House Price Prediction for Houses in Ames,IA

a) \(Pr(X>x\mid Y>y)= .82\)

b) \(Pr(X>x,Y>y)= .615\)

c) \(Pr(X<x\mid Y>y)= .18\)

Number Y<y Number Y>y Total
Number X<x 168 197 365
Number X>x 197 898 1095
Total 365 1095 1460

The probabilities here are not independent. \(.75^{2}\neq.82\) It would be expected that homes with greater lot size would cost more sometimes. (If it were independent, only suckers would use it in their model.)

## # A tibble: 4 x 2
##   `Number Y<y` `Number Y>y`
## *        <dbl>        <dbl>
## 1        168           197 
## 2         91.2         274.
## 3        197           898 
## 4        274.          821.
Number Y<y Number Y>y
Number X<x, observed 168.00 197.00
Number X<x, expected 91.25 273.75
Number X>x, observed 197.00 898.00
Number X>x, expected 273.75 821.25

For a chi-squared test, we calculate \(\sum \frac{(O_{i}-E_{i})^2}{E_{i}}\).

In our case, that’s: \(\frac{(168-91.25)^2}{91.25}+2(\frac{(197-273.75)^2}{273.75} )+ \frac{(898-821.25)^2}{821.25}\) = 114.763. The p-value for 114.763 with 1 df is 0.

The mean of X is 1.051682810^{4}.

The mean of y is 1.80921210^{5}.

The variance of x is9.96256510^{7}.

The variance of y is 6.311111310^{9}.

The correlation between x and y is 0.2638434

The correlation matrix for lot frontage, lot area and overall quality is:

##             LotFrontage   LotArea OverallQual
## LotFrontage   1.0000000 0.4260950   0.2516458
## LotArea       0.4260950 1.0000000   0.1821643
## OverallQual   0.2516458 0.1821643   1.0000000
## 
##  Pearson's product-moment correlation
## 
## data:  train_house_prices$LotArea and train_house_prices$LotFrontage
## t = 16.309, df = 1199, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  0.3786555 0.4713015
## sample estimates:
##      cor 
## 0.426095

The .92 confidence interval for R2 for Lot Area and Lot Frontage is 0.3755136 to 0.4766764.

## 
##  Pearson's product-moment correlation
## 
## data:  train_house_prices$OverallQual and train_house_prices$LotFrontage
## t = 9.0034, df = 1199, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  0.1978967 0.3038861
## sample estimates:
##       cor 
## 0.2516458

The .92 confidence interval for R2 for Overall Quality and Lot Frontage is 0.2010644 to 0.3022272.

## 
##  Pearson's product-moment correlation
## 
## data:  train_house_prices$LotArea and train_house_prices$OverallQual
## t = 4.0629, df = 1458, p-value = 5.106e-05
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  0.0548009 0.1562599
## sample estimates:
##       cor 
## 0.1058057

The .92 confidence interval for R2 for Overall Quality and Lot Area is 0.0552243 to 0.1563871.

Our correlations are all statistically significant. With multicollinearity, we are worried that our model will be statistically significant even though individual parameters may not be. Our correlations may present a problem if we incorporate all of these variables. The familywise error rate for 3 variables at a p-value of .01 is <= 1-(1-.01)^3 = .0297. That is tolerable.

##           [,1]      [,2]      [,3]
## [1,] 1.0000000 0.4260950 0.2516458
## [2,] 0.4260950 1.0000000 0.1821643
## [3,] 0.2516458 0.1821643 1.0000000
##            [,1]        [,2]        [,3]
## [1,]  1.2704570 -0.49967772 -0.22868172
## [2,] -0.4996777  1.23084879 -0.09847491
## [3,] -0.2286817 -0.09847491  1.07548541
##      [,1] [,2] [,3]
## [1,]    1    0    0
## [2,]    0    1    0
## [3,]    0    0    1
##      [,1] [,2] [,3]
## [1,]    1    0    0
## [2,]    0    1    0
## [3,]    0    0    1
## [1] "Our upper triangular is:"
##      [,1]      [,2]       [,3]
## [1,]    1 0.4260950 0.25164580
## [2,]    0 0.8184431 0.07493928
## [3,]    0 0.0000000 0.92981271
## [1] "Our lower triangular is:"
##           [,1]       [,2] [,3]
## [1,] 1.0000000 0.00000000    0
## [2,] 0.4260950 1.00000000    0
## [3,] 0.2516458 0.09156322    1

we ran fitdistr and found a value of 9.50857*10^-5. The reciprocal is 10,526. A maximum likelihood for a gamma distribution can be fitted by its sample mean. Since a gamma with a=1 is an exponential, we are not surprised that the sample mean (below) is less than 10 away from our fitdistr result. An exponential with parameter \(\lambda\) has mean \(\frac{1}{\lambda}\).

##        rate    
##   9.508570e-05 
##  (2.488507e-06)
## [1] 10516.83

The 95th percentile of the fitted distribution is:

## [1] 31505.6

The 5th percentile of the fitted distribution is:

## [1] 539.4428

The 5th percentile of the empirical distribution is:

## [1] 3230

The 95th percentile of the empirical distribution is:

## [1] 17400

The fit for the exponential distribution is not very good for this experience. As a single parameter distribution, the exponential doesn’t work well for a disribution where we want to have a lot of data around a narrow place and then a wide tail. Our distribution contains a lot of data in a narrow range. It is underdispersed. A gamma distribution could work. A lognormal distribution would probably be even better.

—————————————————————–

Our approach includes finding the t-scores for each individual variable. We found correlations for each of our numeric variables. If we had more time, ANOVA or ANCOVA should be used to find interactions between categorical variables. We created a score that balanced t-scores with correlations on equal footing. Because it penalized for numeric variables and not categorical variable, they may have been overrepresented in our sample. We applied a Box-Cox transformation to response variable because house cost data is naturally logarithmic. One can have a house that costs many times the average, but one cannot have a house worth a large negative value. With our list of penalized variables, we built a model by adding the variables highest on the list and removing those with low t-scores within the model. We created a model with increasing R2 until our 18 models were made. We chose our 17th model to submit.

