NeighborhoodBrDale          1   1736.2 5206.4
- tot_bathrooms               1   1739.5 5209.7
- neighborhood_n_ridge_hghts  1   1741.4 5211.6
- bath_pr_sqft                1   1742.1 5212.4
- garage_type_basment         1   1746.1 5216.3
- garage_type_builtIn         1   1746.4 5216.6
- garage_type_no_garage       1   1748.1 5218.3
- exter_qual                  1   1748.8 5219.0
- neighborhood_sawyer         1   1751.3 5221.5
- total_sq_feet               1   1752.0 5222.2
- neighborhood_idottrr        1   1755.4 5225.6
- garage_type_detchd          1   1783.6 5253.8
- central_air                 1   1940.0 5410.2
- student_apt                 1   1940.8 5411.0

Step:  AIC=5202.41
applicants ~ overall_qual + total_sq_feet + tot_bathrooms + exter_qual + 
    central_air + garage_type_basment + garage_type_builtIn + 
    garage_type_detchd + garage_type_no_garage + NeighborhoodBrDale + 
    neighborhood_brk_side + neighborhood_idottrr + neighborhood_meadowv + 
    neighborhood_n_ridge + neighborhood_n_ridge_hghts + neighborhood_sawyer + 
    neighborhood_swisu + neighborhood_veenker + log_rel_price + 
    sale_price_per_sqft + bath_pr_sqft + student_apt + offset(log(num_units))

                             Df Deviance    AIC
- sale_price_per_sqft         1   1733.9 5202.1
- neighborhood_veenker        1   1734.0 5202.2
<none>                            1732.2 5202.4
- neighborhood_swisu          1   1735.5 5203.7
- neighborhood_n_ridge        1   1735.8 5204.0
- log_rel_price               1   1735.9 5204.1
- neighborhood_brk_side       1   1736.2 5204.4
- neighborhood_meadowv        1   1736.6 5204.8
- overall_qual                1   1737.5 5205.7
- NeighborhoodBrDale          1   1737.6 5205.8
- tot_bathrooms               1   1741.2 5209.4
- neighborhood_n_ridge_hghts  1   1742.9 5211.1
- bath_pr_sqft                1   1744.0 5212.2
- garage_type_basment         1   1747.6 5215.8
- garage_type_builtIn         1   1748.2 5216.4
- garage_type_no_garage       1   1749.7 5217.9
- exter_qual                  1   1749.9 5218.1
- neighborhood_sawyer         1   1752.7 5220.9
- total_sq_feet               1   1753.6 5221.8
- neighborhood_idottrr        1   1756.6 5224.8
- garage_type_detchd          1   1786.1 5254.3
- central_air                 1   1942.9 5411.1
- student_apt                 1   1943.5 5411.8

Step:  AIC=5202.14
applicants ~ overall_qual + total_sq_feet + tot_bathrooms + exter_qual + 
    central_air + garage_type_basment + garage_type_builtIn + 
    garage_type_detchd + garage_type_no_garage + NeighborhoodBrDale + 
    neighborhood_brk_side + neighborhood_idottrr + neighborhood_meadowv + 
    neighborhood_n_ridge + neighborhood_n_ridge_hghts + neighborhood_sawyer + 
    neighborhood_swisu + neighborhood_veenker + log_rel_price + 
    bath_pr_sqft + student_apt + offset(log(num_units))

                             Df Deviance    AIC
- neighborhood_veenker        1   1735.9 5202.1
<none>                            1733.9 5202.1
- neighborhood_swisu          1   1737.5 5203.7
- neighborhood_meadowv        1   1738.2 5204.5
- neighborhood_brk_side       1   1738.5 5204.8
- neighborhood_n_ridge        1   1739.2 5205.4
- overall_qual                1   1739.2 5205.4
- NeighborhoodBrDale          1   1739.4 5205.6
- tot_bathrooms               1   1741.2 5207.4
- bath_pr_sqft                1   1744.0 5210.3
- neighborhood_n_ridge_hghts  1   1746.1 5212.3
- garage_type_basment         1   1750.5 5216.7
- garage_type_builtIn         1   1750.8 5217.0
- exter_qual                  1   1751.7 5217.9
- garage_type_no_garage       1   1753.4 5219.6
- neighborhood_sawyer         1   1754.4 5220.7
- neighborhood_idottrr        1   1759.3 5225.5
- total_sq_feet               1   1771.5 5237.7
- garage_type_detchd          1   1789.6 5255.8
- log_rel_price               1   1867.2 5333.5
- student_apt                 1   1944.6 5410.8
- central_air                 1   1958.5 5424.8

