DATA 605 02[46835] : Final Project

1 Overview

Your final is due by the end of the last week of class. You should post your solutions to your GitHub account or RPubs. You are also expected to make a short presentation via YouTube and post that recording to the board. This project will show off your ability to understand the elements of the class.

2 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 \(\frac{(N+1)}{2}\).

2.1 Answer

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   1.000   3.283   5.541   5.506   7.742  10.000
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
## -14.664   1.846   5.482   5.500   9.154  26.766

2.2 Question 1 : 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.

a. P(X>x | X>y)

b. P(X>x, Y>y)

c. P(X<x | X>y)

2.2.1 Answer 1

## [1] 5.540952
## [1] 1.846076

2.2.1.1 (a) P(X>x | X>y)

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

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

## [1] 0.5512679

The probablity of a random number uniformly ranging from 1 to 10 being greater than 5.540952 (median) given that it is greater than 1.8460758 (1st Quartile) is 0.5512679

2.2.1.2 (b) P(X>x, Y>y)

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

## [1] 0.3808

The probablity of a random number uniformly ranging from 1 to 10 being greater than 5.540952 (median) and a random normally distributed number with a mean and standard deviation of 5.5 being greater than 1.8460758 (1st Quartile) is 0.3808

2.2.1.3 (c) P(X<x | X>y)

Probability of X less than its median given that it is greater than the first quantile of Y

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

## [1] 0.4487321

The probablity of a random number uniformly ranging from 1 to 10 being less than 5.540952 (median) given that it is greater than 1.8460758 (1st Quartile) is 0.4487321

2.4 Question 3

Check to see if independence holds by using Fisher’s Exact Test and the Chi Square Test. What is the difference between the two? Which is most appropriate?

2.4.1 Answer 3

## 
##  Fisher's Exact Test for Count Data
## 
## data:  count_data
## p-value = 0.007904
## alternative hypothesis: true odds ratio is not equal to 1
## 95 percent confidence interval:
##  1.032680 1.240419
## sample estimates:
## odds ratio 
##   1.131777
## 
##  Pearson's Chi-squared test with Yates' continuity correction
## 
## data:  count_data
## X-squared = 7.0533, df = 1, p-value = 0.007912

\(H_o\): X and Y are independent. \(H_a\): X and Y are not independent.

Since the P-value is less than the significance level (0.05) for both test, we cannot accept the null hypothesis. Thus, we conclude that there is a relationship between X and Y.

Fisher’s Exact Test is for is used when you have small cell sizes (less than 5). The Chi Square Test is used when the cell sizes are large. It would be appropriate in this case. We ran 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.


3 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?

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.

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 \(\lambda\) of 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.

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.

3.1 Question 1 : Descriptive and Inferential Statistics.

3.1.1 Answer 1

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

## <h4> Id </h4>

##      attribute
## [1,] "Id"     
##      d_table                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               
## [1,] "<table class=\"table\" style=\"margin-left: auto; margin-right: auto;\">\n <thead>\n  <tr>\n   <th style=\"text-align:left;\"> Measure </th>\n   <th style=\"text-align:right;\"> Value </th>\n  </tr>\n </thead>\n<tbody>\n  <tr>\n   <td style=\"text-align:left;\"> Min </td>\n   <td style=\"text-align:right;\"> 1.000 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> First Quartile </td>\n   <td style=\"text-align:right;\"> 364.750 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> Median </td>\n   <td style=\"text-align:right;\"> 730.500 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> Mean </td>\n   <td style=\"text-align:right;\"> 729.967 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> Third Quartile </td>\n   <td style=\"text-align:right;\"> 1094.250 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> Max </td>\n   <td style=\"text-align:right;\"> 1460.000 </td>\n  </tr>\n</tbody>\n</table>"
## <h4> MSSubClass </h4>

##      attribute   
## [1,] "MSSubClass"
##      d_table                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      
## [1,] "<table class=\"table\" style=\"margin-left: auto; margin-right: auto;\">\n <thead>\n  <tr>\n   <th style=\"text-align:left;\"> Measure </th>\n   <th style=\"text-align:right;\"> Value </th>\n  </tr>\n </thead>\n<tbody>\n  <tr>\n   <td style=\"text-align:left;\"> Min </td>\n   <td style=\"text-align:right;\"> 20.00000 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> First Quartile </td>\n   <td style=\"text-align:right;\"> 20.00000 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> Median </td>\n   <td style=\"text-align:right;\"> 50.00000 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> Mean </td>\n   <td style=\"text-align:right;\"> 56.88874 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> Third Quartile </td>\n   <td style=\"text-align:right;\"> 70.00000 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> Max </td>\n   <td style=\"text-align:right;\"> 190.00000 </td>\n  </tr>\n</tbody>\n</table>"
## <h4> MSZoning </h4>

## <table class="table" style="margin-left: auto; margin-right: auto;">
##  <thead>
##   <tr>
##    <th style="text-align:left;"> MSZoning </th>
##    <th style="text-align:right;"> count </th>
##   </tr>
##  </thead>
## <tbody>
##   <tr>
##    <td style="text-align:left;"> C (all) </td>
##    <td style="text-align:right;"> 10 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> FV </td>
##    <td style="text-align:right;"> 65 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> RH </td>
##    <td style="text-align:right;"> 16 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> RL </td>
##    <td style="text-align:right;"> 1147 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> RM </td>
##    <td style="text-align:right;"> 218 </td>
##   </tr>
## </tbody>
## </table>
## <h4> LotFrontage </h4>

##      attribute    
## [1,] "LotFrontage"
##      d_table                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     
## [1,] "<table class=\"table\" style=\"margin-left: auto; margin-right: auto;\">\n <thead>\n  <tr>\n   <th style=\"text-align:left;\"> Measure </th>\n   <th style=\"text-align:right;\"> Value </th>\n  </tr>\n </thead>\n<tbody>\n  <tr>\n   <td style=\"text-align:left;\"> Min </td>\n   <td style=\"text-align:right;\"> 0.00000 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> First Quartile </td>\n   <td style=\"text-align:right;\"> 42.00000 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> Median </td>\n   <td style=\"text-align:right;\"> 63.00000 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> Mean </td>\n   <td style=\"text-align:right;\"> 57.29602 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> Third Quartile </td>\n   <td style=\"text-align:right;\"> 79.00000 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> Max </td>\n   <td style=\"text-align:right;\"> 313.00000 </td>\n  </tr>\n</tbody>\n</table>"
## <h4> LotArea </h4>

##      attribute
## [1,] "LotArea"
##      d_table                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   
## [1,] "<table class=\"table\" style=\"margin-left: auto; margin-right: auto;\">\n <thead>\n  <tr>\n   <th style=\"text-align:left;\"> Measure </th>\n   <th style=\"text-align:right;\"> Value </th>\n  </tr>\n </thead>\n<tbody>\n  <tr>\n   <td style=\"text-align:left;\"> Min </td>\n   <td style=\"text-align:right;\"> 1300.00 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> First Quartile </td>\n   <td style=\"text-align:right;\"> 7538.75 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> Median </td>\n   <td style=\"text-align:right;\"> 9468.50 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> Mean </td>\n   <td style=\"text-align:right;\"> 10448.78 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> Third Quartile </td>\n   <td style=\"text-align:right;\"> 11588.00 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> Max </td>\n   <td style=\"text-align:right;\"> 215245.00 </td>\n  </tr>\n</tbody>\n</table>"
## <h4> Street </h4>

## <table class="table" style="margin-left: auto; margin-right: auto;">
##  <thead>
##   <tr>
##    <th style="text-align:left;"> Street </th>
##    <th style="text-align:right;"> count </th>
##   </tr>
##  </thead>
## <tbody>
##   <tr>
##    <td style="text-align:left;"> Grvl </td>
##    <td style="text-align:right;"> 6 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> Pave </td>
##    <td style="text-align:right;"> 1450 </td>
##   </tr>
## </tbody>
## </table>
## <h4> Alley </h4>

## <table class="table" style="margin-left: auto; margin-right: auto;">
##  <thead>
##   <tr>
##    <th style="text-align:left;"> Alley </th>
##    <th style="text-align:right;"> count </th>
##   </tr>
##  </thead>
## <tbody>
##   <tr>
##    <td style="text-align:left;"> Grvl </td>
##    <td style="text-align:right;"> 50 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> Pave </td>
##    <td style="text-align:right;"> 41 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> NA </td>
##    <td style="text-align:right;"> 1365 </td>
##   </tr>
## </tbody>
## </table>
## <h4> LotShape </h4>

## <table class="table" style="margin-left: auto; margin-right: auto;">
##  <thead>
##   <tr>
##    <th style="text-align:left;"> LotShape </th>
##    <th style="text-align:right;"> count </th>
##   </tr>
##  </thead>
## <tbody>
##   <tr>
##    <td style="text-align:left;"> IR1 </td>
##    <td style="text-align:right;"> 481 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> IR2 </td>
##    <td style="text-align:right;"> 41 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> IR3 </td>
##    <td style="text-align:right;"> 9 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> Reg </td>
##    <td style="text-align:right;"> 925 </td>
##   </tr>
## </tbody>
## </table>
## <h4> LandContour </h4>

## <table class="table" style="margin-left: auto; margin-right: auto;">
##  <thead>
##   <tr>
##    <th style="text-align:left;"> LandContour </th>
##    <th style="text-align:right;"> count </th>
##   </tr>
##  </thead>
## <tbody>
##   <tr>
##    <td style="text-align:left;"> Bnk </td>
##    <td style="text-align:right;"> 61 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> HLS </td>
##    <td style="text-align:right;"> 50 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> Low </td>
##    <td style="text-align:right;"> 36 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> Lvl </td>
##    <td style="text-align:right;"> 1309 </td>
##   </tr>
## </tbody>
## </table>
## <h4> Utilities </h4>

## <table class="table" style="margin-left: auto; margin-right: auto;">
##  <thead>
##   <tr>
##    <th style="text-align:left;"> Utilities </th>
##    <th style="text-align:right;"> count </th>
##   </tr>
##  </thead>
## <tbody>
##   <tr>
##    <td style="text-align:left;"> AllPub </td>
##    <td style="text-align:right;"> 1455 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> NoSeWa </td>
##    <td style="text-align:right;"> 1 </td>
##   </tr>
## </tbody>
## </table>
## <h4> LotConfig </h4>

## <table class="table" style="margin-left: auto; margin-right: auto;">
##  <thead>
##   <tr>
##    <th style="text-align:left;"> LotConfig </th>
##    <th style="text-align:right;"> count </th>
##   </tr>
##  </thead>
## <tbody>
##   <tr>
##    <td style="text-align:left;"> Corner </td>
##    <td style="text-align:right;"> 260 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> CulDSac </td>
##    <td style="text-align:right;"> 94 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> FR2 </td>
##    <td style="text-align:right;"> 47 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> FR3 </td>
##    <td style="text-align:right;"> 4 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> Inside </td>
##    <td style="text-align:right;"> 1051 </td>
##   </tr>
## </tbody>
## </table>
## <h4> LandSlope </h4>

## <table class="table" style="margin-left: auto; margin-right: auto;">
##  <thead>
##   <tr>
##    <th style="text-align:left;"> LandSlope </th>
##    <th style="text-align:right;"> count </th>
##   </tr>
##  </thead>
## <tbody>
##   <tr>
##    <td style="text-align:left;"> Gtl </td>
##    <td style="text-align:right;"> 1378 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> Mod </td>
##    <td style="text-align:right;"> 65 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> Sev </td>
##    <td style="text-align:right;"> 13 </td>
##   </tr>
## </tbody>
## </table>
## <h4> Neighborhood </h4>

## <table class="table" style="margin-left: auto; margin-right: auto;">
##  <thead>
##   <tr>
##    <th style="text-align:left;"> Neighborhood </th>
##    <th style="text-align:right;"> count </th>
##   </tr>
##  </thead>
## <tbody>
##   <tr>
##    <td style="text-align:left;"> Blmngtn </td>
##    <td style="text-align:right;"> 17 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> Blueste </td>
##    <td style="text-align:right;"> 2 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> BrDale </td>
##    <td style="text-align:right;"> 16 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> BrkSide </td>
##    <td style="text-align:right;"> 58 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> ClearCr </td>
##    <td style="text-align:right;"> 28 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> CollgCr </td>
##    <td style="text-align:right;"> 150 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> Crawfor </td>
##    <td style="text-align:right;"> 51 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> Edwards </td>
##    <td style="text-align:right;"> 98 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> Gilbert </td>
##    <td style="text-align:right;"> 79 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> IDOTRR </td>
##    <td style="text-align:right;"> 37 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> MeadowV </td>
##    <td style="text-align:right;"> 17 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> Mitchel </td>
##    <td style="text-align:right;"> 49 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> NAmes </td>
##    <td style="text-align:right;"> 225 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> NoRidge </td>
##    <td style="text-align:right;"> 39 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> NPkVill </td>
##    <td style="text-align:right;"> 9 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> NridgHt </td>
##    <td style="text-align:right;"> 77 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> NWAmes </td>
##    <td style="text-align:right;"> 73 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> OldTown </td>
##    <td style="text-align:right;"> 113 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> Sawyer </td>
##    <td style="text-align:right;"> 74 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> SawyerW </td>
##    <td style="text-align:right;"> 59 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> Somerst </td>
##    <td style="text-align:right;"> 86 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> StoneBr </td>
##    <td style="text-align:right;"> 25 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> SWISU </td>
##    <td style="text-align:right;"> 25 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> Timber </td>
##    <td style="text-align:right;"> 38 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> Veenker </td>
##    <td style="text-align:right;"> 11 </td>
##   </tr>
## </tbody>
## </table>
## <h4> Condition1 </h4>

## <table class="table" style="margin-left: auto; margin-right: auto;">
##  <thead>
##   <tr>
##    <th style="text-align:left;"> Condition1 </th>
##    <th style="text-align:right;"> count </th>
##   </tr>
##  </thead>
## <tbody>
##   <tr>
##    <td style="text-align:left;"> Artery </td>
##    <td style="text-align:right;"> 48 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> Feedr </td>
##    <td style="text-align:right;"> 80 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> Norm </td>
##    <td style="text-align:right;"> 1258 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> PosA </td>
##    <td style="text-align:right;"> 8 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> PosN </td>
##    <td style="text-align:right;"> 18 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> RRAe </td>
##    <td style="text-align:right;"> 11 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> RRAn </td>
##    <td style="text-align:right;"> 26 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> RRNe </td>
##    <td style="text-align:right;"> 2 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> RRNn </td>
##    <td style="text-align:right;"> 5 </td>
##   </tr>
## </tbody>
## </table>
## <h4> Condition2 </h4>

## <table class="table" style="margin-left: auto; margin-right: auto;">
##  <thead>
##   <tr>
##    <th style="text-align:left;"> Condition2 </th>
##    <th style="text-align:right;"> count </th>
##   </tr>
##  </thead>
## <tbody>
##   <tr>
##    <td style="text-align:left;"> Artery </td>
##    <td style="text-align:right;"> 2 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> Feedr </td>
##    <td style="text-align:right;"> 6 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> Norm </td>
##    <td style="text-align:right;"> 1442 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> PosA </td>
##    <td style="text-align:right;"> 1 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> PosN </td>
##    <td style="text-align:right;"> 1 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> RRAe </td>
##    <td style="text-align:right;"> 1 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> RRAn </td>
##    <td style="text-align:right;"> 1 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> RRNn </td>
##    <td style="text-align:right;"> 2 </td>
##   </tr>
## </tbody>
## </table>
## <h4> BldgType </h4>

## <table class="table" style="margin-left: auto; margin-right: auto;">
##  <thead>
##   <tr>
##    <th style="text-align:left;"> BldgType </th>
##    <th style="text-align:right;"> count </th>
##   </tr>
##  </thead>
## <tbody>
##   <tr>
##    <td style="text-align:left;"> 1Fam </td>
##    <td style="text-align:right;"> 1216 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> 2fmCon </td>
##    <td style="text-align:right;"> 31 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> Duplex </td>
##    <td style="text-align:right;"> 52 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> Twnhs </td>
##    <td style="text-align:right;"> 43 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> TwnhsE </td>
##    <td style="text-align:right;"> 114 </td>
##   </tr>
## </tbody>
## </table>
## <h4> HouseStyle </h4>

## <table class="table" style="margin-left: auto; margin-right: auto;">
##  <thead>
##   <tr>
##    <th style="text-align:left;"> HouseStyle </th>
##    <th style="text-align:right;"> count </th>
##   </tr>
##  </thead>
## <tbody>
##   <tr>
##    <td style="text-align:left;"> 1.5Fin </td>
##    <td style="text-align:right;"> 154 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> 1.5Unf </td>
##    <td style="text-align:right;"> 14 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> 1Story </td>
##    <td style="text-align:right;"> 726 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> 2.5Fin </td>
##    <td style="text-align:right;"> 8 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> 2.5Unf </td>
##    <td style="text-align:right;"> 11 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> 2Story </td>
##    <td style="text-align:right;"> 441 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> SFoyer </td>
##    <td style="text-align:right;"> 37 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> SLvl </td>
##    <td style="text-align:right;"> 65 </td>
##   </tr>
## </tbody>
## </table>
## <h4> OverallQual </h4>

##      attribute    
## [1,] "OverallQual"
##      d_table                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      
## [1,] "<table class=\"table\" style=\"margin-left: auto; margin-right: auto;\">\n <thead>\n  <tr>\n   <th style=\"text-align:left;\"> Measure </th>\n   <th style=\"text-align:right;\"> Value </th>\n  </tr>\n </thead>\n<tbody>\n  <tr>\n   <td style=\"text-align:left;\"> Min </td>\n   <td style=\"text-align:right;\"> 1.000000 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> First Quartile </td>\n   <td style=\"text-align:right;\"> 5.000000 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> Median </td>\n   <td style=\"text-align:right;\"> 6.000000 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> Mean </td>\n   <td style=\"text-align:right;\"> 6.088599 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> Third Quartile </td>\n   <td style=\"text-align:right;\"> 7.000000 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> Max </td>\n   <td style=\"text-align:right;\"> 10.000000 </td>\n  </tr>\n</tbody>\n</table>"
## <h4> OverallCond </h4>

##      attribute    
## [1,] "OverallCond"
##      d_table                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     
## [1,] "<table class=\"table\" style=\"margin-left: auto; margin-right: auto;\">\n <thead>\n  <tr>\n   <th style=\"text-align:left;\"> Measure </th>\n   <th style=\"text-align:right;\"> Value </th>\n  </tr>\n </thead>\n<tbody>\n  <tr>\n   <td style=\"text-align:left;\"> Min </td>\n   <td style=\"text-align:right;\"> 1.000000 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> First Quartile </td>\n   <td style=\"text-align:right;\"> 5.000000 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> Median </td>\n   <td style=\"text-align:right;\"> 5.000000 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> Mean </td>\n   <td style=\"text-align:right;\"> 5.576236 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> Third Quartile </td>\n   <td style=\"text-align:right;\"> 6.000000 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> Max </td>\n   <td style=\"text-align:right;\"> 9.000000 </td>\n  </tr>\n</tbody>\n</table>"
## <h4> YearBuilt </h4>

##      attribute  
## [1,] "YearBuilt"
##      d_table                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     
## [1,] "<table class=\"table\" style=\"margin-left: auto; margin-right: auto;\">\n <thead>\n  <tr>\n   <th style=\"text-align:left;\"> Measure </th>\n   <th style=\"text-align:right;\"> Value </th>\n  </tr>\n </thead>\n<tbody>\n  <tr>\n   <td style=\"text-align:left;\"> Min </td>\n   <td style=\"text-align:right;\"> 1872.000 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> First Quartile </td>\n   <td style=\"text-align:right;\"> 1954.000 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> Median </td>\n   <td style=\"text-align:right;\"> 1972.000 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> Mean </td>\n   <td style=\"text-align:right;\"> 1971.185 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> Third Quartile </td>\n   <td style=\"text-align:right;\"> 2000.000 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> Max </td>\n   <td style=\"text-align:right;\"> 2010.000 </td>\n  </tr>\n</tbody>\n</table>"
## <h4> YearRemodAdd </h4>

##      attribute     
## [1,] "YearRemodAdd"
##      d_table                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     
## [1,] "<table class=\"table\" style=\"margin-left: auto; margin-right: auto;\">\n <thead>\n  <tr>\n   <th style=\"text-align:left;\"> Measure </th>\n   <th style=\"text-align:right;\"> Value </th>\n  </tr>\n </thead>\n<tbody>\n  <tr>\n   <td style=\"text-align:left;\"> Min </td>\n   <td style=\"text-align:right;\"> 1950.000 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> First Quartile </td>\n   <td style=\"text-align:right;\"> 1966.750 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> Median </td>\n   <td style=\"text-align:right;\"> 1993.500 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> Mean </td>\n   <td style=\"text-align:right;\"> 1984.819 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> Third Quartile </td>\n   <td style=\"text-align:right;\"> 2004.000 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> Max </td>\n   <td style=\"text-align:right;\"> 2010.000 </td>\n  </tr>\n</tbody>\n</table>"
## <h4> RoofStyle </h4>

## <table class="table" style="margin-left: auto; margin-right: auto;">
##  <thead>
##   <tr>
##    <th style="text-align:left;"> RoofStyle </th>
##    <th style="text-align:right;"> count </th>
##   </tr>
##  </thead>
## <tbody>
##   <tr>
##    <td style="text-align:left;"> Flat </td>
##    <td style="text-align:right;"> 13 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> Gable </td>
##    <td style="text-align:right;"> 1140 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> Gambrel </td>
##    <td style="text-align:right;"> 11 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> Hip </td>
##    <td style="text-align:right;"> 283 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> Mansard </td>
##    <td style="text-align:right;"> 7 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> Shed </td>
##    <td style="text-align:right;"> 2 </td>
##   </tr>
## </tbody>
## </table>
## <h4> RoofMatl </h4>

