DATA605 Final Exam
library(tidyverse)
library(janitor)
library(knitr)
library(kableExtra)
library(mice)
library(psych)
library(matrixcalc)Your final is due by the end of the last week of class. You should post your solutions to your GitHub account or RPubs. You are also expected to make a short presentation via YouTube and post that recording to the board. This project will show off your ability to understand the elements of the class.
1 Problem 1
Using R, generate a random variable X that has 10,000 random uniform numbers from 1 to N, where N can be any number of your choosing greater than or equal to 6. Then generate a random variable Y that has 10,000 random normal numbers with a mean of \(\mu=\sigma=(N+1)/2\).
Answer:
set.seed(123)
N = 10
X <- runif(10000, min = 1, max = N)
Y <- rnorm(10000, mean = (N+1)/2, sd = (N+1)/2)Probability. Calculate as a minimum the below probabilities a through c. Assume the small letter “x” is estimated as the median of the X variable, and the small letter “y” is estimated as the 1st quartile of the Y variable. Interpret the meaning of all probabilities.
1.1 Sub-Question 1
5 points. a. P(X>x | X>y) b. P(X>x, Y>y) c. P(X<x | X>y)
Answer: P(X>x | X>y) = 0.5509642
P(X>x, Y>y) = 0.375
P(X<x | X>y) = 0.4490358
x <- median(X)
y <- quantile(Y, 0.25)
# a
## P(X>x|X>y) = P(X>x n X>y)/P(X>y)
## let P_AgvnB as P(X>x|X>y), P_AnB as P(X>x n PX>y) and P_B as P(X>y)
P_AnB <- sum(X>x & X>y)/10000
P_B <- sum(X>y)/10000
P_AgvnB <- P_AnB/P_B
P_AgvnB## [1] 0.5509642## [1] 0.375## [1] 0.44903581.2 Sub-Question 2
5 points. Investigate whether P(X>x and Y>y)=P(X>x)P(Y>y) by building a table and evaluating the marginal and joint probabilities.
Answer:
According to the marginal and joint probabilities table,
P(X>x and Y>y) = 0.3756
We got P(X>x)P(Y>y) = 0.375 in Q1,
therefore there is very little difference between P(X>x and Y>y) and P(X>x)P(Y>y), the difference is 0.0006.
table(X>x, Y>y, dnn = c('X>x', 'Y>y')) %>%
prop.table() %>%
matrix(2,2) %>%
as.data.frame() %>%
mutate('Row_Name' = c('X<=x', 'X>x'),
'Px_(X)' = V1+V2) %>%
select(Row_Name, everything()) %>%
adorn_totals('row', name = 'Py_(Y)') %>%
as.data.frame() %>%
rename('Y<=y' = V1, 'Y>y' = V2) %>%
remove_rownames() %>%
column_to_rownames('Row_Name') %>%
kable() %>%
kable_styling(bootstrap_options = c('striped','bordered')) %>%
add_header_above(c('Marginal and Joint Probabilities'=4), background = 'lightgray')| Y<=y | Y>y | Px_(X) | |
|---|---|---|---|
| X<=x | 0.1256 | 0.3744 | 0.5 |
| X>x | 0.1244 | 0.3756 | 0.5 |
| Py_(Y) | 0.2500 | 0.7500 | 1.0 |
1.3 Sub-Question 3
5 points. Check to see if independence holds by using Fisher’s Exact Test and the Chi Square Test. What is the difference between the two? Which is most appropriate?
Answer:
Fisher’s Exact Test:
##
## Fisher's Exact Test for Count Data
##
## data: cm
## p-value = 0.7995
## alternative hypothesis: true odds ratio is not equal to 1
## 95 percent confidence interval:
## 0.9242273 1.1100187
## sample estimates:
## odds ratio
## 1.012883Chi Square Test:
##
## Pearson's Chi-squared test with Yates' continuity correction
##
## data: cm
## X-squared = 0.064533, df = 1, p-value = 0.7995What is the difference between the two? Which is most appropriate? The P-value of both tests are the same 0.7995, and is greater than 0.5, therefore for both tests, null hypothesis are accepted. The two variables X & Y are very likely indepentendt of each other.
Despite the idenical results by these the two test in this problem, consider that the dataset is large, both X & Y contains 10000 obervations, for a large data set, Chi-seuqared test is more accurate than Fisher’s exact test in general.
2 Problem 2
You are to register for Kaggle.com (free) and compete in the House Prices: Advanced Regression Techniques competition.
https://www.kaggle.com/c/house-prices-advanced-regression-techniques . I want you to do the following.
Load Data:
data_train <- read_csv('https://raw.githubusercontent.com/oggyluky11/DATA605-FALL-2020/master/Final_Exam/train.csv', na = 'NA')
data_test <- read_csv('https://raw.githubusercontent.com/oggyluky11/DATA605-FALL-2020/master/Final_Exam/test.csv', na = 'NA')2.1 Data Exploration
There are 81 variables and 1460 observations in training set, 80 varaibles and 1459 observations in testing set.
According to the data description, the feature
MSSubClassis a categorical vairable, therefore the data type needs to be converted tofactorinstead ofdouble.Features
MSZoning,Street,*Alley,LotShape,LandContour,Utilities,LotConfig,LandSlope,Neighborhood,Condition1,Condition2,BldgType,HouseStyle,RoofStyle,RoofMatl,Exterior1st,Exterior2nd,MasVnrType,Foundation,Heating,CentralAir,Electrical,*GarageType,PavedDrive,*MiscFeature,SaleType,SaleConditionare nominal categorical variables, therefore the data type needs to be converted tofactorinstead ofcharacters. Note that the varibles marked*are with NA values representing factor level ‘None’ stead of missing value.Features
ExterQual,ExterCond,*BsmtQual,*BsmtCond,*BsmtExposure,*BsmtFinType1,*BsmtFinType2,HeatingQC,KitchenQual,Functional,*FireplaceQu,*GarageFinish,*GarageQual,*GarageCond,*PoolQC,*Fenceare ordinal categorical variabbles, therefore the data type needs to be converted to ORDEREDfactorinstad ofcharacters. Note that the varibles marked*are with NA values representing factor level ‘None’ instead of missing value.Features
MasVnrArea,BsmtFinSF1,BsmtFinSF2,BsmtUnfSF,TotalBsmtSF,1stFlrSF,2ndFlrSF,LowQualFinSF,GrLivArea,BsmtFullBath,BsmtHalfBath,FullBath,HalfBath,Bedroom,Kitchen,TotRmsAbvGrd,Fireplaces,GarageYrBlt,GarageFinish,GarageCars,arageArea,WoodDeckSF,OpenPorchSF,EnclosedPorch,3SsnPorch,ScreenPorch,PoolArea,MiscValare numerical values, no data type conversion is needed however missing value imputation is needed wherever applicable.Features
YearBuilt,YearRemodAdd,MoSoldandYrSoldare time values, no data type conversion however missing value imputation is needed wherever applicable.
