library(purrr)
library(tidyr)
library(ggplot2)
library(Hmisc)
## Warning: package 'Hmisc' was built under R version 3.5.2
## Loading required package: lattice
## Loading required package: survival
## Loading required package: Formula
## 
## Attaching package: 'Hmisc'
## The following objects are masked from 'package:base':
## 
##     format.pval, units
library(dplyr)
## 
## Attaching package: 'dplyr'
## The following objects are masked from 'package:Hmisc':
## 
##     src, summarize
## The following objects are masked from 'package:stats':
## 
##     filter, lag
## The following objects are masked from 'package:base':
## 
##     intersect, setdiff, setequal, union
library(corrplot)
## corrplot 0.84 loaded
library(kableExtra)

Computational Mathematics

Problem 1

Using R, generate a random variable X that has 10,000 random uniform numbers from 1 to N, where N can be any number of your choosing greater than or equal to 6. Then generate a random variable Y that has 10,000 random normal numbers with a mean of \(\mu = \sigma = (N+1)/2\).

Random Variable X

N<-8 
n<-10000

X<-runif(n,min=0,max=N)
hist(X)

Random Variable Y

Y<-rnorm(n,(N+1)/2,(N+1)/2)
hist(Y)
abline(v=(N+1)/2,col="red")

Probability

Calculate as a minimum the below probabilities a through c. Assume the small letter “x” is estimated as the median of the X variable, and the small letter “y” is estimated as the 1st quartile of the Y variable. Interpret the meaning of all probabilities.

x<-median(X)
round(x,2)
## [1] 4.05
y<-quantile(Y,0.25)[[1]]
round(y,2)
## [1] 1.43
  1. \(P(X>x \ | \ X>y)\)

Probability that X is greater than its median given that X is greater than the first quartile of Y

\[P(X>x \ | \ X>y) = \frac{P(X>x \ , \ X>y)}{P(X>y)}\]

Pxxandxy<-sum(X>x & X>y)/n #all the X greater than x and greater than y divided by all possible X
round(Pxxandxy,2)
## [1] 0.5
Pxy<-sum(X>y)/n #all x greater than y divided by all possible X
round(Pxy,2)
## [1] 0.82
Pxxgivenxy=Pxxandxy/Pxy
round(Pxxgivenxy,2)
## [1] 0.61
  1. \(P(X>x, Y>y)\)

Probability that X is grater than all possible x and Y is greater than all possible y

Pxxyy<-(sum(X>x & Y>y))/n
round(Pxxyy,2)
## [1] 0.38
  1. \(P(X<x | X>y)\)

Probability of X greater than its median and greater than the first quantile of Y

\[P(X<x \ | \ X>y) = \frac{P(X<x \ , \ X>y)}{P(X>y)}\]

Pxxandxy<-sum(X<x & X>y)/n
round(Pxxandxy,2)
## [1] 0.32
Pxy<-sum(X>y)/n
round(Pxy,2)
## [1] 0.82
Pxxgivenxy<-Pxxandxy/Pxy
round(Pxxgivenxy,2)
## [1] 0.39

Independance

Investigate whether \(P(X>x \ and \ Y>y)=P(X>x)P(Y>y)\) by building a table and evaluating the marginal and joint probabilities.

We start by building the contingency table with samples/observation of X and Y

m<-matrix( c(sum(X>x & Y<y),sum(X>x & Y>y), sum(X<x & Y<y),sum(X<x & Y>y)), nrow = 2,ncol = 2)
m<-cbind(m,c(m[1,1]+m[1,2],m[2,1]+m[2,2]))
m<-rbind(m,c(m[1,1]+m[2,1],m[1,2]+m[2,2],m[1,3]+m[2,3]))
contingency<-as.data.frame(m)
names(contingency) <- c("X>x","X<x", "Total")
row.names(contingency) <- c("Y<y","Y>y", "Total")
kable(contingency) %>%
  kable_styling(bootstrap_options = "bordered")
X>x X<x Total
Y<y 1239 1261 2500
Y>y 3761 3739 7500
Total 5000 5000 10000

We can now compute the table with probabilities.

mp<-m/m[3,3]
contingency_p<-as.data.frame(mp)
names(contingency_p) <- c("X>x","X<x", "Total")
row.names(contingency_p) <- c("Y<y","Y>y", "Total")
kable(round(contingency_p,2)) %>%
  kable_styling(bootstrap_options = "bordered")
X>x X<x Total
Y<y 0.12 0.13 0.25
Y>y 0.38 0.37 0.75
Total 0.50 0.50 1.00

Now if we compute \(P(X>x \ and \ Y>y)\) as \(P(X>x)P(Y>y)\) we can compare against results in the table

P<-round((sum(X>x)/n)*(sum(Y<y)/n),2)
P
## [1] 0.12
round(P,2)==round(mp[1,1],2)
## [1] TRUE
P<-round((sum(X>x)/n)*(sum(Y>y)/n),2)
P
## [1] 0.38
round(P,2)==round(mp[2,1],2)
## [1] TRUE
P<-round((sum(X<x)/n)*(sum(Y<y)/n),2)
P
## [1] 0.12
round(P,2)==round(mp[1,2],2)
## [1] FALSE
P<-round((sum(X<x)/n)*(sum(Y>y)/n),2)
P
## [1] 0.38
round(P,2)==round(mp[2,2],2)
## [1] FALSE

We find that the results are very similar, so we therefore conclude they are in truth independent. (Note: running the X and Y simulation will sometimes give results that are completely equal or very close)

We run both a fisher and a chi-test. In both of these we state a null hypotheses that the two variables are independent, and a alternative stating that there is dependence.

fisher.test(m,simulate.p.value=TRUE)
## 
##  Fisher's Exact Test for Count Data with simulated p-value (based
##  on 2000 replicates)
## 
## data:  m
## p-value = 0.9905
## alternative hypothesis: two.sided
chisq.test(m, correct=TRUE)
## 
##  Pearson's Chi-squared test
## 
## data:  m
## X-squared = 0.25813, df = 4, p-value = 0.9924

In both cases the p-value is much greater than a reasonable threshold of 0.05, or even 0.1. So we do not reject the null hypothesis of independence and conclude that they are in fact independent (association is not statistically significant). The chi test is better suited for large samples as we have here. (Note: running the X and Y simulation will sometimes give results with p-values at or very close to 1, but in any case they are greater than the reasonable threshold)

Problem 2

You are to register for Kaggle.com (free) and compete in the House Prices: Advanced Regression Techniques competition. https://www.kaggle.com/c/house-prices-advanced-regression-techniques . I want you to do the following.

Descriptive and Inferential Statistics. Provide univariate descriptive statistics and appropriate plots for the training data set. Provide a scatterplot matrix for at least two of the independent variables and the dependent variable. Derive a correlation matrix for any three quantitative variables in the dataset. Test the hypotheses that the correlations between each pairwise set of variables is 0 and provide an 80% confidence interval. Discuss the meaning of your analysis. Would you be worried about familywise error? Why or why not?

train<-read.csv("data/train.csv",header=TRUE,stringsAsFactors=FALSE)

Descriptive Statistics

Provide univariate descriptive statistics and appropriate plots for the training data set.

We first identify the labels of the data we are working with.

colnames(train)
##  [1] "Id"            "MSSubClass"    "MSZoning"      "LotFrontage"  
##  [5] "LotArea"       "Street"        "Alley"         "LotShape"     
##  [9] "LandContour"   "Utilities"     "LotConfig"     "LandSlope"    
## [13] "Neighborhood"  "Condition1"    "Condition2"    "BldgType"     
## [17] "HouseStyle"    "OverallQual"   "OverallCond"   "YearBuilt"    
## [21] "YearRemodAdd"  "RoofStyle"     "RoofMatl"      "Exterior1st"  
## [25] "Exterior2nd"   "MasVnrType"    "MasVnrArea"    "ExterQual"    
## [29] "ExterCond"     "Foundation"    "BsmtQual"      "BsmtCond"     
## [33] "BsmtExposure"  "BsmtFinType1"  "BsmtFinSF1"    "BsmtFinType2" 
## [37] "BsmtFinSF2"    "BsmtUnfSF"     "TotalBsmtSF"   "Heating"      
## [41] "HeatingQC"     "CentralAir"    "Electrical"    "X1stFlrSF"    
## [45] "X2ndFlrSF"     "LowQualFinSF"  "GrLivArea"     "BsmtFullBath" 
## [49] "BsmtHalfBath"  "FullBath"      "HalfBath"      "BedroomAbvGr" 
## [53] "KitchenAbvGr"  "KitchenQual"   "TotRmsAbvGrd"  "Functional"   
## [57] "Fireplaces"    "FireplaceQu"   "GarageType"    "GarageYrBlt"  
## [61] "GarageFinish"  "GarageCars"    "GarageArea"    "GarageQual"   
## [65] "GarageCond"    "PavedDrive"    "WoodDeckSF"    "OpenPorchSF"  
## [69] "EnclosedPorch" "X3SsnPorch"    "ScreenPorch"   "PoolArea"     
## [73] "PoolQC"        "Fence"         "MiscFeature"   "MiscVal"      
## [77] "MoSold"        "YrSold"        "SaleType"      "SaleCondition"
## [81] "SalePrice"

Then we run a histogram of all the variables to identify interesting features. For example, the data shows how many homes had their garages built between 1950 and 1980, but then there was a large dip, with a high spike right before 2010, this probably correlates with the number of auto sales in those periods.

#plot histogram of all numeric variables
train %>%
  keep(is.numeric) %>% 
  gather() %>% 
  ggplot(aes(value)) +
    facet_wrap(~ key, scales = "free",ncol=4) +
  theme( axis.text.x = element_text(angle = 90)) +
    geom_histogram()
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## Warning: Removed 348 rows containing non-finite values (stat_bin).

To see the descriptive statistics we can use both the summary and describe functions, they both produce slightly different data. Of particular interest is describe showing the number of nulls.