## <table class="table" style="margin-left: auto; margin-right: auto;">
##  <thead>
##   <tr>
##    <th style="text-align:left;"> RoofMatl </th>
##    <th style="text-align:right;"> count </th>
##   </tr>
##  </thead>
## <tbody>
##   <tr>
##    <td style="text-align:left;"> CompShg </td>
##    <td style="text-align:right;"> 1432 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> Membran </td>
##    <td style="text-align:right;"> 1 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> Metal </td>
##    <td style="text-align:right;"> 1 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> Roll </td>
##    <td style="text-align:right;"> 1 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> Tar&amp;Grv </td>
##    <td style="text-align:right;"> 11 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> WdShake </td>
##    <td style="text-align:right;"> 5 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> WdShngl </td>
##    <td style="text-align:right;"> 5 </td>
##   </tr>
## </tbody>
## </table>
## <h4> Exterior1st </h4>

## <table class="table" style="margin-left: auto; margin-right: auto;">
##  <thead>
##   <tr>
##    <th style="text-align:left;"> Exterior1st </th>
##    <th style="text-align:right;"> count </th>
##   </tr>
##  </thead>
## <tbody>
##   <tr>
##    <td style="text-align:left;"> AsbShng </td>
##    <td style="text-align:right;"> 20 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> AsphShn </td>
##    <td style="text-align:right;"> 1 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> BrkComm </td>
##    <td style="text-align:right;"> 2 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> BrkFace </td>
##    <td style="text-align:right;"> 50 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> CBlock </td>
##    <td style="text-align:right;"> 1 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> CemntBd </td>
##    <td style="text-align:right;"> 60 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> HdBoard </td>
##    <td style="text-align:right;"> 221 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> ImStucc </td>
##    <td style="text-align:right;"> 1 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> MetalSd </td>
##    <td style="text-align:right;"> 220 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> Plywood </td>
##    <td style="text-align:right;"> 108 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> Stone </td>
##    <td style="text-align:right;"> 2 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> Stucco </td>
##    <td style="text-align:right;"> 24 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> VinylSd </td>
##    <td style="text-align:right;"> 515 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> Wd Sdng </td>
##    <td style="text-align:right;"> 205 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> WdShing </td>
##    <td style="text-align:right;"> 26 </td>
##   </tr>
## </tbody>
## </table>
## <h4> Exterior2nd </h4>

## <table class="table" style="margin-left: auto; margin-right: auto;">
##  <thead>
##   <tr>
##    <th style="text-align:left;"> Exterior2nd </th>
##    <th style="text-align:right;"> count </th>
##   </tr>
##  </thead>
## <tbody>
##   <tr>
##    <td style="text-align:left;"> AsbShng </td>
##    <td style="text-align:right;"> 20 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> AsphShn </td>
##    <td style="text-align:right;"> 3 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> Brk Cmn </td>
##    <td style="text-align:right;"> 7 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> BrkFace </td>
##    <td style="text-align:right;"> 25 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> CBlock </td>
##    <td style="text-align:right;"> 1 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> CmentBd </td>
##    <td style="text-align:right;"> 59 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> HdBoard </td>
##    <td style="text-align:right;"> 206 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> ImStucc </td>
##    <td style="text-align:right;"> 9 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> MetalSd </td>
##    <td style="text-align:right;"> 214 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> Other </td>
##    <td style="text-align:right;"> 1 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> Plywood </td>
##    <td style="text-align:right;"> 142 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> Stone </td>
##    <td style="text-align:right;"> 5 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> Stucco </td>
##    <td style="text-align:right;"> 25 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> VinylSd </td>
##    <td style="text-align:right;"> 504 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> Wd Sdng </td>
##    <td style="text-align:right;"> 197 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> Wd Shng </td>
##    <td style="text-align:right;"> 38 </td>
##   </tr>
## </tbody>
## </table>
## <h4> MasVnrType </h4>

## <table class="table" style="margin-left: auto; margin-right: auto;">
##  <thead>
##   <tr>
##    <th style="text-align:left;"> MasVnrType </th>
##    <th style="text-align:right;"> count </th>
##   </tr>
##  </thead>
## <tbody>
##   <tr>
##    <td style="text-align:left;"> BrkCmn </td>
##    <td style="text-align:right;"> 15 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> BrkFace </td>
##    <td style="text-align:right;"> 444 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> None </td>
##    <td style="text-align:right;"> 863 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> Stone </td>
##    <td style="text-align:right;"> 126 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> NA </td>
##    <td style="text-align:right;"> 8 </td>
##   </tr>
## </tbody>
## </table>
## <h4> MasVnrArea </h4>

##      attribute   
## [1,] "MasVnrArea"
##      d_table                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                
## [1,] "<table class=\"table\" style=\"margin-left: auto; margin-right: auto;\">\n <thead>\n  <tr>\n   <th style=\"text-align:left;\"> Measure </th>\n   <th style=\"text-align:right;\"> Value </th>\n  </tr>\n </thead>\n<tbody>\n  <tr>\n   <td style=\"text-align:left;\"> Min </td>\n   <td style=\"text-align:right;\"> 0.0000 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> First Quartile </td>\n   <td style=\"text-align:right;\"> 0.0000 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> Median </td>\n   <td style=\"text-align:right;\"> 0.0000 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> Mean </td>\n   <td style=\"text-align:right;\"> 102.0877 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> Third Quartile </td>\n   <td style=\"text-align:right;\"> 164.2500 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> Max </td>\n   <td style=\"text-align:right;\"> 1600.0000 </td>\n  </tr>\n</tbody>\n</table>"
## <h4> ExterQual </h4>

## <table class="table" style="margin-left: auto; margin-right: auto;">
##  <thead>
##   <tr>
##    <th style="text-align:left;"> ExterQual </th>
##    <th style="text-align:right;"> count </th>
##   </tr>
##  </thead>
## <tbody>
##   <tr>
##    <td style="text-align:left;"> Ex </td>
##    <td style="text-align:right;"> 49 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> Fa </td>
##    <td style="text-align:right;"> 14 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> Gd </td>
##    <td style="text-align:right;"> 487 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> TA </td>
##    <td style="text-align:right;"> 906 </td>
##   </tr>
## </tbody>
## </table>
## <h4> ExterCond </h4>

## <table class="table" style="margin-left: auto; margin-right: auto;">
##  <thead>
##   <tr>
##    <th style="text-align:left;"> ExterCond </th>
##    <th style="text-align:right;"> count </th>
##   </tr>
##  </thead>
## <tbody>
##   <tr>
##    <td style="text-align:left;"> Ex </td>
##    <td style="text-align:right;"> 3 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> Fa </td>
##    <td style="text-align:right;"> 28 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> Gd </td>
##    <td style="text-align:right;"> 146 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> Po </td>
##    <td style="text-align:right;"> 1 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> TA </td>
##    <td style="text-align:right;"> 1278 </td>
##   </tr>
## </tbody>
## </table>
## <h4> Foundation </h4>

## <table class="table" style="margin-left: auto; margin-right: auto;">
##  <thead>
##   <tr>
##    <th style="text-align:left;"> Foundation </th>
##    <th style="text-align:right;"> count </th>
##   </tr>
##  </thead>
## <tbody>
##   <tr>
##    <td style="text-align:left;"> BrkTil </td>
##    <td style="text-align:right;"> 146 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> CBlock </td>
##    <td style="text-align:right;"> 634 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> PConc </td>
##    <td style="text-align:right;"> 643 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> Slab </td>
##    <td style="text-align:right;"> 24 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> Stone </td>
##    <td style="text-align:right;"> 6 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> Wood </td>
##    <td style="text-align:right;"> 3 </td>
##   </tr>
## </tbody>
## </table>
## <h4> BsmtQual </h4>

## <table class="table" style="margin-left: auto; margin-right: auto;">
##  <thead>
##   <tr>
##    <th style="text-align:left;"> BsmtQual </th>
##    <th style="text-align:right;"> count </th>
##   </tr>
##  </thead>
## <tbody>
##   <tr>
##    <td style="text-align:left;"> Ex </td>
##    <td style="text-align:right;"> 117 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> Fa </td>
##    <td style="text-align:right;"> 35 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> Gd </td>
##    <td style="text-align:right;"> 618 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> TA </td>
##    <td style="text-align:right;"> 649 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> NA </td>
##    <td style="text-align:right;"> 37 </td>
##   </tr>
## </tbody>
## </table>
## <h4> BsmtCond </h4>

## <table class="table" style="margin-left: auto; margin-right: auto;">
##  <thead>
##   <tr>
##    <th style="text-align:left;"> BsmtCond </th>
##    <th style="text-align:right;"> count </th>
##   </tr>
##  </thead>
## <tbody>
##   <tr>
##    <td style="text-align:left;"> Fa </td>
##    <td style="text-align:right;"> 45 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> Gd </td>
##    <td style="text-align:right;"> 65 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> Po </td>
##    <td style="text-align:right;"> 2 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> TA </td>
##    <td style="text-align:right;"> 1307 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> NA </td>
##    <td style="text-align:right;"> 37 </td>
##   </tr>
## </tbody>
## </table>
## <h4> BsmtExposure </h4>

## <table class="table" style="margin-left: auto; margin-right: auto;">
##  <thead>
##   <tr>
##    <th style="text-align:left;"> BsmtExposure </th>
##    <th style="text-align:right;"> count </th>
##   </tr>
##  </thead>
## <tbody>
##   <tr>
##    <td style="text-align:left;"> Av </td>
##    <td style="text-align:right;"> 220 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> Gd </td>
##    <td style="text-align:right;"> 131 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> Mn </td>
##    <td style="text-align:right;"> 114 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> No </td>
##    <td style="text-align:right;"> 953 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> NA </td>
##    <td style="text-align:right;"> 38 </td>
##   </tr>
## </tbody>
## </table>
## <h4> BsmtFinType1 </h4>

## <table class="table" style="margin-left: auto; margin-right: auto;">
##  <thead>
##   <tr>
##    <th style="text-align:left;"> BsmtFinType1 </th>
##    <th style="text-align:right;"> count </th>
##   </tr>
##  </thead>
## <tbody>
##   <tr>
##    <td style="text-align:left;"> ALQ </td>
##    <td style="text-align:right;"> 220 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> BLQ </td>
##    <td style="text-align:right;"> 148 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> GLQ </td>
##    <td style="text-align:right;"> 414 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> LwQ </td>
##    <td style="text-align:right;"> 74 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> Rec </td>
##    <td style="text-align:right;"> 133 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> Unf </td>
##    <td style="text-align:right;"> 430 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> NA </td>
##    <td style="text-align:right;"> 37 </td>
##   </tr>
## </tbody>
## </table>
## <h4> BsmtFinSF1 </h4>

##      attribute   
## [1,] "BsmtFinSF1"
##      d_table                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  
## [1,] "<table class=\"table\" style=\"margin-left: auto; margin-right: auto;\">\n <thead>\n  <tr>\n   <th style=\"text-align:left;\"> Measure </th>\n   <th style=\"text-align:right;\"> Value </th>\n  </tr>\n </thead>\n<tbody>\n  <tr>\n   <td style=\"text-align:left;\"> Min </td>\n   <td style=\"text-align:right;\"> 0.0000 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> First Quartile </td>\n   <td style=\"text-align:right;\"> 0.0000 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> Median </td>\n   <td style=\"text-align:right;\"> 381.0000 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> Mean </td>\n   <td style=\"text-align:right;\"> 436.9911 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> Third Quartile </td>\n   <td style=\"text-align:right;\"> 706.5000 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> Max </td>\n   <td style=\"text-align:right;\"> 2188.0000 </td>\n  </tr>\n</tbody>\n</table>"
## <h4> BsmtFinType2 </h4>

## <table class="table" style="margin-left: auto; margin-right: auto;">
##  <thead>
##   <tr>
##    <th style="text-align:left;"> BsmtFinType2 </th>
##    <th style="text-align:right;"> count </th>
##   </tr>
##  </thead>
## <tbody>
##   <tr>
##    <td style="text-align:left;"> ALQ </td>
##    <td style="text-align:right;"> 19 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> BLQ </td>
##    <td style="text-align:right;"> 33 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> GLQ </td>
##    <td style="text-align:right;"> 14 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> LwQ </td>
##    <td style="text-align:right;"> 46 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> Rec </td>
##    <td style="text-align:right;"> 54 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> Unf </td>
##    <td style="text-align:right;"> 1252 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> NA </td>
##    <td style="text-align:right;"> 38 </td>
##   </tr>
## </tbody>
## </table>
## <h4> BsmtFinSF2 </h4>

##      attribute   
## [1,] "BsmtFinSF2"
##      d_table                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             
## [1,] "<table class=\"table\" style=\"margin-left: auto; margin-right: auto;\">\n <thead>\n  <tr>\n   <th style=\"text-align:left;\"> Measure </th>\n   <th style=\"text-align:right;\"> Value </th>\n  </tr>\n </thead>\n<tbody>\n  <tr>\n   <td style=\"text-align:left;\"> Min </td>\n   <td style=\"text-align:right;\"> 0.0000 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> First Quartile </td>\n   <td style=\"text-align:right;\"> 0.0000 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> Median </td>\n   <td style=\"text-align:right;\"> 0.0000 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> Mean </td>\n   <td style=\"text-align:right;\"> 46.6772 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> Third Quartile </td>\n   <td style=\"text-align:right;\"> 0.0000 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> Max </td>\n   <td style=\"text-align:right;\"> 1474.0000 </td>\n  </tr>\n</tbody>\n</table>"
## <h4> BsmtUnfSF </h4>

##      attribute  
## [1,] "BsmtUnfSF"
##      d_table                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    
## [1,] "<table class=\"table\" style=\"margin-left: auto; margin-right: auto;\">\n <thead>\n  <tr>\n   <th style=\"text-align:left;\"> Measure </th>\n   <th style=\"text-align:right;\"> Value </th>\n  </tr>\n </thead>\n<tbody>\n  <tr>\n   <td style=\"text-align:left;\"> Min </td>\n   <td style=\"text-align:right;\"> 0.0000 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> First Quartile </td>\n   <td style=\"text-align:right;\"> 222.5000 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> Median </td>\n   <td style=\"text-align:right;\"> 477.5000 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> Mean </td>\n   <td style=\"text-align:right;\"> 566.9904 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> Third Quartile </td>\n   <td style=\"text-align:right;\"> 808.0000 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> Max </td>\n   <td style=\"text-align:right;\"> 2336.0000 </td>\n  </tr>\n</tbody>\n</table>"
## <h4> TotalBsmtSF </h4>

##      attribute    
## [1,] "TotalBsmtSF"
##      d_table                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                
## [1,] "<table class=\"table\" style=\"margin-left: auto; margin-right: auto;\">\n <thead>\n  <tr>\n   <th style=\"text-align:left;\"> Measure </th>\n   <th style=\"text-align:right;\"> Value </th>\n  </tr>\n </thead>\n<tbody>\n  <tr>\n   <td style=\"text-align:left;\"> Min </td>\n   <td style=\"text-align:right;\"> 0.000 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> First Quartile </td>\n   <td style=\"text-align:right;\"> 795.000 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> Median </td>\n   <td style=\"text-align:right;\"> 990.500 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> Mean </td>\n   <td style=\"text-align:right;\"> 1050.659 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> Third Quartile </td>\n   <td style=\"text-align:right;\"> 1293.750 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> Max </td>\n   <td style=\"text-align:right;\"> 3206.000 </td>\n  </tr>\n</tbody>\n</table>"
## <h4> Heating </h4>

## <table class="table" style="margin-left: auto; margin-right: auto;">
##  <thead>
##   <tr>
##    <th style="text-align:left;"> Heating </th>
##    <th style="text-align:right;"> count </th>
##   </tr>
##  </thead>
## <tbody>
##   <tr>
##    <td style="text-align:left;"> Floor </td>
##    <td style="text-align:right;"> 1 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> GasA </td>
##    <td style="text-align:right;"> 1424 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> GasW </td>
##    <td style="text-align:right;"> 18 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> Grav </td>
##    <td style="text-align:right;"> 7 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> OthW </td>
##    <td style="text-align:right;"> 2 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> Wall </td>
##    <td style="text-align:right;"> 4 </td>
##   </tr>
## </tbody>
## </table>
## <h4> HeatingQC </h4>

## <table class="table" style="margin-left: auto; margin-right: auto;">
##  <thead>
##   <tr>
##    <th style="text-align:left;"> HeatingQC </th>
##    <th style="text-align:right;"> count </th>
##   </tr>
##  </thead>
## <tbody>
##   <tr>
##    <td style="text-align:left;"> Ex </td>
##    <td style="text-align:right;"> 737 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> Fa </td>
##    <td style="text-align:right;"> 49 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> Gd </td>
##    <td style="text-align:right;"> 241 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> Po </td>
##    <td style="text-align:right;"> 1 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> TA </td>
##    <td style="text-align:right;"> 428 </td>
##   </tr>
## </tbody>
## </table>
## <h4> CentralAir </h4>

## <table class="table" style="margin-left: auto; margin-right: auto;">
##  <thead>
##   <tr>
##    <th style="text-align:left;"> CentralAir </th>
##    <th style="text-align:right;"> count </th>
##   </tr>
##  </thead>
## <tbody>
##   <tr>
##    <td style="text-align:left;"> N </td>
##    <td style="text-align:right;"> 95 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> Y </td>
##    <td style="text-align:right;"> 1361 </td>
##   </tr>
## </tbody>
## </table>
## <h4> Electrical </h4>

## <table class="table" style="margin-left: auto; margin-right: auto;">
##  <thead>
##   <tr>
##    <th style="text-align:left;"> Electrical </th>
##    <th style="text-align:right;"> count </th>
##   </tr>
##  </thead>
## <tbody>
##   <tr>
##    <td style="text-align:left;"> FuseA </td>
##    <td style="text-align:right;"> 94 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> FuseF </td>
##    <td style="text-align:right;"> 27 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> FuseP </td>
##    <td style="text-align:right;"> 3 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> Mix </td>
##    <td style="text-align:right;"> 1 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> SBrkr </td>
##    <td style="text-align:right;"> 1330 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> NA </td>
##    <td style="text-align:right;"> 1 </td>
##   </tr>
## </tbody>
## </table>
## <h4> X1stFlrSF </h4>

##      attribute  
## [1,] "X1stFlrSF"
##      d_table                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   
## [1,] "<table class=\"table\" style=\"margin-left: auto; margin-right: auto;\">\n <thead>\n  <tr>\n   <th style=\"text-align:left;\"> Measure </th>\n   <th style=\"text-align:right;\"> Value </th>\n  </tr>\n </thead>\n<tbody>\n  <tr>\n   <td style=\"text-align:left;\"> Min </td>\n   <td style=\"text-align:right;\"> 334.000 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> First Quartile </td>\n   <td style=\"text-align:right;\"> 882.000 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> Median </td>\n   <td style=\"text-align:right;\"> 1086.000 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> Mean </td>\n   <td style=\"text-align:right;\"> 1157.109 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> Third Quartile </td>\n   <td style=\"text-align:right;\"> 1389.250 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> Max </td>\n   <td style=\"text-align:right;\"> 3228.000 </td>\n  </tr>\n</tbody>\n</table>"
## <h4> X2ndFlrSF </h4>

##      attribute  
## [1,] "X2ndFlrSF"
##      d_table                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          
## [1,] "<table class=\"table\" style=\"margin-left: auto; margin-right: auto;\">\n <thead>\n  <tr>\n   <th style=\"text-align:left;\"> Measure </th>\n   <th style=\"text-align:right;\"> Value </th>\n  </tr>\n </thead>\n<tbody>\n  <tr>\n   <td style=\"text-align:left;\"> Min </td>\n   <td style=\"text-align:right;\"> 0.000 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> First Quartile </td>\n   <td style=\"text-align:right;\"> 0.000 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> Median </td>\n   <td style=\"text-align:right;\"> 0.000 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> Mean </td>\n   <td style=\"text-align:right;\"> 343.533 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> Third Quartile </td>\n   <td style=\"text-align:right;\"> 728.000 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> Max </td>\n   <td style=\"text-align:right;\"> 1818.000 </td>\n  </tr>\n</tbody>\n</table>"
## <h4> LowQualFinSF </h4>

##      attribute     
## [1,] "LowQualFinSF"
##      d_table                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       
## [1,] "<table class=\"table\" style=\"margin-left: auto; margin-right: auto;\">\n <thead>\n  <tr>\n   <th style=\"text-align:left;\"> Measure </th>\n   <th style=\"text-align:right;\"> Value </th>\n  </tr>\n </thead>\n<tbody>\n  <tr>\n   <td style=\"text-align:left;\"> Min </td>\n   <td style=\"text-align:right;\"> 0.000000 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> First Quartile </td>\n   <td style=\"text-align:right;\"> 0.000000 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> Median </td>\n   <td style=\"text-align:right;\"> 0.000000 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> Mean </td>\n   <td style=\"text-align:right;\"> 5.860577 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> Third Quartile </td>\n   <td style=\"text-align:right;\"> 0.000000 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> Max </td>\n   <td style=\"text-align:right;\"> 572.000000 </td>\n  </tr>\n</tbody>\n</table>"
## <h4> GrLivArea </h4>

##      attribute  
## [1,] "GrLivArea"
##      d_table                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    
## [1,] "<table class=\"table\" style=\"margin-left: auto; margin-right: auto;\">\n <thead>\n  <tr>\n   <th style=\"text-align:left;\"> Measure </th>\n   <th style=\"text-align:right;\"> Value </th>\n  </tr>\n </thead>\n<tbody>\n  <tr>\n   <td style=\"text-align:left;\"> Min </td>\n   <td style=\"text-align:right;\"> 334.000 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> First Quartile </td>\n   <td style=\"text-align:right;\"> 1128.000 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> Median </td>\n   <td style=\"text-align:right;\"> 1458.500 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> Mean </td>\n   <td style=\"text-align:right;\"> 1506.502 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> Third Quartile </td>\n   <td style=\"text-align:right;\"> 1775.250 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> Max </td>\n   <td style=\"text-align:right;\"> 3627.000 </td>\n  </tr>\n</tbody>\n</table>"
## <h4> BsmtFullBath </h4>

