Cara 1

#creating custom Control Parameters
custom <- trainControl(method = "repeatedcv",
                       number = 10,
                       repeats = 5,
                       verboseIter = F) #print iterasi

#fitting  Ridge Regression model
set.seed(1234)
ridge <- train(medv~.,train,
               method="glmnet",
               tuneGrid=expand.grid(alpha=0,lambda=seq(0.0001,1,length=10)),
               trControl=custom)
ridge

## glmnet 
## 
## 354 samples
##  13 predictor
## 
## No pre-processing
## Resampling: Cross-Validated (10 fold, repeated 5 times) 
## Summary of sample sizes: 318, 319, 318, 319, 319, 318, ... 
## Resampling results across tuning parameters:
## 
##   lambda  RMSE      Rsquared   MAE     
##   0.0001  4.340939  0.7712224  3.102308
##   0.1112  4.340939  0.7712224  3.102308
##   0.2223  4.340939  0.7712224  3.102308
##   0.3334  4.340939  0.7712224  3.102308
##   0.4445  4.340939  0.7712224  3.102308
##   0.5556  4.340939  0.7712224  3.102308
##   0.6667  4.341042  0.7712146  3.102329
##   0.7778  4.348468  0.7706810  3.099810
##   0.8889  4.356811  0.7700437  3.097963
##   1.0000  4.365780  0.7693706  3.097781
## 
## Tuning parameter 'alpha' was held constant at a value of 0
## RMSE was used to select the optimal model using the smallest value.
## The final values used for the model were alpha = 0 and lambda = 0.5556.

#mean validation score
mean(ridge$resample$RMSE)

## [1] 4.340939

#plotting the model
plot(ridge, main = "Ridge Regression")

#plotting important variables
plot(varImp(ridge,scale=F))

Berdasarkan output di atas, terlihat bahwa peubah yang paling penting adalah peubah nox terhadap model dibandingkan dengan peubah-peubah lainnya.

Cara 2

#Ridge Regression with library(glmnet)
lambdas <- 10^seq(2,-3, by = -.1)
ridge_reg = glmnet(as.matrix(train[,-14]), train[,14], nlambda = 25, alpha = 0,family = 'gaussian', lambda = lambdas)
summary(ridge_reg)

##           Length Class     Mode   
## a0         51    -none-    numeric
## beta      663    dgCMatrix S4     
## df         51    -none-    numeric
## dim         2    -none-    numeric
## lambda     51    -none-    numeric
## dev.ratio  51    -none-    numeric
## nulldev     1    -none-    numeric
## npasses     1    -none-    numeric
## jerr        1    -none-    numeric
## offset      1    -none-    logical
## call        7    -none-    call   
## nobs        1    -none-    numeric

ridge_reg

## 
## Call:  glmnet::glmnet(x = as.matrix(train[, -14]), y = train[, 14],      nlambda = 25, alpha = 0, family = "gaussian", lambda = lambdas) 
## 
##    Df  %Dev  Lambda
## 1  13 30.01 100.000
## 2  13 34.00  79.430
## 3  13 38.04  63.100
## 4  13 42.05  50.120
## 5  13 45.95  39.810
## 6  13 49.70  31.620
## 7  13 53.25  25.120
## 8  13 56.59  19.950
## 9  13 59.69  15.850
## 10 13 62.52  12.590
## 11 13 65.09  10.000
## 12 13 67.36   7.943
## 13 13 69.34   6.310
## 14 13 71.03   5.012
## 15 13 72.44   3.981
## 16 13 73.62   3.162
## 17 13 74.57   2.512
## 18 13 75.34   1.995
## 19 13 75.94   1.585
## 20 13 76.42   1.259
## 21 13 76.79   1.000
## 22 13 77.08   0.794
## 23 13 77.30   0.631
## 24 13 77.46   0.501
## 25 13 77.58   0.398
## 26 13 77.67   0.316
## 27 13 77.73   0.251
## 28 13 77.77   0.200
## 29 13 77.81   0.158
## 30 13 77.83   0.126
## 31 13 77.84   0.100
## 32 13 77.85   0.079
## 33 13 77.86   0.063
## 34 13 77.86   0.050
## 35 13 77.87   0.040
## 36 13 77.87   0.032
## 37 13 77.87   0.025
## 38 13 77.87   0.020
## 39 13 77.87   0.016
## 40 13 77.87   0.013
## 41 13 77.87   0.010
## 42 13 77.87   0.008
## 43 13 77.87   0.006
## 44 13 77.87   0.005
## 45 13 77.87   0.004
## 46 13 77.87   0.003
## 47 13 77.87   0.003
## 48 13 77.87   0.002
## 49 13 77.87   0.002
## 50 13 77.87   0.001
## 51 13 77.87   0.001

set.seed(100)
#tunning parameter lambda dg cv
cv_ridge <- cv.glmnet(as.matrix(train[,-14]), train[,14], alpha = 0, lambda = lambdas)
optimal_lambda <- cv_ridge$lambda.min
optimal_lambda

## [1] 0.1258925

coef(cv_ridge, s="lambda.min")

## 14 x 1 sparse Matrix of class "dgCMatrix"
##                        s1
## (Intercept)  33.512762193
## crim         -0.116541536
## zn            0.045303128
## indus         0.015047943
## chas          2.864206507
## nox         -10.422379184
## rm            3.659253006
## age          -0.012198505
## dis          -1.384865675
## rad           0.227556069
## tax          -0.008280337
## ptratio      -0.902912189
## black         0.008342041
## lstat        -0.623529573

coef(cv_ridge, s=100)

## 14 x 1 sparse Matrix of class "dgCMatrix"
##                       s1
## (Intercept) 23.249596796
## crim        -0.022001298
## zn           0.008746460
## indus       -0.037653796
## chas         0.417908674
## nox         -1.911639790
## rm           0.653628764
## age         -0.007345027
## dis          0.053942947
## rad         -0.019853504
## tax         -0.001407383
## ptratio     -0.143013850
## black        0.001933966
## lstat       -0.064620516

# Compute R^2 from true and predicted values
eval_results <- function(true, predicted, df) {
  SSE <- sum((predicted - true)^2)
  SST <- sum((true - mean(true))^2)
  R_square <- 1 - SSE / SST
  RMSE = sqrt(SSE/nrow(df))
 
  # Model performance metrics
  data.frame(RMSE = RMSE,
             Rsquare = R_square)
}

# Prediction and evaluation on train data
predictions_train <- predict(ridge_reg, s = optimal_lambda, newx = as.matrix(train[,-14]))
eval_results(train[,14], predictions_train, train)

##       RMSE   Rsquare
## 1 4.186191 0.7782747

# Prediction and evaluation on test data
predictions_test <- predict(ridge_reg, s = optimal_lambda, newx = as.matrix(test[,-14]))
eval_results(test[,14], predictions_test, test)

##       RMSE   Rsquare
## 1 5.830073 0.6410751

Berdasarkan output di atas, diperoleh bahwa nilai RMSE data training dan data testing secara berturut-turut, yaitu 4.186191 dan 5.830073. Hal ini menunjukkan bahwa model yang dibuat sudah cukup baik karena menghasilkan nilai RMSE yang kecil.

Dataset

set.seed(123)
x <- cbind(1,matrix( rnorm(100*15,2,1),100,15))
e <- matrix( rnorm(100),100,1)
b <- c(1,rep(0:2,each=5))
y <- x%*%b+e

dt.bangkitan <- data.frame(y,x[, -1])
str(dt.bangkitan)

## 'data.frame':    100 obs. of  16 variables:
##  $ y  : num  26.7 22.7 30.5 29.1 29.2 ...
##  $ X1 : num  1.44 1.77 3.56 2.07 2.13 ...
##  $ X2 : num  1.29 2.26 1.75 1.65 1.05 ...
##  $ X3 : num  4.2 3.31 1.73 2.54 1.59 ...
##  $ X4 : num  1.285 1.247 1.061 0.947 1.563 ...
##  $ X5 : num  1.926 0.831 1.365 1.971 2.671 ...
##  $ X6 : num  1.398 1.006 3.027 2.751 0.491 ...
##  $ X7 : num  3.074 1.973 1.967 0.484 2.79 ...
##  $ X8 : num  1.272 0.46 1.307 2.119 0.635 ...
##  $ X9 : num  2.36 1.34 2.86 3.15 2.28 ...
##  $ X10: num  0.986 1.209 2.3 3.639 3.085 ...
##  $ X11: num  1.004 0.96 1.982 1.868 -0.549 ...
##  $ X12: num  2.916 2.801 1.063 0.599 2.16 ...
##  $ X13: num  2.62 1.24 2.85 1.25 2.63 ...
##  $ X14: num  1.25 1.678 0.852 2.354 2.425 ...
##  $ X15: num  0.914 1.335 2.715 1.568 2.228 ...

Eksplorasi Data

cor.bangkitan <- cor(dt.bangkitan)
cor.bangkitan

##               y          X1            X2           X3          X4           X5
## y    1.00000000  0.06635220 -0.0108389554 -0.111341207  0.18026434  0.124471806
## X1   0.06635220  1.00000000 -0.0495321472 -0.129176009 -0.04407900 -0.192711098
## X2  -0.01083896 -0.04953215  1.0000000000  0.030579031  0.04383271 -0.130622187
## X3  -0.11134121 -0.12917601  0.0305790308  1.000000000 -0.04486571 -0.024848379
## X4   0.18026434 -0.04407900  0.0438327132 -0.044865707  1.00000000 -0.019259855
## X5   0.12447181 -0.19271110 -0.1306221865 -0.024848379 -0.01925986  1.000000000
## X6   0.18148739 -0.05648439  0.1144879233  0.018210080 -0.08991276  0.206617706
## X7   0.25754024 -0.03436677  0.0781128798  0.008685177 -0.06378733 -0.006502516
## X8   0.26562075  0.18157297 -0.0331234961 -0.115029463  0.16789328 -0.140653506
## X9   0.15612088 -0.02260251 -0.0453283184 -0.053281912 -0.16506751 -0.039583467
## X10  0.23309445  0.01100538 -0.0914903545 -0.014442042  0.24521164 -0.016043315
## X11  0.54378073  0.07578378 -0.0237288723 -0.160557106  0.19574314  0.034231649
## X12  0.50269005 -0.12758456  0.0126769273  0.085344716  0.01303423  0.146170450
## X13  0.39313920 -0.04952921  0.0008581215  0.134846380 -0.01789764  0.079731399
## X14  0.56433419  0.13040172 -0.0973757690 -0.027179463  0.09158976  0.103533014
## X15  0.34991851  0.08569836  0.0967633790 -0.229082230  0.12994736 -0.035279575
##              X6            X7            X8            X9         X10
## y    0.18148739  0.2575402402  0.2656207511  0.1561208802  0.23309445
## X1  -0.05648439 -0.0343667704  0.1815729746 -0.0226025134  0.01100538
## X2   0.11448792  0.0781128798 -0.0331234961 -0.0453283184 -0.09149035
## X3   0.01821008  0.0086851768 -0.1150294630 -0.0532819116 -0.01444204
## X4  -0.08991276 -0.0637873268  0.1678932800 -0.1650675124  0.24521164
## X5   0.20661771 -0.0065025161 -0.1406535056 -0.0395834667 -0.01604332
## X6   1.00000000 -0.0646926020  0.0941501419  0.0743634830 -0.02505532
## X7  -0.06469260  1.0000000000  0.0002653148 -0.1289100521 -0.02046957
## X8   0.09415014  0.0002653148  1.0000000000 -0.0008120057  0.02425240
## X9   0.07436348 -0.1289100521 -0.0008120057  1.0000000000 -0.02272065
## X10 -0.02505532 -0.0204695736  0.0242524030 -0.0227206515  1.00000000
## X11 -0.04127698  0.0849030583  0.1458839328 -0.0866610453  0.17228854
## X12  0.03426132  0.1793848678 -0.0433176911 -0.0152440538 -0.10393550
## X13  0.09242346  0.0234258143  0.1675994101  0.1638626335 -0.04332960
## X14 -0.02002915  0.0575698939  0.0472893396 -0.0680598188  0.12692737
## X15 -0.12646758  0.0288381288 -0.0908934275  0.0108933983  0.03891113
##             X11         X12           X13          X14         X15
## y    0.54378073  0.50269005  0.3931391977  0.564334187  0.34991851
## X1   0.07578378 -0.12758456 -0.0495292127  0.130401721  0.08569836
## X2  -0.02372887  0.01267693  0.0008581215 -0.097375769  0.09676338
## X3  -0.16055711  0.08534472  0.1348463800 -0.027179463 -0.22908223
## X4   0.19574314  0.01303423 -0.0178976443  0.091589757  0.12994736
## X5   0.03423165  0.14617045  0.0797313987  0.103533014 -0.03527957
## X6  -0.04127698  0.03426132  0.0924234630 -0.020029147 -0.12646758
## X7   0.08490306  0.17938487  0.0234258143  0.057569894  0.02883813
## X8   0.14588393 -0.04331769  0.1675994101  0.047289340 -0.09089343
## X9  -0.08666105 -0.01524405  0.1638626335 -0.068059819  0.01089340
## X10  0.17228854 -0.10393550 -0.0433295964  0.126927372  0.03891113
## X11  1.00000000  0.01981162  0.0795288323  0.257742514  0.18427179
## X12  0.01981162  1.00000000  0.1486372459  0.227908966  0.01473690
## X13  0.07952883  0.14863725  1.0000000000 -0.008632214 -0.15398824
## X14  0.25774251  0.22790897 -0.0086322143  1.000000000  0.05978406
## X15  0.18427179  0.01473690 -0.1539882385  0.059784059  1.00000000

ggcorrplot(cor.bangkitan, lab = TRUE, type = "lower")

Berdasarkan output dan plot korelasi di atas, dapat diperoleh informasi hubungan atau korelasi antara peubah Y sebagai peubah respon dan peubah-peubah penjelas sera antar peubah penjelas. Korelasi antar peubah ditandai dengan kepekatan warna. Jika semakin pekat warna, maka semakin kuat korelasinya. Sebaliknya, jika semakin pudar warna, maka semakin lemah korelasinya. Terlihat bahwa korelasi paling tinggi dimiliki oleh peubah Y dan peubah X14, yaitu sebesar 0.56.

Regresi Linear

mod1Bangkitan <- lm( y~.,data=dt.bangkitan)
summary(mod1Bangkitan)

## 
## Call:
## lm(formula = y ~ ., data = dt.bangkitan)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -2.10684 -0.46276 -0.01661  0.46989  2.28986 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  1.00143    0.67058   1.493   0.1391    
## X1           0.11730    0.09988   1.174   0.2435    
## X2          -0.06743    0.09221  -0.731   0.4667    
## X3          -0.11002    0.09564  -1.150   0.2533    
## X4           0.19139    0.09006   2.125   0.0365 *  
## X5           0.05484    0.09385   0.584   0.5605    
## X6           1.20593    0.09652  12.494   <2e-16 ***
## X7           0.98520    0.08618  11.432   <2e-16 ***
## X8           0.96980    0.09241  10.495   <2e-16 ***
## X9           0.97923    0.08532  11.477   <2e-16 ***
## X10          0.98632    0.08850  11.145   <2e-16 ***
## X11          1.70147    0.09007  18.891   <2e-16 ***
## X12          2.10295    0.09271  22.682   <2e-16 ***
## X13          1.90424    0.09896  19.243   <2e-16 ***
## X14          2.05354    0.09192  22.340   <2e-16 ***
## X15          1.96807    0.09359  21.028   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8465 on 84 degrees of freedom
## Multiple R-squared:  0.9823, Adjusted R-squared:  0.9791 
## F-statistic: 310.3 on 15 and 84 DF,  p-value: < 2.2e-16

Berdasarkan output di atas, diperoleh informasi bahwa peubah X1, X2, X3, dan X5 tidak nyata atau tidak berpengaruh secara signifikan terhadap peubah Y sebagai peubah respon. Selain itu, diperoleh nilai R-Squared sebesar 0.9823 dan nilai Adjusted R-squared sebesar 0.9791 yang artinya keragaman peubah respon yang dapat dijelaskan oleh keragaman seluruh peubah penjelas sebesar 97.91%.

Regresi Ridge

mod2Bangkitan <- cv.glmnet(x[,-1], y, alpha=0) #pemilihan lambda dgn cv untuk ridge
mod2Bangkitan

## 
## Call:  glmnet::cv.glmnet(x = x[, -1], y = y, alpha = 0) 
## 
## Measure: Mean-Squared Error 
## 
##     Lambda Index Measure     SE Nonzero
## min 0.3288   100  0.9139 0.1418      15
## 1se 0.5746    94  1.0480 0.1789      15

coef(mod2Bangkitan, s="lambda.min")

## 16 x 1 sparse Matrix of class "dgCMatrix"
##                      s1
## (Intercept)  2.19566346
## V1           0.12678129
## V2          -0.05352871
## V3          -0.12646737
## V4           0.21088425
## V5           0.08346725
## V6           1.13201529
## V7           0.94863893
## V8           0.93160983
## V9           0.93343677
## V10          0.93714752
## V11          1.65728283
## V12          2.01983016
## V13          1.82034285
## V14          1.97908284
## V15          1.84975020

Regresi Lasso

mod3Bangkitan <- cv.glmnet(x[, -1], y,alpha=1) #pemilihan lambda dgn cv untuk lambda
mod3Bangkitan

## 
## Call:  glmnet::cv.glmnet(x = x[, -1], y = y, alpha = 1) 
## 
## Measure: Mean-Squared Error 
## 
##      Lambda Index Measure     SE Nonzero
## min 0.01238    61  0.8020 0.1019      15
## 1se 0.10520    38  0.8952 0.1331      12

coef<-coef(mod3Bangkitan, s="lambda.min")

Model Averaging

mod1Bangkitan <- lm(y~.,data=dt.bangkitan, 
                    na.action = na.fail)
mod4Bangkitan <- dredge(global.model=mod1Bangkitan,
                        m.lim=c(10,20))

## Fixed term is "(Intercept)"

mod5Bangkitan <- model.avg(mod4Bangkitan, delta<4)
mod5Bangkitan

## 
## Call:
## model.avg(object = mod4Bangkitan, subset = delta < 4)
## 
## Component models: 
## '2+3+4+5+6+7+10+12+13+14+15'      '2+3+4+5+6+7+9+10+12+13+14+15'    
## '1+2+3+4+5+6+7+10+12+13+14+15'    '2+3+4+5+6+7+12+13+14+15'         
## '2+3+4+5+6+7+8+10+12+13+14+15'    '1+2+3+4+5+6+7+9+10+12+13+14+15'  
## '2+3+4+5+6+7+10+11+12+13+14+15'   '2+3+4+5+6+7+9+12+13+14+15'       
## '2+3+4+5+6+7+8+9+10+12+13+14+15'  '1+2+3+4+5+6+7+8+10+12+13+14+15'  
## '1+2+3+4+5+6+7+10+11+12+13+14+15' '2+3+4+5+6+7+9+10+11+12+13+14+15' 
## '1+2+3+4+5+6+7+12+13+14+15'       '2+3+4+5+6+7+8+12+13+14+15'       
## '2+3+4+5+6+7+11+12+13+14+15'     
## 
## Coefficients: 
##        (Intercept)       X10      X11     X12      X13      X14      X15
## full      1.023856 0.9967599 1.718025 2.09497 1.893608 2.073735 1.986761
## subset    1.023856 0.9967599 1.718025 2.09497 1.893608 2.073735 1.986761
##               X4       X6       X7        X8        X9          X3         X1
## full   0.1378477 1.200413 0.972448 0.9955925 0.9756526 -0.04056454 0.03266817
## subset 0.1790996 1.200413 0.972448 0.9955925 0.9756526 -0.12294580 0.11432606
##                 X2          X5
## full   -0.01553233 0.009591538
## subset -0.07977554 0.059842905

summary(mod5Bangkitan)

## 
## Call:
## model.avg(object = mod4Bangkitan, subset = delta < 4)
## 
## Component model call: 
## lm(formula = y ~ <15 unique rhs>, data = dt.bangkitan, na.action = 
##      na.fail)
## 
## Component models: 
##                                 df  logLik   AICc delta weight
## 2+3+4+5+6+7+10+12+13+14+15      13 -118.86 267.95  0.00   0.18
## 2+3+4+5+6+7+9+10+12+13+14+15    14 -117.85 268.65  0.70   0.13
## 1+2+3+4+5+6+7+10+12+13+14+15    14 -118.03 269.01  1.06   0.10
## 2+3+4+5+6+7+12+13+14+15         12 -120.96 269.51  1.56   0.08
## 2+3+4+5+6+7+8+10+12+13+14+15    14 -118.37 269.68  1.73   0.07
## 1+2+3+4+5+6+7+9+10+12+13+14+15  15 -117.14 269.99  2.04   0.06
## 2+3+4+5+6+7+10+11+12+13+14+15   14 -118.64 270.21  2.26   0.06
## 2+3+4+5+6+7+9+12+13+14+15       13 -120.03 270.29  2.34   0.06
## 2+3+4+5+6+7+8+9+10+12+13+14+15  15 -117.42 270.55  2.60   0.05
## 1+2+3+4+5+6+7+8+10+12+13+14+15  15 -117.57 270.85  2.90   0.04
## 1+2+3+4+5+6+7+10+11+12+13+14+15 15 -117.64 270.99  3.04   0.04
## 2+3+4+5+6+7+9+10+11+12+13+14+15 15 -117.69 271.10  3.15   0.04
## 1+2+3+4+5+6+7+12+13+14+15       13 -120.44 271.12  3.17   0.04
## 2+3+4+5+6+7+8+12+13+14+15       13 -120.64 271.51  3.56   0.03
## 2+3+4+5+6+7+11+12+13+14+15      13 -120.73 271.70  3.75   0.03
## 
## Term codes: 
##  X1 X10 X11 X12 X13 X14 X15  X2  X3  X4  X5  X6  X7  X8  X9 
##   1   2   3   4   5   6   7   8   9  10  11  12  13  14  15 
## 
## Model-averaged coefficients:  
## (full average) 
##              Estimate Std. Error Adjusted SE z value Pr(>|z|)    
## (Intercept)  1.023856   0.597649    0.604755   1.693   0.0905 .  
## X10          0.996760   0.089409    0.090623  10.999   <2e-16 ***
## X11          1.718025   0.090330    0.091582  18.759   <2e-16 ***
## X12          2.094970   0.092302    0.093590  22.384   <2e-16 ***
## X13          1.893608   0.098590    0.099965  18.943   <2e-16 ***
## X14          2.073735   0.091139    0.092411  22.440   <2e-16 ***
## X15          1.986761   0.093113    0.094384  21.050   <2e-16 ***
## X4           0.137848   0.108896    0.109696   1.257   0.2089    
## X6           1.200413   0.094063    0.095369  12.587   <2e-16 ***
## X7           0.972448   0.086441    0.087643  11.096   <2e-16 ***
## X8           0.995593   0.091521    0.092752  10.734   <2e-16 ***
## X9           0.975653   0.085639    0.086818  11.238   <2e-16 ***
## X3          -0.040565   0.079498    0.080030   0.507   0.6122    
## X1           0.032668   0.073846    0.074377   0.439   0.6605    
## X2          -0.015532   0.051114    0.051561   0.301   0.7632    
## X5           0.009592   0.042955    0.043400   0.221   0.8251    
##  
## (conditional average) 
##             Estimate Std. Error Adjusted SE z value Pr(>|z|)    
## (Intercept)  1.02386    0.59765     0.60476   1.693   0.0905 .  
## X10          0.99676    0.08941     0.09062  10.999   <2e-16 ***
## X11          1.71803    0.09033     0.09158  18.759   <2e-16 ***
## X12          2.09497    0.09230     0.09359  22.384   <2e-16 ***
## X13          1.89361    0.09859     0.09997  18.943   <2e-16 ***
## X14          2.07373    0.09114     0.09241  22.440   <2e-16 ***
## X15          1.98676    0.09311     0.09438  21.050   <2e-16 ***
## X4           0.17910    0.08955     0.09081   1.972   0.0486 *  
## X6           1.20041    0.09406     0.09537  12.587   <2e-16 ***
## X7           0.97245    0.08644     0.08764  11.096   <2e-16 ***
## X8           0.99559    0.09152     0.09275  10.734   <2e-16 ***
## X9           0.97565    0.08564     0.08682  11.238   <2e-16 ***
## X3          -0.12295    0.09501     0.09635   1.276   0.2020    
## X1           0.11433    0.09873     0.10012   1.142   0.2535    
## X2          -0.07978    0.09107     0.09236   0.864   0.3877    
## X5           0.05984    0.09222     0.09351   0.640   0.5222    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Berdasarkan output di atas, diperoleh model terbaik dari hasil Model Averaging, yaitu dengan kombinasi 11 peubah penjelas di antaranya X4, X6, X7, X8, X9,X10, X11, X12, X13, X14, dan X15.

Penanganan Missing Value*

Dalam kasus ini kita akan menangani missing value dengan dua cara, yaitu:

• Mereplace missing value pada kolom-kolom yang memiliki banyak sekali missing value (diatas 500)

• Menghapus baris-baris yang mengandung missing value pada kolom-kolom yang memiliki sedikti missing value (dibawah 500)

Berikut dibawah ini adalah sintaks untuk melakukan replace missing value, khususnya jika datanya berupa factor atau string. Kemudian na.omit digunakan untuk menghapus semua baris yang mengandung missing value

dt.house <- dt.house[,-1]
dt.house1 <- dt.house %>% 
  mutate(
    Alley = forcats::fct_explicit_na(Alley, 
                                     na_level="Ukn"),
    FireplaceQu=forcats::fct_explicit_na(FireplaceQu,
                                      na_level="Ukn"),
    PoolQC = forcats::fct_explicit_na(PoolQC, 
                                      na_level="Ukn"),
    Fence = forcats::fct_explicit_na(Fence,
                                     na_level="Ukn"),
    MiscFeature =forcats::fct_explicit_na(MiscFeature,
                                      na_level="Ukn")
  ) %>% na.omit

Kemudian akan dilihat kembali data yang sudah ditangani missing valuenya, sebagai berikut.

plot_intro(data = dt.house1)

skim_without_charts(dt.house1)

Variable type: factor

Variable type: numeric

Berdasarkan output di atas, didapatkan bahwa missing value sudah tertangani. Namun, setelah dilihat kembali ternyata ada kolom yang hanya memiliki satu kategori saja yaitu kolom Utilities sehingga kolom tersebut perlu dihapus saja.

dt.house1 <- dt.house1[,-9]

Memeriksa Sebaran Data

plot_histogram(data = dt.house1,nrow=3,ncol = 3,
               geom_histogram_args = list(fill="steelblue")
               )

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

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

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

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

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

plot_bar(data = dt.house1)

Memeriksa Korelasi Peubah

plot_scatterplot(data = dt.house1 %>%
                   select_if(is.numeric),
                 by="SalePrice",geom_point_args = list(color="steelblue") )

cor_mat <- cor(dt.house1%>%
                   select_if(is.numeric),method = "spearman")
cor_mat[upper.tri(cor_mat,diag = TRUE)] <- NA 
cor_df <- cor_mat   %>%
    as.data.frame() %>% 
    rownames_to_column(var = "Var1") %>%
  pivot_longer(names_to = "Var2",
               values_to = "corr",
               -Var1) %>% na.omit

cor_df %>% filter(abs(corr)>0.6) %>% arrange(desc(abs(corr)))

## # A tibble: 31 × 3
##    Var1         Var2          corr
##    <chr>        <chr>        <dbl>
##  1 GarageYrBlt  YearBuilt    0.895
##  2 X1stFlrSF    TotalBsmtSF  0.877
##  3 GarageArea   GarageCars   0.841
##  4 TotRmsAbvGrd GrLivArea    0.829
##  5 SalePrice    OverallQual  0.823
##  6 GarageYrBlt  YearRemodAdd 0.747
##  7 YearRemodAdd YearBuilt    0.738
##  8 SalePrice    GrLivArea    0.731
##  9 SalePrice    GarageCars   0.681
## 10 SalePrice    FullBath     0.671
## # … with 21 more rows

cor_df %>% filter(abs(corr)<=0.6)  

## # A tibble: 635 × 3
##    Var1        Var2            corr
##    <chr>       <chr>          <dbl>
##  1 LotFrontage MSSubClass  -0.313  
##  2 LotArea     MSSubClass  -0.255  
##  3 OverallQual MSSubClass   0.0992 
##  4 OverallQual LotFrontage  0.238  
##  5 OverallQual LotArea      0.283  
##  6 OverallCond MSSubClass  -0.0763 
##  7 OverallCond LotFrontage -0.0693 
##  8 OverallCond LotArea     -0.0873 
##  9 OverallCond OverallQual -0.264  
## 10 YearBuilt   MSSubClass  -0.00468
## # … with 625 more rows

plot_bar(data = dt.house1,with="SalePrice")

## Seleksi Peubah

regresi1 <- lm(formula = SalePrice~.,data = dt.house1)
broom::tidy(regresi1) %>% mutate(across(where(is.numeric),                                ~ format(round(.x,3),                                             big.mark=",",                                             scientific=F)))

## # A tibble: 239 × 5
##    term            estimate   std.error statistic     p.value
##    <chr>              <dbl>       <dbl>     <dbl>       <dbl>
##  1 (Intercept) -3644762.    1362175.      -2.68   0.00760    
##  2 MSSubClass        -3.79      128.      -0.0295 0.977      
##  3 MSZoningFV     41403.      14265.       2.90   0.00380    
##  4 MSZoningRH     28191.      15384.       1.83   0.0672     
##  5 MSZoningRL     27117.      12657.       2.14   0.0324     
##  6 MSZoningRM     23666.      11795.       2.01   0.0451     
##  7 LotFrontage       77.8        57.4      1.36   0.176      
##  8 LotArea            0.819       0.154    5.31   0.000000143
##  9 StreetPave     53484.      20624.       2.59   0.00967    
## 10 AlleyPave      -4026.       7366.      -0.547  0.585      
## # … with 229 more rows

Forward Stepwise

stepAIC(regresi1, direction = "forward")

## Start:  AIC=22232.61
## SalePrice ~ MSSubClass + MSZoning + LotFrontage + LotArea + Street + 
##     Alley + LotShape + LandContour + LotConfig + LandSlope + 
##     Neighborhood + Condition1 + Condition2 + BldgType + HouseStyle + 
##     OverallQual + OverallCond + YearBuilt + YearRemodAdd + RoofStyle + 
##     RoofMatl + Exterior1st + Exterior2nd + MasVnrType + MasVnrArea + 
##     ExterQual + ExterCond + Foundation + BsmtQual + BsmtCond + 
##     BsmtExposure + BsmtFinType1 + BsmtFinSF1 + BsmtFinType2 + 
##     BsmtFinSF2 + BsmtUnfSF + TotalBsmtSF + Heating + HeatingQC + 
##     CentralAir + Electrical + X1stFlrSF + X2ndFlrSF + LowQualFinSF + 
##     GrLivArea + BsmtFullBath + BsmtHalfBath + FullBath + HalfBath + 
##     BedroomAbvGr + KitchenAbvGr + KitchenQual + TotRmsAbvGrd + 
##     Functional + Fireplaces + FireplaceQu + GarageType + GarageYrBlt + 
##     GarageFinish + GarageCars + GarageArea + GarageQual + GarageCond + 
##     PavedDrive + WoodDeckSF + OpenPorchSF + EnclosedPorch + X3SsnPorch + 
##     ScreenPorch + PoolArea + PoolQC + Fence + MiscFeature + MiscVal + 
##     MoSold + YrSold + SaleType + SaleCondition

## 
## Call:
## lm(formula = SalePrice ~ MSSubClass + MSZoning + LotFrontage + 
##     LotArea + Street + Alley + LotShape + LandContour + LotConfig + 
##     LandSlope + Neighborhood + Condition1 + Condition2 + BldgType + 
##     HouseStyle + OverallQual + OverallCond + YearBuilt + YearRemodAdd + 
##     RoofStyle + RoofMatl + Exterior1st + Exterior2nd + MasVnrType + 
##     MasVnrArea + ExterQual + ExterCond + Foundation + BsmtQual + 
##     BsmtCond + BsmtExposure + BsmtFinType1 + BsmtFinSF1 + BsmtFinType2 + 
##     BsmtFinSF2 + BsmtUnfSF + TotalBsmtSF + Heating + HeatingQC + 
##     CentralAir + Electrical + X1stFlrSF + X2ndFlrSF + LowQualFinSF + 
##     GrLivArea + BsmtFullBath + BsmtHalfBath + FullBath + HalfBath + 
##     BedroomAbvGr + KitchenAbvGr + KitchenQual + TotRmsAbvGrd + 
##     Functional + Fireplaces + FireplaceQu + GarageType + GarageYrBlt + 
##     GarageFinish + GarageCars + GarageArea + GarageQual + GarageCond + 
##     PavedDrive + WoodDeckSF + OpenPorchSF + EnclosedPorch + X3SsnPorch + 
##     ScreenPorch + PoolArea + PoolQC + Fence + MiscFeature + MiscVal + 
##     MoSold + YrSold + SaleType + SaleCondition, data = dt.house1)
## 
## Coefficients:
##          (Intercept)            MSSubClass            MSZoningFV  
##           -3.645e+06            -3.786e+00             4.140e+04  
##           MSZoningRH            MSZoningRL            MSZoningRM  
##            2.819e+04             2.712e+04             2.367e+04  
##          LotFrontage               LotArea            StreetPave  
##            7.779e+01             8.190e-01             5.348e+04  
##            AlleyPave              AlleyUkn           LotShapeIR2  
##           -4.026e+03             2.667e+03             5.613e+03  
##          LotShapeIR3           LotShapeReg        LandContourHLS  
##            1.029e+04             2.903e+03             9.205e+03  
##       LandContourLow        LandContourLvl      LotConfigCulDSac  
##           -1.950e+04             6.102e+03             1.460e+04  
##         LotConfigFR2          LotConfigFR3       LotConfigInside  
##           -1.012e+04            -1.530e+04            -6.373e+02  
##         LandSlopeMod          LandSlopeSev   NeighborhoodBlueste  
##            8.173e+03            -4.098e+04             1.027e+04  
##   NeighborhoodBrDale   NeighborhoodBrkSide   NeighborhoodClearCr  
##            6.490e+03            -6.063e+02            -9.089e+03  
##  NeighborhoodCollgCr   NeighborhoodCrawfor   NeighborhoodEdwards  
##           -6.985e+03             1.228e+04            -1.957e+04  
##  NeighborhoodGilbert    NeighborhoodIDOTRR   NeighborhoodMeadowV  
##           -9.073e+03             1.652e+01            -3.930e+03  
##  NeighborhoodMitchel     NeighborhoodNAmes   NeighborhoodNoRidge  
##           -1.583e+04            -1.350e+04             2.479e+04  
##  NeighborhoodNPkVill   NeighborhoodNridgHt    NeighborhoodNWAmes  
##            1.163e+04             1.960e+04            -1.426e+04  
##  NeighborhoodOldTown    NeighborhoodSawyer   NeighborhoodSawyerW  
##           -9.806e+03            -3.013e+03             1.353e+03  
##  NeighborhoodSomerst   NeighborhoodStoneBr     NeighborhoodSWISU  
##           -1.542e+03             4.677e+04            -5.612e+03  
##   NeighborhoodTimber   NeighborhoodVeenker       Condition1Feedr  
##           -9.291e+03             8.973e+03             1.125e+03  
##       Condition1Norm        Condition1PosA        Condition1PosN  
##            1.254e+04             1.284e+04             4.848e+03  
##       Condition1RRAe        Condition1RRAn        Condition1RRNe  
##           -1.376e+04             1.174e+04             8.855e+03  
##       Condition1RRNn       Condition2Feedr        Condition2Norm  
##            1.099e+04            -1.245e+04            -4.784e+03  
##       Condition2PosA        Condition2PosN        Condition2RRNn  
##            4.334e+04            -2.306e+05             5.630e+03  
##       BldgType2fmCon        BldgTypeDuplex         BldgTypeTwnhs  
##           -5.701e+03            -1.235e+04            -2.380e+04  
##       BldgTypeTwnhsE      HouseStyle1.5Unf      HouseStyle1Story  
##           -1.872e+04             9.230e+03             1.178e+04  
##     HouseStyle2.5Fin      HouseStyle2.5Unf      HouseStyle2Story  
##           -3.152e+04            -1.658e+04            -4.609e+03  
##     HouseStyleSFoyer        HouseStyleSLvl           OverallQual  
##            5.869e+03             4.596e+03             7.158e+03  
##          OverallCond             YearBuilt          YearRemodAdd  
##            5.800e+03             2.669e+02             1.053e+02  
##       RoofStyleGable      RoofStyleGambrel          RoofStyleHip  
##            3.743e+04             4.433e+04             3.594e+04  
##     RoofStyleMansard       RoofMatlCompShg       RoofMatlMembran  
##            5.189e+04             8.076e+04             1.962e+05  
##         RoofMatlRoll       RoofMatlTar&Grv       RoofMatlWdShake  
##            7.634e+04             8.964e+04             5.983e+04  
##      RoofMatlWdShngl    Exterior1stBrkComm    Exterior1stBrkFace  
##            1.368e+05            -4.480e+04             6.533e+02  
##    Exterior1stCBlock    Exterior1stCemntBd    Exterior1stHdBoard  
##           -2.221e+04            -2.781e+04            -1.591e+04  
##   Exterior1stImStucc    Exterior1stMetalSd    Exterior1stPlywood  
##           -2.559e+04            -3.890e+03            -2.103e+04  
##     Exterior1stStone     Exterior1stStucco    Exterior1stVinylSd  
##           -8.940e+03            -1.447e+04            -1.582e+04  
##   Exterior1stWd Sdng    Exterior1stWdShing    Exterior2ndAsphShn  
##           -1.966e+04            -1.325e+04             1.161e+04  
##   Exterior2ndBrk Cmn    Exterior2ndBrkFace     Exterior2ndCBlock  
##            2.313e+04             1.005e+04                    NA  
##   Exterior2ndCmentBd    Exterior2ndHdBoard    Exterior2ndImStucc  
##            3.065e+04             1.232e+04             1.730e+04  
##   Exterior2ndMetalSd      Exterior2ndOther    Exterior2ndPlywood  
##            7.898e+03            -1.684e+04             1.339e+04  
##     Exterior2ndStone     Exterior2ndStucco    Exterior2ndVinylSd  
##            3.773e+03             2.180e+04             1.685e+04  
##   Exterior2ndWd Sdng    Exterior2ndWd Shng     MasVnrTypeBrkFace  
##            2.264e+04             1.075e+04             9.471e+03  
##       MasVnrTypeNone       MasVnrTypeStone            MasVnrArea  
##            1.312e+04             1.720e+04             2.495e+01  
##          ExterQualFa           ExterQualGd           ExterQualTA  
##           -5.516e+03            -2.490e+04            -2.540e+04  
##          ExterCondFa           ExterCondGd           ExterCondTA  
##            1.313e+04             8.983e+03             1.140e+04  
##     FoundationCBlock       FoundationPConc       FoundationStone  
##            5.298e+03             5.715e+03             1.014e+04  
##       FoundationWood            BsmtQualFa            BsmtQualGd  
##           -4.360e+04            -1.032e+04            -1.476e+04  
##           BsmtQualTA            BsmtCondGd            BsmtCondPo  
##           -1.248e+04             1.547e+03             2.783e+04  
##           BsmtCondTA        BsmtExposureGd        BsmtExposureMn  
##            2.950e+03             1.398e+04            -5.879e+03  
##       BsmtExposureNo       BsmtFinType1BLQ       BsmtFinType1GLQ  
##           -6.208e+03             1.227e+03             7.219e+03  
##      BsmtFinType1LwQ       BsmtFinType1Rec       BsmtFinType1Unf  
##           -3.925e+03             6.266e+02             2.749e+03  
##           BsmtFinSF1       BsmtFinType2BLQ       BsmtFinType2GLQ  
##            4.057e+01            -6.054e+03             1.042e+03  
##      BsmtFinType2LwQ       BsmtFinType2Rec       BsmtFinType2Unf  
##           -5.066e+03            -7.131e+03            -3.846e+03  
##           BsmtFinSF2             BsmtUnfSF           TotalBsmtSF  
##            3.366e+01             2.283e+01                    NA  
##          HeatingGasW           HeatingGrav           HeatingOthW  
##           -3.065e+03             1.286e+04            -4.290e+02  
##          HeatingQCFa           HeatingQCGd           HeatingQCPo  
##            1.259e+03            -2.841e+03            -1.118e+03  
##          HeatingQCTA           CentralAirY       ElectricalFuseF  
##           -2.825e+03             6.363e+03             1.742e+03  
##      ElectricalFuseP         ElectricalMix       ElectricalSBrkr  
##            3.979e+03                    NA             5.855e+02  
##            X1stFlrSF             X2ndFlrSF          LowQualFinSF  
##            4.098e+01             6.438e+01             3.465e+01  
##            GrLivArea          BsmtFullBath          BsmtHalfBath  
##                   NA             1.048e+03             8.766e+02  
##             FullBath              HalfBath          BedroomAbvGr  
##            4.885e+03             2.042e+03            -4.021e+03  
##         KitchenAbvGr         KitchenQualFa         KitchenQualGd  
##           -1.819e+04            -1.664e+04            -1.963e+04  
##        KitchenQualTA          TotRmsAbvGrd        FunctionalMaj2  
##           -1.870e+04             1.634e+03            -1.649e+04  
##       FunctionalMin1        FunctionalMin2         FunctionalMod  
##            7.748e+02             1.294e+03            -4.350e+03  
##        FunctionalTyp            Fireplaces         FireplaceQuFa  
##            1.125e+04             6.640e+03            -8.822e+03  
##        FireplaceQuGd         FireplaceQuPo         FireplaceQuTA  
##           -7.029e+03            -4.897e+03            -7.300e+03  
##       FireplaceQuUkn      GarageTypeAttchd     GarageTypeBasment  
##           -1.175e+03             9.003e+03             1.604e+04  
##    GarageTypeBuiltIn     GarageTypeCarPort      GarageTypeDetchd  
##            8.698e+03             1.639e+04             1.307e+04  
##          GarageYrBlt       GarageFinishRFn       GarageFinishUnf  
##           -3.436e+01            -2.018e+03             1.477e+02  
##           GarageCars            GarageArea          GarageQualFa  
##            4.350e+03             1.816e+01            -1.068e+05  
##         GarageQualGd          GarageQualPo          GarageQualTA  
##           -9.457e+04            -1.356e+05            -1.016e+05  
##         GarageCondFa          GarageCondGd          GarageCondPo  
##            1.012e+05             1.072e+05             1.148e+05  
##         GarageCondTA           PavedDriveP           PavedDriveY  
##            1.031e+05            -4.521e+03            -2.342e+02  
##           WoodDeckSF           OpenPorchSF         EnclosedPorch  
##            1.199e+01             3.404e+00             1.134e+01  
##           X3SsnPorch           ScreenPorch              PoolArea  
##            4.206e+01             3.217e+01             6.379e+03  
##             PoolQCFa              PoolQCGd             PoolQCUkn  
##           -7.893e+05            -3.140e+05             3.317e+06  
##            FenceGdWo            FenceMnPrv             FenceMnWw  
##            4.930e+03             5.746e+03             9.522e+02  
##             FenceUkn       MiscFeatureShed       MiscFeatureTenC  
##            6.602e+03            -8.973e+03             7.581e+05  
##       MiscFeatureUkn               MiscVal                MoSold  
##           -1.194e+04             1.960e-01            -4.034e+02  
##               YrSold           SaleTypeCon         SaleTypeConLD  
##           -2.845e+02             1.831e+04             2.177e+04  
##        SaleTypeConLI         SaleTypeConLw           SaleTypeCWD  
##            2.718e+03             2.943e+03             1.329e+04  
##          SaleTypeNew           SaleTypeOth            SaleTypeWD  
##            1.311e+04             2.257e+04            -2.017e+03  
## SaleConditionAdjLand   SaleConditionAlloca   SaleConditionFamily  
##            3.321e+04             6.571e+03            -5.419e+02  
##  SaleConditionNormal  SaleConditionPartial  
##            6.588e+03             5.971e+03

Berdasarkan metode forward stepwise diperoleh bahwa nilai AIC sebesar 22232.61

Backward Stepwise

stepAIC(regresi1, direction = "backward")