summary(train)
##        Id           MSSubClass      MSZoning          LotFrontage    
##  Min.   :   1.0   Min.   : 20.0   Length:1460        Min.   : 21.00  
##  1st Qu.: 365.8   1st Qu.: 20.0   Class :character   1st Qu.: 59.00  
##  Median : 730.5   Median : 50.0   Mode  :character   Median : 69.00  
##  Mean   : 730.5   Mean   : 56.9                      Mean   : 70.05  
##  3rd Qu.:1095.2   3rd Qu.: 70.0                      3rd Qu.: 80.00  
##  Max.   :1460.0   Max.   :190.0                      Max.   :313.00  
##                                                      NA's   :259     
##     LotArea          Street             Alley             LotShape        
##  Min.   :  1300   Length:1460        Length:1460        Length:1460       
##  1st Qu.:  7554   Class :character   Class :character   Class :character  
##  Median :  9478   Mode  :character   Mode  :character   Mode  :character  
##  Mean   : 10517                                                           
##  3rd Qu.: 11602                                                           
##  Max.   :215245                                                           
##                                                                           
##  LandContour         Utilities          LotConfig        
##  Length:1460        Length:1460        Length:1460       
##  Class :character   Class :character   Class :character  
##  Mode  :character   Mode  :character   Mode  :character  
##                                                          
##                                                          
##                                                          
##                                                          
##   LandSlope         Neighborhood        Condition1       
##  Length:1460        Length:1460        Length:1460       
##  Class :character   Class :character   Class :character  
##  Mode  :character   Mode  :character   Mode  :character  
##                                                          
##                                                          
##                                                          
##                                                          
##   Condition2          BldgType          HouseStyle         OverallQual    
##  Length:1460        Length:1460        Length:1460        Min.   : 1.000  
##  Class :character   Class :character   Class :character   1st Qu.: 5.000  
##  Mode  :character   Mode  :character   Mode  :character   Median : 6.000  
##                                                           Mean   : 6.099  
##                                                           3rd Qu.: 7.000  
##                                                           Max.   :10.000  
##                                                                           
##   OverallCond      YearBuilt     YearRemodAdd   RoofStyle        
##  Min.   :1.000   Min.   :1872   Min.   :1950   Length:1460       
##  1st Qu.:5.000   1st Qu.:1954   1st Qu.:1967   Class :character  
##  Median :5.000   Median :1973   Median :1994   Mode  :character  
##  Mean   :5.575   Mean   :1971   Mean   :1985                     
##  3rd Qu.:6.000   3rd Qu.:2000   3rd Qu.:2004                     
##  Max.   :9.000   Max.   :2010   Max.   :2010                     
##                                                                  
##    RoofMatl         Exterior1st        Exterior2nd       
##  Length:1460        Length:1460        Length:1460       
##  Class :character   Class :character   Class :character  
##  Mode  :character   Mode  :character   Mode  :character  
##                                                          
##                                                          
##                                                          
##                                                          
##   MasVnrType          MasVnrArea      ExterQual          ExterCond        
##  Length:1460        Min.   :   0.0   Length:1460        Length:1460       
##  Class :character   1st Qu.:   0.0   Class :character   Class :character  
##  Mode  :character   Median :   0.0   Mode  :character   Mode  :character  
##                     Mean   : 103.7                                        
##                     3rd Qu.: 166.0                                        
##                     Max.   :1600.0                                        
##                     NA's   :8                                             
##   Foundation          BsmtQual           BsmtCond        
##  Length:1460        Length:1460        Length:1460       
##  Class :character   Class :character   Class :character  
##  Mode  :character   Mode  :character   Mode  :character  
##                                                          
##                                                          
##                                                          
##                                                          
##  BsmtExposure       BsmtFinType1         BsmtFinSF1     BsmtFinType2      
##  Length:1460        Length:1460        Min.   :   0.0   Length:1460       
##  Class :character   Class :character   1st Qu.:   0.0   Class :character  
##  Mode  :character   Mode  :character   Median : 383.5   Mode  :character  
##                                        Mean   : 443.6                     
##                                        3rd Qu.: 712.2                     
##                                        Max.   :5644.0                     
##                                                                           
##    BsmtFinSF2        BsmtUnfSF       TotalBsmtSF       Heating         
##  Min.   :   0.00   Min.   :   0.0   Min.   :   0.0   Length:1460       
##  1st Qu.:   0.00   1st Qu.: 223.0   1st Qu.: 795.8   Class :character  
##  Median :   0.00   Median : 477.5   Median : 991.5   Mode  :character  
##  Mean   :  46.55   Mean   : 567.2   Mean   :1057.4                     
##  3rd Qu.:   0.00   3rd Qu.: 808.0   3rd Qu.:1298.2                     
##  Max.   :1474.00   Max.   :2336.0   Max.   :6110.0                     
##                                                                        
##   HeatingQC          CentralAir         Electrical          X1stFlrSF   
##  Length:1460        Length:1460        Length:1460        Min.   : 334  
##  Class :character   Class :character   Class :character   1st Qu.: 882  
##  Mode  :character   Mode  :character   Mode  :character   Median :1087  
##                                                           Mean   :1163  
##                                                           3rd Qu.:1391  
##                                                           Max.   :4692  
##                                                                         
##    X2ndFlrSF     LowQualFinSF       GrLivArea     BsmtFullBath   
##  Min.   :   0   Min.   :  0.000   Min.   : 334   Min.   :0.0000  
##  1st Qu.:   0   1st Qu.:  0.000   1st Qu.:1130   1st Qu.:0.0000  
##  Median :   0   Median :  0.000   Median :1464   Median :0.0000  
##  Mean   : 347   Mean   :  5.845   Mean   :1515   Mean   :0.4253  
##  3rd Qu.: 728   3rd Qu.:  0.000   3rd Qu.:1777   3rd Qu.:1.0000  
##  Max.   :2065   Max.   :572.000   Max.   :5642   Max.   :3.0000  
##                                                                  
##   BsmtHalfBath        FullBath        HalfBath       BedroomAbvGr  
##  Min.   :0.00000   Min.   :0.000   Min.   :0.0000   Min.   :0.000  
##  1st Qu.:0.00000   1st Qu.:1.000   1st Qu.:0.0000   1st Qu.:2.000  
##  Median :0.00000   Median :2.000   Median :0.0000   Median :3.000  
##  Mean   :0.05753   Mean   :1.565   Mean   :0.3829   Mean   :2.866  
##  3rd Qu.:0.00000   3rd Qu.:2.000   3rd Qu.:1.0000   3rd Qu.:3.000  
##  Max.   :2.00000   Max.   :3.000   Max.   :2.0000   Max.   :8.000  
##                                                                    
##   KitchenAbvGr   KitchenQual         TotRmsAbvGrd     Functional       
##  Min.   :0.000   Length:1460        Min.   : 2.000   Length:1460       
##  1st Qu.:1.000   Class :character   1st Qu.: 5.000   Class :character  
##  Median :1.000   Mode  :character   Median : 6.000   Mode  :character  
##  Mean   :1.047                      Mean   : 6.518                     
##  3rd Qu.:1.000                      3rd Qu.: 7.000                     
##  Max.   :3.000                      Max.   :14.000                     
##                                                                        
##    Fireplaces    FireplaceQu         GarageType         GarageYrBlt  
##  Min.   :0.000   Length:1460        Length:1460        Min.   :1900  
##  1st Qu.:0.000   Class :character   Class :character   1st Qu.:1961  
##  Median :1.000   Mode  :character   Mode  :character   Median :1980  
##  Mean   :0.613                                         Mean   :1979  
##  3rd Qu.:1.000                                         3rd Qu.:2002  
##  Max.   :3.000                                         Max.   :2010  
##                                                        NA's   :81    
##  GarageFinish         GarageCars      GarageArea      GarageQual       
##  Length:1460        Min.   :0.000   Min.   :   0.0   Length:1460       
##  Class :character   1st Qu.:1.000   1st Qu.: 334.5   Class :character  
##  Mode  :character   Median :2.000   Median : 480.0   Mode  :character  
##                     Mean   :1.767   Mean   : 473.0                     
##                     3rd Qu.:2.000   3rd Qu.: 576.0                     
##                     Max.   :4.000   Max.   :1418.0                     
##                                                                        
##   GarageCond         PavedDrive          WoodDeckSF      OpenPorchSF    
##  Length:1460        Length:1460        Min.   :  0.00   Min.   :  0.00  
##  Class :character   Class :character   1st Qu.:  0.00   1st Qu.:  0.00  
##  Mode  :character   Mode  :character   Median :  0.00   Median : 25.00  
##                                        Mean   : 94.24   Mean   : 46.66  
##                                        3rd Qu.:168.00   3rd Qu.: 68.00  
##                                        Max.   :857.00   Max.   :547.00  
##                                                                         
##  EnclosedPorch      X3SsnPorch      ScreenPorch        PoolArea      
##  Min.   :  0.00   Min.   :  0.00   Min.   :  0.00   Min.   :  0.000  
##  1st Qu.:  0.00   1st Qu.:  0.00   1st Qu.:  0.00   1st Qu.:  0.000  
##  Median :  0.00   Median :  0.00   Median :  0.00   Median :  0.000  
##  Mean   : 21.95   Mean   :  3.41   Mean   : 15.06   Mean   :  2.759  
##  3rd Qu.:  0.00   3rd Qu.:  0.00   3rd Qu.:  0.00   3rd Qu.:  0.000  
##  Max.   :552.00   Max.   :508.00   Max.   :480.00   Max.   :738.000  
##                                                                      
##     PoolQC             Fence           MiscFeature       
##  Length:1460        Length:1460        Length:1460       
##  Class :character   Class :character   Class :character  
##  Mode  :character   Mode  :character   Mode  :character  
##                                                          
##                                                          
##                                                          
##                                                          
##     MiscVal             MoSold           YrSold       SaleType        
##  Min.   :    0.00   Min.   : 1.000   Min.   :2006   Length:1460       
##  1st Qu.:    0.00   1st Qu.: 5.000   1st Qu.:2007   Class :character  
##  Median :    0.00   Median : 6.000   Median :2008   Mode  :character  
##  Mean   :   43.49   Mean   : 6.322   Mean   :2008                     
##  3rd Qu.:    0.00   3rd Qu.: 8.000   3rd Qu.:2009                     
##  Max.   :15500.00   Max.   :12.000   Max.   :2010                     
##                                                                       
##  SaleCondition        SalePrice     
##  Length:1460        Min.   : 34900  
##  Class :character   1st Qu.:129975  
##  Mode  :character   Median :163000  
##                     Mean   :180921  
##                     3rd Qu.:214000  
##                     Max.   :755000  
## 
describe(train)
## train 
## 
##  81  Variables      1460  Observations
## ---------------------------------------------------------------------------
## Id 
##        n  missing distinct     Info     Mean      Gmd      .05      .10 
##     1460        0     1460        1    730.5      487    73.95   146.90 
##      .25      .50      .75      .90      .95 
##   365.75   730.50  1095.25  1314.10  1387.05 
## 
## lowest :    1    2    3    4    5, highest: 1456 1457 1458 1459 1460
## ---------------------------------------------------------------------------
## MSSubClass 
##        n  missing distinct     Info     Mean      Gmd      .05      .10 
##     1460        0       15     0.94     56.9    43.19       20       20 
##      .25      .50      .75      .90      .95 
##       20       50       70      120      160 
##                                                                       
## Value         20    30    40    45    50    60    70    75    80    85
## Frequency    536    69     4    12   144   299    60    16    58    20
## Proportion 0.367 0.047 0.003 0.008 0.099 0.205 0.041 0.011 0.040 0.014
##                                         
## Value         90   120   160   180   190
## Frequency     52    87    63    10    30
## Proportion 0.036 0.060 0.043 0.007 0.021
## ---------------------------------------------------------------------------
## MSZoning 
##        n  missing distinct 
##     1460        0        5 
##                                                   
## Value      C (all)      FV      RH      RL      RM
## Frequency       10      65      16    1151     218
## Proportion   0.007   0.045   0.011   0.788   0.149
## ---------------------------------------------------------------------------
## LotFrontage 
##        n  missing distinct     Info     Mean      Gmd      .05      .10 
##     1201      259      110    0.998    70.05    24.61       34       44 
##      .25      .50      .75      .90      .95 
##       59       69       80       96      107 
## 
## lowest :  21  24  30  32  33, highest: 160 168 174 182 313
## ---------------------------------------------------------------------------
## LotArea 
##        n  missing distinct     Info     Mean      Gmd      .05      .10 
##     1460        0     1073        1    10517     5718     3312     5000 
##      .25      .50      .75      .90      .95 
##     7554     9478    11602    14382    17401 
## 
## lowest :   1300   1477   1491   1526   1533, highest:  70761 115149 159000 164660 215245
## ---------------------------------------------------------------------------
## Street 
##        n  missing distinct 
##     1460        0        2 
##                       
## Value       Grvl  Pave
## Frequency      6  1454
## Proportion 0.004 0.996
## ---------------------------------------------------------------------------
## Alley 
##        n  missing distinct 
##       91     1369        2 
##                       
## Value       Grvl  Pave
## Frequency     50    41
## Proportion 0.549 0.451
## ---------------------------------------------------------------------------
## LotShape 
##        n  missing distinct 
##     1460        0        4 
##                                   
## Value        IR1   IR2   IR3   Reg
## Frequency    484    41    10   925
## Proportion 0.332 0.028 0.007 0.634
## ---------------------------------------------------------------------------
## LandContour 
##        n  missing distinct 
##     1460        0        4 
##                                   
## Value        Bnk   HLS   Low   Lvl
## Frequency     63    50    36  1311
## Proportion 0.043 0.034 0.025 0.898
## ---------------------------------------------------------------------------
## Utilities 
##        n  missing distinct 
##     1460        0        2 
##                         
## Value      AllPub NoSeWa
## Frequency    1459      1
## Proportion  0.999  0.001
## ---------------------------------------------------------------------------
## LotConfig 
##        n  missing distinct 
##     1460        0        5 
##                                                   
## Value       Corner CulDSac     FR2     FR3  Inside
## Frequency      263      94      47       4    1052
## Proportion   0.180   0.064   0.032   0.003   0.721
## ---------------------------------------------------------------------------
## LandSlope 
##        n  missing distinct 
##     1460        0        3 
##                             
## Value        Gtl   Mod   Sev
## Frequency   1382    65    13
## Proportion 0.947 0.045 0.009
## ---------------------------------------------------------------------------
## Neighborhood 
##        n  missing distinct 
##     1460        0       25 
## 
## lowest : Blmngtn Blueste BrDale  BrkSide ClearCr
## highest: Somerst StoneBr SWISU   Timber  Veenker
## ---------------------------------------------------------------------------
## Condition1 
##        n  missing distinct 
##     1460        0        9 
##                                                                          
## Value      Artery  Feedr   Norm   PosA   PosN   RRAe   RRAn   RRNe   RRNn
## Frequency      48     81   1260      8     19     11     26      2      5
## Proportion  0.033  0.055  0.863  0.005  0.013  0.008  0.018  0.001  0.003
## ---------------------------------------------------------------------------
## Condition2 
##        n  missing distinct 
##     1460        0        8 
##                                                                   
## Value      Artery  Feedr   Norm   PosA   PosN   RRAe   RRAn   RRNn
## Frequency       2      6   1445      1      2      1      1      2
## Proportion  0.001  0.004  0.990  0.001  0.001  0.001  0.001  0.001
## ---------------------------------------------------------------------------
## BldgType 
##        n  missing distinct 
##     1460        0        5 
##                                              
## Value        1Fam 2fmCon Duplex  Twnhs TwnhsE
## Frequency    1220     31     52     43    114
## Proportion  0.836  0.021  0.036  0.029  0.078
## ---------------------------------------------------------------------------
## HouseStyle 
##        n  missing distinct 
##     1460        0        8 
##                                                                   
## Value      1.5Fin 1.5Unf 1Story 2.5Fin 2.5Unf 2Story SFoyer   SLvl
## Frequency     154     14    726      8     11    445     37     65
## Proportion  0.105  0.010  0.497  0.005  0.008  0.305  0.025  0.045
## ---------------------------------------------------------------------------
## OverallQual 
##        n  missing distinct     Info     Mean      Gmd      .05      .10 
##     1460        0       10    0.951    6.099    1.522        4        5 
##      .25      .50      .75      .90      .95 
##        5        6        7        8        8 
##                                                                       
## Value          1     2     3     4     5     6     7     8     9    10
## Frequency      2     3    20   116   397   374   319   168    43    18
## Proportion 0.001 0.002 0.014 0.079 0.272 0.256 0.218 0.115 0.029 0.012
## ---------------------------------------------------------------------------
## OverallCond 
##        n  missing distinct     Info     Mean      Gmd 
##     1460        0        9    0.814    5.575    1.111 
##                                                                 
## Value          1     2     3     4     5     6     7     8     9
## Frequency      1     5    25    57   821   252   205    72    22
## Proportion 0.001 0.003 0.017 0.039 0.562 0.173 0.140 0.049 0.015
## ---------------------------------------------------------------------------
## YearBuilt 
##        n  missing distinct     Info     Mean      Gmd      .05      .10 
##     1460        0      112        1     1971    33.88     1916     1925 
##      .25      .50      .75      .90      .95 
##     1954     1973     2000     2006     2007 
## 
## lowest : 1872 1875 1880 1882 1885, highest: 2006 2007 2008 2009 2010
## ---------------------------------------------------------------------------
## YearRemodAdd 
##        n  missing distinct     Info     Mean      Gmd      .05      .10 
##     1460        0       61    0.997     1985    23.05     1950     1950 
##      .25      .50      .75      .90      .95 
##     1967     1994     2004     2006     2007 
## 
## lowest : 1950 1951 1952 1953 1954, highest: 2006 2007 2008 2009 2010
## ---------------------------------------------------------------------------
## RoofStyle 
##        n  missing distinct 
##     1460        0        6 
##                                                           
## Value         Flat   Gable Gambrel     Hip Mansard    Shed
## Frequency       13    1141      11     286       7       2
## Proportion   0.009   0.782   0.008   0.196   0.005   0.001
## ---------------------------------------------------------------------------
## RoofMatl 
##        n  missing distinct 
##     1460        0        8 
##                                                                           
## Value      ClyTile CompShg Membran   Metal    Roll Tar&Grv WdShake WdShngl
## Frequency        1    1434       1       1       1      11       5       6
## Proportion   0.001   0.982   0.001   0.001   0.001   0.008   0.003   0.004
## ---------------------------------------------------------------------------
## Exterior1st 
##        n  missing distinct 
##     1460        0       15 
##                                                                           
## Value      AsbShng AsphShn BrkComm BrkFace  CBlock CemntBd HdBoard ImStucc
## Frequency       20       1       2      50       1      61     222       1
## Proportion   0.014   0.001   0.001   0.034   0.001   0.042   0.152   0.001
##                                                                   
## Value      MetalSd Plywood   Stone  Stucco VinylSd Wd Sdng WdShing
## Frequency      220     108       2      25     515     206      26
## Proportion   0.151   0.074   0.001   0.017   0.353   0.141   0.018
## ---------------------------------------------------------------------------
## Exterior2nd 
##        n  missing distinct 
##     1460        0       16 
##                                                                           
## Value      AsbShng AsphShn Brk Cmn BrkFace  CBlock CmentBd HdBoard ImStucc
## Frequency       20       3       7      25       1      60     207      10
## Proportion   0.014   0.002   0.005   0.017   0.001   0.041   0.142   0.007
##                                                                           
## Value      MetalSd   Other Plywood   Stone  Stucco VinylSd Wd Sdng Wd Shng
## Frequency      214       1     142       5      26     504     197      38
## Proportion   0.147   0.001   0.097   0.003   0.018   0.345   0.135   0.026
## ---------------------------------------------------------------------------
## MasVnrType 
##        n  missing distinct 
##     1452        8        4 
##                                           
## Value       BrkCmn BrkFace    None   Stone
## Frequency       15     445     864     128
## Proportion   0.010   0.306   0.595   0.088
## ---------------------------------------------------------------------------
## MasVnrArea 
##        n  missing distinct     Info     Mean      Gmd      .05      .10 
##     1452        8      327    0.791    103.7    156.9        0        0 
##      .25      .50      .75      .90      .95 
##        0        0      166      335      456 
## 
## lowest :    0    1   11   14   16, highest: 1115 1129 1170 1378 1600
## ---------------------------------------------------------------------------
## ExterQual 
##        n  missing distinct 
##     1460        0        4 
##                                   
## Value         Ex    Fa    Gd    TA
## Frequency     52    14   488   906
## Proportion 0.036 0.010 0.334 0.621
## ---------------------------------------------------------------------------
## ExterCond 
##        n  missing distinct 
##     1460        0        5 
##                                         
## Value         Ex    Fa    Gd    Po    TA
## Frequency      3    28   146     1  1282
## Proportion 0.002 0.019 0.100 0.001 0.878
## ---------------------------------------------------------------------------
## Foundation 
##        n  missing distinct 
##     1460        0        6 
##                                                     
## Value      BrkTil CBlock  PConc   Slab  Stone   Wood
## Frequency     146    634    647     24      6      3
## Proportion  0.100  0.434  0.443  0.016  0.004  0.002
## ---------------------------------------------------------------------------
## BsmtQual 
##        n  missing distinct 
##     1423       37        4 
##                                   
## Value         Ex    Fa    Gd    TA
## Frequency    121    35   618   649
## Proportion 0.085 0.025 0.434 0.456
## ---------------------------------------------------------------------------
## BsmtCond 
##        n  missing distinct 
##     1423       37        4 
##                                   
## Value         Fa    Gd    Po    TA
## Frequency     45    65     2  1311
## Proportion 0.032 0.046 0.001 0.921
## ---------------------------------------------------------------------------
## BsmtExposure 
##        n  missing distinct 
##     1422       38        4 
##                                   
## Value         Av    Gd    Mn    No
## Frequency    221   134   114   953
## Proportion 0.155 0.094 0.080 0.670
## ---------------------------------------------------------------------------
## BsmtFinType1 
##        n  missing distinct 
##     1423       37        6 
##                                               
## Value        ALQ   BLQ   GLQ   LwQ   Rec   Unf
## Frequency    220   148   418    74   133   430
## Proportion 0.155 0.104 0.294 0.052 0.093 0.302
## ---------------------------------------------------------------------------
## BsmtFinSF1 
##        n  missing distinct     Info     Mean      Gmd      .05      .10 
##     1460        0      637    0.967    443.6    484.5      0.0      0.0 
##      .25      .50      .75      .90      .95 
##      0.0    383.5    712.2   1065.5   1274.0 
## 
## lowest :    0    2   16   20   24, highest: 1904 2096 2188 2260 5644
## ---------------------------------------------------------------------------
## BsmtFinType2 
##        n  missing distinct 
##     1422       38        6 
##                                               
## Value        ALQ   BLQ   GLQ   LwQ   Rec   Unf
## Frequency     19    33    14    46    54  1256
## Proportion 0.013 0.023 0.010 0.032 0.038 0.883
## ---------------------------------------------------------------------------
## BsmtFinSF2 
##        n  missing distinct     Info     Mean      Gmd      .05      .10 
##     1460        0      144    0.305    46.55    86.58      0.0      0.0 
##      .25      .50      .75      .90      .95 
##      0.0      0.0      0.0    117.2    396.2 
## 
## lowest :    0   28   32   35   40, highest: 1080 1085 1120 1127 1474
## ---------------------------------------------------------------------------
## BsmtUnfSF 
##        n  missing distinct     Info     Mean      Gmd      .05      .10 
##     1460        0      780    0.999    567.2    486.6      0.0     74.9 
##      .25      .50      .75      .90      .95 
##    223.0    477.5    808.0   1232.0   1468.0 
## 
## lowest :    0   14   15   23   26, highest: 2042 2046 2121 2153 2336
## ---------------------------------------------------------------------------
## TotalBsmtSF 
##        n  missing distinct     Info     Mean      Gmd      .05      .10 
##     1460        0      721        1     1057    459.5    519.3    636.9 
##      .25      .50      .75      .90      .95 
##    795.8    991.5   1298.2   1602.2   1753.0 
## 
## lowest :    0  105  190  264  270, highest: 3094 3138 3200 3206 6110
## ---------------------------------------------------------------------------
## Heating 
##        n  missing distinct 
##     1460        0        6 
##                                               
## Value      Floor  GasA  GasW  Grav  OthW  Wall
## Frequency      1  1428    18     7     2     4
## Proportion 0.001 0.978 0.012 0.005 0.001 0.003
## ---------------------------------------------------------------------------
## HeatingQC 
##        n  missing distinct 
##     1460        0        5 
##                                         
## Value         Ex    Fa    Gd    Po    TA
## Frequency    741    49   241     1   428
## Proportion 0.508 0.034 0.165 0.001 0.293
## ---------------------------------------------------------------------------
## CentralAir 
##        n  missing distinct 
##     1460        0        2 
##                       
## Value          N     Y
## Frequency     95  1365
## Proportion 0.065 0.935
## ---------------------------------------------------------------------------
## Electrical 
##        n  missing distinct 
##     1459        1        5 
##                                         
## Value      FuseA FuseF FuseP   Mix SBrkr
## Frequency     94    27     3     1  1334
## Proportion 0.064 0.019 0.002 0.001 0.914
## ---------------------------------------------------------------------------
## X1stFlrSF 
##        n  missing distinct     Info     Mean      Gmd      .05      .10 
##     1460        0      753        1     1163    416.4    673.0    756.9 
##      .25      .50      .75      .90      .95 
##    882.0   1087.0   1391.2   1680.0   1831.2 
## 
## lowest :  334  372  438  480  483, highest: 2633 2898 3138 3228 4692
## ---------------------------------------------------------------------------
## X2ndFlrSF 
##        n  missing distinct     Info     Mean      Gmd      .05      .10 
##     1460        0      417    0.817      347    450.2      0.0      0.0 
##      .25      .50      .75      .90      .95 
##      0.0      0.0    728.0    954.2   1141.0 
## 
## lowest :    0  110  167  192  208, highest: 1611 1796 1818 1872 2065
## ---------------------------------------------------------------------------
## LowQualFinSF 
##        n  missing distinct     Info     Mean      Gmd      .05      .10 
##     1460        0       24    0.052    5.845    11.55        0        0 
##      .25      .50      .75      .90      .95 
##        0        0        0        0        0 
## 
## lowest :   0  53  80 120 144, highest: 513 514 515 528 572
## ---------------------------------------------------------------------------
## GrLivArea 
##        n  missing distinct     Info     Mean      Gmd      .05      .10 
##     1460        0      861        1     1515    563.1      848      912 
##      .25      .50      .75      .90      .95 
##     1130     1464     1777     2158     2466 
## 
## lowest :  334  438  480  520  605, highest: 3627 4316 4476 4676 5642
## ---------------------------------------------------------------------------
## BsmtFullBath 
##        n  missing distinct     Info     Mean      Gmd 
##     1460        0        4    0.733   0.4253   0.5085 
##                                   
## Value          0     1     2     3
## Frequency    856   588    15     1
## Proportion 0.586 0.403 0.010 0.001
## ---------------------------------------------------------------------------
## BsmtHalfBath 
##        n  missing distinct     Info     Mean      Gmd 
##     1460        0        3    0.159  0.05753   0.1088 
##                             
## Value          0     1     2
## Frequency   1378    80     2
## Proportion 0.944 0.055 0.001
## ---------------------------------------------------------------------------
## FullBath 
##        n  missing distinct     Info     Mean      Gmd 
##     1460        0        4    0.766    1.565   0.5521 
##                                   
## Value          0     1     2     3
## Frequency      9   650   768    33
## Proportion 0.006 0.445 0.526 0.023
## ---------------------------------------------------------------------------
## HalfBath 
##        n  missing distinct     Info     Mean      Gmd 
##     1460        0        3    0.706   0.3829   0.4852 
##                             
## Value          0     1     2
## Frequency    913   535    12
## Proportion 0.625 0.366 0.008
## ---------------------------------------------------------------------------
## BedroomAbvGr 
##        n  missing distinct     Info     Mean      Gmd 
##     1460        0        8    0.815    2.866    0.818 
##                                                           
## Value          0     1     2     3     4     5     6     8
## Frequency      6    50   358   804   213    21     7     1
## Proportion 0.004 0.034 0.245 0.551 0.146 0.014 0.005 0.001
## ---------------------------------------------------------------------------
## KitchenAbvGr 
##        n  missing distinct     Info     Mean      Gmd 
##     1460        0        4    0.133    1.047  0.09174 
##                                   
## Value          0     1     2     3
## Frequency      1  1392    65     2
## Proportion 0.001 0.953 0.045 0.001
## ---------------------------------------------------------------------------
## KitchenQual 
##        n  missing distinct 
##     1460        0        4 
##                                   
## Value         Ex    Fa    Gd    TA
## Frequency    100    39   586   735
## Proportion 0.068 0.027 0.401 0.503
## ---------------------------------------------------------------------------
## TotRmsAbvGrd 
##        n  missing distinct     Info     Mean      Gmd      .05      .10 
##     1460        0       12    0.958    6.518    1.762        4        5 
##      .25      .50      .75      .90      .95 
##        5        6        7        9       10 
##                                                                       
## Value          2     3     4     5     6     7     8     9    10    11
## Frequency      1    17    97   275   402   329   187    75    47    18
## Proportion 0.001 0.012 0.066 0.188 0.275 0.225 0.128 0.051 0.032 0.012
##                       
## Value         12    14
## Frequency     11     1
## Proportion 0.008 0.001
## ---------------------------------------------------------------------------
## Functional 
##        n  missing distinct 
##     1460        0        7 
##                                                     
## Value       Maj1  Maj2  Min1  Min2   Mod   Sev   Typ
## Frequency     14     5    31    34    15     1  1360
## Proportion 0.010 0.003 0.021 0.023 0.010 0.001 0.932
## ---------------------------------------------------------------------------
## Fireplaces 
##        n  missing distinct     Info     Mean      Gmd 
##     1460        0        4    0.806    0.613   0.6566 
##                                   
## Value          0     1     2     3
## Frequency    690   650   115     5
## Proportion 0.473 0.445 0.079 0.003
## ---------------------------------------------------------------------------
## FireplaceQu 
##        n  missing distinct 
##      770      690        5 
##                                         
## Value         Ex    Fa    Gd    Po    TA
## Frequency     24    33   380    20   313
## Proportion 0.031 0.043 0.494 0.026 0.406
## ---------------------------------------------------------------------------
## GarageType 
##        n  missing distinct 
##     1379       81        6 
##                                                           
## Value       2Types  Attchd Basment BuiltIn CarPort  Detchd
## Frequency        6     870      19      88       9     387
## Proportion   0.004   0.631   0.014   0.064   0.007   0.281
## ---------------------------------------------------------------------------
## GarageYrBlt 
##        n  missing distinct     Info     Mean      Gmd      .05      .10 
##     1379       81       97        1     1979    27.63     1930     1945 
##      .25      .50      .75      .90      .95 
##     1961     1980     2002     2006     2007 
## 
## lowest : 1900 1906 1908 1910 1914, highest: 2006 2007 2008 2009 2010
## ---------------------------------------------------------------------------
## GarageFinish 
##        n  missing distinct 
##     1379       81        3 
##                             
## Value        Fin   RFn   Unf
## Frequency    352   422   605
## Proportion 0.255 0.306 0.439
## ---------------------------------------------------------------------------
## GarageCars 
##        n  missing distinct     Info     Mean      Gmd 
##     1460        0        5    0.802    1.767   0.7609 
##                                         
## Value          0     1     2     3     4
## Frequency     81   369   824   181     5
## Proportion 0.055 0.253 0.564 0.124 0.003
## ---------------------------------------------------------------------------
## GarageArea 
##        n  missing distinct     Info     Mean      Gmd      .05      .10 
##     1460        0      441        1      473    234.9      0.0    240.0 
##      .25      .50      .75      .90      .95 
##    334.5    480.0    576.0    757.1    850.1 
## 
## lowest :    0  160  164  180  186, highest: 1220 1248 1356 1390 1418
## ---------------------------------------------------------------------------
## GarageQual 
##        n  missing distinct 
##     1379       81        5 
##                                         
## Value         Ex    Fa    Gd    Po    TA
## Frequency      3    48    14     3  1311
## Proportion 0.002 0.035 0.010 0.002 0.951
## ---------------------------------------------------------------------------
## GarageCond 
##        n  missing distinct 
##     1379       81        5 
##                                         
## Value         Ex    Fa    Gd    Po    TA
## Frequency      2    35     9     7  1326
## Proportion 0.001 0.025 0.007 0.005 0.962
## ---------------------------------------------------------------------------
## PavedDrive 
##        n  missing distinct 
##     1460        0        3 
##                             
## Value          N     P     Y
## Frequency     90    30  1340
## Proportion 0.062 0.021 0.918
## ---------------------------------------------------------------------------
## WoodDeckSF 
##        n  missing distinct     Info     Mean      Gmd      .05      .10 
##     1460        0      274    0.858    94.24      125        0        0 
##      .25      .50      .75      .90      .95 
##        0        0      168      262      335 
## 
## lowest :   0  12  24  26  28, highest: 668 670 728 736 857
## ---------------------------------------------------------------------------
## OpenPorchSF 
##        n  missing distinct     Info     Mean      Gmd      .05      .10 
##     1460        0      202    0.909    46.66    62.43        0        0 
##      .25      .50      .75      .90      .95 
##        0       25       68      130      175 
## 
## lowest :   0   4   8  10  11, highest: 406 418 502 523 547
## ---------------------------------------------------------------------------
## EnclosedPorch 
##        n  missing distinct     Info     Mean      Gmd      .05      .10 
##     1460        0      120    0.369    21.95    39.39      0.0      0.0 
##      .25      .50      .75      .90      .95 
##      0.0      0.0      0.0    112.0    180.1 
## 
## lowest :   0  19  20  24  30, highest: 301 318 330 386 552
## ---------------------------------------------------------------------------
## X3SsnPorch 
##        n  missing distinct     Info     Mean      Gmd      .05      .10 
##     1460        0       20    0.049     3.41    6.739        0        0 
##      .25      .50      .75      .90      .95 
##        0        0        0        0        0 
##                                                                       
## Value          0    23    96   130   140   144   153   162   168   180
## Frequency   1436     1     1     1     1     2     1     1     3     2
## Proportion 0.984 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.002 0.001
##                                                                       
## Value        182   196   216   238   245   290   304   320   407   508
## Frequency      1     1     2     1     1     1     1     1     1     1
## Proportion 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001
## ---------------------------------------------------------------------------
## ScreenPorch 
##        n  missing distinct     Info     Mean      Gmd      .05      .10 
##     1460        0       76     0.22    15.06    28.27        0        0 
##      .25      .50      .75      .90      .95 
##        0        0        0        0      160 
## 
## lowest :   0  40  53  60  63, highest: 385 396 410 440 480
## ---------------------------------------------------------------------------
## PoolArea 
##        n  missing distinct     Info     Mean      Gmd 
##     1460        0        8    0.014    2.759    5.497 
##                                                           
## Value          0   480   512   519   555   576   648   738
## Frequency   1453     1     1     1     1     1     1     1
## Proportion 0.995 0.001 0.001 0.001 0.001 0.001 0.001 0.001
## ---------------------------------------------------------------------------
## PoolQC 
##        n  missing distinct 
##        7     1453        3 
##                             
## Value         Ex    Fa    Gd
## Frequency      2     2     3
## Proportion 0.286 0.286 0.429
## ---------------------------------------------------------------------------
## Fence 
##        n  missing distinct 
##      281     1179        4 
##                                   
## Value      GdPrv  GdWo MnPrv  MnWw
## Frequency     59    54   157    11
## Proportion 0.210 0.192 0.559 0.039
## ---------------------------------------------------------------------------
## MiscFeature 
##        n  missing distinct 
##       54     1406        4 
##                                   
## Value       Gar2  Othr  Shed  TenC
## Frequency      2     2    49     1
## Proportion 0.037 0.037 0.907 0.019
## ---------------------------------------------------------------------------
## MiscVal 
##        n  missing distinct     Info     Mean      Gmd      .05      .10 
##     1460        0       21    0.103    43.49    85.67        0        0 
##      .25      .50      .75      .90      .95 
##        0        0        0        0        0 
##                                                                       
## Value          0    50   350   400   450   500   550   600   700   800
## Frequency   1408     1     1    11     4    10     1     5     5     1
## Proportion 0.964 0.001 0.001 0.008 0.003 0.007 0.001 0.003 0.003 0.001
##                                                                 
## Value       1150  1200  1300  1400  2000  2500  3500  8300 15500
## Frequency      1     2     1     1     4     1     1     1     1
## Proportion 0.001 0.001 0.001 0.001 0.003 0.001 0.001 0.001 0.001
## ---------------------------------------------------------------------------
## MoSold 
##        n  missing distinct     Info     Mean      Gmd      .05      .10 
##     1460        0       12    0.985    6.322    3.041        2        3 
##      .25      .50      .75      .90      .95 
##        5        6        8       10       11 
##                                                                       
## Value          1     2     3     4     5     6     7     8     9    10
## Frequency     58    52   106   141   204   253   234   122    63    89
## Proportion 0.040 0.036 0.073 0.097 0.140 0.173 0.160 0.084 0.043 0.061
##                       
## Value         11    12
## Frequency     79    59
## Proportion 0.054 0.040
## ---------------------------------------------------------------------------
## YrSold 
##        n  missing distinct     Info     Mean      Gmd 
##     1460        0        5    0.955     2008    1.498 
##                                         
## Value       2006  2007  2008  2009  2010
## Frequency    314   329   304   338   175
## Proportion 0.215 0.225 0.208 0.232 0.120
## ---------------------------------------------------------------------------
## SaleType 
##        n  missing distinct 
##     1460        0        9 
##                                                                 
## Value        COD   Con ConLD ConLI ConLw   CWD   New   Oth    WD
## Frequency     43     2     9     5     5     4   122     3  1267
## Proportion 0.029 0.001 0.006 0.003 0.003 0.003 0.084 0.002 0.868
## ---------------------------------------------------------------------------
## SaleCondition 
##        n  missing distinct 
##     1460        0        6 
##                                                           
## Value      Abnorml AdjLand  Alloca  Family  Normal Partial
## Frequency      101       4      12      20    1198     125
## Proportion   0.069   0.003   0.008   0.014   0.821   0.086
## ---------------------------------------------------------------------------
## SalePrice 
##        n  missing distinct     Info     Mean      Gmd      .05      .10 
##     1460        0      663        1   180921    81086    88000   106475 
##      .25      .50      .75      .90      .95 
##   129975   163000   214000   278000   326100 
## 
## lowest :  34900  35311  37900  39300  40000, highest: 582933 611657 625000 745000 755000
## ---------------------------------------------------------------------------