## Rows: 1,460
## Columns: 81
## $ Id <dbl> 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16...
## $ MSSubClass <dbl> 60, 20, 60, 70, 60, 50, 20, 60, 50, 190, 20, 60, 20, ...
## $ MSZoning <chr> "RL", "RL", "RL", "RL", "RL", "RL", "RL", "RL", "RM",...
## $ LotFrontage <dbl> 65, 80, 68, 60, 84, 85, 75, NA, 51, 50, 70, 85, NA, 9...
## $ LotArea <dbl> 8450, 9600, 11250, 9550, 14260, 14115, 10084, 10382, ...
## $ Street <chr> "Pave", "Pave", "Pave", "Pave", "Pave", "Pave", "Pave...
## $ Alley <chr> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N...
## $ LotShape <chr> "Reg", "Reg", "IR1", "IR1", "IR1", "IR1", "Reg", "IR1...
## $ LandContour <chr> "Lvl", "Lvl", "Lvl", "Lvl", "Lvl", "Lvl", "Lvl", "Lvl...
## $ Utilities <chr> "AllPub", "AllPub", "AllPub", "AllPub", "AllPub", "Al...
## $ LotConfig <chr> "Inside", "FR2", "Inside", "Corner", "FR2", "Inside",...
## $ LandSlope <chr> "Gtl", "Gtl", "Gtl", "Gtl", "Gtl", "Gtl", "Gtl", "Gtl...
## $ Neighborhood <chr> "CollgCr", "Veenker", "CollgCr", "Crawfor", "NoRidge"...
## $ Condition1 <chr> "Norm", "Feedr", "Norm", "Norm", "Norm", "Norm", "Nor...
## $ Condition2 <chr> "Norm", "Norm", "Norm", "Norm", "Norm", "Norm", "Norm...
## $ BldgType <chr> "1Fam", "1Fam", "1Fam", "1Fam", "1Fam", "1Fam", "1Fam...
## $ HouseStyle <chr> "2Story", "1Story", "2Story", "2Story", "2Story", "1....
## $ OverallQual <dbl> 7, 6, 7, 7, 8, 5, 8, 7, 7, 5, 5, 9, 5, 7, 6, 7, 6, 4,...
## $ OverallCond <dbl> 5, 8, 5, 5, 5, 5, 5, 6, 5, 6, 5, 5, 6, 5, 5, 8, 7, 5,...
## $ YearBuilt <dbl> 2003, 1976, 2001, 1915, 2000, 1993, 2004, 1973, 1931,...
## $ YearRemodAdd <dbl> 2003, 1976, 2002, 1970, 2000, 1995, 2005, 1973, 1950,...
## $ RoofStyle <chr> "Gable", "Gable", "Gable", "Gable", "Gable", "Gable",...
## $ RoofMatl <chr> "CompShg", "CompShg", "CompShg", "CompShg", "CompShg"...
## $ Exterior1st <chr> "VinylSd", "MetalSd", "VinylSd", "Wd Sdng", "VinylSd"...
## $ Exterior2nd <chr> "VinylSd", "MetalSd", "VinylSd", "Wd Shng", "VinylSd"...
## $ MasVnrType <chr> "BrkFace", "None", "BrkFace", "None", "BrkFace", "Non...
## $ MasVnrArea <dbl> 196, 0, 162, 0, 350, 0, 186, 240, 0, 0, 0, 286, 0, 30...
## $ ExterQual <chr> "Gd", "TA", "Gd", "TA", "Gd", "TA", "Gd", "TA", "TA",...
## $ ExterCond <chr> "TA", "TA", "TA", "TA", "TA", "TA", "TA", "TA", "TA",...
## $ Foundation <chr> "PConc", "CBlock", "PConc", "BrkTil", "PConc", "Wood"...
## $ BsmtQual <chr> "Gd", "Gd", "Gd", "TA", "Gd", "Gd", "Ex", "Gd", "TA",...
## $ BsmtCond <chr> "TA", "TA", "TA", "Gd", "TA", "TA", "TA", "TA", "TA",...
## $ BsmtExposure <chr> "No", "Gd", "Mn", "No", "Av", "No", "Av", "Mn", "No",...
## $ BsmtFinType1 <chr> "GLQ", "ALQ", "GLQ", "ALQ", "GLQ", "GLQ", "GLQ", "ALQ...
## $ BsmtFinSF1 <dbl> 706, 978, 486, 216, 655, 732, 1369, 859, 0, 851, 906,...
## $ BsmtFinType2 <chr> "Unf", "Unf", "Unf", "Unf", "Unf", "Unf", "Unf", "BLQ...
## $ BsmtFinSF2 <dbl> 0, 0, 0, 0, 0, 0, 0, 32, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0...
## $ BsmtUnfSF <dbl> 150, 284, 434, 540, 490, 64, 317, 216, 952, 140, 134,...
## $ TotalBsmtSF <dbl> 856, 1262, 920, 756, 1145, 796, 1686, 1107, 952, 991,...
## $ Heating <chr> "GasA", "GasA", "GasA", "GasA", "GasA", "GasA", "GasA...
## $ HeatingQC <chr> "Ex", "Ex", "Ex", "Gd", "Ex", "Ex", "Ex", "Ex", "Gd",...
## $ CentralAir <chr> "Y", "Y", "Y", "Y", "Y", "Y", "Y", "Y", "Y", "Y", "Y"...
## $ Electrical <chr> "SBrkr", "SBrkr", "SBrkr", "SBrkr", "SBrkr", "SBrkr",...
## $ `1stFlrSF` <dbl> 856, 1262, 920, 961, 1145, 796, 1694, 1107, 1022, 107...
## $ `2ndFlrSF` <dbl> 854, 0, 866, 756, 1053, 566, 0, 983, 752, 0, 0, 1142,...
## $ LowQualFinSF <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,...
## $ GrLivArea <dbl> 1710, 1262, 1786, 1717, 2198, 1362, 1694, 2090, 1774,...
## $ BsmtFullBath <dbl> 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 0, 1, 0,...
## $ BsmtHalfBath <dbl> 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,...
## $ FullBath <dbl> 2, 2, 2, 1, 2, 1, 2, 2, 2, 1, 1, 3, 1, 2, 1, 1, 1, 2,...
## $ HalfBath <dbl> 1, 0, 1, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0,...
## $ BedroomAbvGr <dbl> 3, 3, 3, 3, 4, 1, 3, 3, 2, 2, 3, 4, 2, 3, 2, 2, 2, 2,...
## $ KitchenAbvGr <dbl> 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1, 1, 2,...
## $ KitchenQual <chr> "Gd", "TA", "Gd", "Gd", "Gd", "TA", "Gd", "TA", "TA",...
## $ TotRmsAbvGrd <dbl> 8, 6, 6, 7, 9, 5, 7, 7, 8, 5, 5, 11, 4, 7, 5, 5, 5, 6...
## $ Functional <chr> "Typ", "Typ", "Typ", "Typ", "Typ", "Typ", "Typ", "Typ...
## $ Fireplaces <dbl> 0, 1, 1, 1, 1, 0, 1, 2, 2, 2, 0, 2, 0, 1, 1, 0, 1, 0,...
## $ FireplaceQu <chr> NA, "TA", "TA", "Gd", "TA", NA, "Gd", "TA", "TA", "TA...
## $ GarageType <chr> "Attchd", "Attchd", "Attchd", "Detchd", "Attchd", "At...
## $ GarageYrBlt <dbl> 2003, 1976, 2001, 1998, 2000, 1993, 2004, 1973, 1931,...
## $ GarageFinish <chr> "RFn", "RFn", "RFn", "Unf", "RFn", "Unf", "RFn", "RFn...
## $ GarageCars <dbl> 2, 2, 2, 3, 3, 2, 2, 2, 2, 1, 1, 3, 1, 3, 1, 2, 2, 2,...
## $ GarageArea <dbl> 548, 460, 608, 642, 836, 480, 636, 484, 468, 205, 384...
## $ GarageQual <chr> "TA", "TA", "TA", "TA", "TA", "TA", "TA", "TA", "Fa",...
## $ GarageCond <chr> "TA", "TA", "TA", "TA", "TA", "TA", "TA", "TA", "TA",...
## $ PavedDrive <chr> "Y", "Y", "Y", "Y", "Y", "Y", "Y", "Y", "Y", "Y", "Y"...
## $ WoodDeckSF <dbl> 0, 298, 0, 0, 192, 40, 255, 235, 90, 0, 0, 147, 140, ...
## $ OpenPorchSF <dbl> 61, 0, 42, 35, 84, 30, 57, 204, 0, 4, 0, 21, 0, 33, 2...
## $ EnclosedPorch <dbl> 0, 0, 0, 272, 0, 0, 0, 228, 205, 0, 0, 0, 0, 0, 176, ...
## $ `3SsnPorch` <dbl> 0, 0, 0, 0, 0, 320, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...
## $ ScreenPorch <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 176, 0, 0, 0, 0, ...
## $ PoolArea <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,...
## $ PoolQC <chr> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N...
## $ Fence <chr> NA, NA, NA, NA, NA, "MnPrv", NA, NA, NA, NA, NA, NA, ...
## $ MiscFeature <chr> NA, NA, NA, NA, NA, "Shed", NA, "Shed", NA, NA, NA, N...
## $ MiscVal <dbl> 0, 0, 0, 0, 0, 700, 0, 350, 0, 0, 0, 0, 0, 0, 0, 0, 7...
## $ MoSold <dbl> 2, 5, 9, 2, 12, 10, 8, 11, 4, 1, 2, 7, 9, 8, 5, 7, 3,...
## $ YrSold <dbl> 2008, 2007, 2008, 2006, 2008, 2009, 2007, 2009, 2008,...
## $ SaleType <chr> "WD", "WD", "WD", "WD", "WD", "WD", "WD", "WD", "WD",...
## $ SaleCondition <chr> "Normal", "Normal", "Normal", "Abnorml", "Normal", "N...
## $ SalePrice <dbl> 208500, 181500, 223500, 140000, 250000, 143000, 30700...## Rows: 1,459
## Columns: 80
## $ Id <dbl> 1461, 1462, 1463, 1464, 1465, 1466, 1467, 1468, 1469,...
## $ MSSubClass <dbl> 20, 20, 60, 60, 120, 60, 20, 60, 20, 20, 120, 160, 16...
## $ MSZoning <chr> "RH", "RL", "RL", "RL", "RL", "RL", "RL", "RL", "RL",...
## $ LotFrontage <dbl> 80, 81, 74, 78, 43, 75, NA, 63, 85, 70, 26, 21, 21, 2...
## $ LotArea <dbl> 11622, 14267, 13830, 9978, 5005, 10000, 7980, 8402, 1...
## $ Street <chr> "Pave", "Pave", "Pave", "Pave", "Pave", "Pave", "Pave...
## $ Alley <chr> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N...
## $ LotShape <chr> "Reg", "IR1", "IR1", "IR1", "IR1", "IR1", "IR1", "IR1...
## $ LandContour <chr> "Lvl", "Lvl", "Lvl", "Lvl", "HLS", "Lvl", "Lvl", "Lvl...
## $ Utilities <chr> "AllPub", "AllPub", "AllPub", "AllPub", "AllPub", "Al...
## $ LotConfig <chr> "Inside", "Corner", "Inside", "Inside", "Inside", "Co...
## $ LandSlope <chr> "Gtl", "Gtl", "Gtl", "Gtl", "Gtl", "Gtl", "Gtl", "Gtl...
## $ Neighborhood <chr> "NAmes", "NAmes", "Gilbert", "Gilbert", "StoneBr", "G...
## $ Condition1 <chr> "Feedr", "Norm", "Norm", "Norm", "Norm", "Norm", "Nor...
## $ Condition2 <chr> "Norm", "Norm", "Norm", "Norm", "Norm", "Norm", "Norm...
## $ BldgType <chr> "1Fam", "1Fam", "1Fam", "1Fam", "TwnhsE", "1Fam", "1F...
## $ HouseStyle <chr> "1Story", "1Story", "2Story", "2Story", "1Story", "2S...
## $ OverallQual <dbl> 5, 6, 5, 6, 8, 6, 6, 6, 7, 4, 7, 6, 5, 6, 7, 9, 8, 9,...
## $ OverallCond <dbl> 6, 6, 5, 6, 5, 5, 7, 5, 5, 5, 5, 5, 5, 6, 6, 5, 5, 5,...
## $ YearBuilt <dbl> 1961, 1958, 1997, 1998, 1992, 1993, 1992, 1998, 1990,...
## $ YearRemodAdd <dbl> 1961, 1958, 1998, 1998, 1992, 1994, 2007, 1998, 1990,...
## $ RoofStyle <chr> "Gable", "Hip", "Gable", "Gable", "Gable", "Gable", "...
## $ RoofMatl <chr> "CompShg", "CompShg", "CompShg", "CompShg", "CompShg"...
## $ Exterior1st <chr> "VinylSd", "Wd Sdng", "VinylSd", "VinylSd", "HdBoard"...
## $ Exterior2nd <chr> "VinylSd", "Wd Sdng", "VinylSd", "VinylSd", "HdBoard"...
## $ MasVnrType <chr> "None", "BrkFace", "None", "BrkFace", "None", "None",...
## $ MasVnrArea <dbl> 0, 108, 0, 20, 0, 0, 0, 0, 0, 0, 0, 504, 492, 0, 0, 1...
## $ ExterQual <chr> "TA", "TA", "TA", "TA", "Gd", "TA", "TA", "TA", "TA",...
## $ ExterCond <chr> "TA", "TA", "TA", "TA", "TA", "TA", "Gd", "TA", "TA",...
## $ Foundation <chr> "CBlock", "CBlock", "PConc", "PConc", "PConc", "PConc...
## $ BsmtQual <chr> "TA", "TA", "Gd", "TA", "Gd", "Gd", "Gd", "Gd", "Gd",...
## $ BsmtCond <chr> "TA", "TA", "TA", "TA", "TA", "TA", "TA", "TA", "TA",...
## $ BsmtExposure <chr> "No", "No", "No", "No", "No", "No", "No", "No", "Gd",...
## $ BsmtFinType1 <chr> "Rec", "ALQ", "GLQ", "GLQ", "ALQ", "Unf", "ALQ", "Unf...
## $ BsmtFinSF1 <dbl> 468, 923, 791, 602, 263, 0, 935, 0, 637, 804, 1051, 1...
## $ BsmtFinType2 <chr> "LwQ", "Unf", "Unf", "Unf", "Unf", "Unf", "Unf", "Unf...
## $ BsmtFinSF2 <dbl> 144, 0, 0, 0, 0, 0, 0, 0, 0, 78, 0, 0, 0, 0, 0, 0, 0,...
## $ BsmtUnfSF <dbl> 270, 406, 137, 324, 1017, 763, 233, 789, 663, 0, 354,...
## $ TotalBsmtSF <dbl> 882, 1329, 928, 926, 1280, 763, 1168, 789, 1300, 882,...
## $ Heating <chr> "GasA", "GasA", "GasA", "GasA", "GasA", "GasA", "GasA...
## $ HeatingQC <chr> "TA", "TA", "Gd", "Ex", "Ex", "Gd", "Ex", "Gd", "Gd",...
## $ CentralAir <chr> "Y", "Y", "Y", "Y", "Y", "Y", "Y", "Y", "Y", "Y", "Y"...
## $ Electrical <chr> "SBrkr", "SBrkr", "SBrkr", "SBrkr", "SBrkr", "SBrkr",...
## $ `1stFlrSF` <dbl> 896, 1329, 928, 926, 1280, 763, 1187, 789, 1341, 882,...
## $ `2ndFlrSF` <dbl> 0, 0, 701, 678, 0, 892, 0, 676, 0, 0, 0, 504, 567, 60...
## $ LowQualFinSF <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,...
## $ GrLivArea <dbl> 896, 1329, 1629, 1604, 1280, 1655, 1187, 1465, 1341, ...
## $ BsmtFullBath <dbl> 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0,...
## $ BsmtHalfBath <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,...
## $ FullBath <dbl> 1, 1, 2, 2, 2, 2, 2, 2, 1, 1, 2, 1, 1, 2, 1, 2, 2, 2,...
## $ HalfBath <dbl> 0, 1, 1, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0,...
## $ BedroomAbvGr <dbl> 2, 3, 3, 3, 2, 3, 3, 3, 2, 2, 2, 2, 3, 3, 2, 3, 3, 3,...
## $ KitchenAbvGr <dbl> 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,...
## $ KitchenQual <chr> "TA", "Gd", "TA", "Gd", "Gd", "TA", "TA", "TA", "Gd",...
## $ TotRmsAbvGrd <dbl> 5, 6, 6, 7, 5, 7, 6, 7, 5, 4, 5, 5, 6, 6, 4, 10, 7, 7...
## $ Functional <chr> "Typ", "Typ", "Typ", "Typ", "Typ", "Typ", "Typ", "Typ...
## $ Fireplaces <dbl> 0, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1,...
## $ FireplaceQu <chr> NA, NA, "TA", "Gd", NA, "TA", NA, "Gd", "Po", NA, "Fa...
## $ GarageType <chr> "Attchd", "Attchd", "Attchd", "Attchd", "Attchd", "At...
## $ GarageYrBlt <dbl> 1961, 1958, 1997, 1998, 1992, 1993, 1992, 1998, 1990,...
## $ GarageFinish <chr> "Unf", "Unf", "Fin", "Fin", "RFn", "Fin", "Fin", "Fin...
## $ GarageCars <dbl> 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 2, 1, 3, 3, 3,...
## $ GarageArea <dbl> 730, 312, 482, 470, 506, 440, 420, 393, 506, 525, 511...
## $ GarageQual <chr> "TA", "TA", "TA", "TA", "TA", "TA", "TA", "TA", "TA",...
## $ GarageCond <chr> "TA", "TA", "TA", "TA", "TA", "TA", "TA", "TA", "TA",...
## $ PavedDrive <chr> "Y", "Y", "Y", "Y", "Y", "Y", "Y", "Y", "Y", "Y", "Y"...
## $ WoodDeckSF <dbl> 140, 393, 212, 360, 0, 157, 483, 0, 192, 240, 203, 27...
## $ OpenPorchSF <dbl> 0, 36, 34, 36, 82, 84, 21, 75, 0, 0, 68, 0, 0, 0, 30,...
## $ EnclosedPorch <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,...
## $ `3SsnPorch` <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,...
## $ ScreenPorch <dbl> 120, 0, 0, 0, 144, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0...
## $ PoolArea <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,...
## $ PoolQC <chr> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N...
## $ Fence <chr> "MnPrv", NA, "MnPrv", NA, NA, NA, "GdPrv", NA, NA, "M...
## $ MiscFeature <chr> NA, "Gar2", NA, NA, NA, NA, "Shed", NA, NA, NA, NA, N...
## $ MiscVal <dbl> 0, 12500, 0, 0, 0, 0, 500, 0, 0, 0, 0, 0, 0, 0, 0, 0,...
## $ MoSold <dbl> 6, 6, 3, 6, 1, 4, 3, 5, 2, 4, 6, 2, 3, 6, 6, 1, 6, 6,...
## $ YrSold <dbl> 2010, 2010, 2010, 2010, 2010, 2010, 2010, 2010, 2010,...
## $ SaleType <chr> "WD", "WD", "WD", "WD", "WD", "WD", "WD", "WD", "WD",...
## $ SaleCondition <chr> "Normal", "Normal", "Normal", "Normal", "Normal", "No...2.2 Data Cleaning
Convert data type of
MSSubClassfromdoubletofactor.Impute missing values to ‘None’ and convert data type of the nominal categorical variables above mentioned from
charactertofactor.Impute missing values to ‘None’ and convert data type of the ordinal categorical variables above mentioned from
characterto ORDEREDfactor.Impute missing values with column means for all other numerical variables.
na_to_none <- function(x){
return(ifelse(is.na(x), 'None', x))
}
replace_mean <- function(x){
return(ifelse(is.na(x), mean(x, na.rm = TRUE), x))
}
data_clean_split <- data_train %>%
mutate(Split = 'Train') %>%
rbind(data_test %>%
mutate(SalePrice = NA,
Split = 'Test')) %>%
mutate(MSSubClass = MSSubClass %>% as.factor()) %>%
mutate_at(c('Alley', 'MiscFeature','BsmtQual', 'BsmtCond', 'BsmtExposure','BsmtFinType1', 'BsmtFinType2', 'FireplaceQu', 'GarageType', 'GarageFinish', 'GarageQual', 'GarageCond', 'PoolQC', 'Fence'), na_to_none) %>%
mutate_at(c('MSZoning','Street', 'Alley', 'LotShape', 'LandContour', 'Utilities', 'LotConfig', 'LandSlope', 'Neighborhood', 'Condition1', 'Condition2', 'BldgType', 'HouseStyle', 'RoofStyle', 'RoofMatl', 'Exterior1st', 'Exterior2nd', 'MasVnrType', 'Foundation', 'Heating', 'CentralAir', 'Electrical','GarageType', 'PavedDrive', 'MiscFeature', 'SaleType', 'SaleCondition'), as.factor) %>%
mutate(ExterQual = factor(ExterQual, levels = c('Po', 'Fa', 'TA', 'Gd', 'Ex'), ordered = TRUE),
ExterCond = factor(ExterCond, levels = c('Po', 'Fa', 'TA', 'Gd', 'Ex'), ordered = TRUE),
BsmtQual = factor(BsmtQual, levels = c('None','Po', 'Fa', 'TA', 'Gd', 'Ex'), ordered = TRUE),
BsmtCond = factor(BsmtCond, levels = c('None','Po', 'Fa', 'TA', 'Gd', 'Ex'), ordered = TRUE),
BsmtExposure = factor(BsmtExposure, levels = c('None','No', 'Mn', 'Av', 'Gd'), ordered = TRUE),
BsmtFinType1 = factor(BsmtFinType1, levels = c('None','Unf', 'LwQ', 'Rec', 'BLQ', 'ALQ', 'GLQ'), ordered = TRUE),
BsmtFinType2 = factor(BsmtFinType2, levels = c('None','Unf', 'LwQ', 'Rec', 'BLQ', 'ALQ', 'GLQ'), ordered = TRUE),
HeatingQC = factor(HeatingQC, levels = c('Po', 'Fa', 'TA', 'Gd', 'Ex'), ordered = TRUE),
KitchenQual = factor(KitchenQual, levels = c('Po', 'Fa', 'TA', 'Gd', 'Ex'), ordered = TRUE),
Functional = factor(Functional, levels = c('Sal', 'Sev', 'Maj2', 'Maj1', 'Mod', 'Min2', 'Min1', 'Typ'), ordered = TRUE), #na exist
FireplaceQu = factor(FireplaceQu, levels = c('None','Po', 'Fa', 'TA', 'Gd', 'Ex'), ordered = TRUE),
GarageFinish = factor(GarageFinish, levels = c('None','Unf', 'RFn', 'Fin'), ordered = TRUE),
GarageQual = factor(GarageFinish, levels = c('None','Unf', 'RFn', 'Fin'), ordered = TRUE),
GarageCond = factor(GarageCond, levels = c('None','Po', 'Fa', 'TA', 'Gd', 'Ex'), ordered = TRUE),
PoolQC = factor(PoolQC, levels = c('None','Fa', 'TA', 'Gd', 'Ex'), ordered = TRUE),
Fence = factor(Fence, levels = c('None','MnWw', 'GdWo', 'MnPrv', 'GdPrv'), ordered = TRUE)
) %>%
mutate_if(is.numeric, replace_mean)
data_train_clean <- data_clean_split %>%
filter(Split == 'Train') %>%
select(-Split)
data_train_cleandata_test_clean <- data_clean_split %>%
filter(Split == 'Test') %>%
select(-c(Split,SalePrice))
data_test_clean2.3 Sub-Question 1
5 points. Descriptive and Inferential Statistics. Provide univariate descriptive statistics and appropriate plots for the training data set. Provide a scatterplot matrix for at least two of the independent variables and the dependent variable. Derive a correlation matrix for any three quantitative variables in the dataset. Test the hypotheses that the correlations between each pairwise set of variables is 0 and provide an 80% confidence interval. Discuss the meaning of your analysis. Would you be worried about familywise error? Why or why not?