## Start:  AIC=22232.61
## SalePrice ~ MSSubClass + MSZoning + LotFrontage + LotArea + Street + 
##     Alley + LotShape + LandContour + LotConfig + LandSlope + 
##     Neighborhood + Condition1 + Condition2 + BldgType + HouseStyle + 
##     OverallQual + OverallCond + YearBuilt + YearRemodAdd + RoofStyle + 
##     RoofMatl + Exterior1st + Exterior2nd + MasVnrType + MasVnrArea + 
##     ExterQual + ExterCond + Foundation + BsmtQual + BsmtCond + 
##     BsmtExposure + BsmtFinType1 + BsmtFinSF1 + BsmtFinType2 + 
##     BsmtFinSF2 + BsmtUnfSF + TotalBsmtSF + Heating + HeatingQC + 
##     CentralAir + Electrical + X1stFlrSF + X2ndFlrSF + LowQualFinSF + 
##     GrLivArea + BsmtFullBath + BsmtHalfBath + FullBath + HalfBath + 
##     BedroomAbvGr + KitchenAbvGr + KitchenQual + TotRmsAbvGrd + 
##     Functional + Fireplaces + FireplaceQu + GarageType + GarageYrBlt + 
##     GarageFinish + GarageCars + GarageArea + GarageQual + GarageCond + 
##     PavedDrive + WoodDeckSF + OpenPorchSF + EnclosedPorch + X3SsnPorch + 
##     ScreenPorch + PoolArea + PoolQC + Fence + MiscFeature + MiscVal + 
##     MoSold + YrSold + SaleType + SaleCondition
## 
## 
## Step:  AIC=22232.61
## SalePrice ~ MSSubClass + MSZoning + LotFrontage + LotArea + Street + 
##     Alley + LotShape + LandContour + LotConfig + LandSlope + 
##     Neighborhood + Condition1 + Condition2 + BldgType + HouseStyle + 
##     OverallQual + OverallCond + YearBuilt + YearRemodAdd + RoofStyle + 
##     RoofMatl + Exterior1st + Exterior2nd + MasVnrType + MasVnrArea + 
##     ExterQual + ExterCond + Foundation + BsmtQual + BsmtCond + 
##     BsmtExposure + BsmtFinType1 + BsmtFinSF1 + BsmtFinType2 + 
##     BsmtFinSF2 + BsmtUnfSF + TotalBsmtSF + Heating + HeatingQC + 
##     CentralAir + Electrical + X1stFlrSF + X2ndFlrSF + LowQualFinSF + 
##     BsmtFullBath + BsmtHalfBath + FullBath + HalfBath + BedroomAbvGr + 
##     KitchenAbvGr + KitchenQual + TotRmsAbvGrd + Functional + 
##     Fireplaces + FireplaceQu + GarageType + GarageYrBlt + GarageFinish + 
##     GarageCars + GarageArea + GarageQual + GarageCond + PavedDrive + 
##     WoodDeckSF + OpenPorchSF + EnclosedPorch + X3SsnPorch + ScreenPorch + 
##     PoolArea + PoolQC + Fence + MiscFeature + MiscVal + MoSold + 
##     YrSold + SaleType + SaleCondition
## 
## 
## Step:  AIC=22232.61
## SalePrice ~ MSSubClass + MSZoning + LotFrontage + LotArea + Street + 
##     Alley + LotShape + LandContour + LotConfig + LandSlope + 
##     Neighborhood + Condition1 + Condition2 + BldgType + HouseStyle + 
##     OverallQual + OverallCond + YearBuilt + YearRemodAdd + RoofStyle + 
##     RoofMatl + Exterior1st + Exterior2nd + MasVnrType + MasVnrArea + 
##     ExterQual + ExterCond + Foundation + BsmtQual + BsmtCond + 
##     BsmtExposure + BsmtFinType1 + BsmtFinSF1 + BsmtFinType2 + 
##     BsmtFinSF2 + BsmtUnfSF + Heating + HeatingQC + CentralAir + 
##     Electrical + X1stFlrSF + X2ndFlrSF + LowQualFinSF + BsmtFullBath + 
##     BsmtHalfBath + FullBath + HalfBath + BedroomAbvGr + KitchenAbvGr + 
##     KitchenQual + TotRmsAbvGrd + Functional + Fireplaces + FireplaceQu + 
##     GarageType + GarageYrBlt + GarageFinish + GarageCars + GarageArea + 
##     GarageQual + GarageCond + PavedDrive + WoodDeckSF + OpenPorchSF + 
##     EnclosedPorch + X3SsnPorch + ScreenPorch + PoolArea + PoolQC + 
##     Fence + MiscFeature + MiscVal + MoSold + YrSold + SaleType + 
##     SaleCondition
## 
##                 Df  Sum of Sq        RSS   AIC
## - Exterior2nd   14 5.3888e+09 4.8216e+11 22217
## - BsmtFinType2   5 6.6766e+08 4.7743e+11 22224
## - SaleType       8 3.6903e+09 4.8046e+11 22225
## - Exterior1st   12 7.2982e+09 4.8406e+11 22225
## - Electrical     3 3.5814e+07 4.7680e+11 22227
## - GarageType     5 1.8370e+09 4.7860e+11 22227
## - FireplaceQu    5 1.9551e+09 4.7872e+11 22227
## - HeatingQC      4 1.1107e+09 4.7788e+11 22227
## - Heating        3 2.4637e+08 4.7701e+11 22227
## - HouseStyle     7 3.9566e+09 4.8072e+11 22228
## - ExterCond      3 4.5644e+08 4.7722e+11 22228
## - Fence          4 1.3478e+09 4.7811e+11 22228
## - RoofStyle      4 1.8194e+09 4.7859e+11 22229
## - BsmtCond       2 2.4985e+08 4.7702e+11 22229
## - SaleCondition  5 2.8915e+09 4.7966e+11 22229
## - PavedDrive     2 2.7183e+08 4.7704e+11 22229
## - GarageFinish   2 5.8511e+08 4.7735e+11 22230
## - Alley          2 8.2989e+08 4.7760e+11 22231
## - LotShape       3 1.7361e+09 4.7850e+11 22231
## - MiscVal        1 2.1888e+05 4.7677e+11 22231
## - MSSubClass     1 4.8177e+05 4.7677e+11 22231
## - OpenPorchSF    1 2.7802e+07 4.7679e+11 22231
## - BsmtHalfBath   1 3.0197e+07 4.7680e+11 22231
## - BsmtFullBath   1 1.0292e+08 4.7687e+11 22231
## - YrSold         1 1.0862e+08 4.7688e+11 22231
## - GarageYrBlt    1 1.1534e+08 4.7688e+11 22231
## - EnclosedPorch  1 2.6601e+08 4.7703e+11 22231
## - HalfBath       1 3.3253e+08 4.7710e+11 22231
## - LowQualFinSF   1 6.8295e+08 4.7745e+11 22232
## - BsmtFinType1   5 4.2613e+09 4.8103e+11 22232
## - CentralAir     1 8.5802e+08 4.7762e+11 22233
## <none>                        4.7677e+11 22233
## - MoSold         1 9.7205e+08 4.7774e+11 22233
## - LotFrontage    1 1.0203e+09 4.7779e+11 22233
## - TotRmsAbvGrd   1 1.0239e+09 4.7779e+11 22233
## - YearRemodAdd   1 1.1693e+09 4.7794e+11 22233
## - GarageCars     1 1.4049e+09 4.7817e+11 22234
## - X3SsnPorch     1 1.4060e+09 4.7817e+11 22234
## - BldgType       4 4.0480e+09 4.8081e+11 22234
## - WoodDeckSF     1 1.4452e+09 4.7821e+11 22234
## - GarageCond     4 4.2208e+09 4.8099e+11 22234
## - FullBath       1 1.6096e+09 4.7838e+11 22234
## - GarageArea     1 2.0340e+09 4.7880e+11 22235
## - Fireplaces     1 2.2468e+09 4.7901e+11 22236
## - MSZoning       4 4.9381e+09 4.8170e+11 22236
## - Foundation     4 5.0095e+09 4.8178e+11 22236
## - MasVnrType     3 4.1661e+09 4.8093e+11 22236
## - ScreenPorch    1 2.4800e+09 4.7925e+11 22236
## - KitchenAbvGr   1 2.5240e+09 4.7929e+11 22236
## - Functional     5 6.1650e+09 4.8293e+11 22237
## - BedroomAbvGr   1 2.8203e+09 4.7959e+11 22237
## - GarageQual     4 6.2857e+09 4.8305e+11 22239
## - YearBuilt      1 3.6947e+09 4.8046e+11 22239
## - Street         1 3.7328e+09 4.8050e+11 22239
## - LandContour    3 5.6008e+09 4.8237e+11 22239
## - Condition1     8 1.0346e+10 4.8711e+11 22240
## - BsmtFinSF2     1 4.6849e+09 4.8145e+11 22241
## - LandSlope      2 5.6024e+09 4.8237e+11 22241
## - BsmtUnfSF      1 6.4715e+09 4.8324e+11 22245
## - LotConfig      4 9.5976e+09 4.8636e+11 22246
## - BsmtQual       3 8.7554e+09 4.8552e+11 22247
## - MasVnrArea     1 7.5537e+09 4.8432e+11 22248
## - ExterQual      3 1.1959e+10 4.8873e+11 22254
## - KitchenQual    3 1.2941e+10 4.8971e+11 22256
## - RoofMatl       6 1.6132e+10 4.9290e+11 22257
## - OverallCond    1 1.3819e+10 4.9059e+11 22262
## - BsmtExposure   3 1.6834e+10 4.9360e+11 22265
## - LotArea        1 1.5621e+10 4.9239e+11 22266
## - MiscFeature    3 1.7999e+10 4.9476e+11 22267
## - X1stFlrSF      1 1.6251e+10 4.9302e+11 22267
## - OverallQual    1 1.6704e+10 4.9347e+11 22268
## - BsmtFinSF1     1 1.8146e+10 4.9491e+11 22272
## - PoolArea       1 2.2151e+10 4.9892e+11 22280
## - PoolQC         3 2.5694e+10 5.0246e+11 22284
## - X2ndFlrSF      1 4.3409e+10 5.2017e+11 22326
## - Condition2     5 6.1503e+10 5.3827e+11 22355
## - Neighborhood  24 8.2665e+10 5.5943e+11 22360
## 
## Step:  AIC=22216.91
## SalePrice ~ MSSubClass + MSZoning + LotFrontage + LotArea + Street + 
##     Alley + LotShape + LandContour + LotConfig + LandSlope + 
##     Neighborhood + Condition1 + Condition2 + BldgType + HouseStyle + 
##     OverallQual + OverallCond + YearBuilt + YearRemodAdd + RoofStyle + 
##     RoofMatl + Exterior1st + MasVnrType + MasVnrArea + ExterQual + 
##     ExterCond + Foundation + BsmtQual + BsmtCond + BsmtExposure + 
##     BsmtFinType1 + BsmtFinSF1 + BsmtFinType2 + BsmtFinSF2 + BsmtUnfSF + 
##     Heating + HeatingQC + CentralAir + Electrical + X1stFlrSF + 
##     X2ndFlrSF + LowQualFinSF + BsmtFullBath + BsmtHalfBath + 
##     FullBath + HalfBath + BedroomAbvGr + KitchenAbvGr + KitchenQual + 
##     TotRmsAbvGrd + Functional + Fireplaces + FireplaceQu + GarageType + 
##     GarageYrBlt + GarageFinish + GarageCars + GarageArea + GarageQual + 
##     GarageCond + PavedDrive + WoodDeckSF + OpenPorchSF + EnclosedPorch + 
##     X3SsnPorch + ScreenPorch + PoolArea + PoolQC + Fence + MiscFeature + 
##     MiscVal + MoSold + YrSold + SaleType + SaleCondition
## 
##                 Df  Sum of Sq        RSS   AIC
## - BsmtFinType2   5 5.3136e+08 4.8269e+11 22208
## - SaleType       8 3.8319e+09 4.8599e+11 22210
## - GarageType     5 1.5020e+09 4.8366e+11 22210
## - Electrical     3 4.6592e+07 4.8220e+11 22211
## - Exterior1st   13 9.0670e+09 4.9122e+11 22211
## - Heating        3 1.9189e+08 4.8235e+11 22211
## - FireplaceQu    5 2.0397e+09 4.8419e+11 22212
## - HeatingQC      4 1.2271e+09 4.8338e+11 22212
## - ExterCond      3 5.1035e+08 4.8267e+11 22212
## - Fence          4 1.4890e+09 4.8364e+11 22212
## - HouseStyle     7 4.2842e+09 4.8644e+11 22213
## - BsmtCond       2 2.2913e+08 4.8238e+11 22213
## - RoofStyle      4 2.0134e+09 4.8417e+11 22214
## - PavedDrive     2 4.2371e+08 4.8258e+11 22214
## - SaleCondition  5 3.1505e+09 4.8531e+11 22214
## - Alley          2 5.5941e+08 4.8271e+11 22214
## - GarageFinish   2 5.9805e+08 4.8275e+11 22214
## - LotShape       3 1.6654e+09 4.8382e+11 22215
## - MiscVal        1 6.2427e+06 4.8216e+11 22215
## - MSSubClass     1 7.0008e+06 4.8216e+11 22215
## - GarageYrBlt    1 1.8041e+07 4.8217e+11 22215
## - OpenPorchSF    1 2.6757e+07 4.8218e+11 22215
## - BsmtHalfBath   1 2.8922e+07 4.8218e+11 22215
## - YrSold         1 1.3116e+08 4.8229e+11 22215
## - EnclosedPorch  1 1.5698e+08 4.8231e+11 22215
## - BsmtFullBath   1 1.9141e+08 4.8235e+11 22215
## - HalfBath       1 5.6359e+08 4.8272e+11 22216
## - CentralAir     1 6.0615e+08 4.8276e+11 22216
## - LowQualFinSF   1 6.1483e+08 4.8277e+11 22216
## - BsmtFinType1   5 4.2269e+09 4.8638e+11 22217
## <none>                        4.8216e+11 22217
## - TotRmsAbvGrd   1 9.2327e+08 4.8308e+11 22217
## - MoSold         1 1.0842e+09 4.8324e+11 22217
## - BldgType       4 3.8716e+09 4.8603e+11 22218
## - GarageCars     1 1.2379e+09 4.8339e+11 22218
## - YearRemodAdd   1 1.3473e+09 4.8350e+11 22218
## - WoodDeckSF     1 1.4125e+09 4.8357e+11 22218
## - LotFrontage    1 1.4525e+09 4.8361e+11 22218
## - X3SsnPorch     1 1.4575e+09 4.8361e+11 22218
## - GarageCond     4 4.3898e+09 4.8654e+11 22219
## - FullBath       1 2.0068e+09 4.8416e+11 22219
## - ScreenPorch    1 2.0209e+09 4.8418e+11 22220
## - GarageArea     1 2.1051e+09 4.8426e+11 22220
## - Foundation     4 4.9410e+09 4.8710e+11 22220
## - Fireplaces     1 2.3944e+09 4.8455e+11 22220
## - MSZoning       4 5.0856e+09 4.8724e+11 22220
## - MasVnrType     3 4.2857e+09 4.8644e+11 22221
## - BedroomAbvGr   1 2.5369e+09 4.8469e+11 22221
## - Functional     5 6.1361e+09 4.8829e+11 22221
## - KitchenAbvGr   1 2.7232e+09 4.8488e+11 22221
## - Street         1 3.2883e+09 4.8544e+11 22222
## - LandContour    3 5.2759e+09 4.8743e+11 22223
## - Condition1     8 9.9875e+09 4.9214e+11 22223
## - YearBuilt      1 3.9169e+09 4.8607e+11 22224
## - GarageQual     4 6.6671e+09 4.8882e+11 22224
## - LandSlope      2 5.6554e+09 4.8781e+11 22226
## - BsmtFinSF2     1 4.9097e+09 4.8706e+11 22226
## - LotConfig      4 9.6193e+09 4.9177e+11 22231
## - MasVnrArea     1 7.4048e+09 4.8956e+11 22232
## - BsmtUnfSF      1 7.6702e+09 4.8983e+11 22232
## - BsmtQual       3 9.9163e+09 4.9207e+11 22233
## - ExterQual      3 1.1439e+10 4.9359e+11 22237
## - KitchenQual    3 1.3525e+10 4.9568e+11 22241
## - RoofMatl       6 1.7311e+10 4.9947e+11 22244
## - LotArea        1 1.4630e+10 4.9679e+11 22248
## - OverallCond    1 1.4996e+10 4.9715e+11 22248
## - BsmtExposure   3 1.7302e+10 4.9946e+11 22250
## - X1stFlrSF      1 1.5610e+10 4.9777e+11 22250
## - MiscFeature    3 1.7741e+10 4.9990e+11 22250
## - OverallQual    1 1.6829e+10 4.9898e+11 22252
## - BsmtFinSF1     1 1.9698e+10 5.0185e+11 22259
## - PoolArea       1 2.2112e+10 5.0427e+11 22264
## - PoolQC         3 2.6891e+10 5.0905e+11 22270
## - X2ndFlrSF      1 4.4831e+10 5.2699e+11 22312
## - Condition2     5 6.0987e+10 5.4314e+11 22337
## - Neighborhood  24 8.3309e+10 5.6546e+11 22343
## 
## Step:  AIC=22208.11
## SalePrice ~ MSSubClass + MSZoning + LotFrontage + LotArea + Street + 
##     Alley + LotShape + LandContour + LotConfig + LandSlope + 
##     Neighborhood + Condition1 + Condition2 + BldgType + HouseStyle + 
##     OverallQual + OverallCond + YearBuilt + YearRemodAdd + RoofStyle + 
##     RoofMatl + Exterior1st + MasVnrType + MasVnrArea + ExterQual + 
##     ExterCond + Foundation + BsmtQual + BsmtCond + BsmtExposure + 
##     BsmtFinType1 + BsmtFinSF1 + BsmtFinSF2 + BsmtUnfSF + Heating + 
##     HeatingQC + CentralAir + Electrical + X1stFlrSF + X2ndFlrSF + 
##     LowQualFinSF + BsmtFullBath + BsmtHalfBath + FullBath + HalfBath + 
##     BedroomAbvGr + KitchenAbvGr + KitchenQual + TotRmsAbvGrd + 
##     Functional + Fireplaces + FireplaceQu + GarageType + GarageYrBlt + 
##     GarageFinish + GarageCars + GarageArea + GarageQual + GarageCond + 
##     PavedDrive + WoodDeckSF + OpenPorchSF + EnclosedPorch + X3SsnPorch + 
##     ScreenPorch + PoolArea + PoolQC + Fence + MiscFeature + MiscVal + 
##     MoSold + YrSold + SaleType + SaleCondition
## 
##                 Df  Sum of Sq        RSS   AIC
## - SaleType       8 3.9277e+09 4.8661e+11 22201
## - GarageType     5 1.4192e+09 4.8411e+11 22201
## - Electrical     3 3.5292e+07 4.8272e+11 22202
## - Heating        3 1.9046e+08 4.8288e+11 22203
## - FireplaceQu    5 2.0357e+09 4.8472e+11 22203
## - Exterior1st   13 9.2953e+09 4.9198e+11 22203
## - ExterCond      3 4.9823e+08 4.8318e+11 22203
## - HeatingQC      4 1.3835e+09 4.8407e+11 22203
## - Fence          4 1.4658e+09 4.8415e+11 22203
## - HouseStyle     7 4.5275e+09 4.8721e+11 22204
## - RoofStyle      4 1.9710e+09 4.8466e+11 22205
## - BsmtCond       2 2.4217e+08 4.8293e+11 22205
## - PavedDrive     2 4.0617e+08 4.8309e+11 22205
## - SaleCondition  5 3.1451e+09 4.8583e+11 22205
## - Alley          2 5.7526e+08 4.8326e+11 22205
## - GarageFinish   2 6.4672e+08 4.8333e+11 22206
## - LotShape       3 1.7091e+09 4.8440e+11 22206
## - MiscVal        1 1.6141e+06 4.8269e+11 22206
## - MSSubClass     1 4.7885e+06 4.8269e+11 22206
## - GarageYrBlt    1 1.4508e+07 4.8270e+11 22206
## - OpenPorchSF    1 2.2696e+07 4.8271e+11 22206
## - BsmtHalfBath   1 4.2994e+07 4.8273e+11 22206
## - YrSold         1 1.3160e+08 4.8282e+11 22206
## - EnclosedPorch  1 1.6249e+08 4.8285e+11 22207
## - BsmtFullBath   1 2.6828e+08 4.8295e+11 22207
## - BsmtFinType1   5 4.0496e+09 4.8674e+11 22207
## - HalfBath       1 5.2275e+08 4.8321e+11 22207
## - CentralAir     1 6.1361e+08 4.8330e+11 22208
## - LowQualFinSF   1 7.1492e+08 4.8340e+11 22208
## <none>                        4.8269e+11 22208
## - MoSold         1 1.0481e+09 4.8373e+11 22209
## - TotRmsAbvGrd   1 1.0522e+09 4.8374e+11 22209
## - BldgType       4 3.8452e+09 4.8653e+11 22209
## - WoodDeckSF     1 1.2665e+09 4.8395e+11 22209
## - GarageCars     1 1.3065e+09 4.8399e+11 22209
## - YearRemodAdd   1 1.3614e+09 4.8405e+11 22209
## - X3SsnPorch     1 1.4509e+09 4.8414e+11 22209
## - LotFrontage    1 1.4709e+09 4.8416e+11 22209
## - GarageCond     4 4.4308e+09 4.8712e+11 22210
## - FullBath       1 1.9472e+09 4.8463e+11 22211
## - ScreenPorch    1 1.9700e+09 4.8466e+11 22211
## - GarageArea     1 2.0879e+09 4.8477e+11 22211
## - Foundation     4 4.9767e+09 4.8766e+11 22211
## - Fireplaces     1 2.4615e+09 4.8515e+11 22212
## - MasVnrType     3 4.2979e+09 4.8698e+11 22212
## - MSZoning       4 5.3025e+09 4.8799e+11 22212
## - Functional     5 6.2166e+09 4.8890e+11 22212
## - KitchenAbvGr   1 2.8036e+09 4.8549e+11 22212
## - BedroomAbvGr   1 2.8063e+09 4.8549e+11 22213
## - Street         1 3.2388e+09 4.8593e+11 22213
## - LandContour    3 5.2087e+09 4.8790e+11 22214
## - Condition1     8 9.8857e+09 4.9257e+11 22214
## - GarageQual     4 6.5756e+09 4.8926e+11 22215
## - YearBuilt      1 4.0710e+09 4.8676e+11 22215
## - LandSlope      2 5.6818e+09 4.8837e+11 22217
## - LotConfig      4 9.7251e+09 4.9241e+11 22222
## - MasVnrArea     1 7.3658e+09 4.9005e+11 22223
## - BsmtUnfSF      1 8.0825e+09 4.9077e+11 22224
## - BsmtQual       3 1.0021e+10 4.9271e+11 22225
## - ExterQual      3 1.1343e+10 4.9403e+11 22228
## - BsmtFinSF2     1 9.6934e+09 4.9238e+11 22228
## - KitchenQual    3 1.3631e+10 4.9632e+11 22233
## - RoofMatl       6 1.7903e+10 5.0059e+11 22236
## - LotArea        1 1.4548e+10 4.9723e+11 22239
## - OverallCond    1 1.5327e+10 4.9801e+11 22240
## - X1stFlrSF      1 1.5454e+10 4.9814e+11 22241
## - BsmtExposure   3 1.8143e+10 5.0083e+11 22243
## - MiscFeature    3 1.8192e+10 5.0088e+11 22243
## - OverallQual    1 1.6811e+10 4.9950e+11 22244
## - BsmtFinSF1     1 2.0081e+10 5.0277e+11 22251
## - PoolArea       1 2.2616e+10 5.0530e+11 22256
## - PoolQC         3 2.7349e+10 5.1004e+11 22262
## - X2ndFlrSF      1 4.5560e+10 5.2825e+11 22305
## - Condition2     5 6.2059e+10 5.4475e+11 22330
## - Neighborhood  24 8.4028e+10 5.6671e+11 22336
## 
## Step:  AIC=22200.98
## SalePrice ~ MSSubClass + MSZoning + LotFrontage + LotArea + Street + 
##     Alley + LotShape + LandContour + LotConfig + LandSlope + 
##     Neighborhood + Condition1 + Condition2 + BldgType + HouseStyle + 
##     OverallQual + OverallCond + YearBuilt + YearRemodAdd + RoofStyle + 
##     RoofMatl + Exterior1st + MasVnrType + MasVnrArea + ExterQual + 
##     ExterCond + Foundation + BsmtQual + BsmtCond + BsmtExposure + 
##     BsmtFinType1 + BsmtFinSF1 + BsmtFinSF2 + BsmtUnfSF + Heating + 
##     HeatingQC + CentralAir + Electrical + X1stFlrSF + X2ndFlrSF + 
##     LowQualFinSF + BsmtFullBath + BsmtHalfBath + FullBath + HalfBath + 
##     BedroomAbvGr + KitchenAbvGr + KitchenQual + TotRmsAbvGrd + 
##     Functional + Fireplaces + FireplaceQu + GarageType + GarageYrBlt + 
##     GarageFinish + GarageCars + GarageArea + GarageQual + GarageCond + 
##     PavedDrive + WoodDeckSF + OpenPorchSF + EnclosedPorch + X3SsnPorch + 
##     ScreenPorch + PoolArea + PoolQC + Fence + MiscFeature + MiscVal + 
##     MoSold + YrSold + SaleCondition
## 
##                 Df  Sum of Sq        RSS   AIC
## - GarageType     5 1.3181e+09 4.8793e+11 22194
## - Electrical     3 7.1675e+06 4.8662e+11 22195
## - Heating        3 1.1153e+08 4.8673e+11 22195
## - HeatingQC      4 1.2076e+09 4.8782e+11 22196
## - FireplaceQu    5 2.1844e+09 4.8880e+11 22196
## - ExterCond      3 6.2404e+08 4.8724e+11 22196
## - Fence          4 1.6078e+09 4.8822e+11 22197
## - Exterior1st   13 9.7519e+09 4.9637e+11 22197
## - HouseStyle     7 4.6306e+09 4.9124e+11 22197
## - BsmtCond       2 1.7730e+08 4.8679e+11 22197
## - RoofStyle      4 2.0713e+09 4.8869e+11 22198
## - PavedDrive     2 5.6819e+08 4.8718e+11 22198
## - GarageFinish   2 6.0956e+08 4.8722e+11 22198
## - Alley          2 7.4987e+08 4.8736e+11 22199
## - LotShape       3 1.7346e+09 4.8835e+11 22199
## - OpenPorchSF    1 7.1093e+05 4.8661e+11 22199
## - GarageYrBlt    1 1.6624e+06 4.8662e+11 22199
## - MSSubClass     1 7.3177e+06 4.8662e+11 22199
## - MiscVal        1 2.2103e+07 4.8664e+11 22199
## - BsmtHalfBath   1 4.7325e+07 4.8666e+11 22199
## - EnclosedPorch  1 9.3348e+07 4.8671e+11 22199
## - YrSold         1 2.0021e+08 4.8681e+11 22199
## - BsmtFullBath   1 2.4536e+08 4.8686e+11 22200
## - HalfBath       1 5.8906e+08 4.8720e+11 22200
## - CentralAir     1 6.1559e+08 4.8723e+11 22200
## - LowQualFinSF   1 6.6289e+08 4.8728e+11 22201
## - BsmtFinType1   5 4.3620e+09 4.9098e+11 22201
## <none>                        4.8661e+11 22201
## - MoSold         1 9.1589e+08 4.8753e+11 22201
## - WoodDeckSF     1 1.1000e+09 4.8771e+11 22201
## - GarageCars     1 1.1894e+09 4.8780e+11 22202
## - TotRmsAbvGrd   1 1.2246e+09 4.8784e+11 22202
## - X3SsnPorch     1 1.3712e+09 4.8799e+11 22202
## - YearRemodAdd   1 1.4243e+09 4.8804e+11 22202
## - ScreenPorch    1 1.6135e+09 4.8823e+11 22203
## - FullBath       1 1.8485e+09 4.8846e+11 22203
## - LotFrontage    1 1.8784e+09 4.8849e+11 22203
## - GarageArea     1 1.9657e+09 4.8858e+11 22203
## - BldgType       4 4.6979e+09 4.9131e+11 22204
## - GarageCond     4 4.8701e+09 4.9148e+11 22204
## - Functional     5 5.9394e+09 4.9255e+11 22204
## - Foundation     4 5.0490e+09 4.9166e+11 22204
## - Street         1 2.4368e+09 4.8905e+11 22204
## - MasVnrType     3 4.2956e+09 4.9091e+11 22205
## - Fireplaces     1 2.6463e+09 4.8926e+11 22205
## - LandContour    3 4.6028e+09 4.9122e+11 22205
## - BedroomAbvGr   1 2.9327e+09 4.8955e+11 22206
## - MSZoning       4 5.6426e+09 4.9226e+11 22206
## - KitchenAbvGr   1 3.0112e+09 4.8963e+11 22206
## - Condition1     8 9.8398e+09 4.9645e+11 22207
## - YearBuilt      1 3.7084e+09 4.9032e+11 22207
## - GarageQual     4 7.0303e+09 4.9364e+11 22209
## - LandSlope      2 6.5162e+09 4.9313e+11 22212
## - MasVnrArea     1 7.2498e+09 4.9386e+11 22215
## - BsmtUnfSF      1 7.8390e+09 4.9445e+11 22217
## - LotConfig      4 1.0873e+10 4.9749e+11 22217
## - BsmtQual       3 1.0260e+10 4.9687e+11 22218
## - ExterQual      3 1.1566e+10 4.9818e+11 22221
## - BsmtFinSF2     1 9.8608e+09 4.9647e+11 22221
## - SaleCondition  5 1.4520e+10 5.0113e+11 22223
## - KitchenQual    3 1.2827e+10 4.9944e+11 22223
## - RoofMatl       6 1.8093e+10 5.0471e+11 22229
## - LotArea        1 1.4105e+10 5.0072e+11 22230
## - OverallCond    1 1.5322e+10 5.0194e+11 22233
## - X1stFlrSF      1 1.6324e+10 5.0294e+11 22235
## - MiscFeature    3 1.8598e+10 5.0521e+11 22236
## - BsmtExposure   3 1.9340e+10 5.0595e+11 22238
## - OverallQual    1 1.7787e+10 5.0440e+11 22238
## - BsmtFinSF1     1 1.9757e+10 5.0637e+11 22243
## - PoolArea       1 2.2776e+10 5.0939e+11 22249
## - PoolQC         3 2.7287e+10 5.1390e+11 22255
## - X2ndFlrSF      1 4.5951e+10 5.3256e+11 22298
## - Condition2     5 6.3396e+10 5.5001e+11 22325
## - Neighborhood  24 8.4170e+10 5.7078e+11 22328
## 
## Step:  AIC=22193.94
## SalePrice ~ MSSubClass + MSZoning + LotFrontage + LotArea + Street + 
##     Alley + LotShape + LandContour + LotConfig + LandSlope + 
##     Neighborhood + Condition1 + Condition2 + BldgType + HouseStyle + 
##     OverallQual + OverallCond + YearBuilt + YearRemodAdd + RoofStyle + 
##     RoofMatl + Exterior1st + MasVnrType + MasVnrArea + ExterQual + 
##     ExterCond + Foundation + BsmtQual + BsmtCond + BsmtExposure + 
##     BsmtFinType1 + BsmtFinSF1 + BsmtFinSF2 + BsmtUnfSF + Heating + 
##     HeatingQC + CentralAir + Electrical + X1stFlrSF + X2ndFlrSF + 
##     LowQualFinSF + BsmtFullBath + BsmtHalfBath + FullBath + HalfBath + 
##     BedroomAbvGr + KitchenAbvGr + KitchenQual + TotRmsAbvGrd + 
##     Functional + Fireplaces + FireplaceQu + GarageYrBlt + GarageFinish + 
##     GarageCars + GarageArea + GarageQual + GarageCond + PavedDrive + 
##     WoodDeckSF + OpenPorchSF + EnclosedPorch + X3SsnPorch + ScreenPorch + 
##     PoolArea + PoolQC + Fence + MiscFeature + MiscVal + MoSold + 
##     YrSold + SaleCondition
## 
##                 Df  Sum of Sq        RSS   AIC
## - Electrical     3 1.1185e+07 4.8794e+11 22188
## - Heating        3 9.8266e+07 4.8803e+11 22188
## - HeatingQC      4 1.1757e+09 4.8911e+11 22189
## - ExterCond      3 5.6130e+08 4.8849e+11 22189
## - FireplaceQu    5 2.4178e+09 4.9035e+11 22189
## - Fence          4 1.7234e+09 4.8966e+11 22190
## - Exterior1st   13 9.9708e+09 4.9790e+11 22190
## - BsmtCond       2 2.1945e+08 4.8815e+11 22190
## - HouseStyle     7 4.9001e+09 4.9283e+11 22191
## - PavedDrive     2 5.1067e+08 4.8844e+11 22191
## - Alley          2 5.8276e+08 4.8852e+11 22191
## - RoofStyle      4 2.4312e+09 4.9036e+11 22191
## - LotShape       3 1.5925e+09 4.8952e+11 22192
## - OpenPorchSF    1 2.2216e+04 4.8793e+11 22192
## - GarageYrBlt    1 2.5024e+05 4.8793e+11 22192
## - MSSubClass     1 3.4663e+05 4.8793e+11 22192
## - MiscVal        1 1.4148e+07 4.8795e+11 22192
## - BsmtHalfBath   1 3.1781e+07 4.8796e+11 22192
## - EnclosedPorch  1 5.7358e+07 4.8799e+11 22192
## - GarageFinish   2 9.8140e+08 4.8891e+11 22192
## - YrSold         1 1.1282e+08 4.8805e+11 22192
## - BsmtFullBath   1 2.2079e+08 4.8815e+11 22192
## - HalfBath       1 4.3974e+08 4.8837e+11 22193
## - CentralAir     1 6.1006e+08 4.8854e+11 22193
## - BsmtFinType1   5 4.2155e+09 4.9215e+11 22193
## - LowQualFinSF   1 7.5750e+08 4.8869e+11 22194
## - MoSold         1 7.9784e+08 4.8873e+11 22194
## <none>                        4.8793e+11 22194
## - WoodDeckSF     1 1.0153e+09 4.8895e+11 22194
## - X3SsnPorch     1 1.2520e+09 4.8918e+11 22195
## - GarageCars     1 1.3232e+09 4.8926e+11 22195
## - YearRemodAdd   1 1.3958e+09 4.8933e+11 22195
## - TotRmsAbvGrd   1 1.4229e+09 4.8936e+11 22195
## - ScreenPorch    1 1.5093e+09 4.8944e+11 22195
## - FullBath       1 1.7108e+09 4.8964e+11 22196
## - LotFrontage    1 1.7429e+09 4.8968e+11 22196
## - BldgType       4 4.6164e+09 4.9255e+11 22196
## - Foundation     4 4.7203e+09 4.9265e+11 22197
## - GarageArea     1 2.1252e+09 4.9006e+11 22197
## - GarageCond     4 4.8273e+09 4.9276e+11 22197
## - MasVnrType     3 4.4260e+09 4.9236e+11 22198
## - Functional     5 6.2369e+09 4.9417e+11 22198
## - LandContour    3 4.5502e+09 4.9248e+11 22198
## - Fireplaces     1 2.7891e+09 4.9072e+11 22198
## - MSZoning       4 5.5497e+09 4.9348e+11 22198
## - Condition1     8 9.4001e+09 4.9733e+11 22199
## - BedroomAbvGr   1 3.2240e+09 4.9116e+11 22199
## - KitchenAbvGr   1 3.4242e+09 4.9136e+11 22200
## - YearBuilt      1 3.4983e+09 4.9143e+11 22200
## - Street         1 3.6283e+09 4.9156e+11 22200
## - GarageQual     4 6.9644e+09 4.9490e+11 22201
## - LandSlope      2 6.8188e+09 4.9475e+11 22205
## - BsmtUnfSF      1 7.6769e+09 4.9561e+11 22209
## - MasVnrArea     1 7.7489e+09 4.9568e+11 22209
## - LotConfig      4 1.0632e+10 4.9856e+11 22210
## - BsmtQual       3 1.0598e+10 4.9853e+11 22211
## - BsmtFinSF2     1 9.7797e+09 4.9771e+11 22214
## - ExterQual      3 1.1871e+10 4.9980e+11 22214
## - KitchenQual    3 1.2748e+10 5.0068e+11 22216
## - SaleCondition  5 1.4966e+10 5.0290e+11 22217
## - RoofMatl       6 1.7983e+10 5.0592e+11 22222
## - LotArea        1 1.3850e+10 5.0178e+11 22223
## - OverallCond    1 1.5553e+10 5.0348e+11 22226
## - MiscFeature    3 1.8443e+10 5.0638e+11 22229
## - X1stFlrSF      1 1.7105e+10 5.0504e+11 22230
## - BsmtExposure   3 1.9319e+10 5.0725e+11 22230
## - OverallQual    1 1.7691e+10 5.0562e+11 22231
## - BsmtFinSF1     1 1.9750e+10 5.0768e+11 22235
## - PoolArea       1 2.2646e+10 5.1058e+11 22242
## - PoolQC         3 2.7274e+10 5.1521e+11 22247
## - X2ndFlrSF      1 5.1897e+10 5.3983e+11 22303
## - Condition2     5 6.3682e+10 5.5161e+11 22318
## - Neighborhood  24 8.5119e+10 5.7305e+11 22322
## 
## Step:  AIC=22187.96
## SalePrice ~ MSSubClass + MSZoning + LotFrontage + LotArea + Street + 
##     Alley + LotShape + LandContour + LotConfig + LandSlope + 
##     Neighborhood + Condition1 + Condition2 + BldgType + HouseStyle + 
##     OverallQual + OverallCond + YearBuilt + YearRemodAdd + RoofStyle + 
##     RoofMatl + Exterior1st + MasVnrType + MasVnrArea + ExterQual + 
##     ExterCond + Foundation + BsmtQual + BsmtCond + BsmtExposure + 
##     BsmtFinType1 + BsmtFinSF1 + BsmtFinSF2 + BsmtUnfSF + Heating + 
##     HeatingQC + CentralAir + X1stFlrSF + X2ndFlrSF + LowQualFinSF + 
##     BsmtFullBath + BsmtHalfBath + FullBath + HalfBath + BedroomAbvGr + 
##     KitchenAbvGr + KitchenQual + TotRmsAbvGrd + Functional + 
##     Fireplaces + FireplaceQu + GarageYrBlt + GarageFinish + GarageCars + 
##     GarageArea + GarageQual + GarageCond + PavedDrive + WoodDeckSF + 
##     OpenPorchSF + EnclosedPorch + X3SsnPorch + ScreenPorch + 
##     PoolArea + PoolQC + Fence + MiscFeature + MiscVal + MoSold + 
##     YrSold + SaleCondition
## 
##                 Df  Sum of Sq        RSS   AIC
## - Heating        3 9.9135e+07 4.8804e+11 22182
## - HeatingQC      4 1.1712e+09 4.8911e+11 22183
## - BsmtCond       3 3.4951e+08 4.8829e+11 22183
## - ExterCond      3 5.6991e+08 4.8851e+11 22183
## - FireplaceQu    5 2.4351e+09 4.9038e+11 22183
## - Fence          4 1.7301e+09 4.8967e+11 22184
## - Exterior1st   13 1.0039e+10 4.9798e+11 22184
## - HouseStyle     7 4.9230e+09 4.9287e+11 22185
## - PavedDrive     2 5.0424e+08 4.8845e+11 22185
## - Alley          2 5.8012e+08 4.8852e+11 22185
## - RoofStyle      4 2.4419e+09 4.9039e+11 22185
## - LotShape       3 1.6436e+09 4.8959e+11 22186
## - OpenPorchSF    1 5.4270e+03 4.8794e+11 22186
## - MSSubClass     1 3.3346e+05 4.8794e+11 22186
## - GarageYrBlt    1 3.8768e+05 4.8794e+11 22186
## - MiscVal        1 1.4125e+07 4.8796e+11 22186
## - BsmtHalfBath   1 3.2312e+07 4.8798e+11 22186
## - EnclosedPorch  1 5.8737e+07 4.8800e+11 22186
## - GarageFinish   2 9.8412e+08 4.8893e+11 22186
## - YrSold         1 1.0999e+08 4.8805e+11 22186
## - BsmtFullBath   1 2.2428e+08 4.8817e+11 22187
## - HalfBath       1 4.4122e+08 4.8838e+11 22187
## - CentralAir     1 6.1309e+08 4.8856e+11 22187
## - BsmtFinType1   5 4.2099e+09 4.9215e+11 22187
## - LowQualFinSF   1 7.4965e+08 4.8869e+11 22188
## - MoSold         1 8.0278e+08 4.8875e+11 22188
## <none>                        4.8794e+11 22188
## - WoodDeckSF     1 1.0214e+09 4.8896e+11 22188
## - X3SsnPorch     1 1.2487e+09 4.8919e+11 22189
## - GarageCars     1 1.3371e+09 4.8928e+11 22189
## - TotRmsAbvGrd   1 1.4174e+09 4.8936e+11 22189
## - YearRemodAdd   1 1.4465e+09 4.8939e+11 22189
## - ScreenPorch    1 1.5136e+09 4.8946e+11 22189
## - FullBath       1 1.7271e+09 4.8967e+11 22190
## - LotFrontage    1 1.7600e+09 4.8970e+11 22190
## - BldgType       4 4.6975e+09 4.9264e+11 22190
## - Foundation     4 4.7287e+09 4.9267e+11 22191
## - GarageCond     4 4.8277e+09 4.9277e+11 22191
## - GarageArea     1 2.1354e+09 4.9008e+11 22191
## - MasVnrType     3 4.4179e+09 4.9236e+11 22192
## - Functional     5 6.2407e+09 4.9418e+11 22192
## - LandContour    3 4.5827e+09 4.9253e+11 22192
## - Fireplaces     1 2.8091e+09 4.9075e+11 22192
## - MSZoning       4 5.5675e+09 4.9351e+11 22192
## - Condition1     8 9.5327e+09 4.9748e+11 22193
## - BedroomAbvGr   1 3.2139e+09 4.9116e+11 22193
## - KitchenAbvGr   1 3.4857e+09 4.9143e+11 22194
## - YearBuilt      1 3.5266e+09 4.9147e+11 22194
## - Street         1 3.6559e+09 4.9160e+11 22194
## - GarageQual     4 7.1047e+09 4.9505e+11 22196
## - LandSlope      2 6.8181e+09 4.9476e+11 22199
## - BsmtUnfSF      1 7.7651e+09 4.9571e+11 22203
## - MasVnrArea     1 7.7709e+09 4.9571e+11 22203
## - LotConfig      4 1.0642e+10 4.9859e+11 22204
## - BsmtQual       3 1.0589e+10 4.9853e+11 22205
## - BsmtFinSF2     1 9.8339e+09 4.9778e+11 22208
## - ExterQual      3 1.1910e+10 4.9985e+11 22208
## - KitchenQual    3 1.2738e+10 5.0068e+11 22210
## - SaleCondition  5 1.5015e+10 5.0296e+11 22211
## - RoofMatl       6 1.8010e+10 5.0595e+11 22216
## - LotArea        1 1.4115e+10 5.0206e+11 22217
## - OverallCond    1 1.5604e+10 5.0355e+11 22220
## - MiscFeature    3 1.8440e+10 5.0638e+11 22223
## - X1stFlrSF      1 1.7262e+10 5.0521e+11 22224
## - BsmtExposure   3 1.9348e+10 5.0729e+11 22225
## - OverallQual    1 1.7781e+10 5.0572e+11 22225
## - BsmtFinSF1     1 1.9867e+10 5.0781e+11 22230
## - PoolArea       1 2.2658e+10 5.1060e+11 22236
## - PoolQC         3 2.7275e+10 5.1522e+11 22242
## - X2ndFlrSF      1 5.2057e+10 5.4000e+11 22297
## - Condition2     5 6.3723e+10 5.5167e+11 22312
## - Neighborhood  24 8.5184e+10 5.7313e+11 22316
## 
## Step:  AIC=22182.18
## SalePrice ~ MSSubClass + MSZoning + LotFrontage + LotArea + Street + 
##     Alley + LotShape + LandContour + LotConfig + LandSlope + 
##     Neighborhood + Condition1 + Condition2 + BldgType + HouseStyle + 
##     OverallQual + OverallCond + YearBuilt + YearRemodAdd + RoofStyle + 
##     RoofMatl + Exterior1st + MasVnrType + MasVnrArea + ExterQual + 
##     ExterCond + Foundation + BsmtQual + BsmtCond + BsmtExposure + 
##     BsmtFinType1 + BsmtFinSF1 + BsmtFinSF2 + BsmtUnfSF + HeatingQC + 
##     CentralAir + X1stFlrSF + X2ndFlrSF + LowQualFinSF + BsmtFullBath + 
##     BsmtHalfBath + FullBath + HalfBath + BedroomAbvGr + KitchenAbvGr + 
##     KitchenQual + TotRmsAbvGrd + Functional + Fireplaces + FireplaceQu + 
##     GarageYrBlt + GarageFinish + GarageCars + GarageArea + GarageQual + 
##     GarageCond + PavedDrive + WoodDeckSF + OpenPorchSF + EnclosedPorch + 
##     X3SsnPorch + ScreenPorch + PoolArea + PoolQC + Fence + MiscFeature + 
##     MiscVal + MoSold + YrSold + SaleCondition
## 
##                 Df  Sum of Sq        RSS   AIC
## - BsmtCond       3 3.0831e+08 4.8835e+11 22177
## - HeatingQC      4 1.2742e+09 4.8932e+11 22177
## - ExterCond      3 5.7653e+08 4.8862e+11 22178
## - FireplaceQu    5 2.4574e+09 4.9050e+11 22178
## - Fence          4 1.7286e+09 4.8977e+11 22178
## - Exterior1st   13 1.0173e+10 4.9822e+11 22179
## - HouseStyle     7 5.0171e+09 4.9306e+11 22179
## - PavedDrive     2 5.6948e+08 4.8861e+11 22180
## - Alley          2 6.0878e+08 4.8865e+11 22180
## - RoofStyle      4 2.4597e+09 4.9050e+11 22180
## - LotShape       3 1.6428e+09 4.8969e+11 22180
## - OpenPorchSF    1 2.4985e+04 4.8804e+11 22180
## - MSSubClass     1 7.0419e+05 4.8804e+11 22180
## - GarageYrBlt    1 3.0585e+06 4.8805e+11 22180
## - MiscVal        1 1.0912e+07 4.8805e+11 22180
## - BsmtHalfBath   1 3.5330e+07 4.8808e+11 22180
## - EnclosedPorch  1 5.6421e+07 4.8810e+11 22180
## - GarageFinish   2 9.7224e+08 4.8901e+11 22180
## - YrSold         1 1.0626e+08 4.8815e+11 22180
## - BsmtFullBath   1 2.3472e+08 4.8828e+11 22181
## - HalfBath       1 4.3024e+08 4.8847e+11 22181
## - CentralAir     1 5.7694e+08 4.8862e+11 22182
## - BsmtFinType1   5 4.1965e+09 4.9224e+11 22182
## - LowQualFinSF   1 7.3995e+08 4.8878e+11 22182
## - MoSold         1 7.8230e+08 4.8882e+11 22182
## <none>                        4.8804e+11 22182
## - WoodDeckSF     1 1.0080e+09 4.8905e+11 22182
## - X3SsnPorch     1 1.2423e+09 4.8928e+11 22183
## - GarageCars     1 1.3643e+09 4.8941e+11 22183
## - TotRmsAbvGrd   1 1.4178e+09 4.8946e+11 22183
## - YearRemodAdd   1 1.5109e+09 4.8955e+11 22184
## - ScreenPorch    1 1.5289e+09 4.8957e+11 22184
## - LotFrontage    1 1.7396e+09 4.8978e+11 22184
## - FullBath       1 1.7427e+09 4.8979e+11 22184
## - Foundation     4 4.6652e+09 4.9271e+11 22185
## - BldgType       4 4.7975e+09 4.9284e+11 22185
## - GarageArea     1 2.1524e+09 4.9020e+11 22185
## - GarageCond     4 4.8560e+09 4.9290e+11 22185
## - MasVnrType     3 4.4130e+09 4.9246e+11 22186
## - Functional     5 6.2847e+09 4.9433e+11 22186
## - LandContour    3 4.5808e+09 4.9262e+11 22186
## - MSZoning       4 5.5376e+09 4.9358e+11 22187
## - Fireplaces     1 2.8432e+09 4.9089e+11 22187
## - BedroomAbvGr   1 3.2406e+09 4.9128e+11 22187
## - Condition1     8 9.6239e+09 4.9767e+11 22188
## - YearBuilt      1 3.5230e+09 4.9157e+11 22188
## - KitchenAbvGr   1 3.7187e+09 4.9176e+11 22189
## - Street         1 3.7309e+09 4.9177e+11 22189
## - GarageQual     4 7.0634e+09 4.9511e+11 22190
## - LandSlope      2 6.8558e+09 4.9490e+11 22193
## - MasVnrArea     1 7.8202e+09 4.9586e+11 22198
## - BsmtUnfSF      1 7.8518e+09 4.9589e+11 22198
## - LotConfig      4 1.0621e+10 4.9866e+11 22198
## - BsmtQual       3 1.0555e+10 4.9860e+11 22200
## - BsmtFinSF2     1 9.8935e+09 4.9794e+11 22202
## - ExterQual      3 1.1968e+10 5.0001e+11 22203
## - KitchenQual    3 1.2790e+10 5.0083e+11 22205
## - SaleCondition  5 1.4979e+10 5.0302e+11 22205
## - RoofMatl       6 1.8089e+10 5.0613e+11 22210
## - LotArea        1 1.4740e+10 5.0278e+11 22213
## - OverallCond    1 1.5543e+10 5.0359e+11 22215
## - MiscFeature    3 1.8451e+10 5.0649e+11 22217
## - X1stFlrSF      1 1.7327e+10 5.0537e+11 22218
## - BsmtExposure   3 1.9398e+10 5.0744e+11 22219
## - OverallQual    1 1.7765e+10 5.0581e+11 22219
## - BsmtFinSF1     1 2.0058e+10 5.0810e+11 22224
## - PoolArea       1 2.2708e+10 5.1075e+11 22230
## - PoolQC         3 2.7309e+10 5.1535e+11 22236
## - X2ndFlrSF      1 5.2359e+10 5.4040e+11 22292
## - Condition2     5 6.3797e+10 5.5184e+11 22307
## - Neighborhood  24 8.5436e+10 5.7348e+11 22311
## 
## Step:  AIC=22176.87
## SalePrice ~ MSSubClass + MSZoning + LotFrontage + LotArea + Street + 
##     Alley + LotShape + LandContour + LotConfig + LandSlope + 
##     Neighborhood + Condition1 + Condition2 + BldgType + HouseStyle + 
##     OverallQual + OverallCond + YearBuilt + YearRemodAdd + RoofStyle + 
##     RoofMatl + Exterior1st + MasVnrType + MasVnrArea + ExterQual + 
##     ExterCond + Foundation + BsmtQual + BsmtExposure + BsmtFinType1 + 
##     BsmtFinSF1 + BsmtFinSF2 + BsmtUnfSF + HeatingQC + CentralAir + 
##     X1stFlrSF + X2ndFlrSF + LowQualFinSF + BsmtFullBath + BsmtHalfBath + 
##     FullBath + HalfBath + BedroomAbvGr + KitchenAbvGr + KitchenQual + 
##     TotRmsAbvGrd + Functional + Fireplaces + FireplaceQu + GarageYrBlt + 
##     GarageFinish + GarageCars + GarageArea + GarageQual + GarageCond + 
##     PavedDrive + WoodDeckSF + OpenPorchSF + EnclosedPorch + X3SsnPorch + 
##     ScreenPorch + PoolArea + PoolQC + Fence + MiscFeature + MiscVal + 
##     MoSold + YrSold + SaleCondition
## 
##                 Df  Sum of Sq        RSS   AIC
## - HeatingQC      4 1.2340e+09 4.8958e+11 22172
## - FireplaceQu    5 2.5184e+09 4.9087e+11 22173
## - ExterCond      3 7.3115e+08 4.8908e+11 22173
## - Fence          4 1.6745e+09 4.9003e+11 22173
## - Exterior1st   13 1.0247e+10 4.9860e+11 22174
## - PavedDrive     2 5.6753e+08 4.8892e+11 22174
## - HouseStyle     7 5.0697e+09 4.9342e+11 22174
## - Alley          2 6.0883e+08 4.8896e+11 22174
## - LotShape       3 1.5903e+09 4.8994e+11 22174
## - RoofStyle      4 2.5711e+09 4.9092e+11 22175
## - OpenPorchSF    1 1.6308e+05 4.8835e+11 22175
## - MSSubClass     1 2.0616e+06 4.8835e+11 22175
## - GarageYrBlt    1 3.4420e+06 4.8835e+11 22175
## - MiscVal        1 1.2729e+07 4.8836e+11 22175
## - BsmtHalfBath   1 2.9879e+07 4.8838e+11 22175
## - EnclosedPorch  1 3.4072e+07 4.8839e+11 22175
## - YrSold         1 6.4453e+07 4.8842e+11 22175
## - GarageFinish   2 9.7896e+08 4.8933e+11 22175
## - BsmtFullBath   1 2.0563e+08 4.8856e+11 22175
## - HalfBath       1 4.9573e+08 4.8885e+11 22176
## - BsmtFinType1   5 4.2387e+09 4.9259e+11 22176
## - CentralAir     1 6.5152e+08 4.8900e+11 22176
## - LowQualFinSF   1 7.2345e+08 4.8907e+11 22177
## - MoSold         1 7.6967e+08 4.8912e+11 22177
## <none>                        4.8835e+11 22177
## - WoodDeckSF     1 9.6745e+08 4.8932e+11 22177
## - X3SsnPorch     1 1.2590e+09 4.8961e+11 22178
## - GarageCars     1 1.3298e+09 4.8968e+11 22178
## - TotRmsAbvGrd   1 1.4684e+09 4.8982e+11 22178
## - YearRemodAdd   1 1.4742e+09 4.8983e+11 22178
## - ScreenPorch    1 1.5425e+09 4.8989e+11 22178
## - FullBath       1 1.7560e+09 4.9011e+11 22179
## - LotFrontage    1 1.7810e+09 4.9013e+11 22179
## - Foundation     4 4.6584e+09 4.9301e+11 22179
## - BldgType       4 4.7730e+09 4.9312e+11 22180
## - GarageArea     1 2.2020e+09 4.9055e+11 22180
## - GarageCond     4 4.9787e+09 4.9333e+11 22180
## - MasVnrType     3 4.4412e+09 4.9279e+11 22181
## - LandContour    3 4.5179e+09 4.9287e+11 22181
## - Functional     5 6.3383e+09 4.9469e+11 22181
## - Fireplaces     1 2.8416e+09 4.9119e+11 22181
## - MSZoning       4 5.5843e+09 4.9394e+11 22181
## - BedroomAbvGr   1 3.1665e+09 4.9152e+11 22182
## - Condition1     8 9.6790e+09 4.9803e+11 22182
## - YearBuilt      1 3.5141e+09 4.9187e+11 22183
## - Street         1 3.6911e+09 4.9204e+11 22183
## - KitchenAbvGr   1 3.8700e+09 4.9222e+11 22184
## - GarageQual     4 6.9675e+09 4.9532e+11 22184
## - LandSlope      2 6.7762e+09 4.9513e+11 22188
## - BsmtUnfSF      1 7.8553e+09 4.9621e+11 22192
## - MasVnrArea     1 7.9231e+09 4.9627e+11 22193
## - LotConfig      4 1.0665e+10 4.9902e+11 22193
## - BsmtQual       3 1.0429e+10 4.9878e+11 22194
## - BsmtFinSF2     1 9.8228e+09 4.9817e+11 22197
## - ExterQual      3 1.1969e+10 5.0032e+11 22197
## - KitchenQual    3 1.2660e+10 5.0101e+11 22199
## - SaleCondition  5 1.4838e+10 5.0319e+11 22200
## - RoofMatl       6 1.8193e+10 5.0654e+11 22205
## - LotArea        1 1.4702e+10 5.0305e+11 22207
## - OverallCond    1 1.5816e+10 5.0417e+11 22210
## - MiscFeature    3 1.8416e+10 5.0677e+11 22211
## - X1stFlrSF      1 1.7334e+10 5.0568e+11 22213
## - BsmtExposure   3 1.9586e+10 5.0794e+11 22214
## - OverallQual    1 1.7793e+10 5.0614e+11 22214
## - BsmtFinSF1     1 2.0310e+10 5.0866e+11 22220
## - PoolArea       1 2.2659e+10 5.1101e+11 22225
## - PoolQC         3 2.7255e+10 5.1561e+11 22230
## - X2ndFlrSF      1 5.2237e+10 5.4059e+11 22286
## - Condition2     5 6.3967e+10 5.5232e+11 22302
## - Neighborhood  24 8.5450e+10 5.7380e+11 22305
## 
## Step:  AIC=22171.64
## SalePrice ~ MSSubClass + MSZoning + LotFrontage + LotArea + Street + 
##     Alley + LotShape + LandContour + LotConfig + LandSlope + 
##     Neighborhood + Condition1 + Condition2 + BldgType + HouseStyle + 
##     OverallQual + OverallCond + YearBuilt + YearRemodAdd + RoofStyle + 
##     RoofMatl + Exterior1st + MasVnrType + MasVnrArea + ExterQual + 
##     ExterCond + Foundation + BsmtQual + BsmtExposure + BsmtFinType1 + 
##     BsmtFinSF1 + BsmtFinSF2 + BsmtUnfSF + CentralAir + X1stFlrSF + 
##     X2ndFlrSF + LowQualFinSF + BsmtFullBath + BsmtHalfBath + 
##     FullBath + HalfBath + BedroomAbvGr + KitchenAbvGr + KitchenQual + 
##     TotRmsAbvGrd + Functional + Fireplaces + FireplaceQu + GarageYrBlt + 
##     GarageFinish + GarageCars + GarageArea + GarageQual + GarageCond + 
##     PavedDrive + WoodDeckSF + OpenPorchSF + EnclosedPorch + X3SsnPorch + 
##     ScreenPorch + PoolArea + PoolQC + Fence + MiscFeature + MiscVal + 
##     MoSold + YrSold + SaleCondition
## 
##                 Df  Sum of Sq        RSS   AIC
## - FireplaceQu    5 2.5563e+09 4.9214e+11 22167
## - Fence          4 1.6623e+09 4.9125e+11 22167
## - ExterCond      3 7.7423e+08 4.9036e+11 22167
## - HouseStyle     7 4.7570e+09 4.9434e+11 22168
## - PavedDrive     2 5.1917e+08 4.9010e+11 22169
## - RoofStyle      4 2.3769e+09 4.9196e+11 22169
## - Alley          2 5.8404e+08 4.9017e+11 22169
## - LotShape       3 1.5240e+09 4.9111e+11 22169
## - GarageFinish   2 8.8160e+08 4.9047e+11 22170
## - MiscVal        1 5.3442e+04 4.8959e+11 22170
## - OpenPorchSF    1 1.1342e+06 4.8959e+11 22170
## - MSSubClass     1 2.2676e+06 4.8959e+11 22170
## - GarageYrBlt    1 8.2252e+06 4.8959e+11 22170
## - EnclosedPorch  1 2.9091e+07 4.8961e+11 22170
## - BsmtHalfBath   1 4.8922e+07 4.8963e+11 22170
## - YrSold         1 5.4579e+07 4.8964e+11 22170
## - BsmtFullBath   1 2.5686e+08 4.8984e+11 22170
## - HalfBath       1 4.2183e+08 4.9001e+11 22171
## - Exterior1st   13 1.1347e+10 5.0093e+11 22171
## - BsmtFinType1   5 4.1542e+09 4.9374e+11 22171
## - CentralAir     1 6.7049e+08 4.9026e+11 22171
## - LowQualFinSF   1 7.1905e+08 4.9030e+11 22171
## - MoSold         1 7.5241e+08 4.9034e+11 22171
## - WoodDeckSF     1 8.6883e+08 4.9045e+11 22172
## <none>                        4.8958e+11 22172
## - ScreenPorch    1 1.2709e+09 4.9086e+11 22173
## - X3SsnPorch     1 1.3247e+09 4.9091e+11 22173
## - GarageCars     1 1.3443e+09 4.9093e+11 22173
## - TotRmsAbvGrd   1 1.5045e+09 4.9109e+11 22173
## - YearRemodAdd   1 1.5938e+09 4.9118e+11 22173
## - FullBath       1 1.7440e+09 4.9133e+11 22174
## - LotFrontage    1 1.8776e+09 4.9146e+11 22174
## - Foundation     4 4.7176e+09 4.9430e+11 22174
## - BldgType       4 4.8516e+09 4.9444e+11 22174
## - GarageArea     1 2.2018e+09 4.9179e+11 22175
## - GarageCond     4 4.9425e+09 4.9453e+11 22175
## - LandContour    3 4.4833e+09 4.9407e+11 22176
## - Functional     5 6.3656e+09 4.9595e+11 22176
## - MasVnrType     3 4.6618e+09 4.9425e+11 22176
## - Fireplaces     1 2.8945e+09 4.9248e+11 22176
## - MSZoning       4 5.6835e+09 4.9527e+11 22176
## - BedroomAbvGr   1 3.3252e+09 4.9291e+11 22177
## - Condition1     8 9.9941e+09 4.9958e+11 22178
## - Street         1 3.6928e+09 4.9328e+11 22178
## - YearBuilt      1 3.8325e+09 4.9342e+11 22178
## - KitchenAbvGr   1 4.0042e+09 4.9359e+11 22179
## - GarageQual     4 7.0622e+09 4.9665e+11 22179
## - LandSlope      2 6.7885e+09 4.9637e+11 22183
## - BsmtUnfSF      1 7.8528e+09 4.9744e+11 22187
## - LotConfig      4 1.0609e+10 5.0019e+11 22187
## - MasVnrArea     1 8.0115e+09 4.9760e+11 22187
## - BsmtQual       3 1.0691e+10 5.0028e+11 22189
## - BsmtFinSF2     1 9.9034e+09 4.9949e+11 22192
## - ExterQual      3 1.1929e+10 5.0151e+11 22192
## - KitchenQual    3 1.2502e+10 5.0209e+11 22193
## - SaleCondition  5 1.4809e+10 5.0439e+11 22194
## - RoofMatl       6 1.7936e+10 5.0752e+11 22199
## - LotArea        1 1.4505e+10 5.0409e+11 22202
## - OverallCond    1 1.6016e+10 5.0560e+11 22205
## - MiscFeature    3 1.8371e+10 5.0796e+11 22206
## - X1stFlrSF      1 1.7395e+10 5.0698e+11 22208
## - BsmtExposure   3 1.9670e+10 5.0926e+11 22209
## - OverallQual    1 1.7915e+10 5.0750e+11 22209
## - BsmtFinSF1     1 2.0143e+10 5.0973e+11 22214
## - PoolArea       1 2.3102e+10 5.1269e+11 22220
## - PoolQC         3 2.7224e+10 5.1681e+11 22225
## - X2ndFlrSF      1 5.2746e+10 5.4233e+11 22282
## - Condition2     5 6.3797e+10 5.5338e+11 22296
## - Neighborhood  24 8.5260e+10 5.7485e+11 22299
## 
## Step:  AIC=22167.33
## SalePrice ~ MSSubClass + MSZoning + LotFrontage + LotArea + Street + 
##     Alley + LotShape + LandContour + LotConfig + LandSlope + 
##     Neighborhood + Condition1 + Condition2 + BldgType + HouseStyle + 
##     OverallQual + OverallCond + YearBuilt + YearRemodAdd + RoofStyle + 
##     RoofMatl + Exterior1st + MasVnrType + MasVnrArea + ExterQual + 
##     ExterCond + Foundation + BsmtQual + BsmtExposure + BsmtFinType1 + 
##     BsmtFinSF1 + BsmtFinSF2 + BsmtUnfSF + CentralAir + X1stFlrSF + 
##     X2ndFlrSF + LowQualFinSF + BsmtFullBath + BsmtHalfBath + 
##     FullBath + HalfBath + BedroomAbvGr + KitchenAbvGr + KitchenQual + 
##     TotRmsAbvGrd + Functional + Fireplaces + GarageYrBlt + GarageFinish + 
##     GarageCars + GarageArea + GarageQual + GarageCond + PavedDrive + 
##     WoodDeckSF + OpenPorchSF + EnclosedPorch + X3SsnPorch + ScreenPorch + 
##     PoolArea + PoolQC + Fence + MiscFeature + MiscVal + MoSold + 
##     YrSold + SaleCondition
## 
##                 Df  Sum of Sq        RSS   AIC
## - ExterCond      3 7.3616e+08 4.9288e+11 22163
## - Fence          4 1.8630e+09 4.9400e+11 22164
## - HouseStyle     7 4.7676e+09 4.9691e+11 22164
## - PavedDrive     2 5.4457e+08 4.9269e+11 22165
## - Alley          2 6.1762e+08 4.9276e+11 22165
## - RoofStyle      4 2.4905e+09 4.9463e+11 22165
## - LotShape       3 1.7796e+09 4.9392e+11 22165
## - GarageYrBlt    1 2.9941e+06 4.9214e+11 22165
## - MiscVal        1 3.0700e+06 4.9214e+11 22165
## - OpenPorchSF    1 3.5298e+06 4.9214e+11 22165
## - MSSubClass     1 9.0944e+06 4.9215e+11 22165
## - EnclosedPorch  1 1.3664e+07 4.9215e+11 22165
## - BsmtHalfBath   1 2.0717e+07 4.9216e+11 22165
## - YrSold         1 3.0776e+07 4.9217e+11 22165
## - GarageFinish   2 9.8648e+08 4.9313e+11 22166
## - BsmtFullBath   1 1.9828e+08 4.9234e+11 22166
## - HalfBath       1 4.6812e+08 4.9261e+11 22166
## - CentralAir     1 6.1704e+08 4.9276e+11 22167
## - LowQualFinSF   1 6.6781e+08 4.9281e+11 22167
## - MoSold         1 7.9379e+08 4.9294e+11 22167
## - WoodDeckSF     1 8.9481e+08 4.9304e+11 22167
## <none>                        4.9214e+11 22167
## - Exterior1st   13 1.1921e+10 5.0406e+11 22168
## - BsmtFinType1   5 4.6581e+09 4.9680e+11 22168
## - X3SsnPorch     1 1.1295e+09 4.9327e+11 22168
## - TotRmsAbvGrd   1 1.1884e+09 4.9333e+11 22168
## - ScreenPorch    1 1.2296e+09 4.9337e+11 22168
## - GarageCars     1 1.3470e+09 4.9349e+11 22168
## - Fireplaces     1 1.4092e+09 4.9355e+11 22169
## - YearRemodAdd   1 1.5858e+09 4.9373e+11 22169
## - FullBath       1 1.6641e+09 4.9381e+11 22169
## - Foundation     4 4.5810e+09 4.9672e+11 22170
## - LotFrontage    1 1.8977e+09 4.9404e+11 22170
## - GarageArea     1 1.9921e+09 4.9413e+11 22170
## - GarageCond     4 4.8637e+09 4.9700e+11 22170
## - BldgType       4 4.9352e+09 4.9708e+11 22170
## - Functional     5 6.1646e+09 4.9831e+11 22171
## - LandContour    3 4.8301e+09 4.9697e+11 22172
## - MasVnrType     3 4.8366e+09 4.9698e+11 22172
## - MSZoning       4 5.8681e+09 4.9801e+11 22172
## - BedroomAbvGr   1 3.4244e+09 4.9557e+11 22173
## - Street         1 3.4773e+09 4.9562e+11 22173
## - YearBuilt      1 3.8347e+09 4.9598e+11 22174
## - KitchenAbvGr   1 3.9562e+09 4.9610e+11 22174
## - Condition1     8 1.0455e+10 5.0260e+11 22174
## - GarageQual     4 6.8605e+09 4.9900e+11 22175
## - LandSlope      2 6.2514e+09 4.9839e+11 22177
## - MasVnrArea     1 7.7929e+09 4.9993e+11 22183
## - LotConfig      4 1.0803e+10 5.0294e+11 22183
## - BsmtUnfSF      1 8.4868e+09 5.0063e+11 22184
## - BsmtQual       3 1.1221e+10 5.0336e+11 22186
## - BsmtFinSF2     1 1.0038e+10 5.0218e+11 22187
## - ExterQual      3 1.1915e+10 5.0406e+11 22188
## - SaleCondition  5 1.5079e+10 5.0722e+11 22190
## - KitchenQual    3 1.4636e+10 5.0678e+11 22193
## - RoofMatl       6 1.9562e+10 5.1170e+11 22198
## - LotArea        1 1.5240e+10 5.0738e+11 22199
## - OverallCond    1 1.6354e+10 5.0850e+11 22201
## - MiscFeature    3 1.8284e+10 5.1043e+11 22201
## - X1stFlrSF      1 1.7941e+10 5.1008e+11 22205
## - OverallQual    1 1.8022e+10 5.1016e+11 22205
## - BsmtExposure   3 2.1439e+10 5.1358e+11 22208
## - BsmtFinSF1     1 2.1506e+10 5.1365e+11 22212
## - PoolArea       1 2.3039e+10 5.1518e+11 22215
## - PoolQC         3 2.7407e+10 5.1955e+11 22221
## - X2ndFlrSF      1 5.4995e+10 5.4714e+11 22281
## - Neighborhood  24 8.4016e+10 5.7616e+11 22292
## - Condition2     5 6.5268e+10 5.5741e+11 22294
## 
## Step:  AIC=22162.97
## SalePrice ~ MSSubClass + MSZoning + LotFrontage + LotArea + Street + 
##     Alley + LotShape + LandContour + LotConfig + LandSlope + 
##     Neighborhood + Condition1 + Condition2 + BldgType + HouseStyle + 
##     OverallQual + OverallCond + YearBuilt + YearRemodAdd + RoofStyle + 
##     RoofMatl + Exterior1st + MasVnrType + MasVnrArea + ExterQual + 
##     Foundation + BsmtQual + BsmtExposure + BsmtFinType1 + BsmtFinSF1 + 
##     BsmtFinSF2 + BsmtUnfSF + CentralAir + X1stFlrSF + X2ndFlrSF + 
##     LowQualFinSF + BsmtFullBath + BsmtHalfBath + FullBath + HalfBath + 
##     BedroomAbvGr + KitchenAbvGr + KitchenQual + TotRmsAbvGrd + 
##     Functional + Fireplaces + GarageYrBlt + GarageFinish + GarageCars + 
##     GarageArea + GarageQual + GarageCond + PavedDrive + WoodDeckSF + 
##     OpenPorchSF + EnclosedPorch + X3SsnPorch + ScreenPorch + 
##     PoolArea + PoolQC + Fence + MiscFeature + MiscVal + MoSold + 
##     YrSold + SaleCondition
## 
##                 Df  Sum of Sq        RSS   AIC
## - Fence          4 1.9533e+09 4.9483e+11 22159
## - HouseStyle     7 4.7381e+09 4.9762e+11 22159
## - Alley          2 5.5856e+08 4.9344e+11 22160
## - PavedDrive     2 6.0593e+08 4.9348e+11 22160
## - RoofStyle      4 2.5331e+09 4.9541e+11 22161
## - MiscVal        1 6.0344e+05 4.9288e+11 22161
## - GarageYrBlt    1 1.0273e+06 4.9288e+11 22161
## - OpenPorchSF    1 7.3155e+06 4.9288e+11 22161
## - BsmtHalfBath   1 9.0175e+06 4.9289e+11 22161
## - MSSubClass     1 1.0564e+07 4.9289e+11 22161
## - EnclosedPorch  1 1.3140e+07 4.9289e+11 22161
## - LotShape       3 1.8230e+09 4.9470e+11 22161
## - YrSold         1 3.1873e+07 4.9291e+11 22161
## - GarageFinish   2 1.0028e+09 4.9388e+11 22161
## - BsmtFullBath   1 1.7938e+08 4.9306e+11 22161
## - HalfBath       1 4.7371e+08 4.9335e+11 22162
## - CentralAir     1 6.4340e+08 4.9352e+11 22162
## - LowQualFinSF   1 6.6871e+08 4.9355e+11 22163
## - MoSold         1 8.2568e+08 4.9370e+11 22163
## - WoodDeckSF     1 8.9239e+08 4.9377e+11 22163
## <none>                        4.9288e+11 22163
## - Exterior1st   13 1.2044e+10 5.0492e+11 22163
## - X3SsnPorch     1 1.1185e+09 4.9400e+11 22163
## - TotRmsAbvGrd   1 1.1634e+09 4.9404e+11 22164
## - BsmtFinType1   5 4.8116e+09 4.9769e+11 22164
## - ScreenPorch    1 1.2684e+09 4.9415e+11 22164
## - GarageCars     1 1.3221e+09 4.9420e+11 22164
## - Fireplaces     1 1.3953e+09 4.9427e+11 22164
## - FullBath       1 1.5053e+09 4.9438e+11 22164
## - YearRemodAdd   1 1.5689e+09 4.9445e+11 22164
## - Foundation     4 4.5932e+09 4.9747e+11 22165
## - LotFrontage    1 1.9249e+09 4.9480e+11 22165
## - GarageCond     4 4.6944e+09 4.9757e+11 22165
## - GarageArea     1 2.0227e+09 4.9490e+11 22165
## - Functional     5 6.1612e+09 4.9904e+11 22167
## - BldgType       4 5.3528e+09 4.9823e+11 22167
## - MasVnrType     3 4.7060e+09 4.9758e+11 22167
## - MSZoning       4 5.8250e+09 4.9870e+11 22168
## - LandContour    3 5.0185e+09 4.9790e+11 22168
## - BedroomAbvGr   1 3.4773e+09 4.9635e+11 22169
## - Street         1 3.5739e+09 4.9645e+11 22169
## - YearBuilt      1 3.8944e+09 4.9677e+11 22170
## - KitchenAbvGr   1 3.9633e+09 4.9684e+11 22170
## - GarageQual     4 6.7060e+09 4.9958e+11 22170
## - Condition1     8 1.0805e+10 5.0368e+11 22171
## - LandSlope      2 6.1162e+09 4.9899e+11 22173
## - MasVnrArea     1 7.6039e+09 5.0048e+11 22178
## - LotConfig      4 1.0564e+10 5.0344e+11 22178
## - BsmtUnfSF      1 8.4701e+09 5.0135e+11 22180
## - BsmtQual       3 1.1272e+10 5.0415e+11 22182
## - BsmtFinSF2     1 9.9403e+09 5.0282e+11 22183
## - ExterQual      3 1.2035e+10 5.0491e+11 22183
## - SaleCondition  5 1.5358e+10 5.0824e+11 22187
## - KitchenQual    3 1.4598e+10 5.0748e+11 22189
## - LotArea        1 1.5024e+10 5.0790e+11 22194
## - RoofMatl       6 1.9995e+10 5.1287e+11 22195
## - OverallCond    1 1.5677e+10 5.0855e+11 22195
## - MiscFeature    3 1.8935e+10 5.1181e+11 22198
## - OverallQual    1 1.7941e+10 5.1082e+11 22200
## - X1stFlrSF      1 1.8332e+10 5.1121e+11 22201
## - BsmtExposure   3 2.1542e+10 5.1442e+11 22204
## - BsmtFinSF1     1 2.1496e+10 5.1437e+11 22208
## - PoolArea       1 2.3598e+10 5.1647e+11 22212
## - PoolQC         3 2.7651e+10 5.2053e+11 22217
## - X2ndFlrSF      1 5.5948e+10 5.4883e+11 22279
## - Neighborhood  24 8.4699e+10 5.7758e+11 22289
## - Condition2     5 6.5208e+10 5.5809e+11 22289
## 
## Step:  AIC=22159.3
## SalePrice ~ MSSubClass + MSZoning + LotFrontage + LotArea + Street + 
##     Alley + LotShape + LandContour + LotConfig + LandSlope + 
##     Neighborhood + Condition1 + Condition2 + BldgType + HouseStyle + 
##     OverallQual + OverallCond + YearBuilt + YearRemodAdd + RoofStyle + 
##     RoofMatl + Exterior1st + MasVnrType + MasVnrArea + ExterQual + 
##     Foundation + BsmtQual + BsmtExposure + BsmtFinType1 + BsmtFinSF1 + 
##     BsmtFinSF2 + BsmtUnfSF + CentralAir + X1stFlrSF + X2ndFlrSF + 
##     LowQualFinSF + BsmtFullBath + BsmtHalfBath + FullBath + HalfBath + 
##     BedroomAbvGr + KitchenAbvGr + KitchenQual + TotRmsAbvGrd + 
##     Functional + Fireplaces + GarageYrBlt + GarageFinish + GarageCars + 
##     GarageArea + GarageQual + GarageCond + PavedDrive + WoodDeckSF + 
##     OpenPorchSF + EnclosedPorch + X3SsnPorch + ScreenPorch + 
##     PoolArea + PoolQC + MiscFeature + MiscVal + MoSold + YrSold + 
##     SaleCondition
## 
##                 Df  Sum of Sq        RSS   AIC
## - HouseStyle     7 4.4820e+09 4.9931e+11 22155
## - PavedDrive     2 4.8490e+08 4.9532e+11 22156
## - Alley          2 6.9457e+08 4.9553e+11 22157
## - RoofStyle      4 2.5960e+09 4.9743e+11 22157
## - GarageYrBlt    1 9.0900e+03 4.9483e+11 22157
## - BsmtHalfBath   1 9.1670e+05 4.9483e+11 22157
## - MiscVal        1 1.7818e+06 4.9483e+11 22157
## - EnclosedPorch  1 1.0883e+07 4.9484e+11 22157
## - OpenPorchSF    1 2.2443e+07 4.9485e+11 22157
## - MSSubClass     1 2.5876e+07 4.9486e+11 22157
## - YrSold         1 3.4268e+07 4.9487e+11 22157
## - LotShape       3 1.8822e+09 4.9671e+11 22157
## - BsmtFullBath   1 1.5412e+08 4.9498e+11 22158
## - GarageFinish   2 1.2011e+09 4.9603e+11 22158
## - HalfBath       1 5.1601e+08 4.9535e+11 22158
## - CentralAir     1 6.4036e+08 4.9547e+11 22159
## - LowQualFinSF   1 7.1723e+08 4.9555e+11 22159
## - WoodDeckSF     1 7.6254e+08 4.9559e+11 22159
## - BsmtFinType1   5 4.4516e+09 4.9928e+11 22159
## <none>                        4.9483e+11 22159
## - TotRmsAbvGrd   1 9.3054e+08 4.9576e+11 22159
## - MoSold         1 9.3846e+08 4.9577e+11 22159
## - Exterior1st   13 1.2057e+10 5.0689e+11 22160
## - X3SsnPorch     1 1.1120e+09 4.9594e+11 22160
## - GarageCars     1 1.2641e+09 4.9609e+11 22160
## - ScreenPorch    1 1.4480e+09 4.9628e+11 22161
## - GarageCond     4 4.2058e+09 4.9904e+11 22161
## - Fireplaces     1 1.5005e+09 4.9633e+11 22161
## - YearRemodAdd   1 1.5224e+09 4.9635e+11 22161
## - FullBath       1 1.5953e+09 4.9643e+11 22161
## - Foundation     4 4.3393e+09 4.9917e+11 22161
## - LotFrontage    1 1.9577e+09 4.9679e+11 22162
## - GarageArea     1 2.1240e+09 4.9695e+11 22162
## - Functional     5 6.2832e+09 5.0111e+11 22163
## - BldgType       4 5.3844e+09 5.0022e+11 22163
## - MSZoning       4 5.5689e+09 5.0040e+11 22164
## - BedroomAbvGr   1 3.1966e+09 4.9803e+11 22164
## - GarageQual     4 6.0880e+09 5.0092e+11 22165
## - MasVnrType     3 5.2382e+09 5.0007e+11 22165
## - LandContour    3 5.2674e+09 5.0010e+11 22165
## - Street         1 3.6311e+09 4.9846e+11 22165
## - KitchenAbvGr   1 3.8294e+09 4.9866e+11 22166
## - YearBuilt      1 3.8591e+09 4.9869e+11 22166
## - Condition1     8 1.0328e+10 5.0516e+11 22166
## - LandSlope      2 5.8980e+09 5.0073e+11 22168
## - MasVnrArea     1 7.6444e+09 5.0248e+11 22174
## - LotConfig      4 1.0508e+10 5.0534e+11 22174
## - BsmtUnfSF      1 8.6270e+09 5.0346e+11 22176
## - BsmtQual       3 1.1387e+10 5.0622e+11 22178
## - BsmtFinSF2     1 9.8751e+09 5.0471e+11 22179
## - ExterQual      3 1.2011e+10 5.0684e+11 22180
## - SaleCondition  5 1.5494e+10 5.1032e+11 22183
## - KitchenQual    3 1.4503e+10 5.0933e+11 22185
## - RoofMatl       6 1.9286e+10 5.1412e+11 22189
## - OverallCond    1 1.5072e+10 5.0990e+11 22190
## - LotArea        1 1.5150e+10 5.0998e+11 22190
## - OverallQual    1 1.7488e+10 5.1232e+11 22195
## - X1stFlrSF      1 1.8770e+10 5.1360e+11 22198
## - MiscFeature    3 2.0921e+10 5.1575e+11 22199
## - BsmtExposure   3 2.1932e+10 5.1676e+11 22201
## - BsmtFinSF1     1 2.1712e+10 5.1654e+11 22204
## - PoolArea       1 2.5265e+10 5.2010e+11 22212
## - PoolQC         3 3.0063e+10 5.2489e+11 22218
## - X2ndFlrSF      1 5.6012e+10 5.5084e+11 22275
## - Neighborhood  24 8.5011e+10 5.7984e+11 22285
## - Condition2     5 6.5657e+10 5.6049e+11 22286
## 
## Step:  AIC=22155.16
## SalePrice ~ MSSubClass + MSZoning + LotFrontage + LotArea + Street + 
##     Alley + LotShape + LandContour + LotConfig + LandSlope + 
##     Neighborhood + Condition1 + Condition2 + BldgType + OverallQual + 
##     OverallCond + YearBuilt + YearRemodAdd + RoofStyle + RoofMatl + 
##     Exterior1st + MasVnrType + MasVnrArea + ExterQual + Foundation + 
##     BsmtQual + BsmtExposure + BsmtFinType1 + BsmtFinSF1 + BsmtFinSF2 + 
##     BsmtUnfSF + CentralAir + X1stFlrSF + X2ndFlrSF + LowQualFinSF + 
##     BsmtFullBath + BsmtHalfBath + FullBath + HalfBath + BedroomAbvGr + 
##     KitchenAbvGr + KitchenQual + TotRmsAbvGrd + Functional + 
##     Fireplaces + GarageYrBlt + GarageFinish + GarageCars + GarageArea + 
##     GarageQual + GarageCond + PavedDrive + WoodDeckSF + OpenPorchSF + 
##     EnclosedPorch + X3SsnPorch + ScreenPorch + PoolArea + PoolQC + 
##     MiscFeature + MiscVal + MoSold + YrSold + SaleCondition
## 
##                 Df  Sum of Sq        RSS   AIC
## - PavedDrive     2 4.2442e+08 4.9974e+11 22152
## - Alley          2 8.3570e+08 5.0015e+11 22153
## - RoofStyle      4 2.7120e+09 5.0202e+11 22153
## - BsmtHalfBath   1 1.2421e+04 4.9931e+11 22153
## - LowQualFinSF   1 2.8228e+06 4.9932e+11 22153
## - OpenPorchSF    1 3.7413e+06 4.9932e+11 22153
## - MiscVal        1 7.6941e+06 4.9932e+11 22153
## - GarageYrBlt    1 2.4980e+07 4.9934e+11 22153
## - EnclosedPorch  1 2.9296e+07 4.9934e+11 22153
## - YrSold         1 3.6856e+07 4.9935e+11 22153
## - BsmtFullBath   1 1.8425e+08 4.9950e+11 22154
## - HalfBath       1 2.1589e+08 4.9953e+11 22154
## - LotShape       3 2.1392e+09 5.0145e+11 22154
## - GarageFinish   2 1.3300e+09 5.0064e+11 22154
## - BsmtFinType1   5 4.2224e+09 5.0354e+11 22154
## - TotRmsAbvGrd   1 6.6337e+08 4.9998e+11 22155
## - WoodDeckSF     1 7.4357e+08 5.0006e+11 22155
## - MoSold         1 7.5977e+08 5.0007e+11 22155
## <none>                        4.9931e+11 22155
## - CentralAir     1 9.3045e+08 5.0024e+11 22155
## - Fireplaces     1 1.1081e+09 5.0042e+11 22156
## - X3SsnPorch     1 1.1235e+09 5.0044e+11 22156
## - Exterior1st   13 1.2428e+10 5.1174e+11 22156
## - ScreenPorch    1 1.3390e+09 5.0065e+11 22156
## - GarageCars     1 1.5489e+09 5.0086e+11 22157
## - YearRemodAdd   1 1.5504e+09 5.0086e+11 22157
## - Foundation     4 4.4466e+09 5.0376e+11 22157
## - FullBath       1 1.7171e+09 5.0103e+11 22157
## - GarageCond     4 4.4952e+09 5.0381e+11 22157
## - LotFrontage    1 1.8858e+09 5.0120e+11 22157
## - MSSubClass     1 1.9834e+09 5.0130e+11 22158
## - GarageArea     1 2.0170e+09 5.0133e+11 22158
## - BldgType       4 5.2199e+09 5.0453e+11 22159
## - Functional     5 6.1545e+09 5.0547e+11 22159
## - BedroomAbvGr   1 2.7137e+09 5.0203e+11 22159
## - Street         1 2.7474e+09 5.0206e+11 22159
## - MasVnrType     3 5.1090e+09 5.0442e+11 22160
## - Condition1     8 9.7888e+09 5.0910e+11 22160
## - LandContour    3 5.2140e+09 5.0453e+11 22161
## - MSZoning       4 6.3353e+09 5.0565e+11 22161
## - GarageQual     4 6.7524e+09 5.0607e+11 22162
## - KitchenAbvGr   1 4.1079e+09 5.0342e+11 22162
## - LandSlope      2 5.3925e+09 5.0471e+11 22163
## - YearBuilt      1 4.9710e+09 5.0428e+11 22164
## - LotConfig      4 1.0630e+10 5.0994e+11 22170
## - BsmtUnfSF      1 7.9743e+09 5.0729e+11 22171
## - MasVnrArea     1 8.2930e+09 5.0761e+11 22171
## - BsmtFinSF2     1 9.0305e+09 5.0834e+11 22173
## - ExterQual      3 1.1765e+10 5.1108e+11 22175
## - BsmtQual       3 1.2163e+10 5.1148e+11 22176
## - SaleCondition  5 1.4998e+10 5.1431e+11 22178
## - KitchenQual    3 1.5602e+10 5.1491e+11 22183
## - LotArea        1 1.4918e+10 5.1423e+11 22185
## - RoofMatl       6 1.9791e+10 5.1910e+11 22186
## - OverallCond    1 1.5326e+10 5.1464e+11 22186
## - OverallQual    1 1.6261e+10 5.1557e+11 22188
## - MiscFeature    3 2.0441e+10 5.1975e+11 22193
## - BsmtFinSF1     1 2.1075e+10 5.2039e+11 22198
## - BsmtExposure   3 2.4022e+10 5.2333e+11 22201
## - X1stFlrSF      1 2.3531e+10 5.2284e+11 22204
## - PoolArea       1 2.4096e+10 5.2341e+11 22205
## - PoolQC         3 3.0154e+10 5.2947e+11 22213
## - Condition2     5 6.4434e+10 5.6375e+11 22278
## - Neighborhood  24 9.0103e+10 5.8942e+11 22289
## - X2ndFlrSF      1 6.7401e+10 5.6671e+11 22292
## 
## Step:  AIC=22152.09
## SalePrice ~ MSSubClass + MSZoning + LotFrontage + LotArea + Street + 
##     Alley + LotShape + LandContour + LotConfig + LandSlope + 
##     Neighborhood + Condition1 + Condition2 + BldgType + OverallQual + 
##     OverallCond + YearBuilt + YearRemodAdd + RoofStyle + RoofMatl + 
##     Exterior1st + MasVnrType + MasVnrArea + ExterQual + Foundation + 
##     BsmtQual + BsmtExposure + BsmtFinType1 + BsmtFinSF1 + BsmtFinSF2 + 
##     BsmtUnfSF + CentralAir + X1stFlrSF + X2ndFlrSF + LowQualFinSF + 
##     BsmtFullBath + BsmtHalfBath + FullBath + HalfBath + BedroomAbvGr + 
##     KitchenAbvGr + KitchenQual + TotRmsAbvGrd + Functional + 
##     Fireplaces + GarageYrBlt + GarageFinish + GarageCars + GarageArea + 
##     GarageQual + GarageCond + WoodDeckSF + OpenPorchSF + EnclosedPorch + 
##     X3SsnPorch + ScreenPorch + PoolArea + PoolQC + MiscFeature + 
##     MiscVal + MoSold + YrSold + SaleCondition
## 
##                 Df  Sum of Sq        RSS   AIC
## - Alley          2 8.5119e+08 5.0059e+11 22150
## - LowQualFinSF   1 2.8496e+06 4.9974e+11 22150
## - OpenPorchSF    1 3.7184e+06 4.9974e+11 22150
## - BsmtHalfBath   1 3.9581e+06 4.9974e+11 22150
## - MiscVal        1 4.4971e+06 4.9974e+11 22150
## - RoofStyle      4 2.7734e+09 5.0251e+11 22150
## - YrSold         1 3.2947e+07 4.9977e+11 22150
## - EnclosedPorch  1 3.8653e+07 4.9978e+11 22150
## - GarageYrBlt    1 4.3337e+07 4.9978e+11 22150
## - HalfBath       1 1.7092e+08 4.9991e+11 22151
## - BsmtFullBath   1 1.7215e+08 4.9991e+11 22151
## - LotShape       3 2.1134e+09 5.0185e+11 22151
## - GarageFinish   2 1.3635e+09 5.0110e+11 22151
## - BsmtFinType1   5 4.1824e+09 5.0392e+11 22151
## - TotRmsAbvGrd   1 7.1187e+08 5.0045e+11 22152
## - WoodDeckSF     1 7.6994e+08 5.0051e+11 22152
## - MoSold         1 7.8965e+08 5.0053e+11 22152
## <none>                        4.9974e+11 22152
## - CentralAir     1 9.2425e+08 5.0066e+11 22152
## - Fireplaces     1 9.8971e+08 5.0073e+11 22152
## - X3SsnPorch     1 1.1627e+09 5.0090e+11 22153
## - Exterior1st   13 1.2321e+10 5.1206e+11 22153
## - ScreenPorch    1 1.3785e+09 5.0112e+11 22153
## - YearRemodAdd   1 1.5526e+09 5.0129e+11 22154
## - GarageCond     4 4.4304e+09 5.0417e+11 22154
## - Foundation     4 4.4377e+09 5.0417e+11 22154
## - GarageCars     1 1.7243e+09 5.0146e+11 22154
## - FullBath       1 1.7277e+09 5.0146e+11 22154
## - LotFrontage    1 1.7875e+09 5.0152e+11 22154
## - MSSubClass     1 1.9224e+09 5.0166e+11 22154
## - GarageArea     1 1.9996e+09 5.0174e+11 22155
## - Functional     5 6.0206e+09 5.0576e+11 22155
## - BldgType       4 5.3875e+09 5.0512e+11 22156
## - Street         1 2.7406e+09 5.0248e+11 22156
## - BedroomAbvGr   1 2.8016e+09 5.0254e+11 22156
## - MasVnrType     3 5.0239e+09 5.0476e+11 22157
## - Condition1     8 9.7220e+09 5.0946e+11 22157
## - MSZoning       4 6.1730e+09 5.0591e+11 22158
## - LandContour    3 5.5218e+09 5.0526e+11 22158
## - GarageQual     4 6.5910e+09 5.0633e+11 22158
## - KitchenAbvGr   1 3.9487e+09 5.0369e+11 22159
## - LandSlope      2 5.3182e+09 5.0506e+11 22160
## - YearBuilt      1 5.4858e+09 5.0522e+11 22162
## - LotConfig      4 1.0585e+10 5.1032e+11 22167
## - BsmtUnfSF      1 8.0059e+09 5.0774e+11 22168
## - MasVnrArea     1 8.2583e+09 5.0800e+11 22168
## - BsmtFinSF2     1 9.1651e+09 5.0890e+11 22170
## - ExterQual      3 1.1654e+10 5.1139e+11 22171
## - BsmtQual       3 1.2333e+10 5.1207e+11 22173
## - SaleCondition  5 1.4865e+10 5.1460e+11 22174
## - KitchenQual    3 1.5677e+10 5.1541e+11 22180
## - LotArea        1 1.4908e+10 5.1465e+11 22182
## - RoofMatl       6 2.0060e+10 5.1980e+11 22183
## - OverallCond    1 1.5628e+10 5.1537e+11 22184
## - OverallQual    1 1.6375e+10 5.1611e+11 22185
## - MiscFeature    3 2.0282e+10 5.2002e+11 22190
## - BsmtFinSF1     1 2.1198e+10 5.2094e+11 22196
## - BsmtExposure   3 2.3897e+10 5.2363e+11 22197
## - X1stFlrSF      1 2.3397e+10 5.2313e+11 22200
## - PoolArea       1 2.3951e+10 5.2369e+11 22201
## - PoolQC         3 3.0007e+10 5.2974e+11 22210
## - Condition2     5 6.4485e+10 5.6422e+11 22275
## - Neighborhood  24 9.0417e+10 5.9015e+11 22286
## - X2ndFlrSF      1 6.7686e+10 5.6742e+11 22289
## 
## Step:  AIC=22149.95
## SalePrice ~ MSSubClass + MSZoning + LotFrontage + LotArea + Street + 
##     LotShape + LandContour + LotConfig + LandSlope + Neighborhood + 
##     Condition1 + Condition2 + BldgType + OverallQual + OverallCond + 
##     YearBuilt + YearRemodAdd + RoofStyle + RoofMatl + Exterior1st + 
##     MasVnrType + MasVnrArea + ExterQual + Foundation + BsmtQual + 