## # A tibble: 81 x 2
##    t.values.continuous tester
##                  <dbl>  <dbl>
##  1                  18   54.1
##  2                  47   37.5
##  3                  62   48.0
##  4                  63   46.2
##  5                  39   43.9
##  6                  44   41.6
##  7                  50   38.1
##  8                  20   47.3
##  9                  21   44.2
## 10                  55   32.2
## 11                  60   43.3
## 12                  57   39.0
## 13                  27   37.1
## 14                  30   55.8
## 15                  35   42.7
## 16                  42   52.5
## 17                  67   40.0
## 18                   4   35.6
## 19                  80   51.3
## 20                  68   35.8
## 21                  45   27.4
## 22                  51   34.2
## 23                  34   50.0
## 24                  66   49.8
## 25                  17   48.6
## 26                   5   39.5
## 27                  43   48.0
## 28                  79   47.6
## 29                  48   43.9
## 30                   3   47.3
## 31                  38   33.7
## 32                  24   46.4
## 33                  52   31.4
## 34                  25   45.8
## 35                  32   45.8
## 36                  13   44.8
## 37                   9   44.2
## 38                  26   44.0
## 39                  14   43.4
## 40                   7   43.4
## # ... with 41 more rows
first.model<-lm(log(train_house_prices$SalePrice)~train_house_prices$OverallQual+train_house_prices$GrLivArea)
summary(first.model)
numeric.variables<-train_house_prices[,c(2,4,5,18,19,20,21,27,35,37,38,39,44,45,46,47,48,49,50,51,52,53,55,57,60,62,63,67,68,69,70,71,72,76,77,78,81)]
correlation.matrix<-cor(numeric.variables, use="complete.obs")
#correlation.matrix
bc.1<-boxcox(train_house_prices$SalePrice~train_house_prices$OverallQual)
lambda.1 <- bc.1$x[which.max(bc.1$y)]
ggplot()+geom_point(aes(x=train_house_prices$SalePrice,y=train_house_prices$GrLivArea))
lambda.1
for (i in 1:1460){train_house_prices$SalePrice[i]<-((train_house_prices$SalePrice[i]^.090606-1)/.090606)}
#------------------------------------------------------
t.values.continuous %>% 
  mutate(tester=(t.values.continuous1+ 24*(1.59-t.values.continuous2-t.values.continuous3)))->t.values.continuous
## 
## Call:
## lm(formula = log(train_house_prices$SalePrice) ~ train_house_prices$OverallQual + 
##     train_house_prices$GrLivArea)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1.78553 -0.09638  0.02084  0.12482  0.76698 
## 
## Coefficients:
##                                 Estimate Std. Error t value Pr(>|t|)    
## (Intercept)                    1.055e+01  2.420e-02  435.95   <2e-16 ***
## train_house_prices$OverallQual 1.789e-01  4.792e-03   37.33   <2e-16 ***
## train_house_prices$GrLivArea   2.536e-04  1.261e-05   20.11   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.2038 on 1457 degrees of freedom
## Multiple R-squared:   0.74,  Adjusted R-squared:  0.7396 
## F-statistic:  2073 on 2 and 1457 DF,  p-value: < 2.2e-16