Scatter Plots

Provide a scatterplot matrix for at least two of the independent variables and the dependent variable.

ggplot(train, aes(LotArea, GarageArea)) +
  geom_point(aes(color=SalePrice)) 

From this plot we can quickly see that homes without a garage have low sales prices. But we can also that the higher priced homes are not necessarily the ones with the highest lot or garage size.

A scattered plot can also help identify a correlation between basement size and sales price.

ggplot(train, aes(LotArea,BsmtUnfSF)) +
  geom_point(aes(color=SalePrice)) 

Here best prices seem to be a moderate size basement and lot, not necessarily very large basements or lots. But to keep in mind, basement size can be linked to lot size, something correlation will help identify.

Correlation

Derive a correlation matrix for any three quantitative variables in the dataset.

correlationData<-dplyr::select(train,SalePrice,LotArea,BsmtUnfSF)
correlationMatrix<-round(cor(correlationData),4)
correlationMatrix
##           SalePrice LotArea BsmtUnfSF
## SalePrice    1.0000  0.2638    0.2145
## LotArea      0.2638  1.0000   -0.0026
## BsmtUnfSF    0.2145 -0.0026    1.0000
corrplot(correlationMatrix,method ="color")

The matrix shows that in fact there isn’t a strong correlation between LotArea and Basement Size, with a correlation very close to zero: -0.0026.
We do however find some correlation between these two variables and the Sale Price.

Hypotheses testing

Test the hypotheses that the correlations between each pairwise set of variables is 0 and provide an 80% confidence interval. Discuss the meaning of your analysis.

Sale Price vs Lot Area

With a low P value, we are confident the correlation between these two variables is not zero, and we are 80% confident it is between 0.2323391 and 0.2947946

cor.test(correlationData$SalePrice,correlationData$LotArea, conf.level = 0.8)
## 
##  Pearson's product-moment correlation
## 
## data:  correlationData$SalePrice and correlationData$LotArea
## t = 10.445, df = 1458, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 80 percent confidence interval:
##  0.2323391 0.2947946
## sample estimates:
##       cor 
## 0.2638434

Sale Price vs Basement Size

With a low P value, we are confident the correlation between these two variables is not zero, and we are 80% confident it is between 0.1822292 and 0.2462680

cor.test(correlationData$SalePrice,correlationData$BsmtUnfSF, conf.level = 0.8)
## 
##  Pearson's product-moment correlation
## 
## data:  correlationData$SalePrice and correlationData$BsmtUnfSF
## t = 8.3847, df = 1458, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 80 percent confidence interval:
##  0.1822292 0.2462680
## sample estimates:
##       cor 
## 0.2144791

Lot Area vs Basement Size

With a high P value, we are confident the correlation between these two variables is in fact zero, and we are 80% confident it is between -0.03617682 and 0.03094600

cor.test(correlationData$LotArea,correlationData$BsmtUnfSF, conf.level = 0.8)
## 
##  Pearson's product-moment correlation
## 
## data:  correlationData$LotArea and correlationData$BsmtUnfSF
## t = -0.099979, df = 1458, p-value = 0.9204
## alternative hypothesis: true correlation is not equal to 0
## 80 percent confidence interval:
##  -0.03617682  0.03094600
## sample estimates:
##         cor 
## -0.00261836

Would you be worried about familywise error? Why or why not?

Familywise error is that of making at least one “type I” error“, or a false positive, rejection of a true null. In our two first cases, the P value is extremely small. Type I error happens when the null is rejected or the P value being smaller than a set threshold. But in our case the P value is very small, so any reasonable threshold (0.1, 0.05, etc.) setting will almost certainly be breached. So I would not be worried about committing a type one error, the null hypothesis can very certainly be rejected. In the last case, now the P value is very large, so again we are far from any reasonable threshold. In this case we can certainly not reject the null.

Linear Algebra and Correlation.

Linear Algebra and Correlation. Invert your correlation matrix from above. (This is known as the precision matrix and contains variance inflation factors on the diagonal.) Multiply the correlation matrix by the precision matrix, and then multiply the precision matrix by the correlation matrix. Conduct LU decomposition on the matrix.

Invert your correlation matrix from above.

precisionMatrix<-solve(correlationMatrix)
round(precisionMatrix,4)
##           SalePrice LotArea BsmtUnfSF
## SalePrice    1.1311 -0.2990   -0.2434
## LotArea     -0.2990  1.0791    0.0669
## BsmtUnfSF   -0.2434  0.0669    1.0524

Multiply the correlation matrix by the precision matrix, and then multiply the precision matrix by the correlation matrix.

round(correlationMatrix %*% precisionMatrix,4)
##           SalePrice LotArea BsmtUnfSF
## SalePrice         1       0         0
## LotArea           0       1         0
## BsmtUnfSF         0       0         1
round(precisionMatrix %*% correlationMatrix,4)
##           SalePrice LotArea BsmtUnfSF
## SalePrice         1       0         0
## LotArea           0       1         0
## BsmtUnfSF         0       0         1

Conduct LU decomposition on the matrix.

We use a function from assignment 2

solve.LDU<-function(A,D=FALSE) {
  #build unity matrix b
  b<-matrix(nrow = nrow(A),ncol = ncol(A))
  for(j in 1:ncol(A)) {
    for(i in 1:nrow(A)) {
      if(i==j) b[i,j]<-1  else b[i,j]=0
    }
  }
  #alternatively b could have been defined by b<-diag(ncol(A))
  Ab<-cbind(A,b)
  for(row in 1:(nrow(Ab)-1)){
    col=row
    for(next.row in (row+1):nrow(Ab)) {
      multiplier<-Ab[next.row,col]/Ab[row,col]
      Ab[next.row,]<-Ab[next.row,]-(multiplier*Ab[row,])
    }
  }
  ru<-Ab[,1:ncol(A)]
  rl<-solve(Ab[,(ncol(A)+1):ncol(Ab)])
  if(D) {
      Ab<-ru
      rd<-diag(diag(ru))
      for(row in 1:nrow(Ab)) {
        Ab[row,]=Ab[row,]/Ab[row,row]  
      }
      rup<-Ab
      result<-list(rl,rd,rup)
      return(result)
  } else {
      result<-list(rl,ru)
      return(result)
  }
}

r<-solve.LDU(correlationMatrix)
L<-r[[1]]
U<-r[[2]]
L
##  SalePrice     LotArea BsmtUnfSF
##     1.0000  0.00000000         0
##     0.2638  1.00000000         0
##     0.2145 -0.06361188         1
U
##           SalePrice   LotArea  BsmtUnfSF
## SalePrice         1 0.2638000  0.2145000
## LotArea           0 0.9304096 -0.0591851
## BsmtUnfSF         0 0.0000000  0.9502249

We can confirm the decomposition by comparing to our original matrix correlationMatrix

round(L %*% U ,4)== round(correlationMatrix,4)
##  SalePrice LotArea BsmtUnfSF
##       TRUE    TRUE      TRUE
##       TRUE    TRUE      TRUE
##       TRUE    TRUE      TRUE

Calculus-Based Probability & Statistics.

Calculus-Based Probability & Statistics. Many times, it makes sense to fit a closed form distribution to data. Select a variable in the Kaggle.com training dataset that is skewed to the right, shift it so that the minimum value is absolutely above zero if necessary. Then load the MASS package and run fitdistr to fit an exponential probability density function. (See https://stat.ethz.ch/R-manual/R-devel/library/MASS/html/fitdistr.html ). Find the optimal value of \(\lambda\) for this distribution, and then take 1000 samples from this exponential distribution using this value (e.g., rexp(1000,\(\lambda\) )). Plot a histogram and compare it with a histogram of your original variable. Using the exponential pdf, find the 5th and 95th percentiles using the cumulative distribution function (CDF). Also generate a 95% confidence interval from the empirical data, assuming normality. Finally, provide the empirical 5th percentile and 95th percentile of the data. Discuss.

Many times, it makes sense to fit a closed form distribution to data. Select a variable in the Kaggle.com training dataset that is skewed to the right, shift it so that the minimum value is absolutely above zero if necessary. Then load the MASS package and run fitdistr to fit an exponential probability density function.

toFit<-train$GrLivArea
min(toFit)
## [1] 334

Selected GrLivArea and found a shift is not necessary.

Then load the MASS package and run fitdistr to fit an exponential probability density function.

library(MASS)
## Warning: package 'MASS' was built under R version 3.5.2
## 
## Attaching package: 'MASS'
## The following object is masked from 'package:dplyr':
## 
##     select
fit <- fitdistr(toFit, "exponential")
fit
##        rate    
##   6.598640e-04 
##  (1.726943e-05)

Find the optimal value of \(\lambda\) for this distribution, and then take 1000 samples from this exponential distribution using this value

l<-fit$estimate
sim<- rexp(1000,l)

Plot a histogram and compare it with a histogram of your original variable.

hist(sim,breaks = 100)

hist(toFit,breaks=100)

sim.df <- data.frame(length = sim)
toFit.df <- data.frame(length = toFit)

sim.df$from <- 'sim'
toFit.df$from <- 'toFit'

both.df <- rbind(sim.df,toFit.df)

ggplot(both.df, aes(length, fill = from)) + geom_density(alpha = 0.2)

Using the exponential pdf, find the 5th and 95th percentiles using the cumulative distribution function (CDF).

quantile(sim, probs=c(0.05, 0.95))
##         5%        95% 
##   61.46133 4445.34043

Also generate a 95% confidence interval from the empirical data, assuming normality.

mean(toFit)
## [1] 1515.464
normal<-rnorm(length(toFit),mean(toFit),sd(toFit))
hist(normal)

quantile(normal, probs=c(0.05, 0.95))
##        5%       95% 
##  703.0199 2359.0967
normal.df <- data.frame(length = normal)

normal.df$from <- 'normal'

all.df <- rbind(both.df,normal.df)

ggplot(all.df, aes(length, fill = from)) + geom_density(alpha = 0.2)

Finally, provide the empirical 5th percentile and 95th percentile of the data. Discuss.

quantile(toFit, probs=c(0.05, 0.95))
##     5%    95% 
##  848.0 2466.1

From this analysis it appears the data select was not very right skew. The exponential simulation does not match our data very well, rather, our selected empirical data matches the normal distribution a lot better. This can be seen in the final density plot, but also on the confidence interval where the limits are much closer than for the exponential approximation.

Modeling

Modeling. Build some type of multiple regression model and submit your model to the competition board. Provide your complete model summary and results with analysis. Report your Kaggle.com user name and score.