##      attribute     
## [1,] "BsmtFullBath"
##      d_table                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           
## [1,] "<table class=\"table\" style=\"margin-left: auto; margin-right: auto;\">\n <thead>\n  <tr>\n   <th style=\"text-align:left;\"> Measure </th>\n   <th style=\"text-align:right;\"> Value </th>\n  </tr>\n </thead>\n<tbody>\n  <tr>\n   <td style=\"text-align:left;\"> Min </td>\n   <td style=\"text-align:right;\"> 0.0000000 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> First Quartile </td>\n   <td style=\"text-align:right;\"> 0.0000000 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> Median </td>\n   <td style=\"text-align:right;\"> 0.0000000 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> Mean </td>\n   <td style=\"text-align:right;\"> 0.4237637 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> Third Quartile </td>\n   <td style=\"text-align:right;\"> 1.0000000 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> Max </td>\n   <td style=\"text-align:right;\"> 3.0000000 </td>\n  </tr>\n</tbody>\n</table>"
## <h4> BsmtHalfBath </h4>

##      attribute     
## [1,] "BsmtHalfBath"
##      d_table                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           
## [1,] "<table class=\"table\" style=\"margin-left: auto; margin-right: auto;\">\n <thead>\n  <tr>\n   <th style=\"text-align:left;\"> Measure </th>\n   <th style=\"text-align:right;\"> Value </th>\n  </tr>\n </thead>\n<tbody>\n  <tr>\n   <td style=\"text-align:left;\"> Min </td>\n   <td style=\"text-align:right;\"> 0.0000000 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> First Quartile </td>\n   <td style=\"text-align:right;\"> 0.0000000 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> Median </td>\n   <td style=\"text-align:right;\"> 0.0000000 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> Mean </td>\n   <td style=\"text-align:right;\"> 0.0570055 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> Third Quartile </td>\n   <td style=\"text-align:right;\"> 0.0000000 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> Max </td>\n   <td style=\"text-align:right;\"> 2.0000000 </td>\n  </tr>\n</tbody>\n</table>"
## <h4> FullBath </h4>

##      attribute 
## [1,] "FullBath"
##      d_table                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     
## [1,] "<table class=\"table\" style=\"margin-left: auto; margin-right: auto;\">\n <thead>\n  <tr>\n   <th style=\"text-align:left;\"> Measure </th>\n   <th style=\"text-align:right;\"> Value </th>\n  </tr>\n </thead>\n<tbody>\n  <tr>\n   <td style=\"text-align:left;\"> Min </td>\n   <td style=\"text-align:right;\"> 0.000000 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> First Quartile </td>\n   <td style=\"text-align:right;\"> 1.000000 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> Median </td>\n   <td style=\"text-align:right;\"> 2.000000 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> Mean </td>\n   <td style=\"text-align:right;\"> 1.561813 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> Third Quartile </td>\n   <td style=\"text-align:right;\"> 2.000000 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> Max </td>\n   <td style=\"text-align:right;\"> 3.000000 </td>\n  </tr>\n</tbody>\n</table>"
## <h4> HalfBath </h4>

##      attribute 
## [1,] "HalfBath"
##      d_table                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           
## [1,] "<table class=\"table\" style=\"margin-left: auto; margin-right: auto;\">\n <thead>\n  <tr>\n   <th style=\"text-align:left;\"> Measure </th>\n   <th style=\"text-align:right;\"> Value </th>\n  </tr>\n </thead>\n<tbody>\n  <tr>\n   <td style=\"text-align:left;\"> Min </td>\n   <td style=\"text-align:right;\"> 0.0000000 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> First Quartile </td>\n   <td style=\"text-align:right;\"> 0.0000000 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> Median </td>\n   <td style=\"text-align:right;\"> 0.0000000 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> Mean </td>\n   <td style=\"text-align:right;\"> 0.3811813 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> Third Quartile </td>\n   <td style=\"text-align:right;\"> 1.0000000 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> Max </td>\n   <td style=\"text-align:right;\"> 2.0000000 </td>\n  </tr>\n</tbody>\n</table>"
## <h4> BedroomAbvGr </h4>

##      attribute     
## [1,] "BedroomAbvGr"
##      d_table                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     
## [1,] "<table class=\"table\" style=\"margin-left: auto; margin-right: auto;\">\n <thead>\n  <tr>\n   <th style=\"text-align:left;\"> Measure </th>\n   <th style=\"text-align:right;\"> Value </th>\n  </tr>\n </thead>\n<tbody>\n  <tr>\n   <td style=\"text-align:left;\"> Min </td>\n   <td style=\"text-align:right;\"> 0.000000 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> First Quartile </td>\n   <td style=\"text-align:right;\"> 2.000000 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> Median </td>\n   <td style=\"text-align:right;\"> 3.000000 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> Mean </td>\n   <td style=\"text-align:right;\"> 2.864698 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> Third Quartile </td>\n   <td style=\"text-align:right;\"> 3.000000 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> Max </td>\n   <td style=\"text-align:right;\"> 8.000000 </td>\n  </tr>\n</tbody>\n</table>"
## <h4> KitchenAbvGr </h4>

##      attribute     
## [1,] "KitchenAbvGr"
##      d_table                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     
## [1,] "<table class=\"table\" style=\"margin-left: auto; margin-right: auto;\">\n <thead>\n  <tr>\n   <th style=\"text-align:left;\"> Measure </th>\n   <th style=\"text-align:right;\"> Value </th>\n  </tr>\n </thead>\n<tbody>\n  <tr>\n   <td style=\"text-align:left;\"> Min </td>\n   <td style=\"text-align:right;\"> 0.000000 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> First Quartile </td>\n   <td style=\"text-align:right;\"> 1.000000 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> Median </td>\n   <td style=\"text-align:right;\"> 1.000000 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> Mean </td>\n   <td style=\"text-align:right;\"> 1.046703 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> Third Quartile </td>\n   <td style=\"text-align:right;\"> 1.000000 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> Max </td>\n   <td style=\"text-align:right;\"> 3.000000 </td>\n  </tr>\n</tbody>\n</table>"
## <h4> KitchenQual </h4>

## <table class="table" style="margin-left: auto; margin-right: auto;">
##  <thead>
##   <tr>
##    <th style="text-align:left;"> KitchenQual </th>
##    <th style="text-align:right;"> count </th>
##   </tr>
##  </thead>
## <tbody>
##   <tr>
##    <td style="text-align:left;"> Ex </td>
##    <td style="text-align:right;"> 96 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> Fa </td>
##    <td style="text-align:right;"> 39 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> Gd </td>
##    <td style="text-align:right;"> 586 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> TA </td>
##    <td style="text-align:right;"> 735 </td>
##   </tr>
## </tbody>
## </table>
## <h4> TotRmsAbvGrd </h4>

##      attribute     
## [1,] "TotRmsAbvGrd"
##      d_table                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      
## [1,] "<table class=\"table\" style=\"margin-left: auto; margin-right: auto;\">\n <thead>\n  <tr>\n   <th style=\"text-align:left;\"> Measure </th>\n   <th style=\"text-align:right;\"> Value </th>\n  </tr>\n </thead>\n<tbody>\n  <tr>\n   <td style=\"text-align:left;\"> Min </td>\n   <td style=\"text-align:right;\"> 2.000000 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> First Quartile </td>\n   <td style=\"text-align:right;\"> 5.000000 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> Median </td>\n   <td style=\"text-align:right;\"> 6.000000 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> Mean </td>\n   <td style=\"text-align:right;\"> 6.506181 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> Third Quartile </td>\n   <td style=\"text-align:right;\"> 7.000000 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> Max </td>\n   <td style=\"text-align:right;\"> 14.000000 </td>\n  </tr>\n</tbody>\n</table>"
## <h4> Functional </h4>

## <table class="table" style="margin-left: auto; margin-right: auto;">
##  <thead>
##   <tr>
##    <th style="text-align:left;"> Functional </th>
##    <th style="text-align:right;"> count </th>
##   </tr>
##  </thead>
## <tbody>
##   <tr>
##    <td style="text-align:left;"> Maj1 </td>
##    <td style="text-align:right;"> 14 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> Maj2 </td>
##    <td style="text-align:right;"> 5 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> Min1 </td>
##    <td style="text-align:right;"> 31 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> Min2 </td>
##    <td style="text-align:right;"> 34 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> Mod </td>
##    <td style="text-align:right;"> 15 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> Sev </td>
##    <td style="text-align:right;"> 1 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> Typ </td>
##    <td style="text-align:right;"> 1356 </td>
##   </tr>
## </tbody>
## </table>
## <h4> Fireplaces </h4>

##      attribute   
## [1,] "Fireplaces"
##      d_table                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           
## [1,] "<table class=\"table\" style=\"margin-left: auto; margin-right: auto;\">\n <thead>\n  <tr>\n   <th style=\"text-align:left;\"> Measure </th>\n   <th style=\"text-align:right;\"> Value </th>\n  </tr>\n </thead>\n<tbody>\n  <tr>\n   <td style=\"text-align:left;\"> Min </td>\n   <td style=\"text-align:right;\"> 0.0000000 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> First Quartile </td>\n   <td style=\"text-align:right;\"> 0.0000000 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> Median </td>\n   <td style=\"text-align:right;\"> 1.0000000 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> Mean </td>\n   <td style=\"text-align:right;\"> 0.6092033 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> Third Quartile </td>\n   <td style=\"text-align:right;\"> 1.0000000 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> Max </td>\n   <td style=\"text-align:right;\"> 3.0000000 </td>\n  </tr>\n</tbody>\n</table>"
## <h4> FireplaceQu </h4>

## <table class="table" style="margin-left: auto; margin-right: auto;">
##  <thead>
##   <tr>
##    <th style="text-align:left;"> FireplaceQu </th>
##    <th style="text-align:right;"> count </th>
##   </tr>
##  </thead>
## <tbody>
##   <tr>
##    <td style="text-align:left;"> Ex </td>
##    <td style="text-align:right;"> 23 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> Fa </td>
##    <td style="text-align:right;"> 33 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> Gd </td>
##    <td style="text-align:right;"> 378 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> Po </td>
##    <td style="text-align:right;"> 20 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> TA </td>
##    <td style="text-align:right;"> 312 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> NA </td>
##    <td style="text-align:right;"> 690 </td>
##   </tr>
## </tbody>
## </table>
## <h4> GarageType </h4>

## <table class="table" style="margin-left: auto; margin-right: auto;">
##  <thead>
##   <tr>
##    <th style="text-align:left;"> GarageType </th>
##    <th style="text-align:right;"> count </th>
##   </tr>
##  </thead>
## <tbody>
##   <tr>
##    <td style="text-align:left;"> 2Types </td>
##    <td style="text-align:right;"> 6 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> Attchd </td>
##    <td style="text-align:right;"> 867 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> Basment </td>
##    <td style="text-align:right;"> 19 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> BuiltIn </td>
##    <td style="text-align:right;"> 87 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> CarPort </td>
##    <td style="text-align:right;"> 9 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> Detchd </td>
##    <td style="text-align:right;"> 387 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> NA </td>
##    <td style="text-align:right;"> 81 </td>
##   </tr>
## </tbody>
## </table>
## <h4> GarageYrBlt </h4>

##      attribute    
## [1,] "GarageYrBlt"
##      d_table                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               
## [1,] "<table class=\"table\" style=\"margin-left: auto; margin-right: auto;\">\n <thead>\n  <tr>\n   <th style=\"text-align:left;\"> Measure </th>\n   <th style=\"text-align:right;\"> Value </th>\n  </tr>\n </thead>\n<tbody>\n  <tr>\n   <td style=\"text-align:left;\"> Min </td>\n   <td style=\"text-align:right;\"> 1900.00 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> First Quartile </td>\n   <td style=\"text-align:right;\"> 1961.00 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> Median </td>\n   <td style=\"text-align:right;\"> 1980.00 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> Mean </td>\n   <td style=\"text-align:right;\"> 1978.44 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> Third Quartile </td>\n   <td style=\"text-align:right;\"> 2002.00 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> Max </td>\n   <td style=\"text-align:right;\"> 2010.00 </td>\n  </tr>\n</tbody>\n</table>"
## <h4> GarageFinish </h4>

## <table class="table" style="margin-left: auto; margin-right: auto;">
##  <thead>
##   <tr>
##    <th style="text-align:left;"> GarageFinish </th>
##    <th style="text-align:right;"> count </th>
##   </tr>
##  </thead>
## <tbody>
##   <tr>
##    <td style="text-align:left;"> Fin </td>
##    <td style="text-align:right;"> 348 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> RFn </td>
##    <td style="text-align:right;"> 422 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> Unf </td>
##    <td style="text-align:right;"> 605 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> NA </td>
##    <td style="text-align:right;"> 81 </td>
##   </tr>
## </tbody>
## </table>
## <h4> GarageCars </h4>

##      attribute   
## [1,] "GarageCars"
##      d_table                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     
## [1,] "<table class=\"table\" style=\"margin-left: auto; margin-right: auto;\">\n <thead>\n  <tr>\n   <th style=\"text-align:left;\"> Measure </th>\n   <th style=\"text-align:right;\"> Value </th>\n  </tr>\n </thead>\n<tbody>\n  <tr>\n   <td style=\"text-align:left;\"> Min </td>\n   <td style=\"text-align:right;\"> 0.000000 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> First Quartile </td>\n   <td style=\"text-align:right;\"> 1.000000 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> Median </td>\n   <td style=\"text-align:right;\"> 2.000000 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> Mean </td>\n   <td style=\"text-align:right;\"> 1.764423 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> Third Quartile </td>\n   <td style=\"text-align:right;\"> 2.000000 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> Max </td>\n   <td style=\"text-align:right;\"> 4.000000 </td>\n  </tr>\n</tbody>\n</table>"
## <h4> GarageArea </h4>

##      attribute   
## [1,] "GarageArea"
##      d_table                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    
## [1,] "<table class=\"table\" style=\"margin-left: auto; margin-right: auto;\">\n <thead>\n  <tr>\n   <th style=\"text-align:left;\"> Measure </th>\n   <th style=\"text-align:right;\"> Value </th>\n  </tr>\n </thead>\n<tbody>\n  <tr>\n   <td style=\"text-align:left;\"> Min </td>\n   <td style=\"text-align:right;\"> 0.0000 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> First Quartile </td>\n   <td style=\"text-align:right;\"> 329.5000 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> Median </td>\n   <td style=\"text-align:right;\"> 478.5000 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> Mean </td>\n   <td style=\"text-align:right;\"> 471.5687 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> Third Quartile </td>\n   <td style=\"text-align:right;\"> 576.0000 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> Max </td>\n   <td style=\"text-align:right;\"> 1390.0000 </td>\n  </tr>\n</tbody>\n</table>"
## <h4> GarageQual </h4>

## <table class="table" style="margin-left: auto; margin-right: auto;">
##  <thead>
##   <tr>
##    <th style="text-align:left;"> GarageQual </th>
##    <th style="text-align:right;"> count </th>
##   </tr>
##  </thead>
## <tbody>
##   <tr>
##    <td style="text-align:left;"> Ex </td>
##    <td style="text-align:right;"> 3 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> Fa </td>
##    <td style="text-align:right;"> 48 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> Gd </td>
##    <td style="text-align:right;"> 14 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> Po </td>
##    <td style="text-align:right;"> 3 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> TA </td>
##    <td style="text-align:right;"> 1307 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> NA </td>
##    <td style="text-align:right;"> 81 </td>
##   </tr>
## </tbody>
## </table>
## <h4> GarageCond </h4>

## <table class="table" style="margin-left: auto; margin-right: auto;">
##  <thead>
##   <tr>
##    <th style="text-align:left;"> GarageCond </th>
##    <th style="text-align:right;"> count </th>
##   </tr>
##  </thead>
## <tbody>
##   <tr>
##    <td style="text-align:left;"> Ex </td>
##    <td style="text-align:right;"> 2 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> Fa </td>
##    <td style="text-align:right;"> 35 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> Gd </td>
##    <td style="text-align:right;"> 9 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> Po </td>
##    <td style="text-align:right;"> 7 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> TA </td>
##    <td style="text-align:right;"> 1322 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> NA </td>
##    <td style="text-align:right;"> 81 </td>
##   </tr>
## </tbody>
## </table>
## <h4> PavedDrive </h4>

## <table class="table" style="margin-left: auto; margin-right: auto;">
##  <thead>
##   <tr>
##    <th style="text-align:left;"> PavedDrive </th>
##    <th style="text-align:right;"> count </th>
##   </tr>
##  </thead>
## <tbody>
##   <tr>
##    <td style="text-align:left;"> N </td>
##    <td style="text-align:right;"> 90 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> P </td>
##    <td style="text-align:right;"> 30 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> Y </td>
##    <td style="text-align:right;"> 1336 </td>
##   </tr>
## </tbody>
## </table>
## <h4> WoodDeckSF </h4>

##      attribute   
## [1,] "WoodDeckSF"
##      d_table                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    
## [1,] "<table class=\"table\" style=\"margin-left: auto; margin-right: auto;\">\n <thead>\n  <tr>\n   <th style=\"text-align:left;\"> Measure </th>\n   <th style=\"text-align:right;\"> Value </th>\n  </tr>\n </thead>\n<tbody>\n  <tr>\n   <td style=\"text-align:left;\"> Min </td>\n   <td style=\"text-align:right;\"> 0.00000 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> First Quartile </td>\n   <td style=\"text-align:right;\"> 0.00000 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> Median </td>\n   <td style=\"text-align:right;\"> 0.00000 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> Mean </td>\n   <td style=\"text-align:right;\"> 93.83379 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> Third Quartile </td>\n   <td style=\"text-align:right;\"> 168.00000 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> Max </td>\n   <td style=\"text-align:right;\"> 857.00000 </td>\n  </tr>\n</tbody>\n</table>"
## <h4> OpenPorchSF </h4>

##      attribute    
## [1,] "OpenPorchSF"
##      d_table                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    
## [1,] "<table class=\"table\" style=\"margin-left: auto; margin-right: auto;\">\n <thead>\n  <tr>\n   <th style=\"text-align:left;\"> Measure </th>\n   <th style=\"text-align:right;\"> Value </th>\n  </tr>\n </thead>\n<tbody>\n  <tr>\n   <td style=\"text-align:left;\"> Min </td>\n   <td style=\"text-align:right;\"> 0.00000 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> First Quartile </td>\n   <td style=\"text-align:right;\"> 0.00000 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> Median </td>\n   <td style=\"text-align:right;\"> 24.00000 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> Mean </td>\n   <td style=\"text-align:right;\"> 46.22115 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> Third Quartile </td>\n   <td style=\"text-align:right;\"> 68.00000 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> Max </td>\n   <td style=\"text-align:right;\"> 547.00000 </td>\n  </tr>\n</tbody>\n</table>"
## <h4> EnclosedPorch </h4>

##      attribute      
## [1,] "EnclosedPorch"
##      d_table                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  
## [1,] "<table class=\"table\" style=\"margin-left: auto; margin-right: auto;\">\n <thead>\n  <tr>\n   <th style=\"text-align:left;\"> Measure </th>\n   <th style=\"text-align:right;\"> Value </th>\n  </tr>\n </thead>\n<tbody>\n  <tr>\n   <td style=\"text-align:left;\"> Min </td>\n   <td style=\"text-align:right;\"> 0.00000 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> First Quartile </td>\n   <td style=\"text-align:right;\"> 0.00000 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> Median </td>\n   <td style=\"text-align:right;\"> 0.00000 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> Mean </td>\n   <td style=\"text-align:right;\"> 22.01442 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> Third Quartile </td>\n   <td style=\"text-align:right;\"> 0.00000 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> Max </td>\n   <td style=\"text-align:right;\"> 552.00000 </td>\n  </tr>\n</tbody>\n</table>"
## <h4> X3SsnPorch </h4>

##      attribute   
## [1,] "X3SsnPorch"
##      d_table                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       
## [1,] "<table class=\"table\" style=\"margin-left: auto; margin-right: auto;\">\n <thead>\n  <tr>\n   <th style=\"text-align:left;\"> Measure </th>\n   <th style=\"text-align:right;\"> Value </th>\n  </tr>\n </thead>\n<tbody>\n  <tr>\n   <td style=\"text-align:left;\"> Min </td>\n   <td style=\"text-align:right;\"> 0.000000 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> First Quartile </td>\n   <td style=\"text-align:right;\"> 0.000000 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> Median </td>\n   <td style=\"text-align:right;\"> 0.000000 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> Mean </td>\n   <td style=\"text-align:right;\"> 3.418956 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> Third Quartile </td>\n   <td style=\"text-align:right;\"> 0.000000 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> Max </td>\n   <td style=\"text-align:right;\"> 508.000000 </td>\n  </tr>\n</tbody>\n</table>"
## <h4> ScreenPorch </h4>

##      attribute    
## [1,] "ScreenPorch"
##      d_table                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  
## [1,] "<table class=\"table\" style=\"margin-left: auto; margin-right: auto;\">\n <thead>\n  <tr>\n   <th style=\"text-align:left;\"> Measure </th>\n   <th style=\"text-align:right;\"> Value </th>\n  </tr>\n </thead>\n<tbody>\n  <tr>\n   <td style=\"text-align:left;\"> Min </td>\n   <td style=\"text-align:right;\"> 0.00000 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> First Quartile </td>\n   <td style=\"text-align:right;\"> 0.00000 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> Median </td>\n   <td style=\"text-align:right;\"> 0.00000 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> Mean </td>\n   <td style=\"text-align:right;\"> 15.10234 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> Third Quartile </td>\n   <td style=\"text-align:right;\"> 0.00000 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> Max </td>\n   <td style=\"text-align:right;\"> 480.00000 </td>\n  </tr>\n</tbody>\n</table>"
## <h4> PoolArea </h4>

##      attribute 
## [1,] "PoolArea"
##      d_table                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       
## [1,] "<table class=\"table\" style=\"margin-left: auto; margin-right: auto;\">\n <thead>\n  <tr>\n   <th style=\"text-align:left;\"> Measure </th>\n   <th style=\"text-align:right;\"> Value </th>\n  </tr>\n </thead>\n<tbody>\n  <tr>\n   <td style=\"text-align:left;\"> Min </td>\n   <td style=\"text-align:right;\"> 0.000000 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> First Quartile </td>\n   <td style=\"text-align:right;\"> 0.000000 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> Median </td>\n   <td style=\"text-align:right;\"> 0.000000 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> Mean </td>\n   <td style=\"text-align:right;\"> 2.055632 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> Third Quartile </td>\n   <td style=\"text-align:right;\"> 0.000000 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> Max </td>\n   <td style=\"text-align:right;\"> 738.000000 </td>\n  </tr>\n</tbody>\n</table>"
## <h4> PoolQC </h4>