Answer:
1. univariate descriptive statistics and appropriate plots for the training data set
- Nominal Categorical Variables
There are total 27 nominal categorical variables.
data_train_nominal <- data_train_clean %>%
select('MSZoning','Street', 'Alley', 'LotShape', 'LandContour', 'Utilities', 'LotConfig', 'LandSlope', 'Neighborhood', 'Condition1', 'Condition2', 'BldgType', 'HouseStyle', 'RoofStyle', 'RoofMatl', 'Exterior1st', 'Exterior2nd', 'MasVnrType', 'Foundation', 'Heating', 'CentralAir', 'Electrical','GarageType', 'PavedDrive', 'MiscFeature', 'SaleType', 'SaleCondition')
data_train_nominal %>%
summary(25) ## MSZoning Street Alley LotShape LandContour Utilities
## C (all): 10 Grvl: 6 Grvl: 50 IR1:484 Bnk: 63 AllPub:1459
## FV : 65 Pave:1454 None:1369 IR2: 41 HLS: 50 NoSeWa: 1
## RH : 16 Pave: 41 IR3: 10 Low: 36
## RL :1151 Reg:925 Lvl:1311
## RM : 218
##
##
##
##
##
##
##
##
##
##
##
##
##
##
##
##
##
##
##
##
## LotConfig LandSlope Neighborhood Condition1 Condition2
## Corner : 263 Gtl:1382 Blmngtn: 17 Artery: 48 Artery: 2
## CulDSac: 94 Mod: 65 Blueste: 2 Feedr : 81 Feedr : 6
## FR2 : 47 Sev: 13 BrDale : 16 Norm :1260 Norm :1445
## FR3 : 4 BrkSide: 58 PosA : 8 PosA : 1
## Inside :1052 ClearCr: 28 PosN : 19 PosN : 2
## CollgCr:150 RRAe : 11 RRAe : 1
## Crawfor: 51 RRAn : 26 RRAn : 1
## Edwards:100 RRNe : 2 RRNn : 2
## Gilbert: 79 RRNn : 5
## IDOTRR : 37
## MeadowV: 17
## Mitchel: 49
## NAmes :225
## NoRidge: 41
## NPkVill: 9
## NridgHt: 77
## NWAmes : 73
## OldTown:113
## Sawyer : 74
## SawyerW: 59
## Somerst: 86
## StoneBr: 25
## SWISU : 25
## Timber : 38
## Veenker: 11
## BldgType HouseStyle RoofStyle RoofMatl Exterior1st
## 1Fam :1220 1.5Fin:154 Flat : 13 ClyTile: 1 AsbShng: 20
## 2fmCon: 31 1.5Unf: 14 Gable :1141 CompShg:1434 AsphShn: 1
## Duplex: 52 1Story:726 Gambrel: 11 Membran: 1 BrkComm: 2
## Twnhs : 43 2.5Fin: 8 Hip : 286 Metal : 1 BrkFace: 50
## TwnhsE: 114 2.5Unf: 11 Mansard: 7 Roll : 1 CBlock : 1
## 2Story:445 Shed : 2 Tar&Grv: 11 CemntBd: 61
## SFoyer: 37 WdShake: 5 HdBoard:222
## SLvl : 65 WdShngl: 6 ImStucc: 1
## MetalSd:220
## Plywood:108
## Stone : 2
## Stucco : 25
## VinylSd:515
## Wd Sdng:206
## WdShing: 26
##
##
##
##
##
##
##
##
##
##
## Exterior2nd MasVnrType Foundation Heating CentralAir Electrical
## AsbShng: 20 BrkCmn : 15 BrkTil:146 Floor: 1 N: 95 FuseA: 94
## AsphShn: 3 BrkFace:445 CBlock:634 GasA :1428 Y:1365 FuseF: 27
## Brk Cmn: 7 None :864 PConc :647 GasW : 18 FuseP: 3
## BrkFace: 25 Stone :128 Slab : 24 Grav : 7 Mix : 1
## CBlock : 1 NA's : 8 Stone : 6 OthW : 2 SBrkr:1334
## CmentBd: 60 Wood : 3 Wall : 4 NA's : 1
## HdBoard:207
## ImStucc: 10
## MetalSd:214
## Other : 1
## Plywood:142
## Stone : 5
## Stucco : 26
## VinylSd:504
## Wd Sdng:197
## Wd Shng: 38
##
##
##
##
##
##
##
##
##
## GarageType PavedDrive MiscFeature SaleType SaleCondition
## 2Types : 6 N: 90 Gar2: 2 COD : 43 Abnorml: 101
## Attchd :870 P: 30 None:1406 Con : 2 AdjLand: 4
## Basment: 19 Y:1340 Othr: 2 ConLD: 9 Alloca : 12
## BuiltIn: 88 Shed: 49 ConLI: 5 Family : 20
## CarPort: 9 TenC: 1 ConLw: 5 Normal :1198
## Detchd :387 CWD : 4 Partial: 125
## None : 81 New : 122
## Oth : 3
## WD :1267
##
##
##
##
##
##
##
##
##
##
##
##
##
##
##
## plot_catorical <- function(df, col){
return(plot(df[col], main = paste0('Histogram: ',col), col = 'deeppink4'))
}
par(mfrow = c(3,2))
for (col in colnames(data_train_nominal)){
plot_catorical(data_train_nominal, col)
}
- Ordinal Categorical Variables
There 16 oridinal categorical variables.
data_train_ordinal <- data_train_clean %>%
select('ExterQual', 'ExterCond', 'BsmtQual', 'BsmtCond', 'BsmtExposure','BsmtFinType1', 'BsmtFinType2','HeatingQC', 'KitchenQual', 'Functional', 'FireplaceQu', 'GarageFinish', 'GarageQual', 'GarageCond', 'PoolQC', 'Fence')
data_train_ordinal %>%
summary(25) ## ExterQual ExterCond BsmtQual BsmtCond BsmtExposure BsmtFinType1
## Po: 0 Po: 1 None: 37 None: 37 None: 38 None: 37
## Fa: 14 Fa: 28 Po : 0 Po : 2 No :953 Unf :430
## TA:906 TA:1282 Fa : 35 Fa : 45 Mn :114 LwQ : 74
## Gd:488 Gd: 146 TA :649 TA :1311 Av :221 Rec :133
## Ex: 52 Ex: 3 Gd :618 Gd : 65 Gd :134 BLQ :148
## Ex :121 Ex : 0 ALQ :220
## GLQ :418
##
## BsmtFinType2 HeatingQC KitchenQual Functional FireplaceQu GarageFinish
## None: 38 Po: 1 Po: 0 Sal : 0 None:690 None: 81
## Unf :1256 Fa: 49 Fa: 39 Sev : 1 Po : 20 Unf :605
## LwQ : 46 TA:428 TA:735 Maj2: 5 Fa : 33 RFn :422
## Rec : 54 Gd:241 Gd:586 Maj1: 14 TA :313 Fin :352
## BLQ : 33 Ex:741 Ex:100 Mod : 15 Gd :380
## ALQ : 19 Min2: 34 Ex : 24
## GLQ : 14 Min1: 31
## Typ :1360
## GarageQual GarageCond PoolQC Fence
## None: 81 None: 81 None:1453 None :1179
## Unf :605 Po : 7 Fa : 2 MnWw : 11
## RFn :422 Fa : 35 TA : 0 GdWo : 54
## Fin :352 TA :1326 Gd : 3 MnPrv: 157
## Gd : 9 Ex : 2 GdPrv: 59
## Ex : 2
##
## par(mfrow = c(3,2))
for (col in colnames(data_train_ordinal)){
plot_catorical(data_train_ordinal, col)
}
- Numerical Variables
There 36 numerical variables excluding Id.
data_train_numeircal <- data_train_clean %>%
select(where(is.numeric), -Id)
data_train_numeircal %>%
summary(25) ## LotFrontage LotArea OverallQual OverallCond
## Min. : 21.00 Min. : 1300 Min. : 1.000 Min. :1.000
## 1st Qu.: 60.00 1st Qu.: 7554 1st Qu.: 5.000 1st Qu.:5.000
## Median : 69.31 Median : 9478 Median : 6.000 Median :5.000
## Mean : 69.92 Mean : 10517 Mean : 6.099 Mean :5.575
## 3rd Qu.: 79.00 3rd Qu.: 11602 3rd Qu.: 7.000 3rd Qu.:6.000
## Max. :313.00 Max. :215245 Max. :10.000 Max. :9.000
## YearBuilt YearRemodAdd MasVnrArea BsmtFinSF1
## Min. :1872 Min. :1950 Min. : 0.0 Min. : 0.0
## 1st Qu.:1954 1st Qu.:1967 1st Qu.: 0.0 1st Qu.: 0.0
## Median :1973 Median :1994 Median : 0.0 Median : 383.5
## Mean :1971 Mean :1985 Mean : 103.7 Mean : 443.6
## 3rd Qu.:2000 3rd Qu.:2004 3rd Qu.: 164.2 3rd Qu.: 712.2
## Max. :2010 Max. :2010 Max. :1600.0 Max. :5644.0
## BsmtFinSF2 BsmtUnfSF TotalBsmtSF 1stFlrSF
## Min. : 0.00 Min. : 0.0 Min. : 0.0 Min. : 334
## 1st Qu.: 0.00 1st Qu.: 223.0 1st Qu.: 795.8 1st Qu.: 882
## Median : 0.00 Median : 477.5 Median : 991.5 Median :1087
## Mean : 46.55 Mean : 567.2 Mean :1057.4 Mean :1163
## 3rd Qu.: 0.00 3rd Qu.: 808.0 3rd Qu.:1298.2 3rd Qu.:1391
## Max. :1474.00 Max. :2336.0 Max. :6110.0 Max. :4692
## 2ndFlrSF LowQualFinSF GrLivArea BsmtFullBath
## Min. : 0 Min. : 0.000 Min. : 334 Min. :0.0000
## 1st Qu.: 0 1st Qu.: 0.000 1st Qu.:1130 1st Qu.:0.0000
## Median : 0 Median : 0.000 Median :1464 Median :0.0000
## Mean : 347 Mean : 5.845 Mean :1515 Mean :0.4253
## 3rd Qu.: 728 3rd Qu.: 0.000 3rd Qu.:1777 3rd Qu.:1.0000
## Max. :2065 Max. :572.000 Max. :5642 Max. :3.0000
## BsmtHalfBath FullBath HalfBath BedroomAbvGr
## Min. :0.00000 Min. :0.000 Min. :0.0000 Min. :0.000
## 1st Qu.:0.00000 1st Qu.:1.000 1st Qu.:0.0000 1st Qu.:2.000
## Median :0.00000 Median :2.000 Median :0.0000 Median :3.000
## Mean :0.05753 Mean :1.565 Mean :0.3829 Mean :2.866
## 3rd Qu.:0.00000 3rd Qu.:2.000 3rd Qu.:1.0000 3rd Qu.:3.000
## Max. :2.00000 Max. :3.000 Max. :2.0000 Max. :8.000
## KitchenAbvGr TotRmsAbvGrd Fireplaces GarageYrBlt
## Min. :0.000 Min. : 2.000 Min. :0.000 Min. :1900
## 1st Qu.:1.000 1st Qu.: 5.000 1st Qu.:0.000 1st Qu.:1962
## Median :1.000 Median : 6.000 Median :1.000 Median :1978
## Mean :1.047 Mean : 6.518 Mean :0.613 Mean :1978
## 3rd Qu.:1.000 3rd Qu.: 7.000 3rd Qu.:1.000 3rd Qu.:2001
## Max. :3.000 Max. :14.000 Max. :3.000 Max. :2010
## GarageCars GarageArea WoodDeckSF OpenPorchSF
## Min. :0.000 Min. : 0.0 Min. : 0.00 Min. : 0.00
## 1st Qu.:1.000 1st Qu.: 334.5 1st Qu.: 0.00 1st Qu.: 0.00
## Median :2.000 Median : 480.0 Median : 0.00 Median : 25.00
## Mean :1.767 Mean : 473.0 Mean : 94.24 Mean : 46.66
## 3rd Qu.:2.000 3rd Qu.: 576.0 3rd Qu.:168.00 3rd Qu.: 68.00
## Max. :4.000 Max. :1418.0 Max. :857.00 Max. :547.00
## EnclosedPorch 3SsnPorch ScreenPorch PoolArea
## Min. : 0.00 Min. : 0.00 Min. : 0.00 Min. : 0.000
## 1st Qu.: 0.00 1st Qu.: 0.00 1st Qu.: 0.00 1st Qu.: 0.000
## Median : 0.00 Median : 0.00 Median : 0.00 Median : 0.000
## Mean : 21.95 Mean : 3.41 Mean : 15.06 Mean : 2.759
## 3rd Qu.: 0.00 3rd Qu.: 0.00 3rd Qu.: 0.00 3rd Qu.: 0.000
## Max. :552.00 Max. :508.00 Max. :480.00 Max. :738.000
## MiscVal MoSold YrSold SalePrice
## Min. : 0.00 Min. : 1.000 Min. :2006 Min. : 34900
## 1st Qu.: 0.00 1st Qu.: 5.000 1st Qu.:2007 1st Qu.:129975
## Median : 0.00 Median : 6.000 Median :2008 Median :163000
## Mean : 43.49 Mean : 6.322 Mean :2008 Mean :180921
## 3rd Qu.: 0.00 3rd Qu.: 8.000 3rd Qu.:2009 3rd Qu.:214000
## Max. :15500.00 Max. :12.000 Max. :2010 Max. :755000plot_numeric<- function(df,col){
data <- df[col] %>%
unlist() %>%
as.numeric()
return(hist(data,
main = paste0('Histogram: ',col),
xlab = col,
col = 'deeppink4'))
}
par(mfrow = c(3,3))
for (col in colnames(data_train_numeircal)){
plot_numeric(data_train_numeircal,col)
}
2. Provide a scatterplot matrix for at least two of the independent variables and the dependent variable.
- 9 nominal categorical variables and dependent variable
3.Derive a correlation matrix for any three quantitative variables in the dataset.