## [1] 0.06060606

## 
## Call:
## lm(formula = train_house_prices$SalePrice ~ train_house_prices$OverallQual)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -2.89568 -0.39473  0.02582  0.39219  2.75968 
## 
## Coefficients:
##                                Estimate Std. Error t value Pr(>|t|)    
## (Intercept)                    17.48976    0.08099  215.95   <2e-16 ***
## train_house_prices$OverallQual  0.70556    0.01295   54.48   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6841 on 1458 degrees of freedom
## Multiple R-squared:  0.6706, Adjusted R-squared:  0.6704 
## F-statistic:  2968 on 1 and 1458 DF,  p-value: < 2.2e-16
## 
## Call:
## lm(formula = train_house_prices$SalePrice ~ train_house_prices[, 
##     18] + train_house_prices[, 47] + train_house_prices[, 62] + 
##     train_house_prices[, 63] + train_house_prices[, 39] + train_house_prices[, 
##     44] + train_house_prices[, 50] + train_house_prices[, 20] + 
##     train_house_prices[, 21] + train_house_prices[, 55])
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -6.6144 -0.2260  0.0187  0.2735  1.6102 
## 
## Coefficients:
##                            Estimate Std. Error t value Pr(>|t|)    
## (Intercept)              -5.664e+00  1.708e+00  -3.316 0.000937 ***
## train_house_prices[, 18]  2.863e-01  1.575e-02  18.181  < 2e-16 ***
## train_house_prices[, 47]  6.616e-04  5.599e-05  11.815  < 2e-16 ***
## train_house_prices[, 62]  2.094e-01  4.027e-02   5.199 2.29e-07 ***
## train_house_prices[, 63]  1.669e-04  1.364e-04   1.224 0.221267    
## train_house_prices[, 39]  2.711e-04  5.683e-05   4.771 2.02e-06 ***
## train_house_prices[, 44]  1.756e-04  6.522e-05   2.693 0.007156 ** 
## train_house_prices[, 50] -6.177e-02  3.549e-02  -1.741 0.081946 .  
## train_house_prices[, 20]  5.537e-03  6.660e-04   8.313  < 2e-16 ***
## train_house_prices[, 21]  6.463e-03  8.418e-04   7.678 2.96e-14 ***
## train_house_prices[, 55]  1.857e-02  1.480e-02   1.255 0.209835    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5017 on 1449 degrees of freedom
## Multiple R-squared:  0.8239, Adjusted R-squared:  0.8227 
## F-statistic: 678.1 on 10 and 1449 DF,  p-value: < 2.2e-16
## 
## Call:
## lm(formula = train_house_prices$SalePrice ~ train_house_prices[, 
##     18] + train_house_prices[, 47] + train_house_prices[, 62] + 
##     train_house_prices[, 60] + train_house_prices[, 39] + train_house_prices[, 
##     44] + train_house_prices[, 50] + train_house_prices[, 20] + 
##     train_house_prices[, 21] + train_house_prices[, 55])
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -6.4622 -0.2267  0.0155  0.2823  1.6218 
## 
## Coefficients:
##                            Estimate Std. Error t value Pr(>|t|)    
## (Intercept)              -4.230e+00  1.861e+00  -2.273  0.02318 *  
## train_house_prices[, 18]  2.939e-01  1.626e-02  18.072  < 2e-16 ***
## train_house_prices[, 47]  6.651e-04  5.635e-05  11.804  < 2e-16 ***
## train_house_prices[, 62]  2.317e-01  3.030e-02   7.647 3.86e-14 ***
## train_house_prices[, 60] -2.716e-03  1.055e-03  -2.574  0.01015 *  
## train_house_prices[, 39]  2.607e-04  5.864e-05   4.445 9.50e-06 ***
## train_house_prices[, 44]  1.793e-04  6.660e-05   2.692  0.00719 ** 
## train_house_prices[, 50] -7.175e-02  3.638e-02  -1.972  0.04878 *  
## train_house_prices[, 20]  6.862e-03  8.807e-04   7.791 1.30e-14 ***
## train_house_prices[, 21]  7.135e-03  9.121e-04   7.823 1.02e-14 ***
## train_house_prices[, 55]  2.040e-02  1.518e-02   1.344  0.17919    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4947 on 1368 degrees of freedom
##   (81 observations deleted due to missingness)
## Multiple R-squared:  0.8131, Adjusted R-squared:  0.8118 
## F-statistic: 595.2 on 10 and 1368 DF,  p-value: < 2.2e-16
## 
## Call:
## lm(formula = train_house_prices$SalePrice ~ train_house_prices[, 
##     18] + train_house_prices[, 47] + train_house_prices[, 62] + 
##     train_house_prices[, 60] + train_house_prices[, 39] + train_house_prices[, 
##     44] + train_house_prices[, 57] + train_house_prices[, 20] + 
##     train_house_prices[, 21] + train_house_prices[, 55])
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -6.2942 -0.2435  0.0104  0.2756  1.5452 
## 
## Coefficients:
##                            Estimate Std. Error t value Pr(>|t|)    
## (Intercept)              -5.383e+00  1.734e+00  -3.104  0.00195 ** 
## train_house_prices[, 18]  2.688e-01  1.607e-02  16.728  < 2e-16 ***
## train_house_prices[, 47]  5.430e-04  5.399e-05  10.057  < 2e-16 ***
## train_house_prices[, 62]  2.244e-01  2.949e-02   7.608 5.14e-14 ***
## train_house_prices[, 60] -1.478e-03  1.038e-03  -1.424  0.15474    
## train_house_prices[, 39]  2.920e-04  5.685e-05   5.136 3.22e-07 ***
## train_house_prices[, 44]  9.738e-05  6.541e-05   1.489  0.13677    
## train_house_prices[, 57]  2.088e-01  2.386e-02   8.754  < 2e-16 ***
## train_house_prices[, 20]  5.919e-03  8.435e-04   7.017 3.55e-12 ***
## train_house_prices[, 21]  7.489e-03  8.880e-04   8.433  < 2e-16 ***
## train_house_prices[, 55]  2.522e-02  1.471e-02   1.714  0.08669 .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4821 on 1368 degrees of freedom
##   (81 observations deleted due to missingness)
## Multiple R-squared:  0.8225, Adjusted R-squared:  0.8212 
## F-statistic: 634.1 on 10 and 1368 DF,  p-value: < 2.2e-16
## 
## Call:
## lm(formula = train_house_prices$SalePrice ~ train_house_prices[, 
##     18] + train_house_prices[, 47] + train_house_prices[, 62] + 
##     train_house_prices[, 60] + train_house_prices[, 39] + train_house_prices[, 
##     44] + train_house_prices[, 57] + train_house_prices[, 20] + 
##     train_house_prices[, 21] + train_house_prices[, 27])
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -6.3961 -0.2389  0.0091  0.2731  1.5879 