##     BsmtExposure + BsmtFinType1 + BsmtFinSF1 + BsmtFinSF2 + BsmtUnfSF + 
##     CentralAir + X1stFlrSF + X2ndFlrSF + LowQualFinSF + BsmtFullBath + 
##     BsmtHalfBath + FullBath + HalfBath + BedroomAbvGr + KitchenAbvGr + 
##     KitchenQual + TotRmsAbvGrd + Functional + Fireplaces + GarageYrBlt + 
##     GarageFinish + GarageCars + GarageArea + GarageQual + GarageCond + 
##     WoodDeckSF + OpenPorchSF + EnclosedPorch + X3SsnPorch + ScreenPorch + 
##     PoolArea + PoolQC + MiscFeature + MiscVal + MoSold + YrSold + 
##     SaleCondition
## 
##                 Df  Sum of Sq        RSS   AIC
## - RoofStyle      4 2.4789e+09 5.0307e+11 22147
## - BsmtHalfBath   1 3.7846e+06 5.0059e+11 22148
## - LowQualFinSF   1 4.5713e+06 5.0059e+11 22148
## - MiscVal        1 5.0709e+06 5.0059e+11 22148
## - EnclosedPorch  1 1.5892e+07 5.0060e+11 22148
## - OpenPorchSF    1 1.6493e+07 5.0060e+11 22148
## - GarageYrBlt    1 2.6725e+07 5.0062e+11 22148
## - YrSold         1 2.8120e+07 5.0062e+11 22148
## - HalfBath       1 1.4470e+08 5.0073e+11 22148
## - LotShape       3 1.9845e+09 5.0257e+11 22148
## - BsmtFullBath   1 1.6033e+08 5.0075e+11 22148
## - GarageFinish   2 1.2811e+09 5.0187e+11 22149
## - BsmtFinType1   5 4.3502e+09 5.0494e+11 22149
## - MoSold         1 6.9010e+08 5.0128e+11 22150
## - Exterior1st   13 1.1935e+10 5.1252e+11 22150
## - WoodDeckSF     1 8.4737e+08 5.0144e+11 22150
## - TotRmsAbvGrd   1 8.7955e+08 5.0147e+11 22150
## - CentralAir     1 8.8702e+08 5.0148e+11 22150
## <none>                        5.0059e+11 22150
## - Fireplaces     1 1.0229e+09 5.0161e+11 22150
## - X3SsnPorch     1 1.2043e+09 5.0179e+11 22151
## - ScreenPorch    1 1.3788e+09 5.0197e+11 22151
## - GarageCars     1 1.4855e+09 5.0207e+11 22151
## - YearRemodAdd   1 1.4914e+09 5.0208e+11 22151
## - FullBath       1 1.6145e+09 5.0220e+11 22152
## - Foundation     4 4.4814e+09 5.0507e+11 22152
## - MSSubClass     1 1.8358e+09 5.0242e+11 22152
## - GarageCond     4 4.6433e+09 5.0523e+11 22152
## - LotFrontage    1 2.0196e+09 5.0261e+11 22152
## - GarageArea     1 2.1801e+09 5.0277e+11 22153
## - Functional     5 6.1768e+09 5.0677e+11 22153
## - Street         1 2.5318e+09 5.0312e+11 22154
## - BedroomAbvGr   1 2.9296e+09 5.0352e+11 22154
## - MSZoning       4 5.7056e+09 5.0629e+11 22154
## - BldgType       4 5.8182e+09 5.0641e+11 22155
## - Condition1     8 9.6278e+09 5.1022e+11 22155
## - MasVnrType     3 5.0153e+09 5.0560e+11 22155
## - LandContour    3 5.5537e+09 5.0614e+11 22156
## - KitchenAbvGr   1 3.7352e+09 5.0432e+11 22156
## - GarageQual     4 6.6485e+09 5.0724e+11 22156
## - LandSlope      2 5.2114e+09 5.0580e+11 22157
## - YearBuilt      1 5.7252e+09 5.0631e+11 22160
## - MasVnrArea     1 7.7445e+09 5.0833e+11 22165
## - LotConfig      4 1.0665e+10 5.1125e+11 22165
## - BsmtUnfSF      1 8.0469e+09 5.0864e+11 22165
## - BsmtFinSF2     1 9.2682e+09 5.0986e+11 22168
## - ExterQual      3 1.1782e+10 5.1237e+11 22169
## - BsmtQual       3 1.2300e+10 5.1289e+11 22171
## - SaleCondition  5 1.5010e+10 5.1560e+11 22172
## - KitchenQual    3 1.5499e+10 5.1609e+11 22177
## - LotArea        1 1.4868e+10 5.1546e+11 22180
## - RoofMatl       6 1.9937e+10 5.2053e+11 22181
## - OverallCond    1 1.5630e+10 5.1622e+11 22182
## - OverallQual    1 1.6457e+10 5.1705e+11 22183
## - MiscFeature    3 2.0016e+10 5.2060e+11 22187
## - BsmtFinSF1     1 2.1214e+10 5.2180e+11 22193
## - BsmtExposure   3 2.3798e+10 5.2439e+11 22195
## - X1stFlrSF      1 2.3174e+10 5.2376e+11 22198
## - PoolArea       1 2.3688e+10 5.2428e+11 22199
## - PoolQC         3 2.9863e+10 5.3045e+11 22207
## - Condition2     5 6.4907e+10 5.6550e+11 22273
## - X2ndFlrSF      1 6.7410e+10 5.6800e+11 22286
## - Neighborhood  24 9.2611e+10 5.9320e+11 22288
## 
## Step:  AIC=22147.35
## SalePrice ~ MSSubClass + MSZoning + LotFrontage + LotArea + Street + 
##     LotShape + LandContour + LotConfig + LandSlope + Neighborhood + 
##     Condition1 + Condition2 + BldgType + OverallQual + OverallCond + 
##     YearBuilt + YearRemodAdd + RoofMatl + Exterior1st + MasVnrType + 
##     MasVnrArea + ExterQual + Foundation + BsmtQual + BsmtExposure + 
##     BsmtFinType1 + BsmtFinSF1 + BsmtFinSF2 + BsmtUnfSF + CentralAir + 
##     X1stFlrSF + X2ndFlrSF + LowQualFinSF + BsmtFullBath + BsmtHalfBath + 
##     FullBath + HalfBath + BedroomAbvGr + KitchenAbvGr + KitchenQual + 
##     TotRmsAbvGrd + Functional + Fireplaces + GarageYrBlt + GarageFinish + 
##     GarageCars + GarageArea + GarageQual + GarageCond + WoodDeckSF + 
##     OpenPorchSF + EnclosedPorch + X3SsnPorch + ScreenPorch + 
##     PoolArea + PoolQC + MiscFeature + MiscVal + MoSold + YrSold + 
##     SaleCondition
## 
##                 Df  Sum of Sq        RSS   AIC
## - LotShape       3 1.7465e+09 5.0481e+11 22145
## - LowQualFinSF   1 4.1765e+06 5.0307e+11 22145
## - BsmtHalfBath   1 1.2093e+07 5.0308e+11 22145
## - YrSold         1 1.7066e+07 5.0308e+11 22145
## - EnclosedPorch  1 2.2911e+07 5.0309e+11 22145
## - MiscVal        1 3.1518e+07 5.0310e+11 22145
## - OpenPorchSF    1 3.7155e+07 5.0310e+11 22145
## - GarageYrBlt    1 6.4492e+07 5.0313e+11 22146
## - BsmtFullBath   1 1.1346e+08 5.0318e+11 22146
## - HalfBath       1 1.9095e+08 5.0326e+11 22146
## - GarageFinish   2 1.1928e+09 5.0426e+11 22146
## - MoSold         1 5.4756e+08 5.0361e+11 22147
## - Exterior1st   13 1.1791e+10 5.1486e+11 22147
## - TotRmsAbvGrd   1 7.7305e+08 5.0384e+11 22147
## - WoodDeckSF     1 8.8077e+08 5.0395e+11 22147
## - CentralAir     1 9.0126e+08 5.0397e+11 22147
## <none>                        5.0307e+11 22147
## - Fireplaces     1 1.0473e+09 5.0411e+11 22148
## - BsmtFinType1   5 4.7929e+09 5.0786e+11 22148
## - X3SsnPorch     1 1.1345e+09 5.0420e+11 22148
## - ScreenPorch    1 1.1940e+09 5.0426e+11 22148
## - MSSubClass     1 1.4502e+09 5.0452e+11 22149
## - FullBath       1 1.4895e+09 5.0456e+11 22149
## - GarageCars     1 1.5052e+09 5.0457e+11 22149
## - YearRemodAdd   1 1.6360e+09 5.0470e+11 22149
## - LotFrontage    1 1.8252e+09 5.0489e+11 22149
## - Foundation     4 4.6207e+09 5.0769e+11 22149
## - GarageCond     4 4.8775e+09 5.0794e+11 22150
## - GarageArea     1 2.1214e+09 5.0519e+11 22150
## - Street         1 2.5604e+09 5.0563e+11 22151
## - Functional     5 6.2780e+09 5.0935e+11 22151
## - BedroomAbvGr   1 2.8120e+09 5.0588e+11 22152
## - BldgType       4 5.7358e+09 5.0880e+11 22152
## - MSZoning       4 5.7446e+09 5.0881e+11 22152
## - MasVnrType     3 4.8733e+09 5.0794e+11 22152
## - Condition1     8 9.6668e+09 5.1273e+11 22152
## - LandContour    3 5.4301e+09 5.0850e+11 22153
## - KitchenAbvGr   1 3.8154e+09 5.0688e+11 22154
## - GarageQual     4 7.0553e+09 5.1012e+11 22155
## - LandSlope      2 5.9874e+09 5.0905e+11 22156
## - YearBuilt      1 5.2239e+09 5.0829e+11 22157
## - MasVnrArea     1 7.6196e+09 5.1069e+11 22162
## - LotConfig      4 1.0703e+10 5.1377e+11 22162
## - BsmtUnfSF      1 8.4346e+09 5.1150e+11 22164
## - BsmtFinSF2     1 9.5878e+09 5.1266e+11 22166
## - ExterQual      3 1.1900e+10 5.1497e+11 22167
## - BsmtQual       3 1.2497e+10 5.1556e+11 22168
## - SaleCondition  5 1.5052e+10 5.1812e+11 22170
## - KitchenQual    3 1.5304e+10 5.1837e+11 22174
## - RoofMatl       6 1.9893e+10 5.2296e+11 22178
## - OverallCond    1 1.5268e+10 5.1834e+11 22178
## - OverallQual    1 1.5527e+10 5.1859e+11 22179
## - LotArea        1 1.5674e+10 5.1874e+11 22179
## - MiscFeature    3 2.0676e+10 5.2374e+11 22185
## - BsmtFinSF1     1 2.1616e+10 5.2468e+11 22191
## - BsmtExposure   3 2.3949e+10 5.2702e+11 22192
## - X1stFlrSF      1 2.3018e+10 5.2609e+11 22194
## - PoolArea       1 2.4239e+10 5.2731e+11 22197
## - PoolQC         3 3.0457e+10 5.3352e+11 22206
## - Condition2     5 6.4792e+10 5.6786e+11 22270
## - X2ndFlrSF      1 6.7755e+10 5.7082e+11 22284
## - Neighborhood  24 9.2641e+10 5.9571e+11 22284
## 
## Step:  AIC=22145.15
## SalePrice ~ MSSubClass + MSZoning + LotFrontage + LotArea + Street + 
##     LandContour + LotConfig + LandSlope + Neighborhood + Condition1 + 
##     Condition2 + BldgType + OverallQual + OverallCond + YearBuilt + 
##     YearRemodAdd + RoofMatl + Exterior1st + MasVnrType + MasVnrArea + 
##     ExterQual + Foundation + BsmtQual + BsmtExposure + BsmtFinType1 + 
##     BsmtFinSF1 + BsmtFinSF2 + BsmtUnfSF + CentralAir + X1stFlrSF + 
##     X2ndFlrSF + LowQualFinSF + BsmtFullBath + BsmtHalfBath + 
##     FullBath + HalfBath + BedroomAbvGr + KitchenAbvGr + KitchenQual + 
##     TotRmsAbvGrd + Functional + Fireplaces + GarageYrBlt + GarageFinish + 
##     GarageCars + GarageArea + GarageQual + GarageCond + WoodDeckSF + 
##     OpenPorchSF + EnclosedPorch + X3SsnPorch + ScreenPorch + 
##     PoolArea + PoolQC + MiscFeature + MiscVal + MoSold + YrSold + 
##     SaleCondition
## 
##                 Df  Sum of Sq        RSS   AIC
## - YrSold         1 3.5495e+06 5.0482e+11 22143
## - EnclosedPorch  1 7.3707e+06 5.0482e+11 22143
## - LowQualFinSF   1 9.2510e+06 5.0482e+11 22143
## - BsmtHalfBath   1 2.5597e+07 5.0484e+11 22143
## - MiscVal        1 2.8474e+07 5.0484e+11 22143
## - OpenPorchSF    1 5.2204e+07 5.0487e+11 22143
## - GarageYrBlt    1 7.6271e+07 5.0489e+11 22143
## - BsmtFullBath   1 1.0992e+08 5.0492e+11 22143
## - HalfBath       1 1.6434e+08 5.0498e+11 22144
## - GarageFinish   2 1.2254e+09 5.0604e+11 22144
## - MoSold         1 5.0732e+08 5.0532e+11 22144
## - Exterior1st   13 1.1723e+10 5.1654e+11 22144
## - WoodDeckSF     1 7.5360e+08 5.0557e+11 22145
## - TotRmsAbvGrd   1 7.8972e+08 5.0560e+11 22145
## - CentralAir     1 8.9832e+08 5.0571e+11 22145
## <none>                        5.0481e+11 22145
## - Fireplaces     1 1.0405e+09 5.0585e+11 22145
## - ScreenPorch    1 1.0644e+09 5.0588e+11 22146
## - X3SsnPorch     1 1.0949e+09 5.0591e+11 22146
## - BsmtFinType1   5 4.9707e+09 5.0978e+11 22146
## - FullBath       1 1.3805e+09 5.0619e+11 22146
## - MSSubClass     1 1.5287e+09 5.0634e+11 22147
## - GarageCars     1 1.5363e+09 5.0635e+11 22147
## - YearRemodAdd   1 1.9057e+09 5.0672e+11 22147
## - LotFrontage    1 1.9882e+09 5.0680e+11 22147
## - GarageArea     1 2.1128e+09 5.0693e+11 22148
## - Foundation     4 4.9441e+09 5.0976e+11 22148
## - Street         1 2.3973e+09 5.0721e+11 22148
## - Functional     5 6.3812e+09 5.1120e+11 22149
## - MasVnrType     3 4.5305e+09 5.0934e+11 22149
## - BedroomAbvGr   1 2.6762e+09 5.0749e+11 22149
## - BldgType       4 5.5907e+09 5.1040e+11 22149
## - GarageCond     4 5.6083e+09 5.1042e+11 22149
## - Condition1     8 9.3918e+09 5.1421e+11 22149
## - MSZoning       4 5.8158e+09 5.1063e+11 22150
## - LandContour    3 5.3465e+09 5.1016e+11 22151
## - KitchenAbvGr   1 4.0641e+09 5.0888e+11 22152
## - YearBuilt      1 5.2178e+09 5.1003e+11 22154
## - GarageQual     4 8.1243e+09 5.1294e+11 22155
## - LandSlope      2 6.4875e+09 5.1130e+11 22155
## - MasVnrArea     1 7.7254e+09 5.1254e+11 22160
## - LotConfig      4 1.1037e+10 5.1585e+11 22161
## - BsmtUnfSF      1 8.2977e+09 5.1311e+11 22161
## - BsmtFinSF2     1 9.9212e+09 5.1474e+11 22164
## - ExterQual      3 1.2222e+10 5.1704e+11 22165
## - BsmtQual       3 1.2496e+10 5.1731e+11 22166
## - SaleCondition  5 1.5107e+10 5.1992e+11 22167
## - KitchenQual    3 1.5339e+10 5.2015e+11 22172
## - RoofMatl       6 1.9358e+10 5.2417e+11 22174
## - OverallCond    1 1.4928e+10 5.1974e+11 22175
## - OverallQual    1 1.5260e+10 5.2007e+11 22176
## - MiscFeature    3 2.0478e+10 5.2529e+11 22183
## - LotArea        1 2.0472e+10 5.2529e+11 22187
## - BsmtExposure   3 2.3372e+10 5.2819e+11 22189
## - BsmtFinSF1     1 2.1694e+10 5.2651e+11 22189
## - X1stFlrSF      1 2.2865e+10 5.2768e+11 22192
## - PoolArea       1 2.4119e+10 5.2893e+11 22194
## - PoolQC         3 3.0129e+10 5.3494e+11 22203
## - Condition2     5 6.7018e+10 5.7183e+11 22272
## - Neighborhood  24 9.1952e+10 5.9677e+11 22280
## - X2ndFlrSF      1 6.7953e+10 5.7277e+11 22281
## 
## Step:  AIC=22143.15
## SalePrice ~ MSSubClass + MSZoning + LotFrontage + LotArea + Street + 
##     LandContour + LotConfig + LandSlope + Neighborhood + Condition1 + 
##     Condition2 + BldgType + OverallQual + OverallCond + YearBuilt + 
##     YearRemodAdd + RoofMatl + Exterior1st + MasVnrType + MasVnrArea + 
##     ExterQual + Foundation + BsmtQual + BsmtExposure + BsmtFinType1 + 
##     BsmtFinSF1 + BsmtFinSF2 + BsmtUnfSF + CentralAir + X1stFlrSF + 
##     X2ndFlrSF + LowQualFinSF + BsmtFullBath + BsmtHalfBath + 
##     FullBath + HalfBath + BedroomAbvGr + KitchenAbvGr + KitchenQual + 
##     TotRmsAbvGrd + Functional + Fireplaces + GarageYrBlt + GarageFinish + 
##     GarageCars + GarageArea + GarageQual + GarageCond + WoodDeckSF + 
##     OpenPorchSF + EnclosedPorch + X3SsnPorch + ScreenPorch + 
##     PoolArea + PoolQC + MiscFeature + MiscVal + MoSold + SaleCondition
## 
##                 Df  Sum of Sq        RSS   AIC
## - EnclosedPorch  1 7.3797e+06 5.0482e+11 22141
## - LowQualFinSF   1 9.0854e+06 5.0483e+11 22141
## - BsmtHalfBath   1 2.6465e+07 5.0484e+11 22141
## - MiscVal        1 2.8834e+07 5.0485e+11 22141
## - OpenPorchSF    1 5.0682e+07 5.0487e+11 22141
## - GarageYrBlt    1 7.6239e+07 5.0489e+11 22141
## - BsmtFullBath   1 1.0813e+08 5.0493e+11 22141
## - HalfBath       1 1.6355e+08 5.0498e+11 22142
## - GarageFinish   2 1.2241e+09 5.0604e+11 22142
## - MoSold         1 5.0614e+08 5.0532e+11 22142
## - Exterior1st   13 1.1720e+10 5.1654e+11 22142
## - WoodDeckSF     1 7.5273e+08 5.0557e+11 22143
## - TotRmsAbvGrd   1 7.9193e+08 5.0561e+11 22143
## - CentralAir     1 8.9931e+08 5.0572e+11 22143
## <none>                        5.0482e+11 22143
## - Fireplaces     1 1.0467e+09 5.0586e+11 22143
## - ScreenPorch    1 1.0619e+09 5.0588e+11 22144
## - X3SsnPorch     1 1.0939e+09 5.0591e+11 22144
## - BsmtFinType1   5 4.9720e+09 5.0979e+11 22144
## - FullBath       1 1.3776e+09 5.0619e+11 22144
## - MSSubClass     1 1.5339e+09 5.0635e+11 22145
## - GarageCars     1 1.5400e+09 5.0636e+11 22145
## - YearRemodAdd   1 1.9032e+09 5.0672e+11 22145
## - LotFrontage    1 1.9847e+09 5.0680e+11 22145
## - GarageArea     1 2.1137e+09 5.0693e+11 22146
## - Foundation     4 4.9680e+09 5.0979e+11 22146
## - Street         1 2.4065e+09 5.0722e+11 22146
## - Functional     5 6.3951e+09 5.1121e+11 22147
## - BedroomAbvGr   1 2.6731e+09 5.0749e+11 22147
## - MasVnrType     3 4.5642e+09 5.0938e+11 22147
## - BldgType       4 5.5874e+09 5.1040e+11 22147
## - GarageCond     4 5.6156e+09 5.1043e+11 22147
## - Condition1     8 9.4040e+09 5.1422e+11 22147
## - MSZoning       4 5.8123e+09 5.1063e+11 22148
## - LandContour    3 5.3453e+09 5.1016e+11 22149
## - KitchenAbvGr   1 4.0947e+09 5.0891e+11 22150
## - YearBuilt      1 5.2260e+09 5.1004e+11 22152
## - GarageQual     4 8.1310e+09 5.1295e+11 22153
## - LandSlope      2 6.4906e+09 5.1131e+11 22153
## - MasVnrArea     1 7.7444e+09 5.1256e+11 22158
## - LotConfig      4 1.1034e+10 5.1585e+11 22159
## - BsmtUnfSF      1 8.2978e+09 5.1312e+11 22159
## - BsmtFinSF2     1 9.9242e+09 5.1474e+11 22163
## - ExterQual      3 1.2263e+10 5.1708e+11 22163
## - BsmtQual       3 1.2493e+10 5.1731e+11 22164
## - SaleCondition  5 1.5542e+10 5.2036e+11 22166
## - KitchenQual    3 1.5336e+10 5.2015e+11 22170
## - RoofMatl       6 1.9435e+10 5.2425e+11 22173
## - OverallCond    1 1.4929e+10 5.1975e+11 22173
## - OverallQual    1 1.5258e+10 5.2008e+11 22174
## - MiscFeature    3 2.0488e+10 5.2531e+11 22181
## - LotArea        1 2.0474e+10 5.2529e+11 22185
## - BsmtExposure   3 2.3566e+10 5.2838e+11 22187
## - BsmtFinSF1     1 2.1691e+10 5.2651e+11 22187
## - X1stFlrSF      1 2.2928e+10 5.2775e+11 22190
## - PoolArea       1 2.4126e+10 5.2894e+11 22192
## - PoolQC         3 3.0134e+10 5.3495e+11 22201
## - Condition2     5 6.7024e+10 5.7184e+11 22270
## - Neighborhood  24 9.2038e+10 5.9685e+11 22278
## - X2ndFlrSF      1 6.8059e+10 5.7288e+11 22280
## 
## Step:  AIC=22141.17
## SalePrice ~ MSSubClass + MSZoning + LotFrontage + LotArea + Street + 
##     LandContour + LotConfig + LandSlope + Neighborhood + Condition1 + 
##     Condition2 + BldgType + OverallQual + OverallCond + YearBuilt + 
##     YearRemodAdd + RoofMatl + Exterior1st + MasVnrType + MasVnrArea + 
##     ExterQual + Foundation + BsmtQual + BsmtExposure + BsmtFinType1 + 
##     BsmtFinSF1 + BsmtFinSF2 + BsmtUnfSF + CentralAir + X1stFlrSF + 
##     X2ndFlrSF + LowQualFinSF + BsmtFullBath + BsmtHalfBath + 
##     FullBath + HalfBath + BedroomAbvGr + KitchenAbvGr + KitchenQual + 
##     TotRmsAbvGrd + Functional + Fireplaces + GarageYrBlt + GarageFinish + 
##     GarageCars + GarageArea + GarageQual + GarageCond + WoodDeckSF + 
##     OpenPorchSF + X3SsnPorch + ScreenPorch + PoolArea + PoolQC + 
##     MiscFeature + MiscVal + MoSold + SaleCondition
## 
##                 Df  Sum of Sq        RSS   AIC
## - LowQualFinSF   1 1.1143e+07 5.0484e+11 22139
## - BsmtHalfBath   1 2.6249e+07 5.0485e+11 22139
## - MiscVal        1 3.0177e+07 5.0485e+11 22139
## - OpenPorchSF    1 5.4133e+07 5.0488e+11 22139
## - GarageYrBlt    1 7.6281e+07 5.0490e+11 22139
## - BsmtFullBath   1 1.1163e+08 5.0494e+11 22139
## - HalfBath       1 1.6497e+08 5.0499e+11 22140
## - GarageFinish   2 1.2210e+09 5.0605e+11 22140
## - MoSold         1 5.1478e+08 5.0534e+11 22140
## - Exterior1st   13 1.1767e+10 5.1659e+11 22140
## - WoodDeckSF     1 7.4669e+08 5.0557e+11 22141
## - TotRmsAbvGrd   1 7.8496e+08 5.0561e+11 22141
## - CentralAir     1 9.0965e+08 5.0573e+11 22141
## <none>                        5.0482e+11 22141
## - Fireplaces     1 1.0514e+09 5.0588e+11 22141
## - ScreenPorch    1 1.0553e+09 5.0588e+11 22142
## - X3SsnPorch     1 1.0894e+09 5.0591e+11 22142
## - BsmtFinType1   5 4.9677e+09 5.0979e+11 22142
## - FullBath       1 1.3734e+09 5.0620e+11 22142
## - MSSubClass     1 1.5289e+09 5.0635e+11 22143
## - GarageCars     1 1.5363e+09 5.0636e+11 22143
## - YearRemodAdd   1 1.9083e+09 5.0673e+11 22143
## - LotFrontage    1 1.9928e+09 5.0682e+11 22144
## - GarageArea     1 2.1320e+09 5.0696e+11 22144
## - Foundation     4 4.9695e+09 5.0979e+11 22144
## - Street         1 2.4484e+09 5.0727e+11 22145
## - BedroomAbvGr   1 2.6657e+09 5.0749e+11 22145
## - Functional     5 6.4008e+09 5.1123e+11 22145
## - MasVnrType     3 4.5714e+09 5.0940e+11 22145
## - BldgType       4 5.5920e+09 5.1042e+11 22145
## - Condition1     8 9.3978e+09 5.1422e+11 22145
## - GarageCond     4 5.6593e+09 5.1048e+11 22145
## - MSZoning       4 5.8279e+09 5.1065e+11 22146
## - LandContour    3 5.3395e+09 5.1016e+11 22147
## - KitchenAbvGr   1 4.0953e+09 5.0892e+11 22148
## - YearBuilt      1 5.3125e+09 5.1014e+11 22151
## - GarageQual     4 8.1728e+09 5.1300e+11 22151
## - LandSlope      2 6.4916e+09 5.1132e+11 22151
## - MasVnrArea     1 7.7383e+09 5.1256e+11 22156
## - LotConfig      4 1.1036e+10 5.1586e+11 22157
## - BsmtUnfSF      1 8.3149e+09 5.1314e+11 22157
## - BsmtFinSF2     1 9.9633e+09 5.1479e+11 22161
## - ExterQual      3 1.2273e+10 5.1710e+11 22161
## - BsmtQual       3 1.2486e+10 5.1731e+11 22162
## - SaleCondition  5 1.5538e+10 5.2036e+11 22164
## - KitchenQual    3 1.5369e+10 5.2019e+11 22168
## - RoofMatl       6 1.9434e+10 5.2426e+11 22171
## - OverallCond    1 1.5073e+10 5.1990e+11 22171
## - OverallQual    1 1.5348e+10 5.2017e+11 22172
## - MiscFeature    3 2.1010e+10 5.2583e+11 22180
## - LotArea        1 2.0480e+10 5.2530e+11 22183
## - BsmtFinSF1     1 2.1697e+10 5.2652e+11 22185
## - BsmtExposure   3 2.3659e+10 5.2848e+11 22185
## - X1stFlrSF      1 2.2922e+10 5.2775e+11 22188
## - PoolArea       1 2.5092e+10 5.2992e+11 22192
## - PoolQC         3 3.0564e+10 5.3539e+11 22200
## - Condition2     5 6.7041e+10 5.7187e+11 22268
## - Neighborhood  24 9.2133e+10 5.9696e+11 22277
## - X2ndFlrSF      1 6.8119e+10 5.7294e+11 22278
## 
## Step:  AIC=22139.19
## SalePrice ~ MSSubClass + MSZoning + LotFrontage + LotArea + Street + 
##     LandContour + LotConfig + LandSlope + Neighborhood + Condition1 + 
##     Condition2 + BldgType + OverallQual + OverallCond + YearBuilt + 
##     YearRemodAdd + RoofMatl + Exterior1st + MasVnrType + MasVnrArea + 
##     ExterQual + Foundation + BsmtQual + BsmtExposure + BsmtFinType1 + 
##     BsmtFinSF1 + BsmtFinSF2 + BsmtUnfSF + CentralAir + X1stFlrSF + 
##     X2ndFlrSF + BsmtFullBath + BsmtHalfBath + FullBath + HalfBath + 
##     BedroomAbvGr + KitchenAbvGr + KitchenQual + TotRmsAbvGrd + 
##     Functional + Fireplaces + GarageYrBlt + GarageFinish + GarageCars + 
##     GarageArea + GarageQual + GarageCond + WoodDeckSF + OpenPorchSF + 
##     X3SsnPorch + ScreenPorch + PoolArea + PoolQC + MiscFeature + 
##     MiscVal + MoSold + SaleCondition
## 
##                 Df  Sum of Sq        RSS   AIC
## - BsmtHalfBath   1 2.6863e+07 5.0486e+11 22137
## - MiscVal        1 2.8200e+07 5.0486e+11 22137
## - OpenPorchSF    1 5.4556e+07 5.0489e+11 22137
## - GarageYrBlt    1 8.4111e+07 5.0492e+11 22137
## - BsmtFullBath   1 1.1248e+08 5.0495e+11 22137
## - HalfBath       1 1.6282e+08 5.0500e+11 22138
## - GarageFinish   2 1.2225e+09 5.0606e+11 22138
## - MoSold         1 5.1525e+08 5.0535e+11 22138
## - Exterior1st   13 1.1783e+10 5.1662e+11 22138
## - WoodDeckSF     1 7.4598e+08 5.0558e+11 22139
## - TotRmsAbvGrd   1 7.7385e+08 5.0561e+11 22139
## - CentralAir     1 9.0896e+08 5.0574e+11 22139
## <none>                        5.0484e+11 22139
## - Fireplaces     1 1.0474e+09 5.0588e+11 22140
## - ScreenPorch    1 1.0572e+09 5.0589e+11 22140
## - X3SsnPorch     1 1.0815e+09 5.0592e+11 22140
## - BsmtFinType1   5 4.9578e+09 5.0979e+11 22140
## - FullBath       1 1.3733e+09 5.0621e+11 22140
## - GarageCars     1 1.5378e+09 5.0637e+11 22141
## - MSSubClass     1 1.5522e+09 5.0639e+11 22141
## - YearRemodAdd   1 1.9171e+09 5.0675e+11 22141
## - LotFrontage    1 1.9961e+09 5.0683e+11 22142
## - GarageArea     1 2.1260e+09 5.0696e+11 22142
## - Foundation     4 4.9586e+09 5.0979e+11 22142
## - Street         1 2.4394e+09 5.0728e+11 22143
## - BedroomAbvGr   1 2.6896e+09 5.0753e+11 22143
## - MasVnrType     3 4.5722e+09 5.0941e+11 22143
## - Functional     5 6.4982e+09 5.1133e+11 22143
## - BldgType       4 5.6151e+09 5.1045e+11 22143
## - Condition1     8 9.3909e+09 5.1423e+11 22143
## - MSZoning       4 5.8188e+09 5.1065e+11 22144
## - GarageCond     4 6.1819e+09 5.1102e+11 22145
## - LandContour    3 5.3345e+09 5.1017e+11 22145
## - KitchenAbvGr   1 4.0847e+09 5.0892e+11 22146
## - YearBuilt      1 5.3578e+09 5.1019e+11 22149
## - LandSlope      2 6.4817e+09 5.1132e+11 22149
## - GarageQual     4 9.1839e+09 5.1402e+11 22151
## - MasVnrArea     1 7.7331e+09 5.1257e+11 22154
## - LotConfig      4 1.1034e+10 5.1587e+11 22155
## - BsmtUnfSF      1 8.3373e+09 5.1317e+11 22155
## - BsmtFinSF2     1 9.9701e+09 5.1481e+11 22159
## - ExterQual      3 1.2289e+10 5.1712e+11 22160
## - BsmtQual       3 1.2476e+10 5.1731e+11 22160
## - SaleCondition  5 1.5528e+10 5.2036e+11 22162
## - KitchenQual    3 1.5375e+10 5.2021e+11 22166
## - RoofMatl       6 1.9468e+10 5.2430e+11 22169
## - OverallCond    1 1.5068e+10 5.1990e+11 22169
## - OverallQual    1 1.5383e+10 5.2022e+11 22170
## - MiscFeature    3 2.1995e+10 5.2683e+11 22180
## - LotArea        1 2.0470e+10 5.2531e+11 22181
## - BsmtFinSF1     1 2.1721e+10 5.2656e+11 22183
## - BsmtExposure   3 2.3728e+10 5.2856e+11 22183
## - X1stFlrSF      1 2.2985e+10 5.2782e+11 22186
## - PoolArea       1 2.7054e+10 5.3189e+11 22194
## - PoolQC         3 3.1406e+10 5.3624e+11 22199
## - Condition2     5 6.7153e+10 5.7199e+11 22266
## - Neighborhood  24 9.2197e+10 5.9703e+11 22275
## - X2ndFlrSF      1 6.9862e+10 5.7470e+11 22279
## 
## Step:  AIC=22137.25
## SalePrice ~ MSSubClass + MSZoning + LotFrontage + LotArea + Street + 
##     LandContour + LotConfig + LandSlope + Neighborhood + Condition1 + 
##     Condition2 + BldgType + OverallQual + OverallCond + YearBuilt + 
##     YearRemodAdd + RoofMatl + Exterior1st + MasVnrType + MasVnrArea + 
##     ExterQual + Foundation + BsmtQual + BsmtExposure + BsmtFinType1 + 
##     BsmtFinSF1 + BsmtFinSF2 + BsmtUnfSF + CentralAir + X1stFlrSF + 
##     X2ndFlrSF + BsmtFullBath + FullBath + HalfBath + BedroomAbvGr + 
##     KitchenAbvGr + KitchenQual + TotRmsAbvGrd + Functional + 
##     Fireplaces + GarageYrBlt + GarageFinish + GarageCars + GarageArea + 
##     GarageQual + GarageCond + WoodDeckSF + OpenPorchSF + X3SsnPorch + 
##     ScreenPorch + PoolArea + PoolQC + MiscFeature + MiscVal + 
##     MoSold + SaleCondition
## 
##                 Df  Sum of Sq        RSS   AIC
## - MiscVal        1 3.0128e+07 5.0489e+11 22135
## - OpenPorchSF    1 5.5735e+07 5.0492e+11 22135
## - GarageYrBlt    1 8.7011e+07 5.0495e+11 22135
## - BsmtFullBath   1 8.9362e+07 5.0495e+11 22135
## - HalfBath       1 1.6088e+08 5.0502e+11 22136
## - GarageFinish   2 1.2157e+09 5.0608e+11 22136
## - MoSold         1 5.0625e+08 5.0537e+11 22136
## - Exterior1st   13 1.1848e+10 5.1671e+11 22137
## - WoodDeckSF     1 7.6087e+08 5.0562e+11 22137
## - TotRmsAbvGrd   1 7.6991e+08 5.0563e+11 22137
## - CentralAir     1 9.0536e+08 5.0577e+11 22137
## <none>                        5.0486e+11 22137
## - ScreenPorch    1 1.0452e+09 5.0591e+11 22138
## - Fireplaces     1 1.0568e+09 5.0592e+11 22138
## - X3SsnPorch     1 1.1141e+09 5.0598e+11 22138
## - BsmtFinType1   5 4.9783e+09 5.0984e+11 22138
## - FullBath       1 1.3465e+09 5.0621e+11 22138
## - GarageCars     1 1.5397e+09 5.0640e+11 22139
## - MSSubClass     1 1.5471e+09 5.0641e+11 22139
## - YearRemodAdd   1 1.9412e+09 5.0680e+11 22140
## - LotFrontage    1 1.9886e+09 5.0685e+11 22140
## - GarageArea     1 2.1358e+09 5.0700e+11 22140
## - Foundation     4 4.9709e+09 5.0983e+11 22140
## - Street         1 2.4382e+09 5.0730e+11 22141
## - BedroomAbvGr   1 2.6627e+09 5.0753e+11 22141
## - MasVnrType     3 4.5557e+09 5.0942e+11 22141
## - Functional     5 6.4730e+09 5.1134e+11 22141
## - BldgType       4 5.6027e+09 5.1047e+11 22141
## - Condition1     8 9.3927e+09 5.1426e+11 22141
## - MSZoning       4 5.7931e+09 5.1066e+11 22142
## - GarageCond     4 6.1728e+09 5.1104e+11 22143
## - LandContour    3 5.4476e+09 5.1031e+11 22143
## - KitchenAbvGr   1 4.0586e+09 5.0892e+11 22144
## - YearBuilt      1 5.3802e+09 5.1024e+11 22147
## - LandSlope      2 6.4559e+09 5.1132e+11 22147
## - GarageQual     4 9.1615e+09 5.1402e+11 22149
## - MasVnrArea     1 7.7238e+09 5.1259e+11 22152
## - LotConfig      4 1.1022e+10 5.1588e+11 22153
## - BsmtUnfSF      1 8.3170e+09 5.1318e+11 22153
## - BsmtFinSF2     1 1.0084e+10 5.1495e+11 22157
## - ExterQual      3 1.2299e+10 5.1716e+11 22158
## - BsmtQual       3 1.2592e+10 5.1745e+11 22158
## - SaleCondition  5 1.5513e+10 5.2038e+11 22160
## - KitchenQual    3 1.5370e+10 5.2023e+11 22164
## - RoofMatl       6 1.9521e+10 5.2438e+11 22167
## - OverallCond    1 1.5275e+10 5.2014e+11 22168
## - OverallQual    1 1.5360e+10 5.2022e+11 22168
## - MiscFeature    3 2.1996e+10 5.2686e+11 22178
## - LotArea        1 2.0457e+10 5.2532e+11 22179
## - BsmtFinSF1     1 2.1914e+10 5.2678e+11 22182
## - BsmtExposure   3 2.3856e+10 5.2872e+11 22182
## - X1stFlrSF      1 2.2979e+10 5.2784e+11 22184
## - PoolArea       1 2.7117e+10 5.3198e+11 22193
## - PoolQC         3 3.1397e+10 5.3626e+11 22197
## - Condition2     5 6.7130e+10 5.7199e+11 22264
## - Neighborhood  24 9.2248e+10 5.9711e+11 22273
## - X2ndFlrSF      1 6.9849e+10 5.7471e+11 22277
## 
## Step:  AIC=22135.32
## SalePrice ~ MSSubClass + MSZoning + LotFrontage + LotArea + Street + 
##     LandContour + LotConfig + LandSlope + Neighborhood + Condition1 + 
##     Condition2 + BldgType + OverallQual + OverallCond + YearBuilt + 
##     YearRemodAdd + RoofMatl + Exterior1st + MasVnrType + MasVnrArea + 
##     ExterQual + Foundation + BsmtQual + BsmtExposure + BsmtFinType1 + 
##     BsmtFinSF1 + BsmtFinSF2 + BsmtUnfSF + CentralAir + X1stFlrSF + 
##     X2ndFlrSF + BsmtFullBath + FullBath + HalfBath + BedroomAbvGr + 
##     KitchenAbvGr + KitchenQual + TotRmsAbvGrd + Functional + 
##     Fireplaces + GarageYrBlt + GarageFinish + GarageCars + GarageArea + 
##     GarageQual + GarageCond + WoodDeckSF + OpenPorchSF + X3SsnPorch + 
##     ScreenPorch + PoolArea + PoolQC + MiscFeature + MoSold + 
##     SaleCondition
## 
##                 Df  Sum of Sq        RSS   AIC
## - OpenPorchSF    1 5.4065e+07 5.0495e+11 22133
## - BsmtFullBath   1 8.6685e+07 5.0498e+11 22134
## - GarageYrBlt    1 8.8040e+07 5.0498e+11 22134
## - HalfBath       1 1.7112e+08 5.0506e+11 22134
## - GarageFinish   2 1.2275e+09 5.0612e+11 22134
## - MoSold         1 5.1374e+08 5.0541e+11 22134
## - Exterior1st   13 1.1823e+10 5.1672e+11 22135
## - WoodDeckSF     1 7.7395e+08 5.0567e+11 22135
## - TotRmsAbvGrd   1 7.8045e+08 5.0567e+11 22135
## - CentralAir     1 8.9557e+08 5.0579e+11 22135
## <none>                        5.0489e+11 22135
## - ScreenPorch    1 1.0245e+09 5.0592e+11 22136
## - Fireplaces     1 1.0296e+09 5.0592e+11 22136
## - X3SsnPorch     1 1.1133e+09 5.0601e+11 22136
## - BsmtFinType1   5 4.9660e+09 5.0986e+11 22136
## - FullBath       1 1.3585e+09 5.0625e+11 22136
## - MSSubClass     1 1.5435e+09 5.0644e+11 22137
## - GarageCars     1 1.5580e+09 5.0645e+11 22137
## - YearRemodAdd   1 1.9172e+09 5.0681e+11 22138
## - LotFrontage    1 1.9858e+09 5.0688e+11 22138
## - GarageArea     1 2.1278e+09 5.0702e+11 22138
## - Foundation     4 4.9424e+09 5.0984e+11 22138
## - Street         1 2.4125e+09 5.0731e+11 22139
## - BedroomAbvGr   1 2.6854e+09 5.0758e+11 22139
## - BldgType       4 5.6040e+09 5.1050e+11 22139
## - MasVnrType     3 4.6869e+09 5.0958e+11 22139
## - Functional     5 6.5618e+09 5.1145e+11 22139
## - Condition1     8 9.4554e+09 5.1435e+11 22140
## - MSZoning       4 5.7638e+09 5.1066e+11 22140
## - GarageCond     4 6.1753e+09 5.1107e+11 22141
## - LandContour    3 5.5051e+09 5.1040e+11 22141
## - KitchenAbvGr   1 4.0441e+09 5.0894e+11 22142
## - YearBuilt      1 5.4383e+09 5.1033e+11 22145
## - LandSlope      2 6.4822e+09 5.1138e+11 22145
## - GarageQual     4 9.2280e+09 5.1412e+11 22147
## - MasVnrArea     1 7.7654e+09 5.1266e+11 22150
## - LotConfig      4 1.1042e+10 5.1593e+11 22151
## - BsmtUnfSF      1 8.2894e+09 5.1318e+11 22151
## - BsmtFinSF2     1 1.0067e+10 5.1496e+11 22155
## - ExterQual      3 1.2301e+10 5.1719e+11 22156
## - BsmtQual       3 1.2606e+10 5.1750e+11 22156
## - SaleCondition  5 1.5498e+10 5.2039e+11 22158
## - KitchenQual    3 1.5454e+10 5.2035e+11 22162
## - RoofMatl       6 1.9545e+10 5.2444e+11 22165
## - OverallCond    1 1.5249e+10 5.2014e+11 22166
## - OverallQual    1 1.5391e+10 5.2028e+11 22166
## - LotArea        1 2.0507e+10 5.2540e+11 22177
## - MiscFeature    3 2.3153e+10 5.2805e+11 22178
## - BsmtFinSF1     1 2.1884e+10 5.2678e+11 22180
## - BsmtExposure   3 2.3849e+10 5.2874e+11 22180
## - X1stFlrSF      1 2.3109e+10 5.2800e+11 22182
## - PoolArea       1 2.7088e+10 5.3198e+11 22191
## - PoolQC         3 3.1371e+10 5.3626e+11 22195
## - Condition2     5 6.7115e+10 5.7201e+11 22262
## - Neighborhood  24 9.2243e+10 5.9714e+11 22271
## - X2ndFlrSF      1 6.9886e+10 5.7478e+11 22275
## 
## Step:  AIC=22133.43
## SalePrice ~ MSSubClass + MSZoning + LotFrontage + LotArea + Street + 
##     LandContour + LotConfig + LandSlope + Neighborhood + Condition1 + 
##     Condition2 + BldgType + OverallQual + OverallCond + YearBuilt + 
##     YearRemodAdd + RoofMatl + Exterior1st + MasVnrType + MasVnrArea + 
##     ExterQual + Foundation + BsmtQual + BsmtExposure + BsmtFinType1 + 
##     BsmtFinSF1 + BsmtFinSF2 + BsmtUnfSF + CentralAir + X1stFlrSF + 
##     X2ndFlrSF + BsmtFullBath + FullBath + HalfBath + BedroomAbvGr + 
##     KitchenAbvGr + KitchenQual + TotRmsAbvGrd + Functional + 
##     Fireplaces + GarageYrBlt + GarageFinish + GarageCars + GarageArea + 
##     GarageQual + GarageCond + WoodDeckSF + X3SsnPorch + ScreenPorch + 
##     PoolArea + PoolQC + MiscFeature + MoSold + SaleCondition
## 
##                 Df  Sum of Sq        RSS   AIC
## - BsmtFullBath   1 8.3760e+07 5.0503e+11 22132
## - GarageYrBlt    1 8.8128e+07 5.0504e+11 22132
## - HalfBath       1 1.6007e+08 5.0511e+11 22132
## - GarageFinish   2 1.2669e+09 5.0621e+11 22132
## - MoSold         1 5.6323e+08 5.0551e+11 22133
## - Exterior1st   13 1.1799e+10 5.1675e+11 22133
## - TotRmsAbvGrd   1 7.7192e+08 5.0572e+11 22133
## - WoodDeckSF     1 8.0266e+08 5.0575e+11 22133
## <none>                        5.0495e+11 22133
## - CentralAir     1 9.4959e+08 5.0590e+11 22134
## - Fireplaces     1 9.9522e+08 5.0594e+11 22134
## - ScreenPorch    1 9.9956e+08 5.0595e+11 22134
## - X3SsnPorch     1 1.1246e+09 5.0607e+11 22134
## - BsmtFinType1   5 4.9294e+09 5.0988e+11 22134
## - FullBath       1 1.3707e+09 5.0632e+11 22134
## - MSSubClass     1 1.5525e+09 5.0650e+11 22135
## - GarageCars     1 1.5925e+09 5.0654e+11 22135
## - YearRemodAdd   1 1.9084e+09 5.0686e+11 22136
## - LotFrontage    1 1.9610e+09 5.0691e+11 22136
## - GarageArea     1 2.1078e+09 5.0705e+11 22136
## - Foundation     4 4.9222e+09 5.0987e+11 22136
## - Street         1 2.4690e+09 5.0742e+11 22137
## - BedroomAbvGr   1 2.6637e+09 5.0761e+11 22137
## - Functional     5 6.5575e+09 5.1150e+11 22138
## - BldgType       4 5.6238e+09 5.1057e+11 22138
## - MasVnrType     3 4.7454e+09 5.0969e+11 22138
## - Condition1     8 9.4365e+09 5.1438e+11 22138
## - MSZoning       4 5.7123e+09 5.1066e+11 22138
## - GarageCond     4 6.1233e+09 5.1107e+11 22139
## - LandContour    3 5.5181e+09 5.1047e+11 22139
## - KitchenAbvGr   1 4.0497e+09 5.0900e+11 22140
## - YearBuilt      1 5.4056e+09 5.1035e+11 22143
## - LandSlope      2 6.4332e+09 5.1138e+11 22143
## - GarageQual     4 9.1744e+09 5.1412e+11 22145
## - MasVnrArea     1 8.0225e+09 5.1297e+11 22149
## - LotConfig      4 1.1054e+10 5.1600e+11 22149
## - BsmtUnfSF      1 8.2663e+09 5.1321e+11 22149
## - BsmtFinSF2     1 1.0043e+10 5.1499e+11 22153
## - ExterQual      3 1.2327e+10 5.1727e+11 22154
## - BsmtQual       3 1.2554e+10 5.1750e+11 22154
## - SaleCondition  5 1.5512e+10 5.2046e+11 22157
## - KitchenQual    3 1.5463e+10 5.2041e+11 22160
## - RoofMatl       6 1.9647e+10 5.2459e+11 22163
## - OverallCond    1 1.5202e+10 5.2015e+11 22164
## - OverallQual    1 1.5615e+10 5.2056e+11 22165
## - LotArea        1 2.0499e+10 5.2545e+11 22175
## - MiscFeature    3 2.3215e+10 5.2816e+11 22177
## - BsmtExposure   3 2.3796e+10 5.2874e+11 22178
## - BsmtFinSF1     1 2.1911e+10 5.2686e+11 22178
## - X1stFlrSF      1 2.3184e+10 5.2813e+11 22181
## - PoolArea       1 2.7183e+10 5.3213e+11 22189
## - PoolQC         3 3.1494e+10 5.3644e+11 22194
## - Condition2     5 6.7076e+10 5.7202e+11 22260
## - Neighborhood  24 9.2713e+10 5.9766e+11 22270
## - X2ndFlrSF      1 7.0015e+10 5.7496e+11 22274
## 
## Step:  AIC=22131.62
## SalePrice ~ MSSubClass + MSZoning + LotFrontage + LotArea + Street + 
##     LandContour + LotConfig + LandSlope + Neighborhood + Condition1 + 
##     Condition2 + BldgType + OverallQual + OverallCond + YearBuilt + 
##     YearRemodAdd + RoofMatl + Exterior1st + MasVnrType + MasVnrArea + 
##     ExterQual + Foundation + BsmtQual + BsmtExposure + BsmtFinType1 + 
##     BsmtFinSF1 + BsmtFinSF2 + BsmtUnfSF + CentralAir + X1stFlrSF + 
##     X2ndFlrSF + FullBath + HalfBath + BedroomAbvGr + KitchenAbvGr + 
##     KitchenQual + TotRmsAbvGrd + Functional + Fireplaces + GarageYrBlt + 
##     GarageFinish + GarageCars + GarageArea + GarageQual + GarageCond + 
##     WoodDeckSF + X3SsnPorch + ScreenPorch + PoolArea + PoolQC + 
##     MiscFeature + MoSold + SaleCondition
## 
##                 Df  Sum of Sq        RSS   AIC
## - GarageYrBlt    1 9.4371e+07 5.0513e+11 22130
## - HalfBath       1 1.5142e+08 5.0518e+11 22130
## - GarageFinish   2 1.2388e+09 5.0627e+11 22130
## - MoSold         1 5.6985e+08 5.0560e+11 22131
## - Exterior1st   13 1.1836e+10 5.1687e+11 22131
## - TotRmsAbvGrd   1 7.8982e+08 5.0582e+11 22131
## - WoodDeckSF     1 8.0223e+08 5.0583e+11 22131
## <none>                        5.0503e+11 22132
## - CentralAir     1 9.7311e+08 5.0600e+11 22132
## - ScreenPorch    1 9.8661e+08 5.0602e+11 22132
## - Fireplaces     1 1.0065e+09 5.0604e+11 22132
## - X3SsnPorch     1 1.1145e+09 5.0615e+11 22132
## - FullBath       1 1.3092e+09 5.0634e+11 22132
## - MSSubClass     1 1.5466e+09 5.0658e+11 22133
## - GarageCars     1 1.5866e+09 5.0662e+11 22133
## - BsmtFinType1   5 5.4577e+09 5.1049e+11 22133
## - YearRemodAdd   1 1.9296e+09 5.0696e+11 22134
## - LotFrontage    1 1.9539e+09 5.0698e+11 22134
## - Foundation     4 4.9445e+09 5.0998e+11 22134
## - GarageArea     1 2.1728e+09 5.0720e+11 22134
## - Street         1 2.4587e+09 5.0749e+11 22135
## - BedroomAbvGr   1 2.6393e+09 5.0767e+11 22135
## - Functional     5 6.5184e+09 5.1155e+11 22136
## - BldgType       4 5.6002e+09 5.1063e+11 22136
## - Condition1     8 9.3712e+09 5.1440e+11 22136
## - MasVnrType     3 4.7291e+09 5.0976e+11 22136
## - MSZoning       4 5.7878e+09 5.1082e+11 22136
## - GarageCond     4 6.1601e+09 5.1119e+11 22137
## - LandContour    3 5.5585e+09 5.1059e+11 22138
## - KitchenAbvGr   1 4.0886e+09 5.0912e+11 22138
## - YearBuilt      1 5.3957e+09 5.1043e+11 22141
## - LandSlope      2 6.4300e+09 5.1146e+11 22142
## - GarageQual     4 9.1616e+09 5.1419e+11 22143
## - MasVnrArea     1 7.9593e+09 5.1299e+11 22147
## - LotConfig      4 1.1058e+10 5.1609e+11 22147
## - BsmtUnfSF      1 8.2455e+09 5.1328e+11 22147
## - ExterQual      3 1.2270e+10 5.1730e+11 22152
## - BsmtQual       3 1.2534e+10 5.1756e+11 22152
## - BsmtFinSF2     1 1.0933e+10 5.1596e+11 22153
## - SaleCondition  5 1.5560e+10 5.2059e+11 22155
## - KitchenQual    3 1.5505e+10 5.2054e+11 22159
## - RoofMatl       6 1.9675e+10 5.2471e+11 22161
## - OverallCond    1 1.5121e+10 5.2015e+11 22162
## - OverallQual    1 1.5570e+10 5.2060e+11 22163
## - LotArea        1 2.0751e+10 5.2578e+11 22174
## - MiscFeature    3 2.3250e+10 5.2828e+11 22175
## - BsmtExposure   3 2.3776e+10 5.2881e+11 22176
## - X1stFlrSF      1 2.3116e+10 5.2815e+11 22179
## - BsmtFinSF1     1 2.3708e+10 5.2874e+11 22180
## - PoolArea       1 2.7184e+10 5.3221e+11 22187
## - PoolQC         3 3.1434e+10 5.3646e+11 22192
## - Condition2     5 6.7290e+10 5.7232e+11 22259
## - Neighborhood  24 9.2630e+10 5.9766e+11 22268
## - X2ndFlrSF      1 6.9934e+10 5.7496e+11 22272
## 
## Step:  AIC=22129.82
## SalePrice ~ MSSubClass + MSZoning + LotFrontage + LotArea + Street + 
##     LandContour + LotConfig + LandSlope + Neighborhood + Condition1 + 
##     Condition2 + BldgType + OverallQual + OverallCond + YearBuilt + 
##     YearRemodAdd + RoofMatl + Exterior1st + MasVnrType + MasVnrArea + 
##     ExterQual + Foundation + BsmtQual + BsmtExposure + BsmtFinType1 + 
##     BsmtFinSF1 + BsmtFinSF2 + BsmtUnfSF + CentralAir + X1stFlrSF + 
##     X2ndFlrSF + FullBath + HalfBath + BedroomAbvGr + KitchenAbvGr + 
##     KitchenQual + TotRmsAbvGrd + Functional + Fireplaces + GarageFinish + 
##     GarageCars + GarageArea + GarageQual + GarageCond + WoodDeckSF + 
##     X3SsnPorch + ScreenPorch + PoolArea + PoolQC + MiscFeature + 
##     MoSold + SaleCondition
## 
##                 Df  Sum of Sq        RSS   AIC
## - HalfBath       1 1.5811e+08 5.0528e+11 22128
## - GarageFinish   2 1.2119e+09 5.0634e+11 22128
## - MoSold         1 5.6335e+08 5.0569e+11 22129
## - Exterior1st   13 1.1946e+10 5.1707e+11 22129
## - WoodDeckSF     1 7.6490e+08 5.0589e+11 22130
## - TotRmsAbvGrd   1 7.7719e+08 5.0590e+11 22130
## - CentralAir     1 9.0452e+08 5.0603e+11 22130
## <none>                        5.0513e+11 22130
## - ScreenPorch    1 1.0004e+09 5.0613e+11 22130
## - Fireplaces     1 1.0986e+09 5.0622e+11 22130
## - X3SsnPorch     1 1.1054e+09 5.0623e+11 22130
## - FullBath       1 1.3007e+09 5.0643e+11 22131
## - MSSubClass     1 1.5450e+09 5.0667e+11 22131
## - GarageCars     1 1.5882e+09 5.0671e+11 22131
## - BsmtFinType1   5 5.4386e+09 5.1056e+11 22132
## - YearRemodAdd   1 1.8424e+09 5.0697e+11 22132
## - LotFrontage    1 2.0503e+09 5.0718e+11 22132
## - GarageArea     1 2.0909e+09 5.0722e+11 22132
## - Foundation     4 4.9159e+09 5.1004e+11 22132
## - Street         1 2.4225e+09 5.0755e+11 22133
## - BedroomAbvGr   1 2.6442e+09 5.0777e+11 22134
## - Functional     5 6.4597e+09 5.1158e+11 22134
## - Condition1     8 9.3334e+09 5.1446e+11 22134
## - BldgType       4 5.5893e+09 5.1071e+11 22134
## - MasVnrType     3 4.7117e+09 5.0984e+11 22134
## - MSZoning       4 5.8363e+09 5.1096e+11 22134
## - GarageCond     4 6.0787e+09 5.1120e+11 22135
## - LandContour    3 5.6902e+09 5.1082e+11 22136
## - KitchenAbvGr   1 4.0831e+09 5.0921e+11 22137
## - YearBuilt      1 5.3229e+09 5.1045e+11 22139
## - LandSlope      2 6.5139e+09 5.1164e+11 22140
## - GarageQual     4 9.1094e+09 5.1423e+11 22141
## - MasVnrArea     1 7.9765e+09 5.1310e+11 22145
## - LotConfig      4 1.1014e+10 5.1614e+11 22145
## - BsmtUnfSF      1 8.3863e+09 5.1351e+11 22146
## - ExterQual      3 1.2213e+10 5.1734e+11 22150
## - BsmtQual       3 1.2500e+10 5.1762e+11 22151
## - BsmtFinSF2     1 1.0996e+10 5.1612e+11 22151
## - SaleCondition  5 1.5539e+10 5.2066e+11 22153
## - KitchenQual    3 1.5509e+10 5.2063e+11 22157
## - RoofMatl       6 1.9935e+10 5.2506e+11 22160
## - OverallQual    1 1.5686e+10 5.2081e+11 22161
## - OverallCond    1 1.5904e+10 5.2103e+11 22162
## - LotArea        1 2.1002e+10 5.2613e+11 22172
## - MiscFeature    3 2.3243e+10 5.2837e+11 22173
## - BsmtExposure   3 2.3771e+10 5.2890e+11 22174
## - X1stFlrSF      1 2.3109e+10 5.2823e+11 22177
## - BsmtFinSF1     1 2.4098e+10 5.2922e+11 22179
## - PoolArea       1 2.7175e+10 5.3230e+11 22185
## - PoolQC         3 3.1369e+10 5.3649e+11 22190
## - Condition2     5 6.7272e+10 5.7240e+11 22257
## - Neighborhood  24 9.3394e+10 5.9852e+11 22267
## - X2ndFlrSF      1 7.0127e+10 5.7525e+11 22270
## 
## Step:  AIC=22128.16
## SalePrice ~ MSSubClass + MSZoning + LotFrontage + LotArea + Street + 
##     LandContour + LotConfig + LandSlope + Neighborhood + Condition1 + 
##     Condition2 + BldgType + OverallQual + OverallCond + YearBuilt + 
##     YearRemodAdd + RoofMatl + Exterior1st + MasVnrType + MasVnrArea + 
##     ExterQual + Foundation + BsmtQual + BsmtExposure + BsmtFinType1 + 
##     BsmtFinSF1 + BsmtFinSF2 + BsmtUnfSF + CentralAir + X1stFlrSF + 
##     X2ndFlrSF + FullBath + BedroomAbvGr + KitchenAbvGr + KitchenQual + 
##     TotRmsAbvGrd + Functional + Fireplaces + GarageFinish + GarageCars + 
##     GarageArea + GarageQual + GarageCond + WoodDeckSF + X3SsnPorch + 
##     ScreenPorch + PoolArea + PoolQC + MiscFeature + MoSold + 
##     SaleCondition
## 
##                 Df  Sum of Sq        RSS   AIC
## - GarageFinish   2 1.1527e+09 5.0644e+11 22127
## - MoSold         1 5.7624e+08 5.0586e+11 22127
## - Exterior1st   13 1.1959e+10 5.1724e+11 22128
## - WoodDeckSF     1 7.5984e+08 5.0604e+11 22128
## - TotRmsAbvGrd   1 8.0969e+08 5.0609e+11 22128
## <none>                        5.0528e+11 22128
## - CentralAir     1 9.3141e+08 5.0621e+11 22128
## - ScreenPorch    1 1.0482e+09 5.0633e+11 22128
## - Fireplaces     1 1.1305e+09 5.0641e+11 22129
## - X3SsnPorch     1 1.1337e+09 5.0642e+11 22129
## - FullBath       1 1.1541e+09 5.0644e+11 22129
## - MSSubClass     1 1.4857e+09 5.0677e+11 22129
## - BsmtFinType1   5 5.3359e+09 5.1062e+11 22130
## - GarageCars     1 1.6735e+09 5.0696e+11 22130
## - YearRemodAdd   1 1.8956e+09 5.0718e+11 22130
## - GarageArea     1 2.0376e+09 5.0732e+11 22131
## - LotFrontage    1 2.0410e+09 5.0732e+11 22131
## - Foundation     4 4.9208e+09 5.1020e+11 22131
## - Street         1 2.4116e+09 5.0769e+11 22131
## - BedroomAbvGr   1 2.6680e+09 5.0795e+11 22132
## - Condition1     8 9.2400e+09 5.1452e+11 22132
## - BldgType       4 5.5326e+09 5.1082e+11 22132
## - MasVnrType     3 4.6180e+09 5.0990e+11 22132
## - Functional     5 6.4865e+09 5.1177e+11 22132
## - MSZoning       4 6.0163e+09 5.1130e+11 22133
## - GarageCond     4 6.0641e+09 5.1135e+11 22133
## - LandContour    3 5.7140e+09 5.1100e+11 22135
## - KitchenAbvGr   1 4.0504e+09 5.0933e+11 22135
## - LandSlope      2 6.4697e+09 5.1175e+11 22138
## - YearBuilt      1 5.8692e+09 5.1115e+11 22139
## - GarageQual     4 9.0808e+09 5.1436e+11 22140
## - MasVnrArea     1 7.9540e+09 5.1324e+11 22143
## - LotConfig      4 1.0944e+10 5.1623e+11 22144
## - BsmtUnfSF      1 8.3807e+09 5.1366e+11 22144
## - ExterQual      3 1.2244e+10 5.1753e+11 22148
## - BsmtQual       3 1.2484e+10 5.1777e+11 22149
## - BsmtFinSF2     1 1.1110e+10 5.1639e+11 22150
## - SaleCondition  5 1.5806e+10 5.2109e+11 22152
## - KitchenQual    3 1.5636e+10 5.2092e+11 22156
## - RoofMatl       6 2.0107e+10 5.2539e+11 22159
## - OverallQual    1 1.5593e+10 5.2088e+11 22159
## - OverallCond    1 1.5798e+10 5.2108e+11 22160
## - LotArea        1 2.0938e+10 5.2622e+11 22171
## - MiscFeature    3 2.3189e+10 5.2847e+11 22171
## - BsmtExposure   3 2.3620e+10 5.2890e+11 22172
## - X1stFlrSF      1 2.3299e+10 5.2858e+11 22176
## - BsmtFinSF1     1 2.4214e+10 5.2950e+11 22177
## - PoolArea       1 2.7196e+10 5.3248e+11 22184
## - PoolQC         3 3.1302e+10 5.3659e+11 22188
## - Condition2     5 6.7572e+10 5.7286e+11 22256
## - Neighborhood  24 9.3354e+10 5.9864e+11 22266
## - X2ndFlrSF      1 8.8909e+10 5.9419e+11 22304
## 
## Step:  AIC=22126.66
## SalePrice ~ MSSubClass + MSZoning + LotFrontage + LotArea + Street + 
##     LandContour + LotConfig + LandSlope + Neighborhood + Condition1 + 
##     Condition2 + BldgType + OverallQual + OverallCond + YearBuilt + 
##     YearRemodAdd + RoofMatl + Exterior1st + MasVnrType + MasVnrArea + 
##     ExterQual + Foundation + BsmtQual + BsmtExposure + BsmtFinType1 + 
##     BsmtFinSF1 + BsmtFinSF2 + BsmtUnfSF + CentralAir + X1stFlrSF + 
##     X2ndFlrSF + FullBath + BedroomAbvGr + KitchenAbvGr + KitchenQual + 
##     TotRmsAbvGrd + Functional + Fireplaces + GarageCars + GarageArea + 
##     GarageQual + GarageCond + WoodDeckSF + X3SsnPorch + ScreenPorch + 
##     PoolArea + PoolQC + MiscFeature + MoSold + SaleCondition
## 
##                 Df  Sum of Sq        RSS   AIC
## - MoSold         1 5.1452e+08 5.0695e+11 22126
## - WoodDeckSF     1 6.8819e+08 5.0712e+11 22126
## - TotRmsAbvGrd   1 8.2249e+08 5.0726e+11 22126
## - CentralAir     1 8.6271e+08 5.0730e+11 22127
## - FullBath       1 9.0240e+08 5.0734e+11 22127
## <none>                        5.0644e+11 22127
## - Exterior1st   13 1.2198e+10 5.1863e+11 22127
## - X3SsnPorch     1 9.9920e+08 5.0744e+11 22127
## - ScreenPorch    1 1.0102e+09 5.0745e+11 22127
## - Fireplaces     1 1.1814e+09 5.0762e+11 22127
## - MSSubClass     1 1.6585e+09 5.0809e+11 22128
## - GarageArea     1 1.7678e+09 5.0820e+11 22129
## - BsmtFinType1   5 5.5120e+09 5.1195e+11 22129
## - LotFrontage    1 1.8056e+09 5.0824e+11 22129
## - YearRemodAdd   1 1.8853e+09 5.0832e+11 22129
## - GarageCars     1 1.9357e+09 5.0837e+11 22129
## - Foundation     4 4.7952e+09 5.1123e+11 22129
## - Functional     5 6.1603e+09 5.1260e+11 22130
## - Street         1 2.4844e+09 5.0892e+11 22130
## - BedroomAbvGr   1 2.4917e+09 5.0893e+11 22130
## - BldgType       4 5.4448e+09 5.1188e+11 22130
## - Condition1     8 9.2415e+09 5.1568e+11 22130
## - MasVnrType     3 4.9021e+09 5.1134e+11 22131
## - GarageCond     4 6.0122e+09 5.1245e+11 22132
## - MSZoning       4 6.2490e+09 5.1268e+11 22132
## - LandContour    3 5.6500e+09 5.1209e+11 22133
## - KitchenAbvGr   1 4.0570e+09 5.1049e+11 22133
## - LandSlope      2 6.4116e+09 5.1285e+11 22136
## - YearBuilt      1 5.5686e+09 5.1200e+11 22137
## - GarageQual     4 9.0165e+09 5.1545e+11 22138
## - LotConfig      4 1.1015e+10 5.1745e+11 22142
## - MasVnrArea     1 8.2320e+09 5.1467e+11 22142
## - BsmtUnfSF      1 8.5381e+09 5.1497e+11 22143
## - ExterQual      3 1.2624e+10 5.1906e+11 22148
## - BsmtQual       3 1.2841e+10 5.1928e+11 22148
## - BsmtFinSF2     1 1.1346e+10 5.1778e+11 22149
## - SaleCondition  5 1.5563e+10 5.2200e+11 22150
## - KitchenQual    3 1.6706e+10 5.2314e+11 22156
## - RoofMatl       6 2.0087e+10 5.2652e+11 22157
## - OverallQual    1 1.5448e+10 5.2188e+11 22158
## - OverallCond    1 1.6249e+10 5.2268e+11 22159
## - LotArea        1 2.0766e+10 5.2720e+11 22169
## - MiscFeature    3 2.2856e+10 5.2929e+11 22169
## - BsmtExposure   3 2.3491e+10 5.2993e+11 22170
## - X1stFlrSF      1 2.2992e+10 5.2943e+11 22173
## - BsmtFinSF1     1 2.4422e+10 5.3086e+11 22176
## - PoolArea       1 2.6844e+10 5.3328e+11 22181
## - PoolQC         3 3.1226e+10 5.3766e+11 22186
## - Condition2     5 6.7187e+10 5.7362e+11 22253
## - Neighborhood  24 9.4273e+10 6.0071e+11 22265
## - X2ndFlrSF      1 8.8976e+10 5.9541e+11 22302
## 
## Step:  AIC=22125.77
## SalePrice ~ MSSubClass + MSZoning + LotFrontage + LotArea + Street + 
##     LandContour + LotConfig + LandSlope + Neighborhood + Condition1 + 
##     Condition2 + BldgType + OverallQual + OverallCond + YearBuilt + 
##     YearRemodAdd + RoofMatl + Exterior1st + MasVnrType + MasVnrArea + 
##     ExterQual + Foundation + BsmtQual + BsmtExposure + BsmtFinType1 + 
##     BsmtFinSF1 + BsmtFinSF2 + BsmtUnfSF + CentralAir + X1stFlrSF + 
##     X2ndFlrSF + FullBath + BedroomAbvGr + KitchenAbvGr + KitchenQual + 
##     TotRmsAbvGrd + Functional + Fireplaces + GarageCars + GarageArea + 
##     GarageQual + GarageCond + WoodDeckSF + X3SsnPorch + ScreenPorch + 
##     PoolArea + PoolQC + MiscFeature + SaleCondition
## 
##                 Df  Sum of Sq        RSS   AIC
## - WoodDeckSF     1 6.3169e+08 5.0758e+11 22125
## - FullBath       1 8.2967e+08 5.0778e+11 22126
## - CentralAir     1 9.0414e+08 5.0785e+11 22126
## - TotRmsAbvGrd   1 9.1019e+08 5.0786e+11 22126
## - Exterior1st   13 1.2182e+10 5.1913e+11 22126
## <none>                        5.0695e+11 22126
## - X3SsnPorch     1 9.8153e+08 5.0793e+11 22126
## - ScreenPorch    1 9.8341e+08 5.0793e+11 22126
## - Fireplaces     1 1.1238e+09 5.0807e+11 22126
## - MSSubClass     1 1.7443e+09 5.0869e+11 22128
## - GarageArea     1 1.8028e+09 5.0875e+11 22128
## - LotFrontage    1 1.8376e+09 5.0879e+11 22128
## - GarageCars     1 1.8714e+09 5.0882e+11 22128
## - YearRemodAdd   1 1.9056e+09 5.0886e+11 22128
## - BsmtFinType1   5 5.7545e+09 5.1270e+11 22128
## - Foundation     4 4.9769e+09 5.1193e+11 22129
## - Functional     5 6.1158e+09 5.1307e+11 22129
## - Condition1     8 9.0185e+09 5.1597e+11 22129
## - Street         1 2.4824e+09 5.0943e+11 22129
## - BedroomAbvGr   1 2.5267e+09 5.0948e+11 22129
## - BldgType       4 5.5381e+09 5.1249e+11 22130
## - MasVnrType     3 4.8790e+09 5.1183e+11 22130
## - GarageCond     4 6.0666e+09 5.1302e+11 22131
## - MSZoning       4 6.3654e+09 5.1332e+11 22131
## - LandContour    3 5.6842e+09 5.1263e+11 22132
## - KitchenAbvGr   1 4.1710e+09 5.1112e+11 22133
## - YearBuilt      1 5.5363e+09 5.1249e+11 22136
## - LandSlope      2 6.5575e+09 5.1351e+11 22136
## - GarageQual     4 9.1616e+09 5.1611e+11 22137
## - MasVnrArea     1 8.3029e+09 5.1525e+11 22142
## - LotConfig      4 1.1210e+10 5.1816e+11 22142
## - BsmtUnfSF      1 8.8659e+09 5.1582e+11 22143
## - ExterQual      3 1.2682e+10 5.1963e+11 22147
## - BsmtQual       3 1.3162e+10 5.2011e+11 22148
## - SaleCondition  5 1.5198e+10 5.2215e+11 22148
## - BsmtFinSF2     1 1.1686e+10 5.1864e+11 22149
## - KitchenQual    3 1.6818e+10 5.2377e+11 22156
## - OverallQual    1 1.5100e+10 5.2205e+11 22156
## - RoofMatl       6 2.0179e+10 5.2713e+11 22157
## - OverallCond    1 1.6448e+10 5.2340e+11 22159
## - MiscFeature    3 2.2588e+10 5.2954e+11 22168
## - LotArea        1 2.0842e+10 5.2779e+11 22168
## - BsmtExposure   3 2.3826e+10 5.3078e+11 22170
## - X1stFlrSF      1 2.2710e+10 5.2966e+11 22172
## - BsmtFinSF1     1 2.4825e+10 5.3178e+11 22176
## - PoolArea       1 2.6677e+10 5.3363e+11 22180
## - PoolQC         3 3.0981e+10 5.3793e+11 22185
## - Condition2     5 6.7589e+10 5.7454e+11 22253
## - Neighborhood  24 9.4034e+10 6.0098e+11 22264
## - X2ndFlrSF      1 8.9093e+10 5.9604e+11 22301
## 
## Step:  AIC=22125.13
## SalePrice ~ MSSubClass + MSZoning + LotFrontage + LotArea + Street + 
##     LandContour + LotConfig + LandSlope + Neighborhood + Condition1 + 
##     Condition2 + BldgType + OverallQual + OverallCond + YearBuilt + 
##     YearRemodAdd + RoofMatl + Exterior1st + MasVnrType + MasVnrArea + 
##     ExterQual + Foundation + BsmtQual + BsmtExposure + BsmtFinType1 + 
##     BsmtFinSF1 + BsmtFinSF2 + BsmtUnfSF + CentralAir + X1stFlrSF + 
##     X2ndFlrSF + FullBath + BedroomAbvGr + KitchenAbvGr + KitchenQual + 
##     TotRmsAbvGrd + Functional + Fireplaces + GarageCars + GarageArea + 
##     GarageQual + GarageCond + X3SsnPorch + ScreenPorch + PoolArea + 
##     PoolQC + MiscFeature + SaleCondition
## 
##                 Df  Sum of Sq        RSS   AIC
## - ScreenPorch    1 7.8528e+08 5.0837e+11 22125
## - FullBath       1 8.0277e+08 5.0838e+11 22125
## - Exterior1st   13 1.2118e+10 5.1970e+11 22125
## - X3SsnPorch     1 8.6904e+08 5.0845e+11 22125
## - TotRmsAbvGrd   1 8.9147e+08 5.0847e+11 22125
## <none>                        5.0758e+11 22125
## - CentralAir     1 9.5287e+08 5.0853e+11 22125
## - Fireplaces     1 1.2018e+09 5.0878e+11 22126
## - LotFrontage    1 1.7358e+09 5.0932e+11 22127
## - GarageArea     1 1.8081e+09 5.0939e+11 22127
## - MSSubClass     1 1.8538e+09 5.0944e+11 22127
## - GarageCars     1 1.9090e+09 5.0949e+11 22127
## - YearRemodAdd   1 1.9827e+09 5.0956e+11 22127
## - Foundation     4 4.8369e+09 5.1242e+11 22128
## - BsmtFinType1   5 5.8167e+09 5.1340e+11 22128
## - Functional     5 5.8865e+09 5.1347e+11 22128
## - BedroomAbvGr   1 2.4299e+09 5.1001e+11 22128
## - Street         1 2.5483e+09 5.1013e+11 22129
## - Condition1     8 9.1943e+09 5.1678e+11 22129
## - BldgType       4 5.6467e+09 5.1323e+11 22129
## - MasVnrType     3 4.7608e+09 5.1234e+11 22129
## - GarageCond     4 5.9416e+09 5.1352e+11 22130
## - MSZoning       4 6.4536e+09 5.1404e+11 22131
## - LandContour    3 5.6444e+09 5.1323e+11 22131
## - KitchenAbvGr   1 4.1590e+09 5.1174e+11 22132
## - YearBuilt      1 5.5913e+09 5.1317e+11 22135
## - LandSlope      2 6.8340e+09 5.1442e+11 22136
## - GarageQual     4 8.9039e+09 5.1649e+11 22136
## - MasVnrArea     1 8.2591e+09 5.1584e+11 22141
## - LotConfig      4 1.1272e+10 5.1885e+11 22141
## - BsmtUnfSF      1 8.7431e+09 5.1633e+11 22142
## - ExterQual      3 1.2656e+10 5.2024e+11 22146
## - SaleCondition  5 1.4784e+10 5.2237e+11 22147
## - BsmtQual       3 1.3212e+10 5.2079e+11 22147
## - BsmtFinSF2     1 1.1961e+10 5.1954e+11 22149
## - KitchenQual    3 1.6614e+10 5.2420e+11 22154
## - OverallQual    1 1.5108e+10 5.2269e+11 22155
## - RoofMatl       6 2.0997e+10 5.2858e+11 22158
## - OverallCond    1 1.7017e+10 5.2460e+11 22159
## - MiscFeature    3 2.2462e+10 5.3004e+11 22167
## - LotArea        1 2.1013e+10 5.2859e+11 22168
## - BsmtExposure   3 2.4593e+10 5.3218e+11 22171
## - X1stFlrSF      1 2.3221e+10 5.3080e+11 22172
## - BsmtFinSF1     1 2.5073e+10 5.3265e+11 22176
## - PoolArea       1 2.6543e+10 5.3412e+11 22179
## - PoolQC         3 3.0652e+10 5.3823e+11 22183
## - Condition2     5 6.7904e+10 5.7549e+11 22253
## - Neighborhood  24 9.4846e+10 6.0243e+11 22265
## - X2ndFlrSF      1 9.0765e+10 5.9835e+11 22303
## 
## Step:  AIC=22124.82
## SalePrice ~ MSSubClass + MSZoning + LotFrontage + LotArea + Street + 
##     LandContour + LotConfig + LandSlope + Neighborhood + Condition1 + 
##     Condition2 + BldgType + OverallQual + OverallCond + YearBuilt + 
##     YearRemodAdd + RoofMatl + Exterior1st + MasVnrType + MasVnrArea + 
##     ExterQual + Foundation + BsmtQual + BsmtExposure + BsmtFinType1 + 
##     BsmtFinSF1 + BsmtFinSF2 + BsmtUnfSF + CentralAir + X1stFlrSF + 
##     X2ndFlrSF + FullBath + BedroomAbvGr + KitchenAbvGr + KitchenQual + 
##     TotRmsAbvGrd + Functional + Fireplaces + GarageCars + GarageArea + 
##     GarageQual + GarageCond + X3SsnPorch + PoolArea + PoolQC + 
##     MiscFeature + SaleCondition
## 
##                 Df  Sum of Sq        RSS   AIC
## - FullBath       1 7.5058e+08 5.0912e+11 22124
## - TotRmsAbvGrd   1 8.0367e+08 5.0917e+11 22125
## - X3SsnPorch     1 8.0370e+08 5.0917e+11 22125
## <none>                        5.0837e+11 22125
## - CentralAir     1 1.0185e+09 5.0939e+11 22125
## - Exterior1st   13 1.2538e+10 5.2091e+11 22126
## - Fireplaces     1 1.4893e+09 5.0986e+11 22126
## - LotFrontage    1 1.6968e+09 5.1006e+11 22127
## - GarageArea     1 1.8569e+09 5.1022e+11 22127
## - GarageCars     1 1.9053e+09 5.1027e+11 22127
## - Functional     5 5.7115e+09 5.1408e+11 22127
## - MSSubClass     1 2.0268e+09 5.1039e+11 22127
## - Foundation     4 4.8571e+09 5.1322e+11 22127
## - YearRemodAdd   1 2.0508e+09 5.1042e+11 22127
## - BsmtFinType1   5 5.8423e+09 5.1421e+11 22127
## - BedroomAbvGr   1 2.2960e+09 5.1066e+11 22128
## - Street         1 2.3174e+09 5.1068e+11 22128
## - MasVnrType     3 4.6674e+09 5.1303e+11 22129
## - Condition1     8 9.4918e+09 5.1786e+11 22129
## - BldgType       4 5.7676e+09 5.1413e+11 22129
## - MSZoning       4 6.4596e+09 5.1483e+11 22131
## - LandContour    3 5.8045e+09 5.1417e+11 22131
## - KitchenAbvGr   1 4.1711e+09 5.1254e+11 22132
## - GarageCond     4 7.0576e+09 5.1543e+11 22132
## - YearBuilt      1 5.3705e+09 5.1374e+11 22134
## - LandSlope      2 7.1550e+09 5.1552e+11 22136
## - GarageQual     4 1.0343e+10 5.1871e+11 22139
## - MasVnrArea     1 8.3957e+09 5.1676e+11 22141
## - LotConfig      4 1.1584e+10 5.1995e+11 22142
## - BsmtUnfSF      1 9.0920e+09 5.1746e+11 22142
## - SaleCondition  5 1.4765e+10 5.2313e+11 22146
## - ExterQual      3 1.2938e+10 5.2131e+11 22146
## - BsmtQual       3 1.3209e+10 5.2158e+11 22147
## - BsmtFinSF2     1 1.2501e+10 5.2087e+11 22149
## - KitchenQual    3 1.6697e+10 5.2506e+11 22154
## - OverallQual    1 1.5127e+10 5.2349e+11 22155
## - RoofMatl       6 2.0469e+10 5.2884e+11 22156
## - OverallCond    1 1.7149e+10 5.2552e+11 22159
## - MiscFeature    3 2.2990e+10 5.3136e+11 22167
## - LotArea        1 2.1336e+10 5.2970e+11 22168
## - BsmtExposure   3 2.4563e+10 5.3293e+11 22170
## - X1stFlrSF      1 2.2850e+10 5.3122e+11 22171
## - BsmtFinSF1     1 2.5711e+10 5.3408e+11 22177
## - PoolArea       1 2.6517e+10 5.3488e+11 22178
## - PoolQC         3 3.0582e+10 5.3895e+11 22183
## - Condition2     5 6.8259e+10 5.7663e+11 22253
## - Neighborhood  24 9.4539e+10 6.0291e+11 22263
## - X2ndFlrSF      1 9.1942e+10 6.0031e+11 22305
## 
## Step:  AIC=22124.43
## SalePrice ~ MSSubClass + MSZoning + LotFrontage + LotArea + Street + 
##     LandContour + LotConfig + LandSlope + Neighborhood + Condition1 + 
##     Condition2 + BldgType + OverallQual + OverallCond + YearBuilt + 
##     YearRemodAdd + RoofMatl + Exterior1st + MasVnrType + MasVnrArea + 
##     ExterQual + Foundation + BsmtQual + BsmtExposure + BsmtFinType1 + 
##     BsmtFinSF1 + BsmtFinSF2 + BsmtUnfSF + CentralAir + X1stFlrSF + 
##     X2ndFlrSF + BedroomAbvGr + KitchenAbvGr + KitchenQual + TotRmsAbvGrd + 
##     Functional + Fireplaces + GarageCars + GarageArea + GarageQual + 
##     GarageCond + X3SsnPorch + PoolArea + PoolQC + MiscFeature + 
##     SaleCondition
## 
##                 Df  Sum of Sq        RSS   AIC
## - TotRmsAbvGrd   1 7.9517e+08 5.0991e+11 22124
## - X3SsnPorch     1 8.9817e+08 5.1002e+11 22124
## <none>                        5.0912e+11 22124
## - CentralAir     1 9.8933e+08 5.1011e+11 22125
## - Fireplaces     1 1.4272e+09 5.1055e+11 22126
## - Exterior1st   13 1.2857e+10 5.2197e+11 22126
## - LotFrontage    1 1.7146e+09 5.1083e+11 22126
## - GarageArea     1 1.8232e+09 5.1094e+11 22126
## - GarageCars     1 1.9053e+09 5.1102e+11 22127
## - BedroomAbvGr   1 1.9321e+09 5.1105e+11 22127
## - Functional     5 5.7657e+09 5.1488e+11 22127
## - BsmtFinType1   5 5.8094e+09 5.1493e+11 22127
## - MSSubClass     1 2.0669e+09 5.1118e+11 22127
## - Foundation     4 4.9351e+09 5.1405e+11 22127
## - YearRemodAdd   1 2.1731e+09 5.1129e+11 22127
## - Street         1 2.3091e+09 5.1143e+11 22127
## - MasVnrType     3 4.6354e+09 5.1375e+11 22128
## - BldgType       4 5.6163e+09 5.1473e+11 22128
## - Condition1     8 9.9308e+09 5.1905e+11 22130
## - KitchenAbvGr   1 3.6758e+09 5.1279e+11 22130
## - MSZoning       4 6.5737e+09 5.1569e+11 22131
## - LandContour    3 6.0919e+09 5.1521e+11 22131
## - GarageCond     4 7.0919e+09 5.1621e+11 22132
## - YearBuilt      1 5.8226e+09 5.1494e+11 22135
## - LandSlope      2 7.4860e+09 5.1660e+11 22136
## - GarageQual     4 1.0509e+10 5.1963e+11 22139
## - MasVnrArea     1 8.2788e+09 5.1740e+11 22140
## - LotConfig      4 1.1225e+10 5.2034e+11 22140
## - BsmtUnfSF      1 9.0786e+09 5.1820e+11 22142
## - SaleCondition  5 1.4725e+10 5.2384e+11 22146
## - ExterQual      3 1.2938e+10 5.2206e+11 22146
## - BsmtQual       3 1.2975e+10 5.2209e+11 22146
## - BsmtFinSF2     1 1.2430e+10 5.2155e+11 22149
## - KitchenQual    3 1.6209e+10 5.2533e+11 22153
## - OverallQual    1 1.5214e+10 5.2433e+11 22155
## - RoofMatl       6 2.0195e+10 5.2931e+11 22155
## - OverallCond    1 1.7321e+10 5.2644e+11 22159
## - MiscFeature    3 2.3158e+10 5.3228e+11 22167
## - LotArea        1 2.1657e+10 5.3078e+11 22168
## - BsmtExposure   3 2.4690e+10 5.3381e+11 22170
## - X1stFlrSF      1 2.5305e+10 5.3442e+11 22176
## - BsmtFinSF1     1 2.5434e+10 5.3455e+11 22176
## - PoolArea       1 2.6484e+10 5.3560e+11 22178
## - PoolQC         3 3.0898e+10 5.4002e+11 22183
## - Condition2     5 6.8482e+10 5.7760e+11 22253
## - Neighborhood  24 9.4294e+10 6.0341e+11 22262
## - X2ndFlrSF      1 1.0101e+11 6.1013e+11 22320
## 
## Step:  AIC=22124.14
## SalePrice ~ MSSubClass + MSZoning + LotFrontage + LotArea + Street + 
##     LandContour + LotConfig + LandSlope + Neighborhood + Condition1 + 
##     Condition2 + BldgType + OverallQual + OverallCond + YearBuilt + 
##     YearRemodAdd + RoofMatl + Exterior1st + MasVnrType + MasVnrArea + 
##     ExterQual + Foundation + BsmtQual + BsmtExposure + BsmtFinType1 + 
##     BsmtFinSF1 + BsmtFinSF2 + BsmtUnfSF + CentralAir + X1stFlrSF + 
##     X2ndFlrSF + BedroomAbvGr + KitchenAbvGr + KitchenQual + Functional + 
##     Fireplaces + GarageCars + GarageArea + GarageQual + GarageCond + 
##     X3SsnPorch + PoolArea + PoolQC + MiscFeature + SaleCondition
## 
##                 Df  Sum of Sq        RSS   AIC
## - X3SsnPorch     1 8.0639e+08 5.1072e+11 22124
## <none>                        5.0991e+11 22124
## - CentralAir     1 1.0725e+09 5.1099e+11 22124
## - BedroomAbvGr   1 1.3271e+09 5.1124e+11 22125
## - Fireplaces     1 1.4530e+09 5.1137e+11 22125
## - Exterior1st   13 1.2913e+10 5.2283e+11 22126
## - GarageArea     1 1.8128e+09 5.1173e+11 22126
## - LotFrontage    1 1.8193e+09 5.1173e+11 22126
## - MSSubClass     1 1.9273e+09 5.1184e+11 22126
## - GarageCars     1 1.9710e+09 5.1188e+11 22126
## - YearRemodAdd   1 2.0988e+09 5.1201e+11 22127
## - Foundation     4 4.9459e+09 5.1486e+11 22127
## - Functional     5 5.9140e+09 5.1583e+11 22127
## - BsmtFinType1   5 5.9599e+09 5.1587e+11 22127
## - Street         1 2.4783e+09 5.1239e+11 22127
## - MasVnrType     3 4.6622e+09 5.1458e+11 22128
## - KitchenAbvGr   1 3.1194e+09 5.1303e+11 22129
## - BldgType       4 5.9795e+09 5.1589e+11 22129
## - MSZoning       4 6.3703e+09 5.1628e+11 22130
## - Condition1     8 1.0164e+10 5.2008e+11 22130
## - LandContour    3 5.9069e+09 5.1582e+11 22131
## - GarageCond     4 7.5267e+09 5.1744e+11 22132
## - YearBuilt      1 5.6826e+09 5.1560e+11 22134
## - LandSlope      2 7.4989e+09 5.1741e+11 22136
## - MasVnrArea     1 8.1522e+09 5.1807e+11 22140
## - GarageQual     4 1.1094e+10 5.2101e+11 22140
## - LotConfig      4 1.1311e+10 5.2122e+11 22140
## - BsmtUnfSF      1 8.7679e+09 5.1868e+11 22141
## - BsmtQual       3 1.2983e+10 5.2290e+11 22146
## - SaleCondition  5 1.4982e+10 5.2490e+11 22146
## - ExterQual      3 1.3701e+10 5.2361e+11 22147
## - BsmtFinSF2     1 1.2187e+10 5.2210e+11 22148
## - KitchenQual    3 1.6583e+10 5.2650e+11 22153
## - RoofMatl       6 1.9993e+10 5.2991e+11 22154
## - OverallQual    1 1.5364e+10 5.2528e+11 22155
## - OverallCond    1 1.7272e+10 5.2718e+11 22159
## - MiscFeature    3 2.3348e+10 5.3326e+11 22167
## - LotArea        1 2.1895e+10 5.3181e+11 22168
## - BsmtExposure   3 2.4627e+10 5.3454e+11 22170
## - BsmtFinSF1     1 2.4997e+10 5.3491e+11 22175
## - PoolArea       1 2.6329e+10 5.3624e+11 22177
## - PoolQC         3 3.0476e+10 5.4039e+11 22182
## - X1stFlrSF      1 3.2646e+10 5.4256e+11 22190
## - Condition2     5 7.0727e+10 5.8064e+11 22256
## - Neighborhood  24 9.4914e+10 6.0483e+11 22263
## - X2ndFlrSF      1 1.5025e+11 6.6016e+11 22405
## 
## Step:  AIC=22123.87
## SalePrice ~ MSSubClass + MSZoning + LotFrontage + LotArea + Street + 
##     LandContour + LotConfig + LandSlope + Neighborhood + Condition1 + 
##     Condition2 + BldgType + OverallQual + OverallCond + YearBuilt + 
##     YearRemodAdd + RoofMatl + Exterior1st + MasVnrType + MasVnrArea + 
##     ExterQual + Foundation + BsmtQual + BsmtExposure + BsmtFinType1 + 
##     BsmtFinSF1 + BsmtFinSF2 + BsmtUnfSF + CentralAir + X1stFlrSF + 
##     X2ndFlrSF + BedroomAbvGr + KitchenAbvGr + KitchenQual + Functional + 
##     Fireplaces + GarageCars + GarageArea + GarageQual + GarageCond + 
##     PoolArea + PoolQC + MiscFeature + SaleCondition
## 
##                 Df  Sum of Sq        RSS   AIC
## <none>                        5.1072e+11 22124
## - CentralAir     1 1.0814e+09 5.1180e+11 22124
## - Exterior1st   13 1.2709e+10 5.2343e+11 22125
## - Fireplaces     1 1.3858e+09 5.1211e+11 22125
## - BedroomAbvGr   1 1.4286e+09 5.1215e+11 22125
## - Foundation     4 4.3786e+09 5.1510e+11 22125
## - GarageArea     1 1.8269e+09 5.1255e+11 22126
## - MSSubClass     1 1.9171e+09 5.1264e+11 22126
## - LotFrontage    1 1.9455e+09 5.1267e+11 22126
## - GarageCars     1 1.9715e+09 5.1269e+11 22126
## - YearRemodAdd   1 2.1072e+09 5.1283e+11 22126
## - Functional     5 5.9016e+09 5.1662e+11 22126
## - BsmtFinType1   5 6.0585e+09 5.1678e+11 22127
## - Street         1 2.4427e+09 5.1316e+11 22127
## - MasVnrType     3 4.5779e+09 5.1530e+11 22128
## - BldgType       4 5.9543e+09 5.1667e+11 22129
## - KitchenAbvGr   1 3.1425e+09 5.1386e+11 22129
## - Condition1     8 1.0119e+10 5.2084e+11 22129
## - MSZoning       4 6.4855e+09 5.1720e+11 22130
## - LandContour    3 5.9483e+09 5.1667e+11 22131
## - GarageCond     4 7.5693e+09 5.1829e+11 22132
## - YearBuilt      1 5.5942e+09 5.1631e+11 22134
## - LandSlope      2 7.5106e+09 5.1823e+11 22136
## - MasVnrArea     1 8.0645e+09 5.1878e+11 22139
## - LotConfig      4 1.1101e+10 5.2182e+11 22139
## - GarageQual     4 1.1164e+10 5.2188e+11 22140
## - BsmtUnfSF      1 9.1527e+09 5.1987e+11 22141
## - BsmtQual       3 1.2868e+10 5.2359e+11 22145
## - SaleCondition  5 1.5094e+10 5.2581e+11 22146
## - ExterQual      3 1.4053e+10 5.2477e+11 22148
## - BsmtFinSF2     1 1.2339e+10 5.2306e+11 22148
## - KitchenQual    3 1.6535e+10 5.2725e+11 22153
## - RoofMatl       6 1.9963e+10 5.3068e+11 22154
## - OverallQual    1 1.5283e+10 5.2600e+11 22154
## - OverallCond    1 1.7236e+10 5.2796e+11 22158
## - MiscFeature    3 2.3453e+10 5.3417e+11 22167
## - LotArea        1 2.2005e+10 5.3272e+11 22168
## - BsmtExposure   3 2.4373e+10 5.3509e+11 22169
## - BsmtFinSF1     1 2.5520e+10 5.3624e+11 22175
## - PoolArea       1 2.6432e+10 5.3715e+11 22177
## - PoolQC         3 3.0537e+10 5.4126e+11 22181
## - X1stFlrSF      1 3.2448e+10 5.4317e+11 22189
## - Condition2     5 7.1161e+10 5.8188e+11 22257
## - Neighborhood  24 9.4448e+10 6.0517e+11 22262
## - X2ndFlrSF      1 1.5092e+11 6.6164e+11 22405