## <table class="table" style="margin-left: auto; margin-right: auto;">
##  <thead>
##   <tr>
##    <th style="text-align:left;"> PoolQC </th>
##    <th style="text-align:right;"> count </th>
##   </tr>
##  </thead>
## <tbody>
##   <tr>
##    <td style="text-align:left;"> Ex </td>
##    <td style="text-align:right;"> 1 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> Fa </td>
##    <td style="text-align:right;"> 2 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> Gd </td>
##    <td style="text-align:right;"> 2 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> NA </td>
##    <td style="text-align:right;"> 1451 </td>
##   </tr>
## </tbody>
## </table>
## <h4> Fence </h4>

## <table class="table" style="margin-left: auto; margin-right: auto;">
##  <thead>
##   <tr>
##    <th style="text-align:left;"> Fence </th>
##    <th style="text-align:right;"> count </th>
##   </tr>
##  </thead>
## <tbody>
##   <tr>
##    <td style="text-align:left;"> GdPrv </td>
##    <td style="text-align:right;"> 59 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> GdWo </td>
##    <td style="text-align:right;"> 54 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> MnPrv </td>
##    <td style="text-align:right;"> 156 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> MnWw </td>
##    <td style="text-align:right;"> 11 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> NA </td>
##    <td style="text-align:right;"> 1176 </td>
##   </tr>
## </tbody>
## </table>
## <h4> MiscFeature </h4>

## <table class="table" style="margin-left: auto; margin-right: auto;">
##  <thead>
##   <tr>
##    <th style="text-align:left;"> MiscFeature </th>
##    <th style="text-align:right;"> count </th>
##   </tr>
##  </thead>
## <tbody>
##   <tr>
##    <td style="text-align:left;"> Gar2 </td>
##    <td style="text-align:right;"> 2 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> Othr </td>
##    <td style="text-align:right;"> 2 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> Shed </td>
##    <td style="text-align:right;"> 49 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> TenC </td>
##    <td style="text-align:right;"> 1 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> NA </td>
##    <td style="text-align:right;"> 1402 </td>
##   </tr>
## </tbody>
## </table>
## <h4> MiscVal </h4>

##      attribute
## [1,] "MiscVal"
##      d_table                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    
## [1,] "<table class=\"table\" style=\"margin-left: auto; margin-right: auto;\">\n <thead>\n  <tr>\n   <th style=\"text-align:left;\"> Measure </th>\n   <th style=\"text-align:right;\"> Value </th>\n  </tr>\n </thead>\n<tbody>\n  <tr>\n   <td style=\"text-align:left;\"> Min </td>\n   <td style=\"text-align:right;\"> 0.00000 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> First Quartile </td>\n   <td style=\"text-align:right;\"> 0.00000 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> Median </td>\n   <td style=\"text-align:right;\"> 0.00000 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> Mean </td>\n   <td style=\"text-align:right;\"> 43.60852 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> Third Quartile </td>\n   <td style=\"text-align:right;\"> 0.00000 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> Max </td>\n   <td style=\"text-align:right;\"> 15500.00000 </td>\n  </tr>\n</tbody>\n</table>"
## <h4> MoSold </h4>

##      attribute
## [1,] "MoSold" 
##      d_table                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      
## [1,] "<table class=\"table\" style=\"margin-left: auto; margin-right: auto;\">\n <thead>\n  <tr>\n   <th style=\"text-align:left;\"> Measure </th>\n   <th style=\"text-align:right;\"> Value </th>\n  </tr>\n </thead>\n<tbody>\n  <tr>\n   <td style=\"text-align:left;\"> Min </td>\n   <td style=\"text-align:right;\"> 1.000000 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> First Quartile </td>\n   <td style=\"text-align:right;\"> 5.000000 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> Median </td>\n   <td style=\"text-align:right;\"> 6.000000 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> Mean </td>\n   <td style=\"text-align:right;\"> 6.326236 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> Third Quartile </td>\n   <td style=\"text-align:right;\"> 8.000000 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> Max </td>\n   <td style=\"text-align:right;\"> 12.000000 </td>\n  </tr>\n</tbody>\n</table>"
## <h4> YrSold </h4>

##      attribute
## [1,] "YrSold" 
##      d_table                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     
## [1,] "<table class=\"table\" style=\"margin-left: auto; margin-right: auto;\">\n <thead>\n  <tr>\n   <th style=\"text-align:left;\"> Measure </th>\n   <th style=\"text-align:right;\"> Value </th>\n  </tr>\n </thead>\n<tbody>\n  <tr>\n   <td style=\"text-align:left;\"> Min </td>\n   <td style=\"text-align:right;\"> 2006.000 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> First Quartile </td>\n   <td style=\"text-align:right;\"> 2007.000 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> Median </td>\n   <td style=\"text-align:right;\"> 2008.000 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> Mean </td>\n   <td style=\"text-align:right;\"> 2007.817 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> Third Quartile </td>\n   <td style=\"text-align:right;\"> 2009.000 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> Max </td>\n   <td style=\"text-align:right;\"> 2010.000 </td>\n  </tr>\n</tbody>\n</table>"
## <h4> SaleType </h4>

## <table class="table" style="margin-left: auto; margin-right: auto;">
##  <thead>
##   <tr>
##    <th style="text-align:left;"> SaleType </th>
##    <th style="text-align:right;"> count </th>
##   </tr>
##  </thead>
## <tbody>
##   <tr>
##    <td style="text-align:left;"> COD </td>
##    <td style="text-align:right;"> 43 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> Con </td>
##    <td style="text-align:right;"> 2 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> ConLD </td>
##    <td style="text-align:right;"> 9 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> ConLI </td>
##    <td style="text-align:right;"> 5 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> ConLw </td>
##    <td style="text-align:right;"> 5 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> CWD </td>
##    <td style="text-align:right;"> 4 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> New </td>
##    <td style="text-align:right;"> 120 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> Oth </td>
##    <td style="text-align:right;"> 3 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> WD </td>
##    <td style="text-align:right;"> 1265 </td>
##   </tr>
## </tbody>
## </table>
## <h4> SaleCondition </h4>

## <table class="table" style="margin-left: auto; margin-right: auto;">
##  <thead>
##   <tr>
##    <th style="text-align:left;"> SaleCondition </th>
##    <th style="text-align:right;"> count </th>
##   </tr>
##  </thead>
## <tbody>
##   <tr>
##    <td style="text-align:left;"> Abnorml </td>
##    <td style="text-align:right;"> 100 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> AdjLand </td>
##    <td style="text-align:right;"> 4 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> Alloca </td>
##    <td style="text-align:right;"> 12 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> Family </td>
##    <td style="text-align:right;"> 20 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> Normal </td>
##    <td style="text-align:right;"> 1197 </td>
##   </tr>
##   <tr>
##    <td style="text-align:left;"> Partial </td>
##    <td style="text-align:right;"> 123 </td>
##   </tr>
## </tbody>
## </table>
## <h4> SalePrice </h4>

##      attribute  
## [1,] "SalePrice"
##      d_table                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    
## [1,] "<table class=\"table\" style=\"margin-left: auto; margin-right: auto;\">\n <thead>\n  <tr>\n   <th style=\"text-align:left;\"> Measure </th>\n   <th style=\"text-align:right;\"> Value </th>\n  </tr>\n </thead>\n<tbody>\n  <tr>\n   <td style=\"text-align:left;\"> Min </td>\n   <td style=\"text-align:right;\"> 34900.0 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> First Quartile </td>\n   <td style=\"text-align:right;\"> 129900.0 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> Median </td>\n   <td style=\"text-align:right;\"> 163000.0 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> Mean </td>\n   <td style=\"text-align:right;\"> 180151.2 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> Third Quartile </td>\n   <td style=\"text-align:right;\"> 214000.0 </td>\n  </tr>\n  <tr>\n   <td style=\"text-align:left;\"> Max </td>\n   <td style=\"text-align:right;\"> 625000.0 </td>\n  </tr>\n</tbody>\n</table>"

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

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.

Here best prices seem to be a moderate size lot, not necessarily very large lots. Over years the prices have gradually increased per lot but not exponentially.

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

TotalBsmtSF GrLivArea YearBuilt
TotalBsmtSF 1.0000000 0.3948292 0.3998666
GrLivArea 0.3948292 1.0000000 0.1926450
YearBuilt 0.3998666 0.1926450 1.0000000
##           SalePrice LotArea BsmtUnfSF
## SalePrice    1.0000  0.2699    0.2207
## LotArea      0.2699  1.0000   -0.0038
## BsmtUnfSF    0.2207 -0.0038    1.0000
  • The first matrix shows there is good correlation between BsmtUnfSF and YearBuilt whereas low correlation between GrLivArea and YearBuilt
  • The matrix shows that in fact there isn???t a strong correlation between LotArea and BsmtUnfSF, with a correlation very close to zero: -0.0038. We do however find some correlation between these two variables and the Sale Price.

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

- TotalBsmtSF vs GrLivArea

## 
##  Pearson's product-moment correlation
## 
## data:  correlation_data$TotalBsmtSF and correlation_data$GrLivArea
## t = 16.387, df = 1454, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 80 percent confidence interval:
##  0.3660790 0.4228263
## sample estimates:
##       cor 
## 0.3948292

With a very low P value, we are confident the correlation between these two variables is not zero, and we are 80% confident it is between 0.3660790 and 0.4228263

  • TotalBsmtSF vs YearBuilt
## 
##  Pearson's product-moment correlation
## 
## data:  correlation_data$TotalBsmtSF and correlation_data$YearBuilt
## t = 16.635, df = 1454, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 80 percent confidence interval:
##  0.3712479 0.4277263
## sample estimates:
##       cor 
## 0.3998666

With a very low P value, we are confident the correlation between these two variables is not zero, and we are 80% confident it is between 0.3712479 and 0.4277263

  • YearBuilt vs GrLivArea
## 
##  Pearson's product-moment correlation
## 
## data:  correlation_data$YearBuilt and correlation_data$GrLivArea
## t = 7.486, df = 1454, p-value = 1.225e-13
## alternative hypothesis: true correlation is not equal to 0
## 80 percent confidence interval:
##  0.1600736 0.2247973
## sample estimates:
##      cor 
## 0.192645

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 0.1600736 and 0.2247973

  • Sale Price vs Lot Area
## 
##  Pearson's product-moment correlation
## 
## data:  correlationData$SalePrice and correlationData$LotArea
## t = 10.687, df = 1454, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 80 percent confidence interval:
##  0.2384211 0.3007466
## sample estimates:
##       cor 
## 0.2698665

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 0.2384211 and 0.3007466. We can conclude that SalePrice and LotArea are significantly correlated with a correlation coefficient of 0.2698665. There is sufficient evidence to conclude there is a significant linear relationship between SalePrice and LotArea because the correlation coefficient is significantly different from zero.

  • Sale Price vs Basement Size
## 
##  Pearson's product-moment correlation
## 
## data:  correlationData$SalePrice and correlationData$BsmtUnfSF
## t = 8.6274, df = 1454, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 80 percent confidence interval:
##  0.1884678 0.2524136
## sample estimates:
##       cor 
## 0.2206778

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 0.1884678 and 0.2524136

  • Lot Area vs Basement Size
## 
##  Pearson's product-moment correlation
## 
## data:  correlationData$LotArea and correlationData$BsmtUnfSF
## t = -0.14391, df = 1454, p-value = 0.8856
## alternative hypothesis: true correlation is not equal to 0
## 80 percent confidence interval:
##  -0.03737706  0.02983752
## sample estimates:
##          cor 
## -0.003774031

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 -0.03737706 and 0.02983752. It means they have no correlation.

Discuss the meaning of your analysis. 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. Type I error happens when the null is rejected or the P value being smaller than a set threshold.

In our first 5 cases, the P value is extremely 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 hypothesis.

3.2 Question 2 : Linear Algebra and Correlation.

3.2.1 Answer 2

Invert your correlation matrix from above. (This is known as the precision matrix and contains variance inflation factors on the diagonal.)

TotalBsmtSF GrLivArea YearBuilt
TotalBsmtSF 1.3601385 -0.4489077 -0.4573942
GrLivArea -0.4489077 1.1867025 -0.0491090
YearBuilt -0.4573942 -0.0491090 1.1923573

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

TotalBsmtSF GrLivArea YearBuilt
TotalBsmtSF 1 0 0
GrLivArea 0 1 0
YearBuilt 0 0 1
TotalBsmtSF GrLivArea YearBuilt
TotalBsmtSF 1 0 0
GrLivArea 0 1 0
YearBuilt 0 0 1

Conduct LU decomposition on the matrix.

TotalBsmtSF GrLivArea YearBuilt
TotalBsmtSF 1.0000000 0.3948292 0.3998666
GrLivArea 0.3948292 1.0000000 0.1926450
YearBuilt 0.3998666 0.1926450 1.0000000
TotalBsmtSF GrLivArea YearBuilt
TotalBsmtSF 1.0000000 0.3948292 0.3998666
GrLivArea 0.3948292 1.0000000 0.1926450
YearBuilt 0.3998666 0.1926450 1.0000000

Let’s confirm the decomposition by comparing to our original matrix correlationMatrix.

##             TotalBsmtSF GrLivArea YearBuilt
## TotalBsmtSF        TRUE      TRUE      TRUE
## GrLivArea          TRUE      TRUE      TRUE
## YearBuilt          TRUE      TRUE      TRUE

3.3 Question 3 : 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).

3.3.1 Answer 3

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, \(\lambda\))).

Using the Square Footage of the Unfinished Basement for this part of the exam. I know it is right skewed because the mean (566.9903846) is larger than the median (477.5) as shown in the figure below:

Have loaded the MASS package. The minimum (0) is not smaller than zero so we don’t need to shift the data. Remember that the maximum value is 2336.

The optimal value for \(\lambda\) is 0.0017637.

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

The original data is not quite exponential, but it’s not a bad approximation. The exponential distribution data has a longer tail than the basement square footage data.

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

##        5%       95% 
##   83.7765 4414.5876

From this analysis it appears the selected data GrLivArea 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.

The PDF would be \(f(x;\lambda) = \lambda e^{-\lambda x}\) where \(x \geq 0\) and otherwise zero.

The CDF would be \(F(x;\lambda) = 1 - e^{-\lambda x}\). lambda is 0.0017637. To find the 5th percentile we need to solve for x in:

\[0.05 = 1 - e^{-0.0017637 x}\]

\[-0.95 = - e^{-0.0017637 x}\]

\[-ln(0.95) = 0.0017637 x\]

\[x = \frac{-ln(0.95)}{0.0017637} = 29.0828047\] For the 95th percentile we need to solve for x in:

\[0.95 = 1 - e^{-0.0017637 x}\]

\[-0.05 = - e^{-0.0017637 x}\]

\[-ln(0.05) = 0.0017637 x\]

\[x = \frac{-ln(0.05)}{0.0017637} = 1698.551394\]

So the 5th and 95th percentiles are approximately 29 and 1699, respectively.

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

      5%      95% 
544.2769 589.7038 

The 95% confidence interval (assuming normality) is 544 to 590. Although what I think was meant was assume the data is normally distributed. Calculate the 5th and 95th percentile. That is found using \(x = \mu + Z \sigma\). The Z is -1.645 for the 5th percentile, and 1.645 for the 95th. So the percentiles would be -160 and 1294.

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

  5%  95% 
   0 1468 
    5%    95% 
 848.0 2450.5 

The actual 5th percentile is 0 and the 95th is 1468. So the findings are summarized in the following table:

Method 5% 95%
Exponential CDF 29 1699
Normal 95% CI 544 590
Normal Percentiles -160 1294
Emperical Percentiles 0 1468

If we model the data as exponentially distributed the 5th percentile is 29. If we model it as normally distributed the 5th is at -160 which in the context of square footage does not make any sense. The actual 5th percentile is 0. The difference is explained to the assumed shape/distibution of the underlying data.

Looking at the 95th percentile we have 393 if the data are exponentially distributed, 1294 if it is normally distributed and 1468 in reality. Again the difference is due to the assumed shape.

I have left out the 95% CI from the discussion because the confidence interval is a way of estimating the mean of the population. We would know if we took 100 estimates that the actual mean falls within the confidence intervals 95% of the time. Within this context it is meaningless.

3.4 Question 4 : 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.

3.4.1 Answer 4

Since there are so many variables I will be using a Generalized Linear Model for Model 1 to detect which variables are the most important and will be using them to build the model. First I will drop out the variables that are missing a lot of data or otherwise meaningless and choose only numerical variables.

Next I will be using Linear Model for Model 2 with only significant variables

3.4.1.1 Build Models

## 
## Call:
## glm(formula = log(SalePrice) ~ log(LotArea) + OverallQual + YearBuilt + 
##     GrLivArea, data = train_int)
## 
## Deviance Residuals: 
##      Min        1Q    Median        3Q       Max  
## -0.92016  -0.07974   0.01003   0.09551   0.52986  
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  2.402e+00  3.386e-01   7.093 2.04e-12 ***
## log(LotArea) 1.525e-01  8.814e-03  17.298  < 2e-16 ***
## OverallQual  1.252e-01  4.603e-03  27.190  < 2e-16 ***
## YearBuilt    3.583e-03  1.726e-04  20.754  < 2e-16 ***
## GrLivArea    2.705e-04  1.127e-05  24.005  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for gaussian family taken to be 0.02541506)
## 
##     Null deviance: 228.259  on 1455  degrees of freedom
## Residual deviance:  36.877  on 1451  degrees of freedom
## AIC: -1208.1
## 
## Number of Fisher Scoring iterations: 2

## 
## Call:
## lm(formula = SalePrice ~ GrLivArea + BsmtFinSF1 + GarageCars + 
##     GrLivArea + LotArea + Fireplaces + YearBuilt + OverallQual + 
##     BedroomAbvGr, data = model2)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.87601 -0.07637  0.01284  0.08626  0.48649 
## 
## Coefficients:
##                Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   5.641e+00  3.310e-01  17.039  < 2e-16 ***
## GrLivArea     2.777e-04  1.335e-05  20.801  < 2e-16 ***
## BsmtFinSF1    1.417e-04  9.778e-06  14.495  < 2e-16 ***
## GarageCars    6.705e-02  7.163e-03   9.361  < 2e-16 ***
## LotArea       3.340e-06  4.197e-07   7.957 3.52e-15 ***
## Fireplaces    4.134e-02  7.201e-03   5.741 1.15e-08 ***
## YearBuilt     2.589e-03  1.739e-04  14.885  < 2e-16 ***
## OverallQual   1.049e-01  4.553e-03  23.036  < 2e-16 ***
## BedroomAbvGr -6.492e-03  6.150e-03  -1.056    0.291    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.1486 on 1447 degrees of freedom
## Multiple R-squared:   0.86,  Adjusted R-squared:  0.8593 
## F-statistic:  1111 on 8 and 1447 DF,  p-value: < 2.2e-16

##              GrLivArea BsmtFinSF1 GarageCars LotArea Fireplaces YearBuilt
## GrLivArea       1.0000     0.1215     0.4741  0.2319     0.4517    0.1926
## BsmtFinSF1      0.1215     1.0000     0.2240  0.1734     0.2362    0.2483
## GarageCars      0.4741     0.2240     1.0000  0.1510     0.2977    0.5367
## LotArea         0.2319     0.1734     0.1510  1.0000     0.2597    0.0066
## Fireplaces      0.4517     0.2362     0.2977  0.2597     1.0000    0.1432
## YearBuilt       0.1926     0.2483     0.5367  0.0066     0.1432    1.0000
## OverallQual     0.5835     0.2131     0.5987  0.0887     0.3874    0.5717
## BedroomAbvGr    0.5401    -0.1219     0.0831  0.1190     0.1040   -0.0726
##              OverallQual BedroomAbvGr
## GrLivArea         0.5835       0.5401
## BsmtFinSF1        0.2131      -0.1219
## GarageCars        0.5987       0.0831
## LotArea           0.0887       0.1190
## Fireplaces        0.3874       0.1040
## YearBuilt         0.5717      -0.0726
## OverallQual       1.0000       0.0968
## BedroomAbvGr      0.0968       1.0000

  • Model 1

Looking at the coefficients for the predictor variables, we can see they all have a positive estimate, though all are very small values. This makes sense, since we can generally assume that the Lot size, Quality, year a property was built, and square footage of the home would have a positive relationships to the price (i.e. large, well-built, new houses on lots of land cost more).

  • Model 2

For Model2, we eliminated several variables with high P values and chose model with more features.

The biggest difference for these models are transforming the response variable, since it is also skewed, but because of its simplicity, we’ll use this for predicting the Sale Price of the properties in the Kaggle dataset. Using R’s predict function, we’ll feed it the third reduced model, the test dataset, and store the results in an object.

3.4.1.2 Prediction

##        Id         SalePrice    
##  Min.   :1461   Min.   :11.04  
##  1st Qu.:1826   1st Qu.:11.73  
##  Median :2190   Median :11.97  
##  Mean   :2190   Mean   :12.01  
##  3rd Qu.:2554   3rd Qu.:12.27  
##  Max.   :2919   Max.   :13.84

Taking this resulting vector, we’ll bind it to the Id column of the test data, then create a .csv from the data.