## 
## Coefficients:
##                            Estimate Std. Error t value Pr(>|t|)    
## (Intercept)              -5.240e+00  1.734e+00  -3.022  0.00256 ** 
## train_house_prices[, 18]  2.642e-01  1.623e-02  16.272  < 2e-16 ***
## train_house_prices[, 47]  6.074e-04  3.739e-05  16.245  < 2e-16 ***
## train_house_prices[, 62]  2.243e-01  2.957e-02   7.585 6.15e-14 ***
## train_house_prices[, 60] -1.395e-03  1.041e-03  -1.340  0.18051    
## train_house_prices[, 39]  2.758e-04  5.675e-05   4.859 1.31e-06 ***
## train_house_prices[, 44]  1.033e-04  6.577e-05   1.571  0.11650    
## train_house_prices[, 57]  2.074e-01  2.396e-02   8.656  < 2e-16 ***
## train_house_prices[, 20]  5.783e-03  8.531e-04   6.779 1.80e-11 ***
## train_house_prices[, 21]  7.520e-03  8.943e-04   8.408  < 2e-16 ***
## train_house_prices[, 27]  8.479e-05  8.159e-05   1.039  0.29890    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.483 on 1360 degrees of freedom
##   (89 observations deleted due to missingness)
## Multiple R-squared:  0.8218, Adjusted R-squared:  0.8205 
## F-statistic: 627.1 on 10 and 1360 DF,  p-value: < 2.2e-16
## 
## Call:
## lm(formula = train_house_prices$SalePrice ~ train_house_prices[, 
##     18] + train_house_prices[, 47] + train_house_prices[, 62] + 
##     train_house_prices[, 63] + train_house_prices[, 39] + train_house_prices[, 
##     44] + train_house_prices[, 57] + train_house_prices[, 20] + 
##     train_house_prices[, 21] + train_house_prices[, 27])
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -6.6390 -0.2354  0.0183  0.2726  1.5710 
## 
## Coefficients:
##                            Estimate Std. Error t value Pr(>|t|)    
## (Intercept)              -6.367e+00  1.580e+00  -4.031 5.85e-05 ***
## train_house_prices[, 18]  2.578e-01  1.564e-02  16.488  < 2e-16 ***
## train_house_prices[, 47]  6.100e-04  3.617e-05  16.865  < 2e-16 ***
## train_house_prices[, 62]  1.755e-01  3.907e-02   4.493 7.60e-06 ***
## train_house_prices[, 63]  2.757e-04  1.327e-04   2.078   0.0379 *  
## train_house_prices[, 39]  2.845e-04  5.504e-05   5.169 2.69e-07 ***
## train_house_prices[, 44]  8.962e-05  6.432e-05   1.393   0.1637    
## train_house_prices[, 57]  2.182e-01  2.348e-02   9.296  < 2e-16 ***
## train_house_prices[, 20]  5.222e-03  6.241e-04   8.367  < 2e-16 ***
## train_house_prices[, 21]  7.247e-03  8.260e-04   8.773  < 2e-16 ***
## train_house_prices[, 27]  5.334e-05  8.194e-05   0.651   0.5151    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4885 on 1441 degrees of freedom
##   (8 observations deleted due to missingness)
## Multiple R-squared:  0.833,  Adjusted R-squared:  0.8318 
## F-statistic: 718.5 on 10 and 1441 DF,  p-value: < 2.2e-16
## 
## Call:
## lm(formula = train_house_prices$SalePrice ~ train_house_prices[, 
##     18] + train_house_prices[, 47] + train_house_prices[, 62] + 
##     train_house_prices[, 63] + train_house_prices[, 39] + train_house_prices[, 
##     44] + train_house_prices[, 57] + train_house_prices[, 20] + 
##     train_house_prices[, 21] + train_house_prices[, 30])
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -6.4313 -0.2366  0.0147  0.2642  1.5723 
## 
## Coefficients:
##                                  Estimate Std. Error t value Pr(>|t|)    
## (Intercept)                    -4.565e+00  1.874e+00  -2.436  0.01497 *  
## train_house_prices[, 18]        2.661e-01  1.600e-02  16.635  < 2e-16 ***
## train_house_prices[, 47]        6.091e-04  3.578e-05  17.022  < 2e-16 ***
## train_house_prices[, 62]        1.825e-01  3.908e-02   4.671 3.28e-06 ***
## train_house_prices[, 63]        2.786e-04  1.320e-04   2.110  0.03499 *  
## train_house_prices[, 39]        2.049e-04  6.407e-05   3.198  0.00141 ** 
## train_house_prices[, 44]        1.541e-04  7.156e-05   2.154  0.03144 *  
## train_house_prices[, 57]        2.104e-01  2.351e-02   8.947  < 2e-16 ***
## train_house_prices[, 20]        4.341e-03  7.962e-04   5.451 5.87e-08 ***
## train_house_prices[, 21]        7.126e-03  8.442e-04   8.441  < 2e-16 ***
## train_house_prices[, 30]CBlock  1.504e-01  5.389e-02   2.792  0.00532 ** 
## train_house_prices[, 30]PConc   1.586e-01  6.505e-02   2.438  0.01489 *  
## train_house_prices[, 30]Slab   -1.645e-01  1.308e-01  -1.258  0.20875    
## train_house_prices[, 30]Stone   1.383e-01  2.032e-01   0.681  0.49619    
## train_house_prices[, 30]Wood   -6.549e-02  2.883e-01  -0.227  0.82035    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4861 on 1445 degrees of freedom
## Multiple R-squared:  0.8351, Adjusted R-squared:  0.8335 
## F-statistic: 522.8 on 14 and 1445 DF,  p-value: < 2.2e-16
## 
## Call:
## lm(formula = train_house_prices$SalePrice ~ train_house_prices[, 
##     18] + train_house_prices[, 47] + train_house_prices[, 62] + 
##     train_house_prices[, 63] + train_house_prices[, 39] + train_house_prices[, 
##     35] + train_house_prices[, 57] + train_house_prices[, 20] + 
##     train_house_prices[, 21] + train_house_prices[, 30])
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -7.0337 -0.2216  0.0310  0.2542  1.5167 
## 
## Coefficients:
##                                  Estimate Std. Error t value Pr(>|t|)    
## (Intercept)                    -3.833e+00  1.852e+00  -2.070   0.0386 *  
## train_house_prices[, 18]        2.699e-01  1.578e-02  17.100  < 2e-16 ***
## train_house_prices[, 47]        6.387e-04  3.387e-05  18.854  < 2e-16 ***
## train_house_prices[, 62]        2.089e-01  3.874e-02   5.393 8.10e-08 ***
## train_house_prices[, 63]        1.875e-04  1.310e-04   1.431   0.1526    
## train_house_prices[, 39]        2.005e-04  4.222e-05   4.749 2.24e-06 ***
## train_house_prices[, 35]        2.223e-04  3.346e-05   6.645 4.29e-11 ***
## train_house_prices[, 57]        1.965e-01  2.321e-02   8.465  < 2e-16 ***
## train_house_prices[, 20]        3.848e-03  7.830e-04   4.914 9.93e-07 ***
## train_house_prices[, 21]        7.263e-03  8.296e-04   8.755  < 2e-16 ***
## train_house_prices[, 30]CBlock  1.296e-01  5.321e-02   2.436   0.0150 *  
## train_house_prices[, 30]PConc   1.501e-01  6.419e-02   2.339   0.0195 *  
## train_house_prices[, 30]Slab   -8.555e-02  1.170e-01  -0.731   0.4649    
## train_house_prices[, 30]Stone   1.666e-01  2.005e-01   0.831   0.4063    
## train_house_prices[, 30]Wood   -1.837e-01  2.851e-01  -0.644   0.5194    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4797 on 1445 degrees of freedom
## Multiple R-squared:  0.8395, Adjusted R-squared:  0.838 
## F-statistic: 539.9 on 14 and 1445 DF,  p-value: < 2.2e-16
## 
## Call:
## lm(formula = train_house_prices$SalePrice ~ train_house_prices[, 
##     18] + train_house_prices[, 47] + train_house_prices[, 62] + 
##     train_house_prices[, 63] + train_house_prices[, 39] + train_house_prices[, 
##     35] + train_house_prices[, 57] + train_house_prices[, 20] + 
##     train_house_prices[, 21] + train_house_prices[, 30] + train_house_prices[, 
##     42])
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -7.0104 -0.2234  0.0282  0.2506  1.5400 