## 
## Call:
## lm(formula = SalePrice ~ MSSubClass + MSZoning + LotFrontage + 
##     LotArea + Street + LandContour + LotConfig + LandSlope + 
##     Neighborhood + Condition1 + Condition2 + BldgType + OverallQual + 
##     OverallCond + YearBuilt + YearRemodAdd + RoofMatl + Exterior1st + 
##     MasVnrType + MasVnrArea + ExterQual + Foundation + BsmtQual + 
##     BsmtExposure + BsmtFinType1 + BsmtFinSF1 + BsmtFinSF2 + BsmtUnfSF + 
##     CentralAir + X1stFlrSF + X2ndFlrSF + BedroomAbvGr + KitchenAbvGr + 
##     KitchenQual + Functional + Fireplaces + GarageCars + GarageArea + 
##     GarageQual + GarageCond + PoolArea + PoolQC + MiscFeature + 
##     SaleCondition, data = dt.house1)
## 
## Coefficients:
##          (Intercept)            MSSubClass            MSZoningFV  
##           -3.958e+06            -1.129e+02             4.526e+04  
##           MSZoningRH            MSZoningRL            MSZoningRM  
##            3.174e+04             3.189e+04             2.686e+04  
##          LotFrontage               LotArea            StreetPave  
##            9.904e+01             8.367e-01             3.639e+04  
##       LandContourHLS        LandContourLow        LandContourLvl  
##            8.930e+03            -1.757e+04             6.721e+03  
##     LotConfigCulDSac          LotConfigFR2          LotConfigFR3  
##            1.543e+04            -8.724e+03            -1.270e+04  
##      LotConfigInside          LandSlopeMod          LandSlopeSev  
##           -8.709e+02             5.975e+03            -4.825e+04  
##  NeighborhoodBlueste    NeighborhoodBrDale   NeighborhoodBrkSide  
##            8.809e+02             7.068e+03            -1.336e+03  
##  NeighborhoodClearCr   NeighborhoodCollgCr   NeighborhoodCrawfor  
##           -1.424e+04            -1.070e+04             9.959e+03  
##  NeighborhoodEdwards   NeighborhoodGilbert    NeighborhoodIDOTRR  
##           -2.059e+04            -1.405e+04             4.492e+02  
##  NeighborhoodMeadowV   NeighborhoodMitchel     NeighborhoodNAmes  
##           -1.023e+04            -1.963e+04            -1.677e+04  
##  NeighborhoodNoRidge   NeighborhoodNPkVill   NeighborhoodNridgHt  
##            1.980e+04             1.491e+04             1.524e+04  
##   NeighborhoodNWAmes   NeighborhoodOldTown    NeighborhoodSawyer  
##           -1.849e+04            -1.207e+04            -7.422e+03  
##  NeighborhoodSawyerW   NeighborhoodSomerst   NeighborhoodStoneBr  
##           -3.558e+03            -5.351e+03             4.050e+04  
##    NeighborhoodSWISU    NeighborhoodTimber   NeighborhoodVeenker  
##           -4.151e+03            -1.521e+04             7.248e+03  
##      Condition1Feedr        Condition1Norm        Condition1PosA  
##            1.008e+03             1.160e+04             3.744e+03  
##       Condition1PosN        Condition1RRAe        Condition1RRAn  
##            2.579e+03            -9.198e+03             1.197e+04  
##       Condition1RRNe        Condition1RRNn       Condition2Feedr  
##            5.861e+03             1.074e+04            -8.273e+03  
##       Condition2Norm        Condition2PosA        Condition2PosN  
##            3.584e+03             4.414e+04            -2.302e+05  
##       Condition2RRNn        BldgType2fmCon        BldgTypeDuplex  
##            1.457e+04             1.341e+04            -8.136e+03  
##        BldgTypeTwnhs        BldgTypeTwnhsE           OverallQual  
##           -1.263e+04            -8.237e+03             6.282e+03  
##          OverallCond             YearBuilt          YearRemodAdd  
##            5.730e+03             2.668e+02             1.276e+02  
##      RoofMatlCompShg       RoofMatlMembran          RoofMatlRoll  
##            1.419e+05             2.213e+05             1.445e+05  
##      RoofMatlTar&Grv       RoofMatlWdShake       RoofMatlWdShngl  
##            1.192e+05             1.492e+05             1.978e+05  
##   Exterior1stBrkComm    Exterior1stBrkFace     Exterior1stCBlock  
##           -3.335e+04             1.734e+04            -1.504e+04  
##   Exterior1stCemntBd    Exterior1stHdBoard    Exterior1stImStucc  
##            7.273e+03            -9.151e+02            -1.298e+04  
##   Exterior1stMetalSd    Exterior1stPlywood      Exterior1stStone  
##            6.721e+03            -4.433e+03            -5.014e+03  
##    Exterior1stStucco    Exterior1stVinylSd    Exterior1stWd Sdng  
##            9.338e+03             3.215e+03             3.493e+03  
##   Exterior1stWdShing     MasVnrTypeBrkFace        MasVnrTypeNone  
##            4.018e+02             1.071e+04             1.428e+04  
##      MasVnrTypeStone            MasVnrArea           ExterQualFa  
##            1.799e+04             2.451e+01            -1.581e+04  
##          ExterQualGd           ExterQualTA      FoundationCBlock  
##           -2.655e+04            -2.748e+04             3.476e+03  
##      FoundationPConc       FoundationStone        FoundationWood  
##            4.836e+03             5.790e+03            -3.992e+04  
##           BsmtQualFa            BsmtQualGd            BsmtQualTA  
##           -1.308e+04            -1.713e+04            -1.710e+04  
##       BsmtExposureGd        BsmtExposureMn        BsmtExposureNo  
##            1.459e+04            -7.404e+03            -7.497e+03  
##      BsmtFinType1BLQ       BsmtFinType1GLQ       BsmtFinType1LwQ  
##            1.111e+03             8.276e+03            -2.912e+03  
##      BsmtFinType1Rec       BsmtFinType1Unf            BsmtFinSF1  
##            2.033e+02             2.859e+03             4.183e+01  
##           BsmtFinSF2             BsmtUnfSF           CentralAirY  
##            3.565e+01             2.394e+01             5.889e+03  
##            X1stFlrSF             X2ndFlrSF          BedroomAbvGr  
##            4.720e+01             5.985e+01            -2.401e+03  
##         KitchenAbvGr         KitchenQualFa         KitchenQualGd  
##           -1.706e+04            -1.966e+04            -2.092e+04  
##        KitchenQualTA        FunctionalMaj2        FunctionalMin1  
##           -1.923e+04            -1.460e+04            -3.200e+02  
##       FunctionalMin2         FunctionalMod         FunctionalTyp  
##           -3.885e+03            -1.199e+03             8.019e+03  
##           Fireplaces            GarageCars            GarageArea  
##            2.495e+03             4.791e+03             1.553e+01  
##         GarageQualFa          GarageQualGd          GarageQualPo  
##           -1.231e+05            -1.152e+05            -1.251e+05  
##         GarageQualTA          GarageCondFa          GarageCondGd  
##           -1.222e+05             1.177e+05             1.174e+05  
##         GarageCondPo          GarageCondTA              PoolArea  
##            1.194e+05             1.198e+05             5.796e+03  
##             PoolQCFa              PoolQCGd             PoolQCUkn  
##           -7.343e+05            -3.021e+05             2.999e+06  
##      MiscFeatureShed       MiscFeatureTenC        MiscFeatureUkn  
##           -1.374e+04             6.987e+05            -1.993e+04  
## SaleConditionAdjLand   SaleConditionAlloca   SaleConditionFamily  
##            3.342e+04             8.397e+03            -5.788e+02  
##  SaleConditionNormal  SaleConditionPartial  
##            4.431e+03             1.814e+04