Step:  AIC=5202.13
applicants ~ overall_qual + total_sq_feet + tot_bathrooms + exter_qual + 
    central_air + garage_type_basment + garage_type_builtIn + 
    garage_type_detchd + garage_type_no_garage + NeighborhoodBrDale + 
    neighborhood_brk_side + neighborhood_idottrr + neighborhood_meadowv + 
    neighborhood_n_ridge + neighborhood_n_ridge_hghts + neighborhood_sawyer + 
    neighborhood_swisu + log_rel_price + bath_pr_sqft + student_apt + 
    offset(log(num_units))

                             Df Deviance    AIC
<none>                            1735.9 5202.1
- neighborhood_swisu          1   1739.5 5203.7
- neighborhood_meadowv        1   1740.2 5204.5
- neighborhood_brk_side       1   1740.6 5204.8
- neighborhood_n_ridge        1   1740.8 5205.0
- overall_qual                1   1741.3 5205.5
- NeighborhoodBrDale          1   1741.4 5205.6
- tot_bathrooms               1   1743.3 5207.5
- bath_pr_sqft                1   1746.2 5210.4
- neighborhood_n_ridge_hghts  1   1747.5 5211.7
- garage_type_basment         1   1752.3 5216.6
- garage_type_builtIn         1   1752.4 5216.6
- exter_qual                  1   1753.5 5217.7
- garage_type_no_garage       1   1755.2 5219.4
- neighborhood_sawyer         1   1756.4 5220.6
- neighborhood_idottrr        1   1761.4 5225.6
- total_sq_feet               1   1773.3 5237.5
- garage_type_detchd          1   1790.9 5255.1
- log_rel_price               1   1868.0 5332.2
- student_apt                 1   1946.3 5410.5
- central_air                 1   1960.3 5424.5

library(dplyr)

final_glm <- glm(
  stepwise_result$formula, 
  data = train,
  family = glm$family
)

AIC(final_glm)

[1] 5202.127

summary(final_glm)

Call:
glm(formula = stepwise_result$formula, family = glm$family, data = train)

Coefficients:
                             Estimate Std. Error z value Pr(>|z|)    
(Intercept)                -2.183e+00  3.149e-01  -6.930 4.20e-12 ***
overall_qual               -4.870e-02  2.096e-02  -2.324 0.020140 *  
total_sq_feet               6.071e-04  9.058e-05   6.702 2.05e-11 ***
tot_bathrooms              -2.298e-01  7.537e-02  -3.049 0.002295 ** 
exter_qual                  1.716e-01  4.078e-02   4.207 2.58e-05 ***
central_airno              -1.798e+00  1.587e-01 -11.332  < 2e-16 ***
garage_type_basment        -6.425e-01  1.755e-01  -3.661 0.000251 ***
garage_type_builtIn        -2.754e-01  7.026e-02  -3.920 8.87e-05 ***
garage_type_detchd         -3.378e-01  4.655e-02  -7.256 4.00e-13 ***
garage_type_no_garage      -3.825e-01  9.100e-02  -4.204 2.62e-05 ***
NeighborhoodBrDale         -5.172e-01  2.396e-01  -2.158 0.030906 *  
neighborhood_brk_side      -2.225e-01  1.056e-01  -2.107 0.035078 *  
neighborhood_idottrr       -8.875e-01  2.015e-01  -4.404 1.06e-05 ***
neighborhood_meadowv       -3.599e-01  1.824e-01  -1.973 0.048472 *  
neighborhood_n_ridge       -1.858e-01  8.568e-02  -2.169 0.030100 *  
neighborhood_n_ridge_hghts -2.378e-01  7.099e-02  -3.350 0.000808 ***
neighborhood_sawyer        -4.018e-01  9.394e-02  -4.277 1.89e-05 ***
neighborhood_swisu          2.794e-01  1.426e-01   1.960 0.050047 .  
log_rel_price              -1.001e+00  8.661e-02 -11.553  < 2e-16 ***
bath_pr_sqft                9.349e+02  2.516e+02   3.715 0.000203 ***
student_apt                 4.941e-01  3.311e-02  14.922  < 2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