## 
## Coefficients:
##                                  Estimate Std. Error t value Pr(>|t|)    
## (Intercept)                    -1.627e+00  1.868e+00  -0.871   0.3840    
## train_house_prices[, 18]        2.652e-01  1.562e-02  16.972  < 2e-16 ***
## train_house_prices[, 47]        6.502e-04  3.354e-05  19.385  < 2e-16 ***
## train_house_prices[, 62]        2.133e-01  3.830e-02   5.569 3.05e-08 ***
## train_house_prices[, 63]        1.516e-04  1.297e-04   1.170   0.2424    
## train_house_prices[, 39]        2.090e-04  4.177e-05   5.005 6.29e-07 ***
## train_house_prices[, 35]        2.194e-04  3.308e-05   6.633 4.63e-11 ***
## train_house_prices[, 57]        1.796e-01  2.313e-02   7.768 1.51e-14 ***
## train_house_prices[, 20]        3.238e-03  7.809e-04   4.146 3.57e-05 ***
## train_house_prices[, 21]        6.624e-03  8.273e-04   8.007 2.40e-15 ***
## train_house_prices[, 30]CBlock  8.372e-02  5.318e-02   1.574   0.1156    
## train_house_prices[, 30]PConc   1.307e-01  6.354e-02   2.057   0.0399 *  
## train_house_prices[, 30]Slab   -3.411e-02  1.160e-01  -0.294   0.7688    
## train_house_prices[, 30]Stone   2.379e-01  1.986e-01   1.198   0.2312    
## train_house_prices[, 30]Wood   -2.210e-01  2.819e-01  -0.784   0.4332    
## train_house_prices[, 42]Y       3.373e-01  5.728e-02   5.889 4.83e-09 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4742 on 1444 degrees of freedom
## Multiple R-squared:  0.8433, Adjusted R-squared:  0.8416 
## F-statistic:   518 on 15 and 1444 DF,  p-value: < 2.2e-16
## 
## Call:
## lm(formula = train_house_prices$SalePrice ~ train_house_prices[, 
##     18] + train_house_prices[, 47] + train_house_prices[, 62] + 
##     train_house_prices[, 63] + train_house_prices[, 39] + train_house_prices[, 
##     35] + train_house_prices[, 57] + train_house_prices[, 20] + 
##     train_house_prices[, 21] + train_house_prices[, 30] + train_house_prices[, 
##     42] + train_house_prices[, 67])
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -6.9003 -0.2212  0.0214  0.2557  1.5518 
## 
## Coefficients:
##                                  Estimate Std. Error t value Pr(>|t|)    
## (Intercept)                    -8.727e-01  1.866e+00  -0.468   0.6401    
## train_house_prices[, 18]        2.671e-01  1.554e-02  17.187  < 2e-16 ***
## train_house_prices[, 47]        6.347e-04  3.356e-05  18.914  < 2e-16 ***
## train_house_prices[, 62]        2.117e-01  3.809e-02   5.557 3.26e-08 ***
## train_house_prices[, 63]        1.468e-04  1.289e-04   1.139   0.2550    
## train_house_prices[, 39]        2.072e-04  4.153e-05   4.990 6.76e-07 ***
## train_house_prices[, 35]        2.069e-04  3.302e-05   6.267 4.85e-10 ***
## train_house_prices[, 57]        1.731e-01  2.305e-02   7.513 1.01e-13 ***
## train_house_prices[, 20]        3.049e-03  7.778e-04   3.920 9.28e-05 ***
## train_house_prices[, 21]        6.429e-03  8.238e-04   7.804 1.15e-14 ***
## train_house_prices[, 30]CBlock  8.386e-02  5.287e-02   1.586   0.1130    
## train_house_prices[, 30]PConc   1.310e-01  6.318e-02   2.074   0.0383 *  
## train_house_prices[, 30]Slab   -2.025e-02  1.154e-01  -0.175   0.8607    
## train_house_prices[, 30]Stone   2.318e-01  1.975e-01   1.174   0.2407    
## train_house_prices[, 30]Wood   -2.209e-01  2.803e-01  -0.788   0.4308    
## train_house_prices[, 42]Y       3.292e-01  5.699e-02   5.776 9.36e-09 ***
## train_house_prices[, 67]        4.407e-04  1.049e-04   4.200 2.83e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4715 on 1443 degrees of freedom
## Multiple R-squared:  0.8452, Adjusted R-squared:  0.8435 
## F-statistic: 492.3 on 16 and 1443 DF,  p-value: < 2.2e-16
## 
## Call:
## lm(formula = train_house_prices$SalePrice ~ train_house_prices[, 
##     18] + train_house_prices[, 47] + train_house_prices[, 62] + 
##     train_house_prices[, 63] + train_house_prices[, 39] + train_house_prices[, 
##     35] + train_house_prices[, 57] + train_house_prices[, 20] + 
##     train_house_prices[, 21] + train_house_prices[, 30] + train_house_prices[, 
##     42] + train_house_prices[, 67] + train_house_prices[, 4])
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -6.9013 -0.2136  0.0278  0.2544  1.5574 
## 
## Coefficients:
##                                  Estimate Std. Error t value Pr(>|t|)    
## (Intercept)                    -1.988e+00  2.113e+00  -0.941 0.346994    
## train_house_prices[, 18]        2.777e-01  1.798e-02  15.441  < 2e-16 ***
## train_house_prices[, 47]        5.878e-04  3.942e-05  14.911  < 2e-16 ***
## train_house_prices[, 62]        2.309e-01  4.270e-02   5.407 7.76e-08 ***
## train_house_prices[, 63]        5.574e-05  1.479e-04   0.377 0.706263    
## train_house_prices[, 39]        1.527e-04  4.862e-05   3.142 0.001721 ** 
## train_house_prices[, 35]        2.153e-04  3.717e-05   5.793 8.88e-09 ***
## train_house_prices[, 57]        1.718e-01  2.720e-02   6.314 3.84e-10 ***
## train_house_prices[, 20]        3.286e-03  8.566e-04   3.836 0.000132 ***
## train_house_prices[, 21]        6.727e-03  9.218e-04   7.297 5.37e-13 ***
## train_house_prices[, 30]CBlock  4.387e-02  5.749e-02   0.763 0.445507    
## train_house_prices[, 30]PConc   1.239e-01  6.928e-02   1.788 0.074012 .  