We start by selecting numeric variables using the distribution plots done before

model_input<-dplyr::select(train, GrLivArea, BedroomAbvGr,BsmtFinSF1,BsmtUnfSF,GarageArea,GarageCars,GarageYrBlt,GrLivArea,LotFrontage,LotArea,Fireplaces,YearBuilt,OverallQual)

model_input$SalePrice<-log(train$SalePrice)

gather(model_input,"VARIABLE","VALUE",-SalePrice) %>%
ggplot(aes(x=VALUE,y=SalePrice)) + 
  geom_point() + facet_wrap(~VARIABLE,scale="free",ncol=4) + 
  labs(x="Variables", y="Sale Price") + 
theme(axis.text.x=element_text(angle=90))
## Warning: Removed 340 rows containing missing values (geom_point).

plotlm<-function(lm) {
  print(summary(lm))
  plot(fitted(lm),resid(lm))
  abline(0, 0)
  hist(resid(lm),breaks = 100)
  qqnorm(resid(lm))
  qqline(resid(lm))  
}

lm1<-lm(SalePrice ~ GrLivArea+BedroomAbvGr+BsmtFinSF1+BsmtUnfSF+GarageArea+GarageCars+GarageYrBlt+GrLivArea+LotFrontage+LotArea+Fireplaces+YearBuilt+OverallQual,data=model_input)

plotlm(lm1)
## 
## Call:
## lm(formula = SalePrice ~ GrLivArea + BedroomAbvGr + BsmtFinSF1 + 
##     BsmtUnfSF + GarageArea + GarageCars + GarageYrBlt + GrLivArea + 
##     LotFrontage + LotArea + Fireplaces + YearBuilt + OverallQual, 
##     data = model_input)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -2.21323 -0.07661  0.00965  0.09168  0.50115 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  5.494e+00  5.432e-01  10.114  < 2e-16 ***
## GrLivArea    1.732e-04  1.714e-05  10.100  < 2e-16 ***
## BedroomAbvGr 1.196e-02  8.499e-03   1.407 0.159678    
## BsmtFinSF1   9.664e-05  1.658e-05   5.828 7.34e-09 ***
## BsmtUnfSF    2.000e-05  1.625e-05   1.231 0.218654    
## GarageArea   2.844e-05  5.457e-05   0.521 0.602300    
## GarageCars   7.380e-02  1.549e-02   4.766 2.13e-06 ***
## GarageYrBlt  5.781e-04  3.963e-04   1.459 0.144885    
## LotFrontage  3.788e-04  2.567e-04   1.476 0.140341    
## LotArea      2.503e-06  7.082e-07   3.534 0.000426 ***
## Fireplaces   6.043e-02  9.666e-03   6.252 5.76e-10 ***
## YearBuilt    2.079e-03  3.194e-04   6.508 1.15e-10 ***
## OverallQual  1.152e-01  6.318e-03  18.230  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.1696 on 1114 degrees of freedom
##   (333 observations deleted due to missingness)
## Multiple R-squared:  0.8195, Adjusted R-squared:  0.8175 
## F-statistic: 421.5 on 12 and 1114 DF,  p-value: < 2.2e-16

We find several variables with high P values. We work our way back by eliminating these and assessing the resulting model.

lm2<-lm(SalePrice ~ GrLivArea+BsmtFinSF1+GarageCars+GrLivArea+LotArea+Fireplaces+YearBuilt+OverallQual+BedroomAbvGr,data=model_input)

plotlm(lm2)
## 
## Call:
## lm(formula = SalePrice ~ GrLivArea + BsmtFinSF1 + GarageCars + 
##     GrLivArea + LotArea + Fireplaces + YearBuilt + OverallQual + 
##     BedroomAbvGr, data = model_input)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -2.18616 -0.08001  0.01038  0.09589  0.50356 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  5.843e+00  3.715e-01  15.730  < 2e-16 ***
## GrLivArea    2.027e-04  1.409e-05  14.388  < 2e-16 ***
## BsmtFinSF1   9.292e-05  1.054e-05   8.814  < 2e-16 ***
## GarageCars   8.585e-02  7.958e-03  10.788  < 2e-16 ***
## LotArea      2.772e-06  4.698e-07   5.900 4.51e-09 ***
## Fireplaces   5.497e-02  8.035e-03   6.842 1.15e-11 ***
## YearBuilt    2.489e-03  1.952e-04  12.754  < 2e-16 ***
## OverallQual  1.110e-01  5.098e-03  21.781  < 2e-16 ***
## BedroomAbvGr 1.174e-02  6.805e-03   1.725   0.0848 .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.1668 on 1451 degrees of freedom
## Multiple R-squared:  0.8265, Adjusted R-squared:  0.8256 
## F-statistic: 864.2 on 8 and 1451 DF,  p-value: < 2.2e-16

correlationData<-dplyr::select(train,GrLivArea,BsmtFinSF1,GarageCars,GrLivArea,LotArea,Fireplaces,YearBuilt,OverallQual,BedroomAbvGr)
correlationMatrix<-round(cor(correlationData),4)
correlationMatrix
##              GrLivArea BsmtFinSF1 GarageCars LotArea Fireplaces YearBuilt
## GrLivArea       1.0000     0.2082     0.4672  0.2631     0.4617    0.1990
## BsmtFinSF1      0.2082     1.0000     0.2241  0.2141     0.2600    0.2495
## GarageCars      0.4672     0.2241     1.0000  0.1549     0.3008    0.5379
## LotArea         0.2631     0.2141     0.1549  1.0000     0.2714    0.0142
## Fireplaces      0.4617     0.2600     0.3008  0.2714     1.0000    0.1477
## YearBuilt       0.1990     0.2495     0.5379  0.0142     0.1477    1.0000
## OverallQual     0.5930     0.2397     0.6007  0.1058     0.3968    0.5723
## BedroomAbvGr    0.5213    -0.1074     0.0861  0.1197     0.1076   -0.0707
##              OverallQual BedroomAbvGr
## GrLivArea         0.5930       0.5213
## BsmtFinSF1        0.2397      -0.1074
## GarageCars        0.6007       0.0861
## LotArea           0.1058       0.1197
## Fireplaces        0.3968       0.1076
## YearBuilt         0.5723      -0.0707
## OverallQual       1.0000       0.1017
## BedroomAbvGr      0.1017       1.0000
corrplot(correlationMatrix,method ="color",type="upper")

lm3<-lm(SalePrice ~ BsmtFinSF1+GarageCars+GrLivArea+LotArea+Fireplaces+YearBuilt+OverallQual,data=model_input)

plotlm(lm3)
## 
## Call:
## lm(formula = SalePrice ~ BsmtFinSF1 + GarageCars + GrLivArea + 
##     LotArea + Fireplaces + YearBuilt + OverallQual, data = model_input)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -2.21416 -0.07986  0.01151  0.09647  0.50045 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 5.864e+00  3.715e-01  15.784  < 2e-16 ***
## BsmtFinSF1  8.922e-05  1.033e-05   8.638  < 2e-16 ***
## GarageCars  8.497e-02  7.947e-03  10.692  < 2e-16 ***
## GrLivArea   2.167e-04  1.152e-05  18.821  < 2e-16 ***
## LotArea     2.787e-06  4.700e-07   5.929 3.80e-09 ***
## Fireplaces  5.362e-02  8.002e-03   6.701 2.95e-11 ***
## YearBuilt   2.492e-03  1.953e-04  12.759  < 2e-16 ***
## OverallQual 1.094e-01  5.008e-03  21.838  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.1669 on 1452 degrees of freedom
## Multiple R-squared:  0.8262, Adjusted R-squared:  0.8253 
## F-statistic: 985.9 on 7 and 1452 DF,  p-value: < 2.2e-16

correlationData<-dplyr::select(train,BsmtFinSF1,GarageCars,GrLivArea,LotArea,Fireplaces,YearBuilt,OverallQual)
correlationMatrix<-round(cor(correlationData),4)
correlationMatrix
##             BsmtFinSF1 GarageCars GrLivArea LotArea Fireplaces YearBuilt
## BsmtFinSF1      1.0000     0.2241    0.2082  0.2141     0.2600    0.2495
## GarageCars      0.2241     1.0000    0.4672  0.1549     0.3008    0.5379
## GrLivArea       0.2082     0.4672    1.0000  0.2631     0.4617    0.1990
## LotArea         0.2141     0.1549    0.2631  1.0000     0.2714    0.0142
## Fireplaces      0.2600     0.3008    0.4617  0.2714     1.0000    0.1477
## YearBuilt       0.2495     0.5379    0.1990  0.0142     0.1477    1.0000
## OverallQual     0.2397     0.6007    0.5930  0.1058     0.3968    0.5723
##             OverallQual
## BsmtFinSF1       0.2397
## GarageCars       0.6007
## GrLivArea        0.5930
## LotArea          0.1058
## Fireplaces       0.3968
## YearBuilt        0.5723
## OverallQual      1.0000
corrplot(correlationMatrix,method ="color",type="upper")

Model 2 and 3 have very similar results, we decide to submit model 2. Not always a model with more features is best, but in this case we do decide on this one.

test<-read.csv("data/test.csv",header=TRUE,stringsAsFactors=FALSE)
test2<-dplyr::select(test,GrLivArea,BsmtFinSF1,GarageCars,GrLivArea,LotArea,Fireplaces,YearBuilt,OverallQual,BedroomAbvGr)
predictions<-predict(lm2,test)
test2$SalePrice <- round(exp(predictions))
test2$Id<-test$Id
test2$SalePrice[is.na(test2$SalePrice)] <- median(test2$SalePrice, na.rm = TRUE)