Berdasarkan metode backward stepwise diperoleh bahwa nilai AIC sebesar 22123.87. Hasil ini menunjukkan bahwa dengan metode backward stepwise memiliki nilai AIC yang lebih kecil dibandingkan dengan metode forward stepwise.

Forward dan Backward Stepwise

stepAIC(regresi1, direction = "both")

## Start:  AIC=22232.61
## SalePrice ~ MSSubClass + MSZoning + LotFrontage + LotArea + Street + 
##     Alley + LotShape + LandContour + LotConfig + LandSlope + 
##     Neighborhood + Condition1 + Condition2 + BldgType + HouseStyle + 
##     OverallQual + OverallCond + YearBuilt + YearRemodAdd + RoofStyle + 
##     RoofMatl + Exterior1st + Exterior2nd + MasVnrType + MasVnrArea + 
##     ExterQual + ExterCond + Foundation + BsmtQual + BsmtCond + 
##     BsmtExposure + BsmtFinType1 + BsmtFinSF1 + BsmtFinType2 + 
##     BsmtFinSF2 + BsmtUnfSF + TotalBsmtSF + Heating + HeatingQC + 
##     CentralAir + Electrical + X1stFlrSF + X2ndFlrSF + LowQualFinSF + 
##     GrLivArea + BsmtFullBath + BsmtHalfBath + FullBath + HalfBath + 
##     BedroomAbvGr + KitchenAbvGr + KitchenQual + TotRmsAbvGrd + 
##     Functional + Fireplaces + FireplaceQu + GarageType + GarageYrBlt + 
##     GarageFinish + GarageCars + GarageArea + GarageQual + GarageCond + 
##     PavedDrive + WoodDeckSF + OpenPorchSF + EnclosedPorch + X3SsnPorch + 
##     ScreenPorch + PoolArea + PoolQC + Fence + MiscFeature + MiscVal + 
##     MoSold + YrSold + SaleType + SaleCondition
## 
## 
## Step:  AIC=22232.61
## SalePrice ~ MSSubClass + MSZoning + LotFrontage + LotArea + Street + 
##     Alley + LotShape + LandContour + LotConfig + LandSlope + 
##     Neighborhood + Condition1 + Condition2 + BldgType + HouseStyle + 
##     OverallQual + OverallCond + YearBuilt + YearRemodAdd + RoofStyle + 
##     RoofMatl + Exterior1st + Exterior2nd + MasVnrType + MasVnrArea + 
##     ExterQual + ExterCond + Foundation + BsmtQual + BsmtCond + 
##     BsmtExposure + BsmtFinType1 + BsmtFinSF1 + BsmtFinType2 + 
##     BsmtFinSF2 + BsmtUnfSF + TotalBsmtSF + Heating + HeatingQC + 
##     CentralAir + Electrical + X1stFlrSF + X2ndFlrSF + LowQualFinSF + 
##     BsmtFullBath + BsmtHalfBath + FullBath + HalfBath + BedroomAbvGr + 
##     KitchenAbvGr + KitchenQual + TotRmsAbvGrd + Functional + 
##     Fireplaces + FireplaceQu + GarageType + GarageYrBlt + GarageFinish + 
##     GarageCars + GarageArea + GarageQual + GarageCond + PavedDrive + 
##     WoodDeckSF + OpenPorchSF + EnclosedPorch + X3SsnPorch + ScreenPorch + 
##     PoolArea + PoolQC + Fence + MiscFeature + MiscVal + MoSold + 
##     YrSold + SaleType + SaleCondition
## 
## 
## Step:  AIC=22232.61
## SalePrice ~ MSSubClass + MSZoning + LotFrontage + LotArea + Street + 
##     Alley + LotShape + LandContour + LotConfig + LandSlope + 
##     Neighborhood + Condition1 + Condition2 + BldgType + HouseStyle + 
##     OverallQual + OverallCond + YearBuilt + YearRemodAdd + RoofStyle + 
##     RoofMatl + Exterior1st + Exterior2nd + MasVnrType + MasVnrArea + 
##     ExterQual + ExterCond + Foundation + BsmtQual + BsmtCond + 
##     BsmtExposure + BsmtFinType1 + BsmtFinSF1 + BsmtFinType2 + 
##     BsmtFinSF2 + BsmtUnfSF + Heating + HeatingQC + CentralAir + 
##     Electrical + X1stFlrSF + X2ndFlrSF + LowQualFinSF + BsmtFullBath + 
##     BsmtHalfBath + FullBath + HalfBath + BedroomAbvGr + KitchenAbvGr + 
##     KitchenQual + TotRmsAbvGrd + Functional + Fireplaces + FireplaceQu + 
##     GarageType + GarageYrBlt + GarageFinish + GarageCars + GarageArea + 
##     GarageQual + GarageCond + PavedDrive + WoodDeckSF + OpenPorchSF + 
##     EnclosedPorch + X3SsnPorch + ScreenPorch + PoolArea + PoolQC + 
##     Fence + MiscFeature + MiscVal + MoSold + YrSold + SaleType + 
##     SaleCondition
## 
##                 Df  Sum of Sq        RSS   AIC
## - Exterior2nd   14 5.3888e+09 4.8216e+11 22217
## - BsmtFinType2   5 6.6766e+08 4.7743e+11 22224
## - SaleType       8 3.6903e+09 4.8046e+11 22225
## - Exterior1st   12 7.2982e+09 4.8406e+11 22225
## - Electrical     3 3.5814e+07 4.7680e+11 22227
## - GarageType     5 1.8370e+09 4.7860e+11 22227
## - FireplaceQu    5 1.9551e+09 4.7872e+11 22227
## - HeatingQC      4 1.1107e+09 4.7788e+11 22227
## - Heating        3 2.4637e+08 4.7701e+11 22227
## - HouseStyle     7 3.9566e+09 4.8072e+11 22228
## - ExterCond      3 4.5644e+08 4.7722e+11 22228
## - Fence          4 1.3478e+09 4.7811e+11 22228
## - RoofStyle      4 1.8194e+09 4.7859e+11 22229
## - BsmtCond       2 2.4985e+08 4.7702e+11 22229
## - SaleCondition  5 2.8915e+09 4.7966e+11 22229
## - PavedDrive     2 2.7183e+08 4.7704e+11 22229
## - GarageFinish   2 5.8511e+08 4.7735e+11 22230
## - Alley          2 8.2989e+08 4.7760e+11 22231
## - LotShape       3 1.7361e+09 4.7850e+11 22231
## - MiscVal        1 2.1888e+05 4.7677e+11 22231
## - MSSubClass     1 4.8177e+05 4.7677e+11 22231
## - OpenPorchSF    1 2.7802e+07 4.7679e+11 22231
## - BsmtHalfBath   1 3.0197e+07 4.7680e+11 22231
## - BsmtFullBath   1 1.0292e+08 4.7687e+11 22231
## - YrSold         1 1.0862e+08 4.7688e+11 22231
## - GarageYrBlt    1 1.1534e+08 4.7688e+11 22231
## - EnclosedPorch  1 2.6601e+08 4.7703e+11 22231
## - HalfBath       1 3.3253e+08 4.7710e+11 22231
## - LowQualFinSF   1 6.8295e+08 4.7745e+11 22232
## - BsmtFinType1   5 4.2613e+09 4.8103e+11 22232
## - CentralAir     1 8.5802e+08 4.7762e+11 22233
## <none>                        4.7677e+11 22233
## - MoSold         1 9.7205e+08 4.7774e+11 22233
## - LotFrontage    1 1.0203e+09 4.7779e+11 22233
## - TotRmsAbvGrd   1 1.0239e+09 4.7779e+11 22233
## - YearRemodAdd   1 1.1693e+09 4.7794e+11 22233
## - GarageCars     1 1.4049e+09 4.7817e+11 22234
## - X3SsnPorch     1 1.4060e+09 4.7817e+11 22234
## - BldgType       4 4.0480e+09 4.8081e+11 22234
## - WoodDeckSF     1 1.4452e+09 4.7821e+11 22234
## - GarageCond     4 4.2208e+09 4.8099e+11 22234
## - FullBath       1 1.6096e+09 4.7838e+11 22234
## - GarageArea     1 2.0340e+09 4.7880e+11 22235
## - Fireplaces     1 2.2468e+09 4.7901e+11 22236
## - MSZoning       4 4.9381e+09 4.8170e+11 22236
## - Foundation     4 5.0095e+09 4.8178e+11 22236
## - MasVnrType     3 4.1661e+09 4.8093e+11 22236
## - ScreenPorch    1 2.4800e+09 4.7925e+11 22236
## - KitchenAbvGr   1 2.5240e+09 4.7929e+11 22236
## - Functional     5 6.1650e+09 4.8293e+11 22237
## - BedroomAbvGr   1 2.8203e+09 4.7959e+11 22237
## - GarageQual     4 6.2857e+09 4.8305e+11 22239
## - YearBuilt      1 3.6947e+09 4.8046e+11 22239
## - Street         1 3.7328e+09 4.8050e+11 22239
## - LandContour    3 5.6008e+09 4.8237e+11 22239
## - Condition1     8 1.0346e+10 4.8711e+11 22240
## - BsmtFinSF2     1 4.6849e+09 4.8145e+11 22241
## - LandSlope      2 5.6024e+09 4.8237e+11 22241
## - BsmtUnfSF      1 6.4715e+09 4.8324e+11 22245
## - LotConfig      4 9.5976e+09 4.8636e+11 22246
## - BsmtQual       3 8.7554e+09 4.8552e+11 22247
## - MasVnrArea     1 7.5537e+09 4.8432e+11 22248
## - ExterQual      3 1.1959e+10 4.8873e+11 22254
## - KitchenQual    3 1.2941e+10 4.8971e+11 22256
## - RoofMatl       6 1.6132e+10 4.9290e+11 22257
## - OverallCond    1 1.3819e+10 4.9059e+11 22262
## - BsmtExposure   3 1.6834e+10 4.9360e+11 22265
## - LotArea        1 1.5621e+10 4.9239e+11 22266
## - MiscFeature    3 1.7999e+10 4.9476e+11 22267
## - X1stFlrSF      1 1.6251e+10 4.9302e+11 22267
## - OverallQual    1 1.6704e+10 4.9347e+11 22268
## - BsmtFinSF1     1 1.8146e+10 4.9491e+11 22272
## - PoolArea       1 2.2151e+10 4.9892e+11 22280
## - PoolQC         3 2.5694e+10 5.0246e+11 22284
## - X2ndFlrSF      1 4.3409e+10 5.2017e+11 22326
## - Condition2     5 6.1503e+10 5.3827e+11 22355
## - Neighborhood  24 8.2665e+10 5.5943e+11 22360
## 
## Step:  AIC=22216.91
## SalePrice ~ MSSubClass + MSZoning + LotFrontage + LotArea + Street + 
##     Alley + LotShape + LandContour + LotConfig + LandSlope + 
##     Neighborhood + Condition1 + Condition2 + BldgType + HouseStyle + 
##     OverallQual + OverallCond + YearBuilt + YearRemodAdd + RoofStyle + 
##     RoofMatl + Exterior1st + MasVnrType + MasVnrArea + ExterQual + 
##     ExterCond + Foundation + BsmtQual + BsmtCond + BsmtExposure + 
##     BsmtFinType1 + BsmtFinSF1 + BsmtFinType2 + BsmtFinSF2 + BsmtUnfSF + 
##     Heating + HeatingQC + CentralAir + Electrical + X1stFlrSF + 
##     X2ndFlrSF + LowQualFinSF + BsmtFullBath + BsmtHalfBath + 
##     FullBath + HalfBath + BedroomAbvGr + KitchenAbvGr + KitchenQual + 
##     TotRmsAbvGrd + Functional + Fireplaces + FireplaceQu + GarageType + 
##     GarageYrBlt + GarageFinish + GarageCars + GarageArea + GarageQual + 
##     GarageCond + PavedDrive + WoodDeckSF + OpenPorchSF + EnclosedPorch + 
##     X3SsnPorch + ScreenPorch + PoolArea + PoolQC + Fence + MiscFeature + 
##     MiscVal + MoSold + YrSold + SaleType + SaleCondition
## 
##                 Df  Sum of Sq        RSS   AIC
## - BsmtFinType2   5 5.3136e+08 4.8269e+11 22208
## - SaleType       8 3.8319e+09 4.8599e+11 22210
## - GarageType     5 1.5020e+09 4.8366e+11 22210
## - Electrical     3 4.6592e+07 4.8220e+11 22211
## - Exterior1st   13 9.0670e+09 4.9122e+11 22211
## - Heating        3 1.9189e+08 4.8235e+11 22211
## - FireplaceQu    5 2.0397e+09 4.8419e+11 22212
## - HeatingQC      4 1.2271e+09 4.8338e+11 22212
## - ExterCond      3 5.1035e+08 4.8267e+11 22212
## - Fence          4 1.4890e+09 4.8364e+11 22212
## - HouseStyle     7 4.2842e+09 4.8644e+11 22213
## - BsmtCond       2 2.2913e+08 4.8238e+11 22213
## - RoofStyle      4 2.0134e+09 4.8417e+11 22214
## - PavedDrive     2 4.2371e+08 4.8258e+11 22214
## - SaleCondition  5 3.1505e+09 4.8531e+11 22214
## - Alley          2 5.5941e+08 4.8271e+11 22214
## - GarageFinish   2 5.9805e+08 4.8275e+11 22214
## - LotShape       3 1.6654e+09 4.8382e+11 22215
## - MiscVal        1 6.2427e+06 4.8216e+11 22215
## - MSSubClass     1 7.0008e+06 4.8216e+11 22215
## - GarageYrBlt    1 1.8041e+07 4.8217e+11 22215
## - OpenPorchSF    1 2.6757e+07 4.8218e+11 22215
## - BsmtHalfBath   1 2.8922e+07 4.8218e+11 22215
## - YrSold         1 1.3116e+08 4.8229e+11 22215
## - EnclosedPorch  1 1.5698e+08 4.8231e+11 22215
## - BsmtFullBath   1 1.9141e+08 4.8235e+11 22215
## - HalfBath       1 5.6359e+08 4.8272e+11 22216
## - CentralAir     1 6.0615e+08 4.8276e+11 22216
## - LowQualFinSF   1 6.1483e+08 4.8277e+11 22216
## - BsmtFinType1   5 4.2269e+09 4.8638e+11 22217
## <none>                        4.8216e+11 22217
## - TotRmsAbvGrd   1 9.2327e+08 4.8308e+11 22217
## - MoSold         1 1.0842e+09 4.8324e+11 22217
## - BldgType       4 3.8716e+09 4.8603e+11 22218
## - GarageCars     1 1.2379e+09 4.8339e+11 22218
## - YearRemodAdd   1 1.3473e+09 4.8350e+11 22218
## - WoodDeckSF     1 1.4125e+09 4.8357e+11 22218
## - LotFrontage    1 1.4525e+09 4.8361e+11 22218
## - X3SsnPorch     1 1.4575e+09 4.8361e+11 22218
## - GarageCond     4 4.3898e+09 4.8654e+11 22219
## - FullBath       1 2.0068e+09 4.8416e+11 22219
## - ScreenPorch    1 2.0209e+09 4.8418e+11 22220
## - GarageArea     1 2.1051e+09 4.8426e+11 22220
## - Foundation     4 4.9410e+09 4.8710e+11 22220
## - Fireplaces     1 2.3944e+09 4.8455e+11 22220
## - MSZoning       4 5.0856e+09 4.8724e+11 22220
## - MasVnrType     3 4.2857e+09 4.8644e+11 22221
## - BedroomAbvGr   1 2.5369e+09 4.8469e+11 22221
## - Functional     5 6.1361e+09 4.8829e+11 22221
## - KitchenAbvGr   1 2.7232e+09 4.8488e+11 22221
## - Street         1 3.2883e+09 4.8544e+11 22222
## - LandContour    3 5.2759e+09 4.8743e+11 22223
## - Condition1     8 9.9875e+09 4.9214e+11 22223
## - YearBuilt      1 3.9169e+09 4.8607e+11 22224
## - GarageQual     4 6.6671e+09 4.8882e+11 22224
## - LandSlope      2 5.6554e+09 4.8781e+11 22226
## - BsmtFinSF2     1 4.9097e+09 4.8706e+11 22226
## - LotConfig      4 9.6193e+09 4.9177e+11 22231
## - MasVnrArea     1 7.4048e+09 4.8956e+11 22232
## - BsmtUnfSF      1 7.6702e+09 4.8983e+11 22232
## + Exterior2nd   14 5.3888e+09 4.7677e+11 22233
## - BsmtQual       3 9.9163e+09 4.9207e+11 22233
## - ExterQual      3 1.1439e+10 4.9359e+11 22237
## - KitchenQual    3 1.3525e+10 4.9568e+11 22241
## - RoofMatl       6 1.7311e+10 4.9947e+11 22244
## - LotArea        1 1.4630e+10 4.9679e+11 22248
## - OverallCond    1 1.4996e+10 4.9715e+11 22248
## - BsmtExposure   3 1.7302e+10 4.9946e+11 22250
## - X1stFlrSF      1 1.5610e+10 4.9777e+11 22250
## - MiscFeature    3 1.7741e+10 4.9990e+11 22250
## - OverallQual    1 1.6829e+10 4.9898e+11 22252
## - BsmtFinSF1     1 1.9698e+10 5.0185e+11 22259
## - PoolArea       1 2.2112e+10 5.0427e+11 22264
## - PoolQC         3 2.6891e+10 5.0905e+11 22270
## - X2ndFlrSF      1 4.4831e+10 5.2699e+11 22312
## - Condition2     5 6.0987e+10 5.4314e+11 22337
## - Neighborhood  24 8.3309e+10 5.6546e+11 22343
## 
## Step:  AIC=22208.11
## SalePrice ~ MSSubClass + MSZoning + LotFrontage + LotArea + Street + 
##     Alley + LotShape + LandContour + LotConfig + LandSlope + 
##     Neighborhood + Condition1 + Condition2 + BldgType + HouseStyle + 
##     OverallQual + OverallCond + YearBuilt + YearRemodAdd + RoofStyle + 
##     RoofMatl + Exterior1st + MasVnrType + MasVnrArea + ExterQual + 
##     ExterCond + Foundation + BsmtQual + BsmtCond + BsmtExposure + 
##     BsmtFinType1 + BsmtFinSF1 + BsmtFinSF2 + BsmtUnfSF + Heating + 
##     HeatingQC + CentralAir + Electrical + X1stFlrSF + X2ndFlrSF + 
##     LowQualFinSF + BsmtFullBath + BsmtHalfBath + FullBath + HalfBath + 
##     BedroomAbvGr + KitchenAbvGr + KitchenQual + TotRmsAbvGrd + 
##     Functional + Fireplaces + FireplaceQu + GarageType + GarageYrBlt + 
##     GarageFinish + GarageCars + GarageArea + GarageQual + GarageCond + 
##     PavedDrive + WoodDeckSF + OpenPorchSF + EnclosedPorch + X3SsnPorch + 
##     ScreenPorch + PoolArea + PoolQC + Fence + MiscFeature + MiscVal + 
##     MoSold + YrSold + SaleType + SaleCondition
## 
##                 Df  Sum of Sq        RSS   AIC
## - SaleType       8 3.9277e+09 4.8661e+11 22201
## - GarageType     5 1.4192e+09 4.8411e+11 22201
## - Electrical     3 3.5292e+07 4.8272e+11 22202
## - Heating        3 1.9046e+08 4.8288e+11 22203
## - FireplaceQu    5 2.0357e+09 4.8472e+11 22203
## - Exterior1st   13 9.2953e+09 4.9198e+11 22203
## - ExterCond      3 4.9823e+08 4.8318e+11 22203
## - HeatingQC      4 1.3835e+09 4.8407e+11 22203
## - Fence          4 1.4658e+09 4.8415e+11 22203
## - HouseStyle     7 4.5275e+09 4.8721e+11 22204
## - RoofStyle      4 1.9710e+09 4.8466e+11 22205
## - BsmtCond       2 2.4217e+08 4.8293e+11 22205
## - PavedDrive     2 4.0617e+08 4.8309e+11 22205
## - SaleCondition  5 3.1451e+09 4.8583e+11 22205
## - Alley          2 5.7526e+08 4.8326e+11 22205
## - GarageFinish   2 6.4672e+08 4.8333e+11 22206
## - LotShape       3 1.7091e+09 4.8440e+11 22206
## - MiscVal        1 1.6141e+06 4.8269e+11 22206
## - MSSubClass     1 4.7885e+06 4.8269e+11 22206
## - GarageYrBlt    1 1.4508e+07 4.8270e+11 22206
## - OpenPorchSF    1 2.2696e+07 4.8271e+11 22206
## - BsmtHalfBath   1 4.2994e+07 4.8273e+11 22206
## - YrSold         1 1.3160e+08 4.8282e+11 22206
## - EnclosedPorch  1 1.6249e+08 4.8285e+11 22207
## - BsmtFullBath   1 2.6828e+08 4.8295e+11 22207
## - BsmtFinType1   5 4.0496e+09 4.8674e+11 22207
## - HalfBath       1 5.2275e+08 4.8321e+11 22207
## - CentralAir     1 6.1361e+08 4.8330e+11 22208
## - LowQualFinSF   1 7.1492e+08 4.8340e+11 22208
## <none>                        4.8269e+11 22208
## - MoSold         1 1.0481e+09 4.8373e+11 22209
## - TotRmsAbvGrd   1 1.0522e+09 4.8374e+11 22209
## - BldgType       4 3.8452e+09 4.8653e+11 22209
## - WoodDeckSF     1 1.2665e+09 4.8395e+11 22209
## - GarageCars     1 1.3065e+09 4.8399e+11 22209
## - YearRemodAdd   1 1.3614e+09 4.8405e+11 22209
## - X3SsnPorch     1 1.4509e+09 4.8414e+11 22209
## - LotFrontage    1 1.4709e+09 4.8416e+11 22209
## - GarageCond     4 4.4308e+09 4.8712e+11 22210
## - FullBath       1 1.9472e+09 4.8463e+11 22211
## - ScreenPorch    1 1.9700e+09 4.8466e+11 22211
## - GarageArea     1 2.0879e+09 4.8477e+11 22211
## - Foundation     4 4.9767e+09 4.8766e+11 22211
## - Fireplaces     1 2.4615e+09 4.8515e+11 22212
## - MasVnrType     3 4.2979e+09 4.8698e+11 22212
## - MSZoning       4 5.3025e+09 4.8799e+11 22212
## - Functional     5 6.2166e+09 4.8890e+11 22212
## - KitchenAbvGr   1 2.8036e+09 4.8549e+11 22212
## - BedroomAbvGr   1 2.8063e+09 4.8549e+11 22213
## - Street         1 3.2388e+09 4.8593e+11 22213
## - LandContour    3 5.2087e+09 4.8790e+11 22214
## - Condition1     8 9.8857e+09 4.9257e+11 22214
## - GarageQual     4 6.5756e+09 4.8926e+11 22215
## - YearBuilt      1 4.0710e+09 4.8676e+11 22215
## + BsmtFinType2   5 5.3136e+08 4.8216e+11 22217
## - LandSlope      2 5.6818e+09 4.8837e+11 22217
## - LotConfig      4 9.7251e+09 4.9241e+11 22222
## - MasVnrArea     1 7.3658e+09 4.9005e+11 22223
## + Exterior2nd   14 5.2525e+09 4.7743e+11 22224
## - BsmtUnfSF      1 8.0825e+09 4.9077e+11 22224
## - BsmtQual       3 1.0021e+10 4.9271e+11 22225
## - ExterQual      3 1.1343e+10 4.9403e+11 22228
## - BsmtFinSF2     1 9.6934e+09 4.9238e+11 22228
## - KitchenQual    3 1.3631e+10 4.9632e+11 22233
## - RoofMatl       6 1.7903e+10 5.0059e+11 22236
## - LotArea        1 1.4548e+10 4.9723e+11 22239
## - OverallCond    1 1.5327e+10 4.9801e+11 22240
## - X1stFlrSF      1 1.5454e+10 4.9814e+11 22241
## - BsmtExposure   3 1.8143e+10 5.0083e+11 22243
## - MiscFeature    3 1.8192e+10 5.0088e+11 22243
## - OverallQual    1 1.6811e+10 4.9950e+11 22244
## - BsmtFinSF1     1 2.0081e+10 5.0277e+11 22251
## - PoolArea       1 2.2616e+10 5.0530e+11 22256
## - PoolQC         3 2.7349e+10 5.1004e+11 22262
## - X2ndFlrSF      1 4.5560e+10 5.2825e+11 22305
## - Condition2     5 6.2059e+10 5.4475e+11 22330
## - Neighborhood  24 8.4028e+10 5.6671e+11 22336
## 
## Step:  AIC=22200.98
## SalePrice ~ MSSubClass + MSZoning + LotFrontage + LotArea + Street + 
##     Alley + LotShape + LandContour + LotConfig + LandSlope + 
##     Neighborhood + Condition1 + Condition2 + BldgType + HouseStyle + 
##     OverallQual + OverallCond + YearBuilt + YearRemodAdd + RoofStyle + 
##     RoofMatl + Exterior1st + MasVnrType + MasVnrArea + ExterQual + 
##     ExterCond + Foundation + BsmtQual + BsmtCond + BsmtExposure + 
##     BsmtFinType1 + BsmtFinSF1 + BsmtFinSF2 + BsmtUnfSF + Heating + 
##     HeatingQC + CentralAir + Electrical + X1stFlrSF + X2ndFlrSF + 
##     LowQualFinSF + BsmtFullBath + BsmtHalfBath + FullBath + HalfBath + 
##     BedroomAbvGr + KitchenAbvGr + KitchenQual + TotRmsAbvGrd + 
##     Functional + Fireplaces + FireplaceQu + GarageType + GarageYrBlt + 
##     GarageFinish + GarageCars + GarageArea + GarageQual + GarageCond + 
##     PavedDrive + WoodDeckSF + OpenPorchSF + EnclosedPorch + X3SsnPorch + 
##     ScreenPorch + PoolArea + PoolQC + Fence + MiscFeature + MiscVal + 
##     MoSold + YrSold + SaleCondition
## 
##                 Df  Sum of Sq        RSS   AIC
## - GarageType     5 1.3181e+09 4.8793e+11 22194
## - Electrical     3 7.1675e+06 4.8662e+11 22195
## - Heating        3 1.1153e+08 4.8673e+11 22195
## - HeatingQC      4 1.2076e+09 4.8782e+11 22196
## - FireplaceQu    5 2.1844e+09 4.8880e+11 22196
## - ExterCond      3 6.2404e+08 4.8724e+11 22196
## - Fence          4 1.6078e+09 4.8822e+11 22197
## - Exterior1st   13 9.7519e+09 4.9637e+11 22197
## - HouseStyle     7 4.6306e+09 4.9124e+11 22197
## - BsmtCond       2 1.7730e+08 4.8679e+11 22197
## - RoofStyle      4 2.0713e+09 4.8869e+11 22198
## - PavedDrive     2 5.6819e+08 4.8718e+11 22198
## - GarageFinish   2 6.0956e+08 4.8722e+11 22198
## - Alley          2 7.4987e+08 4.8736e+11 22199
## - LotShape       3 1.7346e+09 4.8835e+11 22199
## - OpenPorchSF    1 7.1093e+05 4.8661e+11 22199
## - GarageYrBlt    1 1.6624e+06 4.8662e+11 22199
## - MSSubClass     1 7.3177e+06 4.8662e+11 22199
## - MiscVal        1 2.2103e+07 4.8664e+11 22199
## - BsmtHalfBath   1 4.7325e+07 4.8666e+11 22199
## - EnclosedPorch  1 9.3348e+07 4.8671e+11 22199
## - YrSold         1 2.0021e+08 4.8681e+11 22199
## - BsmtFullBath   1 2.4536e+08 4.8686e+11 22200
## - HalfBath       1 5.8906e+08 4.8720e+11 22200
## - CentralAir     1 6.1559e+08 4.8723e+11 22200
## - LowQualFinSF   1 6.6289e+08 4.8728e+11 22201
## - BsmtFinType1   5 4.3620e+09 4.9098e+11 22201
## <none>                        4.8661e+11 22201
## - MoSold         1 9.1589e+08 4.8753e+11 22201
## - WoodDeckSF     1 1.1000e+09 4.8771e+11 22201
## - GarageCars     1 1.1894e+09 4.8780e+11 22202
## - TotRmsAbvGrd   1 1.2246e+09 4.8784e+11 22202
## - X3SsnPorch     1 1.3712e+09 4.8799e+11 22202
## - YearRemodAdd   1 1.4243e+09 4.8804e+11 22202
## - ScreenPorch    1 1.6135e+09 4.8823e+11 22203
## - FullBath       1 1.8485e+09 4.8846e+11 22203
## - LotFrontage    1 1.8784e+09 4.8849e+11 22203
## - GarageArea     1 1.9657e+09 4.8858e+11 22203
## - BldgType       4 4.6979e+09 4.9131e+11 22204
## - GarageCond     4 4.8701e+09 4.9148e+11 22204
## - Functional     5 5.9394e+09 4.9255e+11 22204
## - Foundation     4 5.0490e+09 4.9166e+11 22204
## - Street         1 2.4368e+09 4.8905e+11 22204
## - MasVnrType     3 4.2956e+09 4.9091e+11 22205
## - Fireplaces     1 2.6463e+09 4.8926e+11 22205
## - LandContour    3 4.6028e+09 4.9122e+11 22205
## - BedroomAbvGr   1 2.9327e+09 4.8955e+11 22206
## - MSZoning       4 5.6426e+09 4.9226e+11 22206
## - KitchenAbvGr   1 3.0112e+09 4.8963e+11 22206
## - Condition1     8 9.8398e+09 4.9645e+11 22207
## - YearBuilt      1 3.7084e+09 4.9032e+11 22207
## + SaleType       8 3.9277e+09 4.8269e+11 22208
## - GarageQual     4 7.0303e+09 4.9364e+11 22209
## + BsmtFinType2   5 6.2713e+08 4.8599e+11 22210
## - LandSlope      2 6.5162e+09 4.9313e+11 22212
## - MasVnrArea     1 7.2498e+09 4.9386e+11 22215
## - BsmtUnfSF      1 7.8390e+09 4.9445e+11 22217
## + Exterior2nd   14 5.3715e+09 4.8124e+11 22217
## - LotConfig      4 1.0873e+10 4.9749e+11 22217
## - BsmtQual       3 1.0260e+10 4.9687e+11 22218
## - ExterQual      3 1.1566e+10 4.9818e+11 22221
## - BsmtFinSF2     1 9.8608e+09 4.9647e+11 22221
## - SaleCondition  5 1.4520e+10 5.0113e+11 22223
## - KitchenQual    3 1.2827e+10 4.9944e+11 22223
## - RoofMatl       6 1.8093e+10 5.0471e+11 22229
## - LotArea        1 1.4105e+10 5.0072e+11 22230
## - OverallCond    1 1.5322e+10 5.0194e+11 22233
## - X1stFlrSF      1 1.6324e+10 5.0294e+11 22235
## - MiscFeature    3 1.8598e+10 5.0521e+11 22236
## - BsmtExposure   3 1.9340e+10 5.0595e+11 22238
## - OverallQual    1 1.7787e+10 5.0440e+11 22238
## - BsmtFinSF1     1 1.9757e+10 5.0637e+11 22243
## - PoolArea       1 2.2776e+10 5.0939e+11 22249
## - PoolQC         3 2.7287e+10 5.1390e+11 22255
## - X2ndFlrSF      1 4.5951e+10 5.3256e+11 22298
## - Condition2     5 6.3396e+10 5.5001e+11 22325
## - Neighborhood  24 8.4170e+10 5.7078e+11 22328
## 
## Step:  AIC=22193.94
## SalePrice ~ MSSubClass + MSZoning + LotFrontage + LotArea + Street + 
##     Alley + LotShape + LandContour + LotConfig + LandSlope + 
##     Neighborhood + Condition1 + Condition2 + BldgType + HouseStyle + 
##     OverallQual + OverallCond + YearBuilt + YearRemodAdd + RoofStyle + 
##     RoofMatl + Exterior1st + MasVnrType + MasVnrArea + ExterQual + 
##     ExterCond + Foundation + BsmtQual + BsmtCond + BsmtExposure + 
##     BsmtFinType1 + BsmtFinSF1 + BsmtFinSF2 + BsmtUnfSF + Heating + 
##     HeatingQC + CentralAir + Electrical + X1stFlrSF + X2ndFlrSF + 
##     LowQualFinSF + BsmtFullBath + BsmtHalfBath + FullBath + HalfBath + 
##     BedroomAbvGr + KitchenAbvGr + KitchenQual + TotRmsAbvGrd + 
##     Functional + Fireplaces + FireplaceQu + GarageYrBlt + GarageFinish + 
##     GarageCars + GarageArea + GarageQual + GarageCond + PavedDrive + 
##     WoodDeckSF + OpenPorchSF + EnclosedPorch + X3SsnPorch + ScreenPorch + 
##     PoolArea + PoolQC + Fence + MiscFeature + MiscVal + MoSold + 
##     YrSold + SaleCondition
## 
##                 Df  Sum of Sq        RSS   AIC
## - Electrical     3 1.1185e+07 4.8794e+11 22188
## - Heating        3 9.8266e+07 4.8803e+11 22188
## - HeatingQC      4 1.1757e+09 4.8911e+11 22189
## - ExterCond      3 5.6130e+08 4.8849e+11 22189
## - FireplaceQu    5 2.4178e+09 4.9035e+11 22189
## - Fence          4 1.7234e+09 4.8966e+11 22190
## - Exterior1st   13 9.9708e+09 4.9790e+11 22190
## - BsmtCond       2 2.1945e+08 4.8815e+11 22190
## - HouseStyle     7 4.9001e+09 4.9283e+11 22191
## - PavedDrive     2 5.1067e+08 4.8844e+11 22191
## - Alley          2 5.8276e+08 4.8852e+11 22191
## - RoofStyle      4 2.4312e+09 4.9036e+11 22191
## - LotShape       3 1.5925e+09 4.8952e+11 22192
## - OpenPorchSF    1 2.2216e+04 4.8793e+11 22192
## - GarageYrBlt    1 2.5024e+05 4.8793e+11 22192
## - MSSubClass     1 3.4663e+05 4.8793e+11 22192
## - MiscVal        1 1.4148e+07 4.8795e+11 22192
## - BsmtHalfBath   1 3.1781e+07 4.8796e+11 22192
## - EnclosedPorch  1 5.7358e+07 4.8799e+11 22192
## - GarageFinish   2 9.8140e+08 4.8891e+11 22192
## - YrSold         1 1.1282e+08 4.8805e+11 22192
## - BsmtFullBath   1 2.2079e+08 4.8815e+11 22192
## - HalfBath       1 4.3974e+08 4.8837e+11 22193
## - CentralAir     1 6.1006e+08 4.8854e+11 22193
## - BsmtFinType1   5 4.2155e+09 4.9215e+11 22193
## - LowQualFinSF   1 7.5750e+08 4.8869e+11 22194
## - MoSold         1 7.9784e+08 4.8873e+11 22194
## <none>                        4.8793e+11 22194
## - WoodDeckSF     1 1.0153e+09 4.8895e+11 22194
## - X3SsnPorch     1 1.2520e+09 4.8918e+11 22195
## - GarageCars     1 1.3232e+09 4.8926e+11 22195
## - YearRemodAdd   1 1.3958e+09 4.8933e+11 22195
## - TotRmsAbvGrd   1 1.4229e+09 4.8936e+11 22195
## - ScreenPorch    1 1.5093e+09 4.8944e+11 22195
## - FullBath       1 1.7108e+09 4.8964e+11 22196
## - LotFrontage    1 1.7429e+09 4.8968e+11 22196
## - BldgType       4 4.6164e+09 4.9255e+11 22196
## - Foundation     4 4.7203e+09 4.9265e+11 22197
## - GarageArea     1 2.1252e+09 4.9006e+11 22197
## - GarageCond     4 4.8273e+09 4.9276e+11 22197
## - MasVnrType     3 4.4260e+09 4.9236e+11 22198
## - Functional     5 6.2369e+09 4.9417e+11 22198
## - LandContour    3 4.5502e+09 4.9248e+11 22198
## - Fireplaces     1 2.7891e+09 4.9072e+11 22198
## - MSZoning       4 5.5497e+09 4.9348e+11 22198
## - Condition1     8 9.4001e+09 4.9733e+11 22199
## - BedroomAbvGr   1 3.2240e+09 4.9116e+11 22199
## - KitchenAbvGr   1 3.4242e+09 4.9136e+11 22200
## - YearBuilt      1 3.4983e+09 4.9143e+11 22200
## - Street         1 3.6283e+09 4.9156e+11 22200
## + GarageType     5 1.3181e+09 4.8661e+11 22201
## + SaleType       8 3.8266e+09 4.8411e+11 22201
## - GarageQual     4 6.9644e+09 4.9490e+11 22201
## + BsmtFinType2   5 5.5175e+08 4.8738e+11 22203
## - LandSlope      2 6.8188e+09 4.9475e+11 22205
## - BsmtUnfSF      1 7.6769e+09 4.9561e+11 22209
## - MasVnrArea     1 7.7489e+09 4.9568e+11 22209
## - LotConfig      4 1.0632e+10 4.9856e+11 22210
## + Exterior2nd   14 5.0177e+09 4.8291e+11 22211
## - BsmtQual       3 1.0598e+10 4.9853e+11 22211
## - BsmtFinSF2     1 9.7797e+09 4.9771e+11 22214
## - ExterQual      3 1.1871e+10 4.9980e+11 22214
## - KitchenQual    3 1.2748e+10 5.0068e+11 22216
## - SaleCondition  5 1.4966e+10 5.0290e+11 22217
## - RoofMatl       6 1.7983e+10 5.0592e+11 22222
## - LotArea        1 1.3850e+10 5.0178e+11 22223
## - OverallCond    1 1.5553e+10 5.0348e+11 22226
## - MiscFeature    3 1.8443e+10 5.0638e+11 22229
## - X1stFlrSF      1 1.7105e+10 5.0504e+11 22230
## - BsmtExposure   3 1.9319e+10 5.0725e+11 22230
## - OverallQual    1 1.7691e+10 5.0562e+11 22231
## - BsmtFinSF1     1 1.9750e+10 5.0768e+11 22235
## - PoolArea       1 2.2646e+10 5.1058e+11 22242
## - PoolQC         3 2.7274e+10 5.1521e+11 22247
## - X2ndFlrSF      1 5.1897e+10 5.3983e+11 22303
## - Condition2     5 6.3682e+10 5.5161e+11 22318
## - Neighborhood  24 8.5119e+10 5.7305e+11 22322
## 
## Step:  AIC=22187.96
## SalePrice ~ MSSubClass + MSZoning + LotFrontage + LotArea + Street + 
##     Alley + LotShape + LandContour + LotConfig + LandSlope + 
##     Neighborhood + Condition1 + Condition2 + BldgType + HouseStyle + 
##     OverallQual + OverallCond + YearBuilt + YearRemodAdd + RoofStyle + 
##     RoofMatl + Exterior1st + MasVnrType + MasVnrArea + ExterQual + 
##     ExterCond + Foundation + BsmtQual + BsmtCond + BsmtExposure + 
##     BsmtFinType1 + BsmtFinSF1 + BsmtFinSF2 + BsmtUnfSF + Heating + 
##     HeatingQC + CentralAir + X1stFlrSF + X2ndFlrSF + LowQualFinSF + 
##     BsmtFullBath + BsmtHalfBath + FullBath + HalfBath + BedroomAbvGr + 
##     KitchenAbvGr + KitchenQual + TotRmsAbvGrd + Functional + 
##     Fireplaces + FireplaceQu + GarageYrBlt + GarageFinish + GarageCars + 
##     GarageArea + GarageQual + GarageCond + PavedDrive + WoodDeckSF + 
##     OpenPorchSF + EnclosedPorch + X3SsnPorch + ScreenPorch + 
##     PoolArea + PoolQC + Fence + MiscFeature + MiscVal + MoSold + 
##     YrSold + SaleCondition
## 
##                 Df  Sum of Sq        RSS   AIC
## - Heating        3 9.9135e+07 4.8804e+11 22182
## - HeatingQC      4 1.1712e+09 4.8911e+11 22183
## - BsmtCond       3 3.4951e+08 4.8829e+11 22183
## - ExterCond      3 5.6991e+08 4.8851e+11 22183
## - FireplaceQu    5 2.4351e+09 4.9038e+11 22183
## - Fence          4 1.7301e+09 4.8967e+11 22184
## - Exterior1st   13 1.0039e+10 4.9798e+11 22184
## - HouseStyle     7 4.9230e+09 4.9287e+11 22185
## - PavedDrive     2 5.0424e+08 4.8845e+11 22185
## - Alley          2 5.8012e+08 4.8852e+11 22185
## - RoofStyle      4 2.4419e+09 4.9039e+11 22185
## - LotShape       3 1.6436e+09 4.8959e+11 22186
## - OpenPorchSF    1 5.4270e+03 4.8794e+11 22186
## - MSSubClass     1 3.3346e+05 4.8794e+11 22186
## - GarageYrBlt    1 3.8768e+05 4.8794e+11 22186
## - MiscVal        1 1.4125e+07 4.8796e+11 22186
## - BsmtHalfBath   1 3.2312e+07 4.8798e+11 22186
## - EnclosedPorch  1 5.8737e+07 4.8800e+11 22186
## - GarageFinish   2 9.8412e+08 4.8893e+11 22186
## - YrSold         1 1.0999e+08 4.8805e+11 22186
## - BsmtFullBath   1 2.2428e+08 4.8817e+11 22187
## - HalfBath       1 4.4122e+08 4.8838e+11 22187
## - CentralAir     1 6.1309e+08 4.8856e+11 22187
## - BsmtFinType1   5 4.2099e+09 4.9215e+11 22187
## - LowQualFinSF   1 7.4965e+08 4.8869e+11 22188
## - MoSold         1 8.0278e+08 4.8875e+11 22188
## <none>                        4.8794e+11 22188
## - WoodDeckSF     1 1.0214e+09 4.8896e+11 22188
## - X3SsnPorch     1 1.2487e+09 4.8919e+11 22189
## - GarageCars     1 1.3371e+09 4.8928e+11 22189
## - TotRmsAbvGrd   1 1.4174e+09 4.8936e+11 22189
## - YearRemodAdd   1 1.4465e+09 4.8939e+11 22189
## - ScreenPorch    1 1.5136e+09 4.8946e+11 22189
## - FullBath       1 1.7271e+09 4.8967e+11 22190
## - LotFrontage    1 1.7600e+09 4.8970e+11 22190
## - BldgType       4 4.6975e+09 4.9264e+11 22190
## - Foundation     4 4.7287e+09 4.9267e+11 22191
## - GarageCond     4 4.8277e+09 4.9277e+11 22191
## - GarageArea     1 2.1354e+09 4.9008e+11 22191
## - MasVnrType     3 4.4179e+09 4.9236e+11 22192
## - Functional     5 6.2407e+09 4.9418e+11 22192
## - LandContour    3 4.5827e+09 4.9253e+11 22192
## - Fireplaces     1 2.8091e+09 4.9075e+11 22192
## - MSZoning       4 5.5675e+09 4.9351e+11 22192
## - Condition1     8 9.5327e+09 4.9748e+11 22193
## - BedroomAbvGr   1 3.2139e+09 4.9116e+11 22193
## - KitchenAbvGr   1 3.4857e+09 4.9143e+11 22194
## - YearBuilt      1 3.5266e+09 4.9147e+11 22194
## + Electrical     3 1.1185e+07 4.8793e+11 22194
## - Street         1 3.6559e+09 4.9160e+11 22194
## + GarageType     5 1.3221e+09 4.8662e+11 22195
## + SaleType       8 3.8100e+09 4.8413e+11 22195
## - GarageQual     4 7.1047e+09 4.9505e+11 22196
## + BsmtFinType2   5 5.5531e+08 4.8739e+11 22197
## - LandSlope      2 6.8181e+09 4.9476e+11 22199
## - BsmtUnfSF      1 7.7651e+09 4.9571e+11 22203
## - MasVnrArea     1 7.7709e+09 4.9571e+11 22203
## - LotConfig      4 1.0642e+10 4.9859e+11 22204
## + Exterior2nd   14 4.9574e+09 4.8299e+11 22205
## - BsmtQual       3 1.0589e+10 4.9853e+11 22205
## - BsmtFinSF2     1 9.8339e+09 4.9778e+11 22208
## - ExterQual      3 1.1910e+10 4.9985e+11 22208
## - KitchenQual    3 1.2738e+10 5.0068e+11 22210
## - SaleCondition  5 1.5015e+10 5.0296e+11 22211
## - RoofMatl       6 1.8010e+10 5.0595e+11 22216
## - LotArea        1 1.4115e+10 5.0206e+11 22217
## - OverallCond    1 1.5604e+10 5.0355e+11 22220
## - MiscFeature    3 1.8440e+10 5.0638e+11 22223
## - X1stFlrSF      1 1.7262e+10 5.0521e+11 22224
## - BsmtExposure   3 1.9348e+10 5.0729e+11 22225
## - OverallQual    1 1.7781e+10 5.0572e+11 22225
## - BsmtFinSF1     1 1.9867e+10 5.0781e+11 22230
## - PoolArea       1 2.2658e+10 5.1060e+11 22236
## - PoolQC         3 2.7275e+10 5.1522e+11 22242
## - X2ndFlrSF      1 5.2057e+10 5.4000e+11 22297
## - Condition2     5 6.3723e+10 5.5167e+11 22312
## - Neighborhood  24 8.5184e+10 5.7313e+11 22316
## 
## Step:  AIC=22182.18
## SalePrice ~ MSSubClass + MSZoning + LotFrontage + LotArea + Street + 
##     Alley + LotShape + LandContour + LotConfig + LandSlope + 
##     Neighborhood + Condition1 + Condition2 + BldgType + HouseStyle + 
##     OverallQual + OverallCond + YearBuilt + YearRemodAdd + RoofStyle + 
##     RoofMatl + Exterior1st + MasVnrType + MasVnrArea + ExterQual + 
##     ExterCond + Foundation + BsmtQual + BsmtCond + BsmtExposure + 
##     BsmtFinType1 + BsmtFinSF1 + BsmtFinSF2 + BsmtUnfSF + HeatingQC + 
##     CentralAir + X1stFlrSF + X2ndFlrSF + LowQualFinSF + BsmtFullBath + 
##     BsmtHalfBath + FullBath + HalfBath + BedroomAbvGr + KitchenAbvGr + 
##     KitchenQual + TotRmsAbvGrd + Functional + Fireplaces + FireplaceQu + 
##     GarageYrBlt + GarageFinish + GarageCars + GarageArea + GarageQual + 
##     GarageCond + PavedDrive + WoodDeckSF + OpenPorchSF + EnclosedPorch + 
##     X3SsnPorch + ScreenPorch + PoolArea + PoolQC + Fence + MiscFeature + 
##     MiscVal + MoSold + YrSold + SaleCondition
## 
##                 Df  Sum of Sq        RSS   AIC
## - BsmtCond       3 3.0831e+08 4.8835e+11 22177
## - HeatingQC      4 1.2742e+09 4.8932e+11 22177
## - ExterCond      3 5.7653e+08 4.8862e+11 22178
## - FireplaceQu    5 2.4574e+09 4.9050e+11 22178
## - Fence          4 1.7286e+09 4.8977e+11 22178
## - Exterior1st   13 1.0173e+10 4.9822e+11 22179
## - HouseStyle     7 5.0171e+09 4.9306e+11 22179
## - PavedDrive     2 5.6948e+08 4.8861e+11 22180
## - Alley          2 6.0878e+08 4.8865e+11 22180
## - RoofStyle      4 2.4597e+09 4.9050e+11 22180
## - LotShape       3 1.6428e+09 4.8969e+11 22180
## - OpenPorchSF    1 2.4985e+04 4.8804e+11 22180
## - MSSubClass     1 7.0419e+05 4.8804e+11 22180
## - GarageYrBlt    1 3.0585e+06 4.8805e+11 22180
## - MiscVal        1 1.0912e+07 4.8805e+11 22180
## - BsmtHalfBath   1 3.5330e+07 4.8808e+11 22180
## - EnclosedPorch  1 5.6421e+07 4.8810e+11 22180
## - GarageFinish   2 9.7224e+08 4.8901e+11 22180
## - YrSold         1 1.0626e+08 4.8815e+11 22180
## - BsmtFullBath   1 2.3472e+08 4.8828e+11 22181
## - HalfBath       1 4.3024e+08 4.8847e+11 22181
## - CentralAir     1 5.7694e+08 4.8862e+11 22182
## - BsmtFinType1   5 4.1965e+09 4.9224e+11 22182
## - LowQualFinSF   1 7.3995e+08 4.8878e+11 22182
## - MoSold         1 7.8230e+08 4.8882e+11 22182
## <none>                        4.8804e+11 22182
## - WoodDeckSF     1 1.0080e+09 4.8905e+11 22182
## - X3SsnPorch     1 1.2423e+09 4.8928e+11 22183
## - GarageCars     1 1.3643e+09 4.8941e+11 22183
## - TotRmsAbvGrd   1 1.4178e+09 4.8946e+11 22183
## - YearRemodAdd   1 1.5109e+09 4.8955e+11 22184
## - ScreenPorch    1 1.5289e+09 4.8957e+11 22184
## - LotFrontage    1 1.7396e+09 4.8978e+11 22184
## - FullBath       1 1.7427e+09 4.8979e+11 22184
## - Foundation     4 4.6652e+09 4.9271e+11 22185
## - BldgType       4 4.7975e+09 4.9284e+11 22185
## - GarageArea     1 2.1524e+09 4.9020e+11 22185
## - GarageCond     4 4.8560e+09 4.9290e+11 22185
## - MasVnrType     3 4.4130e+09 4.9246e+11 22186
## - Functional     5 6.2847e+09 4.9433e+11 22186
## - LandContour    3 4.5808e+09 4.9262e+11 22186
## - MSZoning       4 5.5376e+09 4.9358e+11 22187
## - Fireplaces     1 2.8432e+09 4.9089e+11 22187
## - BedroomAbvGr   1 3.2406e+09 4.9128e+11 22187
## - Condition1     8 9.6239e+09 4.9767e+11 22188
## + Heating        3 9.9135e+07 4.8794e+11 22188
## - YearBuilt      1 3.5230e+09 4.9157e+11 22188
## + Electrical     3 1.2054e+07 4.8803e+11 22188
## - KitchenAbvGr   1 3.7187e+09 4.9176e+11 22189
## - Street         1 3.7309e+09 4.9177e+11 22189
## + GarageType     5 1.2993e+09 4.8674e+11 22189
## + SaleType       8 3.7332e+09 4.8431e+11 22190
## - GarageQual     4 7.0634e+09 4.9511e+11 22190
## + BsmtFinType2   5 5.4381e+08 4.8750e+11 22191
## - LandSlope      2 6.8558e+09 4.9490e+11 22193
## - MasVnrArea     1 7.8202e+09 4.9586e+11 22198
## - BsmtUnfSF      1 7.8518e+09 4.9589e+11 22198
## - LotConfig      4 1.0621e+10 4.9866e+11 22198
## + Exterior2nd   14 4.9832e+09 4.8306e+11 22199
## - BsmtQual       3 1.0555e+10 4.9860e+11 22200
## - BsmtFinSF2     1 9.8935e+09 4.9794e+11 22202
## - ExterQual      3 1.1968e+10 5.0001e+11 22203
## - KitchenQual    3 1.2790e+10 5.0083e+11 22205
## - SaleCondition  5 1.4979e+10 5.0302e+11 22205
## - RoofMatl       6 1.8089e+10 5.0613e+11 22210
## - LotArea        1 1.4740e+10 5.0278e+11 22213
## - OverallCond    1 1.5543e+10 5.0359e+11 22215
## - MiscFeature    3 1.8451e+10 5.0649e+11 22217
## - X1stFlrSF      1 1.7327e+10 5.0537e+11 22218
## - BsmtExposure   3 1.9398e+10 5.0744e+11 22219
## - OverallQual    1 1.7765e+10 5.0581e+11 22219
## - BsmtFinSF1     1 2.0058e+10 5.0810e+11 22224
## - PoolArea       1 2.2708e+10 5.1075e+11 22230
## - PoolQC         3 2.7309e+10 5.1535e+11 22236
## - X2ndFlrSF      1 5.2359e+10 5.4040e+11 22292
## - Condition2     5 6.3797e+10 5.5184e+11 22307
## - Neighborhood  24 8.5436e+10 5.7348e+11 22311
## 
## Step:  AIC=22176.87
## SalePrice ~ MSSubClass + MSZoning + LotFrontage + LotArea + Street + 
##     Alley + LotShape + LandContour + LotConfig + LandSlope + 
##     Neighborhood + Condition1 + Condition2 + BldgType + HouseStyle + 
##     OverallQual + OverallCond + YearBuilt + YearRemodAdd + RoofStyle + 
##     RoofMatl + Exterior1st + MasVnrType + MasVnrArea + ExterQual + 
##     ExterCond + Foundation + BsmtQual + BsmtExposure + BsmtFinType1 + 
##     BsmtFinSF1 + BsmtFinSF2 + BsmtUnfSF + HeatingQC + CentralAir + 
##     X1stFlrSF + X2ndFlrSF + LowQualFinSF + BsmtFullBath + BsmtHalfBath + 
##     FullBath + HalfBath + BedroomAbvGr + KitchenAbvGr + KitchenQual + 
##     TotRmsAbvGrd + Functional + Fireplaces + FireplaceQu + GarageYrBlt + 
##     GarageFinish + GarageCars + GarageArea + GarageQual + GarageCond + 
##     PavedDrive + WoodDeckSF + OpenPorchSF + EnclosedPorch + X3SsnPorch + 
##     ScreenPorch + PoolArea + PoolQC + Fence + MiscFeature + MiscVal + 
##     MoSold + YrSold + SaleCondition
## 
##                 Df  Sum of Sq        RSS   AIC
## - HeatingQC      4 1.2340e+09 4.8958e+11 22172
## - FireplaceQu    5 2.5184e+09 4.9087e+11 22173
## - ExterCond      3 7.3115e+08 4.8908e+11 22173
## - Fence          4 1.6745e+09 4.9003e+11 22173
## - Exterior1st   13 1.0247e+10 4.9860e+11 22174
## - PavedDrive     2 5.6753e+08 4.8892e+11 22174
## - HouseStyle     7 5.0697e+09 4.9342e+11 22174
## - Alley          2 6.0883e+08 4.8896e+11 22174
## - LotShape       3 1.5903e+09 4.8994e+11 22174
## - RoofStyle      4 2.5711e+09 4.9092e+11 22175
## - OpenPorchSF    1 1.6308e+05 4.8835e+11 22175
## - MSSubClass     1 2.0616e+06 4.8835e+11 22175
## - GarageYrBlt    1 3.4420e+06 4.8835e+11 22175
## - MiscVal        1 1.2729e+07 4.8836e+11 22175
## - BsmtHalfBath   1 2.9879e+07 4.8838e+11 22175
## - EnclosedPorch  1 3.4072e+07 4.8839e+11 22175
## - YrSold         1 6.4453e+07 4.8842e+11 22175
## - GarageFinish   2 9.7896e+08 4.8933e+11 22175
## - BsmtFullBath   1 2.0563e+08 4.8856e+11 22175
## - HalfBath       1 4.9573e+08 4.8885e+11 22176
## - BsmtFinType1   5 4.2387e+09 4.9259e+11 22176
## - CentralAir     1 6.5152e+08 4.8900e+11 22176
## - LowQualFinSF   1 7.2345e+08 4.8907e+11 22177
## - MoSold         1 7.6967e+08 4.8912e+11 22177
## <none>                        4.8835e+11 22177
## - WoodDeckSF     1 9.6745e+08 4.8932e+11 22177
## - X3SsnPorch     1 1.2590e+09 4.8961e+11 22178
## - GarageCars     1 1.3298e+09 4.8968e+11 22178
## - TotRmsAbvGrd   1 1.4684e+09 4.8982e+11 22178
## - YearRemodAdd   1 1.4742e+09 4.8983e+11 22178
## - ScreenPorch    1 1.5425e+09 4.8989e+11 22178
## - FullBath       1 1.7560e+09 4.9011e+11 22179
## - LotFrontage    1 1.7810e+09 4.9013e+11 22179
## - Foundation     4 4.6584e+09 4.9301e+11 22179
## - BldgType       4 4.7730e+09 4.9312e+11 22180
## - GarageArea     1 2.2020e+09 4.9055e+11 22180
## - GarageCond     4 4.9787e+09 4.9333e+11 22180
## - MasVnrType     3 4.4412e+09 4.9279e+11 22181
## - LandContour    3 4.5179e+09 4.9287e+11 22181
## - Functional     5 6.3383e+09 4.9469e+11 22181
## - Fireplaces     1 2.8416e+09 4.9119e+11 22181
## - MSZoning       4 5.5843e+09 4.9394e+11 22181
## - BedroomAbvGr   1 3.1665e+09 4.9152e+11 22182
## + BsmtCond       3 3.0831e+08 4.8804e+11 22182
## - Condition1     8 9.6790e+09 4.9803e+11 22182
## - YearBuilt      1 3.5141e+09 4.9187e+11 22183
## + Heating        3 5.7939e+07 4.8829e+11 22183
## - Street         1 3.6911e+09 4.9204e+11 22183
## - KitchenAbvGr   1 3.8700e+09 4.9222e+11 22184
## + GarageType     5 1.3200e+09 4.8703e+11 22184
## - GarageQual     4 6.9675e+09 4.9532e+11 22184
## + Electrical     4 8.7174e+07 4.8826e+11 22185
## + SaleType       8 3.6434e+09 4.8471e+11 22185
## + BsmtFinType2   5 5.6221e+08 4.8779e+11 22186
## - LandSlope      2 6.7762e+09 4.9513e+11 22188
## - BsmtUnfSF      1 7.8553e+09 4.9621e+11 22192
## - MasVnrArea     1 7.9231e+09 4.9627e+11 22193
## - LotConfig      4 1.0665e+10 4.9902e+11 22193
## + Exterior2nd   14 4.9649e+09 4.8339e+11 22194
## - BsmtQual       3 1.0429e+10 4.9878e+11 22194
## - BsmtFinSF2     1 9.8228e+09 4.9817e+11 22197
## - ExterQual      3 1.1969e+10 5.0032e+11 22197
## - KitchenQual    3 1.2660e+10 5.0101e+11 22199
## - SaleCondition  5 1.4838e+10 5.0319e+11 22200
## - RoofMatl       6 1.8193e+10 5.0654e+11 22205
## - LotArea        1 1.4702e+10 5.0305e+11 22207
## - OverallCond    1 1.5816e+10 5.0417e+11 22210
## - MiscFeature    3 1.8416e+10 5.0677e+11 22211
## - X1stFlrSF      1 1.7334e+10 5.0568e+11 22213
## - BsmtExposure   3 1.9586e+10 5.0794e+11 22214
## - OverallQual    1 1.7793e+10 5.0614e+11 22214
## - BsmtFinSF1     1 2.0310e+10 5.0866e+11 22220
## - PoolArea       1 2.2659e+10 5.1101e+11 22225
## - PoolQC         3 2.7255e+10 5.1561e+11 22230
## - X2ndFlrSF      1 5.2237e+10 5.4059e+11 22286
## - Condition2     5 6.3967e+10 5.5232e+11 22302
## - Neighborhood  24 8.5450e+10 5.7380e+11 22305
## 
## Step:  AIC=22171.64
## SalePrice ~ MSSubClass + MSZoning + LotFrontage + LotArea + Street + 
##     Alley + LotShape + LandContour + LotConfig + LandSlope + 
##     Neighborhood + Condition1 + Condition2 + BldgType + HouseStyle + 
##     OverallQual + OverallCond + YearBuilt + YearRemodAdd + RoofStyle + 
##     RoofMatl + Exterior1st + MasVnrType + MasVnrArea + ExterQual + 
##     ExterCond + Foundation + BsmtQual + BsmtExposure + BsmtFinType1 + 
##     BsmtFinSF1 + BsmtFinSF2 + BsmtUnfSF + CentralAir + X1stFlrSF + 
##     X2ndFlrSF + LowQualFinSF + BsmtFullBath + BsmtHalfBath + 
##     FullBath + HalfBath + BedroomAbvGr + KitchenAbvGr + KitchenQual + 
##     TotRmsAbvGrd + Functional + Fireplaces + FireplaceQu + GarageYrBlt + 
##     GarageFinish + GarageCars + GarageArea + GarageQual + GarageCond + 
##     PavedDrive + WoodDeckSF + OpenPorchSF + EnclosedPorch + X3SsnPorch + 
##     ScreenPorch + PoolArea + PoolQC + Fence + MiscFeature + MiscVal + 
##     MoSold + YrSold + SaleCondition
## 
##                 Df  Sum of Sq        RSS   AIC
## - FireplaceQu    5 2.5563e+09 4.9214e+11 22167
## - Fence          4 1.6623e+09 4.9125e+11 22167
## - ExterCond      3 7.7423e+08 4.9036e+11 22167
## - HouseStyle     7 4.7570e+09 4.9434e+11 22168
## - PavedDrive     2 5.1917e+08 4.9010e+11 22169
## - RoofStyle      4 2.3769e+09 4.9196e+11 22169
## - Alley          2 5.8404e+08 4.9017e+11 22169
## - LotShape       3 1.5240e+09 4.9111e+11 22169
## - GarageFinish   2 8.8160e+08 4.9047e+11 22170
## - MiscVal        1 5.3442e+04 4.8959e+11 22170
## - OpenPorchSF    1 1.1342e+06 4.8959e+11 22170
## - MSSubClass     1 2.2676e+06 4.8959e+11 22170
## - GarageYrBlt    1 8.2252e+06 4.8959e+11 22170
## - EnclosedPorch  1 2.9091e+07 4.8961e+11 22170
## - BsmtHalfBath   1 4.8922e+07 4.8963e+11 22170
## - YrSold         1 5.4579e+07 4.8964e+11 22170
## - BsmtFullBath   1 2.5686e+08 4.8984e+11 22170
## - HalfBath       1 4.2183e+08 4.9001e+11 22171
## - Exterior1st   13 1.1347e+10 5.0093e+11 22171
## - BsmtFinType1   5 4.1542e+09 4.9374e+11 22171
## - CentralAir     1 6.7049e+08 4.9026e+11 22171
## - LowQualFinSF   1 7.1905e+08 4.9030e+11 22171
## - MoSold         1 7.5241e+08 4.9034e+11 22171
## - WoodDeckSF     1 8.6883e+08 4.9045e+11 22172
## <none>                        4.8958e+11 22172
## - ScreenPorch    1 1.2709e+09 4.9086e+11 22173
## - X3SsnPorch     1 1.3247e+09 4.9091e+11 22173
## - GarageCars     1 1.3443e+09 4.9093e+11 22173
## - TotRmsAbvGrd   1 1.5045e+09 4.9109e+11 22173
## - YearRemodAdd   1 1.5938e+09 4.9118e+11 22173
## - FullBath       1 1.7440e+09 4.9133e+11 22174
## - LotFrontage    1 1.8776e+09 4.9146e+11 22174
## - Foundation     4 4.7176e+09 4.9430e+11 22174
## - BldgType       4 4.8516e+09 4.9444e+11 22174
## - GarageArea     1 2.2018e+09 4.9179e+11 22175
## - GarageCond     4 4.9425e+09 4.9453e+11 22175
## - LandContour    3 4.4833e+09 4.9407e+11 22176
## - Functional     5 6.3656e+09 4.9595e+11 22176
## - MasVnrType     3 4.6618e+09 4.9425e+11 22176
## - Fireplaces     1 2.8945e+09 4.9248e+11 22176
## - MSZoning       4 5.6835e+09 4.9527e+11 22176
## + HeatingQC      4 1.2340e+09 4.8835e+11 22177
## + BsmtCond       3 2.6816e+08 4.8932e+11 22177
## - BedroomAbvGr   1 3.3252e+09 4.9291e+11 22177
## + Heating        3 1.4604e+08 4.8944e+11 22177
## - Condition1     8 9.9941e+09 4.9958e+11 22178
## - Street         1 3.6928e+09 4.9328e+11 22178
## - YearBuilt      1 3.8325e+09 4.9342e+11 22178
## - KitchenAbvGr   1 4.0042e+09 4.9359e+11 22179
## + GarageType     5 1.2851e+09 4.8830e+11 22179
## - GarageQual     4 7.0622e+09 4.9665e+11 22179
## + Electrical     4 6.8482e+07 4.8952e+11 22180
## + SaleType       8 3.4730e+09 4.8611e+11 22180
## + BsmtFinType2   5 6.8081e+08 4.8890e+11 22180
## - LandSlope      2 6.7885e+09 4.9637e+11 22183
## - BsmtUnfSF      1 7.8528e+09 4.9744e+11 22187
## - LotConfig      4 1.0609e+10 5.0019e+11 22187
## - MasVnrArea     1 8.0115e+09 4.9760e+11 22187
## + Exterior2nd   14 5.0286e+09 4.8456e+11 22188
## - BsmtQual       3 1.0691e+10 5.0028e+11 22189
## - BsmtFinSF2     1 9.9034e+09 4.9949e+11 22192
## - ExterQual      3 1.1929e+10 5.0151e+11 22192
## - KitchenQual    3 1.2502e+10 5.0209e+11 22193
## - SaleCondition  5 1.4809e+10 5.0439e+11 22194
## - RoofMatl       6 1.7936e+10 5.0752e+11 22199
## - LotArea        1 1.4505e+10 5.0409e+11 22202
## - OverallCond    1 1.6016e+10 5.0560e+11 22205
## - MiscFeature    3 1.8371e+10 5.0796e+11 22206
## - X1stFlrSF      1 1.7395e+10 5.0698e+11 22208
## - BsmtExposure   3 1.9670e+10 5.0926e+11 22209
## - OverallQual    1 1.7915e+10 5.0750e+11 22209
## - BsmtFinSF1     1 2.0143e+10 5.0973e+11 22214
## - PoolArea       1 2.3102e+10 5.1269e+11 22220
## - PoolQC         3 2.7224e+10 5.1681e+11 22225
## - X2ndFlrSF      1 5.2746e+10 5.4233e+11 22282
## - Condition2     5 6.3797e+10 5.5338e+11 22296
## - Neighborhood  24 8.5260e+10 5.7485e+11 22299
## 
## Step:  AIC=22167.33
## SalePrice ~ MSSubClass + MSZoning + LotFrontage + LotArea + Street + 
##     Alley + LotShape + LandContour + LotConfig + LandSlope + 
##     Neighborhood + Condition1 + Condition2 + BldgType + HouseStyle + 
##     OverallQual + OverallCond + YearBuilt + YearRemodAdd + RoofStyle + 
##     RoofMatl + Exterior1st + MasVnrType + MasVnrArea + ExterQual + 
##     ExterCond + Foundation + BsmtQual + BsmtExposure + BsmtFinType1 + 
##     BsmtFinSF1 + BsmtFinSF2 + BsmtUnfSF + CentralAir + X1stFlrSF + 
##     X2ndFlrSF + LowQualFinSF + BsmtFullBath + BsmtHalfBath + 
##     FullBath + HalfBath + BedroomAbvGr + KitchenAbvGr + KitchenQual + 
##     TotRmsAbvGrd + Functional + Fireplaces + GarageYrBlt + GarageFinish + 
##     GarageCars + GarageArea + GarageQual + GarageCond + PavedDrive + 
##     WoodDeckSF + OpenPorchSF + EnclosedPorch + X3SsnPorch + ScreenPorch + 
##     PoolArea + PoolQC + Fence + MiscFeature + MiscVal + MoSold + 
##     YrSold + SaleCondition
## 
##                 Df  Sum of Sq        RSS   AIC
## - ExterCond      3 7.3616e+08 4.9288e+11 22163
## - Fence          4 1.8630e+09 4.9400e+11 22164
## - HouseStyle     7 4.7676e+09 4.9691e+11 22164
## - PavedDrive     2 5.4457e+08 4.9269e+11 22165
## - Alley          2 6.1762e+08 4.9276e+11 22165
## - RoofStyle      4 2.4905e+09 4.9463e+11 22165
## - LotShape       3 1.7796e+09 4.9392e+11 22165
## - GarageYrBlt    1 2.9941e+06 4.9214e+11 22165
## - MiscVal        1 3.0700e+06 4.9214e+11 22165
## - OpenPorchSF    1 3.5298e+06 4.9214e+11 22165
## - MSSubClass     1 9.0944e+06 4.9215e+11 22165
## - EnclosedPorch  1 1.3664e+07 4.9215e+11 22165
## - BsmtHalfBath   1 2.0717e+07 4.9216e+11 22165
## - YrSold         1 3.0776e+07 4.9217e+11 22165
## - GarageFinish   2 9.8648e+08 4.9313e+11 22166
## - BsmtFullBath   1 1.9828e+08 4.9234e+11 22166
## - HalfBath       1 4.6812e+08 4.9261e+11 22166
## - CentralAir     1 6.1704e+08 4.9276e+11 22167
## - LowQualFinSF   1 6.6781e+08 4.9281e+11 22167
## - MoSold         1 7.9379e+08 4.9294e+11 22167
## - WoodDeckSF     1 8.9481e+08 4.9304e+11 22167
## <none>                        4.9214e+11 22167
## - Exterior1st   13 1.1921e+10 5.0406e+11 22168
## - BsmtFinType1   5 4.6581e+09 4.9680e+11 22168
## - X3SsnPorch     1 1.1295e+09 4.9327e+11 22168
## - TotRmsAbvGrd   1 1.1884e+09 4.9333e+11 22168
## - ScreenPorch    1 1.2296e+09 4.9337e+11 22168
## - GarageCars     1 1.3470e+09 4.9349e+11 22168
## - Fireplaces     1 1.4092e+09 4.9355e+11 22169
## - YearRemodAdd   1 1.5858e+09 4.9373e+11 22169
## - FullBath       1 1.6641e+09 4.9381e+11 22169
## - Foundation     4 4.5810e+09 4.9672e+11 22170
## - LotFrontage    1 1.8977e+09 4.9404e+11 22170
## - GarageArea     1 1.9921e+09 4.9413e+11 22170
## - GarageCond     4 4.8637e+09 4.9700e+11 22170
## - BldgType       4 4.9352e+09 4.9708e+11 22170
## - Functional     5 6.1646e+09 4.9831e+11 22171
## + FireplaceQu    5 2.5563e+09 4.8958e+11 22172
## - LandContour    3 4.8301e+09 4.9697e+11 22172
## - MasVnrType     3 4.8366e+09 4.9698e+11 22172
## - MSZoning       4 5.8681e+09 4.9801e+11 22172
## + HeatingQC      4 1.2720e+09 4.9087e+11 22173
## + BsmtCond       3 3.2971e+08 4.9181e+11 22173
## - BedroomAbvGr   1 3.4244e+09 4.9557e+11 22173
## + Heating        3 1.6300e+08 4.9198e+11 22173
## - Street         1 3.4773e+09 4.9562e+11 22173
## - YearBuilt      1 3.8347e+09 4.9598e+11 22174
## + GarageType     5 1.5215e+09 4.9062e+11 22174
## - KitchenAbvGr   1 3.9562e+09 4.9610e+11 22174
## - Condition1     8 1.0455e+10 5.0260e+11 22174
## - GarageQual     4 6.8605e+09 4.9900e+11 22175
## + Electrical     4 5.7315e+07 4.9208e+11 22175
## + SaleType       8 3.5747e+09 4.8857e+11 22175
## + BsmtFinType2   5 7.1052e+08 4.9143e+11 22176
## - LandSlope      2 6.2514e+09 4.9839e+11 22177
## - MasVnrArea     1 7.7929e+09 4.9993e+11 22183
## - LotConfig      4 1.0803e+10 5.0294e+11 22183
## + Exterior2nd   14 5.1863e+09 4.8696e+11 22184
## - BsmtUnfSF      1 8.4868e+09 5.0063e+11 22184
## - BsmtQual       3 1.1221e+10 5.0336e+11 22186
## - BsmtFinSF2     1 1.0038e+10 5.0218e+11 22187
## - ExterQual      3 1.1915e+10 5.0406e+11 22188
## - SaleCondition  5 1.5079e+10 5.0722e+11 22190
## - KitchenQual    3 1.4636e+10 5.0678e+11 22193
## - RoofMatl       6 1.9562e+10 5.1170e+11 22198
## - LotArea        1 1.5240e+10 5.0738e+11 22199
## - OverallCond    1 1.6354e+10 5.0850e+11 22201
## - MiscFeature    3 1.8284e+10 5.1043e+11 22201
## - X1stFlrSF      1 1.7941e+10 5.1008e+11 22205
## - OverallQual    1 1.8022e+10 5.1016e+11 22205
## - BsmtExposure   3 2.1439e+10 5.1358e+11 22208
## - BsmtFinSF1     1 2.1506e+10 5.1365e+11 22212
## - PoolArea       1 2.3039e+10 5.1518e+11 22215
## - PoolQC         3 2.7407e+10 5.1955e+11 22221
## - X2ndFlrSF      1 5.4995e+10 5.4714e+11 22281
## - Neighborhood  24 8.4016e+10 5.7616e+11 22292
## - Condition2     5 6.5268e+10 5.5741e+11 22294
## 
## Step:  AIC=22162.97
## SalePrice ~ MSSubClass + MSZoning + LotFrontage + LotArea + Street + 
##     Alley + LotShape + LandContour + LotConfig + LandSlope + 
##     Neighborhood + Condition1 + Condition2 + BldgType + HouseStyle + 
##     OverallQual + OverallCond + YearBuilt + YearRemodAdd + RoofStyle + 
##     RoofMatl + Exterior1st + MasVnrType + MasVnrArea + ExterQual + 
##     Foundation + BsmtQual + BsmtExposure + BsmtFinType1 + BsmtFinSF1 + 
##     BsmtFinSF2 + BsmtUnfSF + CentralAir + X1stFlrSF + X2ndFlrSF + 
##     LowQualFinSF + BsmtFullBath + BsmtHalfBath + FullBath + HalfBath + 
##     BedroomAbvGr + KitchenAbvGr + KitchenQual + TotRmsAbvGrd + 
##     Functional + Fireplaces + GarageYrBlt + GarageFinish + GarageCars + 
##     GarageArea + GarageQual + GarageCond + PavedDrive + WoodDeckSF + 
##     OpenPorchSF + EnclosedPorch + X3SsnPorch + ScreenPorch + 
##     PoolArea + PoolQC + Fence + MiscFeature + MiscVal + MoSold + 
##     YrSold + SaleCondition
## 
##                 Df  Sum of Sq        RSS   AIC
## - Fence          4 1.9533e+09 4.9483e+11 22159
## - HouseStyle     7 4.7381e+09 4.9762e+11 22159
## - Alley          2 5.5856e+08 4.9344e+11 22160
## - PavedDrive     2 6.0593e+08 4.9348e+11 22160
## - RoofStyle      4 2.5331e+09 4.9541e+11 22161
## - MiscVal        1 6.0344e+05 4.9288e+11 22161
## - GarageYrBlt    1 1.0273e+06 4.9288e+11 22161
## - OpenPorchSF    1 7.3155e+06 4.9288e+11 22161
## - BsmtHalfBath   1 9.0175e+06 4.9289e+11 22161
## - MSSubClass     1 1.0564e+07 4.9289e+11 22161
## - EnclosedPorch  1 1.3140e+07 4.9289e+11 22161
## - LotShape       3 1.8230e+09 4.9470e+11 22161
## - YrSold         1 3.1873e+07 4.9291e+11 22161
## - GarageFinish   2 1.0028e+09 4.9388e+11 22161
## - BsmtFullBath   1 1.7938e+08 4.9306e+11 22161
## - HalfBath       1 4.7371e+08 4.9335e+11 22162
## - CentralAir     1 6.4340e+08 4.9352e+11 22162
## - LowQualFinSF   1 6.6871e+08 4.9355e+11 22163
## - MoSold         1 8.2568e+08 4.9370e+11 22163
## - WoodDeckSF     1 8.9239e+08 4.9377e+11 22163
## <none>                        4.9288e+11 22163
## - Exterior1st   13 1.2044e+10 5.0492e+11 22163
## - X3SsnPorch     1 1.1185e+09 4.9400e+11 22163
## - TotRmsAbvGrd   1 1.1634e+09 4.9404e+11 22164
## - BsmtFinType1   5 4.8116e+09 4.9769e+11 22164
## - ScreenPorch    1 1.2684e+09 4.9415e+11 22164
## - GarageCars     1 1.3221e+09 4.9420e+11 22164
## - Fireplaces     1 1.3953e+09 4.9427e+11 22164
## - FullBath       1 1.5053e+09 4.9438e+11 22164
## - YearRemodAdd   1 1.5689e+09 4.9445e+11 22164
## - Foundation     4 4.5932e+09 4.9747e+11 22165
## - LotFrontage    1 1.9249e+09 4.9480e+11 22165
## - GarageCond     4 4.6944e+09 4.9757e+11 22165
## - GarageArea     1 2.0227e+09 4.9490e+11 22165
## - Functional     5 6.1612e+09 4.9904e+11 22167
## - BldgType       4 5.3528e+09 4.9823e+11 22167
## + ExterCond      3 7.3616e+08 4.9214e+11 22167
## - MasVnrType     3 4.7060e+09 4.9758e+11 22167
## + FireplaceQu    5 2.5182e+09 4.9036e+11 22167
## - MSZoning       4 5.8250e+09 4.9870e+11 22168
## + BsmtCond       3 4.7827e+08 4.9240e+11 22168
## + HeatingQC      4 1.3129e+09 4.9156e+11 22168
## - LandContour    3 5.0185e+09 4.9790e+11 22168
## + Heating        3 1.7034e+08 4.9271e+11 22169
## - BedroomAbvGr   1 3.4773e+09 4.9635e+11 22169
## - Street         1 3.5739e+09 4.9645e+11 22169
## - YearBuilt      1 3.8944e+09 4.9677e+11 22170
## - KitchenAbvGr   1 3.9633e+09 4.9684e+11 22170
## - GarageQual     4 6.7060e+09 4.9958e+11 22170
## + GarageType     5 1.4296e+09 4.9145e+11 22170
## - Condition1     8 1.0805e+10 5.0368e+11 22171
## + Electrical     4 6.2569e+07 4.9281e+11 22171
## + SaleType       8 3.6368e+09 4.8924e+11 22171
## + BsmtFinType2   5 7.6132e+08 4.9212e+11 22171
## - LandSlope      2 6.1162e+09 4.9899e+11 22173
## - MasVnrArea     1 7.6039e+09 5.0048e+11 22178
## - LotConfig      4 1.0564e+10 5.0344e+11 22178
## + Exterior2nd   14 5.1468e+09 4.8773e+11 22180
## - BsmtUnfSF      1 8.4701e+09 5.0135e+11 22180
## - BsmtQual       3 1.1272e+10 5.0415e+11 22182
## - BsmtFinSF2     1 9.9403e+09 5.0282e+11 22183
## - ExterQual      3 1.2035e+10 5.0491e+11 22183
## - SaleCondition  5 1.5358e+10 5.0824e+11 22187
## - KitchenQual    3 1.4598e+10 5.0748e+11 22189
## - LotArea        1 1.5024e+10 5.0790e+11 22194
## - RoofMatl       6 1.9995e+10 5.1287e+11 22195
## - OverallCond    1 1.5677e+10 5.0855e+11 22195
## - MiscFeature    3 1.8935e+10 5.1181e+11 22198
## - OverallQual    1 1.7941e+10 5.1082e+11 22200
## - X1stFlrSF      1 1.8332e+10 5.1121e+11 22201
## - BsmtExposure   3 2.1542e+10 5.1442e+11 22204
## - BsmtFinSF1     1 2.1496e+10 5.1437e+11 22208
## - PoolArea       1 2.3598e+10 5.1647e+11 22212
## - PoolQC         3 2.7651e+10 5.2053e+11 22217
## - X2ndFlrSF      1 5.5948e+10 5.4883e+11 22279
## - Neighborhood  24 8.4699e+10 5.7758e+11 22289
## - Condition2     5 6.5208e+10 5.5809e+11 22289
## 
## Step:  AIC=22159.3
## SalePrice ~ MSSubClass + MSZoning + LotFrontage + LotArea + Street + 
##     Alley + LotShape + LandContour + LotConfig + LandSlope + 
##     Neighborhood + Condition1 + Condition2 + BldgType + HouseStyle + 
##     OverallQual + OverallCond + YearBuilt + YearRemodAdd + RoofStyle + 
##     RoofMatl + Exterior1st + MasVnrType + MasVnrArea + ExterQual + 
##     Foundation + BsmtQual + BsmtExposure + BsmtFinType1 + BsmtFinSF1 + 
##     BsmtFinSF2 + BsmtUnfSF + CentralAir + X1stFlrSF + X2ndFlrSF + 
##     LowQualFinSF + BsmtFullBath + BsmtHalfBath + FullBath + HalfBath + 
##     BedroomAbvGr + KitchenAbvGr + KitchenQual + TotRmsAbvGrd + 
##     Functional + Fireplaces + GarageYrBlt + GarageFinish + GarageCars + 
##     GarageArea + GarageQual + GarageCond + PavedDrive + WoodDeckSF + 
##     OpenPorchSF + EnclosedPorch + X3SsnPorch + ScreenPorch + 
##     PoolArea + PoolQC + MiscFeature + MiscVal + MoSold + YrSold + 
##     SaleCondition
## 
##                 Df  Sum of Sq        RSS   AIC
## - HouseStyle     7 4.4820e+09 4.9931e+11 22155
## - PavedDrive     2 4.8490e+08 4.9532e+11 22156
## - Alley          2 6.9457e+08 4.9553e+11 22157
## - RoofStyle      4 2.5960e+09 4.9743e+11 22157
## - GarageYrBlt    1 9.0900e+03 4.9483e+11 22157
## - BsmtHalfBath   1 9.1670e+05 4.9483e+11 22157
## - MiscVal        1 1.7818e+06 4.9483e+11 22157
## - EnclosedPorch  1 1.0883e+07 4.9484e+11 22157
## - OpenPorchSF    1 2.2443e+07 4.9485e+11 22157
## - MSSubClass     1 2.5876e+07 4.9486e+11 22157
## - YrSold         1 3.4268e+07 4.9487e+11 22157
## - LotShape       3 1.8822e+09 4.9671e+11 22157
## - BsmtFullBath   1 1.5412e+08 4.9498e+11 22158
## - GarageFinish   2 1.2011e+09 4.9603e+11 22158
## - HalfBath       1 5.1601e+08 4.9535e+11 22158
## - CentralAir     1 6.4036e+08 4.9547e+11 22159
## - LowQualFinSF   1 7.1723e+08 4.9555e+11 22159
## - WoodDeckSF     1 7.6254e+08 4.9559e+11 22159
## - BsmtFinType1   5 4.4516e+09 4.9928e+11 22159
## <none>                        4.9483e+11 22159
## - TotRmsAbvGrd   1 9.3054e+08 4.9576e+11 22159
## - MoSold         1 9.3846e+08 4.9577e+11 22159
## - Exterior1st   13 1.2057e+10 5.0689e+11 22160
## - X3SsnPorch     1 1.1120e+09 4.9594e+11 22160
## - GarageCars     1 1.2641e+09 4.9609e+11 22160
## - ScreenPorch    1 1.4480e+09 4.9628e+11 22161
## - GarageCond     4 4.2058e+09 4.9904e+11 22161
## - Fireplaces     1 1.5005e+09 4.9633e+11 22161
## - YearRemodAdd   1 1.5224e+09 4.9635e+11 22161
## - FullBath       1 1.5953e+09 4.9643e+11 22161
## - Foundation     4 4.3393e+09 4.9917e+11 22161
## - LotFrontage    1 1.9577e+09 4.9679e+11 22162
## - GarageArea     1 2.1240e+09 4.9695e+11 22162
## + Fence          4 1.9533e+09 4.9288e+11 22163
## - Functional     5 6.2832e+09 5.0111e+11 22163
## - BldgType       4 5.3844e+09 5.0022e+11 22163
## + FireplaceQu    5 2.7076e+09 4.9212e+11 22163
## + ExterCond      3 8.2647e+08 4.9400e+11 22164
## - MSZoning       4 5.5689e+09 5.0040e+11 22164
## + BsmtCond       3 4.3238e+08 4.9440e+11 22164
## - BedroomAbvGr   1 3.1966e+09 4.9803e+11 22164
## + HeatingQC      4 1.3261e+09 4.9350e+11 22164
## - GarageQual     4 6.0880e+09 5.0092e+11 22165
## - MasVnrType     3 5.2382e+09 5.0007e+11 22165
## - LandContour    3 5.2674e+09 5.0010e+11 22165
## + Heating        3 1.7519e+08 4.9466e+11 22165
## - Street         1 3.6311e+09 4.9846e+11 22165
## - KitchenAbvGr   1 3.8294e+09 4.9866e+11 22166
## - YearBuilt      1 3.8591e+09 4.9869e+11 22166
## - Condition1     8 1.0328e+10 5.0516e+11 22166
## + GarageType     5 1.5269e+09 4.9330e+11 22166
## + SaleType       8 3.8383e+09 4.9099e+11 22167
## + Electrical     4 5.4368e+07 4.9478e+11 22167
## + BsmtFinType2   5 7.6456e+08 4.9407e+11 22168
## - LandSlope      2 5.8980e+09 5.0073e+11 22168
## - MasVnrArea     1 7.6444e+09 5.0248e+11 22174
## - LotConfig      4 1.0508e+10 5.0534e+11 22174
## + Exterior2nd   14 5.2026e+09 4.8963e+11 22176
## - BsmtUnfSF      1 8.6270e+09 5.0346e+11 22176
## - BsmtQual       3 1.1387e+10 5.0622e+11 22178
## - BsmtFinSF2     1 9.8751e+09 5.0471e+11 22179
## - ExterQual      3 1.2011e+10 5.0684e+11 22180
## - SaleCondition  5 1.5494e+10 5.1032e+11 22183
## - KitchenQual    3 1.4503e+10 5.0933e+11 22185
## - RoofMatl       6 1.9286e+10 5.1412e+11 22189
## - OverallCond    1 1.5072e+10 5.0990e+11 22190
## - LotArea        1 1.5150e+10 5.0998e+11 22190
## - OverallQual    1 1.7488e+10 5.1232e+11 22195
## - X1stFlrSF      1 1.8770e+10 5.1360e+11 22198
## - MiscFeature    3 2.0921e+10 5.1575e+11 22199
## - BsmtExposure   3 2.1932e+10 5.1676e+11 22201
## - BsmtFinSF1     1 2.1712e+10 5.1654e+11 22204
## - PoolArea       1 2.5265e+10 5.2010e+11 22212
## - PoolQC         3 3.0063e+10 5.2489e+11 22218
## - X2ndFlrSF      1 5.6012e+10 5.5084e+11 22275
## - Neighborhood  24 8.5011e+10 5.7984e+11 22285
## - Condition2     5 6.5657e+10 5.6049e+11 22286
## 
## Step:  AIC=22155.16
## SalePrice ~ MSSubClass + MSZoning + LotFrontage + LotArea + Street + 
##     Alley + LotShape + LandContour + LotConfig + LandSlope + 
##     Neighborhood + Condition1 + Condition2 + BldgType + OverallQual + 
##     OverallCond + YearBuilt + YearRemodAdd + RoofStyle + RoofMatl + 
##     Exterior1st + MasVnrType + MasVnrArea + ExterQual + Foundation + 
##     BsmtQual + BsmtExposure + BsmtFinType1 + BsmtFinSF1 + BsmtFinSF2 + 
##     BsmtUnfSF + CentralAir + X1stFlrSF + X2ndFlrSF + LowQualFinSF + 
##     BsmtFullBath + BsmtHalfBath + FullBath + HalfBath + BedroomAbvGr + 
##     KitchenAbvGr + KitchenQual + TotRmsAbvGrd + Functional + 
##     Fireplaces + GarageYrBlt + GarageFinish + GarageCars + GarageArea + 
##     GarageQual + GarageCond + PavedDrive + WoodDeckSF + OpenPorchSF + 
##     EnclosedPorch + X3SsnPorch + ScreenPorch + PoolArea + PoolQC + 
##     MiscFeature + MiscVal + MoSold + YrSold + SaleCondition
## 
##                 Df  Sum of Sq        RSS   AIC
## - PavedDrive     2 4.2442e+08 4.9974e+11 22152
## - Alley          2 8.3570e+08 5.0015e+11 22153
## - RoofStyle      4 2.7120e+09 5.0202e+11 22153
## - BsmtHalfBath   1 1.2421e+04 4.9931e+11 22153
## - LowQualFinSF   1 2.8228e+06 4.9932e+11 22153
## - OpenPorchSF    1 3.7413e+06 4.9932e+11 22153
## - MiscVal        1 7.6941e+06 4.9932e+11 22153
## - GarageYrBlt    1 2.4980e+07 4.9934e+11 22153
## - EnclosedPorch  1 2.9296e+07 4.9934e+11 22153
## - YrSold         1 3.6856e+07 4.9935e+11 22153
## - BsmtFullBath   1 1.8425e+08 4.9950e+11 22154
## - HalfBath       1 2.1589e+08 4.9953e+11 22154
## - LotShape       3 2.1392e+09 5.0145e+11 22154
## - GarageFinish   2 1.3300e+09 5.0064e+11 22154
## - BsmtFinType1   5 4.2224e+09 5.0354e+11 22154
## - TotRmsAbvGrd   1 6.6337e+08 4.9998e+11 22155
## - WoodDeckSF     1 7.4357e+08 5.0006e+11 22155
## - MoSold         1 7.5977e+08 5.0007e+11 22155
## <none>                        4.9931e+11 22155
## - CentralAir     1 9.3045e+08 5.0024e+11 22155
## - Fireplaces     1 1.1081e+09 5.0042e+11 22156
## - X3SsnPorch     1 1.1235e+09 5.0044e+11 22156
## - Exterior1st   13 1.2428e+10 5.1174e+11 22156
## - ScreenPorch    1 1.3390e+09 5.0065e+11 22156
## - GarageCars     1 1.5489e+09 5.0086e+11 22157
## - YearRemodAdd   1 1.5504e+09 5.0086e+11 22157
## - Foundation     4 4.4466e+09 5.0376e+11 22157
## - FullBath       1 1.7171e+09 5.0103e+11 22157
## - GarageCond     4 4.4952e+09 5.0381e+11 22157
## - LotFrontage    1 1.8858e+09 5.0120e+11 22157
## - MSSubClass     1 1.9834e+09 5.0130e+11 22158
## - GarageArea     1 2.0170e+09 5.0133e+11 22158
## - BldgType       4 5.2199e+09 5.0453e+11 22159
## - Functional     5 6.1545e+09 5.0547e+11 22159
## - BedroomAbvGr   1 2.7137e+09 5.0203e+11 22159
## - Street         1 2.7474e+09 5.0206e+11 22159
## + FireplaceQu    5 2.7229e+09 4.9659e+11 22159
## + HouseStyle     7 4.4820e+09 4.9483e+11 22159
## + Fence          4 1.6973e+09 4.9762e+11 22159
## + ExterCond      3 7.6541e+08 4.9855e+11 22160
## + BsmtCond       3 5.4342e+08 4.9877e+11 22160
## - MasVnrType     3 5.1090e+09 5.0442e+11 22160
## - Condition1     8 9.7888e+09 5.0910e+11 22160
## - LandContour    3 5.2140e+09 5.0453e+11 22161
## + Heating        3 2.1342e+08 4.9910e+11 22161
## + HeatingQC      4 1.0198e+09 4.9829e+11 22161
## - MSZoning       4 6.3353e+09 5.0565e+11 22161
## + GarageType     5 1.8405e+09 4.9747e+11 22161
## - GarageQual     4 6.7524e+09 5.0607e+11 22162
## - KitchenAbvGr   1 4.1079e+09 5.0342e+11 22162
## + SaleType       8 3.8820e+09 4.9543e+11 22163
## - LandSlope      2 5.3925e+09 5.0471e+11 22163
## + BsmtFinType2   5 9.4526e+08 4.9837e+11 22163
## + Electrical     4 2.7908e+07 4.9928e+11 22163
## - YearBuilt      1 4.9710e+09 5.0428e+11 22164
## - LotConfig      4 1.0630e+10 5.0994e+11 22170
## - BsmtUnfSF      1 7.9743e+09 5.0729e+11 22171
## - MasVnrArea     1 8.2930e+09 5.0761e+11 22171
## + Exterior2nd   14 5.3775e+09 4.9394e+11 22171
## - BsmtFinSF2     1 9.0305e+09 5.0834e+11 22173
## - ExterQual      3 1.1765e+10 5.1108e+11 22175
## - BsmtQual       3 1.2163e+10 5.1148e+11 22176
## - SaleCondition  5 1.4998e+10 5.1431e+11 22178
## - KitchenQual    3 1.5602e+10 5.1491e+11 22183
## - LotArea        1 1.4918e+10 5.1423e+11 22185
## - RoofMatl       6 1.9791e+10 5.1910e+11 22186
## - OverallCond    1 1.5326e+10 5.1464e+11 22186
## - OverallQual    1 1.6261e+10 5.1557e+11 22188
## - MiscFeature    3 2.0441e+10 5.1975e+11 22193
## - BsmtFinSF1     1 2.1075e+10 5.2039e+11 22198
## - BsmtExposure   3 2.4022e+10 5.2333e+11 22201
## - X1stFlrSF      1 2.3531e+10 5.2284e+11 22204
## - PoolArea       1 2.4096e+10 5.2341e+11 22205
## - PoolQC         3 3.0154e+10 5.2947e+11 22213
## - Condition2     5 6.4434e+10 5.6375e+11 22278
## - Neighborhood  24 9.0103e+10 5.8942e+11 22289
## - X2ndFlrSF      1 6.7401e+10 5.6671e+11 22292
## 
## Step:  AIC=22152.09
## SalePrice ~ MSSubClass + MSZoning + LotFrontage + LotArea + Street + 
##     Alley + LotShape + LandContour + LotConfig + LandSlope + 
##     Neighborhood + Condition1 + Condition2 + BldgType + OverallQual + 
##     OverallCond + YearBuilt + YearRemodAdd + RoofStyle + RoofMatl + 
##     Exterior1st + MasVnrType + MasVnrArea + ExterQual + Foundation + 
##     BsmtQual + BsmtExposure + BsmtFinType1 + BsmtFinSF1 + BsmtFinSF2 + 
##     BsmtUnfSF + CentralAir + X1stFlrSF + X2ndFlrSF + LowQualFinSF + 
##     BsmtFullBath + BsmtHalfBath + FullBath + HalfBath + BedroomAbvGr + 
##     KitchenAbvGr + KitchenQual + TotRmsAbvGrd + Functional + 
##     Fireplaces + GarageYrBlt + GarageFinish + GarageCars + GarageArea + 
##     GarageQual + GarageCond + WoodDeckSF + OpenPorchSF + EnclosedPorch + 
##     X3SsnPorch + ScreenPorch + PoolArea + PoolQC + MiscFeature + 
##     MiscVal + MoSold + YrSold + SaleCondition
## 
##                 Df  Sum of Sq        RSS   AIC
## - Alley          2 8.5119e+08 5.0059e+11 22150
## - LowQualFinSF   1 2.8496e+06 4.9974e+11 22150
## - OpenPorchSF    1 3.7184e+06 4.9974e+11 22150
## - BsmtHalfBath   1 3.9581e+06 4.9974e+11 22150
## - MiscVal        1 4.4971e+06 4.9974e+11 22150
## - RoofStyle      4 2.7734e+09 5.0251e+11 22150
## - YrSold         1 3.2947e+07 4.9977e+11 22150
## - EnclosedPorch  1 3.8653e+07 4.9978e+11 22150
## - GarageYrBlt    1 4.3337e+07 4.9978e+11 22150
## - HalfBath       1 1.7092e+08 4.9991e+11 22151
## - BsmtFullBath   1 1.7215e+08 4.9991e+11 22151
## - LotShape       3 2.1134e+09 5.0185e+11 22151
## - GarageFinish   2 1.3635e+09 5.0110e+11 22151
## - BsmtFinType1   5 4.1824e+09 5.0392e+11 22151
## - TotRmsAbvGrd   1 7.1187e+08 5.0045e+11 22152
## - WoodDeckSF     1 7.6994e+08 5.0051e+11 22152
## - MoSold         1 7.8965e+08 5.0053e+11 22152
## <none>                        4.9974e+11 22152
## - CentralAir     1 9.2425e+08 5.0066e+11 22152
## - Fireplaces     1 9.8971e+08 5.0073e+11 22152
## - X3SsnPorch     1 1.1627e+09 5.0090e+11 22153
## - Exterior1st   13 1.2321e+10 5.1206e+11 22153
## - ScreenPorch    1 1.3785e+09 5.0112e+11 22153
## - YearRemodAdd   1 1.5526e+09 5.0129e+11 22154
## - GarageCond     4 4.4304e+09 5.0417e+11 22154
## - Foundation     4 4.4377e+09 5.0417e+11 22154
## - GarageCars     1 1.7243e+09 5.0146e+11 22154
## - FullBath       1 1.7277e+09 5.0146e+11 22154
## - LotFrontage    1 1.7875e+09 5.0152e+11 22154
## - MSSubClass     1 1.9224e+09 5.0166e+11 22154
## - GarageArea     1 1.9996e+09 5.0174e+11 22155
## + PavedDrive     2 4.2442e+08 4.9931e+11 22155
## - Functional     5 6.0206e+09 5.0576e+11 22155
## - BldgType       4 5.3875e+09 5.0512e+11 22156
## - Street         1 2.7406e+09 5.0248e+11 22156
## + FireplaceQu    5 2.7399e+09 4.9700e+11 22156
## - BedroomAbvGr   1 2.8016e+09 5.0254e+11 22156
## + ExterCond      3 8.2022e+08 4.9892e+11 22156
## + HouseStyle     7 4.4215e+09 4.9532e+11 22156
## + Fence          4 1.5834e+09 4.9815e+11 22157
## + BsmtCond       3 5.6410e+08 4.9917e+11 22157
## - MasVnrType     3 5.0239e+09 5.0476e+11 22157
## - Condition1     8 9.7220e+09 5.0946e+11 22157
## + Heating        3 3.0785e+08 4.9943e+11 22157
## - MSZoning       4 6.1730e+09 5.0591e+11 22158
## + HeatingQC      4 1.0327e+09 4.9870e+11 22158
## - LandContour    3 5.5218e+09 5.0526e+11 22158
## + GarageType     5 1.7951e+09 4.9794e+11 22158
## - GarageQual     4 6.5910e+09 5.0633e+11 22158
## - KitchenAbvGr   1 3.9487e+09 5.0369e+11 22159
## + SaleType       8 3.9879e+09 4.9575e+11 22159
## - LandSlope      2 5.3182e+09 5.0506e+11 22160
## + Electrical     4 3.8794e+07 4.9970e+11 22160
## + BsmtFinType2   5 9.3543e+08 4.9880e+11 22160
## - YearBuilt      1 5.4858e+09 5.0522e+11 22162
## - LotConfig      4 1.0585e+10 5.1032e+11 22167
## - BsmtUnfSF      1 8.0059e+09 5.0774e+11 22168
## + Exterior2nd   14 5.4993e+09 4.9424e+11 22168
## - MasVnrArea     1 8.2583e+09 5.0800e+11 22168
## - BsmtFinSF2     1 9.1651e+09 5.0890e+11 22170
## - ExterQual      3 1.1654e+10 5.1139e+11 22171
## - BsmtQual       3 1.2333e+10 5.1207e+11 22173
## - SaleCondition  5 1.4865e+10 5.1460e+11 22174
## - KitchenQual    3 1.5677e+10 5.1541e+11 22180
## - LotArea        1 1.4908e+10 5.1465e+11 22182
## - RoofMatl       6 2.0060e+10 5.1980e+11 22183
## - OverallCond    1 1.5628e+10 5.1537e+11 22184
## - OverallQual    1 1.6375e+10 5.1611e+11 22185
## - MiscFeature    3 2.0282e+10 5.2002e+11 22190
## - BsmtFinSF1     1 2.1198e+10 5.2094e+11 22196
## - BsmtExposure   3 2.3897e+10 5.2363e+11 22197
## - X1stFlrSF      1 2.3397e+10 5.2313e+11 22200
## - PoolArea       1 2.3951e+10 5.2369e+11 22201
## - PoolQC         3 3.0007e+10 5.2974e+11 22210
## - Condition2     5 6.4485e+10 5.6422e+11 22275
## - Neighborhood  24 9.0417e+10 5.9015e+11 22286
## - X2ndFlrSF      1 6.7686e+10 5.6742e+11 22289
## 
## Step:  AIC=22149.95
## SalePrice ~ MSSubClass + MSZoning + LotFrontage + LotArea + Street + 
##     LotShape + LandContour + LotConfig + LandSlope + Neighborhood + 
##     Condition1 + Condition2 + BldgType + OverallQual + OverallCond + 
##     YearBuilt + YearRemodAdd + RoofStyle + RoofMatl + Exterior1st + 
##     MasVnrType + MasVnrArea + ExterQual + Foundation + BsmtQual + 
##     BsmtExposure + BsmtFinType1 + BsmtFinSF1 + BsmtFinSF2 + BsmtUnfSF + 
##     CentralAir + X1stFlrSF + X2ndFlrSF + LowQualFinSF + BsmtFullBath + 
##     BsmtHalfBath + FullBath + HalfBath + BedroomAbvGr + KitchenAbvGr + 
##     KitchenQual + TotRmsAbvGrd + Functional + Fireplaces + GarageYrBlt + 
##     GarageFinish + GarageCars + GarageArea + GarageQual + GarageCond + 
##     WoodDeckSF + OpenPorchSF + EnclosedPorch + X3SsnPorch + ScreenPorch + 
##     PoolArea + PoolQC + MiscFeature + MiscVal + MoSold + YrSold + 
##     SaleCondition
## 
##                 Df  Sum of Sq        RSS   AIC
## - RoofStyle      4 2.4789e+09 5.0307e+11 22147
## - BsmtHalfBath   1 3.7846e+06 5.0059e+11 22148
## - LowQualFinSF   1 4.5713e+06 5.0059e+11 22148
## - MiscVal        1 5.0709e+06 5.0059e+11 22148
## - EnclosedPorch  1 1.5892e+07 5.0060e+11 22148
## - OpenPorchSF    1 1.6493e+07 5.0060e+11 22148
## - GarageYrBlt    1 2.6725e+07 5.0062e+11 22148
## - YrSold         1 2.8120e+07 5.0062e+11 22148
## - HalfBath       1 1.4470e+08 5.0073e+11 22148
## - LotShape       3 1.9845e+09 5.0257e+11 22148
## - BsmtFullBath   1 1.6033e+08 5.0075e+11 22148
## - GarageFinish   2 1.2811e+09 5.0187e+11 22149
## - BsmtFinType1   5 4.3502e+09 5.0494e+11 22149
## - MoSold         1 6.9010e+08 5.0128e+11 22150
## - Exterior1st   13 1.1935e+10 5.1252e+11 22150
## - WoodDeckSF     1 8.4737e+08 5.0144e+11 22150
## - TotRmsAbvGrd   1 8.7955e+08 5.0147e+11 22150
## - CentralAir     1 8.8702e+08 5.0148e+11 22150
## <none>                        5.0059e+11 22150
## - Fireplaces     1 1.0229e+09 5.0161e+11 22150
## - X3SsnPorch     1 1.2043e+09 5.0179e+11 22151
## - ScreenPorch    1 1.3788e+09 5.0197e+11 22151
## - GarageCars     1 1.4855e+09 5.0207e+11 22151
## - YearRemodAdd   1 1.4914e+09 5.0208e+11 22151
## - FullBath       1 1.6145e+09 5.0220e+11 22152
## - Foundation     4 4.4814e+09 5.0507e+11 22152
## - MSSubClass     1 1.8358e+09 5.0242e+11 22152
## - GarageCond     4 4.6433e+09 5.0523e+11 22152
## + Alley          2 8.5119e+08 4.9974e+11 22152
## - LotFrontage    1 2.0196e+09 5.0261e+11 22152
## - GarageArea     1 2.1801e+09 5.0277e+11 22153
## + PavedDrive     2 4.3990e+08 5.0015e+11 22153
## - Functional     5 6.1768e+09 5.0677e+11 22153
## - Street         1 2.5318e+09 5.0312e+11 22154
## + FireplaceQu    5 2.7893e+09 4.9780e+11 22154
## + HouseStyle     7 4.5484e+09 4.9604e+11 22154
## + Fence          4 1.7318e+09 4.9886e+11 22154
## + ExterCond      3 7.5971e+08 4.9983e+11 22154
## - BedroomAbvGr   1 2.9296e+09 5.0352e+11 22154
## - MSZoning       4 5.7056e+09 5.0629e+11 22154
## - BldgType       4 5.8182e+09 5.0641e+11 22155
## + BsmtCond       3 5.4155e+08 5.0005e+11 22155
## - Condition1     8 9.6278e+09 5.1022e+11 22155
## - MasVnrType     3 5.0153e+09 5.0560e+11 22155
## + Heating        3 3.4190e+08 5.0025e+11 22155
## + HeatingQC      4 1.0256e+09 4.9956e+11 22156
## - LandContour    3 5.5537e+09 5.0614e+11 22156
## - KitchenAbvGr   1 3.7352e+09 5.0432e+11 22156
## + GarageType     5 1.6505e+09 4.9894e+11 22156
## - GarageQual     4 6.6485e+09 5.0724e+11 22156
## + SaleType       8 4.2443e+09 4.9634e+11 22157
## - LandSlope      2 5.2114e+09 5.0580e+11 22157
## + BsmtFinType2   5 9.7149e+08 4.9962e+11 22158
## + Electrical     4 4.3063e+07 5.0055e+11 22158
## - YearBuilt      1 5.7252e+09 5.0631e+11 22160
## - MasVnrArea     1 7.7445e+09 5.0833e+11 22165
## - LotConfig      4 1.0665e+10 5.1125e+11 22165
## - BsmtUnfSF      1 8.0469e+09 5.0864e+11 22165
## + Exterior2nd   14 5.2241e+09 4.9536e+11 22167
## - BsmtFinSF2     1 9.2682e+09 5.0986e+11 22168
## - ExterQual      3 1.1782e+10 5.1237e+11 22169
## - BsmtQual       3 1.2300e+10 5.1289e+11 22171
## - SaleCondition  5 1.5010e+10 5.1560e+11 22172
## - KitchenQual    3 1.5499e+10 5.1609e+11 22177
## - LotArea        1 1.4868e+10 5.1546e+11 22180
## - RoofMatl       6 1.9937e+10 5.2053e+11 22181
## - OverallCond    1 1.5630e+10 5.1622e+11 22182
## - OverallQual    1 1.6457e+10 5.1705e+11 22183
## - MiscFeature    3 2.0016e+10 5.2060e+11 22187
## - BsmtFinSF1     1 2.1214e+10 5.2180e+11 22193
## - BsmtExposure   3 2.3798e+10 5.2439e+11 22195
## - X1stFlrSF      1 2.3174e+10 5.2376e+11 22198
## - PoolArea       1 2.3688e+10 5.2428e+11 22199
## - PoolQC         3 2.9863e+10 5.3045e+11 22207
## - Condition2     5 6.4907e+10 5.6550e+11 22273
## - X2ndFlrSF      1 6.7410e+10 5.6800e+11 22286
## - Neighborhood  24 9.2611e+10 5.9320e+11 22288
## 
## Step:  AIC=22147.35
## SalePrice ~ MSSubClass + MSZoning + LotFrontage + LotArea + Street + 
##     LotShape + LandContour + LotConfig + LandSlope + Neighborhood + 
##     Condition1 + Condition2 + BldgType + OverallQual + OverallCond + 
##     YearBuilt + YearRemodAdd + RoofMatl + Exterior1st + MasVnrType + 
##     MasVnrArea + ExterQual + Foundation + BsmtQual + BsmtExposure + 
##     BsmtFinType1 + BsmtFinSF1 + BsmtFinSF2 + BsmtUnfSF + CentralAir + 
##     X1stFlrSF + X2ndFlrSF + LowQualFinSF + BsmtFullBath + BsmtHalfBath + 
##     FullBath + HalfBath + BedroomAbvGr + KitchenAbvGr + KitchenQual + 
##     TotRmsAbvGrd + Functional + Fireplaces + GarageYrBlt + GarageFinish + 
##     GarageCars + GarageArea + GarageQual + GarageCond + WoodDeckSF + 
##     OpenPorchSF + EnclosedPorch + X3SsnPorch + ScreenPorch + 
##     PoolArea + PoolQC + MiscFeature + MiscVal + MoSold + YrSold + 
##     SaleCondition
## 
##                 Df  Sum of Sq        RSS   AIC
## - LotShape       3 1.7465e+09 5.0481e+11 22145
## - LowQualFinSF   1 4.1765e+06 5.0307e+11 22145
## - BsmtHalfBath   1 1.2093e+07 5.0308e+11 22145
## - YrSold         1 1.7066e+07 5.0308e+11 22145
## - EnclosedPorch  1 2.2911e+07 5.0309e+11 22145
## - MiscVal        1 3.1518e+07 5.0310e+11 22145
## - OpenPorchSF    1 3.7155e+07 5.0310e+11 22145
## - GarageYrBlt    1 6.4492e+07 5.0313e+11 22146
## - BsmtFullBath   1 1.1346e+08 5.0318e+11 22146
## - HalfBath       1 1.9095e+08 5.0326e+11 22146
## - GarageFinish   2 1.1928e+09 5.0426e+11 22146
## - MoSold         1 5.4756e+08 5.0361e+11 22147
## - Exterior1st   13 1.1791e+10 5.1486e+11 22147
## - TotRmsAbvGrd   1 7.7305e+08 5.0384e+11 22147
## - WoodDeckSF     1 8.8077e+08 5.0395e+11 22147
## - CentralAir     1 9.0126e+08 5.0397e+11 22147
## <none>                        5.0307e+11 22147
## - Fireplaces     1 1.0473e+09 5.0411e+11 22148
## - BsmtFinType1   5 4.7929e+09 5.0786e+11 22148
## - X3SsnPorch     1 1.1345e+09 5.0420e+11 22148
## - ScreenPorch    1 1.1940e+09 5.0426e+11 22148
## - MSSubClass     1 1.4502e+09 5.0452e+11 22149
## - FullBath       1 1.4895e+09 5.0456e+11 22149
## - GarageCars     1 1.5052e+09 5.0457e+11 22149
## - YearRemodAdd   1 1.6360e+09 5.0470e+11 22149
## - LotFrontage    1 1.8252e+09 5.0489e+11 22149
## - Foundation     4 4.6207e+09 5.0769e+11 22149
## - GarageCond     4 4.8775e+09 5.0794e+11 22150
## + RoofStyle      4 2.4789e+09 5.0059e+11 22150
## - GarageArea     1 2.1214e+09 5.0519e+11 22150
## + Alley          2 5.5670e+08 5.0251e+11 22150
## + PavedDrive     2 4.9947e+08 5.0257e+11 22150
## - Street         1 2.5604e+09 5.0563e+11 22151
## - Functional     5 6.2780e+09 5.0935e+11 22151
## + FireplaceQu    5 2.8655e+09 5.0020e+11 22151
## + HouseStyle     7 4.6235e+09 4.9844e+11 22151
## + ExterCond      3 9.0255e+08 5.0216e+11 22151
## - BedroomAbvGr   1 2.8120e+09 5.0588e+11 22152
## + Fence          4 1.7487e+09 5.0132e+11 22152
## - BldgType       4 5.7358e+09 5.0880e+11 22152
## - MSZoning       4 5.7446e+09 5.0881e+11 22152
## + BsmtCond       3 7.2358e+08 5.0234e+11 22152
## - MasVnrType     3 4.8733e+09 5.0794e+11 22152
## - Condition1     8 9.6668e+09 5.1273e+11 22152
## + Heating        3 3.7468e+08 5.0269e+11 22153
## + GarageType     5 2.1153e+09 5.0095e+11 22153
## - LandContour    3 5.4301e+09 5.0850e+11 22153
## + HeatingQC      4 8.8451e+08 5.0218e+11 22153
## - KitchenAbvGr   1 3.8154e+09 5.0688e+11 22154
## + SaleType       8 4.2519e+09 4.9882e+11 22154
## - GarageQual     4 7.0553e+09 5.1012e+11 22155
## + Electrical     4 2.0917e+07 5.0305e+11 22155
## + BsmtFinType2   5 8.5526e+08 5.0221e+11 22156
## - LandSlope      2 5.9874e+09 5.0905e+11 22156
## - YearBuilt      1 5.2239e+09 5.0829e+11 22157
## - MasVnrArea     1 7.6196e+09 5.1069e+11 22162
## - LotConfig      4 1.0703e+10 5.1377e+11 22162
## + Exterior2nd   14 5.4104e+09 4.9766e+11 22164
## - BsmtUnfSF      1 8.4346e+09 5.1150e+11 22164
## - BsmtFinSF2     1 9.5878e+09 5.1266e+11 22166
## - ExterQual      3 1.1900e+10 5.1497e+11 22167
## - BsmtQual       3 1.2497e+10 5.1556e+11 22168
## - SaleCondition  5 1.5052e+10 5.1812e+11 22170
## - KitchenQual    3 1.5304e+10 5.1837e+11 22174
## - RoofMatl       6 1.9893e+10 5.2296e+11 22178
## - OverallCond    1 1.5268e+10 5.1834e+11 22178
## - OverallQual    1 1.5527e+10 5.1859e+11 22179
## - LotArea        1 1.5674e+10 5.1874e+11 22179
## - MiscFeature    3 