GrLivArea BsmtFinSF1 GarageCars LotArea Fireplaces YearBuilt OverallQual BedroomAbvGr SalePrice Id
896 468 1 11622 0 1961 5 2 114616 1461
1329 923 1 14267 0 1958 6 3 152290 1462
1629 791 2 13830 1 1997 5 3 180078 1463
1604 602 2 9978 1 1998 6 3 191382 1464
1280 263 2 5005 0 1992 8 2 192296 1465
1655 0 2 10000 1 1993 6 3 175958 1466
1187 935 2 7980 0 1992 6 3 167690 1467
1465 0 2 8402 1 1998 6 3 168189 1468
1341 637 2 10176 1 1990 7 2 195886 1469
882 804 2 8400 0 1970 4 2 116748 1470
1337 1051 2 5858 1 1999 7 2 209343 1471
987 156 1 1680 0 1971 6 2 123991 1472
1092 300 1 1680 0 1971 5 3 116558 1473
1456 514 2 2280 1 1975 6 3 166576 1474
836 0 1 2280 0 1975 7 2 130766 1475
2334 0 3 12858 1 2009 9 3 327500 1476
1544 0 3 12883 0 2009 8 3 227228 1477
1698 110 3 11520 1 2005 9 3 274688 1478
1822 28 3 14122 1 2005 8 3 255252 1479
2696 1373 3 14300 2 2003 9 3 453610 1480
2250 578 3 13650 1 2002 8 3 307882 1481
1370 24 2 7132 1 2006 8 2 207440 1482
1324 0 2 18494 0 2005 6 3 163435 1483
1145 16 2 3203 0 2006 7 2 165981 1484
1374 326 2 13300 1 2004 7 3 196920 1485
1733 0 2 8577 1 2004 7 3 204489 1486
2475 0 3 17433 1 1998 8 4 300686 1487
1595 0 3 8987 1 2005 8 2 236178 1488
1218 0 2 9215 0 2009 7 2 173768 1489
1468 1414 2 10440 1 2005 6 2 212246 1490
1659 0 2 11920 0 2004 7 3 194375 1491
1012 0 1 9800 0 1920 5 2 99013 1492
1494 126 2 15410 2 1974 6 3 173057 1493
2349 250 3 13143 1 1993 8 4 292726 1494
2225 1129 3 11134 1 1992 8 4 317375 1495
1488 1298 2 4835 1 2004 7 2 228250 1496
1680 0 2 3515 0 2004 7 2 191338 1497
1200 280 2 3215 0 2004 7 2 174065 1498
1200 368 2 2544 0 2004 7 2 175855 1499
1236 376 2 2544 0 2005 6 2 160531 1500
1512 466 2 2980 0 2000 6 2 173539 1501
1080 244 2 2403 0 2003 7 2 166617 1502
1418 1032 3 12853 1 2010 8 1 268821 1503
1848 484 2 7379 1 2000 8 3 247542 1504
1492 833 2 8000 1 2002 7 3 213694 1505
1829 506 2 10456 0 1967 6 4 177091 1506
2495 1137 2 10791 1 1993 6 4 260033 1507
1891 687 2 18837 1 1978 6 3 205169 1508
1645 329 2 9600 0 1971 6 4 165335 1509
1232 698 2 9600 0 1966 5 3 138968 1510
1209 1059 2 9900 0 1966 5 3 145478 1511
1510 1010 2 9680 0 1967 5 3 157357 1512
1775 0 2 10600 0 1964 6 3 162253 1513
1728 1500 0 13260 0 1962 5 6 153536 1514
2461 670 2 9724 2 1952 5 3 204063 1515
1556 300 2 17360 1 1949 6 3 163359 1516
1128 944 1 11380 1 1966 6 2 153215 1517
1604 0 2 8267 0 1958 5 4 135228 1518
1480 1188 2 8197 0 2003 7 3 215602 1519
1143 856 1 8050 0 1959 5 3 126668 1520
1206 936 1 10725 0 1959 5 3 131544 1521
1580 734 2 10032 2 1959 6 3 182524 1522
1337 0 1 8382 0 1956 4 3 105909 1523
1064 339 1 10950 0 1952 5 2 114940 1524
972 648 1 10895 0 1955 5 3 117185 1525
988 532 1 13587 0 1958 5 2 118511 1526
985 0 2 7898 0 1920 4 2 94025 1527
1224 481 1 8064 0 1948 6 3 132605 1528
1175 588 2 7635 0 1960 5 3 131727 1529
1395 717 2 9760 1 1963 6 2 168628 1530
1844 48 1 4800 2 1900 4 3 113969 1531
936 579 0 4485 1 1920 5 2 100760 1532
1347 274 2 5805 0 1957 5 3 130335 1533
1251 0 1 6900 0 1938 6 3 121138 1534
1633 780 1 11851 1 1948 5 3 147295 1535
1245 176 1 8239 0 1920 5 3 107039 1536
832 0 2 9656 1 1923 2 2 77190 1537
1566 0 1 9600 0 1900 8 3 149132 1538
2268 0 2 9000 0 1890 8 3 188470 1539
2256 0 0 9045 0 1910 5 4 125495 1540
1470 283 2 10560 0 1922 6 2 140079 1541
1612 788 1 5830 0 1950 5 3 138582 1542
2068 474 1 7793 1 1922 7 3 181052 1543
765 188 1 5000 0 1925 4 2 85228 1544
1132 452 1 6000 0 1939 6 2 125715 1545
1196 264 2 6000 2 1940 6 3 144168 1546
1453 360 1 6360 2 1942 5 3 133006 1547
1416 300 1 6000 0 1948 6 3 135388 1548
1040 276 2 6240 0 1936 5 2 114288 1549
1536 448 2 6240 1 1930 5 4 136138 1550
1068 960 1 6120 1 1923 6 2 132763 1551
1962 0 2 8094 1 1915 4 4 125330 1552
1560 0 0 12900 0 1912 6 3 117733 1553
1324 0 1 3068 0 1920 6 3 116490 1554
1675 766 1 15263 2 1959 5 3 161310 1555
1224 0 1 10632 0 1917 5 3 103818 1556
1392 1026 0 9900 0 1915 5 3 116750 1557
919 368 1 6001 0 1940 6 3 116636 1558
1884 73 0 6449 0 1907 4 4 101289 1559
1680 736 2 6048 1 1910 5 2 141889 1560
1832 704 0 10773 0 1967 4 4 129377 1561
892 240 1 7800 0 1966 5 3 110150 1562
864 775 1 7832 0 1968 5 2 119304 1563
1373 1319 2 7424 2 1978 5 3 175545 1564
1440 267 2 11227 2 1968 5 4 151067 1565
1483 1092 2 20062 2 1977 7 1 227842 1566
756 0 2 9259 0 1927 4 2 90255 1567
1981 964 2 17082 1 1978 6 4 216098 1568
1610 288 1 18600 1 1938 3 4 109585 1569
1074 104 1 11479 1 1950 6 3 127768 1570
1531 192 1 9350 1 1947 4 3 117324 1571
1172 954 1 9525 0 1954 5 3 128444 1572
1508 1346 2 17485 2 2009 7 1 256166 1573
1298 0 2 11200 0 1964 5 3 128228 1574
1433 1433 2 11980 2 1987 7 1 235566 1575
1802 860 4 12361 1 1993 6 3 238638 1576
1222 24 2 7360 0 2010 7 2 173926 1577
1445 0 2 14235 0 1900 6 3 126974 1578
965 870 2 11105 0 1996 5 2 144554 1579
1692 353 2 9337 1 1997 7 3 209260 1580
1026 198 1 15240 0 1977 5 3 119873 1581
876 480 2 7480 0 1972 5 3 123092 1582
1978 1682 3 10389 1 2003 8 3 331077 1583
2098 0 2 9375 1 1997 7 4 221391 1584
848 672 2 4435 0 2003 6 1 151460 1585
640 0 1 8777 0 1945 3 2 76974 1586
992 0 1 8842 0 1954 5 3 106486 1587
1196 1070 1 10044 0 1968 5 3 136534 1588
1120 0 2 11792 0 1948 4 2 106329 1589
1096 528 1 6305 1 1975 6 3 143144 1590
960 0 0 6410 0 1958 4 3 89070 1591
1296 133 1 4853 1 1924 5 2 113085 1592
856 238 2 7890 1 1939 6 2 126691 1593
2650 0 0 7200 0 1967 4 6 143336 1594
1666 0 0 9839 1 1931 5 3 118305 1595
2133 426 1 10452 2 1941 7 4 200928 1596
2177 375 2 15600 0 1950 5 5 166755 1597
1652 343 2 19645 0 1994 7 3 203644 1598
1034 747 2 3907 1 1989 8 1 199482 1599
1191 76 2 3907 1 1989 8 2 188242 1600
540 480 1 8154 0 1941 2 1 71729 1601
1107 308 1 9140 0 1921 6 2 117985 1602
952 0 1 8712 0 1896 4 3 81569 1603
1646 1373 2 3811 1 2004 8 2 266778 1604
1916 615 3 11050 1 1998 8 3 276765 1605
1285 679 2 9620 1 1977 6 3 167510 1606
2048 0 2 12760 0 1976 6 5 179516 1607
1346 78 3 11896 1 2008 7 3 202876 1608
1214 0 2 9803 0 2009 7 2 173917 1609
1444 0 2 9802 0 2006 5 3 148177 1610
1264 42 2 15300 1 1965 5 2 136243 1611
1430 0 2 10114 0 2004 5 3 146993 1612
1344 0 2 11875 1 1999 5 3 148529 1613
945 915 1 2394 1 1973 5 2 129041 1614
1092 176 0 1476 0 1970 4 3 96121 1615
1092 0 0 1900 0 1970 4 3 93886 1616
1092 294 1 1890 0 1972 4 3 105208 1617
874 469 1 6953 0 1971 5 3 114368 1618
833 207 2 12887 0 1984 5 2 123707 1619
2432 0 2 7700 0 1985 5 4 182163 1620
1274 458 2 10475 0 1991 5 3 145406 1621
1479 476 1 10544 0 1969 5 5 134592 1622
1803 1341 2 9892 2 1994 8 3 285646 1623
1797 944 2 12961 1 1993 6 3 211317 1624
882 564 1 13008 0 1956 6 2 127470 1625
1434 844 2 10200 1 1974 6 4 176529 1626
1608 847 2 10179 1 1997 6 3 197985 1627
2283 850 3 11792 1 2003 8 4 319680 1628
1628 284 2 8400 1 1996 7 3 202413 1629
2522 1965 2 7296 1 2004 8 1 376801 1630
1478 341 2 7380 0 1998 8 2 210301 1631
1734 741 2 8013 0 1995 8 2 237620 1632
1382 189 2 8923 1 1998 7 3 187814 1633
1636 476 2 7500 1 1998 6 3 188109 1634
1516 600 2 8803 1 1994 6 3 184062 1635
1190 0 2 7250 1 1993 6 3 153228 1636
1934 400 2 11900 1 1977 5 3 174942 1637
2050 0 2 13250 1 1978 7 4 210684 1638
1671 363 2 10928 1 1978 6 3 179541 1639
2673 602 2 12388 1 1980 7 4 273414 1640
1707 832 2 11088 1 1978 6 3 193913 1641
1884 622 2 7000 1 2003 7 3 231077 1642
1874 0 2 7500 1 2000 8 3 232900 1643
1811 225 2 8470 1 2002 8 3 238274 1644
1621 1333 2 9373 2 1975 5 3 188198 1645
1116 888 2 10140 1 1974 6 3 163646 1646
1193 636 2 11050 1 1975 7 3 180167 1647
1180 0 2 7830 0 1970 5 2 125438 1648
1050 500 1 8510 0 1971 5 3 121254 1649
864 726 2 7038 0 1970 4 3 113627 1650
864 240 2 9000 0 1971 4 3 107038 1651
987 254 1 1680 0 1973 6 2 126378 1652
987 110 1 1680 0 1972 6 2 123504 1653
1548 306 2 2308 1 1976 6 3 166368 1654
1055 435 2 2280 1 1975 7 2 164725 1655
1456 389 2 2349 1 1977 6 3 164538 1656
1548 320 2 2364 1 1978 6 3 167595 1657
1456 279 2 2364 1 1978 6 3 162421 1658
836 536 1 2104 0 1976 7 2 141370 1659
1120 644 2 10710 1 1966 5 3 139845 1660
2772 1360 3 14257 3 2007 9 4 483747 1661
2690 986 3 12350 1 2009 9 3 415050 1662
2020 1232 3 12350 1 2008 9 3 355888 1663
2674 2288 3 13693 2 2007 10 2 578548 1664
1736 0 3 11578 1 2008 9 3 275492 1665
1782 1531 3 16870 2 2004 8 3 327699 1666
2520 1230 3 23303 1 2007 8 5 375893 1667
1743 1015 3 10367 1 2008 9 3 317448 1668
1531 1037 3 10872 1 2006 9 2 301136 1669
1808 1142 3 13514 1 2008 9 3 332578 1670
1760 1262 2 12878 1 2003 7 3 249299 1671
2452 1972 3 15274 1 2003 9 3 444205 1672
2400 0 3 13262 1 2003 8 4 294197 1673
1606 0 3 9658 1 2006 8 3 236507 1674
1358 836 2 6904 1 2005 6 2 187442 1675
1306 881 2 5122 1 2005 6 1 186037 1676
1358 876 2 10307 1 2007 7 2 212846 1677
2492 2146 3 14836 1 2004 10 2 515204 1678
2200 1557 3 15262 1 2003 8 3 351623 1679
1884 800 2 7390 1 2008 9 2 298418 1680
1456 0 2 6472 1 2008 9 2 235848 1681
1712 1196 3 16770 1 2002 8 3 292459 1682
1405 0 2 3480 1 2003 7 2 184253 1683
1456 0 2 10928 1 2005 7 3 191336 1684
1490 0 2 8918 1 2005 6 3 172755 1685
1220 16 2 3182 1 2005 7 2 176158 1686
1374 0 2 9434 1 2004 7 3 185616 1687
1630 0 2 7984 1 2004 7 3 198330 1688
1594 0 2 10125 1 2004 7 3 197766 1689
1489 652 2 8965 1 2003 7 3 209322 1690
1342 494 2 8174 1 2003 7 3 195980 1691
2004 651 3 12891 1 2002 8 4 287931 1692
1374 241 2 9734 0 2004 7 3 184472 1693
1514 683 2 8433 1 2000 6 3 188817 1694
1430 0 2 7750 1 1999 7 3 185057 1695
2312 913 3 15896 1 1999 7 4 293761 1696
1430 0 2 7848 1 1999 7 3 185118 1697
2687 1173 3 12720 2 2000 8 4 388374 1698
2063 236 3 10750 2 1994 8 3 281536 1699
2061 816 2 9085 1 1995 7 3 246079 1700
2232 624 2 11692 1 1993 8 3 279876 1701
1696 0 3 11194 0 2008 8 3 235082 1702
1658 0 3 10206 1 2008 8 3 241634 1703
1702 1294 3 10130 1 2007 8 3 293009 1704
1432 379 2 9139 1 2006 8 3 221980 1705
2490 2158 3 11128 2 2005 9 2 479319 1706
1436 0 2 7993 0 2008 7 3 182199 1707
1402 0 2 8640 0 2008 7 3 180877 1708
1530 0 3 12606 1 2007 9 3 260394 1709
1448 24 2 7500 1 2006 8 2 212243 1710
1795 682 3 10603 1 2006 8 3 275415 1711
1836 0 2 8125 1 2008 8 3 235769 1712
1662 1430 3 10625 1 2006 7 3 265747 1713
1553 771 2 8736 0 2003 7 3 207764 1714
1653 410 2 8127 0 2003 7 3 202548 1715
1218 0 2 9605 0 2007 7 3 171976 1716
1141 54 2 7500 0 2006 7 3 168007 1717
1158 0 0 7500 0 2004 6 3 131223 1718
1812 0 2 10628 0 2004 7 3 201938 1719
1512 516 3 10141 0 2004 8 3 237010 1720
1114 0 2 13072 0 2004 7 3 167719 1721
1114 0 0 13072 0 2004 5 3 118914 1722
1114 836 2 12450 0 2003 5 3 152373 1723
1450 0 3 7328 0 2008 7 2 196431 1724
2122 637 2 11492 1 1996 7 4 245024 1725
1730 52 2 7703 0 1992 6 3 171887 1726
1332 0 2 7175 0 1990 6 2 152703 1727
1540 36 2 9109 0 1994 7 3 182467 1728
1400 331 2 10274 0 1986 6 3 162032 1729
1882 0 2 8250 2 1981 6 4 187021 1730
980 68 2 9750 0 1962 5 3 117345 1731
864 660 2 8499 0 1961 5 3 122737 1732
864 864 1 9079 0 1961 5 2 119144 1733
1020 544 1 9316 0 1965 5 3 119457 1734
912 624 1 7791 0 1963 5 3 116051 1735
912 140 1 7150 0 1962 5 3 107846 1736
2014 1733 3 15676 2 1980 8 2 338840 1737
1755 601 2 11949 1 1991 7 3 219075 1738
3005 0 3 2880 1 2004 7 3 305447 1739
1726 0 2 3830 1 2008 6 2 183952 1740
1256 962 2 4217 1 2008 6 1 186473 1741
1512 507 2 2998 0 2000 6 2 174561 1742
1452 549 2 3768 0 1999 7 3 190556 1743
1694 1252 2 14694 1 1977 8 2 256993 1744
1740 121 2 15417 0 1981 7 2 194040 1745
2499 0 2 9600 1 1976 8 4 260490 1746
2067 560 2 12732 2 1974 7 3 237507 1747
2640 0 2 10400 1 1967 6 5 213754 1748
1336 553 2 9600 1 1969 5 3 147184 1749
1216 955 1 9000 0 1969 6 3 149878 1750
2288 432 2 13774 2 1977 7 4 249182 1751
864 648 1 7130 0 1967 5 2 116599 1752
1568 0 2 9600 0 1967 5 3 138547 1753
2061 698 2 9600 1 1974 7 4 228102 1754
1320 962 2 16500 1 1971 6 3 177384 1755
894 734 2 7436 1 1960 4 2 117410 1756
864 403 1 8125 0 1959 5 3 109962 1757
1362 775 3 9450 1 1957 4 3 142731 1758
1728 625 2 13495 1 1956 5 3 162406 1759
1313 310 2 9350 1 1961 5 3 138284 1760
1292 998 2 10500 2 1964 5 3 159802 1761
2140 388 2 8970 1 1965 5 4 176376 1762
1576 568 2 11475 1 1961 6 4 171470 1763
960 100 1 9768 0 1955 5 2 108362 1764
1691 1173 2 9900 0 1967 6 2 189427 1765
1453 1312 2 10573 1 1961 6 3 184782 1766
1567 1387 2 14695 2 1966 6 2 207682 1767
1144 856 1 8760 0 1956 5 3 126022 1768
1329 544 2 12285 2 1960 7 3 185908 1769
988 708 1 9240 0 1959 6 3 132478 1770
1202 435 1 8750 0 1956 5 3 120646 1771
1382 172 1 8750 0 1955 5 3 121873 1772
1200 155 1 10400 2 1956 4 3 113969 1773
1866 0 2 9482 0 1958 5 4 146026 1774
1062 490 1 8128 0 1954 6 3 128948 1775
1112 308 2 13070 0 1951 5 2 124573 1776
793 700 1 8480 0 1945 5 2 109284 1777
1031 931 1 7626 0 1952 5 2 122493 1778
1210 0 1 9533 0 1953 5 2 113837 1779
1527 699 2 11419 1 1948 7 3 186216 1780
1200 390 1 9600 0 1950 5 3 118301 1781
792 0 1 5470 0 1958 3 2 82128 1782
1352 0 2 10800 0 1939 5 4 121057 1783
1039 0 1 8146 0 1900 4 2 84823 1784
1078 0 1 10230 0 1925 5 3 101643 1785
2377 0 2 10410 1 1915 4 3 142654 1786
1690 0 2 7200 0 1910 7 4 150326 1787
599 0 0 5400 0 1940 2 2 62547 1788
846 0 2 10800 0 1920 5 2 101448 1789
725 0 1 10800 0 1890 3 1 69265 1790
2544 0 3 9671 0 1969 6 6 212752 1791
1380 384 1 10143 0 1963 6 3 142983 1792
1040 872 2 11500 1 1967 6 3 157709 1793
951 745 2 8010 0 1958 6 2 140926 1794
1105 546 1 10454 0 1957 6 3 133596 1795
1142 0 1 9000 1 1958 6 2 130749 1796
1133 621 2 8064 0 1950 6 3 141766 1797
1041 0 1 7350 0 1958 5 3 108527 1798
732 630 1 7200 0 1952 5 2 107871 1799
1183 433 1 8000 0 1959 5 3 120610 1800
1461 0 1 10800 0 1949 4 4 107821 1801
1495 120 2 8064 0 1948 6 3 145259 1802
1806 0 2 7570 0 1964 6 4 160960 1803
941 941 2 8604 0 1978 5 2 137291 1804
1045 826 1 7936 1 1963 6 3 143496 1805
1378 0 1 4080 0 1935 6 3 123348 1806
1944 633 2 10307 0 1910 6 4 160541 1807
1306 0 2 15660 0 1910 5 3 113425 1808
1464 0 0 9900 0 1910 5 3 101664 1809
1558 421 2 6406 1 1939 5 3 140653 1810
1701 0 0 7627 0 1920 4 4 98929 1811
1447 0 0 10134 0 1910 5 3 101264 1812
1328 384 1 6000 0 1950 5 3 121014 1813
861 0 2 7404 0 1920 4 2 90693 1814
612 0 1 5925 0 1940 2 1 67682 1815
792 0 1 8520 0 1923 5 2 93471 1816
1510 0 2 9600 0 1910 4 3 105918 1817
2007 0 1 8400 0 1900 6 3 136116 1818
1288 0 1 3600 1 1917 6 3 119481 1819
816 0 0 3300 1 1910 4 2 78463 1820
1480 0 1 5400 0 1920 6 3 122599 1821
1521 0 3 9720 0 1910 6 4 139276 1822
797 0 0 9392 0 1900 3 2 67059 1823
1432 0 1 6615 1 1923 6 3 127581 1824
1654 0 1 4960 1 1930 5 3 123730 1825
1142 220 1 6000 0 1924 5 3 104973 1826