tblTable<-tbl_df(test2)
tblTable %>% kable() %>% kable_styling() %>% scroll_box(width = "800px", height = "400px")
GrLivArea BsmtFinSF1 GarageCars LotArea Fireplaces YearBuilt OverallQual BedroomAbvGr SalePrice Id
896 468 1 11622 0 1961 5 2 114285 1461
1329 923 1 14267 0 1958 6 3 147141 1462
1629 791 2 13830 1 1997 5 3 175140 1463
1604 602 2 9978 1 1998 6 3 189770 1464
1280 263 2 5005 0 1992 8 2 195447 1465
1655 0 2 10000 1 1993 6 3 179079 1466
1187 935 2 7980 0 1992 6 3 166797 1467
1465 0 2 8402 1 1998 6 3 173700 1468
1341 637 2 10176 1 1990 7 2 195526 1469
882 804 2 8400 0 1970 4 2 116205 1470
1337 1051 2 5858 1 1999 7 2 205159 1471
987 156 1 1680 0 1971 6 2 126031 1472
1092 300 1 1680 0 1971 5 3 118142 1473
1456 514 2 2280 1 1975 6 3 168855 1474
836 0 1 2280 0 1975 7 2 136194 1475
2334 0 3 12858 1 2009 9 3 327733 1476
1544 0 3 12883 0 2009 8 3 236538 1477
1698 110 3 11520 1 2005 9 3 287099 1478
1822 28 3 14122 1 2005 8 3 263358 1479
2696 1373 3 14300 2 2003 9 3 418719 1480
2250 578 3 13650 1 2002 8 3 299648 1481
1370 24 2 7132 1 2006 8 2 214228 1482
1324 0 2 18494 0 2005 6 3 167197 1483
1145 16 2 3203 0 2006 7 2 171363 1484
1374 326 2 13300 1 2004 7 3 202093 1485
1733 0 2 8577 1 2004 7 3 208121 1486
2475 0 3 17433 1 1998 8 4 300900 1487
1595 0 3 8987 1 2005 8 2 244429 1488
1218 0 2 9215 0 2009 7 2 177901 1489
1468 1414 2 10440 1 2005 6 2 200470 1490
1659 0 2 11920 0 2004 7 3 195862 1491
1012 0 1 9800 0 1920 5 2 100646 1492
1494 126 2 15410 2 1974 6 3 179392 1493
2349 250 3 13143 1 1993 8 4 292987 1494
2225 1129 3 11134 1 1992 8 4 307541 1495
1488 1298 2 4835 1 2004 7 2 218537 1496
1680 0 2 3515 0 2004 7 2 189926 1497
1200 280 2 3215 0 2004 7 2 176711 1498
1200 368 2 2544 0 2004 7 2 177831 1499
1236 376 2 2544 0 2005 6 2 160826 1500
1512 466 2 2980 0 2000 6 2 169592 1501
1080 244 2 2403 0 2003 7 2 171076 1502
1418 1032 3 12853 1 2010 8 1 262530 1503
1848 484 2 7379 1 2000 8 3 245715 1504
1492 833 2 8000 1 2002 7 3 212744 1505
1829 506 2 10456 0 1967 6 4 174762 1506
2495 1137 2 10791 1 1993 6 4 239293 1507
1891 687 2 18837 1 1978 6 3 197683 1508
1645 329 2 9600 0 1971 6 4 166878 1509
1232 698 2 9600 0 1966 5 3 138740 1510
1209 1059 2 9900 0 1966 5 3 142925 1511
1510 1010 2 9680 0 1967 5 3 151511 1512
1775 0 2 10600 0 1964 6 3 161848 1513
1728 1500 0 13260 0 1962 5 6 144225 1514
2461 670 2 9724 2 1952 5 3 191441 1515
1556 300 2 17360 1 1949 6 3 165093 1516
1128 944 1 11380 1 1966 6 2 149567 1517
1604 0 2 8267 0 1958 5 4 138557 1518
1480 1188 2 8197 0 2003 7 3 208243 1519
1143 856 1 8050 0 1959 5 3 124173 1520
1206 936 1 10725 0 1959 5 3 127650 1521
1580 734 2 10032 2 1959 6 3 183324 1522
1337 0 1 8382 0 1956 4 3 106046 1523
1064 339 1 10950 0 1952 5 2 114034 1524
972 648 1 10895 0 1955 5 3 117403 1525
988 532 1 13587 0 1958 5 2 116894 1526
985 0 2 7898 0 1920 4 2 97093 1527
1224 481 1 8064 0 1948 6 3 132548 1528
1175 588 2 7635 0 1960 5 3 133013 1529
1395 717 2 9760 1 1963 6 2 166445 1530
1844 48 1 4800 2 1900 4 3 113491 1531
936 579 0 4485 1 1920 5 2 99923 1532
1347 274 2 5805 0 1957 5 3 132105 1533
1251 0 1 6900 0 1938 6 3 123916 1534
1633 780 1 11851 1 1948 5 3 141467 1535
1245 176 1 8239 0 1920 5 3 108052 1536
832 0 2 9656 1 1923 2 2 80631 1537
1566 0 1 9600 0 1900 8 3 151176 1538
2268 0 2 9000 0 1890 8 3 184943 1539
2256 0 0 9045 0 1910 5 4 118443 1540
1470 283 2 10560 0 1922 6 2 139036 1541
1612 788 1 5830 0 1950 5 3 131877 1542
2068 474 1 7793 1 1922 7 3 173805 1543
765 188 1 5000 0 1925 4 2 87104 1544
1132 452 1 6000 0 1939 6 2 124679 1545
1196 264 2 6000 2 1940 6 3 153127 1546
1453 360 1 6360 2 1942 5 3 134474 1547
1416 300 1 6000 0 1948 6 3 134738 1548
1040 276 2 6240 0 1936 5 2 116599 1549
1536 448 2 6240 1 1930 5 4 139600 1550
1068 960 1 6120 1 1923 6 2 131033 1551
1962 0 2 8094 1 1915 4 4 126503 1552
1560 0 0 12900 0 1912 6 3 115389 1553
1324 0 1 3068 0 1920 6 3 118983 1554
1675 766 1 15263 2 1959 5 3 156193 1555
1224 0 1 10632 0 1917 5 3 105759 1556
1392 1026 0 9900 0 1915 5 3 109695 1557
919 368 1 6001 0 1940 6 3 120180 1558
1884 73 0 6449 0 1907 4 4 97524 1559
1680 736 2 6048 1 1910 5 2 137132 1560
1832 704 0 10773 0 1967 4 4 120244 1561
892 240 1 7800 0 1966 5 3 113328 1562
864 775 1 7832 0 1968 5 2 117643 1563
1373 1319 2 7424 2 1978 5 3 172893 1564
1440 267 2 11227 2 1968 5 4 158521 1565
1483 1092 2 20062 2 1977 7 1 218118 1566
756 0 2 9259 0 1927 4 2 94675 1567
1981 964 2 17082 1 1978 6 4 207996 1568
1610 288 1 18600 1 1938 3 4 108327 1569
1074 104 1 11479 1 1950 6 3 133077 1570
1531 192 1 9350 1 1947 4 3 116314 1571
1172 954 1 9525 0 1954 5 3 124998 1572
1508 1346 2 17485 2 2009 7 1 241343 1573
1298 0 2 11200 0 1964 5 3 131707 1574
1433 1433 2 11980 2 1987 7 1 223425 1575
1802 860 4 12361 1 1993 6 3 238837 1576
1222 24 2 7360 0 2010 7 2 177970 1577
1445 0 2 14235 0 1900 6 3 130390 1578
965 870 2 11105 0 1996 5 2 142818 1579
1692 353 2 9337 1 1997 7 3 210039 1580
1026 198 1 15240 0 1977 5 3 121699 1581
876 480 2 7480 0 1972 5 3 127643 1582
1978 1682 3 10389 1 2003 8 3 312156 1583
2098 0 2 9375 1 1997 7 4 223326 1584
848 672 2 4435 0 2003 6 1 151063 1585
640 0 1 8777 0 1945 3 2 79322 1586
992 0 1 8842 0 1954 5 3 110087 1587
1196 1070 1 10044 0 1968 5 3 131661 1588
1120 0 2 11792 0 1948 4 2 108151 1589
1096 528 1 6305 1 1975 6 3 145864 1590
960 0 0 6410 0 1958 4 3 90117 1591
1296 133 1 4853 1 1924 5 2 113609 1592
856 238 2 7890 1 1939 6 2 133750 1593
2650 0 0 7200 0 1967 4 6 134761 1594
1666 0 0 9839 1 1931 5 3 115878 1595
2133 426 1 10452 2 1941 7 4 197952 1596
2177 375 2 15600 0 1950 5 5 163111 1597
1652 343 2 19645 0 1994 7 3 201217 1598
1034 747 2 3907 1 1989 8 1 200963 1599
1191 76 2 3907 1 1989 8 2 197223 1600
540 480 1 8154 0 1941 2 1 71049 1601
1107 308 1 9140 0 1921 6 2 118060 1602
952 0 1 8712 0 1896 4 3 84554 1603
1646 1373 2 3811 1 2004 8 2 253195 1604
1916 615 3 11050 1 1998 8 3 276214 1605
1285 679 2 9620 1 1977 6 3 169870 1606
2048 0 2 12760 0 1976 6 5 181513 1607
1346 78 3 11896 1 2008 7 3 215276 1608
1214 0 2 9803 0 2009 7 2 178046 1609
1444 0 2 9802 0 2006 5 3 150032 1610
1264 42 2 15300 1 1965 5 2 139029 1611
1430 0 2 10114 0 2004 5 3 148993 1612
1344 0 2 11875 1 1999 5 3 153526 1613
945 915 1 2394 1 1973 5 2 127667 1614
1092 176 0 1476 0 1970 4 3 95623 1615
1092 0 0 1900 0 1970 4 3 94183 1616
1092 294 1 1890 0 1972 4 3 105991 1617
874 469 1 6953 0 1971 5 3 116514 1618
833 207 2 12887 0 1984 5 2 127520 1619
2432 0 2 7700 0 1985 5 4 174997 1620
1274 458 2 10475 0 1991 5 3 145980 1621
1479 476 1 10544 0 1969 5 5 135606 1622
1803 1341 2 9892 2 1994 8 3 276355 1623
1797 944 2 12961 1 1993 6 3 202864 1624
882 564 1 13008 0 1956 6 2 127385 1625
1434 844 2 10200 1 1974 6 4 178832 1626
1608 847 2 10179 1 1997 6 3 193922 1627
2283 850 3 11792 1 2003 8 4 312201 1628
1628 284 2 8400 1 1996 7 3 204961 1629
2522 1965 2 7296 1 2004 8 1 318834 1630
1478 341 2 7380 0 1998 8 2 209389 1631
1734 741 2 8013 0 1995 8 2 227590 1632
1382 189 2 8923 1 1998 7 3 194523 1633
1636 476 2 7500 1 1998 6 3 187489 1634
1516 600 2 8803 1 1994 6 3 183933 1635
1190 0 2 7250 1 1993 6 3 161732 1636
1934 400 2 11900 1 1977 5 3 170026 1637
2050 0 2 13250 1 1978 7 4 213225 1638
1671 363 2 10928 1 1978 6 3 179475 1639
2673 602 2 12388 1 1980 7 4 256511 1640
1707 832 2 11088 1 1978 6 3 188926 1641
1884 622 2 7000 1 2003 7 3 225804 1642
1874 0 2 7500 1 2000 8 3 236229 1643
1811 225 2 8470 1 2002 8 3 239992 1644
1621 1333 2 9373 2 1975 5 3 181669 1645
1116 888 2 10140 1 1974 6 3 166363 1646
1193 636 2 11050 1 1975 7 3 185382 1647
1180 0 2 7830 0 1970 5 2 127807 1648
1050 500 1 8510 0 1971 5 3 121618 1649
864 726 2 7038 0 1970 4 3 115864 1650
864 240 2 9000 0 1971 4 3 111630 1651
987 254 1 1680 0 1973 6 2 127818 1652
987 110 1 1680 0 1972 6 2 125806 1653
1548 306 2 2308 1 1976 6 3 169175 1654
1055 435 2 2280 1 1975 7 2 170668 1655
1456 389 2 2349 1 1977 6 3 167771 1656
1548 320 2 2364 1 1978 6 3 170267 1657
1456 279 2 2364 1 1978 6 3 166485 1658
836 536 1 2104 0 1976 7 2 143436 1659
1120 644 2 10710 1 1966 5 3 143012 1660
2772 1360 3 14257 3 2007 9 4 458493 1661
2690 986 3 12350 1 2009 9 3 385515 1662
2020 1232 3 12350 1 2008 9 3 343480 1663
2674 2288 3 13693 2 2007 10 2 505397 1664
1736 0 3 11578 1 2008 9 3 288570 1665
1782 1531 3 16870 2 2004 8 3 318993 1666
2520 1230 3 23303 1 2007 8 5 358025 1667
1743 1015 3 10367 1 2008 9 3 316498 1668
1531 1037 3 10872 1 2006 9 2 299187 1669
1808 1142 3 13514 1 2008 9 3 327346 1670
1760 1262 2 12878 1 2003 7 3 237529 1671
2452 1972 3 15274 1 2003 9 3 399864 1672
2400 0 3 13262 1 2003 8 4 296622 1673
1606 0 3 9658 1 2006 8 3 248947 1674
1358 836 2 6904 1 2005 6 2 183985 1675
1306 881 2 5122 1 2005 6 1 179795 1676
1358 876 2 10307 1 2007 7 2 209354 1677
2492 2146 3 14836 1 2004 10 2 453041 1678
2200 1557 3 15262 1 2003 8 3 327144 1679
1884 800 2 7390 1 2008 9 2 287172 1680
1456 0 2 6472 1 2008 9 2 243822 1681
1712 1196 3 16770 1 2002 8 3 287040 1682
1405 0 2 3480 1 2003 7 2 189289 1683
1456 0 2 10928 1 2005 7 3 198536 1684
1490 0 2 8918 1 2005 6 3 177905 1685
1220 16 2 3182 1 2005 7 2 183352 1686
1374 0 2 9434 1 2004 7 3 193973 1687
1630 0 2 7984 1 2004 7 3 203486 1688
1594 0 2 10125 1 2004 7 3 203208 1689
1489 652 2 8965 1 2003 7 3 210151 1690
1342 494 2 8174 1 2003 7 3 200568 1691
2004 651 3 12891 1 2002 8 4 289790 1692
1374 241 2 9734 0 2004 7 3 187912 1693
1514 683 2 8433 1 2000 6 3 187877 1694
1430 0 2 7750 1 1999 7 3 192859 1695
2312 913 3 15896 1 1999 7 4 283088 1696
1430 0 2 7848 1 1999 7 3 192911 1697
2687 1173 3 12720 2 2000 8 4 367101 1698
2063 236 3 10750 2 1994 8 3 287132 1699
2061 816 2 9085 1 1995 7 3 234966 1700
2232 624 2 11692 1 1993 8 3 267616 1701
1696 0 3 11194 0 2008 8 3 242197 1702
1658 0 3 10206 1 2008 8 3 253226 1703
1702 1294 3 10130 1 2007 8 3 287361 1704
1432 379 2 9139 1 2006 8 3 228126 1705
2490 2158 3 11128 2 2005 9 2 425316 1706
1436 0 2 7993 0 2008 7 3 187032 1707
1402 0 2 8640 0 2008 7 3 186080 1708
1530 0 3 12606 1 2007 9 3 276868 1709
1448 24 2 7500 1 2006 8 2 217865 1710
1795 682 3 10603 1 2006 8 3 276316 1711
1836 0 2 8125 1 2008 8 3 239546 1712
1662 1430 3 10625 1 2006 7 3 258038 1713
1553 771 2 8736 0 2003 7 3 203619 1714
1653 410 2 8127 0 2003 7 3 200595 1715
1218 0 2 9605 0 2007 7 3 179301 1716
1141 54 2 7500 0 2006 7 3 175941 1717
1158 0 0 7500 0 2004 6 3 131743 1718
1812 0 2 10628 0 2004 7 3 201310 1719
1512 516 3 10141 0 2004 8 3 241657 1720
1114 0 2 13072 0 2004 7 3 175937 1721
1114 0 0 13072 0 2004 5 3 118669 1722
1114 836 2 12450 0 2003 5 3 151640 1723
1450 0 3 7328 0 2008 7 2 201620 1724
2122 637 2 11492 1 1996 7 4 238906 1725
1730 52 2 7703 0 1992 6 3 171406 1726
1332 0 2 7175 0 1990 6 2 154523 1727
1540 36 2 9109 0 1994 7 3 185666 1728
1400 331 2 10274 0 1986 6 3 163245 1729
1882 0 2 8250 2 1981 6 4 193607 1730
980 68 2 9750 0 1962 5 3 123154 1731
864 660 2 8499 0 1961 5 3 126340 1732
864 864 1 9079 0 1961 5 2 116974 1733
1020 544 1 9316 0 1965 5 3 119844 1734
912 624 1 7791 0 1963 5 3 117041 1735
912 140 1 7150 0 1962 5 3 111418 1736
2014 1733 3 15676 2 1980 8 2 316139 1737
1755 601 2 11949 1 1991 7 3 216029 1738
3005 0 3 2880 1 2004 7 3 288886 1739
1726 0 2 3830 1 2008 6 2 183226 1740
1256 962 2 4217 1 2008 6 1 180218 1741
1512 507 2 2998 0 2000 6 2 170248 1742
1452 549 2 3768 0 1999 7 3 190837 1743
1694 1252 2 14694 1 1977 8 2 243619 1744
1740 121 2 15417 0 1981 7 2 189764 1745
2499 0 2 9600 1 1976 8 4 257062 1746
2067 560 2 12732 2 1974 7 3 232683 1747
2640 0 2 10400 1 1967 6 5 210054 1748
1336 553 2 9600 1 1969 5 3 148807 1749
1216 955 1 9000 0 1969 6 3 146092 1750
2288 432 2 13774 2 1977 7 4 245838 1751
864 648 1 7130 0 1967 5 2 115748 1752
1568 0 2 9600 0 1967 5 3 139539 1753
2061 698 2 9600 1 1974 7 4 223490 1754
1320 962 2 16500 1 1971 6 3 176366 1755
894 734 2 7436 1 1960 4 2 118948 1756
864 403 1 8125 0 1959 5 3 112531 1757
1362 775 3 9450 1 1957 4 3 144470 1758
1728 625 2 13495 1 1956 5 3 158736 1759
1313 310 2 9350 1 1961 5 3 141855 1760
1292 998 2 10500 2 1964 5 3 160791 1761
2140 388 2 8970 1 1965 5 4 172490 1762
1576 568 2 11475 1 1961 6 4 174297 1763
960 100 1 9768 0 1955 5 2 109661 1764
1691 1173 2 9900 0 1967 6 2 176340 1765
1453 1312 2 10573 1 1961 6 3 179599 1766
1567 1387 2 14695 2 1966 6 2 197930 1767
1144 856 1 8760 0 1956 5 3 123517 1768
1329 544 2 12285 2 1960 7 3 192963 1769
988 708 1 9240 0 1959 6 3 133065 1770
1202 435 1 8750 0 1956 5 3 120179 1771
1382 172 1 8750 0 1955 5 3 121334 1772
1200 155 1 10400 2 1956 4 3 117453 1773
1866 0 2 9482 0 1958 5 4 146608 1774
1062 490 1 8128 0 1954 6 3 130328 1775
1112 308 2 13070 0 1951 5 2 125535 1776
793 700 1 8480 0 1945 5 2 108944 1777
1031 931 1 7626 0 1952 5 2 118582 1778
1210 0 1 9533 0 1953 5 2 113653 1779
1527 699 2 11419 1 1948 7 3 186754 1780
1200 390 1 9600 0 1950 5 3 118134 1781
792 0 1 5470 0 1958 3 2 83723 1782
1352 0 2 10800 0 1939 5 4 126460 1783
1039 0 1 8146 0 1900 4 2 85770 1784
1078 0 1 10230 0 1925 5 3 104623 1785
2377 0 2 10410 1 1915 4 3 136877 1786
1690 0 2 7200 0 1910 7 4 155767 1787
599 0 0 5400 0 1940 2 2 63212 1788
846 0 2 10800 0 1920 5 2 106334 1789
725 0 1 10800 0 1890 3 1 69945 1790
2544 0 3 9671 0 1969 6 6 215611 1791
1380 384 1 10143 0 1963 6 3 141551 1792
1040 872 2 11500 1 1967 6 3 161357 1793
951 745 2 8010 0 1958 6 2 141882 1794
1105 546 1 10454 0 1957 6 3 134007 1795
1142 0 1 9000 1 1958 6 2 133801 1796
1133 621 2 8064 0 1950 6 3 144364 1797
1041 0 1 7350 0 1958 5 3 111835 1798
732 630 1 7200 0 1952 5 2 108401 1799
1183 433 1 8000 0 1959 5 3 120342 1800
1461 0 1 10800 0 1949 4 4 108855 1801
1495 120 2 8064 0 1948 6 3 147553 1802
1806 0 2 7570 0 1964 6 4 163413 1803
941 941 2 8604 0 1978 5 2 135852 1804
1045 826 1 7936 1 1963 6 3 144702 1805
1378 0 1 4080 0 1935 6 3 125220 1806
1944 633 2 10307 0 1910 6 4 156999 1807
1306 0 2 15660 0 1910 5 3 116763 1808
1464 0 0 9900 0 1910 5 3 99934 1809
1558 421 2 6406 1 1939 5 3 141438 1810
1701 0 0 7627 0 1920 4 4 96722 1811
1447 0 0 10134 0 1910 5 3 99655 1812
1328 384 1 6000 0 1950 5 3 119969 1813
861 0 2 7404 0 1920 4 2 94554 1814
612 0 1 5925 0 1940 2 1 68354 1815
792 0 1 8520 0 1923 5 2 96634 1816
1510 0 2 9600 0 1910 4 3 107089 1817
2007 0 1 8400 0 1900 6 3 131951 1818
1288 0 1 3600 1 1917 6 3 124047 1819
816 0 0 3300 1 1910 4 2 80403 1820
1480 0 1 5400 0 1920 6 3 123602 1821