2.0676e+10 5.2374e+11 22185
## - BsmtFinSF1     1 2.1616e+10 5.2468e+11 22191
## - BsmtExposure   3 2.3949e+10 5.2702e+11 22192
## - X1stFlrSF      1 2.3018e+10 5.2609e+11 22194
## - PoolArea       1 2.4239e+10 5.2731e+11 22197
## - PoolQC         3 3.0457e+10 5.3352e+11 22206
## - Condition2     5 6.4792e+10 5.6786e+11 22270
## - X2ndFlrSF      1 6.7755e+10 5.7082e+11 22284
## - Neighborhood  24 9.2641e+10 5.9571e+11 22284
## 
## Step:  AIC=22145.15
## SalePrice ~ MSSubClass + MSZoning + LotFrontage + LotArea + Street + 
##     LandContour + LotConfig + LandSlope + Neighborhood + Condition1 + 
##     Condition2 + BldgType + OverallQual + OverallCond + YearBuilt + 
##     YearRemodAdd + RoofMatl + Exterior1st + MasVnrType + MasVnrArea + 
##     ExterQual + Foundation + BsmtQual + BsmtExposure + BsmtFinType1 + 
##     BsmtFinSF1 + BsmtFinSF2 + BsmtUnfSF + CentralAir + X1stFlrSF + 
##     X2ndFlrSF + LowQualFinSF + BsmtFullBath + BsmtHalfBath + 
##     FullBath + HalfBath + BedroomAbvGr + KitchenAbvGr + KitchenQual + 
##     TotRmsAbvGrd + Functional + Fireplaces + GarageYrBlt + GarageFinish + 
##     GarageCars + GarageArea + GarageQual + GarageCond + WoodDeckSF + 
##     OpenPorchSF + EnclosedPorch + X3SsnPorch + ScreenPorch + 
##     PoolArea + PoolQC + MiscFeature + MiscVal + MoSold + YrSold + 
##     SaleCondition
## 
##                 Df  Sum of Sq        RSS   AIC
## - YrSold         1 3.5495e+06 5.0482e+11 22143
## - EnclosedPorch  1 7.3707e+06 5.0482e+11 22143
## - LowQualFinSF   1 9.2510e+06 5.0482e+11 22143
## - BsmtHalfBath   1 2.5597e+07 5.0484e+11 22143
## - MiscVal        1 2.8474e+07 5.0484e+11 22143
## - OpenPorchSF    1 5.2204e+07 5.0487e+11 22143
## - GarageYrBlt    1 7.6271e+07 5.0489e+11 22143
## - BsmtFullBath   1 1.0992e+08 5.0492e+11 22143
## - HalfBath       1 1.6434e+08 5.0498e+11 22144
## - GarageFinish   2 1.2254e+09 5.0604e+11 22144
## - MoSold         1 5.0732e+08 5.0532e+11 22144
## - Exterior1st   13 1.1723e+10 5.1654e+11 22144
## - WoodDeckSF     1 7.5360e+08 5.0557e+11 22145
## - TotRmsAbvGrd   1 7.8972e+08 5.0560e+11 22145
## - CentralAir     1 8.9832e+08 5.0571e+11 22145
## <none>                        5.0481e+11 22145
## - Fireplaces     1 1.0405e+09 5.0585e+11 22145
## - ScreenPorch    1 1.0644e+09 5.0588e+11 22146
## - X3SsnPorch     1 1.0949e+09 5.0591e+11 22146
## - BsmtFinType1   5 4.9707e+09 5.0978e+11 22146
## - FullBath       1 1.3805e+09 5.0619e+11 22146
## - MSSubClass     1 1.5287e+09 5.0634e+11 22147
## - GarageCars     1 1.5363e+09 5.0635e+11 22147
## - YearRemodAdd   1 1.9057e+09 5.0672e+11 22147
## + LotShape       3 1.7465e+09 5.0307e+11 22147
## - LotFrontage    1 1.9882e+09 5.0680e+11 22147
## - GarageArea     1 2.1128e+09 5.0693e+11 22148
## - Foundation     4 4.9441e+09 5.0976e+11 22148
## + PavedDrive     2 4.7403e+08 5.0434e+11 22148
## + Alley          2 4.7397e+08 5.0434e+11 22148
## + RoofStyle      4 2.2409e+09 5.0257e+11 22148
## - Street         1 2.3973e+09 5.0721e+11 22148
## + FireplaceQu    5 3.1078e+09 5.0171e+11 22148
## + HouseStyle     7 4.8499e+09 4.9996e+11 22149
## - Functional     5 6.3812e+09 5.1120e+11 22149
## - MasVnrType     3 4.5305e+09 5.0934e+11 22149
## - BedroomAbvGr   1 2.6762e+09 5.0749e+11 22149
## + ExterCond      3 9.5076e+08 5.0386e+11 22149
## - BldgType       4 5.5907e+09 5.1040e+11 22149
## - GarageCond     4 5.6083e+09 5.1042e+11 22149
## - Condition1     8 9.3918e+09 5.1421e+11 22149
## + Fence          4 1.7650e+09 5.0305e+11 22149
## - MSZoning       4 5.8158e+09 5.1063e+11 22150
## + BsmtCond       3 6.6000e+08 5.0415e+11 22150
## + Heating        3 3.7338e+08 5.0444e+11 22150
## + GarageType     5 2.1850e+09 5.0263e+11 22150
## - LandContour    3 5.3465e+09 5.1016e+11 22151
## + HeatingQC      4 8.7383e+08 5.0394e+11 22151
## - KitchenAbvGr   1 4.0641e+09 5.0888e+11 22152
## + SaleType       8 4.2289e+09 5.0058e+11 22152
## + Electrical     4 4.0669e+07 5.0477e+11 22153
## + BsmtFinType2   5 8.4078e+08 5.0397e+11 22153
## - YearBuilt      1 5.2178e+09 5.1003e+11 22154
## - GarageQual     4 8.1243e+09 5.1294e+11 22155
## - LandSlope      2 6.4875e+09 5.1130e+11 22155
## - MasVnrArea     1 7.7254e+09 5.1254e+11 22160
## - LotConfig      4 1.1037e+10 5.1585e+11 22161
## - BsmtUnfSF      1 8.2977e+09 5.1311e+11 22161
## + Exterior2nd   14 5.3959e+09 4.9942e+11 22161
## - BsmtFinSF2     1 9.9212e+09 5.1474e+11 22164
## - ExterQual      3 1.2222e+10 5.1704e+11 22165
## - BsmtQual       3 1.2496e+10 5.1731e+11 22166
## - SaleCondition  5 1.5107e+10 5.1992e+11 22167
## - KitchenQual    3 1.5339e+10 5.2015e+11 22172
## - RoofMatl       6 1.9358e+10 5.2417e+11 22174
## - OverallCond    1 1.4928e+10 5.1974e+11 22175
## - OverallQual    1 1.5260e+10 5.2007e+11 22176
## - MiscFeature    3 2.0478e+10 5.2529e+11 22183
## - LotArea        1 2.0472e+10 5.2529e+11 22187
## - BsmtExposure   3 2.3372e+10 5.2819e+11 22189
## - BsmtFinSF1     1 2.1694e+10 5.2651e+11 22189
## - X1stFlrSF      1 2.2865e+10 5.2768e+11 22192
## - PoolArea       1 2.4119e+10 5.2893e+11 22194
## - PoolQC         3 3.0129e+10 5.3494e+11 22203
## - Condition2     5 6.7018e+10 5.7183e+11 22272
## - Neighborhood  24 9.1952e+10 5.9677e+11 22280
## - X2ndFlrSF      1 6.7953e+10 5.7277e+11 22281
## 
## Step:  AIC=22143.15
## SalePrice ~ MSSubClass + MSZoning + LotFrontage + LotArea + Street + 
##     LandContour + LotConfig + LandSlope + Neighborhood + Condition1 + 
##     Condition2 + BldgType + OverallQual + OverallCond + YearBuilt + 
##     YearRemodAdd + RoofMatl + Exterior1st + MasVnrType + MasVnrArea + 
##     ExterQual + Foundation + BsmtQual + BsmtExposure + BsmtFinType1 + 
##     BsmtFinSF1 + BsmtFinSF2 + BsmtUnfSF + CentralAir + X1stFlrSF + 
##     X2ndFlrSF + LowQualFinSF + BsmtFullBath + BsmtHalfBath + 
##     FullBath + HalfBath + BedroomAbvGr + KitchenAbvGr + KitchenQual + 
##     TotRmsAbvGrd + Functional + Fireplaces + GarageYrBlt + GarageFinish + 
##     GarageCars + GarageArea + GarageQual + GarageCond + WoodDeckSF + 
##     OpenPorchSF + EnclosedPorch + X3SsnPorch + ScreenPorch + 
##     PoolArea + PoolQC + MiscFeature + MiscVal + MoSold + SaleCondition
## 
##                 Df  Sum of Sq        RSS   AIC
## - EnclosedPorch  1 7.3797e+06 5.0482e+11 22141
## - LowQualFinSF   1 9.0854e+06 5.0483e+11 22141
## - BsmtHalfBath   1 2.6465e+07 5.0484e+11 22141
## - MiscVal        1 2.8834e+07 5.0485e+11 22141
## - OpenPorchSF    1 5.0682e+07 5.0487e+11 22141
## - GarageYrBlt    1 7.6239e+07 5.0489e+11 22141
## - BsmtFullBath   1 1.0813e+08 5.0493e+11 22141
## - HalfBath       1 1.6355e+08 5.0498e+11 22142
## - GarageFinish   2 1.2241e+09 5.0604e+11 22142
## - MoSold         1 5.0614e+08 5.0532e+11 22142
## - Exterior1st   13 1.1720e+10 5.1654e+11 22142
## - WoodDeckSF     1 7.5273e+08 5.0557e+11 22143
## - TotRmsAbvGrd   1 7.9193e+08 5.0561e+11 22143
## - CentralAir     1 8.9931e+08 5.0572e+11 22143
## <none>                        5.0482e+11 22143
## - Fireplaces     1 1.0467e+09 5.0586e+11 22143
## - ScreenPorch    1 1.0619e+09 5.0588e+11 22144
## - X3SsnPorch     1 1.0939e+09 5.0591e+11 22144
## - BsmtFinType1   5 4.9720e+09 5.0979e+11 22144
## - FullBath       1 1.3776e+09 5.0619e+11 22144
## - MSSubClass     1 1.5339e+09 5.0635e+11 22145
## - GarageCars     1 1.5400e+09 5.0636e+11 22145
## + YrSold         1 3.5495e+06 5.0481e+11 22145
## - YearRemodAdd   1 1.9032e+09 5.0672e+11 22145
## + LotShape       3 1.7330e+09 5.0308e+11 22145
## - LotFrontage    1 1.9847e+09 5.0680e+11 22145
## - GarageArea     1 2.1137e+09 5.0693e+11 22146
## - Foundation     4 4.9680e+09 5.0979e+11 22146
## + Alley          2 4.7312e+08 5.0434e+11 22146
## + PavedDrive     2 4.7310e+08 5.0434e+11 22146
## + RoofStyle      4 2.2365e+09 5.0258e+11 22146
## - Street         1 2.4065e+09 5.0722e+11 22146
## + FireplaceQu    5 3.0898e+09 5.0173e+11 22146
## + HouseStyle     7 4.8509e+09 4.9997e+11 22147
## - Functional     5 6.3951e+09 5.1121e+11 22147
## - BedroomAbvGr   1 2.6731e+09 5.0749e+11 22147
## - MasVnrType     3 4.5642e+09 5.0938e+11 22147
## + ExterCond      3 9.5163e+08 5.0387e+11 22147
## - BldgType       4 5.5874e+09 5.1040e+11 22147
## - GarageCond     4 5.6156e+09 5.1043e+11 22147
## + Fence          4 1.7655e+09 5.0305e+11 22147
## - Condition1     8 9.4040e+09 5.1422e+11 22147
## - MSZoning       4 5.8123e+09 5.1063e+11 22148
## + BsmtCond       3 6.3688e+08 5.0418e+11 22148
## + Heating        3 3.7296e+08 5.0444e+11 22148
## + GarageType     5 2.1468e+09 5.0267e+11 22149
## - LandContour    3 5.3453e+09 5.1016e+11 22149
## + HeatingQC      4 8.7303e+08 5.0394e+11 22149
## + SaleType       8 4.2314e+09 5.0059e+11 22150
## - KitchenAbvGr   1 4.0947e+09 5.0891e+11 22150
## + Electrical     4 4.1258e+07 5.0478e+11 22151
## + BsmtFinType2   5 8.4172e+08 5.0398e+11 22151
## - YearBuilt      1 5.2260e+09 5.1004e+11 22152
## - GarageQual     4 8.1310e+09 5.1295e+11 22153
## - LandSlope      2 6.4906e+09 5.1131e+11 22153
## - MasVnrArea     1 7.7444e+09 5.1256e+11 22158
## - LotConfig      4 1.1034e+10 5.1585e+11 22159
## - BsmtUnfSF      1 8.2978e+09 5.1312e+11 22159
## + Exterior2nd   14 5.3985e+09 4.9942e+11 22159
## - BsmtFinSF2     1 9.9242e+09 5.1474e+11 22163
## - ExterQual      3 1.2263e+10 5.1708e+11 22163
## - BsmtQual       3 1.2493e+10 5.1731e+11 22164
## - SaleCondition  5 1.5542e+10 5.2036e+11 22166
## - KitchenQual    3 1.5336e+10 5.2015e+11 22170
## - RoofMatl       6 1.9435e+10 5.2425e+11 22173
## - OverallCond    1 1.4929e+10 5.1975e+11 22173
## - OverallQual    1 1.5258e+10 5.2008e+11 22174
## - MiscFeature    3 2.0488e+10 5.2531e+11 22181
## - LotArea        1 2.0474e+10 5.2529e+11 22185
## - BsmtExposure   3 2.3566e+10 5.2838e+11 22187
## - BsmtFinSF1     1 2.1691e+10 5.2651e+11 22187
## - X1stFlrSF      1 2.2928e+10 5.2775e+11 22190
## - PoolArea       1 2.4126e+10 5.2894e+11 22192
## - PoolQC         3 3.0134e+10 5.3495e+11 22201
## - Condition2     5 6.7024e+10 5.7184e+11 22270
## - Neighborhood  24 9.2038e+10 5.9685e+11 22278
## - X2ndFlrSF      1 6.8059e+10 5.7288e+11 22280
## 
## Step:  AIC=22141.17
## SalePrice ~ MSSubClass + MSZoning + LotFrontage + LotArea + Street + 
##     LandContour + LotConfig + LandSlope + Neighborhood + Condition1 + 
##     Condition2 + BldgType + OverallQual + OverallCond + YearBuilt + 
##     YearRemodAdd + RoofMatl + Exterior1st + MasVnrType + MasVnrArea + 
##     ExterQual + Foundation + BsmtQual + BsmtExposure + BsmtFinType1 + 
##     BsmtFinSF1 + BsmtFinSF2 + BsmtUnfSF + CentralAir + X1stFlrSF + 
##     X2ndFlrSF + LowQualFinSF + BsmtFullBath + BsmtHalfBath + 
##     FullBath + HalfBath + BedroomAbvGr + KitchenAbvGr + KitchenQual + 
##     TotRmsAbvGrd + Functional + Fireplaces + GarageYrBlt + GarageFinish + 
##     GarageCars + GarageArea + GarageQual + GarageCond + WoodDeckSF + 
##     OpenPorchSF + X3SsnPorch + ScreenPorch + PoolArea + PoolQC + 
##     MiscFeature + MiscVal + MoSold + SaleCondition
## 
##                 Df  Sum of Sq        RSS   AIC
## - LowQualFinSF   1 1.1143e+07 5.0484e+11 22139
## - BsmtHalfBath   1 2.6249e+07 5.0485e+11 22139
## - MiscVal        1 3.0177e+07 5.0485e+11 22139
## - OpenPorchSF    1 5.4133e+07 5.0488e+11 22139
## - GarageYrBlt    1 7.6281e+07 5.0490e+11 22139
## - BsmtFullBath   1 1.1163e+08 5.0494e+11 22139
## - HalfBath       1 1.6497e+08 5.0499e+11 22140
## - GarageFinish   2 1.2210e+09 5.0605e+11 22140
## - MoSold         1 5.1478e+08 5.0534e+11 22140
## - Exterior1st   13 1.1767e+10 5.1659e+11 22140
## - WoodDeckSF     1 7.4669e+08 5.0557e+11 22141
## - TotRmsAbvGrd   1 7.8496e+08 5.0561e+11 22141
## - CentralAir     1 9.0965e+08 5.0573e+11 22141
## <none>                        5.0482e+11 22141
## - Fireplaces     1 1.0514e+09 5.0588e+11 22141
## - ScreenPorch    1 1.0553e+09 5.0588e+11 22142
## - X3SsnPorch     1 1.0894e+09 5.0591e+11 22142
## - BsmtFinType1   5 4.9677e+09 5.0979e+11 22142
## - FullBath       1 1.3734e+09 5.0620e+11 22142
## - MSSubClass     1 1.5289e+09 5.0635e+11 22143
## - GarageCars     1 1.5363e+09 5.0636e+11 22143
## + EnclosedPorch  1 7.3797e+06 5.0482e+11 22143
## + YrSold         1 3.5585e+06 5.0482e+11 22143
## - YearRemodAdd   1 1.9083e+09 5.0673e+11 22143
## + LotShape       3 1.7175e+09 5.0311e+11 22143
## - LotFrontage    1 1.9928e+09 5.0682e+11 22144
## - GarageArea     1 2.1320e+09 5.0696e+11 22144
## - Foundation     4 4.9695e+09 5.0979e+11 22144
## + PavedDrive     2 4.7652e+08 5.0435e+11 22144
## + Alley          2 4.6089e+08 5.0436e+11 22144
## + RoofStyle      4 2.2406e+09 5.0258e+11 22144
## - Street         1 2.4484e+09 5.0727e+11 22145
## + FireplaceQu    5 3.0650e+09 5.0176e+11 22145
## + HouseStyle     7 4.8577e+09 4.9997e+11 22145
## - BedroomAbvGr   1 2.6657e+09 5.0749e+11 22145
## - Functional     5 6.4008e+09 5.1123e+11 22145
## - MasVnrType     3 4.5714e+09 5.0940e+11 22145
## + ExterCond      3 9.5336e+08 5.0387e+11 22145
## - BldgType       4 5.5920e+09 5.1042e+11 22145
## - Condition1     8 9.3978e+09 5.1422e+11 22145
## + Fence          4 1.7576e+09 5.0307e+11 22145
## - GarageCond     4 5.6593e+09 5.1048e+11 22145
## - MSZoning       4 5.8279e+09 5.1065e+11 22146
## + BsmtCond       3 6.3118e+08 5.0419e+11 22146
## + Heating        3 3.6826e+08 5.0446e+11 22146
## + GarageType     5 2.1414e+09 5.0268e+11 22147
## - LandContour    3 5.3395e+09 5.1016e+11 22147
## + HeatingQC      4 8.7165e+08 5.0395e+11 22147
## - KitchenAbvGr   1 4.0953e+09 5.0892e+11 22148
## + SaleType       8 4.2032e+09 5.0062e+11 22148
## + Electrical     4 3.8862e+07 5.0479e+11 22149
## + BsmtFinType2   5 8.4542e+08 5.0398e+11 22149
## - YearBuilt      1 5.3125e+09 5.1014e+11 22151
## - GarageQual     4 8.1728e+09 5.1300e+11 22151
## - LandSlope      2 6.4916e+09 5.1132e+11 22151
## - MasVnrArea     1 7.7383e+09 5.1256e+11 22156
## - LotConfig      4 1.1036e+10 5.1586e+11 22157
## - BsmtUnfSF      1 8.3149e+09 5.1314e+11 22157
## + Exterior2nd   14 5.3720e+09 4.9945e+11 22158
## - BsmtFinSF2     1 9.9633e+09 5.1479e+11 22161
## - ExterQual      3 1.2273e+10 5.1710e+11 22161
## - BsmtQual       3 1.2486e+10 5.1731e+11 22162
## - SaleCondition  5 1.5538e+10 5.2036e+11 22164
## - KitchenQual    3 1.5369e+10 5.2019e+11 22168
## - RoofMatl       6 1.9434e+10 5.2426e+11 22171
## - OverallCond    1 1.5073e+10 5.1990e+11 22171
## - OverallQual    1 1.5348e+10 5.2017e+11 22172
## - MiscFeature    3 2.1010e+10 5.2583e+11 22180
## - LotArea        1 2.0480e+10 5.2530e+11 22183
## - BsmtFinSF1     1 2.1697e+10 5.2652e+11 22185
## - BsmtExposure   3 2.3659e+10 5.2848e+11 22185
## - X1stFlrSF      1 2.2922e+10 5.2775e+11 22188
## - PoolArea       1 2.5092e+10 5.2992e+11 22192
## - PoolQC         3 3.0564e+10 5.3539e+11 22200
## - Condition2     5 6.7041e+10 5.7187e+11 22268
## - Neighborhood  24 9.2133e+10 5.9696e+11 22277
## - X2ndFlrSF      1 6.8119e+10 5.7294e+11 22278
## 
## Step:  AIC=22139.19
## SalePrice ~ MSSubClass + MSZoning + LotFrontage + LotArea + Street + 
##     LandContour + LotConfig + LandSlope + Neighborhood + Condition1 + 
##     Condition2 + BldgType + OverallQual + OverallCond + YearBuilt + 
##     YearRemodAdd + RoofMatl + Exterior1st + MasVnrType + MasVnrArea + 
##     ExterQual + Foundation + BsmtQual + BsmtExposure + BsmtFinType1 + 
##     BsmtFinSF1 + BsmtFinSF2 + BsmtUnfSF + CentralAir + X1stFlrSF + 
##     X2ndFlrSF + BsmtFullBath + BsmtHalfBath + FullBath + HalfBath + 
##     BedroomAbvGr + KitchenAbvGr + KitchenQual + TotRmsAbvGrd + 
##     Functional + Fireplaces + GarageYrBlt + GarageFinish + GarageCars + 
##     GarageArea + GarageQual + GarageCond + WoodDeckSF + OpenPorchSF + 
##     X3SsnPorch + ScreenPorch + PoolArea + PoolQC + MiscFeature + 
##     MiscVal + MoSold + SaleCondition
## 
##                 Df  Sum of Sq        RSS   AIC
## - BsmtHalfBath   1 2.6863e+07 5.0486e+11 22137
## - MiscVal        1 2.8200e+07 5.0486e+11 22137
## - OpenPorchSF    1 5.4556e+07 5.0489e+11 22137
## - GarageYrBlt    1 8.4111e+07 5.0492e+11 22137
## - BsmtFullBath   1 1.1248e+08 5.0495e+11 22137
## - HalfBath       1 1.6282e+08 5.0500e+11 22138
## - GarageFinish   2 1.2225e+09 5.0606e+11 22138
## - MoSold         1 5.1525e+08 5.0535e+11 22138
## - Exterior1st   13 1.1783e+10 5.1662e+11 22138
## - WoodDeckSF     1 7.4598e+08 5.0558e+11 22139
## - TotRmsAbvGrd   1 7.7385e+08 5.0561e+11 22139
## - CentralAir     1 9.0896e+08 5.0574e+11 22139
## <none>                        5.0484e+11 22139
## - Fireplaces     1 1.0474e+09 5.0588e+11 22140
## - ScreenPorch    1 1.0572e+09 5.0589e+11 22140
## - X3SsnPorch     1 1.0815e+09 5.0592e+11 22140
## - BsmtFinType1   5 4.9578e+09 5.0979e+11 22140
## - FullBath       1 1.3733e+09 5.0621e+11 22140
## - GarageCars     1 1.5378e+09 5.0637e+11 22141
## - MSSubClass     1 1.5522e+09 5.0639e+11 22141
## + LowQualFinSF   1 1.1143e+07 5.0482e+11 22141
## + GrLivArea      1 1.1143e+07 5.0482e+11 22141
## + EnclosedPorch  1 9.4373e+06 5.0483e+11 22141
## + YrSold         1 3.3752e+06 5.0483e+11 22141
## - YearRemodAdd   1 1.9171e+09 5.0675e+11 22141
## + LotShape       3 1.7222e+09 5.0311e+11 22142
## - LotFrontage    1 1.9961e+09 5.0683e+11 22142
## - GarageArea     1 2.1260e+09 5.0696e+11 22142
## - Foundation     4 4.9586e+09 5.0979e+11 22142
## + PavedDrive     2 4.7829e+08 5.0436e+11 22142
## + Alley          2 4.6180e+08 5.0437e+11 22142
## + RoofStyle      4 2.2405e+09 5.0260e+11 22142
## - Street         1 2.4394e+09 5.0728e+11 22143
## + FireplaceQu    5 3.0563e+09 5.0178e+11 22143
## - BedroomAbvGr   1 2.6896e+09 5.0753e+11 22143
## - MasVnrType     3 4.5722e+09 5.0941e+11 22143
## + ExterCond      3 9.4522e+08 5.0389e+11 22143
## - Functional     5 6.4982e+09 5.1133e+11 22143
## - BldgType       4 5.6151e+09 5.1045e+11 22143
## - Condition1     8 9.3909e+09 5.1423e+11 22143
## + Fence          4 1.7395e+09 5.0310e+11 22143
## - MSZoning       4 5.8188e+09 5.1065e+11 22144
## + BsmtCond       3 6.2827e+08 5.0421e+11 22144
## + HouseStyle     7 4.1629e+09 5.0067e+11 22144
## + Heating        3 3.6587e+08 5.0447e+11 22144
## - GarageCond     4 6.1819e+09 5.1102e+11 22145
## + GarageType     5 2.1169e+09 5.0272e+11 22145
## - LandContour    3 5.3345e+09 5.1017e+11 22145
## + HeatingQC      4 8.6654e+08 5.0397e+11 22145
## - KitchenAbvGr   1 4.0847e+09 5.0892e+11 22146
## + SaleType       8 4.2099e+09 5.0063e+11 22146
## + Electrical     4 3.8502e+07 5.0480e+11 22147
## + BsmtFinType2   5 8.3162e+08 5.0400e+11 22147
## - YearBuilt      1 5.3578e+09 5.1019e+11 22149
## - LandSlope      2 6.4817e+09 5.1132e+11 22149
## - GarageQual     4 9.1839e+09 5.1402e+11 22151
## - MasVnrArea     1 7.7331e+09 5.1257e+11 22154
## - LotConfig      4 1.1034e+10 5.1587e+11 22155
## - BsmtUnfSF      1 8.3373e+09 5.1317e+11 22155
## + Exterior2nd   14 5.3799e+09 4.9946e+11 22156
## - BsmtFinSF2     1 9.9701e+09 5.1481e+11 22159
## - ExterQual      3 1.2289e+10 5.1712e+11 22160
## - BsmtQual       3 1.2476e+10 5.1731e+11 22160
## - SaleCondition  5 1.5528e+10 5.2036e+11 22162
## - KitchenQual    3 1.5375e+10 5.2021e+11 22166
## - RoofMatl       6 1.9468e+10 5.2430e+11 22169
## - OverallCond    1 1.5068e+10 5.1990e+11 22169
## - OverallQual    1 1.5383e+10 5.2022e+11 22170
## - MiscFeature    3 2.1995e+10 5.2683e+11 22180
## - LotArea        1 2.0470e+10 5.2531e+11 22181
## - BsmtFinSF1     1 2.1721e+10 5.2656e+11 22183
## - BsmtExposure   3 2.3728e+10 5.2856e+11 22183
## - X1stFlrSF      1 2.2985e+10 5.2782e+11 22186
## - PoolArea       1 2.7054e+10 5.3189e+11 22194
## - PoolQC         3 3.1406e+10 5.3624e+11 22199
## - Condition2     5 6.7153e+10 5.7199e+11 22266
## - Neighborhood  24 9.2197e+10 5.9703e+11 22275
## - X2ndFlrSF      1 6.9862e+10 5.7470e+11 22279
## 
## Step:  AIC=22137.25
## SalePrice ~ MSSubClass + MSZoning + LotFrontage + LotArea + Street + 
##     LandContour + LotConfig + LandSlope + Neighborhood + Condition1 + 
##     Condition2 + BldgType + OverallQual + OverallCond + YearBuilt + 
##     YearRemodAdd + RoofMatl + Exterior1st + MasVnrType + MasVnrArea + 
##     ExterQual + Foundation + BsmtQual + BsmtExposure + BsmtFinType1 + 
##     BsmtFinSF1 + BsmtFinSF2 + BsmtUnfSF + CentralAir + X1stFlrSF + 
##     X2ndFlrSF + BsmtFullBath + FullBath + HalfBath + BedroomAbvGr + 
##     KitchenAbvGr + KitchenQual + TotRmsAbvGrd + Functional + 
##     Fireplaces + GarageYrBlt + GarageFinish + GarageCars + GarageArea + 
##     GarageQual + GarageCond + WoodDeckSF + OpenPorchSF + X3SsnPorch + 
##     ScreenPorch + PoolArea + PoolQC + MiscFeature + MiscVal + 
##     MoSold + SaleCondition
## 
##                 Df  Sum of Sq        RSS   AIC
## - MiscVal        1 3.0128e+07 5.0489e+11 22135
## - OpenPorchSF    1 5.5735e+07 5.0492e+11 22135
## - GarageYrBlt    1 8.7011e+07 5.0495e+11 22135
## - BsmtFullBath   1 8.9362e+07 5.0495e+11 22135
## - HalfBath       1 1.6088e+08 5.0502e+11 22136
## - GarageFinish   2 1.2157e+09 5.0608e+11 22136
## - MoSold         1 5.0625e+08 5.0537e+11 22136
## - Exterior1st   13 1.1848e+10 5.1671e+11 22137
## - WoodDeckSF     1 7.6087e+08 5.0562e+11 22137
## - TotRmsAbvGrd   1 7.6991e+08 5.0563e+11 22137
## - CentralAir     1 9.0536e+08 5.0577e+11 22137
## <none>                        5.0486e+11 22137
## - ScreenPorch    1 1.0452e+09 5.0591e+11 22138
## - Fireplaces     1 1.0568e+09 5.0592e+11 22138
## - X3SsnPorch     1 1.1141e+09 5.0598e+11 22138
## - BsmtFinType1   5 4.9783e+09 5.0984e+11 22138
## - FullBath       1 1.3465e+09 5.0621e+11 22138
## - GarageCars     1 1.5397e+09 5.0640e+11 22139
## - MSSubClass     1 1.5471e+09 5.0641e+11 22139
## + BsmtHalfBath   1 2.6863e+07 5.0484e+11 22139
## + LowQualFinSF   1 1.1757e+07 5.0485e+11 22139
## + GrLivArea      1 1.1757e+07 5.0485e+11 22139
## + EnclosedPorch  1 9.2532e+06 5.0485e+11 22139
## + YrSold         1 4.2244e+06 5.0486e+11 22139
## - YearRemodAdd   1 1.9412e+09 5.0680e+11 22140
## + LotShape       3 1.7355e+09 5.0313e+11 22140
## - LotFrontage    1 1.9886e+09 5.0685e+11 22140
## - GarageArea     1 2.1358e+09 5.0700e+11 22140
## - Foundation     4 4.9709e+09 5.0983e+11 22140
## + Alley          2 4.5943e+08 5.0440e+11 22140
## + PavedDrive     2 4.5515e+08 5.0441e+11 22140
## + RoofStyle      4 2.2673e+09 5.0260e+11 22140
## - Street         1 2.4382e+09 5.0730e+11 22141
## + FireplaceQu    5 3.0285e+09 5.0183e+11 22141
## - BedroomAbvGr   1 2.6627e+09 5.0753e+11 22141
## - MasVnrType     3 4.5557e+09 5.0942e+11 22141
## - Functional     5 6.4730e+09 5.1134e+11 22141
## + ExterCond      3 9.2185e+08 5.0394e+11 22141
## - BldgType       4 5.6027e+09 5.1047e+11 22141
## - Condition1     8 9.3927e+09 5.1426e+11 22141
## + Fence          4 1.7147e+09 5.0315e+11 22142
## - MSZoning       4 5.7931e+09 5.1066e+11 22142
## + BsmtCond       3 6.1273e+08 5.0425e+11 22142
## + HouseStyle     7 4.1628e+09 5.0070e+11 22142
## + Heating        3 3.6576e+08 5.0450e+11 22143
## - GarageCond     4 6.1728e+09 5.1104e+11 22143
## + GarageType     5 2.1104e+09 5.0275e+11 22143
## - LandContour    3 5.4476e+09 5.1031e+11 22143
## + HeatingQC      4 8.7685e+08 5.0399e+11 22143
## - KitchenAbvGr   1 4.0586e+09 5.0892e+11 22144
## + SaleType       8 4.2140e+09 5.0065e+11 22144
## + Electrical     4 3.8070e+07 5.0482e+11 22145
## + BsmtFinType2   5 8.4604e+08 5.0402e+11 22145
## - YearBuilt      1 5.3802e+09 5.1024e+11 22147
## - LandSlope      2 6.4559e+09 5.1132e+11 22147
## - GarageQual     4 9.1615e+09 5.1402e+11 22149
## - MasVnrArea     1 7.7238e+09 5.1259e+11 22152
## - LotConfig      4 1.1022e+10 5.1588e+11 22153
## - BsmtUnfSF      1 8.3170e+09 5.1318e+11 22153
## + Exterior2nd   14 5.4011e+09 4.9946e+11 22154
## - BsmtFinSF2     1 1.0084e+10 5.1495e+11 22157
## - ExterQual      3 1.2299e+10 5.1716e+11 22158
## - BsmtQual       3 1.2592e+10 5.1745e+11 22158
## - SaleCondition  5 1.5513e+10 5.2038e+11 22160
## - KitchenQual    3 1.5370e+10 5.2023e+11 22164
## - RoofMatl       6 1.9521e+10 5.2438e+11 22167
## - OverallCond    1 1.5275e+10 5.2014e+11 22168
## - OverallQual    1 1.5360e+10 5.2022e+11 22168
## - MiscFeature    3 2.1996e+10 5.2686e+11 22178
## - LotArea        1 2.0457e+10 5.2532e+11 22179
## - BsmtFinSF1     1 2.1914e+10 5.2678e+11 22182
## - BsmtExposure   3 2.3856e+10 5.2872e+11 22182
## - X1stFlrSF      1 2.2979e+10 5.2784e+11 22184
## - PoolArea       1 2.7117e+10 5.3198e+11 22193
## - PoolQC         3 3.1397e+10 5.3626e+11 22197
## - Condition2     5 6.7130e+10 5.7199e+11 22264
## - Neighborhood  24 9.2248e+10 5.9711e+11 22273
## - X2ndFlrSF      1 6.9849e+10 5.7471e+11 22277
## 
## Step:  AIC=22135.32
## SalePrice ~ MSSubClass + MSZoning + LotFrontage + LotArea + Street + 
##     LandContour + LotConfig + LandSlope + Neighborhood + Condition1 + 
##     Condition2 + BldgType + OverallQual + OverallCond + YearBuilt + 
##     YearRemodAdd + RoofMatl + Exterior1st + MasVnrType + MasVnrArea + 
##     ExterQual + Foundation + BsmtQual + BsmtExposure + BsmtFinType1 + 
##     BsmtFinSF1 + BsmtFinSF2 + BsmtUnfSF + CentralAir + X1stFlrSF + 
##     X2ndFlrSF + BsmtFullBath + FullBath + HalfBath + BedroomAbvGr + 
##     KitchenAbvGr + KitchenQual + TotRmsAbvGrd + Functional + 
##     Fireplaces + GarageYrBlt + GarageFinish + GarageCars + GarageArea + 
##     GarageQual + GarageCond + WoodDeckSF + OpenPorchSF + X3SsnPorch + 
##     ScreenPorch + PoolArea + PoolQC + MiscFeature + MoSold + 
##     SaleCondition
## 
##                 Df  Sum of Sq        RSS   AIC
## - OpenPorchSF    1 5.4065e+07 5.0495e+11 22133
## - BsmtFullBath   1 8.6685e+07 5.0498e+11 22134
## - GarageYrBlt    1 8.8040e+07 5.0498e+11 22134
## - HalfBath       1 1.7112e+08 5.0506e+11 22134
## - GarageFinish   2 1.2275e+09 5.0612e+11 22134
## - MoSold         1 5.1374e+08 5.0541e+11 22134
## - Exterior1st   13 1.1823e+10 5.1672e+11 22135
## - WoodDeckSF     1 7.7395e+08 5.0567e+11 22135
## - TotRmsAbvGrd   1 7.8045e+08 5.0567e+11 22135
## - CentralAir     1 8.9557e+08 5.0579e+11 22135
## <none>                        5.0489e+11 22135
## - ScreenPorch    1 1.0245e+09 5.0592e+11 22136
## - Fireplaces     1 1.0296e+09 5.0592e+11 22136
## - X3SsnPorch     1 1.1133e+09 5.0601e+11 22136
## - BsmtFinType1   5 4.9660e+09 5.0986e+11 22136
## - FullBath       1 1.3585e+09 5.0625e+11 22136
## - MSSubClass     1 1.5435e+09 5.0644e+11 22137
## - GarageCars     1 1.5580e+09 5.0645e+11 22137
## + MiscVal        1 3.0128e+07 5.0486e+11 22137
## + BsmtHalfBath   1 2.8791e+07 5.0486e+11 22137
## + EnclosedPorch  1 1.0510e+07 5.0488e+11 22137
## + LowQualFinSF   1 9.6794e+06 5.0488e+11 22137
## + GrLivArea      1 9.6794e+06 5.0488e+11 22137
## + YrSold         1 4.6798e+06 5.0489e+11 22137
## - YearRemodAdd   1 1.9172e+09 5.0681e+11 22138
## + LotShape       3 1.7310e+09 5.0316e+11 22138
## - LotFrontage    1 1.9858e+09 5.0688e+11 22138
## - GarageArea     1 2.1278e+09 5.0702e+11 22138
## - Foundation     4 4.9424e+09 5.0984e+11 22138
## + Alley          2 4.5718e+08 5.0444e+11 22138
## + RoofStyle      4 2.2930e+09 5.0260e+11 22138
## + PavedDrive     2 4.5031e+08 5.0444e+11 22138
## - Street         1 2.4125e+09 5.0731e+11 22139
## + FireplaceQu    5 3.0168e+09 5.0188e+11 22139
## - BedroomAbvGr   1 2.6854e+09 5.0758e+11 22139
## + ExterCond      3 9.4726e+08 5.0395e+11 22139
## - BldgType       4 5.6040e+09 5.1050e+11 22139
## - MasVnrType     3 4.6869e+09 5.0958e+11 22139
## - Functional     5 6.5618e+09 5.1145e+11 22139
## + Fence          4 1.7218e+09 5.0317e+11 22140
## - Condition1     8 9.4554e+09 5.1435e+11 22140
## - MSZoning       4 5.7638e+09 5.1066e+11 22140
## + BsmtCond       3 6.2227e+08 5.0427e+11 22140
## + HouseStyle     7 4.1646e+09 5.0073e+11 22140
## + Heating        3 3.6395e+08 5.0453e+11 22141
## - GarageCond     4 6.1753e+09 5.1107e+11 22141
## + GarageType     5 2.0855e+09 5.0281e+11 22141
## - LandContour    3 5.5051e+09 5.1040e+11 22141
## + HeatingQC      4 8.3456e+08 5.0406e+11 22142
## - KitchenAbvGr   1 4.0441e+09 5.0894e+11 22142
## + SaleType       8 4.2441e+09 5.0065e+11 22142
## + Electrical     4 3.9389e+07 5.0485e+11 22143
## + BsmtFinType2   5 8.5146e+08 5.0404e+11 22144
## - YearBuilt      1 5.4383e+09 5.1033e+11 22145
## - LandSlope      2 6.4822e+09 5.1138e+11 22145
## - GarageQual     4 9.2280e+09 5.1412e+11 22147
## - MasVnrArea     1 7.7654e+09 5.1266e+11 22150
## - LotConfig      4 1.1042e+10 5.1593e+11 22151
## - BsmtUnfSF      1 8.2894e+09 5.1318e+11 22151
## + Exterior2nd   14 5.3930e+09 4.9950e+11 22152
## - BsmtFinSF2     1 1.0067e+10 5.1496e+11 22155
## - ExterQual      3 1.2301e+10 5.1719e+11 22156
## - BsmtQual       3 1.2606e+10 5.1750e+11 22156
## - SaleCondition  5 1.5498e+10 5.2039e+11 22158
## - KitchenQual    3 1.5454e+10 5.2035e+11 22162
## - RoofMatl       6 1.9545e+10 5.2444e+11 22165
## - OverallCond    1 1.5249e+10 5.2014e+11 22166
## - OverallQual    1 1.5391e+10 5.2028e+11 22166
## - LotArea        1 2.0507e+10 5.2540e+11 22177
## - MiscFeature    3 2.3153e+10 5.2805e+11 22178
## - BsmtFinSF1     1 2.1884e+10 5.2678e+11 22180
## - BsmtExposure   3 2.3849e+10 5.2874e+11 22180
## - X1stFlrSF      1 2.3109e+10 5.2800e+11 22182
## - PoolArea       1 2.7088e+10 5.3198e+11 22191
## - PoolQC         3 3.1371e+10 5.3626e+11 22195
## - Condition2     5 6.7115e+10 5.7201e+11 22262
## - Neighborhood  24 9.2243e+10 5.9714e+11 22271
## - X2ndFlrSF      1 6.9886e+10 5.7478e+11 22275
## 
## Step:  AIC=22133.43
## SalePrice ~ MSSubClass + MSZoning + LotFrontage + LotArea + Street + 
##     LandContour + LotConfig + LandSlope + Neighborhood + Condition1 + 
##     Condition2 + BldgType + OverallQual + OverallCond + YearBuilt + 
##     YearRemodAdd + RoofMatl + Exterior1st + MasVnrType + MasVnrArea + 
##     ExterQual + Foundation + BsmtQual + BsmtExposure + BsmtFinType1 + 
##     BsmtFinSF1 + BsmtFinSF2 + BsmtUnfSF + CentralAir + X1stFlrSF + 
##     X2ndFlrSF + BsmtFullBath + FullBath + HalfBath + BedroomAbvGr + 
##     KitchenAbvGr + KitchenQual + TotRmsAbvGrd + Functional + 
##     Fireplaces + GarageYrBlt + GarageFinish + GarageCars + GarageArea + 
##     GarageQual + GarageCond + WoodDeckSF + X3SsnPorch + ScreenPorch + 
##     PoolArea + PoolQC + MiscFeature + MoSold + SaleCondition
## 
##                 Df  Sum of Sq        RSS   AIC
## - BsmtFullBath   1 8.3760e+07 5.0503e+11 22132
## - GarageYrBlt    1 8.8128e+07 5.0504e+11 22132
## - HalfBath       1 1.6007e+08 5.0511e+11 22132
## - GarageFinish   2 1.2669e+09 5.0621e+11 22132
## - MoSold         1 5.6323e+08 5.0551e+11 22133
## - Exterior1st   13 1.1799e+10 5.1675e+11 22133
## - TotRmsAbvGrd   1 7.7192e+08 5.0572e+11 22133
## - WoodDeckSF     1 8.0266e+08 5.0575e+11 22133
## <none>                        5.0495e+11 22133
## - CentralAir     1 9.4959e+08 5.0590e+11 22134
## - Fireplaces     1 9.9522e+08 5.0594e+11 22134
## - ScreenPorch    1 9.9956e+08 5.0595e+11 22134
## - X3SsnPorch     1 1.1246e+09 5.0607e+11 22134
## - BsmtFinType1   5 4.9294e+09 5.0988e+11 22134
## - FullBath       1 1.3707e+09 5.0632e+11 22134
## - MSSubClass     1 1.5525e+09 5.0650e+11 22135
## - GarageCars     1 1.5925e+09 5.0654e+11 22135
## + OpenPorchSF    1 5.4065e+07 5.0489e+11 22135
## + BsmtHalfBath   1 2.9936e+07 5.0492e+11 22135
## + MiscVal        1 2.8458e+07 5.0492e+11 22135
## + EnclosedPorch  1 1.4526e+07 5.0493e+11 22135
## + LowQualFinSF   1 1.0139e+07 5.0494e+11 22135
## + GrLivArea      1 1.0139e+07 5.0494e+11 22135
## + YrSold         1 2.8496e+06 5.0494e+11 22135
## - YearRemodAdd   1 1.9084e+09 5.0686e+11 22136
## + LotShape       3 1.7469e+09 5.0320e+11 22136
## - LotFrontage    1 1.9610e+09 5.0691e+11 22136
## - GarageArea     1 2.1078e+09 5.0705e+11 22136
## - Foundation     4 4.9222e+09 5.0987e+11 22136
## + RoofStyle      4 2.3201e+09 5.0263e+11 22136
## + Alley          2 4.7155e+08 5.0448e+11 22136
## + PavedDrive     2 4.5323e+08 5.0449e+11 22137
## - Street         1 2.4690e+09 5.0742e+11 22137
## + FireplaceQu    5 3.0594e+09 5.0189e+11 22137
## - BedroomAbvGr   1 2.6637e+09 5.0761e+11 22137
## + ExterCond      3 9.6177e+08 5.0399e+11 22137
## - Functional     5 6.5575e+09 5.1150e+11 22138
## - BldgType       4 5.6238e+09 5.1057e+11 22138
## + Fence          4 1.7451e+09 5.0320e+11 22138
## - MasVnrType     3 4.7454e+09 5.0969e+11 22138
## - Condition1     8 9.4365e+09 5.1438e+11 22138
## - MSZoning       4 5.7123e+09 5.1066e+11 22138
## + BsmtCond       3 6.2191e+08 5.0433e+11 22138
## + HouseStyle     7 4.1502e+09 5.0080e+11 22138
## - GarageCond     4 6.1233e+09 5.1107e+11 22139
## + Heating        3 3.5942e+08 5.0459e+11 22139
## + GarageType     5 2.0651e+09 5.0288e+11 22139
## - LandContour    3 5.5181e+09 5.1047e+11 22139
## + HeatingQC      4 8.3935e+08 5.0411e+11 22140
## + SaleType       8 4.2943e+09 5.0065e+11 22140
## - KitchenAbvGr   1 4.0497e+09 5.0900e+11 22140
## + Electrical     4 4.1855e+07 5.0491e+11 22141
## + BsmtFinType2   5 8.6275e+08 5.0408e+11 22142
## - YearBuilt      1 5.4056e+09 5.1035e+11 22143
## - LandSlope      2 6.4332e+09 5.1138e+11 22143
## - GarageQual     4 9.1744e+09 5.1412e+11 22145
## - MasVnrArea     1 8.0225e+09 5.1297e+11 22149
## - LotConfig      4 1.1054e+10 5.1600e+11 22149
## - BsmtUnfSF      1 8.2663e+09 5.1321e+11 22149
## + Exterior2nd   14 5.4038e+09 4.9954e+11 22150
## - BsmtFinSF2     1 1.0043e+10 5.1499e+11 22153
## - ExterQual      3 1.2327e+10 5.1727e+11 22154
## - BsmtQual       3 1.2554e+10 5.1750e+11 22154
## - SaleCondition  5 1.5512e+10 5.2046e+11 22157
## - KitchenQual    3 1.5463e+10 5.2041e+11 22160
## - RoofMatl       6 1.9647e+10 5.2459e+11 22163
## - OverallCond    1 1.5202e+10 5.2015e+11 22164
## - OverallQual    1 1.5615e+10 5.2056e+11 22165
## - LotArea        1 2.0499e+10 5.2545e+11 22175
## - MiscFeature    3 2.3215e+10 5.2816e+11 22177
## - BsmtExposure   3 2.3796e+10 5.2874e+11 22178
## - BsmtFinSF1     1 2.1911e+10 5.2686e+11 22178
## - X1stFlrSF      1 2.3184e+10 5.2813e+11 22181
## - PoolArea       1 2.7183e+10 5.3213e+11 22189
## - PoolQC         3 3.1494e+10 5.3644e+11 22194
## - Condition2     5 6.7076e+10 5.7202e+11 22260
## - Neighborhood  24 9.2713e+10 5.9766e+11 22270
## - X2ndFlrSF      1 7.0015e+10 5.7496e+11 22274
## 
## Step:  AIC=22131.62
## SalePrice ~ MSSubClass + MSZoning + LotFrontage + LotArea + Street + 
##     LandContour + LotConfig + LandSlope + Neighborhood + Condition1 + 
##     Condition2 + BldgType + OverallQual + OverallCond + YearBuilt + 
##     YearRemodAdd + RoofMatl + Exterior1st + MasVnrType + MasVnrArea + 
##     ExterQual + Foundation + BsmtQual + BsmtExposure + BsmtFinType1 + 
##     BsmtFinSF1 + BsmtFinSF2 + BsmtUnfSF + CentralAir + X1stFlrSF + 
##     X2ndFlrSF + FullBath + HalfBath + BedroomAbvGr + KitchenAbvGr + 
##     KitchenQual + TotRmsAbvGrd + Functional + Fireplaces + GarageYrBlt + 
##     GarageFinish + GarageCars + GarageArea + GarageQual + GarageCond + 
##     WoodDeckSF + X3SsnPorch + ScreenPorch + PoolArea + PoolQC + 
##     MiscFeature + MoSold + SaleCondition
## 
##                 Df  Sum of Sq        RSS   AIC
## - GarageYrBlt    1 9.4371e+07 5.0513e+11 22130
## - HalfBath       1 1.5142e+08 5.0518e+11 22130
## - GarageFinish   2 1.2388e+09 5.0627e+11 22130
## - MoSold         1 5.6985e+08 5.0560e+11 22131
## - Exterior1st   13 1.1836e+10 5.1687e+11 22131
## - TotRmsAbvGrd   1 7.8982e+08 5.0582e+11 22131
## - WoodDeckSF     1 8.0223e+08 5.0583e+11 22131
## <none>                        5.0503e+11 22132
## - CentralAir     1 9.7311e+08 5.0600e+11 22132
## - ScreenPorch    1 9.8661e+08 5.0602e+11 22132
## - Fireplaces     1 1.0065e+09 5.0604e+11 22132
## - X3SsnPorch     1 1.1145e+09 5.0615e+11 22132
## - FullBath       1 1.3092e+09 5.0634e+11 22132
## - MSSubClass     1 1.5466e+09 5.0658e+11 22133
## - GarageCars     1 1.5866e+09 5.0662e+11 22133
## - BsmtFinType1   5 5.4577e+09 5.1049e+11 22133
## + BsmtFullBath   1 8.3760e+07 5.0495e+11 22133
## + OpenPorchSF    1 5.1140e+07 5.0498e+11 22134
## + MiscVal        1 2.5944e+07 5.0500e+11 22134
## + EnclosedPorch  1 1.8840e+07 5.0501e+11 22134
## + LowQualFinSF   1 1.0598e+07 5.0502e+11 22134
## + GrLivArea      1 1.0598e+07 5.0502e+11 22134
## + BsmtHalfBath   1 5.2573e+06 5.0503e+11 22134
## + YrSold         1 1.1000e+06 5.0503e+11 22134
## - YearRemodAdd   1 1.9296e+09 5.0696e+11 22134
## - LotFrontage    1 1.9539e+09 5.0698e+11 22134
## + LotShape       3 1.7333e+09 5.0330e+11 22134
## - Foundation     4 4.9445e+09 5.0998e+11 22134
## - GarageArea     1 2.1728e+09 5.0720e+11 22134
## + Alley          2 4.6662e+08 5.0456e+11 22135
## + PavedDrive     2 4.5830e+08 5.0457e+11 22135
## + RoofStyle      4 2.2391e+09 5.0279e+11 22135
## - Street         1 2.4587e+09 5.0749e+11 22135
## + FireplaceQu    5 3.0469e+09 5.0198e+11 22135
## - BedroomAbvGr   1 2.6393e+09 5.0767e+11 22135
## + ExterCond      3 9.4740e+08 5.0408e+11 22136
## - Functional     5 6.5184e+09 5.1155e+11 22136
## - BldgType       4 5.6002e+09 5.1063e+11 22136
## - Condition1     8 9.3712e+09 5.1440e+11 22136
## - MasVnrType     3 4.7291e+09 5.0976e+11 22136
## + Fence          4 1.7369e+09 5.0329e+11 22136
## - MSZoning       4 5.7878e+09 5.1082e+11 22136
## + BsmtCond       3 6.1457e+08 5.0442e+11 22136
## + HouseStyle     7 4.1774e+09 5.0085e+11 22137
## + Heating        3 3.7541e+08 5.0466e+11 22137
## - GarageCond     4 6.1601e+09 5.1119e+11 22137
## + GarageType     5 2.0463e+09 5.0298e+11 22137
## - LandContour    3 5.5585e+09 5.1059e+11 22138
## + HeatingQC      4 8.6108e+08 5.0417e+11 22138
## + SaleType       8 4.2549e+09 5.0078e+11 22138
## - KitchenAbvGr   1 4.0886e+09 5.0912e+11 22138
## + Electrical     4 4.1285e+07 5.0499e+11 22140
## + BsmtFinType2   5 8.8241e+08 5.0415e+11 22140
## - YearBuilt      1 5.3957e+09 5.1043e+11 22141
## - LandSlope      2 6.4300e+09 5.1146e+11 22142
## - GarageQual     4 9.1616e+09 5.1419e+11 22143
## - MasVnrArea     1 7.9593e+09 5.1299e+11 22147
## - LotConfig      4 1.1058e+10 5.1609e+11 22147
## - BsmtUnfSF      1 8.2455e+09 5.1328e+11 22147
## + Exterior2nd   14 5.4353e+09 4.9960e+11 22148
## - ExterQual      3 1.2270e+10 5.1730e+11 22152
## - BsmtQual       3 1.2534e+10 5.1756e+11 22152
## - BsmtFinSF2     1 1.0933e+10 5.1596e+11 22153
## - SaleCondition  5 1.5560e+10 5.2059e+11 22155
## - KitchenQual    3 1.5505e+10 5.2054e+11 22159
## - RoofMatl       6 1.9675e+10 5.2471e+11 22161
## - OverallCond    1 1.5121e+10 5.2015e+11 22162
## - OverallQual    1 1.5570e+10 5.2060e+11 22163
## - LotArea        1 2.0751e+10 5.2578e+11 22174
## - MiscFeature    3 2.3250e+10 5.2828e+11 22175
## - BsmtExposure   3 2.3776e+10 5.2881e+11 22176
## - X1stFlrSF      1 2.3116e+10 5.2815e+11 22179
## - BsmtFinSF1     1 2.3708e+10 5.2874e+11 22180
## - PoolArea       1 2.7184e+10 5.3221e+11 22187
## - PoolQC         3 3.1434e+10 5.3646e+11 22192
## - Condition2     5 6.7290e+10 5.7232e+11 22259
## - Neighborhood  24 9.2630e+10 5.9766e+11 22268
## - X2ndFlrSF      1 6.9934e+10 5.7496e+11 22272
## 
## Step:  AIC=22129.82
## SalePrice ~ MSSubClass + MSZoning + LotFrontage + LotArea + Street + 
##     LandContour + LotConfig + LandSlope + Neighborhood + Condition1 + 
##     Condition2 + BldgType + OverallQual + OverallCond + YearBuilt + 
##     YearRemodAdd + RoofMatl + Exterior1st + MasVnrType + MasVnrArea + 
##     ExterQual + Foundation + BsmtQual + BsmtExposure + BsmtFinType1 + 
##     BsmtFinSF1 + BsmtFinSF2 + BsmtUnfSF + CentralAir + X1stFlrSF + 
##     X2ndFlrSF + FullBath + HalfBath + BedroomAbvGr + KitchenAbvGr + 
##     KitchenQual + TotRmsAbvGrd + Functional + Fireplaces + GarageFinish + 
##     GarageCars + GarageArea + GarageQual + GarageCond + WoodDeckSF + 
##     X3SsnPorch + ScreenPorch + PoolArea + PoolQC + MiscFeature + 
##     MoSold + SaleCondition
## 
##                 Df  Sum of Sq        RSS   AIC
## - HalfBath       1 1.5811e+08 5.0528e+11 22128
## - GarageFinish   2 1.2119e+09 5.0634e+11 22128
## - MoSold         1 5.6335e+08 5.0569e+11 22129
## - Exterior1st   13 1.1946e+10 5.1707e+11 22129
## - WoodDeckSF     1 7.6490e+08 5.0589e+11 22130
## - TotRmsAbvGrd   1 7.7719e+08 5.0590e+11 22130
## - CentralAir     1 9.0452e+08 5.0603e+11 22130
## <none>                        5.0513e+11 22130
## - ScreenPorch    1 1.0004e+09 5.0613e+11 22130
## - Fireplaces     1 1.0986e+09 5.0622e+11 22130
## - X3SsnPorch     1 1.1054e+09 5.0623e+11 22130
## - FullBath       1 1.3007e+09 5.0643e+11 22131
## - MSSubClass     1 1.5450e+09 5.0667e+11 22131
## - GarageCars     1 1.5882e+09 5.0671e+11 22131
## - BsmtFinType1   5 5.4386e+09 5.1056e+11 22132
## + GarageYrBlt    1 9.4371e+07 5.0503e+11 22132
## + BsmtFullBath   1 9.0002e+07 5.0504e+11 22132
## + OpenPorchSF    1 5.1123e+07 5.0507e+11 22132
## + MiscVal        1 2.6840e+07 5.0510e+11 22132
## + EnclosedPorch  1 2.0194e+07 5.0510e+11 22132
## + LowQualFinSF   1 1.8806e+07 5.0511e+11 22132
## + GrLivArea      1 1.8806e+07 5.0511e+11 22132
## - YearRemodAdd   1 1.8424e+09 5.0697e+11 22132
## + BsmtHalfBath   1 6.0487e+06 5.0512e+11 22132
## + YrSold         1 1.0266e+06 5.0512e+11 22132
## + LotShape       3 1.7483e+09 5.0338e+11 22132
## - LotFrontage    1 2.0503e+09 5.0718e+11 22132
## - GarageArea     1 2.0909e+09 5.0722e+11 22132
## - Foundation     4 4.9159e+09 5.1004e+11 22132
## + PavedDrive     2 4.8487e+08 5.0464e+11 22133
## + RoofStyle      4 2.2884e+09 5.0284e+11 22133
## + Alley          2 4.3432e+08 5.0469e+11 22133
## - Street         1 2.4225e+09 5.0755e+11 22133
## + FireplaceQu    5 3.0264e+09 5.0210e+11 22133
## - BedroomAbvGr   1 2.6442e+09 5.0777e+11 22134
## - Functional     5 6.4597e+09 5.1158e+11 22134
## + ExterCond      3 9.3601e+08 5.0419e+11 22134
## - Condition1     8 9.3334e+09 5.1446e+11 22134
## - BldgType       4 5.5893e+09 5.1071e+11 22134
## - MasVnrType     3 4.7117e+09 5.0984e+11 22134
## + Fence          4 1.6965e+09 5.0343e+11 22134
## - MSZoning       4 5.8363e+09 5.1096e+11 22134
## + BsmtCond       3 6.1341e+08 5.0451e+11 22135
## + HouseStyle     7 4.2544e+09 5.0087e+11 22135
## - GarageCond     4 6.0787e+09 5.1120e+11 22135
## + Heating        3 4.0290e+08 5.0472e+11 22135
## + GarageType     5 2.0418e+09 5.0308e+11 22135
## + HeatingQC      4 8.6152e+08 5.0426e+11 22136
## - LandContour    3 5.6902e+09 5.1082e+11 22136
## + SaleType       8 4.2285e+09 5.0090e+11 22137
## - KitchenAbvGr   1 4.0831e+09 5.0921e+11 22137
## + Electrical     4 4.4302e+07 5.0508e+11 22138
## + BsmtFinType2   5 8.8958e+08 5.0424e+11 22138
## - YearBuilt      1 5.3229e+09 5.1045e+11 22139
## - LandSlope      2 6.5139e+09 5.1164e+11 22140
## - GarageQual     4 9.1094e+09 5.1423e+11 22141
## - MasVnrArea     1 7.9765e+09 5.1310e+11 22145
## - LotConfig      4 1.1014e+10 5.1614e+11 22145
## - BsmtUnfSF      1 8.3863e+09 5.1351e+11 22146
## + Exterior2nd   14 5.3608e+09 4.9976e+11 22146
## - ExterQual      3 1.2213e+10 5.1734e+11 22150
## - BsmtQual       3 1.2500e+10 5.1762e+11 22151
## - BsmtFinSF2     1 1.0996e+10 5.1612e+11 22151
## - SaleCondition  5 1.5539e+10 5.2066e+11 22153
## - KitchenQual    3 1.5509e+10 5.2063e+11 22157
## - RoofMatl       6 1.9935e+10 5.2506e+11 22160
## - OverallQual    1 1.5686e+10 5.2081e+11 22161
## - OverallCond    1 1.5904e+10 5.2103e+11 22162
## - LotArea        1 2.1002e+10 5.2613e+11 22172
## - MiscFeature    3 2.3243e+10 5.2837e+11 22173
## - BsmtExposure   3 2.3771e+10 5.2890e+11 22174
## - X1stFlrSF      1 2.3109e+10 5.2823e+11 22177
## - BsmtFinSF1     1 2.4098e+10 5.2922e+11 22179
## - PoolArea       1 2.7175e+10 5.3230e+11 22185
## - PoolQC         3 3.1369e+10 5.3649e+11 22190
## - Condition2     5 6.7272e+10 5.7240e+11 22257
## - Neighborhood  24 9.3394e+10 5.9852e+11 22267
## - X2ndFlrSF      1 7.0127e+10 5.7525e+11 22270
## 
## Step:  AIC=22128.16
## SalePrice ~ MSSubClass + MSZoning + LotFrontage + LotArea + Street + 
##     LandContour + LotConfig + LandSlope + Neighborhood + Condition1 + 
##     Condition2 + BldgType + OverallQual + OverallCond + YearBuilt + 
##     YearRemodAdd + RoofMatl + Exterior1st + MasVnrType + MasVnrArea + 
##     ExterQual + Foundation + BsmtQual + BsmtExposure + BsmtFinType1 + 
##     BsmtFinSF1 + BsmtFinSF2 + BsmtUnfSF + CentralAir + X1stFlrSF + 
##     X2ndFlrSF + FullBath + BedroomAbvGr + KitchenAbvGr + KitchenQual + 
##     TotRmsAbvGrd + Functional + Fireplaces + GarageFinish + GarageCars + 
##     GarageArea + GarageQual + GarageCond + WoodDeckSF + X3SsnPorch + 
##     ScreenPorch + PoolArea + PoolQC + MiscFeature + MoSold + 
##     SaleCondition
## 
##                 Df  Sum of Sq        RSS   AIC
## - GarageFinish   2 1.1527e+09 5.0644e+11 22127
## - MoSold         1 5.7624e+08 5.0586e+11 22127
## - Exterior1st   13 1.1959e+10 5.1724e+11 22128
## - WoodDeckSF     1 7.5984e+08 5.0604e+11 22128
## - TotRmsAbvGrd   1 8.0969e+08 5.0609e+11 22128
## <none>                        5.0528e+11 22128
## - CentralAir     1 9.3141e+08 5.0621e+11 22128
## - ScreenPorch    1 1.0482e+09 5.0633e+11 22128
## - Fireplaces     1 1.1305e+09 5.0641e+11 22129
## - X3SsnPorch     1 1.1337e+09 5.0642e+11 22129
## - FullBath       1 1.1541e+09 5.0644e+11 22129
## - MSSubClass     1 1.4857e+09 5.0677e+11 22129
## - BsmtFinType1   5 5.3359e+09 5.1062e+11 22130
## - GarageCars     1 1.6735e+09 5.0696e+11 22130
## + HalfBath       1 1.5811e+08 5.0513e+11 22130
## + GarageYrBlt    1 1.0106e+08 5.0518e+11 22130
## + BsmtFullBath   1 8.1063e+07 5.0520e+11 22130
## + OpenPorchSF    1 4.0583e+07 5.0524e+11 22130
## + MiscVal        1 3.6544e+07 5.0525e+11 22130
## + EnclosedPorch  1 2.1597e+07 5.0526e+11 22130
## + LowQualFinSF   1 1.5830e+07 5.0527e+11 22130
## + GrLivArea      1 1.5830e+07 5.0527e+11 22130
## + BsmtHalfBath   1 6.0396e+06 5.0528e+11 22130
## + YrSold         1 7.9409e+05 5.0528e+11 22130
## - YearRemodAdd   1 1.8956e+09 5.0718e+11 22130
## + LotShape       3 1.7197e+09 5.0356e+11 22130
## - GarageArea     1 2.0376e+09 5.0732e+11 22131
## - LotFrontage    1 2.0410e+09 5.0732e+11 22131
## - Foundation     4 4.9208e+09 5.1020e+11 22131
## + RoofStyle      4 2.3310e+09 5.0295e+11 22131
## + PavedDrive     2 4.4196e+08 5.0484e+11 22131
## + Alley          2 4.1038e+08 5.0487e+11 22131
## - Street         1 2.4116e+09 5.0769e+11 22131
## + FireplaceQu    5 3.0401e+09 5.0224e+11 22132
## - BedroomAbvGr   1 2.6680e+09 5.0795e+11 22132
## - Condition1     8 9.2400e+09 5.1452e+11 22132
## - BldgType       4 5.5326e+09 5.1082e+11 22132
## + ExterCond      3 9.4453e+08 5.0434e+11 22132
## - MasVnrType     3 4.6180e+09 5.0990e+11 22132
## - Functional     5 6.4865e+09 5.1177e+11 22132
## + Fence          4 1.7299e+09 5.0355e+11 22132
## + BsmtCond       3 6.5874e+08 5.0462e+11 22133
## - MSZoning       4 6.0163e+09 5.1130e+11 22133
## - GarageCond     4 6.0641e+09 5.1135e+11 22133
## + Heating        3 3.8217e+08 5.0490e+11 22133
## + HouseStyle     7 3.9736e+09 5.0131e+11 22134
## + GarageType     5 1.8663e+09 5.0342e+11 22134
## + HeatingQC      4 8.2559e+08 5.0446e+11 22134
## - LandContour    3 5.7140e+09 5.1100e+11 22135
## + SaleType       8 4.2719e+09 5.0101e+11 22135
## - KitchenAbvGr   1 4.0504e+09 5.0933e+11 22135
## + Electrical     4 4.3840e+07 5.0524e+11 22136
## + BsmtFinType2   5 8.6021e+08 5.0442e+11 22136
## - LandSlope      2 6.4697e+09 5.1175e+11 22138
## - YearBuilt      1 5.8692e+09 5.1115e+11 22139
## - GarageQual     4 9.0808e+09 5.1436e+11 22140
## - MasVnrArea     1 7.9540e+09 5.1324e+11 22143
## - LotConfig      4 1.0944e+10 5.1623e+11 22144
## - BsmtUnfSF      1 8.3807e+09 5.1366e+11 22144
## + Exterior2nd   14 5.4517e+09 4.9983e+11 22144
## - ExterQual      3 1.2244e+10 5.1753e+11 22148
## - BsmtQual       3 1.2484e+10 5.1777e+11 22149
## - BsmtFinSF2     1 1.1110e+10 5.1639e+11 22150
## - SaleCondition  5 1.5806e+10 5.2109e+11 22152
## - KitchenQual    3 1.5636e+10 5.2092e+11 22156
## - RoofMatl       6 2.0107e+10 5.2539e+11 22159
## - OverallQual    1 1.5593e+10 5.2088e+11 22159
## - OverallCond    1 1.5798e+10 5.2108e+11 22160
## - LotArea        1 2.0938e+10 5.2622e+11 22171
## - MiscFeature    3 2.3189e+10 5.2847e+11 22171
## - BsmtExposure   3 2.3620e+10 5.2890e+11 22172
## - X1stFlrSF      1 2.3299e+10 5.2858e+11 22176
## - BsmtFinSF1     1 2.4214e+10 5.2950e+11 22177
## - PoolArea       1 2.7196e+10 5.3248e+11 22184
## - PoolQC         3 3.1302e+10 5.3659e+11 22188
## - Condition2     5 6.7572e+10 5.7286e+11 22256
## - Neighborhood  24 9.3354e+10 5.9864e+11 22266
## - X2ndFlrSF      1 8.8909e+10 5.9419e+11 22304
## 
## Step:  AIC=22126.66
## SalePrice ~ MSSubClass + MSZoning + LotFrontage + LotArea + Street + 
##     LandContour + LotConfig + LandSlope + Neighborhood + Condition1 + 
##     Condition2 + BldgType + OverallQual + OverallCond + YearBuilt + 
##     YearRemodAdd + RoofMatl + Exterior1st + MasVnrType + MasVnrArea + 
##     ExterQual + Foundation + BsmtQual + BsmtExposure + BsmtFinType1 + 
##     BsmtFinSF1 + BsmtFinSF2 + BsmtUnfSF + CentralAir + X1stFlrSF + 
##     X2ndFlrSF + FullBath + BedroomAbvGr + KitchenAbvGr + KitchenQual + 
##     TotRmsAbvGrd + Functional + Fireplaces + GarageCars + GarageArea + 
##     GarageQual + GarageCond + WoodDeckSF + X3SsnPorch + ScreenPorch + 
##     PoolArea + PoolQC + MiscFeature + MoSold + SaleCondition
## 
##                 Df  Sum of Sq        RSS   AIC
## - MoSold         1 5.1452e+08 5.0695e+11 22126
## - WoodDeckSF     1 6.8819e+08 5.0712e+11 22126
## - TotRmsAbvGrd   1 8.2249e+08 5.0726e+11 22126
## - CentralAir     1 8.6271e+08 5.0730e+11 22127
## - FullBath       1 9.0240e+08 5.0734e+11 22127
## <none>                        5.0644e+11 22127
## - Exterior1st   13 1.2198e+10 5.1863e+11 22127
## - X3SsnPorch     1 9.9920e+08 5.0744e+11 22127
## - ScreenPorch    1 1.0102e+09 5.0745e+11 22127
## - Fireplaces     1 1.1814e+09 5.0762e+11 22127
## + GarageFinish   2 1.1527e+09 5.0528e+11 22128
## - MSSubClass     1 1.6585e+09 5.0809e+11 22128
## + HalfBath       1 9.8923e+07 5.0634e+11 22128
## - GarageArea     1 1.7678e+09 5.0820e+11 22129
## + OpenPorchSF    1 7.7013e+07 5.0636e+11 22129
## - BsmtFinType1   5 5.5120e+09 5.1195e+11 22129
## + GarageYrBlt    1 7.2252e+07 5.0636e+11 22129
## + BsmtFullBath   1 5.4949e+07 5.0638e+11 22129
## - LotFrontage    1 1.8056e+09 5.0824e+11 22129
## + MiscVal        1 4.6339e+07 5.0639e+11 22129
## + EnclosedPorch  1 1.7021e+07 5.0642e+11 22129
## + LowQualFinSF   1 1.6316e+07 5.0642e+11 22129
## + GrLivArea      1 1.6316e+07 5.0642e+11 22129
## + BsmtHalfBath   1 5.5197e+06 5.0643e+11 22129
## + YrSold         1 2.5103e+05 5.0644e+11 22129
## - YearRemodAdd   1 1.8853e+09 5.0832e+11 22129
## - GarageCars     1 1.9357e+09 5.0837e+11 22129
## + LotShape       3 1.7639e+09 5.0467e+11 22129
## - Foundation     4 4.7952e+09 5.1123e+11 22129
## + PavedDrive     2 4.7421e+08 5.0596e+11 22130
## + RoofStyle      4 2.2660e+09 5.0417e+11 22130
## + FireplaceQu    5 3.1850e+09 5.0325e+11 22130
## + Alley          2 3.5960e+08 5.0608e+11 22130
## - Functional     5 6.1603e+09 5.1260e+11 22130
## - Street         1 2.4844e+09 5.0892e+11 22130
## - BedroomAbvGr   1 2.4917e+09 5.0893e+11 22130
## - BldgType       4 5.4448e+09 5.1188e+11 22130
## - Condition1     8 9.2415e+09 5.1568e+11 22130
## + Fence          4 1.9234e+09 5.0451e+11 22131
## + ExterCond      3 9.9144e+08 5.0544e+11 22131
## - MasVnrType     3 4.9021e+09 5.1134e+11 22131
## + BsmtCond       3 6.6409e+08 5.0577e+11 22131
## + GarageType     5 2.3649e+09 5.0407e+11 22132
## - GarageCond     4 6.0122e+09 5.1245e+11 22132
## + HouseStyle     7 4.1023e+09 5.0233e+11 22132
## + Heating        3 3.6357e+08 5.0607e+11 22132
## - MSZoning       4 6.2490e+09 5.1268e+11 22132
## - LandContour    3 5.6500e+09 5.1209e+11 22133
## + HeatingQC      4 6.9167e+08 5.0574e+11 22133
## - KitchenAbvGr   1 4.0570e+09 5.1049e+11 22133
## + SaleType       8 4.2576e+09 5.0218e+11 22133
## + Electrical     4 4.2946e+07 5.0639e+11 22135
## + BsmtFinType2   5 8.8868e+08 5.0555e+11 22135
## - LandSlope      2 6.4116e+09 5.1285e+11 22136
## - YearBuilt      1 5.5686e+09 5.1200e+11 22137
## - GarageQual     4 9.0165e+09 5.1545e+11 22138
## - LotConfig      4 1.1015e+10 5.1745e+11 22142
## - MasVnrArea     1 8.2320e+09 5.1467e+11 22142
## + Exterior2nd   14 5.4598e+09 5.0098e+11 22143
## - BsmtUnfSF      1 8.5381e+09 5.1497e+11 22143
## - ExterQual      3 1.2624e+10 5.1906e+11 22148
## - BsmtQual       3 1.2841e+10 5.1928e+11 22148
## - BsmtFinSF2     1 1.1346e+10 5.1778e+11 22149
## - SaleCondition  5 1.5563e+10 5.2200e+11 22150
## - KitchenQual    3 1.6706e+10 5.2314e+11 22156
## - RoofMatl       6 2.0087e+10 5.2652e+11 22157
## - OverallQual    1 1.5448e+10 5.2188e+11 22158
## - OverallCond    1 1.6249e+10 5.2268e+11 22159
## - LotArea        1 2.0766e+10 5.2720e+11 22169
## - MiscFeature    3 2.2856e+10 5.2929e+11 22169
## - BsmtExposure   3 2.3491e+10 5.2993e+11 22170
## - X1stFlrSF      1 2.2992e+10 5.2943e+11 22173
## - BsmtFinSF1     1 2.4422e+10 5.3086e+11 22176
## - PoolArea       1 2.6844e+10 5.3328e+11 22181
## - PoolQC         3 3.1226e+10 5.3766e+11 22186
## - Condition2     5 6.7187e+10 5.7362e+11 22253
## - Neighborhood  24 9.4273e+10 6.0071e+11 22265
## - X2ndFlrSF      1 8.8976e+10 5.9541e+11 22302
## 
## Step:  AIC=22125.77
## SalePrice ~ MSSubClass + MSZoning + LotFrontage + LotArea + Street + 
##     LandContour + LotConfig + LandSlope + Neighborhood + Condition1 + 
##     Condition2 + BldgType + OverallQual + OverallCond + YearBuilt + 
##     YearRemodAdd + RoofMatl + Exterior1st + MasVnrType + MasVnrArea + 
##     ExterQual + Foundation + BsmtQual + BsmtExposure + BsmtFinType1 + 
##     BsmtFinSF1 + BsmtFinSF2 + BsmtUnfSF + CentralAir + X1stFlrSF + 
##     X2ndFlrSF + FullBath + BedroomAbvGr + KitchenAbvGr + KitchenQual + 
##     TotRmsAbvGrd + Functional + Fireplaces + GarageCars + GarageArea + 
##     GarageQual + GarageCond + WoodDeckSF + X3SsnPorch + ScreenPorch + 
##     PoolArea + PoolQC + MiscFeature + SaleCondition
## 
##                 Df  Sum of Sq        RSS   AIC
## - WoodDeckSF     1 6.3169e+08 5.0758e+11 22125
## - FullBath       1 8.2967e+08 5.0778e+11 22126
## - CentralAir     1 9.0414e+08 5.0785e+11 22126
## - TotRmsAbvGrd   1 9.1019e+08 5.0786e+11 22126
## - Exterior1st   13 1.2182e+10 5.1913e+11 22126
## <none>                        5.0695e+11 22126
## - X3SsnPorch     1 9.8153e+08 5.0793e+11 22126
## - ScreenPorch    1 9.8341e+08 5.0793e+11 22126
## - Fireplaces     1 1.1238e+09 5.0807e+11 22126
## + MoSold         1 5.1452e+08 5.0644e+11 22127
## + GarageFinish   2 1.0910e+09 5.0586e+11 22127
## + OpenPorchSF    1 1.2883e+08 5.0682e+11 22128
## - MSSubClass     1 1.7443e+09 5.0869e+11 22128
## + HalfBath       1 1.1073e+08 5.0684e+11 22128
## + GarageYrBlt    1 6.7194e+07 5.0688e+11 22128
## + BsmtFullBath   1 6.0293e+07 5.0689e+11 22128
## + MiscVal        1 5.4848e+07 5.0690e+11 22128
## - GarageArea     1 1.8028e+09 5.0875e+11 22128
## + EnclosedPorch  1 3.2114e+07 5.0692e+11 22128
## - LotFrontage    1 1.8376e+09 5.0879e+11 22128
## + LowQualFinSF   1 1.5851e+07 5.0693e+11 22128
## + GrLivArea      1 1.5851e+07 5.0693e+11 22128
## + YrSold         1 1.0100e+07 5.0694e+11 22128
## + BsmtHalfBath   1 1.8569e+06 5.0695e+11 22128
## - GarageCars     1 1.8714e+09 5.0882e+11 22128
## - YearRemodAdd   1 1.9056e+09 5.0886e+11 22128
## + LotShape       3 1.7314e+09 5.0522e+11 22128
## - BsmtFinType1   5 5.7545e+09 5.1270e+11 22128
## - Foundation     4 4.9769e+09 5.1193e+11 22129
## + PavedDrive     2 5.0242e+08 5.0645e+11 22129
## + FireplaceQu    5 3.2616e+09 5.0369e+11 22129
## - Functional     5 6.1158e+09 5.1307e+11 22129
## - Condition1     8 9.0185e+09 5.1597e+11 22129
## + Alley          2 3.1754e+08 5.0663e+11 22129
## + RoofStyle      4 2.1583e+09 5.0479e+11 22129
## - Street         1 2.4824e+09 5.0943e+11 22129
## - BedroomAbvGr   1 2.5267e+09 5.0948e+11 22129
## + Fence          4 1.9980e+09 5.0495e+11 22129
## + ExterCond      3 1.0138e+09 5.0594e+11 22130
## - BldgType       4 5.5381e+09 5.1249e+11 22130
## - MasVnrType     3 4.8790e+09 5.1183e+11 22130
## + BsmtCond       3 6.9766e+08 5.0625e+11 22130
## - GarageCond     4 6.0666e+09 5.1302e+11 22131
## + GarageType     5 2.2202e+09 5.0473e+11 22131
## + Heating        3 3.4236e+08 5.0661e+11 22131
## + HouseStyle     7 3.8919e+09 5.0306e+11 22131
## - MSZoning       4 6.3654e+09 5.1332e+11 22131
## - LandContour    3 5.6842e+09 5.1263e+11 22132
## + HeatingQC      4 7.0226e+08 5.0625e+11 22132
## + SaleType       8 4.1987e+09 5.0275e+11 22133
## - KitchenAbvGr   1 4.1710e+09 5.1112e+11 22133
## + Electrical     4 4.1864e+07 5.0691e+11 22134
## + BsmtFinType2   5 8.3556e+08 5.0611e+11 22134
## - YearBuilt      1 5.5363e+09 5.1249e+11 22136
## - LandSlope      2 6.5575e+09 5.1351e+11 22136
## - GarageQual     4 9.1616e+09 5.1611e+11 22137
## - MasVnrArea     1 8.3029e+09 5.1525e+11 22142
## - LotConfig      4 1.1210e+10 5.1816e+11 22142
## + Exterior2nd   14 5.5062e+09 5.0144e+11 22142
## - BsmtUnfSF      1 8.8659e+09 5.1582e+11 22143
## - ExterQual      3 1.2682e+10 5.1963e+11 22147
## - BsmtQual       3 1.3162e+10 5.2011e+11 22148
## - SaleCondition  5 1.5198e+10 5.2215e+11 22148
## - BsmtFinSF2     1 1.1686e+10 5.1864e+11 22149
## - KitchenQual    3 1.6818e+10 5.2377e+11 22156
## - OverallQual    1 1.5100e+10 5.2205e+11 22156
## - RoofMatl       6 2.0179e+10 5.2713e+11 22157
## - OverallCond    1 1.6448e+10 5.2340e+11 22159
## - MiscFeature    3 2.2588e+10 5.2954e+11 22168
## - LotArea        1 2.0842e+10 5.2779e+11 22168
## - BsmtExposure   3 2.3826e+10 5.3078e+11 22170
## - X1stFlrSF      1 2.2710e+10 5.2966e+11 22172
## - BsmtFinSF1     1 2.4825e+10 5.3178e+11 22176
## - PoolArea       1 2.6677e+10 5.3363e+11 22180
## - PoolQC         3 3.0981e+10 5.3793e+11 22185
## - Condition2     5 6.7589e+10 5.7454e+11 22253
## - Neighborhood  24 9.4034e+10 6.0098e+11 22264
## - X2ndFlrSF      1 8.9093e+10 5.9604e+11 22301
## 
## Step:  AIC=22125.13
## SalePrice ~ MSSubClass + MSZoning + LotFrontage + LotArea + Street + 
##     LandContour + LotConfig + LandSlope + Neighborhood + Condition1 + 
##     Condition2 + BldgType + OverallQual + OverallCond + YearBuilt + 
##     YearRemodAdd + RoofMatl + Exterior1st + MasVnrType + MasVnrArea + 
##     ExterQual + Foundation + BsmtQual + BsmtExposure + BsmtFinType1 + 
##     BsmtFinSF1 + BsmtFinSF2 + BsmtUnfSF + CentralAir + X1stFlrSF + 
##     X2ndFlrSF + FullBath + BedroomAbvGr + KitchenAbvGr + KitchenQual + 
##     TotRmsAbvGrd + Functional + Fireplaces + GarageCars + GarageArea + 
##     GarageQual + GarageCond + X3SsnPorch + ScreenPorch + PoolArea + 
##     PoolQC + MiscFeature + SaleCondition
## 
##                 Df  Sum of Sq        RSS   AIC
## - ScreenPorch    1 7.8528e+08 5.0837e+11 22125
## - FullBath       1 8.0277e+08 5.0838e+11 22125
## - Exterior1st   13 1.2118e+10 5.1970e+11 22125
## - X3SsnPorch     1 8.6904e+08 5.0845e+11 22125
## - TotRmsAbvGrd   1 8.9147e+08 5.0847e+11 22125
## <none>                        5.0758e+11 22125
## - CentralAir     1 9.5287e+08 5.0853e+11 22125
## - Fireplaces     1 1.2018e+09 5.0878e+11 22126
## + WoodDeckSF     1 6.3169e+08 5.0695e+11 22126
## + MoSold         1 4.5803e+08 5.0712e+11 22126
## + OpenPorchSF    1 1.6051e+08 5.0742e+11 22127
## - LotFrontage    1 1.7358e+09 5.0932e+11 22127
## + HalfBath       1 1.0873e+08 5.0747e+11 22127
## + GarageFinish   2 1.0292e+09 5.0655e+11 22127
## + MiscVal        1 6.8546e+07 5.0751e+11 22127
## + BsmtFullBath   1 5.9505e+07 5.0752e+11 22127
## - GarageArea     1 1.8081e+09 5.0939e+11 22127
## + GarageYrBlt    1 3.9077e+07 5.0754e+11 22127
## + EnclosedPorch  1 1.8009e+07 5.0756e+11 22127
## + LowQualFinSF   1 1.2835e+07 5.0757e+11 22127
## + GrLivArea      1 1.2835e+07 5.0757e+11 22127
## + YrSold         1 1.0340e+07 5.0757e+11 22127
## + BsmtHalfBath   1 6.4642e+06 5.0758e+11 22127
## - MSSubClass     1 1.8538e+09 5.0944e+11 22127
## - GarageCars     1 1.9090e+09 5.0949e+11 22127
## - YearRemodAdd   1 1.9827e+09 5.0956e+11 22127
## - Foundation     4 4.8369e+09 5.1242e+11 22128
## - BsmtFinType1   5 5.8167e+09 5.1340e+11 22128
## + LotShape       3 1.6241e+09 5.0596e+11 22128
## - Functional     5 5.8865e+09 5.1347e+11 22128
## + FireplaceQu    5 3.3012e+09 5.0428e+11 22128
## + PavedDrive     2 5.1080e+08 5.0707e+11 22128
## + Alley          2 3.7440e+08 5.0721e+11 22128
## + RoofStyle      4 2.2121e+09 5.0537e+11 22128
## - BedroomAbvGr   1 2.4299e+09 5.1001e+11 22128
## - Street         1 2.5483e+09 5.1013e+11 22129
## - Condition1     8 9.1943e+09 5.1678e+11 22129
## + ExterCond      3 1.0041e+09 5.0658e+11 22129
## + Fence          4 1.8901e+09 5.0569e+11 22129
## - BldgType       4 5.6467e+09 5.1323e+11 22129
## - MasVnrType     3 4.7608e+09 5.1234e+11 22129
## + BsmtCond       3 6.4751e+08 5.0693e+11 22130
## - GarageCond     4 5.9416e+09 5.1352e+11 22130
## + Heating        3 3.3779e+08 5.0724e+11 22130
## + GarageType     5 2.1456e+09 5.0544e+11 22131
## + HouseStyle     7 3.8807e+09 5.0370e+11 22131
## - MSZoning       4 6.4536e+09 5.1404e+11 22131
## - LandContour    3 5.6444e+09 5.1323e+11 22131
## + HeatingQC      4 6.3537e+08 5.0695e+11 22132
## - KitchenAbvGr   1 4.1590e+09 5.1174e+11 22132
## + SaleType       8 4.1204e+09 5.0346e+11 22132
## + Electrical     4 4.1159e+07 5.0754e+11 22133
## + BsmtFinType2   5 7.9832e+08 5.0678e+11 22133
## - YearBuilt      1 5.5913e+09 5.1317e+11 22135
## - LandSlope      2 6.8340e+09 5.1442e+11 22136
## - GarageQual     4 8.9039e+09 5.1649e+11 22136
## - MasVnrArea     1 8.2591e+09 5.1584e+11 22141
## - LotConfig      4 1.1272e+10 5.1885e+11 22141
## + Exterior2nd   14 5.5035e+09 5.0208e+11 22141
## - BsmtUnfSF      1 8.7431e+09 5.1633e+11 22142
## - ExterQual      3 1.2656e+10 5.2024e+11 22146
## - SaleCondition  5 1.4784e+10 5.2237e+11 22147
## - BsmtQual       3 1.3212e+10 5.2079e+11 22147
## - BsmtFinSF2     1 1.1961e+10 5.1954e+11 22149
## - KitchenQual    3 1.6614e+10 5.2420e+11 22154
## - OverallQual    1 1.5108e+10 5.2269e+11 22155
## - RoofMatl       6 2.0997e+10 5.2858e+11 22158
## - OverallCond    1 1.7017e+10 5.2460e+11 22159
## - MiscFeature    3 2.2462e+10 5.3004e+11 22167
## - LotArea        1 2.1013e+10 5.2859e+11 22168
## - BsmtExposure   3 2.4593e+10 5.3218e+11 22171
## - X1stFlrSF      1 2.3221e+10 5.3080e+11 22172
## - BsmtFinSF1     1 2.5073e+10 5.3265e+11 22176
## - PoolArea       1 2.6543e+10 5.3412e+11 22179
## - PoolQC         3 3.0652e+10 5.3823e+11 22183
## - Condition2     5 6.7904e+10 5.7549e+11 22253
## - Neighborhood  24 9.4846e+10 6.0243e+11 22265
## - X2ndFlrSF      1 9.0765e+10 5.9835e+11 22303
## 
## Step:  AIC=22124.82
## SalePrice ~ MSSubClass + MSZoning + LotFrontage + LotArea + Street + 
##     LandContour + LotConfig + LandSlope + Neighborhood + Condition1 + 
##     Condition2 + BldgType + OverallQual + OverallCond + YearBuilt + 
##     YearRemodAdd + RoofMatl + Exterior1st + MasVnrType + MasVnrArea + 
##     ExterQual + Foundation + BsmtQual + BsmtExposure + BsmtFinType1 + 
##     BsmtFinSF1 + BsmtFinSF2 + BsmtUnfSF + CentralAir + X1stFlrSF + 
##     X2ndFlrSF + FullBath + BedroomAbvGr + KitchenAbvGr + KitchenQual + 
##     TotRmsAbvGrd + Functional + Fireplaces + GarageCars + GarageArea + 
##     GarageQual + GarageCond + X3SsnPorch + PoolArea + PoolQC + 
##     MiscFeature + SaleCondition
## 
##                 Df  Sum of Sq        RSS   AIC
## - FullBath       1 7.5058e+08 5.0912e+11 22124
## - TotRmsAbvGrd   1 8.0367e+08 5.0917e+11 22125
## - X3SsnPorch     1 8.0370e+08 5.0917e+11 22125
## <none>                        5.0837e+11 22125
## - CentralAir     1 1.0185e+09 5.0939e+11 22125
## + ScreenPorch    1 7.8528e+08 5.0758e+11 22125
## - Exterior1st   13 1.2538e+10 5.2091e+11 22126
## + MoSold         1 4.4385e+08 5.0792e+11 22126
## + WoodDeckSF     1 4.3356e+08 5.0793e+11 22126
## - Fireplaces     1 1.4893e+09 5.0986e+11 22126
## - LotFrontage    1 1.6968e+09 5.1006e+11 22127
## + HalfBath       1 1.4442e+08 5.0822e+11 22127
## + OpenPorchSF    1 1.1057e+08 5.0826e+11 22127
## + GarageFinish   2 1.0086e+09 5.0736e+11 22127
## + GarageYrBlt    1 5.2449e+07 5.0831e+11 22127
## + BsmtFullBath   1 4.9497e+07 5.0832e+11 22127
## + MiscVal        1 3.7592e+07 5.0833e+11 22127
## + LowQualFinSF   1 1.5881e+07 5.0835e+11 22127
## + GrLivArea      1 1.5881e+07 5.0835e+11 22127
## + YrSold         1 1.4517e+07 5.0835e+11 22127
## - GarageArea     1 1.8569e+09 5.1022e+11 22127
## + BsmtHalfBath   1 1.9383e+06 5.0837e+11 22127
## + EnclosedPorch  1 1.3027e+06 5.0837e+11 22127
## - GarageCars     1 1.9053e+09 5.1027e+11 22127
## - Functional     5 5.7115e+09 5.1408e+11 22127
## - MSSubClass     1 2.0268e+09 5.1039e+11 22127
## - Foundation     4 4.8571e+09 5.1322e+11 22127
## - YearRemodAdd   1 2.0508e+09 5.1042e+11 22127
## - BsmtFinType1   5 5.8423e+09 5.1421e+11 22127
## + LotShape       3 1.5395e+09 5.0683e+11 22128
## + PavedDrive     2 5.3237e+08 5.0784e+11 22128
## + FireplaceQu    5 3.2784e+09 5.0509e+11 22128
## - BedroomAbvGr   1 2.2960e+09 5.1066e+11 22128
## - Street         1 2.3174e+09 5.1068e+11 22128
## + Alley          2 3.6664e+08 5.0800e+11 22128
## + RoofStyle      4 2.0778e+09 5.0629e+11 22128
## + Fence          4 2.0163e+09 5.0635e+11 22129
## + ExterCond      3 1.0028e+09 5.0736e+11 22129
## - MasVnrType     3 4.6674e+09 5.1303e+11 22129
## - Condition1     8 9.4918e+09 5.1786e+11 22129
## - BldgType       4 5.7676e+09 5.1413e+11 22129
## + BsmtCond       3 6.9518e+08 5.0767e+11 22129
## + Heating        3 3.5378e+08 5.0801e+11 22130
## + GarageType     5 2.0807e+09 5.0629e+11 22130
## + HouseStyle     7 3.8040e+09 5.0456e+11 22131
## - MSZoning       4 6.4596e+09 5.1483e+11 22131
## - LandContour    3 5.8045e+09 5.1417e+11 22131
## + HeatingQC      4 5.2967e+08 5.0784e+11 22132
## - KitchenAbvGr   1 4.1711e+09 5.1254e+11 22132
## - GarageCond     4 7.0576e+09 5.1543e+11 22132
## + SaleType       8 3.8941e+09 5.0447e+11 22132
## + Electrical     4 4.1445e+07 5.0833e+11 22133
## + BsmtFinType2   5 7.6731e+08 5.0760e+11 22133
## - YearBuilt      1 5.3705e+09 5.1374e+11 22134
## - LandSlope      2 7.1550e+09 5.1552e+11 22136
## - GarageQual     4 1.0343e+10 5.1871e+11 22139
## - MasVnrArea     1 8.3957e+09 5.1676e+11 22141
## + Exterior2nd   14 5.2993e+09 5.0307e+11 22141
## - LotConfig      4 1.1584e+10 5.1995e+11 22142
## - BsmtUnfSF      1 9.0920e+09 5.1746e+11 22142
## - SaleCondition  5 1.4765e+10 5.2313e+11 22146
## - ExterQual      3 1.2938e+10 5.2131e+11 22146
## - BsmtQual       3 1.3209e+10 5.2158e+11 22147
## - BsmtFinSF2     1 1.2501e+10 5.2087e+11 22149
## - KitchenQual    3 1.6697e+10 5.2506e+11 22154
## - OverallQual    1 1.5127e+10 5.2349e+11 22155
## - RoofMatl       6 2.0469e+10 5.2884e+11 22156
## - OverallCond    1 1.7149e+10 5.2552e+11 22159
## - MiscFeature    3 2.2990e+10 5.3136e+11 22167
## - LotArea        1 2.1336e+10 5.2970e+11 22168
## - BsmtExposure   3 2.4563e+10 5.3293e+11 22170
## - X1stFlrSF      1 2.2850e+10 5.3122e+11 22171
## - BsmtFinSF1     1 2.5711e+10 5.3408e+11 22177
## - PoolArea       1 2.6517e+10 5.3488e+11 22178
## - PoolQC         3 3.0582e+10 5.3895e+11 22183
## - Condition2     5 6.8259e+10 5.7663e+11 22253
## - Neighborhood  24 9.4539e+10 6.0291e+11 22263
## - X2ndFlrSF      1 9.1942e+10 6.0031e+11 22305
## 
## Step:  AIC=22124.43
## SalePrice ~ MSSubClass + MSZoning + LotFrontage + LotArea + Street + 
##     LandContour + LotConfig + LandSlope + Neighborhood + Condition1 + 
##     Condition2 + BldgType + OverallQual + OverallCond + YearBuilt + 
##     YearRemodAdd + RoofMatl + Exterior1st + MasVnrType + MasVnrArea + 
##     ExterQual + Foundation + BsmtQual + BsmtExposure + BsmtFinType1 + 
##     BsmtFinSF1 + BsmtFinSF2 + BsmtUnfSF + CentralAir + X1stFlrSF + 
##     X2ndFlrSF + BedroomAbvGr + KitchenAbvGr + KitchenQual + TotRmsAbvGrd + 
##     Functional + Fireplaces + GarageCars + GarageArea + GarageQual + 
##     GarageCond + X3SsnPorch + PoolArea + PoolQC + MiscFeature + 
##     SaleCondition
## 
##                 Df  Sum of Sq        RSS   AIC
## - TotRmsAbvGrd   1 7.9517e+08 5.0991e+11 22124
## - X3SsnPorch     1 8.9817e+08 5.1002e+11 22124
## <none>                        5.0912e+11 22124
## - CentralAir     1 9.8933e+08 5.1011e+11 22125
## + FullBath       1 7.5058e+08 5.0837e+11 22125
## + ScreenPorch    1 7.3309e+08 5.0838e+11 22125
## - Fireplaces     1 1.4272e+09 5.1055e+11 22126
## + WoodDeckSF     1 4.1784e+08 5.0870e+11 22126
## + MoSold         1 3.8122e+08 5.0874e+11 22126
## - Exterior1st   13 1.2857e+10 5.2197e+11 22126
## - LotFrontage    1 1.7146e+09 5.1083e+11 22126
## + OpenPorchSF    1 1.3580e+08 5.0898e+11 22126
## + GarageYrBlt    1 4.4381e+07 5.0907e+11 22126
## - GarageArea     1 1.8232e+09 5.1094e+11 22126
## + MiscVal        1 3.6819e+07 5.0908e+11 22126
## + YrSold         1 1.7783e+07 5.0910e+11 22126
## + LowQualFinSF   1 1.6957e+07 5.0910e+11 22126
## + GrLivArea      1 1.6957e+07 5.0910e+11 22126
## + BsmtFullBath   1 1.5458e+07 5.0910e+11 22126
## + BsmtHalfBath   1 1.8839e+06 5.0912e+11 22126
## + HalfBath       1 8.6732e+05 5.0912e+11 22126
## + EnclosedPorch  1 2.9982e+04 5.0912e+11 22126
## - GarageCars     1 1.9053e+09 5.1102e+11 22127
## - BedroomAbvGr   1 1.9321e+09 5.1105e+11 22127
## + GarageFinish   2 8.0106e+08 5.0832e+11 22127
## - Functional     5 5.7657e+09 5.1488e+11 22127
## - BsmtFinType1   5 5.8094e+09 5.1493e+11 22127
## - MSSubClass     1 2.0669e+09 5.1118e+11 22127
## - Foundation     4 4.9351e+09 5.1405e+11 22127
## - YearRemodAdd   1 2.1731e+09 5.1129e+11 22127
## + PavedDrive     2 5.8456e+08 5.0853e+11 22127
## + LotShape       3 1.4816e+09 5.0764e+11 22127
## - Street         1 2.3091e+09 5.1143e+11 22127
## + FireplaceQu    5 3.1583e+09 5.0596e+11 22128
## + Alley          2 3.5263e+08 5.0877e+11 22128
## + Fence          4 2.0165e+09 5.0710e+11 22128
## + RoofStyle      4 1.9309e+09 5.0719e+11 22128
## - MasVnrType     3 4.6354e+09 5.1375e+11 22128
## - BldgType       4 5.6163e+09 5.1473e+11 22128
## + ExterCond      3 9.1039e+08 5.0821e+11 22129
## + BsmtCond       3 6.7046e+08 5.0845e+11 22129
## - Condition1     8 9.9308e+09 5.1905e+11 22130
## + Heating        3 3.8601e+08 5.0873e+11 22130
## + HouseStyle     7 4.0590e+09 5.0506e+11 22130
## + GarageType     5 1.9687e+09 5.0715e+11 22130
## - KitchenAbvGr   1 3.6758e+09 5.1279e+11 22130
## - MSZoning       4 6.5737e+09 5.1569e+11 22131
## + HeatingQC      4 5.5413e+08 5.0856e+11 22131
## - LandContour    3 6.0919e+09 5.1521e+11 22131
## - GarageCond     4 7.0919e+09 5.1621e+11 22132
## + SaleType       8 3.8899e+09 5.0523e+11 22132
## + Electrical     4 4.3081e+07 5.0907e+11 22132
## + BsmtFinType2   5 7.6354e+08 5.0835e+11 22133
## - YearBuilt      1 5.8226e+09 5.1494e+11 22135
## - LandSlope      2 7.4860e+09 5.1660e+11 22136
## - GarageQual     4 1.0509e+10 5.1963e+11 22139
## - MasVnrArea     1 8.2788e+09 5.1740e+11 22140
## - LotConfig      4 1.1225e+10 5.2034e+11 22140
## + Exterior2nd   14 5.4053e+09 5.0371e+11 22141
## - BsmtUnfSF      1 9.0786e+09 5.1820e+11 22142
## - SaleCondition  5 1.4725e+10 5.2384e+11 22146
## - ExterQual      3 1.2938e+10 5.2206e+11 22146
## - BsmtQual       3 1.2975e+10 5.2209e+11 22146
## - BsmtFinSF2     1 1.2430e+10 5.2155e+11 22149
## - KitchenQual    3 1.6209e+10 5.2533e+11 22153
## - OverallQual    1 1.5214e+10 5.2433e+11 22155
## - RoofMatl       6 2.0195e+10 5.2931e+11 22155
## - OverallCond    1 1.7321e+10 5.2644e+11 22159
## - MiscFeature    3 2.3158e+10 5.3228e+11 22167
## - LotArea        1 2.1657e+10 5.3078e+11 22168
## - BsmtExposure   3 2.4690e+10 5.3381e+11 22170
## - X1stFlrSF      1 2.5305e+10 5.3442e+11 22176
## - BsmtFinSF1     1 2.5434e+10 5.3455e+11 22176
## - PoolArea       1 2.6484e+10 5.3560e+11 22178
## - PoolQC         3 3.0898e+10 5.4002e+11 22183
## - Condition2     5 6.8482e+10 5.7760e+11 22253
## - Neighborhood  24 9.4294e+10 6.0341e+11 22262
## - X2ndFlrSF      1 1.0101e+11 6.1013e+11 22320
## 
## Step:  AIC=22124.14
## SalePrice ~ MSSubClass + MSZoning + LotFrontage + LotArea + Street + 
##     LandContour + LotConfig + LandSlope + Neighborhood + Condition1 + 
##     Condition2 + BldgType + OverallQual + OverallCond + YearBuilt + 
##     YearRemodAdd + RoofMatl + Exterior1st + MasVnrType + MasVnrArea + 
##     ExterQual + Foundation + BsmtQual + BsmtExposure + BsmtFinType1 + 
##     BsmtFinSF1 + BsmtFinSF2 + BsmtUnfSF + CentralAir + X1stFlrSF + 
##     X2ndFlrSF + BedroomAbvGr + KitchenAbvGr + KitchenQual + Functional + 
##     Fireplaces + GarageCars + GarageArea + GarageQual + GarageCond + 
##     X3SsnPorch + PoolArea + PoolQC + MiscFeature + SaleCondition
## 
##                 Df  Sum of Sq        RSS   AIC
## - X3SsnPorch     1 8.0639e+08 5.1072e+11 22124
## <none>                        5.0991e+11 22124
## + TotRmsAbvGrd   1 7.9517e+08 5.0912e+11 22124
## - CentralAir     1 1.0725e+09 5.1099e+11 22124
## + FullBath       1 7.4208e+08 5.0917e+11 22125
## + ScreenPorch    1 6.4917e+08 5.0926e+11 22125
## - BedroomAbvGr   1 1.3271e+09 5.1124e+11 22125
## + MoSold         1 4.5388e+08 5.0946e+11 22125
## - Fireplaces     1 1.4530e+09 5.1137e+11 22125
## + WoodDeckSF     1 4.1289e+08 5.0950e+11 22125
## - Exterior1st   13 1.2913e+10 5.2283e+11 22126
## + OpenPorchSF    1 1.2642e+08 5.0979e+11 22126
## - GarageArea     1 1.8128e+09 5.1173e+11 22126
## + MiscVal        1 5.1825e+07 5.0986e+11 22126
## - LotFrontage    1 1.8193e+09 5.1173e+11 22126
## + GarageYrBlt    1 3.4851e+07 5.0988e+11 22126
## + BsmtFullBath   1 2.3777e+07 5.0989e+11 22126
## + YrSold         1 1.5584e+07 5.0990e+11 22126
## + BsmtHalfBath   1 4.3335e+06 5.0991e+11 22126
## + EnclosedPorch  1 3.8861e+06 5.0991e+11 22126
## + LowQualFinSF   1 8.1918e+04 5.0991e+11 22126
## + GrLivArea      1 8.1918e+04 5.0991e+11 22126
## + HalfBath       1 6.4365e+04 5.0991e+11 22126
## - MSSubClass     1 1.9273e+09 5.1184e+11 22126
## - GarageCars     1 1.9710e+09 5.1188e+11 22126
## + GarageFinish   2 8.1782e+08 5.0910e+11 22126
## - YearRemodAdd   1 2.0988e+09 5.1201e+11 22127
## - Foundation     4 4.9459e+09 5.1486e+11 22127
## - Functional     5 5.9140e+09 5.1583e+11 22127
## + PavedDrive     2 6.2453e+08 5.0929e+11 22127
## - BsmtFinType1   5 5.9599e+09 5.1587e+11 22127
## + LotShape       3 1.4947e+09 5.0842e+11 22127
## + Alley          2 4.5473e+08 5.0946e+11 22127
## - Street         1 2.4783e+09 5.1239e+11 22127
## + FireplaceQu    5 2.9067e+09 5.0701e+11 22128
## - MasVnrType     3 4.6622e+09 5.1458e+11 22128
## + Fence          4 1.8477e+09 5.0807e+11 22128
## + ExterCond      3 9.1738e+08 5.0900e+11 22128
## + RoofStyle      4 1.8347e+09 5.0808e+11 22128
## + BsmtCond       3 7.1283e+08 5.0920e+11 22129
## - KitchenAbvGr   1 3.1194e+09 5.1303e+11 22129
## - BldgType       4 5.9795e+09 5.1589e+11 22129
## + Heating        3 3.6245e+08 5.0955e+11 22129
## - MSZoning       4 6.3703e+09 5.1628e+11 22130
## + GarageType     5 2.0542e+09 5.0786e+11 22130
## - Condition1     8 1.0164e+10 5.2008e+11 22130
## + HouseStyle     7 3.6126e+09 5.0630e+11 22130
## - LandContour    3 5.9069e+09 5.1582e+11 22131
## + HeatingQC      4 5.7040e+08 5.0934e+11 22131
## + SaleType       8 3.9828e+09 5.0593e+11 22132
## + Electrical     4 3.9185e+07 5.0987e+11 22132
## - GarageCond     4 7.5267e+09 5.1744e+11 22132
## + BsmtFinType2   5 8.6962e+08 5.0904e+11 22132
## - YearBuilt      1 5.6826e+09 5.1560e+11 22134
## - LandSlope      2 7.4989e+09 5.1741e+11 22136
## - MasVnrArea     1 8.1522e+09 5.1807e+11 22140
## - GarageQual     4 1.1094e+10 5.2101e+11 22140
## - LotConfig      4 1.1311e+10 5.2122e+11 22140
## - BsmtUnfSF      1 8.7679e+09 5.1868e+11 22141
## + Exterior2nd   14 5.1784e+09 5.0473e+11 22141
## - BsmtQual       3 1.2983e+10 5.2290e+11 22146
## - SaleCondition  5 1.4982e+10 5.2490e+11 22146
## - ExterQual      3 1.3701e+10 5.2361e+11 22147
## - BsmtFinSF2     1 1.2187e+10 5.2210e+11 22148
## - KitchenQual    3 1.6583e+10 5.2650e+11 22153
## - RoofMatl       6 1.9993e+10 5.2991e+11 22154
## - OverallQual    1 1.5364e+10 5.2528e+11 22155
## - OverallCond    1 1.7272e+10 5.2718e+11 22159
## - MiscFeature    3 2.3348e+10 5.3326e+11 22167
## - LotArea        1 2.1895e+10 5.3181e+11 22168
## - BsmtExposure   3 2.4627e+10 5.3454e+11 22170
## - BsmtFinSF1     1 2.4997e+10 5.3491e+11 22175
## - PoolArea       1 2.6329e+10 5.3624e+11 22177
## - PoolQC         3 3.0476e+10 5.4039e+11 22182
## - X1stFlrSF      1 3.2646e+10 5.4256e+11 22190
## - Condition2     5 7.0727e+10 5.8064e+11 22256
## - Neighborhood  24 9.4914e+10 6.0483e+11 22263
## - X2ndFlrSF      1 1.5025e+11 6.6016e+11 22405
## 
## Step:  AIC=22123.87
## SalePrice ~ MSSubClass + MSZoning + LotFrontage + LotArea + Street + 
##     LandContour + LotConfig + LandSlope + Neighborhood + Condition1 + 
##     Condition2 + BldgType + OverallQual + OverallCond + YearBuilt + 
##     YearRemodAdd + RoofMatl + Exterior1st + MasVnrType + MasVnrArea + 
##     ExterQual + Foundation + BsmtQual + BsmtExposure + BsmtFinType1 + 
##     BsmtFinSF1 + BsmtFinSF2 + BsmtUnfSF + CentralAir + X1stFlrSF + 
##     X2ndFlrSF + BedroomAbvGr + KitchenAbvGr + KitchenQual + Functional + 
##     Fireplaces + GarageCars + GarageArea + GarageQual + GarageCond + 
##     PoolArea + PoolQC + MiscFeature + SaleCondition
## 
##                 Df  Sum of Sq        RSS   AIC
## <none>                        5.1072e+11 22124
## + FullBath       1 8.3147e+08 5.0989e+11 22124
## + X3SsnPorch     1 8.0639e+08 5.0991e+11 22124
## - CentralAir     1 1.0814e+09 5.1180e+11 22124
## + TotRmsAbvGrd   1 7.0338e+08 5.1002e+11 22124
## + ScreenPorch    1 5.9158e+08 5.1013e+11 22125
## - Exterior1st   13 1.2709e+10 5.2343e+11 22125
## - Fireplaces     1 1.3858e+09 5.1211e+11 22125
## - BedroomAbvGr   1 1.4286e+09 5.1215e+11 22125
## + MoSold         1 4.3576e+08 5.1028e+11 22125
## + WoodDeckSF     1 3.3290e+08 5.1039e+11 22125
## - Foundation     4 4.3786e+09 5.1510e+11 22125
## + OpenPorchSF    1 1.3741e+08 5.1058e+11 22126
## + MiscVal        1 5.0120e+07 5.1067e+11 22126
## - GarageArea     1 1.8269e+09 5.1255e+11 22126
## + GarageYrBlt    1 3.3218e+07 5.1069e+11 22126
## + BsmtFullBath   1 1.7720e+07 5.1070e+11 22126
## + YrSold         1 1.6279e+07 5.1070e+11 22126
## + EnclosedPorch  1 6.9135e+06 5.1071e+11 22126
## + LowQualFinSF   1 5.9888e+05 5.1072e+11 22126
## + GrLivArea      1 5.9888e+05 5.1072e+11 22126
## + HalfBath       1 1.2392e+05 5.1072e+11 22126
## + BsmtHalfBath   1 1.2700e+02 5.1072e+11 22126
## - MSSubClass     1 1.9171e+09 5.1264e+11 22126
## - LotFrontage    1 1.9455e+09 5.1267e+11 22126
## - GarageCars     1 1.9715e+09 5.1269e+11 22126
## + GarageFinish   2 7.0616e+08 5.1001e+11 22126
## - YearRemodAdd   1 2.1072e+09 5.1283e+11 22126
## - Functional     5 5.9016e+09 5.1662e+11 22126
## + PavedDrive     2 6.3984e+08 5.1008e+11 22127
## + LotShape       3 1.4829e+09 5.0924e+11 22127
## - BsmtFinType1   5 6.0585e+09 5.1678e+11 22127
## + Alley          2 4.7389e+08 5.1025e+11 22127
## - Street         1 2.4427e+09 5.1316e+11 22127
## - MasVnrType     3 4.5779e+09 5.1530e+11 22128
## + Fence          4 1.8419e+09 5.0888e+11 22128
## + FireplaceQu    5 2.7651e+09 5.0795e+11 22128
## + ExterCond      3 8.9427e+08 5.0983e+11 22128
## + RoofStyle      4 1.8124e+09 5.0891e+11 22128
## + BsmtCond       3 7.4297e+08 5.0998e+11 22128
## - BldgType       4 5.9543e+09 5.1667e+11 22129
## - KitchenAbvGr   1 3.1425e+09 5.1386e+11 22129
## + Heating        3 3.6680e+08 5.1035e+11 22129
## - Condition1     8 1.0119e+10 5.2084e+11 22129
## - MSZoning       4 6.4855e+09 5.1720e+11 22130
## + GarageType     5 1.8496e+09 5.0887e+11 22130
## + HouseStyle     7 3.5668e+09 5.0715e+11 22130
## + HeatingQC      4 6.3534e+08 5.1008e+11 22131
## - LandContour    3 5.9483e+09 5.1667e+11 22131
## + SaleType       8 3.9498e+09 5.0677e+11 22131
## + Electrical     4 3.8760e+07 5.1068e+11 22132
## - GarageCond     4 7.5693e+09 5.1829e+11 22132
## + BsmtFinType2   5 8.3696e+08 5.0988e+11 22132
## - YearBuilt      1 5.5942e+09 5.1631e+11 22134
## - LandSlope      2 7.5106e+09 5.1823e+11 22136
## - MasVnrArea     1 8.0645e+09 5.1878e+11 22139
## - LotConfig      4 1.1101e+10 5.2182e+11 22139
## - GarageQual     4 1.1164e+10 5.2188e+11 22140
## + Exterior2nd   14 5.1852e+09 5.0553e+11 22141
## - BsmtUnfSF      1 9.1527e+09 5.1987e+11 22141
## - BsmtQual       3 1.2868e+10 5.2359e+11 22145
## - SaleCondition  5 1.5094e+10 5.2581e+11 22146
## - ExterQual      3 1.4053e+10 5.2477e+11 22148
## - BsmtFinSF2     1 1.2339e+10 5.2306e+11 22148
## - KitchenQual    3 1.6535e+10 5.2725e+11 22153
## - RoofMatl       6 1.9963e+10 5.3068e+11 22154
## - OverallQual    1 1.5283e+10 5.2600e+11 22154
## - OverallCond    1 1.7236e+10 5.2796e+11 22158
## - MiscFeature    3 2.3453e+10 5.3417e+11 22167
## - LotArea        1 2.2005e+10 5.3272e+11 22168
## - BsmtExposure   3 2.4373e+10 5.3509e+11 22169
## - BsmtFinSF1     1 2.5520e+10 5.3624e+11 22175
## - PoolArea       1 2.6432e+10 5.3715e+11 22177
## - PoolQC         3 3.0537e+10 5.4126e+11 22181
## - X1stFlrSF      1 3.2448e+10 5.4317e+11 22189
## - Condition2     5 7.1161e+10 5.8188e+11 22257
## - Neighborhood  24 9.4448e+10 6.0517e+11 22262
## - X2ndFlrSF      1 1.5092e+11 6.6164e+11 22405