(Dispersion parameter for poisson family taken to be 1)

    Null deviance: 2784.1  on 1144  degrees of freedom
Residual deviance: 1735.9  on 1124  degrees of freedom
AIC: 5202.1

Number of Fisher Scoring iterations: 5

plot(final_glm)

Task 8 - Fit a LASSO

#THE ONLY CHANGES NEEDED
#1. Replace "WEIGHT_VARIABLE" with the weight variable that you used for the GLM
#2. In the  "lasso_formula" below, use your formula from task 6
#3. Use the same FAMILY from task 6.  Type ?glmnet into the console to read the possible options

lasso_formula <- applicants ~ . + offset(log(num_units)) - neighborhood_n_ames - garage_type_attchd - num_units - log_sale_price 

lasso_x_train <- model.matrix(lasso_formula, data = train)
lasso_x_test <- model.matrix(lasso_formula, data = test)

control <-trainControl(method="cv", number=15)
lassoGrid <- expand.grid(alpha = 1, lambda = seq(0.0001,0.01,by = 0.0005))

#Fit a lasso and inspect the variables which have zero coefficients.
#Note that the glmnet library only allows the identity link function
lasso <- train(x = lasso_x_train, 
               y = train_y, 
               method = 'glmnet', 
               family = "poisson",

               trControl = control, 
               tuneGrid = lassoGrid) 

#This code gets the coefficients from the LASSO which are zero
lasso_results <- varImp(lasso,scale=F)
lasso_coefficients <- lasso_results$importance

#Show the coefficients which are zero
variables_with_zeros <- colnames(lasso_x_train)[which(lasso_coefficients$Overall==0)]
print("Variables with Coefficients of Zero:")

[1] "Variables with Coefficients of Zero:"

cat( paste( variables_with_zeros, collapse='\n' ) )

sale_price
year_sold
month_sold
tot_bathrooms
lot_area
neighborhood_gilbert
neighborhood_n_w_ames
log_rel_price

Task 9 - Create a bagged tree model

The following code creates eight samples of the data. 20% of records are taken, with replacement, from the data randomly.

sample1 <- train %>% sample_frac(0.2,replace=T)
sample2 <- train %>% sample_frac(0.2,replace=T)
sample3 <- train %>% sample_frac(0.2,replace=T)
sample4 <- train %>% sample_frac(0.2,replace=T)
sample5 <- train %>% sample_frac(0.2,replace=T)
sample6 <- train %>% sample_frac(0.2,replace=T)
sample7 <- train %>% sample_frac(0.2,replace=T)
sample8 <- train %>% sample_frac(0.2,replace=T)

This is the setting for the decision tree paramters. Make your adjustments here to test out different paramters.

#ctrl <- rpart.control(minbucket = 5, cp = 0.01, maxdepth = 5)
ctrl <- rpart.control(minbucket = 10, cp = 0.001, maxdepth = 5)
#ctrl <- rpart.control(minbucket = 10, cp = 0.01, maxdepth = 7)

The following code sets up a decision tree using all the variables in the dataframe. Each tree uses only 20% of the records. The number of units are used as the weights.