1521 0 3 9720 0 1910 6 4 147805 1822
797 0 0 9392 0 1900 3 2 67301 1823
1432 0 1 6615 1 1923 6 3 130731 1824
1654 0 1 4960 1 1930 5 3 123958 1825
1142 220 1 6000 0 1924 5 3 106652 1826
995 0 1 6120 0 1925 5 2 100525 1827
1582 273 1 6120 1 1938 5 3 128232 1828
1072 134 5 8635 0 1925 5 2 146766 1829
1768 0 2 8094 0 1915 6 3 142070 1830
1944 0 1 9928 0 1915 7 3 151756 1831
2128 0 0 3000 0 1922 5 4 116932 1832
1930 522 1 6876 0 1927 6 4 146943 1833
1427 0 1 5775 0 1915 6 3 120894 1834
1864 169 0 5852 0 1902 7 6 138029 1835
1666 0 1 5160 0 1927 6 3 130521 1836
892 749 0 5160 0 1923 4 1 85018 1837
1403 276 1 10320 0 1915 6 3 124998 1838
704 0 1 4280 0 1946 4 2 88903 1839
1200 1200 0 10800 0 1987 5 3 128594 1840
1152 1152 1 10547 0 1978 5 2 133417 1841
1112 0 1 9780 0 1934 5 4 108869 1842
1052 527 1 11625 1 1967 5 3 128696 1843
1034 456 2 8014 1 1978 6 3 157822 1844
1774 0 1 15400 1 1961 5 4 142895 1845
1138 588 2 15312 1 1960 6 3 159213 1846
2071 0 1 15584 1 1956 5 4 149961 1847
660 0 0 9000 0 1947 2 2 65777 1848
1383 0 2 15635 0 1954 4 2 117030 1849
1073 257 1 9571 0 1956 5 2 114073 1850
1639 342 1 9350 1 1946 6 3 150163 1851
1089 173 1 7440 1 1954 5 3 120073 1852
1049 552 1 4235 0 1984 5 2 123259 1853
1061 460 2 10778 0 1990 7 1 170280 1854
1338 70 2 19255 1 1983 6 2 167184 1855
1879 474 2 10560 1 1993 7 3 219176 1856
2016 0 2 26400 1 1880 5 4 137811 1857
2228 0 2 7018 0 1979 5 6 169028 1858
1535 0 2 7018 0 1979 5 4 143467 1859
1229 1094 2 7040 2 1979 5 2 162758 1860
1513 0 2 7007 0 1979 5 4 142824 1861
2787 820 4 11855 2 2000 7 6 361040 1862
2787 820 4 7939 2 2000 7 6 357142 1863
2787 820 4 7976 2 2000 7 6 357178 1864
1680 1021 3 10933 1 2009 9 1 306644 1865
1720 1104 3 10816 1 2008 9 3 318037 1866
1468 0 3 9178 1 2008 8 3 242964 1867
1838 1359 2 11422 2 2007 8 3 289181 1868
1290 902 2 6762 1 2007 7 2 204963 1869
1254 872 3 10324 0 2008 8 2 236756 1870
1498 24 3 11645 1 2005 8 3 244838 1871
1422 0 2 11646 1 2005 6 3 176801 1872
1759 800 2 16698 1 1992 7 3 223714 1873
990 755 1 9757 0 1994 5 3 130729 1874
1463 950 2 14753 0 1998 7 3 204154 1875
1772 606 2 8750 1 1998 6 3 195750 1876
1444 1259 2 10739 0 2002 7 3 209048 1877
1492 24 2 11166 1 2001 7 3 198582 1878
907 625 1 16269 0 1978 5 3 124269 1879
914 710 2 6950 0 1979 5 2 131964 1880
1611 1234 3 11664 0 2002 7 3 235688 1881
2184 0 2 12334 1 2003 8 4 259887 1882
1725 0 2 8749 0 2002 7 3 195786 1883
1870 0 2 11250 0 2001 7 3 202524 1884
1513 1246 2 15750 1 1999 8 2 248650 1885
1828 1360 2 12782 1 2002 8 3 270824 1886
1417 1111 2 8750 1 1997 7 3 212800 1887
1602 1478 3 10200 1 2007 8 3 286506 1888
1396 0 2 11069 1 2007 6 3 176467 1889
1149 399 1 10682 0 1960 4 3 107680 1890
1072 547 2 3675 0 2005 6 2 158555 1891
876 332 1 6410 0 1959 4 3 99810 1892
1368 1078 1 11767 0 1950 5 3 131081 1893
1678 0 0 10926 0 1959 5 6 122476 1894
1560 546 1 11767 1 1956 5 2 137479 1895
1298 626 1 8212 2 1941 5 3 133929 1896
1268 832 1 6300 2 1938 5 3 133968 1897
1242 0 1 5707 1 1935 6 3 129280 1898
1232 0 2 8574 1 1916 6 3 135160 1899
1228 0 1 7155 1 1918 7 3 138640 1900
1567 728 2 13680 2 1940 5 2 155726 1901
1273 793 1 14680 0 1960 5 2 127907 1902
2480 246 2 8145 2 1940 7 5 228228 1903
1112 154 1 9100 1 1954 5 2 119565 1904
1561 65 2 13339 1 1960 6 3 164338 1905
1523 312 1 15600 1 1949 5 3 134178 1906
1906 784 2 17500 2 1954 6 3 198391 1907
1032 0 2 1733 1 1980 6 2 147603 1908
1229 471 2 1488 1 1980 6 2 160380 1909
1229 0 2 1612 1 1980 6 2 153565 1910
1982 454 2 13607 1 1986 6 3 198120 1911
2365 803 2 17597 2 1971 7 3 254343 1912
2168 0 2 8660 0 1900 5 5 136192 1913
572 0 1 10200 0 1925 4 2 83507 1914
1648 1476 2 3843 1 2007 8 2 257673 1915
810 0 1 21780 0 1910 2 1 69000 1916
2052 445 3 10125 1 2000 8 3 280160 1917
926 767 1 9750 1 1977 6 2 144490 1918
1287 841 2 9360 2 1977 6 2 180009 1919
1595 55 2 11070 0 1991 5 2 148563 1920
2036 1758 3 13438 1 2008 9 3 362950 1921
1641 1115 3 14463 0 2008 9 3 299559 1922
2237 462 2 9839 1 1980 6 3 203554 1923
1479 904 2 14419 1 1987 7 3 209455 1924
2014 0 2 9157 0 2003 7 3 208352 1925
1978 1640 3 12633 1 2007 9 2 349005 1926
1008 532 1 12518 0 1968 5 3 121387 1927
1404 594 2 13383 1 1969 5 3 153045 1928
796 720 1 7689 0 1972 5 2 116549 1929
1091 114 1 7706 0 1993 6 2 137713 1930
883 718 2 7669 1 1992 5 2 143497 1931
1287 330 2 10429 0 1992 5 3 144977 1932
1632 496 2 10457 1 1969 5 4 159409 1933
1604 706 2 8702 1 1997 6 3 190461 1934
1470 476 2 8139 1 1995 6 3 180255 1935
1604 851 2 9535 0 1998 6 3 183598 1936
1636 138 2 15038 1 1996 6 3 184607 1937
1384 450 2 14137 0 1996 5 3 152570 1938
1682 656 2 6264 1 1997 8 1 233334 1939
1280 0 2 5070 0 1992 8 2 190763 1940
1633 0 2 11184 1 1998 6 3 181108 1941
1709 504 2 14067 0 1991 6 3 180716 1942
1337 319 2 5950 1 1989 8 2 208966 1943
2500 16 3 13543 1 2005 8 5 308496 1944
1884 1337 3 15401 1 2004 9 2 332979 1945
1474 0 2 31220 2 1952 6 3 174665 1946
1710 1034 2 8118 1 2007 9 2 283180 1947
1488 0 2 47280 1 1950 6 3 172479 1948
1688 983 2 12680 1 1988 7 2 217054 1949
1260 747 2 10825 0 1983 7 3 183210 1950
2064 1206 2 18559 2 1978 7 3 253459 1951
1782 864 2 14450 1 1979 7 3 217541 1952
1211 890 2 13068 1 1976 6 3 171865 1953
2044 0 2 10400 1 1980 7 3 209867 1954
1308 280 2 9743 0 1969 5 3 136597 1955
2840 988 4 12511 2 1978 7 4 343410 1956
1444 0 2 10400 1 1976 6 2 162733 1957
2340 1023 3 14311 1 1996 8 4 317614 1958
1792 0 2 9000 0 1974 5 4 150093 1959
936 252 1 10295 0 1969 4 2 102711 1960
864 119 2 7560 0 1971 5 3 122854 1961
987 458 1 1680 0 1973 6 2 130264 1962
987 483 1 1890 0 1972 6 2 130318 1963
1302 350 1 1680 0 1972 5 3 124162 1964
1456 286 2 2308 0 1975 6 4 158333 1965
1055 378 2 2529 0 1977 7 2 161599 1966
1582 1012 3 12704 0 2007 8 3 260440 1967
2464 1728 3 13693 1 2007 8 4 356791 1968
1950 1375 3 14418 1 2007 9 2 340268 1969
2748 1420 3 13418 1 2006 9 4 409073 1970
2790 1082 4 12539 1 2005 10 4 484427 1971
2331 1249 3 12151 1 2005 9 3 363484 1972
2088 40 3 8899 1 2007 8 4 278882 1973
2332 856 3 10574 1 2004 8 4 315214 1974
2470 2257 3 12720 2 2003 10 1 471877 1975
1575 1149 3 10845 1 2003 8 2 270916 1976
2649 1075 3 16900 1 2001 8 4 346516 1977
2690 0 3 16451 1 2003 8 4 317375 1978
1866 372 3 10110 1 2008 9 2 301887 1979
1367 20 2 12304 1 2005 7 2 193808 1980
1800 1204 3 8232 1 2007 9 2 319350 1981
1342 846 2 6240 1 2006 8 2 229356 1982
1342 24 2 6240 1 2006 8 2 212490 1983
1626 0 2 2448 0 2003 7 2 186838 1984
1455 1073 3 3940 1 2003 7 2 230497 1985
1576 1087 3 3940 1 2004 7 2 237118 1986
1246 0 2 3710 1 2007 7 2 185237 1987
1515 0 2 9024 1 2004 6 3 178417 1988
1720 0 2 8010 1 2002 7 3 206218 1989
1986 0 2 8396 1 2003 7 4 220998 1990
1358 876 2 7301 1 2007 7 2 207617 1991
1892 544 2 8220 1 2000 7 3 223621 1992
1414 0 2 7750 1 2002 7 3 193675 1993
2322 870 2 12460 1 1999 7 4 256830 1994
1651 0 2 8390 1 1999 7 3 202053 1995
2199 0 2 9660 1 1997 8 3 251944 1996
2172 0 3 11000 1 2000 9 4 312169 1997
2006 1660 3 11675 1 1998 8 2 306899 1998
2125 851 2 10990 2 1996 7 4 257275 1999
2501 0 3 11929 1 1995 8 4 295693 2000
2197 228 3 10010 1 1993 7 4 251525 2001
1578 1096 3 13253 1 2006 7 3 247727 2002
1861 0 3 9801 1 2007 8 3 262912 2003
1874 729 3 9428 1 2007 8 3 281790 2004
1460 666 2 10037 1 2006 8 3 236212 2005
1372 24 2 8640 0 2007 8 3 206620 2006
1660 0 3 10625 1 2007 8 3 252992 2007
1218 902 2 7500 0 2007 7 2 191581 2008
1696 80 2 10110 0 2003 6 3 176584 2009
1663 0 2 12774 0 2003 7 3 195997 2010
1175 80 0 13072 0 2005 6 3 135595 2011
1162 0 2 9260 0 2007 7 3 177107 2012
1609 362 2 8453 0 1995 6 3 173792 2013
1680 602 2 8480 0 1993 6 3 179405 2014
1657 537 2 14565 0 1994 7 3 202218 2015
1677 472 2 8450 0 2001 6 3 180691 2016
1737 397 2 8285 0 1992 7 3 198377 2017
984 53 1 9100 1 1963 5 3 119422 2018
864 764 1 8100 1 1961 5 3 123551 2019
890 890 1 8450 0 1968 5 3 121153 2020
864 489 1 6360 0 1963 5 3 114010 2021
1430 800 2 19508 2 1974 6 3 190678 2022
1641 190 2 10759 1 1972 5 4 156517 2023
2683 704 2 9205 2 1990 6 4 249304 2024
2786 520 2 11025 1 1993 9 4 334664 2025
1245 24 2 3435 0 2004 7 1 172212 2026
1200 390 2 3180 0 2005 6 2 160146 2027
1392 0 2 3180 0 2007 7 2 180330 2028
1549 550 2 2280 0 1999 6 3 173471 2029
1638 1027 2 4765 1 2000 9 2 271542 2030
1310 1004 2 4538 1 2001 9 1 251040 2031
1419 964 2 4385 1 2001 9 2 258606 2032
1557 1141 2 4109 1 1999 9 2 268804 2033
1404 600 2 2160 0 1999 7 3 189042 2034
1789 681 2 10646 1 2001 7 3 223859 2035
1586 612 2 2645 0 1999 8 3 219723 2036
1607 813 2 2645 0 1999 8 3 224821 2037
2393 128 2 3951 1 1998 10 2 322932 2038
1239 560 2 11064 1 1995 8 1 213167 2039
2944 410 3 24572 1 1977 9 3 367517 2040
1671 1044 2 16280 1 1976 8 3 241111 2041
1812 0 2 7500 1 2002 7 3 209803 2042
1427 828 2 11104 0 1969 6 4 167106 2043
1740 301 2 11050 1 1968 6 4 178653 2044
1620 603 2 15387 1 1967 7 4 202301 2045
1625 0 2 9750 0 1965 5 4 142177 2046
1464 732 2 8814 0 1968 5 4 148017 2047
925 260 2 8125 0 1965 5 3 124349 2048
1728 0 2 11072 0 1965 5 6 149171 2049
1670 583 2 13355 0 1971 7 4 193908 2050
1014 0 1 7785 0 1956 5 2 109513 2051
1114 0 2 9900 0 1961 5 3 125488 2052
1118 528 1 11332 0 1960 5 3 121233 2053
906 120 1 4882 0 1937 4 2 91736 2054
1496 658 2 9600 0 1960 5 3 143663 2055
1337 32 1 9600 1 1950 5 3 124126 2056
1036 531 1 7584 0 1953 5 3 115996 2057
1988 575 2 14670 1 1966 6 4 193685 2058
1176 621 1 8856 2 1957 5 3 136146 2059
1440 1053 1 9840 0 1959 5 2 133408 2060
1570 958 2 13200 1 1958 6 3 177925 2061
1104 774 1 10425 0 1956 5 3 122152 2062
882 148 1 11556 0 1952 5 2 108152 2063
1152 500 2 9373 0 1953 5 3 129671 2064
950 624 2 12774 0 1953 5 2 125620 2065
1790 0 2 14250 2 1957 6 3 179888 2066
1764 0 1 8838 1 1957 5 4 138647 2067
1824 0 2 12436 0 1957 5 5 147922 2068
869 0 1 10122 0 1948 4 1 92799 2069
1159 0 1 7506 0 1925 5 3 105555 2070
672 0 1 5400 0 1940 4 2 87290 2071
1436 0 4 10836 1 1922 5 3 152883 2072
1044 744 2 10180 1 1968 5 3 142640 2073
1312 637 2 11355 1 1958 7 3 182211 2074
1081 697 1 12929 0 1960 6 3 137193 2075
876 432 2 7200 1 1951 5 2 125834 2076
1256 476 1 8000 0 1959 5 3 122625 2077
1027 520 1 8000 0 1962 5 3 118423 2078
1320 315 2 8064 0 1948 6 3 145014 2079
984 0 1 6390 0 1954 6 2 120561 2080
1278 673 1 7200 0 1954 6 4 139772 2081
1800 0 0 8513 0 1961 5 6 125328 2082
1588 370 2 7200 0 1955 5 3 139806 2083
825 0 1 7200 0 1954 5 2 104703 2084
1117 0 1 7590 0 1963 5 3 115070 2085
1133 96 1 9836 0 2008 6 3 146495 2086
1323 0 2 9184 0 1948 5 3 126499 2087
1360 0 1 4800 0 1910 5 2 103898 2088
672 0 1 4800 0 1940 5 2 97379 2089
1456 0 1 6000 0 1915 6 4 123119 2090
1594 0 0 11426 0 1910 4 3 92208 2091
1656 0 2 7628 0 1940 4 2 116831 2092
1740 360 1 7308 1 1920 5 2 126559 2093
1027 0 0 5400 1 1920 7 2 120743 2094
1436 590 2 10800 2 1940 6 3 167925 2095
899 0 1 6756 0 1910 5 2 95142 2096
1080 0 0 5914 0 1890 5 3 86994 2097
1499 445 3 9000 1 1946 5 3 156428 2098
407 0 1 7311 0 1946 2 1 66815 2099
1588 0 0 12205 0 1949 3 5 93177 2100
1627 0 2 9142 0 1900 5 4 120783 2101
1450 116 1 5350 0 1920 7 3 138749 2102
1017 0 1 9143 0 1900 5 2 95681 2103
2350 234 2 9600 0 1920 5 4 150409 2104
1540 0 0 6000 0 1905 5 3 99153 2105
1086 0 2 11340 0 1920 2 2 80126 2106
2495 0 2 10800 1 1890 7 5 188379 2107
984 200 1 9750 0 1959 5 2 112332 2108
1093 0 1 8516 0 1958 4 2 100285 2109
1143 406 1 7111 1 1928 5 2 114815 2110
1668 0 1 7425 0 1945 7 3 153556 2111
1738 175 1 7010 1 1935 5 3 130498 2112
1210 600 1 5000 0 1941 5 3 116537 2113
1290 0 1 5870 0 1900 6 3 113303 2114
1672 521 1 6000 1 1940 6 3 150028 2115
949 0 2 6000 1 1924 5 2 114330 2116
1497 201 1 6000 0 1937 6 3 132048 2117
1342 264 1 6000 1 1939 6 2 135073 2118
1013 0 1 5000 0 1926 6 3 114003 2119
1216 68 1 5520 1 1920 5 3 111512 2120
896 NA 1 5940 0 1946 4 2 160380 2121
1136 80 1 6240 0 1929 4 2 94224 2122
808 0 1 6120 0 1945 5 1 100540 2123
2009 300 2 6240 1 1939 7 4 193525 2124
1902 203 2 6120 0 1923 5 4 136658 2125
1716 0 2 9144 0 1915 6 4 142654 2126
1984 196 1 8094 0 1910 6 5 140260 2127
1609 0 1 4347 0 1910 6 3 123397 2128
768 0 2 6291 0 1930 6 1 117035 2129
1536 372 1 10266 0 1952 6 4 143720 2130
1969 0 2 6876 1 1938 6 4 166943 2131
1308 0 2 10320 0 1915 5 2 115176 2132
1040 0 2 7200 0 1925 6 2 123893 2133
1236 121 1 7006 1 1925 6 3 127832 2134
759 0 2 10320 0 1912 5 1 101085 2135
1344 0 0 10320 0 1915 3 3 79179 2136
1054 0 1 9488 0 1947 5 3 109750 2137
1075 784 2 11235 0 1963 5 3 135075 2138
1096 528 2 13014 1 1978 6 3 163137 2139
992 758 1 10265 0 1967 5 3 122488 2140
1034 450 2 7703 1 1978 6 3 157598 2141
1073 221 1 9981 0 1967 5 3 118362 2142
1126 104 2 7400 0 1984 5 2 132012 2143
1140 1300 2 12900 0 1920 5 3 129611 2144
960 634 1 9239 0 1963 5 3 118771 2145
1188 776 2 14175 1 1956 6 1 157790 2146
1721 988 2 10532 2 1960 5 3 173516 2147
1350 336 3 8375 0 1941 5 2 138570 2148
904 704 3 10200 0 1970 5 3 143185 2149
1524 599 2 20270 2 1979 7 3 216278 2150
1079 0 1 5190 1 1948 7 2 142476 2151
1518 1035 0 19550 2 1940 5 2 135811 2152
1509 870 1 9571 1 1956 5 3 141018 2153
864 864 0 9350 0 1975 5 2 111241 2154
1269 324 1 9360 0 1962 6 3 136992 2155
2814 779 2 9771 1 1995 6 4 247458 2156
1626 1271 2 9938 1 1994 7 3 224396 2157
2200 355 2 14171 1 1993 7 4 236426 2158
2037 0 2 10541 1 1996 7 3 218170 2159
1356 0 2 10616 1 2007 7 3 195354 2160
1615 0 3 9345 1 2007 8 3 249807 2161
2276 2085 3 11778 2 2008 9 3 413093 2162
1766 1153 3 11778 2 2008 9 3 341615 2163
1511 770 3 11454 1 1995 8 3 256500 2164
1643 262 2 11500 1 1966 6 2 169856 2165
990 722 2 9750 0 1994 5 3 142009 2166
1418 1308 2 8696 1 1997 7 3 216742 2167
1771 688 2 13142 0 1997 6 3 188475 2168
1652 527 2 8998 0 2000 7 3 201725 2169
1823 663 2 12192 0 2000 7 3 213377 2170
1174 781 2 12250 0 1978 5 3 143420 2171
1076 294 2 9216 1 1975 5 3 139735 2172
1558 88 2 14330 0 1975 5 2 143421 2173
2161 0 2 10400 1 2001 7 3 226437 2174
1947 1194 3 9720 1 2001 9 3 329009 2175
1786 1538 3 14860 1 2002 8 3 299198 2176
2327 0 2 10905 1 2003 7 4 238467 2177
1764 0 2 11690 1 1999 8 3 233138 2178
848 662 2 4426 0 2004 6 1 151295 2179
1838 1593 3 10126 0 1997 6 2 221937 2180
1445 24 2 9750 0 2004 7 3 186839 2181
1564 56 3 11058 0 2007 7 3 211513 2182
1361 24 2 9627 0 2007 7 3 184998 2183
1092 609 1 9825 0 1966 5 3 122821 2184
1033 456 2 12102 0 1976 5 3 134505 2185
1127 1033 2 6500 1 1976 6 3 168134 2186
1117 368 2 9638 1 1977 6 3 159514 2187
1398 288 2 7200 1 1976 6 3 166070 2188