4. Test the hypothesis that the correlations between each pairwise set of variables is 0 and provide an 80% confidence interval. Discuss the meaning of your analysis. Would you be worried about familywise error? Why or why not?
SalePricevsGrLivAreaP-value is very small, the 80% confidence internal does not include 0, therefore the null hypothesis that the true correlation equal zero is rejected.SalePricevsOverallQualP-value is very small, the 80% confidence internal does not include 0, therefore the null hypothesis that the true correlation equal zero is rejected.OverallQualvsGrLivAreaP-value is very small, the 80% confidence internal does not include 0, therefore the null hypothesis that the true correlation equal zero is rejected.
From this hypothesis testing, it is inferred that there are high correlation among size of general living size, rates of the finish of the house and the sale price, which means GrLivArea and OverallQual, as independent variables, have good explainability on the dependent variable SalePrice.
Familywise error rate (FWE or FWER) is the probability of a coming to at least one false conclusion in a series of hypothesis tests. It is the probability of making at least one Type I Error. It is also called alpha inflation or cumulative Type I error.
\(FWE \leq 1-(1-\alpha)^{c}\) where \(\alpha\) is the alpha level for an individual test (e.g. 0.5) and \(c\) is the number of comparisons/tests.
In this question, \(\alpha = 0.2\) for an 80% confidence interval and \(c=3\) for three variables used for the hypothesis test.
Therefore, \(FWE \leq 1-(1-0.2)^{3} = 0.488\)
FWE can be reduced by increasing the confidence interval, therefore we have less concern on this.
cor.test(data_train_clean$SalePrice, data_train_clean$GrLivArea, method="pearson", conf.level = 0.8)##
## Pearson's product-moment correlation
##
## data: data_train_clean$SalePrice and data_train_clean$GrLivArea
## t = 38.348, df = 1458, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 80 percent confidence interval:
## 0.6915087 0.7249450
## sample estimates:
## cor
## 0.7086245##
## Pearson's product-moment correlation
##
## data: data_train_clean$SalePrice and data_train_clean$OverallQual
## t = 49.364, df = 1458, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 80 percent confidence interval:
## 0.7780752 0.8032204
## sample estimates:
## cor
## 0.7909816##
## Pearson's product-moment correlation
##
## data: data_train_clean$OverallQual and data_train_clean$GrLivArea
## t = 28.121, df = 1458, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 80 percent confidence interval:
## 0.5708061 0.6143422
## sample estimates:
## cor
## 0.59300742.4 Sub-Question 2
5 points. Linear Algebra and Correlation. Invert your correlation matrix from above. (This is known as the precision matrix and contains variance inflation factors on the diagonal.) Multiply the correlation matrix by the precision matrix, and then multiply the precision matrix by the correlation matrix. Conduct LU decomposition on the matrix.
1. Precision Matrix
cor_mat <- cor(data_train_clean[c('SalePrice', 'GrLivArea', 'OverallQual')], method = 'pearson') %>%
as.matrix()
cor_mat## SalePrice GrLivArea OverallQual
## SalePrice 1.0000000 0.7086245 0.7909816
## GrLivArea 0.7086245 1.0000000 0.5930074
## OverallQual 0.7909816 0.5930074 1.0000000## SalePrice GrLivArea OverallQual
## SalePrice 3.498623 -1.2927630 -2.0007280
## GrLivArea -1.292763 2.0200794 -0.1753704
## OverallQual -2.000728 -0.1753704 2.68653502. Multiply the correlation matrix by the precision matrix
## SalePrice GrLivArea OverallQual
## SalePrice 1 0 0
## GrLivArea 0 1 0
## OverallQual 0 0 13. multiply the precision matrix by the correlation matrix
## SalePrice GrLivArea OverallQual
## SalePrice 1 0 0
## GrLivArea 0 1 0
## OverallQual 0 0 14. Conduct LU decomposition on the matrix
## $L
## [,1] [,2] [,3]
## [1,] 1.0000000 0.00000000 0
## [2,] 0.7086245 1.00000000 0
## [3,] 0.7909816 0.06527753 1
##
## $U
## [,1] [,2] [,3]
## [1,] 1 0.7086245 0.79098160
## [2,] 0 0.4978513 0.03249851
## [3,] 0 0.0000000 0.372226692.5 Sub-Question 3
5 points. Calculus-Based Probability & Statistics. Many times, it makes sense to fit a closed form distribution to data. Select a variable in the Kaggle.com training dataset that is skewed to the right, shift it so that the minimum value is absolutely above zero if necessary. Then load the MASS package and run fitdistr to fit an exponential probability density function. (See https://stat.ethz.ch/R-manual/R-devel/library/MASS/html/fitdistr.html ). Find the optimal value of \(\lambda\) for this distribution, and then take 1000 samples from this exponential distribution using this value (e.g., rexp(1000, \(\lambda\))). Plot a histogram and compare it with a histogram of your original variable. Using the exponential pdf, find the 5th and 95th percentiles using the cumulative distribution function (CDF). Also generate a 95% confidence interval from the empirical data, assuming normality. Finally, provide the empirical 5th percentile and 95th percentile of the data. Discuss.
1. Select a variable in the Kaggle.com training dataset that is skewed to the right, shift it so that the minimum value is absolutely above zero if necessary
From the Descriptive and Inferential Statistics section, we can see variable WoodDeckSF is smoothly right skewed. The minimum is zero so add 1 to all observations to have minimum value absolitely above zero.
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.00 0.00 0.00 94.24 168.00 857.00
data_skewed <- data_train_clean$WoodDeckSF+1
hist(data_skewed, col = 'deeppink4', main = 'Histogram: Sifted WoodDeckSF', xlab = 'WoodDeckSF + 1')
2. Then load the MASS package and run fitdistr to fit an exponential probability density function. (See https://stat.ethz.ch/R-manual/R-devel/library/MASS/html/fitdistr.html ). Find the optimal value of \(\lambda\) for this distribution, and then take 1000 samples from this exponential distribution using this value (e.g., rexp(1000, \(\lambda\))).
##
## Attaching package: 'MASS'## The following object is masked from 'package:dplyr':
##
## select## rate
## 0.010499292
## (0.000274779)par(mfrow = c(1,2))
hist(exp_samp, probability = TRUE, col = 'deeppink4', breaks = 30, main = 'Histogram: Exp_Sample')
hist(data_skewed, probability = TRUE, col = 'deeppink4', breaks = 30, main = 'Histogram: WoodDeckSF + 1', xlab = 'WoodDeckSF + 1')
3. Using the exponential pdf, find the 5th and 95th percentiles using the cumulative distribution function (CDF).
The 5th and 95th are 4.885405 and 285.327084 respectively.
## [1] 4.885405 285.3270844. Also generate a 95% confidence interval from the empirical data, assuming normality.
The 95% CI with normlity assumption is {-150.415, 340.904}. However in actual practice, the interval should be right truncated at zero.
## [1] -150.415 340.9045. Finally, provide the empirical 5th percentile and 95th percentile of the data. Discuss.
The 5th & 95th percentile of the data is 1 and 336 repective. The result make sense since the data is shifted with minimum value = 1. Since multiple independent variables like WoodDeckSF contain 0 because not all houses have the area that were calculated, like wook deck, basement, etc. Therefore the probability model should concidered mulipulating zeros.
## 5% 95%
## 1 3362.6 Sub-Question 4
10 points. Modeling. Build some type of multiple regression model and submit your model to the competition board. Provide your complete model summary and results with analysis. Report your Kaggle.com user name and score.
Build Model with Step wise Approach
data_lm_null <- lm(SalePrice ~ 1, data = data_train_clean[complete.cases(data_train_clean), ])
data_lm_full <- lm(SalePrice ~ ., data = data_train_clean[complete.cases(data_train_clean), ])
stepAIC(data_lm_null, direction = 'both', scope = list(lower = data_lm_null, upper = data_lm_full))## Start: AIC=32738.89
## SalePrice ~ 1
##
## Df Sum of Sq RSS AIC
## + OverallQual 1 5.6937e+12 3.4274e+12 31321
## + Neighborhood 24 4.9702e+12 4.1509e+12 31645
## + GrLivArea 1 4.5989e+12 4.5222e+12 31723
## + ExterQual 3 4.3268e+12 4.7943e+12 31812
## + BsmtQual 4 4.2210e+12 4.9001e+12 31845
## + KitchenQual 3 4.1445e+12 4.9766e+12 31866
## + GarageCars 1 3.7331e+12 5.3880e+12 31977
## + GarageArea 1 3.5343e+12 5.5868e+12 32030
## + TotalBsmtSF 1 3.4308e+12 5.6903e+12 32056
## + `1stFlrSF` 1 3.3603e+12 5.7608e+12 32074
## + FullBath 1 2.8881e+12 6.2330e+12 32188
## + GarageFinish 3 2.7926e+12 6.3285e+12 32215
## + GarageQual 3 2.7926e+12 6.3285e+12 32215
## + FireplaceQu 5 2.6892e+12 6.4319e+12 32242
## + TotRmsAbvGrd 1 2.6240e+12 6.4971e+12 32249
## + YearBuilt 1 2.4975e+12 6.6236e+12 32277
## + YearRemodAdd 1 2.3491e+12 6.7720e+12 32309
## + Foundation 5 2.3400e+12 6.7811e+12 32319
## + GarageType 6 2.2878e+12 6.8333e+12 32332
## + MSSubClass 14 2.2617e+12 6.8594e+12 32353
## + MasVnrArea 1 2.0795e+12 7.0416e+12 32365
## + GarageYrBlt 1 2.0230e+12 7.0981e+12 32377
## + Fireplaces 1 2.0061e+12 7.1150e+12 32380
## + BsmtFinType1 6 1.9155e+12 7.2056e+12 32409
## + HeatingQC 4 1.7822e+12 7.3389e+12 32431
## + MasVnrType 3 1.7138e+12 7.4073e+12 32443
## + BsmtFinSF1 1 1.3449e+12 7.7762e+12 32509
## + BsmtExposure 4 1.3455e+12 7.7756e+12 32515
## + Exterior1st 14 1.3926e+12 7.7285e+12 32526
## + Exterior2nd 15 1.4015e+12 7.7196e+12 32527
## + SaleCondition 5 1.2192e+12 7.9019e+12 32541
## + SaleType 8 1.2356e+12 7.8855e+12 32544
## + LotFrontage 1 1.0130e+12 8.1081e+12 32570
## + WoodDeckSF 1 9.6139e+11 8.1597e+12 32579
## + `2ndFlrSF` 1 9.5065e+11 8.1704e+12 32581
## + MSZoning 4 9.8354e+11 8.1376e+12 32581
## + OpenPorchSF 1 8.8358e+11 8.2375e+12 32593
## + HalfBath 1 7.2705e+11 8.3941e+12 32620
## + HouseStyle 7 7.9373e+11 8.3274e+12 32621
## + GarageCond 5 7.4344e+11 8.3777e+12 32626
## + LotShape 3 7.1725e+11 8.4039e+12 32626
## + LotArea 1 6.3893e+11 8.4822e+12 32636
## + CentralAir 1 5.7732e+11 8.5438e+12 32646