995 0 1 6120 0 1925 5 2 98611 1827
1582 273 1 6120 1 1938 5 3 129203 1828
1072 134 5 8635 0 1925 5 2 135391 1829
1768 0 2 8094 0 1915 6 3 141458 1830
1944 0 1 9928 0 1915 7 3 155219 1831
2128 0 0 3000 0 1922 5 4 122436 1832
1930 522 1 6876 0 1927 6 4 152082 1833
1427 0 1 5775 0 1915 6 3 119403 1834
1864 169 0 5852 0 1902 7 6 136017 1835
1666 0 1 5160 0 1927 6 3 131353 1836
892 749 0 5160 0 1923 4 1 89559 1837
1403 276 1 10320 0 1915 6 3 125228 1838
704 0 1 4280 0 1946 4 2 85944 1839
1200 1200 0 10800 0 1987 5 3 137108 1840
1152 1152 1 10547 0 1978 5 2 141180 1841
1112 0 1 9780 0 1934 5 4 104189 1842
1052 527 1 11625 1 1967 5 3 126933 1843
1034 456 2 8014 1 1978 6 3 150951 1844
1774 0 1 15400 1 1961 5 4 142601 1845
1138 588 2 15312 1 1960 6 3 154830 1846
2071 0 1 15584 1 1956 5 4 152964 1847
660 0 0 9000 0 1947 2 2 65562 1848
1383 0 2 15635 0 1954 4 2 117677 1849
1073 257 1 9571 0 1956 5 2 114553 1850
1639 342 1 9350 1 1946 6 3 151924 1851
1089 173 1 7440 1 1954 5 3 116295 1852
1049 552 1 4235 0 1984 5 2 125317 1853
1061 460 2 10778 0 1990 7 1 171032 1854
1338 70 2 19255 1 1983 6 2 164622 1855
1879 474 2 10560 1 1993 7 3 222825 1856
2016 0 2 26400 1 1880 5 4 137190 1857
2228 0 2 7018 0 1979 5 6 166910 1858
1535 0 2 7018 0 1979 5 4 139490 1859
1229 1094 2 7040 2 1979 5 2 164649 1860
1513 0 2 7007 0 1979 5 4 138635 1861
2787 820 4 11855 2 2000 7 6 359962 1862
2787 820 4 7939 2 2000 7 6 355284 1863
2787 820 4 7976 2 2000 7 6 355328 1864
1680 1021 3 10933 1 2009 9 1 317708 1865
1720 1104 3 10816 1 2008 9 3 319910 1866
1468 0 3 9178 1 2008 8 3 228430 1867
1838 1359 2 11422 2 2007 8 3 300602 1868
1290 902 2 6762 1 2007 7 2 207168 1869
1254 872 3 10324 0 2008 8 2 236127 1870
1498 24 3 11645 1 2005 8 3 231235 1871
1422 0 2 11646 1 2005 6 3 171075 1872
1759 800 2 16698 1 1992 7 3 229793 1873
990 755 1 9757 0 1994 5 3 131772 1874
1463 950 2 14753 0 1998 7 3 209335 1875
1772 606 2 8750 1 1998 6 3 199815 1876
1444 1259 2 10739 0 2002 7 3 216892 1877
1492 24 2 11166 1 2001 7 3 192072 1878
907 625 1 16269 0 1978 5 3 123956 1879
914 710 2 6950 0 1979 5 2 131490 1880
1611 1234 3 11664 0 2002 7 3 242833 1881
2184 0 2 12334 1 2003 8 4 258298 1882
1725 0 2 8749 0 2002 7 3 194873 1883
1870 0 2 11250 0 2001 7 3 204053 1884
1513 1246 2 15750 1 1999 8 2 259411 1885
1828 1360 2 12782 1 2002 8 3 285262 1886
1417 1111 2 8750 1 1997 7 3 215440 1887
1602 1478 3 10200 1 2007 8 3 292582 1888
1396 0 2 11069 1 2007 6 3 170397 1889
1149 399 1 10682 0 1960 4 3 108305 1890
1072 547 2 3675 0 2005 6 2 157742 1891
876 332 1 6410 0 1959 4 3 97787 1892
1368 1078 1 11767 0 1950 5 3 137639 1893
1678 0 0 10926 0 1959 5 6 120529 1894
1560 546 1 11767 1 1956 5 2 143440 1895
1298 626 1 8212 2 1941 5 3 132774 1896
1268 832 1 6300 2 1938 5 3 133668 1897
1242 0 1 5707 1 1935 6 3 124464 1898
1232 0 2 8574 1 1916 6 3 127573 1899
1228 0 1 7155 1 1918 7 3 132403 1900
1567 728 2 13680 2 1940 5 2 158701 1901
1273 793 1 14680 0 1960 5 2 134285 1902
2480 246 2 8145 2 1940 7 5 226799 1903
1112 154 1 9100 1 1954 5 2 118139 1904
1561 65 2 13339 1 1960 6 3 160626 1905
1523 312 1 15600 1 1949 5 3 135730 1906
1906 784 2 17500 2 1954 6 3 203669 1907
1032 0 2 1733 1 1980 6 2 140115 1908
1229 471 2 1488 1 1980 6 2 158081 1909
1229 0 2 1612 1 1980 6 2 147934 1910
1982 454 2 13607 1 1986 6 3 204246 1911
2365 803 2 17597 2 1971 7 3 269313 1912
2168 0 2 8660 0 1900 5 5 135405 1913
572 0 1 10200 0 1925 4 2 80034 1914
1648 1476 2 3843 1 2007 8 2 272992 1915
810 0 1 21780 0 1910 2 1 69763 1916
2052 445 3 10125 1 2000 8 3 281162 1917
926 767 1 9750 1 1977 6 2 144560 1918
1287 841 2 9360 2 1977 6 2 179742 1919
1595 55 2 11070 0 1991 5 2 151416 1920
2036 1758 3 13438 1 2008 9 3 386543 1921
1641 1115 3 14463 0 2008 9 3 304448 1922
2237 462 2 9839 1 1980 6 3 213397 1923
1479 904 2 14419 1 1987 7 3 211370 1924
2014 0 2 9157 0 2003 7 3 211993 1925
1978 1640 3 12633 1 2007 9 2 374513 1926
1008 532 1 12518 0 1968 5 3 121071 1927
1404 594 2 13383 1 1969 5 3 152782 1928
796 720 1 7689 0 1972 5 2 117316 1929
1091 114 1 7706 0 1993 6 2 137032 1930
883 718 2 7669 1 1992 5 2 141013 1931
1287 330 2 10429 0 1992 5 3 143658 1932
1632 496 2 10457 1 1969 5 4 157933 1933
1604 706 2 8702 1 1997 6 3 192898 1934
1470 476 2 8139 1 1995 6 3 178626 1935
1604 851 2 9535 0 1998 6 3 189946 1936
1636 138 2 15038 1 1996 6 3 182933 1937
1384 450 2 14137 0 1996 5 3 153564 1938
1682 656 2 6264 1 1997 8 1 242586 1939
1280 0 2 5070 0 1992 8 2 185301 1940
1633 0 2 11184 1 1998 6 3 177866 1941
1709 504 2 14067 0 1991 6 3 185626 1942
1337 319 2 5950 1 1989 8 2 204289 1943
2500 16 3 13543 1 2005 8 5 303054 1944
1884 1337 3 15401 1 2004 9 2 350044 1945
1474 0 2 31220 2 1952 6 3 168353 1946
1710 1034 2 8118 1 2007 9 2 293883 1947
1488 0 2 47280 1 1950 6 3 170216 1948
1688 983 2 12680 1 1988 7 2 227265 1949
1260 747 2 10825 0 1983 7 3 182516 1950
2064 1206 2 18559 2 1978 7 3 267934 1951
1782 864 2 14450 1 1979 7 3 223962 1952
1211 890 2 13068 1 1976 6 3 170600 1953
2044 0 2 10400 1 1980 7 3 210786 1954
1308 280 2 9743 0 1969 5 3 134875 1955
2840 988 4 12511 2 1978 7 4 358795 1956
1444 0 2 10400 1 1976 6 2 160047 1957
2340 1023 3 14311 1 1996 8 4 329627 1958
1792 0 2 9000 0 1974 5 4 148865 1959
936 252 1 10295 0 1969 4 2 102870 1960
864 119 2 7560 0 1971 5 3 116293 1961
987 458 1 1680 0 1973 6 2 130085 1962
987 483 1 1890 0 1972 6 2 130300 1963
1302 350 1 1680 0 1972 5 3 124759 1964
1456 286 2 2308 0 1975 6 4 153760 1965
1055 378 2 2529 0 1977 7 2 157727 1966
1582 1012 3 12704 0 2007 8 3 263529 1967
2464 1728 3 13693 1 2007 8 4 387118 1968
1950 1375 3 14418 1 2007 9 2 360054 1969
2748 1420 3 13418 1 2006 9 4 443779 1970
2790 1082 4 12539 1 2005 10 4 505477 1971
2331 1249 3 12151 1 2005 9 3 385662 1972
2088 40 3 8899 1 2007 8 4 270172 1973
2332 856 3 10574 1 2004 8 4 323856 1974
2470 2257 3 12720 2 2003 10 1 540430 1975
1575 1149 3 10845 1 2003 8 2 276693 1976
2649 1075 3 16900 1 2001 8 4 369715 1977
2690 0 3 16451 1 2003 8 4 322285 1978
1866 372 3 10110 1 2008 9 2 301561 1979
1367 20 2 12304 1 2005 7 2 189282 1980
1800 1204 3 8232 1 2007 9 2 330202 1981
1342 846 2 6240 1 2006 8 2 230579 1982
1342 24 2 6240 1 2006 8 2 205221 1983
1626 0 2 2448 0 2003 7 2 187334 1984
1455 1073 3 3940 1 2003 7 2 232959 1985
1576 1087 3 3940 1 2004 7 2 242024 1986
1246 0 2 3710 1 2007 7 2 178266 1987
1515 0 2 9024 1 2004 6 3 173570 1988
1720 0 2 8010 1 2002 7 3 202317 1989
1986 0 2 8396 1 2003 7 4 217259 1990
1358 876 2 7301 1 2007 7 2 210720 1991
1892 544 2 8220 1 2000 7 3 228200 1992
1414 0 2 7750 1 2002 7 3 185673 1993
2322 870 2 12460 1 1999 7 4 270676 1994
1651 0 2 8390 1 1999 7 3 197192 1995
2199 0 2 9660 1 1997 8 3 254757 1996
2172 0 3 11000 1 2000 9 4 302023 1997
2006 1660 3 11675 1 1998 8 2 331906 1998
2125 851 2 10990 2 1996 7 4 263009 1999
2501 0 3 11929 1 1995 8 4 295048 2000
2197 228 3 10010 1 1993 7 4 249275 2001
1578 1096 3 13253 1 2006 7 3 249799 2002
1861 0 3 9801 1 2007 8 3 254642 2003
1874 729 3 9428 1 2007 8 3 283027 2004
1460 666 2 10037 1 2006 8 3 233700 2005
1372 24 2 8640 0 2007 8 3 199375 2006
1660 0 3 10625 1 2007 8 3 241481 2007
1218 902 2 7500 0 2007 7 2 195324 2008
1696 80 2 10110 0 2003 6 3 177306 2009
1663 0 2 12774 0 2003 7 3 194642 2010
1175 80 0 13072 0 2005 6 3 136205 2011
1162 0 2 9260 0 2007 7 3 169127 2012
1609 362 2 8453 0 1995 6 3 175466 2013
1680 602 2 8480 0 1993 6 3 184212 2014
1657 537 2 14565 0 1994 7 3 206085 2015
1677 472 2 8450 0 2001 6 3 184461 2016
1737 397 2 8285 0 1992 7 3 201243 2017
984 53 1 9100 1 1963 5 3 114298 2018
864 764 1 8100 1 1961 5 3 121236 2019
890 890 1 8450 0 1968 5 3 121603 2020
864 489 1 6360 0 1963 5 3 111808 2021
1430 800 2 19508 2 1974 6 3 189627 2022
1641 190 2 10759 1 1972 5 4 152945 2023
2683 704 2 9205 2 1990 6 4 265052 2024
2786 520 2 11025 1 1993 9 4 354115 2025
1245 24 2 3435 0 2004 7 1 171206 2026
1200 390 2 3180 0 2005 6 2 159589 2027
1392 0 2 3180 0 2007 7 2 177809 2028
1549 550 2 2280 0 1999 6 3 175417 2029
1638 1027 2 4765 1 2000 9 2 279465 2030
1310 1004 2 4538 1 2001 9 1 256429 2031
1419 964 2 4385 1 2001 9 2 260981 2032
1557 1141 2 4109 1 1999 9 2 276375 2033
1404 600 2 2160 0 1999 7 3 188382 2034
1789 681 2 10646 1 2001 7 3 228544 2035
1586 612 2 2645 0 1999 8 3 220793 2036
1607 813 2 2645 0 1999 8 3 228502 2037
2393 128 2 3951 1 1998 10 2 334326 2038
1239 560 2 11064 1 1995 8 1 213916 2039
2944 410 3 24572 1 1977 9 3 393579 2040
1671 1044 2 16280 1 1976 8 3 247003 2041
1812 0 2 7500 1 2002 7 3 207199 2042
1427 828 2 11104 0 1969 6 4 167002 2043
1740 301 2 11050 1 1968 6 4 175705 2044
1620 603 2 15387 1 1967 7 4 199352 2045
1625 0 2 9750 0 1965 5 4 139194 2046
1464 732 2 8814 0 1968 5 4 148346 2047
925 260 2 8125 0 1965 5 3 119032 2048
1728 0 2 11072 0 1965 5 6 142011 2049
1670 583 2 13355 0 1971 7 4 194095 2050
1014 0 1 7785 0 1956 5 2 108015 2051
1114 0 2 9900 0 1961 5 3 120374 2052
1118 528 1 11332 0 1960 5 3 121716 2053
906 120 1 4882 0 1937 4 2 90515 2054
1496 658 2 9600 0 1960 5 3 146402 2055
1337 32 1 9600 1 1950 5 3 121739 2056
1036 531 1 7584 0 1953 5 3 115435 2057
1988 575 2 14670 1 1966 6 4 197044 2058
1176 621 1 8856 2 1957 5 3 133971 2059
1440 1053 1 9840 0 1959 5 2 143228 2060
1570 958 2 13200 1 1958 6 3 181726 2061
1104 774 1 10425 0 1956 5 3 123876 2062
882 148 1 11556 0 1952 5 2 106573 2063
1152 500 2 9373 0 1953 5 3 127683 2064
950 624 2 12774 0 1953 5 2 125071 2065
1790 0 2 14250 2 1957 6 3 175929 2066
1764 0 1 8838 1 1957 5 4 137690 2067
1824 0 2 12436 0 1957 5 5 144446 2068
869 0 1 10122 0 1948 4 1 92823 2069
1159 0 1 7506 0 1925 5 3 103014 2070
672 0 1 5400 0 1940 4 2 84185 2071
1436 0 4 10836 1 1922 5 3 142258 2072
1044 744 2 10180 1 1968 5 3 139353 2073
1312 637 2 11355 1 1958 7 3 178410 2074
1081 697 1 12929 0 1960 6 3 137771 2075
876 432 2 7200 1 1951 5 2 121349 2076
1256 476 1 8000 0 1959 5 3 123832 2077
1027 520 1 8000 0 1962 5 3 117841 2078
1320 315 2 8064 0 1948 6 3 142246 2079
984 0 1 6390 0 1954 6 2 117800 2080
1278 673 1 7200 0 1954 6 4 139176 2081
1800 0 0 8513 0 1961 5 6 124324 2082
1588 370 2 7200 0 1955 5 3 141193 2083
825 0 1 7200 0 1954 5 2 101763 2084
1117 0 1 7590 0 1963 5 3 112376 2085
1133 96 1 9836 0 2008 6 3 143851 2086
1323 0 2 9184 0 1948 5 3 123051 2087
1360 0 1 4800 0 1910 5 2 104512 2088
672 0 1 4800 0 1940 5 2 93308 2089
1456 0 1 6000 0 1915 6 4 119680 2090
1594 0 0 11426 0 1910 4 3 95391 2091
1656 0 2 7628 0 1940 4 2 119196 2092
1740 360 1 7308 1 1920 5 2 131823 2093
1027 0 0 5400 1 1920 7 2 117776 2094
1436 590 2 10800 2 1940 6 3 164000 2095
899 0 1 6756 0 1910 5 2 92556 2096
1080 0 0 5914 0 1890 5 3 85623 2097
1499 445 3 9000 1 1946 5 3 152498 2098
407 0 1 7311 0 1946 2 1 65239 2099
1588 0 0 12205 0 1949 3 5 93878 2100
1627 0 2 9142 0 1900 5 4 117464 2101
1450 116 1 5350 0 1920 7 3 137242 2102
1017 0 1 9143 0 1900 5 2 93941 2103
2350 234 2 9600 0 1920 5 4 156551 2104
1540 0 0 6000 0 1905 5 3 101171 2105
1086 0 2 11340 0 1920 2 2 79307 2106
2495 0 2 10800 1 1890 7 5 187066 2107
984 200 1 9750 0 1959 5 2 111789 2108
1093 0 1 8516 0 1958 4 2 100177 2109
1143 406 1 7111 1 1928 5 2 114691 2110
1668 0 1 7425 0 1945 7 3 154083 2111
1738 175 1 7010 1 1935 5 3 132426 2112
1210 600 1 5000 0 1941 5 3 117579 2113
1290 0 1 5870 0 1900 6 3 110603 2114
1672 521 1 6000 1 1940 6 3 153116 2115
949 0 2 6000 1 1924 5 2 108182 2116
1497 201 1 6000 0 1937 6 3 132706 2117
1342 264 1 6000 1 1939 6 2 135237 2118
1013 0 1 5000 0 1926 6 3 109227 2119
1216 68 1 5520 1 1920 5 3 107996 2120
896 NA 1 5940 0 1946 4 2 157815 2121
1136 80 1 6240 0 1929 4 2 94400 2122
808 0 1 6120 0 1945 5 1 99237 2123
2009 300 2 6240 1 1939 7 4 191928 2124
1902 203 2 6120 0 1923 5 4 137101 2125
1716 0 2 9144 0 1915 6 4 139014 2126
1984 196 1 8094 0 1910 6 5 140721 2127
1609 0 1 4347 0 1910 6 3 123388 2128
768 0 2 6291 0 1930 6 1 112179 2129
1536 372 1 10266 0 1952 6 4 143996 2130
1969 0 2 6876 1 1938 6 4 163717 2131
1308 0 2 10320 0 1915 5 2 113670 2132
1040 0 2 7200 0 1925 6 2 119012 2133
1236 121 1 7006 1 1925 6 3 123712 2134
759 0 2 10320 0 1912 5 1 97472 2135
1344 0 0 10320 0 1915 3 3 80876 2136
1054 0 1 9488 0 1947 5 3 106620 2137
1075 784 2 11235 0 1963 5 3 134361 2138
1096 528 2 13014 1 1978 6 3 157761 2139
992 758 1 10265 0 1967 5 3 123206 2140
1034 450 2 7703 1 1978 6 3 150666 2141
1073 221 1 9981 0 1967 5 3 116663 2142
1126 104 2 7400 0 1984 5 2 129847 2143
1140 1300 2 12900 0 1920 5 3 132418 2144
960 634 1 9239 0 1963 5 3 118346 2145
1188 776 2 14175 1 1956 6 1 161046 2146
1721 988 2 10532 2 1960 5 3 177933 2147
1350 336 3 8375 0 1941 5 2 137063 2148
904 704 3 10200 0 1970 5 3 137472 2149
1524 599 2 20270 2 1979 7 3 213375 2150
1079 0 1 5190 1 1948 7 2 137285 2151
1518 1035 0 19550 2 1940 5 2 145828 2152
1509 870 1 9571 1 1956 5 3 146035 2153
864 864 0 9350 0 1975 5 2 115633 2154
1269 324 1 9360 0 1962 6 3 136755 2155
2814 779 2 9771 1 1995 6 4 270542 2156
1626 1271 2 9938 1 1994 7 3 232665 2157
2200 355 2 14171 1 1993 7 4 240864 2158
2037 0 2 10541 1 1996 7 3 219376 2159
1356 0 2 10616 1 2007 7 3 186867 2160
1615 0 3 9345 1 2007 8 3 237465 2161
2276 2085 3 11778 2 2008 9 3 448557 2162
1766 1153 3 11778 2 2008 9 3 341148 2163
1511 770 3 11454 1 1995 8 3 251201 2164
1643 262 2 11500 1 1966 6 2 171684 2165
990 722 2 9750 0 1994 5 3 140250 2166
1418 1308 2 8696 1 1997 7 3 221562 2167
1771 688 2 13142 0 1997 6 3 196267 2168
1652 527 2 8998 0 2000 7 3 204880 2169
1823 663 2 12192 0 2000 7 3 221374 2170
1174 781 2 12250 0 1978 5 3 144000 2171
1076 294 2 9216 1 1975 5 3 133890 2172
1558 88 2 14330 0 1975 5 2 146044 2173
2161 0 2 10400 1 2001 7 3 229911 2174
1947 1194 3 9720 1 2001 9 3 337665 2175
1786 1538 3 14860 1 2002 8 3 311365 2176
2327 0 2 10905 1 2003 7 4 240848 2177
1764 0 2 11690 1 1999 8 3 228484 2178
848 662 2 4426 0 2004 6 1 151633 2179
1838 1593 3 10126 0 1997 6 2 242213 2180
1445 24 2 9750 0 2004 7 3 182457 2181
1564 56 3 11058 0 2007 7 3 205056 2182
1361 24 2 9627 0 2007 7 3 179566 2183
1092 609 1 9825 0 1966 5 3 123526 2184
1033 456 2 12102 0 1976 5 3 131489 2185
1127 1033 2 6500 1 1976 6 3 166389 2186
1117 368 2 9638 1 1977 6 3 152990 2187
1398 288 2 7200 1 1976 6 3 161796 2188
3820 0 2 47007 2 1959 5 5 308130 2189
1152 0 0 6012 0 1955 4 2 93704 2190
1152 0 0 6845 0 1955 4 2 93965 2191
784 784 0 6931 0 1955 4 2 94834 2192
1053 0 0 12180 0 1938 5 2 98902 2193
1137 0 0 8050 0 1947 5 4 100884 2194