3820 0 2 47007 2 1959 5 5 273707 2189
1152 0 0 6012 0 1955 4 2 91810 2190
1152 0 0 6845 0 1955 4 2 92022 2191
784 784 0 6931 0 1955 4 2 91883 2192
1053 0 0 12180 0 1938 5 2 98050 2193
1137 0 0 8050 0 1947 5 4 103227 2194
930 767 1 9520 0 1953 4 2 103191 2195
1204 0 1 7692 0 1954 4 3 102516 2196
1292 224 1 5142 0 1923 4 3 97948 2197
1424 0 1 7290 1 1921 7 2 143699 2198
1920 281 2 7804 2 1930 6 4 176172 2199
1316 379 1 8969 1 1926 6 2 132569 2200
1264 0 2 15564 0 1914 6 3 130630 2201
1512 406 1 7609 1 1925 8 3 173627 2202
1603 0 2 9650 1 1923 6 4 150477 2203
1938 606 1 11700 1 1937 5 4 145717 2204
1374 0 1 9260 0 1938 5 3 114439 2205
1091 500 1 7801 1 1951 6 2 135874 2206
1873 210 2 9670 2 1935 8 4 220311 2207
2161 435 2 12392 2 1950 7 3 220618 2208
1898 1116 2 26073 2 1956 5 3 188137 2209
1032 366 2 1879 1 1980 6 2 152771 2210
919 299 1 7000 0 1926 6 2 114292 2211
1090 0 1 6000 0 1940 6 3 120236 2212
1200 0 0 8155 0 1930 5 4 100251 2213
1656 257 1 6000 1 1967 5 3 139660 2214
912 0 1 7392 0 1930 5 2 100440 2215
1955 330 1 9000 0 1958 5 4 141074 2216
733 0 2 14584 0 1952 1 2 72941 2217
1361 0 1 5280 0 1895 4 2 89708 2218
1049 0 1 5150 0 1910 4 2 87382 2219
864 0 1 9000 0 1920 4 3 88242 2220
1648 1476 2 3843 1 2007 8 2 257673 2221
1646 1474 2 3811 1 2004 7 2 228721 2222
2032 700 3 23730 0 1996 7 3 248823 2223
1820 0 3 11050 1 1996 7 3 227818 2224
1872 0 2 10260 0 1976 5 4 153844 2225
1689 1383 2 9990 1 1991 4 3 163389 2226
1501 893 2 4084 1 1986 7 2 201355 2227
1537 1036 3 11563 0 2006 8 3 257193 2228
1780 770 2 12852 1 2007 8 3 257124 2229
1442 0 2 9802 0 2006 5 3 149971 2230
1612 0 3 12018 0 2008 7 3 213569 2231
1495 0 2 12890 1 1989 6 3 173027 2232
1256 920 2 18265 1 1986 6 3 180895 2233
1440 1029 2 11202 1 2003 8 3 242298 2234
1675 1223 2 7915 0 1999 6 3 192425 2235
1728 1011 2 11449 1 2007 8 3 259179 2236
1964 1571 3 11447 1 2005 8 3 310525 2237
1344 1309 4 8940 0 1997 7 2 237334 2238
1092 0 0 9278 0 2007 5 2 116407 2239
1189 864 2 4500 0 1997 6 2 164292 2240
1200 865 3 14137 0 1964 4 3 137557 2241
1040 769 2 4224 0 1975 5 3 135339 2242
1475 318 1 2665 1 1976 5 4 138807 2243
988 501 1 1974 0 1973 4 2 104846 2244
988 437 1 1596 1 1973 4 1 108715 2245
1160 785 1 17979 0 1968 5 3 130119 2246
1092 358 0 1477 0 1970 6 3 121439 2247
816 534 1 6490 0 1983 5 2 117818 2248
845 638 1 6600 0 1982 5 3 120812 2249
889 647 2 12395 0 1984 5 3 135760 2250
1836 0 1 56600 0 1900 5 4 131903 2251
1587 838 2 10667 1 1971 6 3 181090 2252
1384 0 2 8872 1 1997 6 3 170668 2253
1694 186 2 10147 1 1994 6 3 184180 2254
1714 871 2 8637 1 1999 6 3 198716 2255
1553 414 2 7875 0 1996 7 3 193111 2256
2299 0 2 7500 1 1999 6 5 210578 2257
1187 0 2 9556 0 1992 7 3 171624 2258
1642 0 2 7655 1 1993 6 3 177450 2259
1128 550 2 18160 1 1964 6 3 161182 2260
1179 248 2 4740 0 1988 8 2 189186 2261
1321 926 2 5118 1 1990 8 1 217844 2262
2541 986 3 12328 1 2005 8 4 335308 2263
2338 1101 3 51974 2 2006 9 4 429657 2264
1424 1047 3 41600 0 1969 5 3 178748 2265
1612 797 2 8035 1 2006 9 2 270826 2266
2234 1558 2 14082 1 2006 8 1 296563 2267
2042 1152 3 13870 1 2006 10 3 382387 2268
1284 256 2 10960 0 1984 6 3 157857 2269
1479 321 2 12090 1 1981 7 3 194211 2270
1664 1328 2 12299 1 1978 7 3 219890 2271
1930 758 2 11339 1 1979 7 4 222661 2272
1177 781 2 11850 0 1984 6 3 162593 2273
1353 903 2 10400 1 1979 6 2 175044 2274
1220 492 2 13001 1 1971 6 2 161933 2275
1324 624 2 8991 1 1976 7 3 189548 2276
1877 931 2 8000 1 1974 6 4 196024 2277
1422 566 2 9457 0 1970 5 3 143799 2278
914 81 1 7920 0 1970 5 3 113325 2279
914 314 1 17199 0 1961 4 2 102765 2280
1337 0 2 4113 1 2001 6 2 166538 2281
1337 930 2 10943 1 1997 6 2 183207 2282
1092 312 1 2205 0 1973 6 3 133017 2283
1218 0 1 2058 0 1973 6 4 134069 2284
1055 632 1 2304 0 1978 7 2 152130 2285
988 725 1 7150 0 1966 5 3 120664 2286
1816 1151 3 12469 1 2006 9 3 325577 2287
1694 0 3 11825 1 2006 8 3 254955 2288
2122 1518 3 14333 1 2007 8 2 319453 2289
2656 1304 3 13641 1 2007 9 3 393797 2290
2550 0 3 13440 1 2006 8 4 308224 2291
2046 1430 3 15431 2 2005 10 2 410818 2292
2552 1812 3 13891 2 2007 9 3 427359 2293
2758 0 3 13654 1 2005 9 4 358575 2294
2290 1684 3 17169 1 2007 10 2 422436 2295
2152 0 2 16659 1 2007 8 3 260857 2296
2100 778 3 9709 2 2007 8 3 313337 2297
1802 0 3 13615 1 2006 9 3 292653 2298
2956 0 3 13069 1 2004 8 5 336587 2299
2385 938 3 14277 1 2003 8 3 319787 2300
1818 669 3 12568 1 2007 8 3 279482 2301
1614 1178 3 9926 0 2005 7 3 235230 2302
1721 119 2 9254 0 2005 8 3 223002 2303
1828 0 3 10732 0 2006 8 3 247213 2304
1302 866 2 3901 1 2005 6 1 178793 2305
1302 1030 2 3903 1 2005 6 1 181540 2306
1362 762 2 6289 1 2005 6 2 182561 2307
1554 24 2 4590 1 2006 8 2 220809 2308
1577 848 2 7841 1 2005 9 2 269372 2309
1324 24 2 6240 1 2006 8 2 211716 2310
1405 1000 2 3242 1 2003 7 2 207584 2311
1496 0 2 15810 0 2007 6 3 172704 2312
1536 0 2 10237 1 2005 6 3 180230 2313
1458 0 2 13204 0 2006 7 3 189654 2314
1495 0 2 8857 1 2006 6 3 178499 2315
1746 0 3 9729 1 2006 6 3 205148 2316
1326 918 2 12216 0 2005 6 3 179016 2317
1504 0 2 8229 0 2007 6 3 169387 2318
1456 0 2 7713 0 2007 7 3 187179 2319
1258 0 2 7697 0 2007 7 3 179807 2320
1589 1084 3 3621 1 2003 8 2 264696 2321
1266 0 2 3710 1 2007 7 2 185990 2322
1119 779 2 16219 0 2004 7 2 188767 2323
1374 192 2 11084 1 2004 7 3 198370 2324
1525 0 2 10936 1 2006 7 3 201839 2325
1394 0 2 11950 1 2003 7 3 195637 2326
1948 0 2 7875 1 2003 7 4 218985 2327
1995 574 2 8740 1 2002 7 4 233172 2328
1690 520 2 9487 1 2000 6 3 192336 2329
1644 0 2 9649 1 1999 6 3 181192 2330
2551 1181 3 12191 2 1997 8 4 354205 2331
3078 672 3 10557 1 1998 9 4 396803 2332
2582 1048 3 11002 1 1998 8 4 332960 2333
2385 0 3 10790 1 1998 7 4 259583 2334
2202 335 2 11762 1 1992 8 4 261402 2335
2538 1225 3 9044 1 1996 8 4 332003 2336
1369 0 2 9910 0 2007 7 3 185030 2337
1542 1220 3 11830 1 2007 8 3 277589 2338
1534 28 2 10612 1 2006 8 3 226341 2339
1966 1572 3 12291 1 2007 10 1 381722 2340
1528 0 2 9965 1 2007 7 3 201921 2341
1538 769 2 8847 0 2005 8 3 228002 2342
1506 778 2 8251 1 2005 7 3 214001 2343
1977 0 3 9605 0 2006 7 3 227304 2344
1830 0 3 8778 0 2006 8 3 245977 2345
1338 24 2 8640 0 2007 8 3 205201 2346
1335 0 2 9000 0 2006 7 3 182841 2347
1792 350 2 8640 0 2007 8 3 231902 2348
1588 0 2 10411 0 2007 5 3 155123 2349
1880 745 3 12217 1 2007 8 3 284745 2350
1584 0 2 10440 1 2007 8 2 225846 2351
1685 0 3 11824 1 2006 8 2 251520 2352
2443 0 3 10625 1 2004 6 4 238476 2353
1100 0 0 7500 0 2006 6 3 130853 2354
1143 0 0 7500 0 2006 7 3 147501 2355
1094 729 2 12450 0 2003 5 3 149532 2356
1486 0 2 7441 0 2006 7 3 187711 2357
1820 480 2 11613 0 1993 6 3 184081 2358
1266 0 1 8012 2 1980 6 2 152702 2359
894 138 1 6285 0 1977 5 2 113597 2360
1040 812 2 7476 0 1968 5 3 134743 2361
2503 727 2 19522 1 1990 7 3 259110 2362
1037 787 2 10751 0 1974 5 2 136008 2363
1055 968 2 12712 1 1973 6 2 164374 2364
1378 851 2 4379 1 2004 8 2 228812 2365
1151 60 2 3523 0 2006 8 2 192677 2366
1565 60 2 3784 0 2006 8 2 209697 2367
1352 937 2 3606 1 2006 7 2 205905 2368
1550 0 2 5330 0 2006 8 2 208791 2369
1501 565 2 2280 1 1999 6 3 181752 2370
1573 417 2 2117 0 2000 6 3 172527 2371
1358 0 2 7321 0 1999 7 3 179684 2372
2048 964 2 8010 2 2003 8 3 285290 2373
2362 901 2 8413 2 1998 8 3 298860 2374
1494 457 2 9466 1 1994 8 1 220804 2375
2362 1732 2 12000 1 1980 7 3 264096 2376
2497 1632 2 17778 2 1981 8 2 319633 2377
1152 0 2 11700 0 1968 6 3 144513 2378
2411 915 2 8000 1 1970 6 4 215949 2379
1082 973 2 8723 0 1969 6 3 155063 2380
1295 910 2 11700 0 1968 6 3 161890 2381
1610 346 2 11358 1 1972 7 3 195076 2382
1594 0 2 9547 1 1993 7 2 195100 2383
2075 819 2 10530 1 1993 7 3 235470 2384
1093 792 2 10738 1 1966 6 3 161149 2385
1052 617 1 10800 0 1963 6 3 135591 2386
1107 474 1 8050 0 1967 5 3 121364 2387
1224 0 3 10899 0 1964 4 2 124938 2388
1074 438 2 7450 1 1956 5 2 132794 2389
1187 311 2 14357 1 1961 5 2 138587 2390
964 700 2 8243 1 1961 5 3 136623 2391
894 0 1 8680 0 1960 5 3 109496 2392
1200 654 2 8800 1 1966 7 3 180706 2393
1042 494 2 9200 0 1965 6 3 145850 2394
2154 414 2 8800 1 1964 6 5 195471 2395
1374 54 1 11382 1 1964 6 3 145718 2396
1652 1386 2 22002 1 1959 6 3 193377 2397
908 130 2 12172 0 1940 5 2 114987 2398
666 299 0 5000 0 1946 3 2 74644 2399
670 144 0 3500 0 1945 3 2 73149 2400
808 150 1 5175 0 1958 5 2 106268 2401
1150 368 1 9600 0 1955 5 2 116787 2402
1560 0 3 8668 0 1968 5 4 153579 2403
1280 602 2 10050 1 1966 5 3 146883 2404
1254 600 2 9600 1 1961 6 3 161020 2405
936 873 1 8760 0 1957 6 2 131313 2406
1008 908 1 6860 0 1956 5 3 120106 2407
1053 288 2 8250 0 1963 5 3 127359 2408
1144 0 1 9100 1 1960 5 3 121840 2409
1721 668 2 9736 3 1957 6 4 199261 2410
922 512 1 9770 0 1957 5 2 113631 2411
1411 780 1 12198 1 1955 5 3 137752 2412
1216 288 1 10050 0 1955 5 3 119019 2413
1154 408 1 11556 0 1953 5 3 118754 2414
1560 0 2 8078 0 1958 5 4 137255 2415
948 441 2 10950 0 1952 6 2 136914 2416
1040 85 1 7942 0 1953 6 3 124581 2417
925 114 1 8540 0 1956 5 3 110214 2418
1540 150 1 7150 0 1955 4 4 112707 2419
925 793 1 8400 2 1955 5 3 130658 2420
1647 595 1 9532 1 1953 4 3 125548 2421
924 292 1 15783 0 1952 5 2 111848 2422
1544 0 0 14190 0 1890 4 3 87514 2423
1728 198 1 12099 1 1953 5 3 138432 2424
3086 0 3 21281 0 1935 5 4 199613 2425
1281 1030 2 10284 0 1925 4 1 114287 2426
1534 0 0 10800 0 1895 5 3 97891 2427
1651 242 1 10090 2 1963 7 4 186229 2428
888 192 1 8700 0 1961 5 3 111616 2429
952 952 1 8300 0 1968 6 3 137829 2430
1238 432 1 7200 1 1950 5 3 125430 2431
1040 574 1 7500 0 1959 5 3 118281 2432
1170 625 1 7315 1 1958 5 3 128526 2433
1242 739 1 7903 0 1960 5 3 125581 2434
1377 1098 1 8000 2 1960 5 3 148992 2435
925 0 1 7000 0 1961 5 3 109948 2436
864 110 1 6600 0 1962 5 2 108582 2437
936 734 1 6760 1 1962 5 3 124866 2438
960 0 2 6978 0 1926 5 2 109293 2439
1296 276 2 6000 0 1927 6 3 135687 2440
1022 782 1 4480 1 1922 5 2 113467 2441
967 0 1 3153 1 1920 5 2 103445 2442
1072 0 2 7200 2 1940 5 2 129302 2443
1174 130 2 9000 1 1900 5 2 115048 2444
1141 122 1 5925 0 1900 4 3 89056 2445
1798 0 2 9639 0 1900 4 4 112056 2446
1772 0 2 10337 0 1910 8 3 176441 2447
1642 196 1 9863 1 1927 6 4 143255 2448
1232 168 2 4571 0 1910 5 3 113298 2449
1650 259 2 8398 0 1910 6 3 140452 2450
1358 316 1 3600 1 1930 5 3 119765 2451
2454 0 2 13500 1 1879 7 3 178890 2452
968 0 1 8626 0 1956 4 2 97320 2453
1382 0 1 11800 1 1949 4 1 109568 2454
1060 317 1 6854 1 1925 5 1 109762 2455
1435 910 1 8674 0 1950 5 3 129698 2456
1274 306 1 6125 0 1939 5 3 114664 2457
1232 276 1 6000 2 1939 6 3 141365 2458
884 0 1 6120 0 1939 5 2 101774 2459
1409 52 2 6240 1 1938 6 3 147741 2460
1322 48 1 6240 0 1939 5 4 114413 2461
1426 0 1 6240 1 1930 5 3 118780 2462
1281 351 2 6120 0 1926 5 2 120222 2463
2264 0 1 7755 0 1918 6 4 146831 2464
1376 0 2 8850 0 1920 6 3 133139 2465
1316 0 2 8550 0 1926 5 4 120787 2466
1344 336 2 5700 1 1929 7 3 163337 2467
1173 0 1 5680 0 1901 5 3 99213 2468
1214 0 1 5680 0 1901 5 2 98874 2469
2294 375 2 13200 1 1963 6 5 202325 2470
1952 354 1 9780 2 1950 7 4 193482 2471
2180 375 2 10320 1 1915 6 3 170005 2472
1315 681 2 4330 0 1958 4 3 121788 2473
1484 0 1 10320 0 1910 4 3 97958 2474
2267 288 2 12888 2 1937 7 3 215568 2475
1282 485 1 4484 0 1942 5 2 115751 2476
999 925 1 11235 0 1963 5 3 123678 2477
1452 785 2 11235 1 1964 5 2 152639 2478
1005 513 2 14299 0 1964 4 3 117496 2479
1020 68 2 14149 1 1964 5 3 133445 2480
1040 249 1 11677 0 1966 5 3 118140 2481
868 748 2 8425 0 1971 5 2 129142 2482
897 168 1 8665 0 1968 5 3 113520 2483
943 114 2 8398 0 1967 5 2 122385 2484
912 216 1 8169 0 1966 5 3 113651 2485
1375 386 1 14175 1 1956 5 3 132889 2486
2654 267 2 16779 1 1920 5 4 172936 2487
1302 258 1 6960 2 1940 7 2 158907 2488
1299 736 2 11375 1 1954 6 3 162517 2489
1176 190 1 13770 2 1958 5 3 132926 2490
998 0 2 9000 0 1945 4 3 105144 2491
1522 299 2 11075 1 1984 6 3 175779 2492
1325 300 2 17541 1 1948 5 3 140703 2493
1630 587 2 22692 1 1953 5 3 157886 2494
1242 0 1 17808 0 1946 4 2 102936 2495
2422 353 2 12671 2 1954 6 4 211272 2496
1626 491 1 10512 0 1954 6 3 147097 2497
864 453 1 5400 0 1958 5 3 111925 2498
943 0 1 11515 0 1958 4 3 99252 2499
1038 283 1 3869 0 1984 5 2 119827 2500
1342 557 1 9280 0 1951 5 4 125144 2501
1480 1080 1 11100 1 1951 5 4 143459 2502
1362 0 1 7550 0 1920 4 4 98372 2503
1822 0 2 23920 1 1984 6 4 190490 2504
1958 497 2 9317 1 1994 7 3 222978 2505
1651 0 3 9178 1 2007 8 3 251520 2506
2140 0 3 10481 0 2006 8 3 263170 2507
1651 0 3 10235 1 2007 8 3 252258 2508
1546 20 3 11750 0 2005 7 3 209397 2509
1500 36 2 8760 1 2006 8 3 223802 2510
1270 0 2 7242 0 2005 7 2 177034 2511
1795 0 2 9316 0 2005 7 3 200387 2512
1873 608 2 8883 1 1988 7 3 217896 2513
1743 51 2 20064 2 1976 8 0 229944 2514
1022 550 2 14217 0 1994 5 3 142419 2515
1308 539 2 10021 0 1997 6 3 167773 2516
990 420 1 8428 0 1994 5 3 126256 2517
1097 549 1 16561 0 1996 5 3 134225 2518
1873 342 2 10820 1 1999 7 3 219653 2519
1753 638 2 12352 1 1998 7 3 220740 2520
1690 0 2 9543 0 2001 7 3 194346 2521
1842 841 2 8826 1 2000 7 3 227943 2522
894 663 2 11800 0 1974 5 3 132535 2523
1025 502 2 8660 1 1976 5 3 141131 2524
1009 755 2 9720 1 1977 5 3 144804 2525
1040 539 2 8982 0 1977 5 3 134906 2526
907 60 1 16300 0 1977 5 3 117630 2527
879 330 2 9675 0 1975 5 3 127671 2528
864 671 2 7200 0 1972 5 3 129513 2529
875 385 2 7200 0 1972 4 3 113113 2530
1673 1412 2 11354 1 2000 7 3 233902 2531
1932 654 2 8749 1 2003 7 3 229802 2532
1729 0 2 8158 0 2002 7 3 195624 2533
1592 408 2 11927 1 1994 8 3 231108 2534
2439 1198 2 12728 1 2001 8 4 304714 2535
1992 762 2 15295 2 1996 7 3 248417 2536
1341 915 2 17227 1 1999 8 1 231083 2537
1476 0 2 8145 0 2007 7 3 188165 2538
1190 709 2 8769 0 2005 7 2 186837 2539
1330 0 2 8334 1 2006 6 3 172377 2540
1491 0 2 8333 1 2006 7 3 199012 2541
1536 0 2 9045 0 2005 5 3 152157 2542
936 936 1 9825 1 1967 5 2 128408 2543
1088 132 2 8308 0 1963 4 2 111831 2544
1351 130 2 16287 1 1925 5 3 131026 2545
1179 0 2 8240 0 1960 6 2 139436 2546
1044 504 2 6285 1 1976 6 3 157305 2547
2233 0 2 9555 0 1979 5 5 168405 2548
1408 611 2 7023 0 2005 5 3 156043 2549
5095 4010 3 39290 2 2008 10 2 1042704 2550
1072 467 2 3675 0 2005 6 2 157380 2551
960 77 1 6400 0 1959 5 2 109495 2552
1152 0 0 6882 0 1955 4 2 92032 2553
1195 0 0 8741 0 1946 5 4 104388 2554
865 144 1 10042 1 1920 6 2 116966 2555