## train_house_prices[, 30]Slab   -1.669e-01  1.327e-01  -1.258 0.208717    
## train_house_prices[, 30]Stone   2.647e-01  2.044e-01   1.295 0.195628    
## train_house_prices[, 30]Wood   -5.595e-01  3.545e-01  -1.578 0.114848    
## train_house_prices[, 42]Y       3.430e-01  6.121e-02   5.604 2.60e-08 ***
## train_house_prices[, 67]        4.053e-04  1.258e-04   3.222 0.001306 ** 
## train_house_prices[, 4]         1.862e-03  6.837e-04   2.723 0.006562 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.487 on 1183 degrees of freedom
##   (259 observations deleted due to missingness)
## Multiple R-squared:  0.8483, Adjusted R-squared:  0.8461 
## F-statistic: 389.1 on 17 and 1183 DF,  p-value: < 2.2e-16
## 
## Call:
## lm(formula = train_house_prices$SalePrice ~ train_house_prices[, 
##     18] + train_house_prices[, 47] + train_house_prices[, 62] + 
##     train_house_prices[, 63] + train_house_prices[, 39] + train_house_prices[, 
##     35] + train_house_prices[, 57] + train_house_prices[, 20] + 
##     train_house_prices[, 21] + train_house_prices[, 30] + train_house_prices[, 
##     42] + train_house_prices[, 67] + train_house_prices[, 4] + 
##     train_house_prices[, 80])
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -7.0024 -0.2247  0.0191  0.2524  1.7705 
## 
## Coefficients:
##                                   Estimate Std. Error t value Pr(>|t|)    
## (Intercept)                     -4.354e-01  2.124e+00  -0.205 0.837641    
## train_house_prices[, 18]         2.731e-01  1.774e-02  15.393  < 2e-16 ***
## train_house_prices[, 47]         6.006e-04  3.891e-05  15.437  < 2e-16 ***
## train_house_prices[, 62]         2.423e-01  4.231e-02   5.728 1.29e-08 ***
## train_house_prices[, 63]        -1.577e-05  1.466e-04  -0.108 0.914333    
## train_house_prices[, 39]         1.485e-04  4.831e-05   3.073 0.002167 ** 
## train_house_prices[, 35]         2.316e-04  3.689e-05   6.278 4.83e-10 ***
## train_house_prices[, 57]         1.586e-01  2.690e-02   5.896 4.85e-09 ***
## train_house_prices[, 20]         2.948e-03  8.506e-04   3.466 0.000548 ***
## train_house_prices[, 21]         6.149e-03  9.154e-04   6.718 2.87e-11 ***
## train_house_prices[, 30]CBlock   5.511e-02  5.677e-02   0.971 0.331903    
## train_house_prices[, 30]PConc    1.195e-01  6.832e-02   1.748 0.080650 .  
## train_house_prices[, 30]Slab    -1.553e-01  1.325e-01  -1.172 0.241458    
## train_house_prices[, 30]Stone    2.839e-01  2.014e-01   1.410 0.158884    
## train_house_prices[, 30]Wood    -5.647e-01  3.492e-01  -1.617 0.106152    
## train_house_prices[, 42]Y        3.586e-01  6.053e-02   5.925 4.10e-09 ***
## train_house_prices[, 67]         4.157e-04  1.244e-04   3.341 0.000861 ***
## train_house_prices[, 4]          1.794e-03  6.738e-04   2.663 0.007848 ** 
## train_house_prices[, 80]AdjLand  3.281e-01  2.481e-01   1.323 0.186230    
## train_house_prices[, 80]Alloca   2.980e-02  1.655e-01   0.180 0.857143    
## train_house_prices[, 80]Family  -3.227e-03  1.249e-01  -0.026 0.979397    
## train_house_prices[, 80]Normal   2.845e-01  5.536e-02   5.139 3.23e-07 ***
## train_house_prices[, 80]Partial  4.186e-01  7.420e-02   5.642 2.10e-08 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4795 on 1178 degrees of freedom
##   (259 observations deleted due to missingness)
## Multiple R-squared:  0.8535, Adjusted R-squared:  0.8508 
## F-statistic:   312 on 22 and 1178 DF,  p-value: < 2.2e-16
## 
## Call:
## lm(formula = train_house_prices$SalePrice ~ train_house_prices[, 
##     18] + train_house_prices[, 47] + train_house_prices[, 62] + 
##     train_house_prices[, 63] + train_house_prices[, 39] + train_house_prices[, 
##     35] + train_house_prices[, 57] + train_house_prices[, 20] + 
##     train_house_prices[, 21] + train_house_prices[, 30] + train_house_prices[, 
##     42] + train_house_prices[, 67] + train_house_prices[, 4] + 
##     train_house_prices[, 80] + train_house_prices[, 68])
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -7.0026 -0.2231  0.0193  0.2528  1.7717 
## 
## Coefficients:
##                                   Estimate Std. Error t value Pr(>|t|)    
## (Intercept)                     -4.159e-01  2.130e+00  -0.195 0.845232    
## train_house_prices[, 18]         2.730e-01  1.776e-02  15.368  < 2e-16 ***
## train_house_prices[, 47]         5.998e-04  3.939e-05  15.229  < 2e-16 ***
## train_house_prices[, 62]         2.429e-01  4.252e-02   5.712 1.41e-08 ***
## train_house_prices[, 63]        -1.772e-05  1.473e-04  -0.120 0.904295    
## train_house_prices[, 39]         1.482e-04  4.837e-05   3.063 0.002237 ** 
## train_house_prices[, 35]         2.316e-04  3.691e-05   6.275 4.90e-10 ***
## train_house_prices[, 57]         1.585e-01  2.693e-02   5.886 5.15e-09 ***
## train_house_prices[, 20]         2.948e-03  8.510e-04   3.464 0.000551 ***
## train_house_prices[, 21]         6.140e-03  9.186e-04   6.684 3.59e-11 ***
## train_house_prices[, 30]CBlock   5.507e-02  5.680e-02   0.970 0.332483    
## train_house_prices[, 30]PConc    1.190e-01  6.845e-02   1.738 0.082462 .  
## train_house_prices[, 30]Slab    -1.549e-01  1.326e-01  -1.168 0.243004    
## train_house_prices[, 30]Stone    2.835e-01  2.015e-01   1.407 0.159723    
## train_house_prices[, 30]Wood    -5.644e-01  3.494e-01  -1.615 0.106489    
## train_house_prices[, 42]Y        3.593e-01  6.077e-02   5.913 4.40e-09 ***
## train_house_prices[, 67]         4.168e-04  1.248e-04   3.341 0.000860 ***
## train_house_prices[, 4]          1.795e-03  6.741e-04   2.662 0.007869 ** 
## train_house_prices[, 80]AdjLand  3.282e-01  2.482e-01   1.322 0.186267    
## train_house_prices[, 80]Alloca   3.070e-02  1.657e-01   0.185 0.853044    
## train_house_prices[, 80]Family  -2.561e-03  1.251e-01  -0.020 0.983664    
## train_house_prices[, 80]Normal   2.847e-01  5.541e-02   5.139 3.23e-07 ***
## train_house_prices[, 80]Partial  4.186e-01  7.423e-02   5.639 2.14e-08 ***
## train_house_prices[, 68]         3.171e-05  2.320e-04   0.137 0.891305    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4797 on 1177 degrees of freedom
##   (259 observations deleted due to missingness)
## Multiple R-squared:  0.8535, Adjusted R-squared:  0.8507 
## F-statistic: 298.2 on 23 and 1177 DF,  p-value: < 2.2e-16
## 
## Call:
## lm(formula = train_house_prices$SalePrice ~ train_house_prices[, 
##     18] + train_house_prices[, 47] + train_house_prices[, 62] + 
##     train_house_prices[, 63] + train_house_prices[, 39] + train_house_prices[, 
##     35] + train_house_prices[, 57] + train_house_prices[, 20] + 
##     train_house_prices[, 21] + train_house_prices[, 30] + train_house_prices[, 
##     42] + train_house_prices[, 67] + train_house_prices[, 4] + 
##     train_house_prices[, 80] + train_house_prices[, 68] + train_house_prices[, 
##     45])
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -6.9034 -0.2233  0.0184  0.2508  1.7887 