## 
## Call:
## lm(formula = SalePrice ~ MSSubClass + MSZoning + LotFrontage + 
##     LotArea + Street + LandContour + LotConfig + LandSlope + 
##     Neighborhood + Condition1 + Condition2 + BldgType + OverallQual + 
##     OverallCond + YearBuilt + YearRemodAdd + RoofMatl + Exterior1st + 
##     MasVnrType + MasVnrArea + ExterQual + Foundation + BsmtQual + 
##     BsmtExposure + BsmtFinType1 + BsmtFinSF1 + BsmtFinSF2 + BsmtUnfSF + 
##     CentralAir + X1stFlrSF + X2ndFlrSF + BedroomAbvGr + KitchenAbvGr + 
##     KitchenQual + Functional + Fireplaces + GarageCars + GarageArea + 
##     GarageQual + GarageCond + PoolArea + PoolQC + MiscFeature + 
##     SaleCondition, data = dt.house1)
## 
## Coefficients:
##          (Intercept)            MSSubClass            MSZoningFV  
##           -3.958e+06            -1.129e+02             4.526e+04  
##           MSZoningRH            MSZoningRL            MSZoningRM  
##            3.174e+04             3.189e+04             2.686e+04  
##          LotFrontage               LotArea            StreetPave  
##            9.904e+01             8.367e-01             3.639e+04  
##       LandContourHLS        LandContourLow        LandContourLvl  
##            8.930e+03            -1.757e+04             6.721e+03  
##     LotConfigCulDSac          LotConfigFR2          LotConfigFR3  
##            1.543e+04            -8.724e+03            -1.270e+04  
##      LotConfigInside          LandSlopeMod          LandSlopeSev  
##           -8.709e+02             5.975e+03            -4.825e+04  
##  NeighborhoodBlueste    NeighborhoodBrDale   NeighborhoodBrkSide  
##            8.809e+02             7.068e+03            -1.336e+03  
##  NeighborhoodClearCr   NeighborhoodCollgCr   NeighborhoodCrawfor  
##           -1.424e+04            -1.070e+04             9.959e+03  
##  NeighborhoodEdwards   NeighborhoodGilbert    NeighborhoodIDOTRR  
##           -2.059e+04            -1.405e+04             4.492e+02  
##  NeighborhoodMeadowV   NeighborhoodMitchel     NeighborhoodNAmes  
##           -1.023e+04            -1.963e+04            -1.677e+04  
##  NeighborhoodNoRidge   NeighborhoodNPkVill   NeighborhoodNridgHt  
##            1.980e+04             1.491e+04             1.524e+04  
##   NeighborhoodNWAmes   NeighborhoodOldTown    NeighborhoodSawyer  
##           -1.849e+04            -1.207e+04            -7.422e+03  
##  NeighborhoodSawyerW   NeighborhoodSomerst   NeighborhoodStoneBr  
##           -3.558e+03            -5.351e+03             4.050e+04  
##    NeighborhoodSWISU    NeighborhoodTimber   NeighborhoodVeenker  
##           -4.151e+03            -1.521e+04             7.248e+03  
##      Condition1Feedr        Condition1Norm        Condition1PosA  
##            1.008e+03             1.160e+04             3.744e+03  
##       Condition1PosN        Condition1RRAe        Condition1RRAn  
##            2.579e+03            -9.198e+03             1.197e+04  
##       Condition1RRNe        Condition1RRNn       Condition2Feedr  
##            5.861e+03             1.074e+04            -8.273e+03  
##       Condition2Norm        Condition2PosA        Condition2PosN  
##            3.584e+03             4.414e+04            -2.302e+05  
##       Condition2RRNn        BldgType2fmCon        BldgTypeDuplex  
##            1.457e+04             1.341e+04            -8.136e+03  
##        BldgTypeTwnhs        BldgTypeTwnhsE           OverallQual  
##           -1.263e+04            -8.237e+03             6.282e+03  
##          OverallCond             YearBuilt          YearRemodAdd  
##            5.730e+03             2.668e+02             1.276e+02  
##      RoofMatlCompShg       RoofMatlMembran          RoofMatlRoll  
##            1.419e+05             2.213e+05             1.445e+05  
##      RoofMatlTar&Grv       RoofMatlWdShake       RoofMatlWdShngl  
##            1.192e+05             1.492e+05             1.978e+05  
##   Exterior1stBrkComm    Exterior1stBrkFace     Exterior1stCBlock  
##           -3.335e+04             1.734e+04            -1.504e+04  
##   Exterior1stCemntBd    Exterior1stHdBoard    Exterior1stImStucc  
##            7.273e+03            -9.151e+02            -1.298e+04  
##   Exterior1stMetalSd    Exterior1stPlywood      Exterior1stStone  
##            6.721e+03            -4.433e+03            -5.014e+03  
##    Exterior1stStucco    Exterior1stVinylSd    Exterior1stWd Sdng  
##            9.338e+03             3.215e+03             3.493e+03  
##   Exterior1stWdShing     MasVnrTypeBrkFace        MasVnrTypeNone  
##            4.018e+02             1.071e+04             1.428e+04  
##      MasVnrTypeStone            MasVnrArea           ExterQualFa  
##            1.799e+04             2.451e+01            -1.581e+04  
##          ExterQualGd           ExterQualTA      FoundationCBlock  
##           -2.655e+04            -2.748e+04             3.476e+03  
##      FoundationPConc       FoundationStone        FoundationWood  
##            4.836e+03             5.790e+03            -3.992e+04  
##           BsmtQualFa            BsmtQualGd            BsmtQualTA  
##           -1.308e+04            -1.713e+04            -1.710e+04  
##       BsmtExposureGd        BsmtExposureMn        BsmtExposureNo  
##            1.459e+04            -7.404e+03            -7.497e+03  
##      BsmtFinType1BLQ       BsmtFinType1GLQ       BsmtFinType1LwQ  
##            1.111e+03             8.276e+03            -2.912e+03  
##      BsmtFinType1Rec       BsmtFinType1Unf            BsmtFinSF1  
##            2.033e+02             2.859e+03             4.183e+01  
##           BsmtFinSF2             BsmtUnfSF           CentralAirY  
##            3.565e+01             2.394e+01             5.889e+03  
##            X1stFlrSF             X2ndFlrSF          BedroomAbvGr  
##            4.720e+01             5.985e+01            -2.401e+03  
##         KitchenAbvGr         KitchenQualFa         KitchenQualGd  
##           -1.706e+04            -1.966e+04            -2.092e+04  
##        KitchenQualTA        FunctionalMaj2        FunctionalMin1  
##           -1.923e+04            -1.460e+04            -3.200e+02  
##       FunctionalMin2         FunctionalMod         FunctionalTyp  
##           -3.885e+03            -1.199e+03             8.019e+03  
##           Fireplaces            GarageCars            GarageArea  
##            2.495e+03             4.791e+03             1.553e+01  
##         GarageQualFa          GarageQualGd          GarageQualPo  
##           -1.231e+05            -1.152e+05            -1.251e+05  
##         GarageQualTA          GarageCondFa          GarageCondGd  
##           -1.222e+05             1.177e+05             1.174e+05  
##         GarageCondPo          GarageCondTA              PoolArea  
##            1.194e+05             1.198e+05             5.796e+03  
##             PoolQCFa              PoolQCGd             PoolQCUkn  
##           -7.343e+05            -3.021e+05             2.999e+06  
##      MiscFeatureShed       MiscFeatureTenC        MiscFeatureUkn  
##           -1.374e+04             6.987e+05            -1.993e+04  
## SaleConditionAdjLand   SaleConditionAlloca   SaleConditionFamily  
##            3.342e+04             8.397e+03            -5.788e+02  
##  SaleConditionNormal  SaleConditionPartial  
##            4.431e+03             1.814e+04