768 544 1 8172 1 1955 4 2 103465 2556
864 682 2 8172 0 1955 4 3 111512 2557
2592 371 0 10890 0 1923 5 6 139486 2558
1422 319 1 7223 0 1926 5 3 114881 2559
1298 113 1 6821 1 1921 6 2 126512 2560
1098 246 1 4000 1 1930 7 2 139460 2561
1436 0 1 6720 1 1921 6 3 130226 2562
1461 0 1 7155 1 1926 6 3 132686 2563
1718 0 2 7230 1 1927 7 4 172675 2564
1226 0 2 13108 1 1951 5 2 131914 2565
1755 189 1 7810 1 1930 4 4 117516 2566
1355 533 2 6221 0 1941 5 3 130400 2567
1560 540 2 25485 3 1960 6 3 198239 2568
1488 813 2 21579 2 1968 6 3 191398 2569
1045 330 2 1782 1 1980 6 2 152621 2570
1680 0 2 17871 0 1995 4 4 141793 2571
1020 577 2 3907 0 1988 8 1 186238 2572
1696 434 2 20693 2 1971 7 3 216450 2573
2726 0 2 18044 1 1986 8 2 275933 2574
1215 375 2 7000 0 1940 6 3 139527 2575
1601 0 0 7288 0 1925 5 3 105888 2576
1828 548 NA 9060 0 1923 5 3 160380 2577
816 0 1 3672 0 1922 5 2 95571 2578
845 0 1 11067 0 1939 2 1 72508 2579
1991 0 0 8250 0 1895 5 4 107896 2580
1073 967 2 6565 0 1957 4 3 119523 2581
1001 737 1 6060 0 1930 5 2 109114 2582
1625 1573 2 5568 1 2006 8 2 259391 2583
1299 1001 2 12150 1 1979 6 2 175572 2584
1392 585 3 10000 1 2002 5 3 178767 2585
1409 1392 2 12864 1 2002 7 1 218158 2586
1478 1239 2 9928 1 1991 7 3 215496 2587
918 224 1 8750 0 1975 7 3 145648 2588
1026 924 2 8410 1 1974 6 2 161215 2589
1501 949 2 4054 2 1987 7 2 214359 2590
2279 0 2 19958 1 1958 6 4 193744 2591
1689 0 2 8368 0 2006 7 3 196100 2592
1564 583 2 8298 1 2006 8 2 235461 2593
1240 215 2 10331 0 1985 7 3 174296 2594
1312 250 2 6718 0 2001 8 2 201889 2595
1922 1329 3 11305 1 2002 8 2 295203 2596
1491 0 2 7777 1 1996 6 3 173450 2597
2486 766 2 11800 1 2003 7 5 268234 2598
1824 0 3 12633 1 2006 10 3 327591 2599
2034 0 4 43500 0 1953 3 2 152904 2600
936 16 2 6710 0 1996 6 0 141419 2601
1092 252 1 1504 0 1972 4 3 105465 2602
992 503 1 1533 0 1970 4 2 104042 2603
1092 384 0 1495 0 1970 4 3 97494 2604
1092 0 1 1890 0 1976 4 3 104167 2605
1008 923 2 9129 1 1977 5 1 143406 2606
1356 1148 2 15957 1 1977 6 3 183199 2607
1676 1112 2 33983 2 1977 5 3 193639 2608
1432 531 2 8286 1 1977 5 3 153906 2609
796 796 0 6723 0 1971 5 2 107164 2610
1608 811 1 27697 0 1961 4 3 129044 2611
1178 1090 2 11000 0 1976 5 3 146475 2612
816 596 1 11625 0 1983 5 2 120198 2613
887 516 1 10447 0 1984 5 3 122371 2614
1293 468 2 11027 0 1954 6 2 147967 2615
1024 773 1 10533 2 1956 6 2 148191 2616
1797 1127 3 11765 1 1957 5 3 183355 2617
1390 1110 2 39384 2 1957 6 1 192595 2618
1851 0 2 11727 1 1969 7 3 197088 2619
1525 700 2 8238 1 1997 6 3 187090 2620
1671 0 2 13041 1 1995 6 3 182086 2621
1776 0 2 9783 1 1996 6 3 184790 2622
2064 0 2 13128 1 2005 8 4 255469 2623
2212 60 3 13751 1 2005 7 3 255565 2624
2687 0 2 13108 0 1994 8 4 266930 2625
1169 705 2 8076 1 1993 6 3 172342 2626
1204 0 2 3701 0 1987 8 2 184820 2627
2798 1218 3 16023 1 2005 9 3 402725 2628
3390 0 3 18062 1 2006 10 5 467660 2629
2473 205 3 12292 1 2006 9 4 344511 2630
2698 1206 3 16052 1 2006 10 4 446848 2631
2795 0 3 15922 1 2005 9 4 363553 2632
1714 1191 2 8147 1 2005 9 2 286169 2633
2000 1416 3 18261 2 2005 9 3 370948 2634
1102 850 2 10464 1 1980 6 2 165985 2635
1857 0 2 10530 1 1978 7 4 203504 2636
1083 1005 2 9927 1 1976 7 2 185313 2637
2318 788 2 9512 1 2005 7 3 253411 2638
1875 548 2 10530 1 1975 6 3 188672 2639
1103 755 2 10000 0 1974 6 3 155061 2640
874 20 2 7200 0 1971 4 3 109047 2641
1419 951 2 8773 0 2002 6 2 177798 2642
1092 0 2 2760 0 1973 6 3 141016 2643
1365 402 2 2160 1 1973 5 3 146033 2644
1030 282 1 1890 0 1972 6 3 130550 2645
948 276 1 1680 0 1972 6 2 126755 2646
1092 382 1 1680 0 1972 6 3 133358 2647
1069 727 2 4043 1 1975 6 2 158148 2648
1387 373 1 7514 1 1967 5 3 134244 2649
1055 120 1 2280 0 1976 7 2 144332 2650
1456 70 2 2179 1 1976 6 3 162389 2651
2589 1369 3 16387 1 2006 9 4 397483 2652
1618 0 3 16163 1 2004 8 2 249883 2653
1740 0 3 12228 0 2006 7 4 220798 2654
1868 1505 3 14780 1 2005 9 2 337382 2655
2206 0 3 13975 1 2005 9 4 320900 2656
2091 1290 2 9942 1 2005 9 3 317006 2657
2253 0 2 12867 1 2005 8 3 262160 2658
2389 0 3 10672 1 2006 8 4 296046 2659
2358 880 3 11643 1 2005 8 4 319323 2660
1792 1232 3 13758 1 2005 9 2 322986 2661
1780 1383 3 14828 1 2004 9 2 326910 2662
1914 994 3 13215 1 2004 8 3 292050 2663
1565 472 2 5911 1 2005 9 2 258106 2664
1686 1023 3 7740 1 2006 9 1 302104 2665
1666 415 2 6373 1 2006 9 2 263043 2666
1456 0 2 10237 1 2005 6 3 177330 2667
1492 0 2 10237 0 2006 7 3 189402 2668
1326 0 2 11660 0 2006 6 3 164535 2669
2373 0 3 11631 1 2004 8 4 294404 2670
1492 0 2 9073 0 2006 7 3 188792 2671
1364 453 2 3087 1 2006 7 2 197045 2672
1511 1038 2 2938 1 2002 7 2 212135 2673
1548 1059 2 3072 1 2004 7 2 215298 2674
1142 16 2 3010 0 2005 7 2 170741 2675
1598 0 2 9171 1 2004 7 3 202836 2676
1889 732 2 8658 1 2000 6 3 203769 2677
2322 0 3 12104 0 2006 7 4 248362 2678
1976 791 3 9660 1 1998 8 3 283111 2679
2234 505 3 9545 1 2000 8 3 291845 2680
2855 1182 3 9233 1 2000 9 4 398192 2681
2726 527 3 10019 1 1995 8 4 323309 2682
3500 292 3 17242 1 1993 9 4 419793 2683
2494 380 3 10236 1 1994 8 4 303697 2684
2799 247 3 12585 1 1993 8 3 316647 2685
1964 0 2 12447 1 2005 8 3 246955 2686
1670 1562 3 15218 1 2006 8 2 292667 2687
1504 0 2 10936 0 2006 8 3 212573 2688
1278 24 2 8640 0 2006 8 2 199857 2689
2640 1836 3 13162 1 2006 9 3 410842 2690
1716 0 2 8125 0 2005 6 3 175896 2691
1142 24 0 7733 0 2005 6 3 132023 2692
1400 0 2 11024 0 2005 7 3 185845 2693
1131 0 0 13072 0 2005 6 3 133395 2694
1686 0 2 7800 0 2005 7 3 195186 2695
1585 0 2 7632 0 2005 7 3 191141 2696
1837 0 2 8304 0 1997 6 3 176797 2697
1731 758 2 9370 0 1992 6 3 183912 2698
1398 904 2 7175 0 1990 6 2 170327 2699
1217 278 2 7175 0 1991 6 2 155299 2700
1320 274 2 9019 0 1994 6 3 162418 2701
988 36 2 9100 0 1962 5 3 122767 2702
1654 0 2 8927 0 1977 6 4 164282 2703
1211 612 2 9240 1 1962 5 2 141548 2704
984 554 1 9308 0 1965 5 3 119081 2705
909 162 1 8450 0 1968 5 3 113666 2706
925 181 2 8638 0 1963 5 2 121566 2707
1024 712 1 13052 0 1965 5 3 123097 2708
912 644 0 8020 0 1964 5 3 107949 2709
941 659 1 8789 1 1967 5 3 126388 2710
2646 1023 2 14330 4 1974 7 3 306264 2711
2826 1118 3 11025 3 1992 8 3 382729 2712
1143 0 2 3628 1 2004 7 1 177918 2713
1223 0 2 2544 0 2005 7 2 173086 2714
1524 353 2 2998 0 2000 6 2 168238 2715
1080 0 2 4447 0 2003 7 2 168191 2716
1694 0 1 8314 1 1997 7 3 186086 2717
1568 0 2 7180 1 2001 8 3 222377 2718
1193 962 2 13110 0 1972 5 2 142902 2719
1334 553 2 10140 0 1967 7 3 175192 2720
1051 758 2 9600 0 1968 5 3 135161 2721
1770 361 2 8640 0 1968 5 4 152080 2722
976 760 2 9360 1 1968 6 2 155254 2723
898 744 1 8400 0 1968 5 3 119698 2724
1051 799 1 9759 0 1966 5 3 123951 2725
1141 602 1 9600 0 1967 5 3 124198 2726
1565 901 1 8800 2 1965 6 3 172329 2727
1488 260 2 10368 1 1964 6 3 165168 2728
1440 360 2 9350 1 1964 5 4 149067 2729
1248 632 1 10800 0 1960 5 3 125494 2730
816 574 1 8550 1 1934 6 2 124290 2731
1043 0 1 9724 1 1947 5 2 114419 2732
1433 915 2 9600 1 1961 5 3 153860 2733
1624 40 1 10858 1 1952 5 2 131230 2734
1216 996 1 9600 0 1951 5 3 125696 2735
1728 0 1 9462 1 1949 5 3 133582 2736
936 486 1 9888 0 1954 5 2 112871 2737
1584 0 2 8917 0 1967 5 4 141377 2738
1246 939 2 12700 2 1964 6 3 178117 2739
1008 0 2 9723 0 1963 6 2 136253 2740
1364 623 1 8400 1 1957 5 3 133725 2741
1336 203 2 9610 1 1958 6 3 156620 2742
1370 678 1 10000 1 1956 5 3 134836 2743
1124 914 1 10152 1 1956 6 3 146582 2744
1050 824 1 8092 0 1954 6 3 134097 2745
1008 658 1 12778 0 1952 5 2 116729 2746
1575 0 2 10170 1 1951 6 2 156930 2747
1145 271 2 7700 0 1956 5 3 127120 2748
1005 488 1 11050 1 1956 5 2 121947 2749
1056 144 1 13600 0 1955 5 3 114813 2750
884 741 1 15428 0 1951 5 2 115271 2751
2039 0 3 21299 3 1941 7 3 238505 2752
1384 494 2 13300 0 1956 5 2 136741 2753
2640 1018 3 22136 1 1925 5 5 209505 2754
1312 0 2 7500 0 1947 6 3 140035 2755
713 0 1 10410 0 1930 3 2 77905 2756
715 0 2 10914 0 1929 3 2 84831 2757
720 0 1 7008 0 1900 4 1 79211 2758
1595 338 2 7200 1 1915 6 3 149180 2759
1760 0 2 10818 1 1910 4 4 120835 2760
1146 580 1 10184 1 1963 6 3 145260 2761
1207 701 1 9510 0 1962 6 3 140162 2762
1773 913 2 10800 2 1961 6 3 195219 2763
1472 0 2 11650 1 1959 7 2 175911 2764
2448 636 2 18275 2 1962 7 3 249502 2765
1521 455 1 12144 0 1950 4 3 114313 2766
1040 0 2 8544 0 1950 3 2 94845 2767
1556 0 0 8512 0 1960 5 4 116223 2768
1150 781 1 7000 0 1961 5 3 123741 2769
1045 809 2 7400 0 1962 7 3 165843 2770
864 468 1 7000 0 1962 5 3 113706 2771
1025 953 0 7000 0 1962 5 3 112784 2772
2014 0 2 9856 0 1900 5 5 132444 2773
1668 276 1 9600 0 1948 5 3 127884 2774
1657 284 1 5520 1 1920 4 4 112651 2775
1416 381 2 9600 0 1900 6 3 132582 2776
1428 208 2 6451 0 1900 7 4 146586 2777
1004 0 1 3960 1 1930 7 2 133721 2778
1951 0 2 7745 0 1900 4 4 114980 2779
1032 143 1 7741 0 1924 6 2 114921 2780
844 0 1 5633 0 1925 5 2 97363 2781
864 0 1 7200 0 1950 4 2 93507 2782
1376 0 1 7614 0 1905 3 2 83089 2783
960 576 2 6000 0 1955 5 3 125057 2784
1566 0 2 6000 0 1924 5 5 127027 2785
492 416 1 7830 0 1921 3 1 74296 2786
1182 310 1 9576 0 1945 6 3 128930 2787
840 0 1 5747 0 1920 3 2 76971 2788
2104 0 2 6300 0 1910 7 5 170977 2789
1248 0 0 5976 0 1920 5 2 95871 2790
960 0 2 9750 0 1958 5 3 120676 2791
1020 0 0 4761 0 1918 3 2 72701 2792
1827 0 1 11737 1 1924 6 2 142333 2793
1162 347 1 6120 0 1930 3 3 88112 2794
1324 0 1 6120 0 1930 5 3 110089 2795
816 0 1 11672 0 1925 5 2 98447 2796
2486 0 2 33120 1 1962 6 5 214150 2797
1430 0 2 10320 0 1924 4 3 109321 2798
1330 0 1 7518 0 1910 5 3 105277 2799
819 0 0 9000 0 1919 5 2 88405 2800
984 343 1 7200 0 1930 6 3 118899 2801
1422 329 1 12375 1 1951 5 3 131146 2802
1921 0 2 11136 0 1964 6 4 168928 2803
1640 0 2 21370 1 1950 5 3 148150 2804
1032 0 1 8250 1 1935 5 2 110353 2805
879 0 1 5220 0 1936 5 2 100663 2806
1073 510 1 5500 0 2004 7 2 162492 2807
1064 779 2 11327 1 1967 5 3 143786 2808
934 456 1 10366 0 1964 6 2 129064 2809
1059 773 1 9000 0 1966 5 3 123593 2810
1458 194 2 9535 1 1967 5 3 146770 2811
1040 794 2 7176 1 1978 6 3 162678 2812
1967 0 2 9662 0 1977 5 6 160694 2813
1949 483 2 8235 0 1977 5 6 166797 2814
872 0 1 17529 1 1924 5 2 106654 2815
1830 810 2 20355 2 1967 7 2 225165 2816
1000 104 2 13050 2 1963 5 1 136858 2817
810 535 2 10820 0 1971 5 2 125965 2818
1700 397 1 1700 0 1980 7 2 170197 2819
1350 799 2 9375 1 1954 4 3 131544 2820
1150 230 1 6488 2 1942 5 3 124989 2821
2009 0 3 19950 2 1928 6 4 195964 2822
3672 425 2 19800 2 1935 6 5 269733 2823
1560 612 2 11679 1 1962 5 3 154761 2824
1488 0 2 12048 1 1952 5 3 140689 2825
1057 0 1 10519 0 1955 5 3 112346 2826
1609 468 1 9525 0 1953 6 5 148971 2827
2559 549 2 12128 1 1989 6 4 228098 2828
1440 261 4 9069 0 1993 6 2 194592 2829
1876 0 3 11003 0 2005 7 3 223006 2830
1208 393 2 7488 0 2005 7 2 181449 2831
1846 1576 2 13377 1 2006 6 3 224687 2832
1590 1122 3 11645 0 2005 8 2 258415 2833
1809 0 2 10984 0 2005 7 3 201888 2834
1614 56 2 9316 1 2005 7 3 205149 2835
1596 0 2 9316 0 2005 7 3 192465 2836
1388 853 2 12000 1 1968 6 3 173517 2837
1100 0 2 13015 0 1996 5 3 137707 2838
1499 0 2 12438 1 1995 6 3 175553 2839
1425 846 2 8685 0 1998 7 3 197292 2840
1749 500 2 9272 0 1999 7 3 204861 2841
1779 894 2 13426 1 1999 7 3 228494 2842
1388 509 1 8340 0 1977 6 3 147783 2843
1282 595 3 10385 0 1978 6 3 174532 2844
864 437 1 7200 0 1972 5 3 116301 2845
1762 456 2 9930 0 2002 7 3 206473 2846
1755 639 2 9468 1 1999 6 3 196554 2847
1358 872 2 11088 1 2002 8 1 228762 2848
1909 0 2 8726 0 2002 7 4 205613 2849
2214 920 3 10566 1 1999 8 3 302195 2850
2049 0 2 21533 1 1996 7 4 228129 2851
1939 796 3 11250 1 1998 7 3 252691 2852
1995 685 2 11250 1 1995 7 4 233137 2853
848 717 2 4435 0 2003 6 1 151696 2854
1390 1000 2 8810 0 2003 7 3 201279 2855
1737 0 2 8581 0 2006 7 3 198135 2856
1611 0 2 8400 0 2005 7 3 192561 2857
1336 996 2 8772 0 2005 7 3 199986 2858
1436 173 2 8777 0 1910 4 3 106960 2859
1012 976 0 7840 0 1975 6 4 131953 2860
1176 847 1 16133 0 1969 5 2 129423 2861
1724 0 2 7162 1 2003 7 3 206414 2862
914 475 0 8050 0 2002 6 2 129068 2863
2314 0 2 11060 1 2003 7 3 235166 2864
1072 547 2 3675 0 2005 6 2 158555 2865
1709 0 2 2522 0 2004 7 3 192770 2866
936 0 1 6956 0 1948 4 3 95461 2867
1338 0 2 7822 0 1915 6 3 130112 2868
1669 0 1 8707 0 1924 4 4 106076 2869
1482 691 2 16012 1 1954 4 3 136246 2870
1414 0 0 8248 1 1922 4 3 95928 2871
498 0 1 8088 0 1922 2 1 64250 2872
1273 0 1 11388 0 1910 4 3 94134 2873
1551 930 1 10890 0 1938 5 3 129912 2874
1340 780 1 6430 0 1945 6 3 137862 2875
1479 424 1 7000 2 1926 7 3 163469 2876
1510 305 1 4899 0 1920 6 3 127753 2877
1636 0 1 9399 1 1919 7 4 153705 2878
1465 646 1 10164 2 1939 5 3 138858 2879
1288 384 1 6191 0 1941 5 4 117800 2880
1550 0 1 21780 1 1920 6 3 138606 2881
1717 602 1 12400 1 1940 5 2 137336 2882
1671 526 2 8170 1 1929 7 4 180972 2883
1609 0 3 12320 2 1932 7 3 197346 2884
1801 0 2 14210 1 1930 6 3 159537 2885
2315 760 1 15600 3 1950 5 4 185957 2886
976 305 1 7288 0 1942 5 2 107819 2887
1285 374 2 7000 0 1926 6 3 136662 2888
672 0 0 8534 0 1925 4 2 77846 2889
641 0 1 7030 0 1925 4 2 83942 2890
1638 0 1 9060 0 1957 6 4 143033 2891
729 0 0 12366 0 1945 3 2 74862 2892
1396 0 0 9000 0 1951 5 4 110170 2893
936 0 0 8520 0 1916 3 2 71863 2894
1778 1573 2 5748 1 2005 8 2 267030 2895
1646 1564 2 3842 1 2004 8 2 257751 2896
1625 776 2 23580 1 1979 6 3 191837 2897
1664 0 2 8385 0 1978 6 4 164778 2898
1491 0 2 9116 0 2001 8 3 208337 2899
1210 576 2 11080 0 1975 6 3 156704 2900
1650 909 2 50102 2 1958 6 2 208211 2901
1403 1136 2 8098 0 2000 6 2 179064 2902
1960 1350 3 13618 2 2005 8 3 323082 2903
1838 1455 3 11577 1 2005 9 3 334737 2904
1600 0 1 31250 0 1951 1 3 84352 2905
1368 1243 4 7020 0 1997 7 2 235775 2906
1304 0 1 2665 1 1977 5 3 128975 2907
874 441 1 10172 0 1968 5 3 116380 2908
1652 149 3 11836 0 1970 5 4 160850 2909
630 522 0 1470 0 1970 4 1 87831 2910
1092 252 1 1484 0 1972 4 3 105459 2911
1360 119 1 13384 1 1969 5 3 133197 2912
1092 408 1 1533 0 1970 4 3 106482 2913
1092 0 0 1526 0 1970 4 3 94085 2914
1092 0 0 1936 0 1970 4 3 94192 2915
1092 252 1 1894 0 1970 4 3 105055 2916
1224 1224 2 20000 1 1960 5 4 157663 2917
970 337 0 10441 0 1992 5 3 114583 2918
2000 758 3 9627 1 1993 7 3 250650 2919
write.csv(dplyr::select(test2, Id, SalePrice), "data/predictions.csv", row.names = FALSE)

Kaglee submittion

Kaggle UserID: PKowalchuk