## 
## Coefficients:
##                                   Estimate Std. Error t value Pr(>|t|)    
## (Intercept)                     -4.731e-01  2.129e+00  -0.222 0.824190    
## train_house_prices[, 18]         2.738e-01  1.776e-02  15.418  < 2e-16 ***
## train_house_prices[, 47]         7.089e-04  7.772e-05   9.121  < 2e-16 ***
## train_house_prices[, 62]         2.434e-01  4.250e-02   5.728 1.29e-08 ***
## train_house_prices[, 63]        -2.863e-05  1.474e-04  -0.194 0.845960    
## train_house_prices[, 39]         6.191e-05  7.174e-05   0.863 0.388310    
## train_house_prices[, 35]         2.322e-04  3.688e-05   6.295 4.33e-10 ***
## train_house_prices[, 57]         1.540e-01  2.705e-02   5.692 1.58e-08 ***
## train_house_prices[, 20]         3.121e-03  8.570e-04   3.642 0.000282 ***
## train_house_prices[, 21]         5.988e-03  9.226e-04   6.491 1.26e-10 ***
## train_house_prices[, 30]CBlock   4.966e-02  5.685e-02   0.874 0.382564    
## train_house_prices[, 30]PConc    1.177e-01  6.840e-02   1.721 0.085488 .  
## train_house_prices[, 30]Slab    -2.429e-01  1.431e-01  -1.697 0.089931 .  
## train_house_prices[, 30]Stone    2.885e-01  2.014e-01   1.433 0.152249    
## train_house_prices[, 30]Wood    -5.686e-01  3.492e-01  -1.629 0.103665    
## train_house_prices[, 42]Y        3.591e-01  6.073e-02   5.913 4.41e-09 ***
## train_house_prices[, 67]         4.090e-04  1.248e-04   3.278 0.001076 ** 
## train_house_prices[, 4]          1.656e-03  6.789e-04   2.439 0.014857 *  
## train_house_prices[, 80]AdjLand  3.094e-01  2.483e-01   1.246 0.212960    
## train_house_prices[, 80]Alloca   7.272e-03  1.662e-01   0.044 0.965107    
## train_house_prices[, 80]Family  -5.326e-03  1.250e-01  -0.043 0.966020    
## train_house_prices[, 80]Normal   2.871e-01  5.539e-02   5.183 2.56e-07 ***
## train_house_prices[, 80]Partial  4.193e-01  7.418e-02   5.652 1.99e-08 ***
## train_house_prices[, 68]         6.047e-05  2.325e-04   0.260 0.794846    
## train_house_prices[, 45]        -1.267e-04  7.783e-05  -1.628 0.103853    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4793 on 1176 degrees of freedom
##   (259 observations deleted due to missingness)
## Multiple R-squared:  0.8539, Adjusted R-squared:  0.8509 
## F-statistic: 286.3 on 24 and 1176 DF,  p-value: < 2.2e-16
## 
## Call:
## lm(formula = train_house_prices$SalePrice ~ train_house_prices[, 
##     18] + train_house_prices[, 47] + train_house_prices[, 62] + 
##     train_house_prices[, 63] + train_house_prices[, 39] + train_house_prices[, 
##     35] + train_house_prices[, 57] + train_house_prices[, 20] + 
##     train_house_prices[, 21] + train_house_prices[, 30] + train_house_prices[, 
##     42] + train_house_prices[, 67] + train_house_prices[, 4] + 
##     train_house_prices[, 80] + train_house_prices[, 68] + train_house_prices[, 
##     45] + train_house_prices[, 51])
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -6.9255 -0.2270  0.0185  0.2479  1.7490 
## 
## Coefficients:
##                                   Estimate Std. Error t value Pr(>|t|)    
## (Intercept)                     -1.263e-02  2.147e+00  -0.006  0.99531    
## train_house_prices[, 18]         2.743e-01  1.775e-02  15.453  < 2e-16 ***
## train_house_prices[, 47]         7.188e-04  7.792e-05   9.224  < 2e-16 ***
## train_house_prices[, 62]         2.406e-01  4.251e-02   5.660 1.90e-08 ***
## train_house_prices[, 63]        -1.976e-05  1.474e-04  -0.134  0.89336    
## train_house_prices[, 39]         6.220e-05  7.169e-05   0.868  0.38576    
## train_house_prices[, 35]         2.294e-04  3.690e-05   6.217 7.01e-10 ***
## train_house_prices[, 57]         1.499e-01  2.716e-02   5.521 4.14e-08 ***
## train_house_prices[, 20]         2.842e-03  8.744e-04   3.250  0.00119 ** 
## train_house_prices[, 21]         6.029e-03  9.224e-04   6.536 9.40e-11 ***
## train_house_prices[, 30]CBlock   4.525e-02  5.689e-02   0.796  0.42648    
## train_house_prices[, 30]PConc    1.211e-01  6.839e-02   1.770  0.07699 .  
## train_house_prices[, 30]Slab    -2.270e-01  1.434e-01  -1.583  0.11361    
## train_house_prices[, 30]Stone    3.006e-01  2.014e-01   1.493  0.13577    
## train_house_prices[, 30]Wood    -5.600e-01  3.490e-01  -1.605  0.10886    
## train_house_prices[, 42]Y        3.543e-01  6.076e-02   5.831 7.11e-09 ***
## train_house_prices[, 67]         4.073e-04  1.247e-04   3.267  0.00112 ** 
## train_house_prices[, 4]          1.661e-03  6.785e-04   2.448  0.01453 *  
## train_house_prices[, 80]AdjLand  3.000e-01  2.482e-01   1.209  0.22689    
## train_house_prices[, 80]Alloca  -1.320e-02  1.666e-01  -0.079  0.93687    
## train_house_prices[, 80]Family  -2.545e-03  1.249e-01  -0.020  0.98375    
## train_house_prices[, 80]Normal   2.847e-01  5.538e-02   5.141 3.20e-07 ***
## train_house_prices[, 80]Partial  4.159e-01  7.416e-02   5.608 2.56e-08 ***
## train_house_prices[, 68]         3.538e-05  2.329e-04   0.152  0.87927    
## train_house_prices[, 45]        -1.770e-04  8.399e-05  -2.107  0.03529 *  
## train_house_prices[, 51]         5.980e-02  3.767e-02   1.588  0.11265    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.479 on 1175 degrees of freedom
##   (259 observations deleted due to missingness)
## Multiple R-squared:  0.8542, Adjusted R-squared:  0.8511 
## F-statistic: 275.3 on 25 and 1175 DF,  p-value: < 2.2e-16
## 
## Call:
## lm(formula = train_house_prices$SalePrice ~ train_house_prices[, 
##     18] + train_house_prices[, 47] + train_house_prices[, 62] + 
##     train_house_prices[, 63] + train_house_prices[, 39] + train_house_prices[, 
##     35] + train_house_prices[, 57] + train_house_prices[, 20] + 
##     train_house_prices[, 21] + train_house_prices[, 30] + train_house_prices[, 
##     42] + train_house_prices[, 67] + train_house_prices[, 4] + 
##     train_house_prices[, 80] + train_house_prices[, 68] + train_house_prices[, 
##     45] + train_house_prices[, 51] + train_house_prices[, 34])
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -6.2868 -0.2262  0.0249  0.2458  1.8604 