930 767 1 9520 0 1953 4 2 105719 2195
1204 0 1 7692 0 1954 4 3 101307 2196
1292 224 1 5142 0 1923 4 3 98060 2197
1424 0 1 7290 1 1921 7 2 141881 2198
1920 281 2 7804 2 1930 6 4 172103 2199
1316 379 1 8969 1 1926 6 2 133270 2200
1264 0 2 15564 0 1914 6 3 125763 2201
1512 406 1 7609 1 1925 8 3 171878 2202
1603 0 2 9650 1 1923 6 4 143586 2203
1938 606 1 11700 1 1937 5 4 150958 2204
1374 0 1 9260 0 1938 5 3 113758 2205
1091 500 1 7801 1 1951 6 2 135349 2206
1873 210 2 9670 2 1935 8 4 211438 2207
2161 435 2 12392 2 1950 7 3 224825 2208
1898 1116 2 26073 2 1956 5 3 198393 2209
1032 366 2 1879 1 1980 6 2 147647 2210
919 299 1 7000 0 1926 6 2 112491 2211
1090 0 1 6000 0 1940 6 3 116093 2212
1200 0 0 8155 0 1930 5 4 98279 2213
1656 257 1 6000 1 1967 5 3 141789 2214
912 0 1 7392 0 1930 5 2 98035 2215
1955 330 1 9000 0 1958 5 4 146438 2216
733 0 2 14584 0 1952 1 2 71100 2217
1361 0 1 5280 0 1895 4 2 90692 2218
1049 0 1 5150 0 1910 4 2 86420 2219
864 0 1 9000 0 1920 4 3 84783 2220
1648 1476 2 3843 1 2007 8 2 272992 2221
1646 1474 2 3811 1 2004 7 2 243676 2222
2032 700 3 23730 0 1996 7 3 259400 2223
1820 0 3 11050 1 1996 7 3 221247 2224
1872 0 2 10260 0 1976 5 4 153645 2225
1689 1383 2 9990 1 1991 4 3 174288 2226
1501 893 2 4084 1 1986 7 2 205932 2227
1537 1036 3 11563 0 2006 8 3 259477 2228
1780 770 2 12852 1 2007 8 3 262338 2229
1442 0 2 9802 0 2006 5 3 148095 2230
1612 0 3 12018 0 2008 7 3 207363 2231
1495 0 2 12890 1 1989 6 3 168192 2232
1256 920 2 18265 1 1986 6 3 181148 2233
1440 1029 2 11202 1 2003 8 3 243729 2234
1675 1223 2 7915 0 1999 6 3 203641 2235
1728 1011 2 11449 1 2007 8 3 266311 2236
1964 1571 3 11447 1 2005 8 3 327484 2237
1344 1309 4 8940 0 1997 7 2 239934 2238
1092 0 0 9278 0 2007 5 2 118378 2239
1189 864 2 4500 0 1997 6 2 167406 2240
1200 865 3 14137 0 1964 4 3 137162 2241
1040 769 2 4224 0 1975 5 3 133798 2242
1475 318 1 2665 1 1976 5 4 136782 2243
988 501 1 1974 0 1973 4 2 106247 2244
988 437 1 1596 1 1973 4 1 110307 2245
1160 785 1 17979 0 1968 5 3 133311 2246
1092 358 0 1477 0 1970 6 3 121654 2247
816 534 1 6490 0 1983 5 2 117746 2248
845 638 1 6600 0 1982 5 3 119416 2249
889 647 2 12395 0 1984 5 3 132647 2250
1836 0 1 56600 0 1900 5 4 136405 2251
1587 838 2 10667 1 1971 6 3 184087 2252
1384 0 2 8872 1 1997 6 3 164280 2253
1694 186 2 10147 1 1994 6 3 183188 2254
1714 871 2 8637 1 1999 6 3 204600 2255
1553 414 2 7875 0 1996 7 3 193409 2256
2299 0 2 7500 1 1999 6 5 209198 2257
1187 0 2 9556 0 1992 7 3 163982 2258
1642 0 2 7655 1 1993 6 3 173956 2259
1128 550 2 18160 1 1964 6 3 156652 2260
1179 248 2 4740 0 1988 8 2 184495 2261
1321 926 2 5118 1 1990 8 1 223057 2262
2541 986 3 12328 1 2005 8 4 352557 2263
2338 1101 3 51974 2 2006 9 4 448708 2264
1424 1047 3 41600 0 1969 5 3 184698 2265
1612 797 2 8035 1 2006 9 2 275754 2266
2234 1558 2 14082 1 2006 8 1 337612 2267
2042 1152 3 13870 1 2006 10 3 393144 2268
1284 256 2 10960 0 1984 6 3 154789 2269
1479 321 2 12090 1 1981 7 3 190123 2270
1664 1328 2 12299 1 1978 7 3 229224 2271
1930 758 2 11339 1 1979 7 4 226031 2272
1177 781 2 11850 0 1984 6 3 162346 2273
1353 903 2 10400 1 1979 6 2 178743 2274
1220 492 2 13001 1 1971 6 2 160572 2275
1324 624 2 8991 1 1976 7 3 185727 2276
1877 931 2 8000 1 1974 6 4 200635 2277
1422 566 2 9457 0 1970 5 3 145209 2278
914 81 1 7920 0 1970 5 3 109528 2279
914 314 1 17199 0 1961 4 2 103389 2280
1337 0 2 4113 1 2001 6 2 162304 2281
1337 930 2 10943 1 1997 6 2 187493 2282
1092 312 1 2205 0 1973 6 3 130571 2283
1218 0 1 2058 0 1973 6 4 128471 2284
1055 632 1 2304 0 1978 7 2 153185 2285
988 725 1 7150 0 1966 5 3 120913 2286
1816 1151 3 12469 1 2006 9 3 330863 2287
1694 0 3 11825 1 2006 8 3 244118 2288
2122 1518 3 14333 1 2007 8 2 346927 2289
2656 1304 3 13641 1 2007 9 3 429732 2290
2550 0 3 13440 1 2006 8 4 309286 2291
2046 1430 3 15431 2 2005 10 2 430586 2292
2552 1812 3 13891 2 2007 9 3 467995 2293
2758 0 3 13654 1 2005 9 4 363233 2294
2290 1684 3 17169 1 2007 10 2 463379 2295
2152 0 2 16659 1 2007 8 3 264151 2296
2100 778 3 9709 2 2007 8 3 316565 2297
1802 0 3 13615 1 2006 9 3 281044 2298
2956 0 3 13069 1 2004 8 5 341759 2299
2385 938 3 14277 1 2003 8 3 337955 2300
1818 669 3 12568 1 2007 8 3 279213 2301
1614 1178 3 9926 0 2005 7 3 241588 2302
1721 119 2 9254 0 2005 8 3 221949 2303
1828 0 3 10732 0 2006 8 3 242226 2304
1302 866 2 3901 1 2005 6 1 184681 2305
1302 1030 2 3903 1 2005 6 1 189026 2306
1362 762 2 6289 1 2005 6 2 185311 2307
1554 24 2 4590 1 2006 8 2 216470 2308
1577 848 2 7841 1 2005 9 2 274179 2309
1324 24 2 6240 1 2006 8 2 204198 2310
1405 1000 2 3242 1 2003 7 2 212140 2311
1496 0 2 15810 0 2007 6 3 170783 2312
1536 0 2 10237 1 2005 6 3 175748 2313
1458 0 2 13204 0 2006 7 3 185571 2314
1495 0 2 8857 1 2006 6 3 173408 2315
1746 0 3 9729 1 2006 6 3 199400 2316
1326 918 2 12216 0 2005 6 3 182383 2317
1504 0 2 8229 0 2007 6 3 166883 2318
1456 0 2 7713 0 2007 7 3 182569 2319
1258 0 2 7697 0 2007 7 3 172793 2320
1589 1084 3 3621 1 2003 8 2 268663 2321
1266 0 2 3710 1 2007 7 2 179259 2322
1119 779 2 16219 0 2004 7 2 190774 2323
1374 192 2 11084 1 2004 7 3 191791 2324
1525 0 2 10936 1 2006 7 3 195549 2325
1394 0 2 11950 1 2003 7 3 187739 2326
1948 0 2 7875 1 2003 7 4 214604 2327
1995 574 2 8740 1 2002 7 4 235922 2328
1690 520 2 9487 1 2000 6 3 194430 2329
1644 0 2 9649 1 1999 6 3 177958 2330
2551 1181 3 12191 2 1997 8 4 370852 2331
3078 672 3 10557 1 1998 9 4 424405 2332
2582 1048 3 11002 1 1998 8 4 351720 2333
2385 0 3 10790 1 1998 7 4 258268 2334
2202 335 2 11762 1 1992 8 4 264068 2335
2538 1225 3 9044 1 1996 8 4 352125 2336
1369 0 2 9910 0 2007 7 3 179524 2337
1542 1220 3 11830 1 2007 8 3 278930 2338
1534 28 2 10612 1 2006 8 3 218347 2339
1966 1572 3 12291 1 2007 10 1 412773 2340
1528 0 2 9965 1 2007 7 3 195584 2341
1538 769 2 8847 0 2005 8 3 230994 2342
1506 778 2 8251 1 2005 7 3 214700 2343
1977 0 3 9605 0 2006 7 3 226466 2344
1830 0 3 8778 0 2006 8 3 240784 2345
1338 24 2 8640 0 2007 8 3 197502 2346
1335 0 2 9000 0 2006 7 3 176839 2347
1792 350 2 8640 0 2007 8 3 234634 2348
1588 0 2 10411 0 2007 5 3 154937 2349
1880 745 3 12217 1 2007 8 3 286802 2350
1584 0 2 10440 1 2007 8 2 222407 2351
1685 0 3 11824 1 2006 8 2 245094 2352
2443 0 3 10625 1 2004 6 4 239894 2353
1100 0 0 7500 0 2006 6 3 129797 2354
1143 0 0 7500 0 2006 7 3 145883 2355
1094 729 2 12450 0 2003 5 3 149248 2356
1486 0 2 7441 0 2006 7 3 183454 2357
1820 480 2 11613 0 1993 6 3 190212 2358
1266 0 1 8012 2 1980 6 2 148815 2359
894 138 1 6285 0 1977 5 2 111928 2360
1040 812 2 7476 0 1968 5 3 133642 2361
2503 727 2 19522 1 1990 7 3 280816 2362
1037 787 2 10751 0 1974 5 2 137517 2363
1055 968 2 12712 1 1973 6 2 164777 2364
1378 851 2 4379 1 2004 8 2 230420 2365
1151 60 2 3523 0 2006 8 2 185998 2366
1565 60 2 3784 0 2006 8 2 208841 2367
1352 937 2 3606 1 2006 7 2 209051 2368
1550 0 2 5330 0 2006 8 2 207279 2369
1501 565 2 2280 1 1999 6 3 180784 2370
1573 417 2 2117 0 2000 6 3 173647 2371
1358 0 2 7321 0 1999 7 3 173799 2372
2048 964 2 8010 2 2003 8 3 294821 2373
2362 901 2 8413 2 1998 8 3 315148 2374
1494 457 2 9466 1 1994 8 1 224499 2375
2362 1732 2 12000 1 1980 7 3 295886 2376
2497 1632 2 17778 2 1981 8 2 360647 2377
1152 0 2 11700 0 1968 6 3 138404 2378
2411 915 2 8000 1 1970 6 4 229788 2379
1082 973 2 8723 0 1969 6 3 154669 2380
1295 910 2 11700 0 1968 6 3 163836 2381
1610 346 2 11358 1 1972 7 3 192838 2382
1594 0 2 9547 1 1993 7 2 193093 2383
2075 819 2 10530 1 1993 7 3 247056 2384
1093 792 2 10738 1 1966 6 3 157433 2385
1052 617 1 10800 0 1963 6 3 135213 2386
1107 474 1 8050 0 1967 5 3 121285 2387
1224 0 3 10899 0 1964 4 2 121621 2388
1074 438 2 7450 1 1956 5 2 130097 2389
1187 311 2 14357 1 1961 5 2 136685 2390
964 700 2 8243 1 1961 5 3 132154 2391
894 0 1 8680 0 1960 5 3 105193 2392
1200 654 2 8800 1 1966 7 3 175488 2393
1042 494 2 9200 0 1965 6 3 141674 2394
2154 414 2 8800 1 1964 6 5 195474 2395
1374 54 1 11382 1 1964 6 3 142930 2396
1652 1386 2 22002 1 1959 6 3 203959 2397
908 130 2 12172 0 1940 5 2 111224 2398
666 299 0 5000 0 1946 3 2 74887 2399
670 144 0 3500 0 1945 3 2 72786 2400
808 150 1 5175 0 1958 5 2 103833 2401
1150 368 1 9600 0 1955 5 2 118589 2402
1560 0 3 8668 0 1968 5 4 146793 2403
1280 602 2 10050 1 1966 5 3 145011 2404
1254 600 2 9600 1 1961 6 3 157551 2405
936 873 1 8760 0 1957 6 2 133629 2406
1008 908 1 6860 0 1956 5 3 121475 2407
1053 288 2 8250 0 1963 5 3 123242 2408
1144 0 1 9100 1 1960 5 3 117679 2409
1721 668 2 9736 3 1957 6 4 193517 2410
922 512 1 9770 0 1957 5 2 114263 2411
1411 780 1 12198 1 1955 5 3 141184 2412
1216 288 1 10050 0 1955 5 3 118826 2413
1154 408 1 11556 0 1953 5 3 118784 2414
1560 0 2 8078 0 1958 5 4 133502 2415
948 441 2 10950 0 1952 6 2 134102 2416
1040 85 1 7942 0 1953 6 3 120625 2417
925 114 1 8540 0 1956 5 3 106670 2418
1540 150 1 7150 0 1955 4 4 112958 2419
925 793 1 8400 2 1955 5 3 127180 2420
1647 595 1 9532 1 1953 4 3 130374 2421
924 292 1 15783 0 1952 5 2 111611 2422
1544 0 0 14190 0 1890 4 3 90157 2423
1728 198 1 12099 1 1953 5 3 141189 2424
3086 0 3 21281 0 1935 5 4 214755 2425
1281 1030 2 10284 0 1925 4 1 121407 2426
1534 0 0 10800 0 1895 5 3 100012 2427
1651 242 1 10090 2 1963 7 4 181047 2428
888 192 1 8700 0 1961 5 3 108201 2429
952 952 1 8300 0 1968 6 3 138540 2430
1238 432 1 7200 1 1950 5 3 124345 2431
1040 574 1 7500 0 1959 5 3 118056 2432
1170 625 1 7315 1 1958 5 3 128076 2433
1242 739 1 7903 0 1960 5 3 128326 2434
1377 1098 1 8000 2 1960 5 3 152316 2435
925 0 1 7000 0 1961 5 3 105782 2436
864 110 1 6600 0 1962 5 2 106461 2437
936 734 1 6760 1 1962 5 3 122927 2438
960 0 2 6978 0 1926 5 2 105001 2439
1296 276 2 6000 0 1927 6 3 132173 2440
1022 782 1 4480 1 1922 5 2 114161 2441
967 0 1 3153 1 1920 5 2 99673 2442
1072 0 2 7200 2 1940 5 2 122088 2443
1174 130 2 9000 1 1900 5 2 111343 2444
1141 122 1 5925 0 1900 4 3 87555 2445
1798 0 2 9639 0 1900 4 4 111096 2446
1772 0 2 10337 0 1910 8 3 173719 2447
1642 196 1 9863 1 1927 6 4 141113 2448
1232 168 2 4571 0 1910 5 3 109658 2449
1650 259 2 8398 0 1910 6 3 140332 2450
1358 316 1 3600 1 1930 5 3 118647 2451
2454 0 2 13500 1 1879 7 3 183754 2452
968 0 1 8626 0 1956 4 2 96295 2453
1382 0 1 11800 1 1949 4 1 112471 2454
1060 317 1 6854 1 1925 5 1 110437 2455
1435 910 1 8674 0 1950 5 3 135517 2456
1274 306 1 6125 0 1939 5 3 114640 2457
1232 276 1 6000 2 1939 6 3 136052 2458
884 0 1 6120 0 1939 5 2 99146 2459
1409 52 2 6240 1 1938 6 3 141793 2460
1322 48 1 6240 0 1939 5 4 111325 2461
1426 0 1 6240 1 1930 5 3 116637 2462
1281 351 2 6120 0 1926 5 2 120301 2463
2264 0 1 7755 0 1918 6 4 151840 2464
1376 0 2 8850 0 1920 6 3 128845 2465
1316 0 2 8550 0 1926 5 4 115019 2466
1344 336 2 5700 1 1929 7 3 157017 2467
1173 0 1 5680 0 1901 5 3 96595 2468
1214 0 1 5680 0 1901 5 2 98337 2469
2294 375 2 13200 1 1963 6 5 204565 2470
1952 354 1 9780 2 1950 7 4 193163 2471
2180 375 2 10320 1 1915 6 3 175623 2472
1315 681 2 4330 0 1958 4 3 122938 2473
1484 0 1 10320 0 1910 4 3 98573 2474
2267 288 2 12888 2 1937 7 3 219626 2475
1282 485 1 4484 0 1942 5 2 118886 2476
999 925 1 11235 0 1963 5 3 125506 2477
1452 785 2 11235 1 1964 5 2 156928 2478
1005 513 2 14299 0 1964 4 3 115655 2479
1020 68 2 14149 1 1964 5 3 126146 2480
1040 249 1 11677 0 1966 5 3 116416 2481
868 748 2 8425 0 1971 5 2 128478 2482
897 168 1 8665 0 1968 5 3 110068 2483
943 114 2 8398 0 1967 5 2 118662 2484
912 216 1 8169 0 1966 5 3 110524 2485
1375 386 1 14175 1 1956 5 3 133409 2486
2654 267 2 16779 1 1920 5 4 182691 2487
1302 258 1 6960 2 1940 7 2 155571 2488
1299 736 2 11375 1 1954 6 3 160666 2489
1176 190 1 13770 2 1958 5 3 128450 2490
998 0 2 9000 0 1945 4 3 100392 2491
1522 299 2 11075 1 1984 6 3 173466 2492
1325 300 2 17541 1 1948 5 3 137680 2493
1630 587 2 22692 1 1953 5 3 160847 2494
1242 0 1 17808 0 1946 4 2 104406 2495
2422 353 2 12671 2 1954 6 4 216174 2496
1626 491 1 10512 0 1954 6 3 152039 2497
864 453 1 5400 0 1958 5 3 109457 2498
943 0 1 11515 0 1958 4 3 96429 2499
1038 283 1 3869 0 1984 5 2 120114 2500
1342 557 1 9280 0 1951 5 4 125382 2501
1480 1080 1 11100 1 1951 5 4 147117 2502
1362 0 1 7550 0 1920 4 4 96260 2503
1822 0 2 23920 1 1984 6 4 187414 2504
1958 497 2 9317 1 1994 7 3 228155 2505
1651 0 3 9178 1 2007 8 3 239717 2506
2140 0 3 10481 0 2006 8 3 263928 2507
1651 0 3 10235 1 2007 8 3 240565 2508
1546 20 3 11750 0 2005 7 3 202414 2509
1500 36 2 8760 1 2006 8 3 215205 2510
1270 0 2 7242 0 2005 7 2 173334 2511
1795 0 2 9316 0 2005 7 3 200627 2512
1873 608 2 8883 1 1988 7 3 222554 2513
1743 51 2 20064 2 1976 8 0 235595 2514
1022 550 2 14217 0 1994 5 3 140169 2515
1308 539 2 10021 0 1997 6 3 167228 2516
990 420 1 8428 0 1994 5 3 125105 2517
1097 549 1 16561 0 1996 5 3 135570 2518
1873 342 2 10820 1 1999 7 3 221941 2519
1753 638 2 12352 1 1998 7 3 224431 2520
1690 0 2 9543 0 2001 7 3 193000 2521
1842 841 2 8826 1 2000 7 3 235205 2522
894 663 2 11800 0 1974 5 3 129473 2523
1025 502 2 8660 1 1976 5 3 136056 2524
1009 755 2 9720 1 1977 5 3 141261 2525
1040 539 2 8982 0 1977 5 3 132264 2526
907 60 1 16300 0 1977 5 3 114133 2527
879 330 2 9675 0 1975 5 3 122438 2528
864 671 2 7200 0 1972 5 3 125931 2529
875 385 2 7200 0 1972 4 3 109220 2530
1673 1412 2 11354 1 2000 7 3 245402 2531
1932 654 2 8749 1 2003 7 3 236620 2532
1729 0 2 8158 0 2002 7 3 194705 2533
1592 408 2 11927 1 1994 8 3 228007 2534
2439 1198 2 12728 1 2001 8 4 327295 2535
1992 762 2 15295 2 1996 7 3 255573 2536
1341 915 2 17227 1 1999 8 1 238689 2537
1476 0 2 8145 0 2007 7 3 183851 2538
1190 709 2 8769 0 2005 7 2 188404 2539
1330 0 2 8334 1 2006 6 3 165352 2540
1491 0 2 8333 1 2006 7 3 192034 2541
1536 0 2 9045 0 2005 5 3 151236 2542
936 936 1 9825 1 1967 5 2 130307 2543
1088 132 2 8308 0 1963 4 2 110339 2544
1351 130 2 16287 1 1925 5 3 127018 2545
1179 0 2 8240 0 1960 6 2 135898 2546
1044 504 2 6285 1 1976 6 3 150744 2547
2233 0 2 9555 0 1979 5 5 169662 2548
1408 611 2 7023 0 2005 5 3 158086 2549
5095 4010 3 39290 2 2008 10 2 1579681 2550
1072 467 2 3675 0 2005 6 2 155963 2551
960 77 1 6400 0 1959 5 2 107913 2552
1152 0 0 6882 0 1955 4 2 93976 2553
1195 0 0 8741 0 1946 5 4 102493 2554
865 144 1 10042 1 1920 6 2 112379 2555
768 544 1 8172 1 1955 4 2 102126 2556
864 682 2 8172 0 1955 4 3 109033 2557
2592 371 0 10890 0 1923 5 6 149155 2558
1422 319 1 7223 0 1926 5 3 116135 2559
1298 113 1 6821 1 1921 6 2 125156 2560
1098 246 1 4000 1 1930 7 2 135861 2561
1436 0 1 6720 1 1921 6 3 127108 2562