## + Electrical 4 5.4447e+11 8.5766e+12 32658
## + RoofStyle 5 5.3977e+11 8.5813e+12 32660
## + PavedDrive 2 4.9770e+11 8.6234e+12 32661
## + BsmtFullBath 1 4.6171e+11 8.6594e+12 32666
## + BsmtUnfSF 1 4.2440e+11 8.6967e+12 32672
## + BsmtCond 4 4.5588e+11 8.6652e+12 32672
## + Fence 4 3.2257e+11 8.7985e+12 32695
## + BldgType 4 3.1413e+11 8.8070e+12 32696
## + BedroomAbvGr 1 2.6970e+11 8.8514e+12 32697
## + RoofMatl 7 2.9023e+11 8.8309e+12 32706
## + BsmtFinType2 6 2.7582e+11 8.8453e+12 32706
## + LandContour 3 2.3817e+11 8.8829e+12 32706
## + Condition1 8 2.9749e+11 8.8236e+12 32707
## + ExterCond 4 2.1487e+11 8.9062e+12 32712
## + Alley 2 1.8654e+11 8.9346e+12 32713
## + KitchenAbvGr 1 1.7231e+11 8.9488e+12 32713
## + PoolQC 3 1.9562e+11 8.9255e+12 32713
## + LotConfig 4 1.9714e+11 8.9240e+12 32715
## + EnclosedPorch 1 1.5138e+11 8.9697e+12 32717
## + ScreenPorch 1 1.1650e+11 9.0046e+12 32722
## + Functional 6 1.5168e+11 8.9694e+12 32727
## + Heating 5 1.3200e+11 8.9891e+12 32728
## + PoolArea 1 7.9061e+10 9.0420e+12 32728
## + OverallCond 1 5.3185e+10 9.0679e+12 32732
## + MiscFeature 4 6.4230e+10 9.0569e+12 32737
## + `3SsnPorch` 1 1.8663e+10 9.1024e+12 32738
## + MoSold 1 1.8540e+10 9.1026e+12 32738
## + Condition2 7 9.0937e+10 9.0302e+12 32738
## + Street 1 1.5325e+10 9.1058e+12 32738
## + LandSlope 2 2.5545e+10 9.0956e+12 32739
## <none> 9.1211e+12 32739
## + YrSold 1 6.2443e+09 9.1149e+12 32740
## + LowQualFinSF 1 5.8277e+09 9.1153e+12 32740
## + Id 1 5.7866e+09 9.1153e+12 32740
## + MiscVal 1 4.0075e+09 9.1171e+12 32740
## + BsmtHalfBath 1 2.3411e+09 9.1188e+12 32741
## + Utilities 1 1.8610e+09 9.1192e+12 32741
## + BsmtFinSF2 1 9.7704e+08 9.1201e+12 32741
##
## Step: AIC=31320.66
## SalePrice ~ OverallQual
##
## Df Sum of Sq RSS AIC
## + GrLivArea 1 8.1532e+11 2.6121e+12 30928
## + Neighborhood 24 7.9949e+11 2.6279e+12 30983
## + `1stFlrSF` 1 6.2641e+11 2.8010e+12 31030
## + TotalBsmtSF 1 4.5847e+11 2.9689e+12 31114
## + TotRmsAbvGrd 1 4.3018e+11 2.9972e+12 31128
## + GarageArea 1 4.2917e+11 2.9982e+12 31129
## + BsmtQual 4 4.2836e+11 2.9990e+12 31135
## + GarageCars 1 3.9113e+11 3.0363e+12 31147
## + KitchenQual 3 3.9748e+11 3.0299e+12 31148
## + BsmtFinSF1 1 3.7571e+11 3.0517e+12 31154
## + ExterQual 3 3.2782e+11 3.0996e+12 31181
## + LotArea 1 3.0116e+11 3.1262e+12 31189
## + MSSubClass 14 3.4213e+11 3.0853e+12 31196
## + MasVnrArea 1 2.5444e+11 3.1730e+12 31211
## + Fireplaces 1 2.5377e+11 3.1736e+12 31211
## + BsmtExposure 4 2.5129e+11 3.1761e+12 31218
## + FireplaceQu 5 2.5486e+11 3.1725e+12 31219
## + LotFrontage 1 2.1435e+11 3.2130e+12 31229
## + FullBath 1 2.0805e+11 3.2193e+12 31232
## + MSZoning 4 2.0269e+11 3.2247e+12 31240
## + BsmtFullBath 1 1.7979e+11 3.2476e+12 31244
## + WoodDeckSF 1 1.7506e+11 3.2523e+12 31247
## + BldgType 4 1.8265e+11 3.2448e+12 31249
## + GarageFinish 3 1.6414e+11 3.2633e+12 31255
## + GarageQual 3 1.6414e+11 3.2633e+12 31255
## + BsmtFinType1 6 1.6367e+11 3.2637e+12 31262
## + GarageType 6 1.5697e+11 3.2704e+12 31265
## + LotShape 3 1.3467e+11 3.2927e+12 31268
## + SaleCondition 5 1.1626e+11 3.3111e+12 31281
## + LandSlope 2 1.0026e+11 3.3271e+12 31282
## + RoofMatl 7 1.1516e+11 3.3122e+12 31285
## + RoofStyle 5 9.9955e+10 3.3274e+12 31288
## + SaleType 8 1.1331e+11 3.3141e+12 31288
## + LandContour 3 8.6547e+10 3.3409e+12 31290
## + `2ndFlrSF` 1 7.5100e+10 3.3523e+12 31291
## + BedroomAbvGr 1 7.1756e+10 3.3556e+12 31292
## + YearRemodAdd 1 6.8879e+10 3.3585e+12 31293
## + YearBuilt 1 6.8824e+10 3.3586e+12 31293
## + MasVnrType 3 6.9621e+10 3.3578e+12 31297
## + PoolQC 3 6.7596e+10 3.3598e+12 31298
## + Foundation 5 7.6282e+10 3.3511e+12 31298
## + LotConfig 4 6.8789e+10 3.3586e+12 31299
## + OpenPorchSF 1 5.1606e+10 3.3758e+12 31301
## + HeatingQC 4 6.4549e+10 3.3628e+12 31301
## + GarageYrBlt 1 4.6961e+10 3.3804e+12 31303
## + HouseStyle 7 7.3696e+10 3.3537e+12 31303
## + HalfBath 1 4.4437e+10 3.3830e+12 31304
## + Alley 2 4.7074e+10 3.3803e+12 31305
## + Exterior1st 14 9.5465e+10 3.3319e+12 31308
## + Exterior2nd 15 9.9128e+10 3.3283e+12 31308
## + ScreenPorch 1 3.3707e+10 3.3937e+12 31308
## + PavedDrive 2 2.6774e+10 3.4006e+12 31313
## + PoolArea 1 1.5533e+10 3.4119e+12 31316
## + EnclosedPorch 1 1.4349e+10 3.4130e+12 31317
## + CentralAir 1 1.3156e+10 3.4142e+12 31317
## + BsmtFinSF2 1 1.1626e+10 3.4158e+12 31318
## + Heating 5 2.7841e+10 3.3996e+12 31319
## + BsmtUnfSF 1 8.3629e+09 3.4190e+12 31319
## + Electrical 4 1.8970e+10 3.4084e+12 31321
## <none> 3.4274e+12 31321
## + `3SsnPorch` 1 3.9363e+09 3.4235e+12 31321
## + Functional 6 2.6091e+10 3.4013e+12 31322
## + GarageCond 5 2.1375e+10 3.4060e+12 31322
## + Condition1 8 3.5167e+10 3.3922e+12 31322
## + BsmtHalfBath 1 2.0739e+09 3.4253e+12 31322
## + Utilities 1 1.5121e+09 3.4259e+12 31322
## + MoSold 1 7.5014e+08 3.4266e+12 31322
## + KitchenAbvGr 1 6.9205e+08 3.4267e+12 31322
## + YrSold 1 3.6469e+08 3.4270e+12 31323
## + Street 1 2.7448e+08 3.4271e+12 31323
## + OverallCond 1 1.8709e+08 3.4272e+12 31323
## + MiscVal 1 1.2340e+08 3.4273e+12 31323
## + LowQualFinSF 1 2.1048e+07 3.4274e+12 31323
## + Id 1 2.1764e+05 3.4274e+12 31323
## + BsmtFinType2 6 2.1894e+10 3.4055e+12 31323
## + BsmtCond 4 9.9406e+09 3.4175e+12 31324
## + Fence 4 9.8232e+09 3.4176e+12 31324
## + ExterCond 4 8.9254e+09 3.4185e+12 31325
## + Condition2 7 2.2957e+10 3.4044e+12 31325
## + MiscFeature 4 1.8220e+09 3.4256e+12 31328
## - OverallQual 1 5.6937e+12 9.1211e+12 32739
##
## Step: AIC=30928.49
## SalePrice ~ OverallQual + GrLivArea
##
## Df Sum of Sq RSS AIC
## + Neighborhood 24 6.6416e+11 1.9479e+12 30551
## + BsmtQual 4 4.1158e+11 2.2005e+12 30688
## + MSSubClass 14 4.2852e+11 2.1836e+12 30696
## + HouseStyle 7 3.4978e+11 2.2623e+12 30734
## + KitchenQual 3 3.2199e+11 2.2901e+12 30744
## + BsmtFinSF1 1 2.9080e+11 2.3213e+12 30759
## + ExterQual 3 2.8308e+11 2.3290e+12 30768
## + TotalBsmtSF 1 2.5781e+11 2.3543e+12 30780
## + BsmtExposure 4 2.5909e+11 2.3530e+12 30785
## + GarageArea 1 2.3096e+11 2.3811e+12 30796
## + GarageCars 1 2.2787e+11 2.3842e+12 30798
## + `1stFlrSF` 1 2.2062e+11 2.3915e+12 30802
## + BsmtFinType1 6 2.3683e+11 2.3753e+12 30803
## + YearBuilt 1 2.1654e+11 2.3955e+12 30805
## + BsmtFullBath 1 2.1219e+11 2.3999e+12 30808
## + `2ndFlrSF` 1 1.9574e+11 2.4163e+12 30817
## + RoofMatl 7 1.9313e+11 2.4190e+12 30831
## + MSZoning 4 1.5964e+11 2.4524e+12 30845
## + GarageFinish 3 1.3758e+11 2.4745e+12 30856
## + GarageQual 3 1.3758e+11 2.4745e+12 30856
## + SaleCondition 5 1.3640e+11 2.4757e+12 30861
## + Foundation 5 1.3025e+11 2.4818e+12 30864
## + LotArea 1 1.1268e+11 2.4994e+12 30867
## + SaleType 8 1.3419e+11 2.4779e+12 30868
## + GarageYrBlt 1 1.0970e+11 2.5024e+12 30868
## + MasVnrArea 1 1.0960e+11 2.5025e+12 30868
## + LandContour 3 1.1072e+11 2.5014e+12 30872
## + YearRemodAdd 1 9.9210e+10 2.5129e+12 30874
## + BedroomAbvGr 1 9.2921e+10 2.5192e+12 30878
## + WoodDeckSF 1 8.9858e+10 2.5222e+12 30880
## + GarageType 6 1.0039e+11 2.5117e+12 30884
## + MasVnrType 3 8.8629e+10 2.5235e+12 30884
## + FireplaceQu 5 9.5313e+10 2.5168e+12 30885
## + Exterior2nd 15 1.2833e+11 2.4837e+12 30885
## + LotShape 3 8.4523e+10 2.5276e+12 30887
## + Exterior1st 14 1.1437e+11 2.4977e+12 30892
## + BldgType 4 7.4735e+10 2.5373e+12 30894
## + HeatingQC 4 7.2906e+10 2.5392e+12 30895
## + RoofStyle 5 7.3781e+10 2.5383e+12 30897
## + Fireplaces 1 5.9315e+10 2.5528e+12 30897
## + Alley 2 6.0655e+10 2.5514e+12 30898
## + PavedDrive 2 5.1771e+10 2.5603e+12 30903
## + KitchenAbvGr 1 4.6548e+10 2.5655e+12 30904
## + LandSlope 2 4.9653e+10 2.5624e+12 30905
## + Condition1 8 7.0741e+10 2.5413e+12 30905
## + LotFrontage 1 4.2861e+10 2.5692e+12 30906
## + EnclosedPorch 1 4.1278e+10 2.5708e+12 30907
## + PoolQC 3 4.6226e+10 2.5659e+12 30909
## + LotConfig 4 4.8837e+10 2.5632e+12 30909
## + CentralAir 1 3.8190e+10 2.5739e+12 30909
## + LowQualFinSF 1 3.2394e+10 2.5797e+12 30912
## + BsmtUnfSF 1 2.5274e+10 2.5868e+12 30916
## + Condition2 7 4.6252e+10 2.5658e+12 30917
## + Heating 5 3.8594e+10 2.5735e+12 30917
## + BsmtCond 4 3.2007e+10 2.5801e+12 30919
## + GarageCond 5 3.0265e+10 2.5818e+12 30922
## + Electrical 4 2.4782e+10 2.5873e+12 30923
## + Functional 6 3.0659e+10 2.5814e+12 30923
## + ScreenPorch 1 1.2765e+10 2.5993e+12 30923
## + HalfBath 1 8.4495e+09 2.6036e+12 30926
## + TotRmsAbvGrd 1 7.2247e+09 2.6049e+12 30926
## + BsmtFinSF2 1 6.2441e+09 2.6058e+12 30927
## + Fence 4 1.6421e+10 2.5957e+12 30927
## <none> 2.6121e+12 30928
## + `3SsnPorch` 1 3.5823e+09 2.6085e+12 30929
## + FullBath 1 3.2650e+09 2.6088e+12 30929
## + OpenPorchSF 1 2.5819e+09 2.6095e+12 30929
## + MoSold 1 1.7656e+09 2.6103e+12 30930
## + BsmtHalfBath 1 1.5926e+09 2.6105e+12 30930
## + Id 1 9.3882e+08 2.6111e+12 30930
## + Utilities 1 9.3208e+08 2.6111e+12 30930
## + Street 1 7.1939e+08 2.6114e+12 30930
## + PoolArea 1 5.7290e+08 2.6115e+12 30930
## + OverallCond 1 1.3875e+08 2.6119e+12 30930
## + MiscVal 1 5.2399e+07 2.6120e+12 30930
## + YrSold 1 1.8700e+07 2.6121e+12 30930
## + ExterCond 4 1.0609e+10 2.6015e+12 30931
## + BsmtFinType2 6 1.2783e+10 2.5993e+12 30933
## + MiscFeature 4 1.6057e+09 2.6105e+12 30936
## - GrLivArea 1 8.1532e+11 3.4274e+12 31321
## - OverallQual 1 1.9101e+12 4.5222e+12 31723
##
## Step: AIC=30550.8
## SalePrice ~ OverallQual + GrLivArea + Neighborhood
##
## Df Sum of Sq RSS AIC
## + MSSubClass 14 2.6728e+11 1.6806e+12 30365
## + BsmtQual 4 2.1657e+11 1.7314e+12 30388
## + KitchenQual 3 1.8764e+11 1.7603e+12 30410
## + BsmtExposure 4 1.7538e+11 1.7726e+12 30422
## + BsmtFinSF1 1 1.5902e+11 1.7889e+12 30429
## + RoofMatl 7 1.6059e+11 1.7873e+12 30440
## + HouseStyle 7 1.5685e+11 1.7911e+12 30443
## + ExterQual 3 1.3663e+11 1.8113e+12 30451
## + TotalBsmtSF 1 1.1953e+11 1.8284e+12 30461
## + BldgType 4 1.2683e+11 1.8211e+12 30461
## + BsmtFullBath 1 1.1089e+11 1.8370e+12 30468
## + `1stFlrSF` 1 1.0733e+11 1.8406e+12 30471
## + BsmtFinType1 6 1.1490e+11 1.8330e+12 30475
## + `2ndFlrSF` 1 9.8256e+10 1.8497e+12 