## 
## Coefficients:
##                                   Estimate Std. Error t value Pr(>|t|)    
## (Intercept)                      1.723e+00  2.230e+00   0.773  0.43990    
## train_house_prices[, 18]         2.735e-01  1.801e-02  15.181  < 2e-16 ***
## train_house_prices[, 47]         7.755e-04  8.881e-05   8.731  < 2e-16 ***
## train_house_prices[, 62]         2.289e-01  4.278e-02   5.351 1.06e-07 ***
## train_house_prices[, 63]         1.962e-05  1.475e-04   0.133  0.89421    
## train_house_prices[, 39]         7.183e-05  8.537e-05   0.841  0.40029    
## train_house_prices[, 35]         1.357e-05  5.071e-05   0.268  0.78911    
## train_house_prices[, 57]         1.487e-01  2.729e-02   5.450 6.17e-08 ***
## train_house_prices[, 20]         2.060e-03  8.982e-04   2.293  0.02200 *  
## train_house_prices[, 21]         5.983e-03  9.426e-04   6.347 3.17e-10 ***
## train_house_prices[, 30]CBlock   2.257e-02  5.720e-02   0.395  0.69321    
## train_house_prices[, 30]PConc    1.250e-01  6.847e-02   1.825  0.06821 .  
## train_house_prices[, 30]Stone    3.128e-01  1.996e-01   1.567  0.11733    
## train_house_prices[, 30]Wood    -6.401e-01  3.459e-01  -1.851  0.06448 .  
## train_house_prices[, 42]Y        3.759e-01  6.321e-02   5.947 3.62e-09 ***
## train_house_prices[, 67]         4.011e-04  1.245e-04   3.220  0.00132 ** 
## train_house_prices[, 4]          1.892e-03  6.765e-04   2.797  0.00524 ** 
## train_house_prices[, 80]AdjLand  2.997e-01  2.804e-01   1.069  0.28523    
## train_house_prices[, 80]Alloca  -6.773e-02  1.902e-01  -0.356  0.72187    
## train_house_prices[, 80]Family   4.149e-02  1.241e-01   0.334  0.73816    
## train_house_prices[, 80]Normal   2.752e-01  5.524e-02   4.982 7.28e-07 ***
## train_house_prices[, 80]Partial  4.509e-01  7.403e-02   6.091 1.53e-09 ***
## train_house_prices[, 68]        -1.444e-05  2.316e-04  -0.062  0.95028    
## train_house_prices[, 45]        -2.223e-04  9.539e-05  -2.330  0.01996 *  
## train_house_prices[, 51]         7.899e-02  3.788e-02   2.085  0.03727 *  
## train_house_prices[, 34]BLQ     -7.213e-02  5.867e-02  -1.229  0.21919    
## train_house_prices[, 34]GLQ      1.243e-02  5.197e-02   0.239  0.81094    
## train_house_prices[, 34]LwQ     -1.299e-01  7.311e-02  -1.777  0.07590 .  
## train_house_prices[, 34]Rec     -6.069e-02  5.952e-02  -1.020  0.30816    
## train_house_prices[, 34]Unf     -2.950e-01  5.560e-02  -5.306 1.34e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4736 on 1140 degrees of freedom
##   (290 observations deleted due to missingness)
## Multiple R-squared:  0.855,  Adjusted R-squared:  0.8513 
## F-statistic: 231.8 on 29 and 1140 DF,  p-value: < 2.2e-16
## 
## Call:
## lm(formula = train_house_prices$SalePrice ~ train_house_prices[, 
##     18] + train_house_prices[, 47] + train_house_prices[, 62] + 
##     train_house_prices[, 63] + train_house_prices[, 35] + train_house_prices[, 
##     57] + train_house_prices[, 20] + train_house_prices[, 21] + 
##     train_house_prices[, 42] + train_house_prices[, 67] + train_house_prices[, 
##     4] + train_house_prices[, 80] + train_house_prices[, 45] + 
##     train_house_prices[, 51] + train_house_prices[, 34])
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -6.1868 -0.2250  0.0250  0.2481  1.8471 
## 
## Coefficients:
##                                   Estimate Std. Error t value Pr(>|t|)    
## (Intercept)                     -6.412e-01  1.932e+00  -0.332  0.73996    
## train_house_prices[, 18]         2.774e-01  1.761e-02  15.753  < 2e-16 ***
## train_house_prices[, 47]         8.467e-04  5.828e-05  14.529  < 2e-16 ***
## train_house_prices[, 62]         2.307e-01  4.254e-02   5.424 7.11e-08 ***
## train_house_prices[, 63]         3.816e-05  1.470e-04   0.260  0.79520    
## train_house_prices[, 35]         2.404e-05  4.852e-05   0.495  0.62035    
## train_house_prices[, 57]         1.452e-01  2.719e-02   5.341 1.11e-07 ***
## train_house_prices[, 20]         2.983e-03  7.139e-04   4.178 3.16e-05 ***
## train_house_prices[, 21]         6.279e-03  9.201e-04   6.824 1.43e-11 ***
## train_house_prices[, 42]Y        3.599e-01  6.253e-02   5.757 1.10e-08 ***
## train_house_prices[, 67]         3.767e-04  1.244e-04   3.029  0.00251 ** 
## train_house_prices[, 4]          1.611e-03  6.666e-04   2.416  0.01584 *  
## train_house_prices[, 80]AdjLand  3.157e-01  2.811e-01   1.123  0.26160    
## train_house_prices[, 80]Alloca  -9.253e-02  1.901e-01  -0.487  0.62647    
## train_house_prices[, 80]Family   2.705e-02  1.243e-01   0.218  0.82783    
## train_house_prices[, 80]Normal   2.748e-01  5.537e-02   4.963 7.99e-07 ***
## train_house_prices[, 80]Partial  4.580e-01  7.404e-02   6.186 8.57e-10 ***
## train_house_prices[, 45]        -2.773e-04  6.229e-05  -4.452 9.33e-06 ***
## train_house_prices[, 51]         6.926e-02  3.767e-02   1.839  0.06624 .  
## train_house_prices[, 34]BLQ     -7.178e-02  5.879e-02  -1.221  0.22233    
## train_house_prices[, 34]GLQ      3.389e-02  5.037e-02   0.673  0.50116    
## train_house_prices[, 34]LwQ     -1.215e-01  7.305e-02  -1.663  0.09666 .  
## train_house_prices[, 34]Rec     -6.067e-02  5.961e-02  -1.018  0.30901    
## train_house_prices[, 34]Unf     -2.667e-01  5.420e-02  -4.920 9.93e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4751 on 1146 degrees of freedom
##   (290 observations deleted due to missingness)
## Multiple R-squared:  0.8533, Adjusted R-squared:  0.8503 
## F-statistic: 289.8 on 23 and 1146 DF,  p-value: < 2.2e-16

We will submit model 17 to the test data from kaggle.com. The final score was .20812