1461 0 1 7155 1 1926 6 3 129849 2563
1718 0 2 7230 1 1927 7 4 165014 2564
1226 0 2 13108 1 1951 5 2 128300 2565
1755 189 1 7810 1 1930 4 4 118046 2566
1355 533 2 6221 0 1941 5 3 130192 2567
1560 540 2 25485 3 1960 6 3 194294 2568
1488 813 2 21579 2 1968 6 3 191405 2569
1045 330 2 1782 1 1980 6 2 147379 2570
1680 0 2 17871 0 1995 4 4 141322 2571
1020 577 2 3907 0 1988 8 1 185640 2572
1696 434 2 20693 2 1971 7 3 214463 2573
2726 0 2 18044 1 1986 8 2 296687 2574
1215 375 2 7000 0 1940 6 3 135998 2575
1601 0 0 7288 0 1925 5 3 108834 2576
1828 548 0 9060 0 1923 5 3 125370 2577
816 0 1 3672 0 1922 5 2 92345 2578
845 0 1 11067 0 1939 2 1 73267 2579
1991 0 0 8250 0 1895 5 4 111853 2580
1073 967 2 6565 0 1957 4 3 120288 2581
1001 737 1 6060 0 1930 5 2 111057 2582
1625 1573 2 5568 1 2006 8 2 275883 2583
1299 1001 2 12150 1 1979 6 2 179592 2584
1392 585 3 10000 1 2002 5 3 175139 2585
1409 1392 2 12864 1 2002 7 1 232748 2586
1478 1239 2 9928 1 1991 7 3 220559 2587
918 224 1 8750 0 1975 7 3 140197 2588
1026 924 2 8410 1 1974 6 2 160537 2589
1501 949 2 4054 2 1987 7 2 216873 2590
2279 0 2 19958 1 1958 6 4 196310 2591
1689 0 2 8368 0 2006 7 3 194695 2592
1564 583 2 8298 1 2006 8 2 237897 2593
1240 215 2 10331 0 1985 7 3 168918 2594
1312 250 2 6718 0 2001 8 2 199358 2595
1922 1329 3 11305 1 2002 8 2 312227 2596
1491 0 2 7777 1 1996 6 3 168181 2597
2486 766 2 11800 1 2003 7 5 279606 2598
1824 0 3 12633 1 2006 10 3 313009 2599
2034 0 4 43500 0 1953 3 2 158924 2600
936 16 2 6710 0 1996 6 0 140858 2601
1092 252 1 1504 0 1972 4 3 104449 2602
992 503 1 1533 0 1970 4 2 105416 2603
1092 384 0 1495 0 1970 4 3 99003 2604
1092 0 1 1890 0 1976 4 3 101965 2605
1008 923 2 9129 1 1977 5 1 146226 2606
1356 1148 2 15957 1 1977 6 3 186493 2607
1676 1112 2 33983 2 1977 5 3 202111 2608
1432 531 2 8286 1 1977 5 3 153169 2609
796 796 0 6723 0 1971 5 2 110253 2610
1608 811 1 27697 0 1961 4 3 138411 2611
1178 1090 2 11000 0 1976 5 3 149212 2612
816 596 1 11625 0 1983 5 2 120840 2613
887 516 1 10447 0 1984 5 3 120906 2614
1293 468 2 11027 0 1954 6 2 148959 2615
1024 773 1 10533 2 1956 6 2 147135 2616
1797 1127 3 11765 1 1957 5 3 189479 2617
1390 1110 2 39384 2 1957 6 1 203009 2618
1851 0 2 11727 1 1969 7 3 195040 2619
1525 700 2 8238 1 1997 6 3 188260 2620
1671 0 2 13041 1 1995 6 3 179472 2621
1776 0 2 9783 1 1996 6 3 183256 2622
2064 0 2 13128 1 2005 8 4 251796 2623
2212 60 3 13751 1 2005 7 3 256970 2624
2687 0 2 13108 0 1994 8 4 279148 2625
1169 705 2 8076 1 1993 6 3 168810 2626
1204 0 2 3701 0 1987 8 2 178280 2627
2798 1218 3 16023 1 2005 9 3 442830 2628
3390 0 3 18062 1 2006 10 5 486025 2629
2473 205 3 12292 1 2006 9 4 344810 2630
2698 1206 3 16052 1 2006 10 4 475704 2631
2795 0 3 15922 1 2005 9 4 369775 2632
1714 1191 2 8147 1 2005 9 2 299305 2633
2000 1416 3 18261 2 2005 9 3 383163 2634
1102 850 2 10464 1 1980 6 2 165925 2635
1857 0 2 10530 1 1978 7 4 197883 2636
1083 1005 2 9927 1 1976 7 2 185113 2637
2318 788 2 9512 1 2005 7 3 270525 2638
1875 548 2 10530 1 1975 6 3 193288 2639
1103 755 2 10000 0 1974 6 3 153459 2640
874 20 2 7200 0 1971 4 3 103417 2641
1419 951 2 8773 0 2002 6 2 185646 2642
1092 0 2 2760 0 1973 6 3 133834 2643
1365 402 2 2160 1 1973 5 3 143142 2644
1030 282 1 1890 0 1972 6 3 127333 2645
948 276 1 1680 0 1972 6 2 125082 2646
1092 382 1 1680 0 1972 6 3 131301 2647
1069 727 2 4043 1 1975 6 2 156108 2648
1387 373 1 7514 1 1967 5 3 134442 2649
1055 120 1 2280 0 1976 7 2 141716 2650
1456 70 2 2179 1 1976 6 3 156769 2651
2589 1369 3 16387 1 2006 9 4 425753 2652
1618 0 3 16163 1 2004 8 2 242827 2653
1740 0 3 12228 0 2006 7 4 212523 2654
1868 1505 3 14780 1 2005 9 2 357073 2655
2206 0 3 13975 1 2005 9 4 311944 2656
2091 1290 2 9942 1 2005 9 3 336868 2657
2253 0 2 12867 1 2005 8 3 266860 2658
2389 0 3 10672 1 2006 8 4 293041 2659
2358 880 3 11643 1 2005 8 4 329337 2660
1792 1232 3 13758 1 2005 9 2 335201 2661
1780 1383 3 14828 1 2004 9 2 341649 2662
1914 994 3 13215 1 2004 8 3 298596 2663
1565 472 2 5911 1 2005 9 2 257421 2664
1686 1023 3 7740 1 2006 9 1 312515 2665
1666 415 2 6373 1 2006 9 2 263701 2666
1456 0 2 10237 1 2005 6 3 171887 2667
1492 0 2 10237 0 2006 7 3 185484 2668
1326 0 2 11660 0 2006 6 3 160250 2669
2373 0 3 11631 1 2004 8 4 291166 2670
1492 0 2 9073 0 2006 7 3 184764 2671
1364 453 2 3087 1 2006 7 2 195504 2672
1511 1038 2 2938 1 2002 7 2 218867 2673
1548 1059 2 3072 1 2004 7 2 223037 2674
1142 16 2 3010 0 2005 7 2 165307 2675
1598 0 2 9171 1 2004 7 3 197356 2676
1889 732 2 8658 1 2000 6 3 211159 2677
2322 0 3 12104 0 2006 7 4 249699 2678
1976 791 3 9660 1 1998 8 3 287187 2679
2234 505 3 9545 1 2000 8 3 297686 2680
2855 1182 3 9233 1 2000 9 4 429146 2681
2726 527 3 10019 1 1995 8 4 336276 2682
3500 292 3 17242 1 1993 9 4 456416 2683
2494 380 3 10236 1 1994 8 4 308218 2684
2799 247 3 12585 1 1993 8 3 333088 2685
1964 0 2 12447 1 2005 8 3 245935 2686
1670 1562 3 15218 1 2006 8 2 308030 2687
1504 0 2 10936 0 2006 8 3 207167 2688
1278 24 2 8640 0 2006 8 2 194998 2689
2640 1836 3 13162 1 2006 9 3 459405 2690
1716 0 2 8125 0 2005 6 3 176028 2691
1142 24 0 7733 0 2005 6 3 131529 2692
1400 0 2 11024 0 2005 7 3 180812 2693
1131 0 0 13072 0 2005 6 3 133034 2694
1686 0 2 7800 0 2005 7 3 193662 2695
1585 0 2 7632 0 2005 7 3 188200 2696
1837 0 2 8304 0 1997 6 3 178419 2697
1731 758 2 9370 0 1992 6 3 191090 2698
1398 904 2 7175 0 1990 6 2 176787 2699
1217 278 2 7175 0 1991 6 2 154246 2700
1320 274 2 9019 0 1994 6 3 159815 2701
988 36 2 9100 0 1962 5 3 116820 2702
1654 0 2 8927 0 1977 6 4 160313 2703
1211 612 2 9240 1 1962 5 2 141528 2704
984 554 1 9308 0 1965 5 3 118433 2705
909 162 1 8450 0 1968 5 3 110262 2706
925 181 2 8638 0 1963 5 2 118064 2707
1024 712 1 13052 0 1965 5 3 124009 2708
912 644 0 8020 0 1964 5 3 109198 2709
941 659 1 8789 1 1967 5 3 124222 2710
2646 1023 2 14330 4 1974 7 3 325262 2711
2826 1118 3 11025 3 1992 8 3 409214 2712
1143 0 2 3628 1 2004 7 1 172971 2713
1223 0 2 2544 0 2005 7 2 168423 2714
1524 353 2 2998 0 2000 6 2 171362 2715
1080 0 2 4447 0 2003 7 2 162056 2716
1694 0 1 8314 1 1997 7 3 185607 2717
1568 0 2 7180 1 2001 8 3 214252 2718
1193 962 2 13110 0 1972 5 2 147610 2719
1334 553 2 10140 0 1967 7 3 173502 2720
1051 758 2 9600 0 1968 5 3 133976 2721
1770 361 2 8640 0 1968 5 4 153141 2722
976 760 2 9360 1 1968 6 2 152786 2723
898 744 1 8400 0 1968 5 3 119358 2724
1051 799 1 9759 0 1966 5 3 125433 2725
1141 602 1 9600 0 1967 5 3 125324 2726
1565 901 1 8800 2 1965 6 3 176047 2727
1488 260 2 10368 1 1964 6 3 161883 2728
1440 360 2 9350 1 1964 5 4 144451 2729
1248 632 1 10800 0 1960 5 3 127837 2730
816 574 1 8550 1 1934 6 2 121568 2731
1043 0 1 9724 1 1947 5 2 111591 2732
1433 915 2 9600 1 1961 5 3 155900 2733
1624 40 1 10858 1 1952 5 2 134100 2734
1216 996 1 9600 0 1951 5 3 129820 2735
1728 0 1 9462 1 1949 5 3 134676 2736
936 486 1 9888 0 1954 5 2 113447 2737
1584 0 2 8917 0 1967 5 4 137949 2738
1246 939 2 12700 2 1964 6 3 175044 2739
1008 0 2 9723 0 1963 6 2 131254 2740
1364 623 1 8400 1 1957 5 3 135267 2741
1336 203 2 9610 1 1958 6 3 151188 2742
1370 678 1 10000 1 1956 5 3 136930 2743
1124 914 1 10152 1 1956 6 3 146936 2744
1050 824 1 8092 0 1954 6 3 134733 2745
1008 658 1 12778 0 1952 5 2 119126 2746
1575 0 2 10170 1 1951 6 2 155456 2747
1145 271 2 7700 0 1956 5 3 123635 2748
1005 488 1 11050 1 1956 5 2 121654 2749
1056 144 1 13600 0 1955 5 3 112694 2750
884 741 1 15428 0 1951 5 2 117187 2751
2039 0 3 21299 3 1941 7 3 229209 2752
1384 494 2 13300 0 1956 5 2 139841 2753
2640 1018 3 22136 1 1925 5 5 221793 2754
1312 0 2 7500 0 1947 6 3 135128 2755
713 0 1 10410 0 1930 3 2 75972 2756
715 0 2 10914 0 1929 3 2 81212 2757
720 0 1 7008 0 1900 4 1 77841 2758
1595 338 2 7200 1 1915 6 3 146969 2759
1760 0 2 10818 1 1910 4 4 118038 2760
1146 580 1 10184 1 1963 6 3 143595 2761
1207 701 1 9510 0 1962 6 3 141869 2762
1773 913 2 10800 2 1961 6 3 199057 2763
1472 0 2 11650 1 1959 7 2 172139 2764
2448 636 2 18275 2 1962 7 3 263545 2765
1521 455 1 12144 0 1950 4 3 118533 2766
1040 0 2 8544 0 1950 3 2 93108 2767
1556 0 0 8512 0 1960 5 4 117393 2768
1150 781 1 7000 0 1961 5 3 125783 2769
1045 809 2 7400 0 1962 7 3 162409 2770
864 468 1 7000 0 1962 5 3 111426 2771
1025 953 0 7000 0 1962 5 3 116717 2772
2014 0 2 9856 0 1900 5 5 130255 2773
1668 276 1 9600 0 1948 5 3 131876 2774
1657 284 1 5520 1 1920 4 4 112594 2775
1416 381 2 9600 0 1900 6 3 130902 2776
1428 208 2 6451 0 1900 7 4 139930 2777
1004 0 1 3960 1 1930 7 2 127808 2778
1951 0 2 7745 0 1900 4 4 115187 2779
1032 143 1 7741 0 1924 6 2 113232 2780
844 0 1 5633 0 1925 5 2 94408 2781
864 0 1 7200 0 1950 4 2 91674 2782
1376 0 1 7614 0 1905 3 2 84811 2783
960 576 2 6000 0 1955 5 3 121622 2784
1566 0 2 6000 0 1924 5 5 120824 2785
492 416 1 7830 0 1921 3 1 73886 2786
1182 310 1 9576 0 1945 6 3 127582 2787
840 0 1 5747 0 1920 3 2 75503 2788
2104 0 2 6300 0 1910 7 5 167048 2789
1248 0 0 5976 0 1920 5 2 97608 2790
960 0 2 9750 0 1958 5 3 114385 2791
1020 0 0 4761 0 1918 3 2 73599 2792
1827 0 1 11737 1 1924 6 2 146150 2793
1162 347 1 6120 0 1930 3 3 88536 2794
1324 0 1 6120 0 1930 5 3 108744 2795
816 0 1 11672 0 1925 5 2 95585 2796
2486 0 2 33120 1 1962 6 5 218110 2797
1430 0 2 10320 0 1924 4 3 107672 2798
1330 0 1 7518 0 1910 5 3 103913 2799
819 0 0 9000 0 1919 5 2 87299 2800
984 343 1 7200 0 1930 6 3 115779 2801
1422 329 1 12375 1 1951 5 3 131556 2802
1921 0 2 11136 0 1964 6 4 168174 2803
1640 0 2 21370 1 1950 5 3 146621 2804
1032 0 1 8250 1 1935 5 2 107318 2805
879 0 1 5220 0 1936 5 2 97948 2806
1073 510 1 5500 0 2004 7 2 163585 2807
1064 779 2 11327 1 1967 5 3 141001 2808
934 456 1 10366 0 1964 6 2 128882 2809
1059 773 1 9000 0 1966 5 3 124932 2810
1458 194 2 9535 1 1967 5 3 143924 2811
1040 794 2 7176 1 1978 6 3 158179 2812
1967 0 2 9662 0 1977 5 6 155809 2813
1949 483 2 8235 0 1977 5 6 165227 2814
872 0 1 17529 1 1924 5 2 102913 2815
1830 810 2 20355 2 1967 7 2 233609 2816
1000 104 2 13050 2 1963 5 1 132298 2817
810 535 2 10820 0 1971 5 2 123651 2818
1700 397 1 1700 0 1980 7 2 177793 2819
1350 799 2 9375 1 1954 4 3 132418 2820
1150 230 1 6488 2 1942 5 3 120091 2821
2009 0 3 19950 2 1928 6 4 187809 2822
3672 425 2 19800 2 1935 6 5 299331 2823
1560 612 2 11679 1 1962 5 3 156190 2824
1488 0 2 12048 1 1952 5 3 136959 2825
1057 0 1 10519 0 1955 5 3 109318 2826
1609 468 1 9525 0 1953 6 5 148011 2827
2559 549 2 12128 1 1989 6 4 242101 2828
1440 261 4 9069 0 1993 6 2 189365 2829
1876 0 3 11003 0 2005 7 3 220661 2830
1208 393 2 7488 0 2005 7 2 180282 2831
1846 1576 2 13377 1 2006 6 3 242641 2832
1590 1122 3 11645 0 2005 8 2 267670 2833
1809 0 2 10984 0 2005 7 3 202534 2834
1614 56 2 9316 1 2005 7 3 200429 2835
1596 0 2 9316 0 2005 7 3 189841 2836
1388 853 2 12000 1 1968 6 3 173983 2837
1100 0 2 13015 0 1996 5 3 132651 2838
1499 0 2 12438 1 1995 6 3 170757 2839
1425 846 2 8685 0 1998 7 3 200011 2840
1749 500 2 9272 0 1999 7 3 209319 2841
1779 894 2 13426 1 1999 7 3 235863 2842
1388 509 1 8340 0 1977 6 3 150337 2843
1282 595 3 10385 0 1978 6 3 170572 2844
864 437 1 7200 0 1972 5 3 113923 2845
1762 456 2 9930 0 2002 7 3 210861 2846
1755 639 2 9468 1 1999 6 3 200805 2847
1358 872 2 11088 1 2002 8 1 235344 2848
1909 0 2 8726 0 2002 7 4 203746 2849
2214 920 3 10566 1 1999 8 3 314230 2850
2049 0 2 21533 1 1996 7 4 226861 2851
1939 796 3 11250 1 1998 7 3 257492 2852
1995 685 2 11250 1 1995 7 4 237341 2853
848 717 2 4435 0 2003 6 1 152429 2854
1390 1000 2 8810 0 2003 7 3 205171 2855
1737 0 2 8581 0 2006 7 3 197448 2856
1611 0 2 8400 0 2005 7 3 190051 2857
1336 996 2 8772 0 2005 7 3 203025 2858
1436 173 2 8777 0 1910 4 3 106047 2859
1012 976 0 7840 0 1975 6 4 133521 2860
1176 847 1 16133 0 1969 5 2 135481 2861
1724 0 2 7162 1 2003 7 3 202492 2862
914 475 0 8050 0 2002 6 2 131580 2863
2314 0 2 11060 1 2003 7 3 241668 2864
1072 547 2 3675 0 2005 6 2 157742 2865
1709 0 2 2522 0 2004 7 3 191002 2866
936 0 1 6956 0 1948 4 3 92365 2867
1338 0 2 7822 0 1915 6 3 125422 2868
1669 0 1 8707 0 1924 4 4 106328 2869
1482 691 2 16012 1 1954 4 3 138308 2870
1414 0 0 8248 1 1922 4 3 96524 2871
498 0 1 8088 0 1922 2 1 63042 2872
1273 0 1 11388 0 1910 4 3 93295 2873
1551 930 1 10890 0 1938 5 3 137069 2874
1340 780 1 6430 0 1945 6 3 140998 2875
1479 424 1 7000 2 1926 7 3 160321 2876
1510 305 1 4899 0 1920 6 3 128870 2877
1636 0 1 9399 1 1919 7 4 148821 2878
1465 646 1 10164 2 1939 5 3 139658 2879
1288 384 1 6191 0 1941 5 4 116238 2880
1550 0 1 21780 1 1920 6 3 137607 2881
1717 602 1 12400 1 1940 5 2 145206 2882
1671 526 2 8170 1 1929 7 4 176947 2883
1609 0 3 12320 2 1932 7 3 185044 2884
1801 0 2 14210 1 1930 6 3 157869 2885
2315 760 1 15600 3 1950 5 4 194977 2886
976 305 1 7288 0 1942 5 2 107452 2887
1285 374 2 7000 0 1926 6 3 133714 2888
672 0 0 8534 0 1925 4 2 76524 2889
641 0 1 7030 0 1925 4 2 80723 2890
1638 0 1 9060 0 1957 6 4 141784 2891
729 0 0 12366 0 1945 3 2 74673 2892
1396 0 0 9000 0 1951 5 4 109884 2893
936 0 0 8520 0 1916 3 2 72434 2894
1778 1573 2 5748 1 2005 8 2 287285 2895
1646 1564 2 3842 1 2004 8 2 274126 2896
1625 776 2 23580 1 1979 6 3 196568 2897
1664 0 2 8385 0 1978 6 4 160884 2898
1491 0 2 9116 0 2001 8 3 202531 2899
1210 576 2 11080 0 1975 6 3 155085 2900
1650 909 2 50102 2 1958 6 2 218953 2901
1403 1136 2 8098 0 2000 6 2 188328 2902
1960 1350 3 13618 2 2005 8 3 332820 2903
1838 1455 3 11577 1 2005 9 3 345618 2904
1600 0 1 31250 0 1951 1 3 88622 2905
1368 1243 4 7020 0 1997 7 2 237760 2906
1304 0 1 2665 1 1977 5 3 125827 2907
874 441 1 10172 0 1968 5 3 114255 2908
1652 149 3 11836 0 1970 5 4 156249 2909
630 522 0 1470 0 1970 4 1 89955 2910
1092 252 1 1484 0 1972 4 3 104442 2911
1360 119 1 13384 1 1969 5 3 131950 2912
1092 408 1 1533 0 1970 4 3 106243 2913
1092 0 0 1526 0 1970 4 3 93768 2914
1092 0 0 1936 0 1970 4 3 93897 2915
1092 252 1 1894 0 1970 4 3 104045 2916
1224 1224 2 20000 1 1960 5 4 157689 2917
970 337 0 10441 0 1992 5 3 115160 2918
2000 758 3 9627 1 1993 7 3 255744 2919

These seven variables explain 80% of the variability in the sale price. I will use this model to make the Kaggle submission.

My Kaggle score is 0.15845 and my username is debkabiraj. I am ranked 3487 on the leaderboard.

3.4.1.3 Prediction Submission Scores

3.4.1.3.1 Model 1
Submission1 Score

Submission1 Score

Submission1 Rank

Submission1 Rank

3.4.1.3.2 Model 2
Submission2 Score

Submission2 Score

Submission2 Rank

Submission2 Rank

3.4.1.4 Results


Debabrata Kabiraj

May 21, 2020