30478
## + GarageCars 1 9.2578e+10 1.8553e+12 30482
## + GarageArea 1 9.1532e+10 1.8564e+12 30483
## + SaleCondition 5 7.4025e+10 1.8739e+12 30505
## + LotArea 1 6.2031e+10 1.8859e+12 30506
## + GarageFinish 3 6.5729e+10 1.8822e+12 30507
## + GarageQual 3 6.5729e+10 1.8822e+12 30507
## + SaleType 8 7.2195e+10 1.8757e+12 30512
## + YearBuilt 1 4.8020e+10 1.8999e+12 30517
## + BedroomAbvGr 1 4.4208e+10 1.9037e+12 30520
## + WoodDeckSF 1 4.1405e+10 1.9065e+12 30522
## + YearRemodAdd 1 4.1055e+10 1.9069e+12 30522
## + Fireplaces 1 4.0714e+10 1.9072e+12 30522
## + FireplaceQu 5 4.9588e+10 1.8983e+12 30523
## + KitchenAbvGr 1 3.8200e+10 1.9097e+12 30524
## + OverallCond 1 3.7413e+10 1.9105e+12 30525
## + LandContour 3 4.2300e+10 1.9056e+12 30525
## + Exterior2nd 15 6.7328e+10 1.8806e+12 30530
## + MasVnrArea 1 3.0261e+10 1.9177e+12 30530
## + RoofStyle 5 4.0366e+10 1.9076e+12 30530
## + PoolQC 3 3.4187e+10 1.9137e+12 30531
## + Exterior1st 14 6.1467e+10 1.8865e+12 30532
## + LotConfig 4 3.1156e+10 1.9168e+12 30535
## + MasVnrType 3 2.8411e+10 1.9195e+12 30536
## + LandSlope 2 2.4210e+10 1.9237e+12 30537
## + MSZoning 4 2.7395e+10 1.9205e+12 30538
## + BsmtUnfSF 1 1.9006e+10 1.9289e+12 30539
## + ScreenPorch 1 1.7287e+10 1.9306e+12 30540
## + LotShape 3 2.1952e+10 1.9260e+12 30540
## + HeatingQC 4 2.4548e+10 1.9234e+12 30540
## + GarageYrBlt 1 1.6529e+10 1.9314e+12 30540
## + CentralAir 1 1.5803e+10 1.9321e+12 30541
## + Foundation 5 2.5269e+10 1.9227e+12 30542
## + LotFrontage 1 1.4226e+10 1.9337e+12 30542
## + Alley 2 1.6347e+10 1.9316e+12 30543
## + BsmtCond 4 2.0702e+10 1.9272e+12 30543
## + Condition2 7 2.8367e+10 1.9196e+12 30544
## + Functional 6 2.2783e+10 1.9251e+12 30546
## + GarageType 6 2.2388e+10 1.9255e+12 30546
## + PavedDrive 2 1.1566e+10 1.9364e+12 30546
## + HalfBath 1 7.1005e+09 1.9408e+12 30548
## + EnclosedPorch 1 6.9606e+09 1.9410e+12 30548
## + Condition1 8 2.5033e+10 1.9229e+12 30548
## + OpenPorchSF 1 6.3767e+09 1.9416e+12 30548
## + LowQualFinSF 1 5.9303e+09 1.9420e+12 30548
## + `3SsnPorch` 1 4.3850e+09 1.9435e+12 30550
## + BsmtHalfBath 1 4.0388e+09 1.9439e+12 30550
## + BsmtFinType2 6 1.6991e+10 1.9309e+12 30550
## + MoSold 1 3.5731e+09 1.9444e+12 30550
## + Utilities 1 3.5060e+09 1.9444e+12 30550
## + Heating 5 1.3721e+10 1.9342e+12 30551
## + BsmtFinSF2 1 2.8131e+09 1.9451e+12 30551
## <none> 1.9479e+12 30551
## + GarageCond 5 1.3154e+10 1.9348e+12 30551
## + ExterCond 4 1.0028e+10 1.9379e+12 30551
## + TotRmsAbvGrd 1 9.6096e+08 1.9470e+12 30552
## + PoolArea 1 5.7196e+08 1.9474e+12 30552
## + Id 1 3.3513e+08 1.9476e+12 30553
## + Electrical 4 8.3103e+09 1.9396e+12 30553
## + Street 1 2.7029e+08 1.9477e+12 30553
## + FullBath 1 2.0857e+08 1.9477e+12 30553
## + YrSold 1 4.6303e+07 1.9479e+12 30553
## + MiscVal 1 9.5682e+06 1.9479e+12 30553
## + Fence 4 2.1713e+09 1.9458e+12 30557
## + MiscFeature 4 9.5678e+08 1.9470e+12 30558
## - OverallQual 1 4.3178e+11 2.3797e+12 30839
## - Neighborhood 24 6.6416e+11 2.6121e+12 30929
## - GrLivArea 1 6.7998e+11 2.6279e+12 30983
##
## Step: AIC=30364.65
## SalePrice ~ OverallQual + GrLivArea + Neighborhood + MSSubClass
##
## Df Sum of Sq RSS AIC
## + RoofMatl 7 1.7746e+11 1.5032e+12 30217
## + BsmtQual 4 1.4544e+11 1.5352e+12 30241
## + BsmtExposure 4 1.4464e+11 1.5360e+12 30242
## + KitchenQual 3 1.2710e+11 1.5535e+12 30257
## + BsmtFinSF1 1 1.0135e+11 1.5793e+12 30276
## + ExterQual 3 9.7965e+10 1.5827e+12 30284
## + BsmtFullBath 1 8.7366e+10 1.5933e+12 30289
## + BsmtFinType1 6 9.7365e+10 1.5833e+12 30290
## + GarageCars 1 5.9482e+10 1.6212e+12 30314
## + BsmtUnfSF 1 5.3419e+10 1.6272e+12 30320
## + PoolQC 3 4.5379e+10 1.6353e+12 30331
## + BedroomAbvGr 1 3.8351e+10 1.6423e+12 30333
## + GarageArea 1 3.7228e+10 1.6434e+12 30334
## + GarageFinish 3 4.0923e+10 1.6397e+12 30335
## + GarageQual 3 4.0923e+10 1.6397e+12 30335
## + YearBuilt 1 3.4996e+10 1.6457e+12 30336
## + OverallCond 1 3.3814e+10 1.6468e+12 30337
## + LotArea 1 3.3437e+10 1.6472e+12 30338
## + LandContour 3 3.6228e+10 1.6444e+12 30339
## + YearRemodAdd 1 3.1639e+10 1.6490e+12 30339
## + SaleCondition 5 3.8619e+10 1.6420e+12 30341
## + WoodDeckSF 1 2.5464e+10 1.6552e+12 30345
## + KitchenAbvGr 1 2.5145e+10 1.6555e+12 30345
## + SaleType 8 4.0575e+10 1.6401e+12 30345
## + TotalBsmtSF 1 2.2173e+10 1.6585e+12 30347
## + Condition2 7 3.5780e+10 1.6449e+12 30347
## + MasVnrArea 1 2.1244e+10 1.6594e+12 30348
## + Fireplaces 1 2.0931e+10 1.6597e+12 30349
## + FireplaceQu 5 2.7714e+10 1.6529e+12 30351
## + HouseStyle 7 3.1329e+10 1.6493e+12 30351
## + LandSlope 2 1.7407e+10 1.6632e+12 30354
## + Functional 6 2.5868e+10 1.6548e+12 30354
## + ScreenPorch 1 1.3736e+10 1.6669e+12 30355
## + GarageYrBlt 1 1.2616e+10 1.6680e+12 30356
## + LotConfig 4 1.8851e+10 1.6618e+12 30356
## + MasVnrType 3 1.6253e+10 1.6644e+12 30357
## + BsmtCond 4 1.8207e+10 1.6624e+12 30357
## + LotShape 3 1.5208e+10 1.6654e+12 30358
## + HeatingQC 4 1.7366e+10 1.6633e+12 30358
## + Exterior1st 14 3.9569e+10 1.6411e+12 30358
## + Foundation 5 1.7154e+10 1.6635e+12 30360
## + CentralAir 1 7.3471e+09 1.6733e+12 30360
## + Condition1 8 2.2757e+10 1.6579e+12 30361
## + `1stFlrSF` 1 6.4575e+09 1.6742e+12 30361
## + HalfBath 1 5.7749e+09 1.6749e+12 30362
## + BsmtHalfBath 1 5.0596e+09 1.6756e+12 30362
## + EnclosedPorch 1 4.4410e+09 1.6762e+12 30363
## + MoSold 1 4.3005e+09 1.6763e+12 30363
## + LowQualFinSF 1 4.0960e+09 1.6766e+12 30363
## + Utilities 1 4.0938e+09 1.6766e+12 30363
## + Exterior2nd 15 3.6056e+10 1.6446e+12 30363
## + PavedDrive 2 6.2036e+09 1.6744e+12 30363
## + `2ndFlrSF` 1 3.7559e+09 1.6769e+12 30363
## + LotFrontage 1 3.0458e+09 1.6776e+12 30364
## + Electrical 4 9.5867e+09 1.6711e+12 30364
## + ExterCond 4 9.4654e+09 1.6712e+12 30365
## <none> 1.6806e+12 30365
## + OpenPorchSF 1 2.2369e+09 1.6784e+12 30365
## + Heating 5 1.1264e+10 1.6694e+12 30365
## + `3SsnPorch` 1 1.7201e+09 1.6789e+12 30365
## + RoofStyle 5 1.0550e+10 1.6701e+12 30366
## + TotRmsAbvGrd 1 1.3030e+09 1.6793e+12 30366
## + BsmtFinType2 6 1.2812e+10 1.6678e+12 30366
## + Street 1 4.5384e+08 1.6802e+12 30366
## + Id 1 2.1664e+08 1.6804e+12 30367
## + BsmtFinSF2 1 1.5767e+08 1.6805e+12 30367
## + GarageCond 5 9.3535e+09 1.6713e+12 30367
## + FullBath 1 8.3918e+07 1.6806e+12 30367
## + MiscVal 1 7.4222e+07 1.6806e+12 30367
## + YrSold 1 4.8441e+07 1.6806e+12 30367
## + PoolArea 1 2.6639e+07 1.6806e+12 30367
## + BldgType 3 4.1900e+09 1.6765e+12 30367
## + MSZoning 4 5.2463e+09 1.6754e+12 30368
## + Alley 2 5.7093e+08 1.6801e+12 30368
## + GarageType 6 6.9343e+09 1.6737e+12 30371
## + Fence 4 1.2976e+09 1.6793e+12 30372
## + MiscFeature 4 4.7733e+08 1.6802e+12 30372
## - MSSubClass 14 2.6728e+11 1.9479e+12 30551
## - OverallQual 1 3.4597e+11 2.0266e+12 30634
## - Neighborhood 24 5.0292e+11 2.1836e+12 30697
## - GrLivArea 1 6.4100e+11 2.3216e+12 30832
##
## Step: AIC=30216.73
## SalePrice ~ OverallQual + GrLivArea + Neighborhood + MSSubClass +
## RoofMatl
##
## Df Sum of Sq RSS AIC
## + BsmtFinSF1 1 1.8959e+11 1.3136e+12 30023
## + BsmtExposure 4 1.5050e+11 1.3527e+12 30072
## + BsmtQual 4 1.4991e+11 1.3533e+12 30072
## + KitchenQual 3 1.2995e+11 1.3732e+12 30092
## + ExterQual 3 1.1742e+11 1.3858e+12 30105
## + BsmtFullBath 1 9.9787e+10 1.4034e+12 30119
## + BsmtFinType1 6 1.0248e+11 1.4007e+12 30126
## + TotalBsmtSF 1 7.4677e+10 1.4285e+12 30145
## + BsmtUnfSF 1 6.5004e+10 1.4382e+12 30155
## + BedroomAbvGr 1 5.7408e+10 1.4458e+12 30162
## + YearBuilt 1 4.9609e+10 1.4536e+12 30170
## + GarageCars 1 4.6300e+10 1.4569e+12 30173
## + GarageArea 1 4.5358e+10 1.4578e+12 30174
## + LotArea 1 4.1540e+10 1.4616e+12 30178
## + SaleCondition 5 4.8462e+10 1.4547e+12 30179
## + SaleType 8 5.2032e+10 1.4512e+12 30182
## + GarageFinish 3 4.0532e+10 1.4627e+12 30183
## + GarageQual 3 4.0532e+10 1.4627e+12 30183
## + OverallCond 1 3.5990e+10 1.4672e+12 30184
## + YearRemodAdd 1 3.4140e+10 1.4690e+12 30185
## + Condition2 7 4.3440e+10 1.4597e+12 30188
## + HouseStyle 7 4.1399e+10 1.4618e+12 30190
## + KitchenAbvGr 1 2.9210e+10 1.4740e+12 30190
## + MasVnrArea 1 2.7118e+10 1.4761e+12 30192
## + `1stFlrSF` 1 2.6280e+10 1.4769e+12 30193
## + Functional 6 3.3609e+10 1.4696e+12 30196
## + Fireplaces 1 2.2458e+10 1.4807e+12 30197
## + MasVnrType 3 2.4547e+10 1.4786e+12 30199
## + LandContour 3 2.2960e+10 1.4802e+12 30200
## + PoolQC 3 2.2645e+10 1.4805e+12 30201
## + WoodDeckSF 1 1.8547e+10 1.4846e+12 30201
## + `2ndFlrSF` 1 1.7300e+10 1.4859e+12 30202
## + BsmtCond 4 2.0226e+10 1.4830e+12 30205
## + GarageYrBlt 1 1.3760e+10 1.4894e+12 30205
## + PoolArea 1 1.3447e+10 1.4897e+12 30206
## + Foundation 5 2.0770e+10 1.4824e+12 30207
## + LandSlope 2 1.4557e+10 1.4886e+12 30207
## + FireplaceQu 5 2.0666e+10 1.4825e+12 30207
## + HeatingQC 4 1.8123e+10 1.4851e+12 30207
## + LotConfig 4 1.8019e+10 1.4852e+12 30207
## + ScreenPorch 1 9.8496e+09 1.4933e+12 30209
## + LotShape 3 1.3947e+10 1.4892e+12 30209
## + LowQualFinSF 1 9.6011e+09 1.4936e+12 30209
## + MoSold 1 7.9190e+09 1.4953e+12 30211
## + CentralAir 1 7.0249e+09 1.4962e+12 30212
## + RoofStyle 5 1.4357e+10 1.4888e+12 30213
## + Exterior1st 14 3.2047e+10 1.4711e+12 30214
## + TotRmsAbvGrd 1 5.4480e+09 1.4977e+12 30214
## + Condition1 8 1.9797e+10 1.4834e+12 30214
## + PavedDrive 2 6.6726e+09 1.4965e+12 30214
## + BsmtHalfBath 1 4.4347e+09 1.4988e+12 30214
## + Utilities 1 4.0758e+09 1.4991e+12 30215
## + Electrical 4 1.0242e+10 1.4929e+12 30215
## + ExterCond 4 1.0146e+10 1.4930e+12 30215
## + EnclosedPorch 1 3.9215e+09 1.4993e+12 30215
## + HalfBath 1 3.4827e+09 1.4997e+12 30215
## + BsmtFinType2 6 1.3742e+10 1.4894e+12 30215
## + OpenPorchSF 1 3.3870e+09 1.4998e+12 30216
## + LotFrontage 1 3.2359e+09 1.5000e+12 30216
## + Heating 5 1.0679e+10 1.4925e+12 30216
## <none> 1.5032e+12 30217
## + `3SsnPorch` 1 1.4257e+09 1.5018e+12 30217
## + GarageCond 5 9.1471e+09 1.4940e+12 30218
## + FullBath 1 8.0641e+08 1.5024e+12 30218
## + Street 1 4.6066e+08 1.5027e+12 30218
## + MiscVal 1 