Berdasarkan metode forward dan backward stepwise diperoleh bahwa nilai AIC sebesar 22123.87. Hasil ini menunjukkan bahwa nilai AIC yang diperoleh dengan metode forward dan backward stepwise lebih kecil dibandingkan dengan metode forward stepwise maupun backward stepwise.Oleh karena itu, dapat disimpulkan bahwa model terbaik adalah model dengan metode forward dan backward stepwise karena memiliki nilai AIC yang lebih kecil dibandingkan dengan model dengan metode lainnya.

Pemilihan Banyaknya Klaster

Koefisien Silhoutte

Koefisien Silhoutte digunakan untuk melihat kualitas dan kekuatan klaster, seberapa baik atau buruknya suatu obyek ditempatkan dalam suatu klaster. Semakin besar koefisien Silhoutte, maka struktur yang terbentuk sangat baik atau klaster yang terbentuk sudah sesuai.

#Complete Lingkage
fviz_nbclust(data.stdz, FUNcluster = hcut, method = "silhouette", hc_method = "complete")

Pada Complete Linkage diperoleh bahwa nilai koefisien Silhoutte terbesar saat jumlah klaster=5 atau k=5

#Average Lingkage
fviz_nbclust(data.stdz, FUNcluster = hcut, method = "silhouette", hc_method = "average", hc_metric="euclidean")

Pada Average Linkage diperoleh bahwa nilai koefisien Silhoutte terbesar saat jumlah klaster=5 atau k=5

#Centroid Lingkage
fviz_nbclust(data.stdz, FUNcluster = hcut, method = "silhouette", hc_method = "centroid", hc_metric="euclidean")

Pada Centroid Linkage diperoleh bahwa nilai koefisien Silhoutte terbesar saat jumlah klaster=2 atau k=2

#Single Lingkage
fviz_nbclust(data.stdz, FUNcluster = hcut, method = "silhouette", hc_method = "single", hc_metric="euclidean")

Pada Single Linkage diperoleh bahwa nilai koefisien Silhoutte terbesar saat jumlah klaster=2 atau k=2

#Ward Linkage
fviz_nbclust(data.stdz, FUNcluster = hcut, method = "silhouette", hc_method = "ward.D", hc_metric="euclidean")

Pada Ward Linkage diperoleh bahwa nilai koefisien Silhoutte terbesar saat jumlah klaster=6 atau k=6

Dendogram

fviz_dend(hclust(dist(data.stdz, method = "euclidean"), method = "average"))

## Warning: The `<scale>` argument of `guides()` cannot be `FALSE`. Use "none" instead as
## of ggplot2 3.3.4.
## ℹ The deprecated feature was likely used in the factoextra package.
##   Please report the issue at <]8;;https://github.com/kassambara/factoextra/issueshttps://github.com/kassambara/factoextra/issues]8;;>.

fviz_dend(hclust(dist(data.stdz, method = "euclidean"), method = "centroid"))

fviz_dend(hclust(dist(data.stdz, method = "euclidean"), method = "single"))

fviz_dend(hclust(dist(data.stdz, method = "euclidean"), method = "ward"))

## The "ward" method has been renamed to "ward.D"; note new "ward.D2"

fviz_dend(hclust(dist(data.stdz, method = "euclidean"), method = "complete"))

hc.data <- eclust(data.ok, stand = TRUE, FUNcluster = "hclust", k=5, hc_method = "complete", hc_metric = "euclidean", graph = F)

#cluster dari setiap pengamatan
hc.data$cluster

##   [1] 1 2 1 2 1 2 1 2 3 2 3 2 3 2 1 2 1 2 3 2 1 2 3 2 3 2 3 1 3 2 3 2 3 2 3 2 3
##  [38] 2 3 2 3 2 3 1 3 2 3 1 1 1 3 1 1 3 3 3 3 3 1 3 3 1 3 3 3 1 1 3 1 1 3 3 3 3
##  [75] 3 1 1 1 1 3 3 1 3 3 1 3 3 1 1 3 3 1 3 1 1 1 3 1 3 1 1 3 3 1 3 1 3 3 3 3 3
## [112] 1 1 1 1 1 3 3 3 3 1 1 1 4 1 4 5 4 5 4 5 4 1 4 5 4 5 4 5 4 5 4 1 4 5 4 5 4
## [149] 5 4 5 4 5 4 5 4 5 4 5 4 5 4 5 4 5 4 5 4 5 4 5 4 5 4 5 4 5 4 5 4 5 4 5 4 5
## [186] 4 5 4 5 4 5 4 5 4 5 4 5 4 5 4

aggregate(data.ok, by=list(cluster=hc.data$cluster), FUN = mean)

##   cluster      Age Annual Income Spending Score
## 1       1 28.35417      50.29167       45.93750
## 2       2 24.80952      25.61905       80.23810
## 3       3 55.33333      47.31579       41.08772
## 4       4 32.69231      86.53846       82.12821
## 5       5 41.68571      88.22857       17.28571

dataklaster <- data.frame("Observasi"=c(seq(1:200)),"Klaster"=hc.data$cluster)

kable(aggregate(Observasi~Klaster,dataklaster,paste,collapse=", "),align = c("c","l"))

ggplot(datamallcust, 
       aes(x = datamallcust$`Spending Score` , y = datamallcust$`Annual Income`)) + 
  geom_point(stat = "identity", aes(color = as.factor(hc.data$cluster))) +
  scale_color_discrete(name = " ", 
                       breaks=c("1", "2", "3", "4", "5"),
                       labels=c("Klaster 1", "Klaster 2",
                                "Klaster 3", "Klaster 4",
                                "Klaster 5")) +
  ggtitle("Segmentasi Pelanggan", 
          subtitle = "dengan Menggunakan Analisis Gerombol Berhierarki")

## Warning: Use of `` datamallcust$`Spending Score` `` is discouraged.
## ℹ Use `Spending Score` instead.

## Warning: Use of `` datamallcust$`Annual Income` `` is discouraged.
## ℹ Use `Annual Income` instead.

fviz_cluster(hc.data)

Pemilihan Banyaknya Klaster

#Penentuan k dengan within sum square
fviz_nbclust(data.stdz, FUNcluster = kmeans, method = "wss")

Untuk menentukan banyaknya klaster berdasarkan garis yang membentuk siku (elbow) dan hal ini bersifat subjektif yang berarti setiap individu dapat berbeda. Berdasarkan gambar di atas, dipilih bahwa yang membentuk siku (elbow) pada k=2 sehingga ditetapkan bahwa k=2.

#Ditetapkan k=2
kmeans.data <- eclust(data.ok, stand = TRUE, FUNcluster = "kmeans", k=2, graph = F)

kmeans.data$centers 

##          Age Annual Income Spending Score
## 1 -0.7508891   0.002621995      0.7407935
## 2  0.7071480  -0.002469258     -0.6976405

Berdasarkan hasil di atas, memunculkan centroid pada data yang masih terstandarisasi sehingga sulit untuk diinterpretasikan.

kmeans.data$cluster

##   [1] 1 1 2 1 1 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2
##  [38] 1 2 1 2 1 2 1 2 1 2 1 1 1 2 1 1 2 2 2 2 2 1 2 2 1 2 2 2 1 2 2 1 1 2 2 2 2
##  [75] 2 1 2 2 1 2 2 1 2 2 1 2 2 1 1 2 2 1 2 2 1 1 2 1 2 1 1 2 2 1 2 1 2 2 2 2 2
## [112] 1 2 1 1 1 2 2 2 2 1 2 1 1 1 1 2 1 2 1 2 1 1 1 2 1 2 1 2 1 2 1 1 1 2 1 2 1
## [149] 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2
## [186] 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1

aggregate(data.ok, by=list(cluster=kmeans.data$cluster), FUN = mean)

##   cluster      Age Annual Income Spending Score
## 1       1 28.36082      60.62887       69.32990
## 2       2 48.72816      60.49515       32.18447

datakmeans <- data.frame("Observasi"=c(seq(1:200)),"Klaster"=kmeans.data$cluster)

kable(aggregate(Observasi~Klaster,datakmeans,paste,collapse=", "),align = c("c","l"))

Berdasarkan analisis gerombol tak berhierarki yang telah dilakukan diperoleh bahwa peubah Age, peubah Annual Income, dan peubah Spending Score yang dikelompokkan menjadi dua klaster. Selain itu, terlihat bahwa pada klaster satu terdiri dari pelanggan yang kisaran umurnya 28 tahun memiliki pendapatan tahunan dan spending score yang cukup tinggi. Sedangkan, pada klaster 2 terdiri dari pelanggan yang kisaran umurnya 48 tahun memiliki pendapatan tahunan yang tinggi, tetapi memiliki spending score yang rendah. Oleh karena itu, dapat disimpulkan bahwa pelanggan yang berusia muda dan memiliki pendapatan tahunan yang cukup tinggi cenderung sering mengunjungi mall dan menghabiskan uangnya di mall.

ggplot(datamallcust, aes(x = datamallcust$`Spending Score` , y = datamallcust$`Annual Income`)) + 
  geom_point(stat = "identity", aes(color = as.factor(kmeans.data$cluster))) +
  scale_color_discrete(name = " ", 
                       breaks=c("1", "2"),
                       labels=c("Cluster 1", "Cluster 2")) +
 ggtitle("Segmentasi Pelanggan", 
  subtitle = "dengan Menggunakan Analisis Gerombol Tak Berhierarki")

## Warning: Use of `` datamallcust$`Spending Score` `` is discouraged.
## ℹ Use `Spending Score` instead.

## Warning: Use of `` datamallcust$`Annual Income` `` is discouraged.
## ℹ Use `Annual Income` instead.

Interpretasi:

• Pelanggan pada klaster satu cenderung memiliki pendapatan tahunan dan spending score yang sedang-sedang saja. Namun, terdapat pula pelanggan yang memiliki pendapatan tahunan dan spending score yang rendah. Begitupun sebaliknya.

• Pelanggan pada klaster dua cenderung memiliki pendapatan tahunan dan spending score yang sedang-sedang saja seperti pada pelanggan klaster satu. Namun, terdapat pelanggan yang memiliki pendapatan tahunan yang rendah, tetapi memiliki spending score yang tinggi. Selain itu, terdapat pula pelanggan yang memiliki pendapatan tahunan dan spending score yang tinggi.

fviz_cluster(kmeans.data)