tree1 <- rpart(data = sample1, lasso_formula, weights = sample1$num_units, control = ctrl)
tree2 <- rpart(data = sample2, lasso_formula, weights = sample2$num_units, control = ctrl)
tree3 <- rpart(data = sample3, lasso_formula, weights = sample3$num_units, control = ctrl)
tree4 <- rpart(data = sample4, lasso_formula, weights = sample4$num_units, control = ctrl)
tree5 <- rpart(data = sample5, lasso_formula, weights = sample5$num_units, control = ctrl)
tree6 <- rpart(data = sample6, lasso_formula, weights = sample6$num_units, control = ctrl)
tree7 <- rpart(data = sample7, lasso_formula, weights = sample7$num_units, control = ctrl)
tree8 <- rpart(data = sample8, lasso_formula, weights = sample8$num_units, control = ctrl)

rpart.plot(tree1, cex = .7)

rpart.plot(tree2, cex = .7)

rpart.plot(tree3, cex = .7)

rpart.plot(tree4, cex = .7)

rpart.plot(tree5, cex = .7)

rpart.plot(tree6, cex = .7)

rpart.plot(tree7, cex = .7)

rpart.plot(tree8, cex = .7)

#make predictions
tree1_pred <- predict(tree1, newdata = test, type = "vector")
tree2_pred <- predict(tree2, newdata = test, type = "vector")
tree3_pred <- predict(tree3, newdata = test, type = "vector")
tree4_pred <- predict(tree4, newdata = test, type = "vector")
tree5_pred <- predict(tree5, newdata = test, type = "vector")
tree6_pred <- predict(tree6, newdata = test, type = "vector")
tree7_pred <- predict(tree7, newdata = test, type = "vector")
tree8_pred <- predict(tree8, newdata = test, type = "vector")

#UPDATE THIS FORMULA TO PERFORM BAGGING
trees_pred <- (tree1_pred + tree2_pred + tree3_pred+ tree4_pred+ tree5_pred+ tree6_pred+ tree7_pred+ tree8_pred)/8

LLfunction <- function(targets, predicted_values){
  p_v_zero <- ifelse(predicted_values <= 0, 0, predicted_values)
  p_v_pos <- ifelse(predicted_values <= 0, 0.000001 ,predicted_values)
  return(sum(targets*log(p_v_pos)) - sum(p_v_zero))
}
# "targets" is a vector containing the actual values for the target variable
# "predicted_values" is a vector containing the predicted values for the target variable

LLfunction(test$applicants, trees_pred)

[1] 343.9751

LLfunction(test$applicants, tree1_pred)

[1] 264.3733

Task 10 - Measure the variable importance with a Random Forest

#NO CHANGES NEEDED
RF <- randomForest( applicants ~ . + neighborhood_n_ames - garage_type_attchd - num_units - log_sale_price,
                   data = train,
                   weights = train_number_of_units, 
                   ntree=400,
                   importance=TRUE)

imp_RF <- importance(RF)
imp_DF <- data.frame(Variables = row.names(imp_RF), MSE = imp_RF[,1])
imp_DF <- imp_DF[order(imp_DF$MSE, decreasing = TRUE),]

ggplot(imp_DF[1:30,], aes(x=reorder(Variables, MSE), y=MSE, fill=MSE)) + geom_bar(stat = 'identity') + labs(x = 'Variables', y= '% increase MSE if variable is randomly permuted') + coord_flip() + theme(legend.position="none")

Task 11 - Compare model performance

#This function will calculate the log-liklihood based on a Poisson model for the number of applicants
LLfunction <- function(targets, predicted_values){
  p_v_zero <- ifelse(predicted_values <= 0, 0, predicted_values)
  p_v_pos <- ifelse(predicted_values <= 0, 0.000001, predicted_values)
  return(sum(targets*log(p_v_pos)) - sum(p_v_zero))
}
print("loglikelihood")

[1] "loglikelihood"

glm_pred <- predict(final_glm, type="response", newdata = test)
lasso_pred <- exp(predict(lasso,newdata = lasso_x_test, weights = test_number_of_units))
RF_pred <- predict(RF, type="response", newdata = test)

tibble(Model = c("GLM", "LASSO", "Bagged Trees", "Random Forest"),
       LogLikelihood = c(LLfunction(test$applicants,glm_pred),
                         LLfunction(test$applicants,lasso_pred),
                         LLfunction(test$applicants, trees_pred),
                         LLfunction(test$applicants,RF_pred)))

# A tibble: 4 × 2
  Model         LogLikelihood
  <chr>                 <dbl>
1 GLM                    237.
2 LASSO               -54465.
3 Bagged Trees           344.
4 Random Forest          444.

Task 12 - Executive Summary