4.8918e+07 1.5031e+12 30219
## + BsmtFinSF2 1 3.4035e+07 1.5032e+12 30219
## + YrSold 1 1.2731e+07 1.5032e+12 30219
## + Id 1 1.2696e+07 1.5032e+12 30219
## + BldgType 3 4.0896e+09 1.4991e+12 30219
## + Exterior2nd 15 2.8561e+10 1.4746e+12 30219
## + MSZoning 4 5.7423e+09 1.4974e+12 30219
## + Alley 2 6.8784e+08 1.5025e+12 30220
## + GarageType 6 8.7122e+09 1.4945e+12 30220
## + Fence 4 3.8914e+09 1.4993e+12 30221
## + MiscFeature 4 8.4358e+08 1.5023e+12 30224
## - RoofMatl 7 1.7746e+11 1.6806e+12 30365
## - MSSubClass 14 2.8415e+11 1.7873e+12 30440
## - OverallQual 1 3.1767e+11 1.8209e+12 30493
## - Neighborhood 24 4.4385e+11 1.9470e+12 30544
## - GrLivArea 1 7.1682e+11 2.2200e+12 30781
##
## Step: AIC=30023.11
## SalePrice ~ OverallQual + GrLivArea + Neighborhood + MSSubClass +
## RoofMatl + BsmtFinSF1
##
## Df Sum of Sq RSS AIC
## + BsmtQual 4 1.0306e+11 1.2105e+12 29913
## + KitchenQual 3 9.9265e+10 1.2143e+12 29915
## + ExterQual 3 9.9089e+10 1.2145e+12 29915
## + BsmtExposure 4 7.6182e+10 1.2374e+12 29944
## + Condition2 7 6.4758e+10 1.2488e+12 29964
## + SaleCondition 5 5.7551e+10 1.2560e+12 29968
## + SaleType 8 5.7040e+10 1.2566e+12 29975
## + GarageCars 1 3.6436e+10 1.2772e+12 29984
## + YearBuilt 1 3.5246e+10 1.2784e+12 29986
## + YearRemodAdd 1 3.4336e+10 1.2793e+12 29987
## + OverallCond 1 3.2846e+10 1.2808e+12 29988
## + GarageArea 1 2.9260e+10 1.2843e+12 29992
## + LotArea 1 2.8106e+10 1.2855e+12 29994
## + BedroomAbvGr 1 2.3997e+10 1.2896e+12 29998
## + TotalBsmtSF 1 2.1590e+10 1.2920e+12 30001
## + Functional 6 2.6957e+10 1.2866e+12 30005
## + GarageFinish 3 2.0132e+10 1.2935e+12 30007
## + GarageQual 3 2.0132e+10 1.2935e+12 30007
## + GarageYrBlt 1 1.5180e+10 1.2984e+12 30008
## + LandContour 3 1.8491e+10 1.2951e+12 30009
## + HeatingQC 4 2.0219e+10 1.2934e+12 30009
## + MasVnrArea 1 1.4807e+10 1.2988e+12 30009
## + PoolQC 3 1.6264e+10 1.2973e+12 30011
## + KitchenAbvGr 1 1.2355e+10 1.3012e+12 30011
## + LotConfig 4 1.7199e+10 1.2964e+12 30012
## + Condition1 8 2.3559e+10 1.2900e+12 30013
## + PoolArea 1 1.0776e+10 1.3028e+12 30013
## + FireplaceQu 5 1.7568e+10 1.2960e+12 30014
## + MasVnrType 3 1.3573e+10 1.3000e+12 30014
## + BsmtUnfSF 1 9.5232e+09 1.3041e+12 30015
## + Foundation 5 1.6689e+10 1.2969e+12 30015
## + WoodDeckSF 1 9.0974e+09 1.3045e+12 30015
## + HouseStyle 7 1.9683e+10 1.2939e+12 30015
## + Fireplaces 1 8.8487e+09 1.3047e+12 30015
## + LotShape 3 1.1694e+10 1.3019e+12 30016
## + ScreenPorch 1 7.9973e+09 1.3056e+12 30016
## + LowQualFinSF 1 7.1055e+09 1.3065e+12 30017
## + `1stFlrSF` 1 6.7446e+09 1.3069e+12 30018
## + MoSold 1 6.3246e+09 1.3073e+12 30018
## + Exterior1st 14 2.9319e+10 1.2843e+12 30018
## + Heating 5 1.3029e+10 1.3006e+12 30019
## + BsmtFinType2 6 1.4538e+10 1.2991e+12 30019
## + BsmtCond 4 1.0914e+10 1.3027e+12 30019
## + BsmtFullBath 1 4.1276e+09 1.3095e+12 30021
## + BsmtFinSF2 1 3.9838e+09 1.3096e+12 30021
## + BsmtFinType1 6 1.2693e+10 1.3009e+12 30021
## + CentralAir 1 3.6331e+09 1.3100e+12 30021
## + LotFrontage 1 3.5337e+09 1.3101e+12 30021
## + LandSlope 2 5.1343e+09 1.3085e+12 30021
## + `2ndFlrSF` 1 3.1257e+09 1.3105e+12 30022
## + EnclosedPorch 1 2.3782e+09 1.3112e+12 30023
## + ExterCond 4 7.7073e+09 1.3059e+12 30023
## + OpenPorchSF 1 2.1488e+09 1.3114e+12 30023
## + Utilities 1 2.0700e+09 1.3115e+12 30023
## <none> 1.3136e+12 30023
## + HalfBath 1 1.6464e+09 1.3120e+12 30023
## + RoofStyle 5 8.5309e+09 1.3051e+12 30024
## + BsmtHalfBath 1 1.2683e+09 1.3123e+12 30024
## + `3SsnPorch` 1 1.1681e+09 1.3124e+12 30024
## + Exterior2nd 15 2.6107e+10 1.2875e+12 30024
## + FullBath 1 7.0127e+08 1.3129e+12 30024
## + BldgType 3 4.2641e+09 1.3093e+12 30024
## + MSZoning 4 5.7763e+09 1.3078e+12 30025
## + PavedDrive 2 2.0233e+09 1.3116e+12 30025
## + Id 1 1.2163e+08 1.3135e+12 30025
## + Street 1 8.2664e+07 1.3135e+12 30025
## + TotRmsAbvGrd 1 5.8815e+07 1.3135e+12 30025
## + MiscVal 1 4.4952e+07 1.3136e+12 30025
## + YrSold 1 9.2333e+05 1.3136e+12 30025
## + Electrical 4 4.4447e+09 1.3092e+12 30026
## + Alley 2 3.0567e+08 1.3133e+12 30027
## + Fence 4 3.7720e+09 1.3098e+12 30027
## + GarageType 6 7.0112e+09 1.3066e+12 30027
## + GarageCond 5 4.9700e+09 1.3086e+12 30028
## + MiscFeature 4 7.6709e+08 1.3128e+12 30030
## - MSSubClass 14 2.0993e+11 1.5235e+12 30210
## - BsmtFinSF1 1 1.8959e+11 1.5032e+12 30217
## - RoofMatl 7 2.6570e+11 1.5793e+12 30276
## - OverallQual 1 2.7493e+11 1.5885e+12 30297
## - Neighborhood 24 3.9622e+11 1.7098e+12 30358
## - GrLivArea 1 6.2632e+11 1.9399e+12 30587
##
## Step: AIC=29912.56
## SalePrice ~ OverallQual + GrLivArea + Neighborhood + MSSubClass +
## RoofMatl + BsmtFinSF1 + BsmtQual
##
## Df Sum of Sq RSS AIC
## + Condition2 7 7.2123e+10 1.1384e+12 29837
## + KitchenQual 3 6.4333e+10 1.1462e+12 29839
## + BsmtExposure 4 6.2691e+10 1.1478e+12 29843
## + ExterQual 3 5.3899e+10 1.1566e+12 29853
## + OverallCond 1 4.5015e+10 1.1655e+12 29860
## + LotArea 1 3.4420e+10 1.1761e+12 29873
## + YearRemodAdd 1 2.9559e+10 1.1810e+12 29879
## + GarageCars 1 2.9331e+10 1.1812e+12 29879
## + SaleCondition 5 3.5145e+10 1.1754e+12 29880
## + TotalBsmtSF 1 2.7106e+10 1.1834e+12 29882
## + GarageArea 1 2.4596e+10 1.1859e+12 29885
## + YearBuilt 1 2.2290e+10 1.1882e+12 29888
## + SaleType 8 3.2343e+10 1.1782e+12 29889
## + Functional 6 2.7495e+10 1.1830e+12 29891
## + BedroomAbvGr 1 1.4135e+10 1.1964e+12 29898
## + KitchenAbvGr 1 1.2908e+10 1.1976e+12 29899
## + Fireplaces 1 1.2824e+10 1.1977e+12 29899
## + LandContour 3 1.5817e+10 1.1947e+12 29900
## + LotConfig 4 1.7314e+10 1.1932e+12 29900
## + PoolQC 3 1.5368e+10 1.1952e+12 29900
## + PoolArea 1 1.0943e+10 1.1996e+12 29901
## + Condition1 8 2.2420e+10 1.1881e+12 29901
## + HouseStyle 7 2.0399e+10 1.1901e+12 29902
## + HeatingQC 4 1.5356e+10 1.1952e+12 29902
## + BsmtUnfSF 1 9.2211e+09 1.2013e+12 29904
## + LotShape 3 1.2010e+10 1.1985e+12 29904
## + ScreenPorch 1 8.5455e+09 1.2020e+12 29904
## + MasVnrArea 1 8.0882e+09 1.2025e+12 29905
## + LowQualFinSF 1 7.5140e+09 1.2030e+12 29906
## + BsmtCond 3 1.0671e+10 1.1999e+12 29906
## + WoodDeckSF 1 7.3389e+09 1.2032e+12 29906
## + GarageYrBlt 1 7.2552e+09 1.2033e+12 29906
## + GarageFinish 3 1.0414e+10 1.2001e+12 29906
## + GarageQual 3 1.0414e+10 1.2001e+12 29906
## + CentralAir 1 6.0861e+09 1.2045e+12 29907
## + `1stFlrSF` 1 5.7924e+09 1.2047e+12 29908
## + Heating 5 1.2072e+10 1.1985e+12 29908
## + ExterCond 4 1.0245e+10 1.2003e+12 29908
## + LandSlope 2 6.2911e+09 1.2042e+12 29909
## + MasVnrType 3 7.6935e+09 1.2028e+12 29909
## + BsmtFinSF2 1 4.1690e+09 1.2064e+12 29910
## + Exterior1st 14 2.5581e+10 1.1850e+12 29910
## + BsmtFullBath 1 4.0872e+09 1.2065e+12 29910
## + MoSold 1 3.9368e+09 1.2066e+12 29910
## + BsmtFinType2 6 1.1685e+10 1.1989e+12 29911
## + BsmtFinType1 5 9.6610e+09 1.2009e+12 29911
## + Foundation 5 9.4204e+09 1.2011e+12 29911
## + MSZoning 4 7.4853e+09 1.2031e+12 29912
## + `2ndFlrSF` 1 2.4284e+09 1.2081e+12 29912
## + LotFrontage 1 1.6946e+09 1.2088e+12 29913
## <none> 1.2105e+12 29913
## + `3SsnPorch` 1 1.5342e+09 1.2090e+12 29913
## + FullBath 1 1.4692e+09 1.2091e+12 29913
## + Utilities 1 1.3096e+09 1.2092e+12 29913
## + EnclosedPorch 1 1.2606e+09 1.2093e+12 29913
## + FireplaceQu 5 7.6620e+09 1.2029e+12 29913
## + HalfBath 1 9.3974e+08 1.2096e+12 29913
## + BsmtHalfBath 1 5.5231e+08 1.2100e+12 29914
## + OpenPorchSF 1 4.7915e+08 1.2101e+12 29914
## + PavedDrive 2 2.0800e+09 1.2085e+12 29914
## + Id 1 3.6423e+08 1.2102e+12 29914
## + Street 1 2.2739e+08 1.2103e+12 29914
## + TotRmsAbvGrd 1 1.6571e+08 1.2104e+12 29914
## + MiscVal 1 1.1938e+08 1.2104e+12 29914
## + Electrical 4 5.0633e+09 1.2055e+12 29915
## + GarageCond 5 6.6969e+09 1.2038e+12 29915
## + YrSold 1 2.4436e+06 1.2105e+12 29915
## + BldgType 3 2.2915e+09 1.2082e+12 29916
## + Alley 2 9.8568e+07 1.2104e+12 29916
## + GarageType 6 6.3450e+09 1.2042e+12 29917
## + RoofStyle 5 4.3446e+09 1.2062e+12 29917
## + Fence 4 1.6691e+09 1.2089e+12 29919
## + MiscFeature 4 7.7922e+08 1.2098e+12 29920
## + Exterior2nd 15 1.8853e+10 1.1917e+12 29920
## - BsmtQual 4 1.0306e+11 1.3136e+12 30023
## - MSSubClass 14 1.6159e+11 1.3721e+12 30066
## - BsmtFinSF1 1 1.4273e+11 1.3533e+12 30072
## - OverallQual 1 1.8101e+11 1.3916e+12 30113
## - Neighborhood 24 2.7913e+11 1.4897e+12 30166
## - RoofMatl 7 2.5874e+11 1.4693e+12 30180
## - GrLivArea 1 5.6228e+11 1.7728e+12 30464
##
## Step: AIC=29837.42
## SalePrice ~ OverallQual + GrLivArea + Neighborhood + MSSubClass +
## RoofMatl + BsmtFinSF1 + BsmtQual + Condition2
##
## Df Sum of Sq RSS AIC
## + KitchenQual 3 6.8801e+10 1.0696e+12 29753
## + ExterQual 3 6.5035e+10 1.0734e+12 29758
## + BsmtExposure 4 6.3681e+10 1.0747e+12 29762
## + OverallCond 1 4.2662e+10 1.0958e+12 29784
## + LotArea 1 3.8508e+10 1.0999e+12 29790
## + SaleCondition 5 4.3428e+10 1.0950e+12 29791
## + TotalBsmtSF 1 3.2094e+10 1.1063e+12 29798
## + SaleType 8 4.1770e+10 1.0966e+12 29799
## + YearRemodAdd 1 2.8904e+10 1.1095e+12 29802
## + GarageCars 1 2.8096e+10 1.1103e+12 29803
## + GarageArea 1 2.6008e+10 1.1124e+12 29806
## + YearBuilt 1 2.5719e+10 1.1127e+12 29806
## + Functional 6 3.0553e+10 1.1079e+12 29810
## + BedroomAbvGr 1 1.9971e+10 1.1184e+12 29814
## + KitchenAbvGr 1 1.2738e+10 1.1257e+12 29823
## + MasVnrArea 1 1.2638e+10 1.1258e+12 29823
## + HouseStyle 7 2.1773e+10 1.1166e+12 29823
## + BsmtUnfSF 1 1.1806e+10 1.1266e+12 29824
## + Exterior1st 14 3.1756e+10 1.1067e+12 29824
## + LotConfig 4 1.6179e+10 1.1222e+12 29825
## + HeatingQC 4 1.5569e+10 1.1228e+12 29825
## + PoolQC 3 1.3986e+10 1.1244e+12 29826
## + PoolArea 1 9.8755e+09 1.1285e+12 29827
## + Fireplaces 1 9.2163e+09 1.1292e+12 29828
## + LotShape 3 1.1564e+10 1.1269e+12 29829
## + LandContour 3 1.1481e+10 1.1269e+12 29829
## + GarageYrBlt 1 8.1597e+09 1.1303e+12 29829
## + GarageFinish 3 1.0372e+10 1.1280e+12 29830
## + GarageQual 3 1.0372e+10 1.1280e+12 29830
## + ScreenPorch 1 7.1729e+09 1.1312e+12 29830
## + BsmtCond 3 1.0261e+10 1.1282e+12 29830
## + `1stFlrSF` 1 6.8722e+09 1.1315e+12 29831
## + WoodDeckSF 1 6.7775e+09 1.1316e+12 29831
## + LowQualFinSF 1 6.5087e+09 1.1319e+12 29831
## + Heating 5 1.1946e+10 1.1265e+12 29832
## + CentralAir 1 5.4737e+09 1.1329e+12 29832
## + BsmtFinType1 5 1.0938e+10 1.1275e+12 29833
## + MasVnrType 3 7.3242e+09 1.1311e+12 29834
## + BsmtFinSF2 1 4.1098e+09 1.1343e+12 29834
## + Condition1 8 1.4974e+10 1.1234e+12 29834
## + LandSlope 2 5.5222e+09 1.1329e+12 29834
## + BsmtFinType2 6 1.1731e+10 1.1267e+12 29834
## + Foundation 5 1.0161e+10 1.1283e+12 29834
## + `2ndFlrSF` 1 3.3620e+09 1.1351e+12 29835
## + LotFrontage 1 3.2278e+09 1.1352e+12 29835
## + MoSold 1 3.1937e+09 1.1352e+12 29835
## + Exterior2nd 15 2.4774e+10 1.1136e+12 29836
## + MSZoning 4 7.5691e+09 1.1308e+12 29836
## + BsmtFullBath 1 2.6714e+09 1.1357e+12 29836
## + ExterCond 4 6.3734e+09 1.1320e+12 29837
## <none> 1.1384e+12 29837
## + `3SsnPorch` 1 1.2689e+09 1.1371e+12 29838
## + TotRmsAbvGrd 1 1.2522e+09 1.1372e+12 29838
## + RoofStyle 5 7.4410e+09 1.1310e+12 29838
## + Utilities 1 1.1047e+09 1.1373e+12 29838
## + EnclosedPorch 1 1.1007e+09 1.1373e+12 29838
## + FullBath 1 7.8009e+08 1.1376e+12 29838
## + OpenPorchSF 1 6.8561e+08 1.1377e+12 29839
## + Electrical 4 5.2999e+09 1.1331e+12 29839
## + HalfBath 1 5.2297e+08 1.1379e+12 29839
## + MiscVal 1 4.5827e+08 1.1380e+12 29839
## + BsmtHalfBath 1 4.4284e+08 1.1380e+12 29839
## + Id 1 4.0386e+08 1.1380e+12 29839
## + Street 1 2.3119e+08 1.1382e+12 29839
## + PavedDrive 2 1.6932e+09 1.1367e+12 29839
## + YrSold 1 1.2649e+07 1.1384e+12 29839
## + FireplaceQu 5 6.0641e+09 1.1324e+12 29840
## + GarageCond 5 5.8984e+09 1.1325e+12 29840
## + GarageType 6 7.1317e+09 1.1313e+12 29840
## + BldgType 3 2.4012e+09 1.1360e+12 29840
## + Alley 2 1.1376e+08 1.1383e+12 29841
## + Fence 4 1.6528e+09 1.1368e+12 29843
## + MiscFeature 4 1.1994e+09 1.1372e+12 29844
## - Condition2 7 7.2123e+10 1.2105e+12 29913
## - BsmtQual 4 1.1042e+11 1.2488e+12 29964
## - MSSubClass 14 1.6786e+11 1.3063e+12 30009
## - BsmtFinSF1 1 1.6170e+11 1.3001e+12 30028
## - OverallQual 1 1.8120e+11 1.3196e+12 30050
## - Neighborhood 24 2.5887e+11 1.3973e+12 30087
## - RoofMatl 7 2.7775e+11 1.4162e+12 30140
## - GrLivArea 1 5.9741e+11 1.7358e+12 30448
##
## Step: AIC=29752.97
## SalePrice ~ OverallQual + GrLivArea + Neighborhood + MSSubClass +
## RoofMatl + BsmtFinSF1 + BsmtQual + Condition2 + KitchenQual
##
## Df Sum of Sq RSS AIC
## + BsmtExposure 4 6.8849e+10 1.0008e+12 29664
## + LotArea 1 4.0458e+10 1.0292e+12 29699
## + SaleCondition 5 4.1172e+10 1.0284e+12 29706
## + OverallCond 1 3.2106e+10 1.0375e+12 29711
## + ExterQual 3 3.3914e+10 1.0357e+12 29712
## + TotalBsmtSF 1 2.8873e+10 1.0407e+12 29715
## + GarageCars 1 2.5861e+10 1.0438e+12 29720
## + SaleType 8 3.5620e+10 1.0340e+12 29720
## + GarageArea 1 2.4466e+10 1.0451e+12 29721
## + YearBuilt 1 2.2057e+10 1.0476e+12 29725
## + Functional 6 2.7543e+10 1.0421e+12 29727
## + YearRemodAdd 1 1.5447e+10 1.0542e+12 29734
## + MasVnrArea 1 1.4736e+10 1.0549e+12 29735
## + LotConfig 4 1.8116e+10 1.0515e+12 29736
## + BedroomAbvGr 1 1.3321e+10 1.0563e+12 29737
## + KitchenAbvGr 1 1.1599e+10 1.0580e+12 29739
## + HouseStyle 7 1.9811e+10 1.0498e+12 29740
## + PoolQC 3 1.3075e+10 1.0565e+12 29741
## + BsmtUnfSF 1 1.0017e+10 1.0596e+12 29741
## + LandContour 3 1.2105e+10 1.0575e+12 29743
## + LotShape 3 1.2056e+10 1.0576e+12 29743
## + PoolArea 1 8.7435e+09 1.0609e+12 29743
## + Fireplaces 1 8.7164e+09 1.0609e+12 29743
## + LowQualFinSF 1 7.5066e+09 1.0621e+12 29745
## + WoodDeckSF 1 6.9592e+09 1.0627e+12 29746
## + BsmtCond 3 9.3743e+09 1.0602e+12 29746
## + ScreenPorch 1 6.0115e+09 1.0636e+12 29747
## + `1stFlrSF` 1 6.0078e+09 1.0636e+12 29747
## + GarageYrBlt 1 5.5382e+09 1.0641e+12 29747
## + HeatingQC 4 9.3819e+09 1.0602e+12 29748
## + CentralAir 1 4.9217e+09 1.0647e+12 29748
## + BsmtFinType2 6 1.2131e+10 1.0575e+12 29748
## + Exterior1st 14 2.3727e+10 1.0459e+12 29748
## + LandSlope 2 5.9199e+09 1.0637e+12 29749
## + BsmtFinSF2 1 4.2439e+09 1.0654e+12 29749
## + GarageFinish 3 7.0313e+09 1.0626e+12 29749
## + GarageQual 3 7.0313e+09 1.0626e+12 29749
## + LotFrontage 1 3.3861e+09 1.0662e+12 29750
## + Heating 5 9.0611e+09 1.0606e+12 29751
## + MoSold 1 3.0380e+09 1.0666e+12 29751
## + Condition1 8 1.3265e+10 1.0563e+12 29751
## + MasVnrType 3 5.5787e+09 1.0640e+12 29751
## + `2ndFlrSF` 1 2.5939e+09 1.0670e+12 29751
## + MSZoning 4 6.6748e+09 1.0629e+12 29752
## + Foundation 5 7.7685e+09 1.0618e+12 29752
## + TotRmsAbvGrd 1 1.7164e+09 1.0679e+12 29753
## + BsmtFullBath 1 1.6902e+09 1.0679e+12 29753
## <none> 1.0696e+12 29753
## + BsmtFinType1 5 7.3296e+09 1.0623e+12 29753
## + GarageCond 5 7.3017e+09 1.0623e+12 29753
## + Utilities 1 1.4117e+09 1.0682e+12 29753
## + RoofStyle 5 7.2494e+09 1.0624e+12 29753
## + EnclosedPorch 1 1.3688e+09 1.0682e+12 29753
## + FullBath 1 1.2184e+09 1.0684e+12 29753
## + `3SsnPorch` 1 1.0925e+09 1.0685e+12 29754
## + MiscVal 1 7.2525e+08 1.0689e+12 29754
## + ExterCond 4 5.0669e+09 1.0645e+12 29754
## + OpenPorchSF 1 4.9072e+08 1.0691e+12 29754
## + Street 1 3.4617e+08 1.0693e+12 29755
## + BsmtHalfBath 1 3.1241e+08 1.0693e+12 29755
## + YrSold 1 1.3193e+08 1.0695e+12 29755
## + HalfBath 1 1.1223e+08 1.0695e+12 29755
## + PavedDrive 2 1.5763e+09 1.0680e+12 29755
## + Id 1 2.0005e+07 1.0696e+12 29755
## + Electrical 4 4.2011e+09 1.0654e+12 29755
## + GarageType 6 6.9084e+09 1.0627e+12 29756
## + BldgType 3 2.1761e+09 1.0674e+12 29756
## + Alley 2 8.3443e+07 1.0695e+12 29757
## + Fence 4 1.9417e+09 1.0677e+12 29758
## + FireplaceQu 5 3.3664e+09 1.0662e+12 29758
## + MiscFeature 4 1.5345e+09 1.0681e+12 29759
## + Exterior2nd 15 1.3367e+10 1.0562e+12 29765
## - KitchenQual 3 6.8801e+10 1.1384e+12 29837
## - Condition2 7 7.6591e+10 1.1462e+12 29839
## - BsmtQual 4 7.2129e+10 1.1417e+12 29840
## - OverallQual 1 1.1825e+11 1.1879e+12 29903
## - MSSubClass 14 1.4442e+11 1.2140e+12 29909
## - BsmtFinSF1 1 1.4342e+11 1.2130e+12 29934
## - Neighborhood 24 2.1927e+11 1.2889e+12 29976
## - RoofMatl 7 2.7460e+11 1.3442e+12 30071
## - GrLivArea 1 5.3870e+11 1.6083e+12 30343
##
## Step: AIC=29664.43
## SalePrice ~ OverallQual + GrLivArea + Neighborhood + MSSubClass +
## RoofMatl + BsmtFinSF1 + BsmtQual + Condition2 + KitchenQual +
## BsmtExposure
##
## Df Sum of Sq RSS AIC
## + OverallCond 1 3.3081e+10 9.6768e+11 29618
## + SaleCondition 5 3.8161e+10 9.6260e+11 29618
## + ExterQual 3 3.0459e+10 9.7031e+11 29626
## + LotArea 1 2.6177e+10 9.7459e+11 29628
## + GarageCars 1 2.2365e+10 9.7840e+11 29634
## + GarageArea 1 2.2267e+10 9.7850e+11 29634
## + SaleType 8 3.1286e+10 9.6948e+11 29634
## + YearBuilt 1 2.1399e+10 9.7937e+11 29635
## + TotalBsmtSF 1 1.9111e+10 9.8165e+11 29639
## + Functional 6 2.4046e+10 9.7672e+11 29641
## + YearRemodAdd 1 1.4957e+10 9.8581e+11 29645
## + PoolQC 3 1.6894e+10 9.8387e+11 29646
## + LotConfig 4 1.7320e+10 9.8345e+11 29647
## + PoolArea 1 1.1906e+10 9.8886e+11 29649
## + MasVnrArea 1 1.0855e+10 9.8991e+11 29651
## + BedroomAbvGr 1 9.2367e+09 9.9153e+11 29653
## + BsmtUnfSF 1 8.5801e+09 9.9219e+11 29654
## + HeatingQC 4 1.1875e+10 9.8889e+11 29655
## + BsmtCond 3 1.0275e+10 9.9049e+11 29656
## + HouseStyle 7 1.5126e+10 9.8564e+11 29656
## + Exterior1st 14 2.4550e+10 9.7622e+11 29656
## + LotShape 3 9.4306e+09 9.9134e+11 29657
## + KitchenAbvGr 1 6.3528e+09 9.9441e+11 29657
## + LowQualFinSF 1 6.2423e+09 9.9452e+11 29657
## + Fireplaces 1 5.4693e+09 9.9530e+11 29659
## + CentralAir 1 5.3368e+09 9.9543e+11 29659
## + GarageYrBlt 1 5.2686e+09 9.9550e+11 29659
## + ScreenPorch 1 5.0736e+09 9.9569e+11 29659
## + GarageFinish 3 7.1309e+09 9.9364e+11 29660
## + GarageQual 3 7.1309e+09 9.9364e+11 29660
## + MSZoning 4 8.0220e+09 9.9274e+11 29661
## + GarageCond 5 9.2017e+09 9.9156e+11 29661
## + Heating 5 8.6153e+09 9.9215e+11 29662
## + WoodDeckSF 1 3.1114e+09 9.9765e+11 29662
## + Condition1 8 1.2464e+10 9.8830e+11 29662
## + LandContour 3 5.2937e+09 9.9547e+11 29663
## + MoSold 1 2.4666e+09 9.9830e+11 29663
## + FullBath 1 2.0673e+09 9.9870e+11 29663
## + GarageType 6 8.9048e+09 9.9186e+11 29664
## + ExterCond 4 6.0663e+09 9.9470e+11 29664
## + `1stFlrSF` 1 1.8909e+09 9.9888e+11 29664
## + `3SsnPorch` 1 1.5483e+09 9.9922e+11 29664
## + LotFrontage 1 1.5225e+09 9.9924e+11 29664
## + EnclosedPorch 1 1.4551e+09 9.9931e+11 29664
## <none> 1.0008e+12 29664
## + BsmtFinSF2 1 1.2870e+09 9.9948e+11 29665
## + PavedDrive 2 2.4075e+09 9.9836e+11 29665
## + Foundation 5 6.4706e+09 9.9430e+11 29665
## + Utilities 1 8.4725e+08 9.9992e+11 29665
## + MasVnrType 3 3.5546e+09 9.9721e+11 29665
## + BsmtFinType1 5 6.2948e+09 9.9447e+11 29665
## + MiscVal 1 7.0444e+08 1.0001e+12 29665
## + BsmtFullBath 1 6.8123e+08 1.0001e+12 29665
## + TotRmsAbvGrd 1 4.1890e+08 1.0003e+12 29666
## + OpenPorchSF 1 3.8551e+08 1.0004e+12 29666
## + `2ndFlrSF` 1 3.7297e+08 1.0004e+12 29666
## + RoofStyle 5 5.7754e+09 9.9499e+11 29666
## + HalfBath 1 2.4538e+08 1.0005e+12 29666
## + BsmtHalfBath 1 4.0387e+07 1.0007e+12 29666
## + Street 1 3.2803e+07 1.0007e+12 29666
## + Id 1 1.1757e+07 1.0008e+12 29666
## + YrSold 1 6.1793e+05 1.0008e+12 29666
## + BldgType 3 1.5679e+09 9.9920e+11 29668
## + Electrical 4 2.9274e+09 9.9784e+11 29668
## + LandSlope 2 1.4174e+08 1.0006e+12 29668
## + Alley 2 9.9920e+06 1.0008e+12 29668
## + BsmtFinType2 6 5.4752e+09 9.9529e+11 29669
## + MiscFeature 4 1.3292e+09 9.9944e+11 29671
## + Fence 4 1.1654e+09 9.9960e+11 29671
## + FireplaceQu 5 1.8687e+09 9.9890e+11 29672
## + Exterior2nd 15 1.3779e+10 9.8699e+11 29674
## - BsmtQual 4 5.8704e+10 1.0595e+12 29739
## - BsmtExposure 4 6.8849e+10 1.0696e+12 29753
## - Condition2 7 7.7946e+10 1.0787e+12 29759
## - KitchenQual 3 7.3969e+10 1.0747e+12 29762
## - BsmtFinSF1 1 9.0013e+10 1.0908e+12 29787
## - OverallQual 1 1.0025e+11 1.1010e+12 29801
## - MSSubClass 14 1.4511e+11 1.1459e+12 29833
## - Neighborhood 24 2.1833e+11 1.2191e+12 29903
## - RoofMatl 7 2.6097e+11 1.2617e+12 29987
## - GrLivArea 1 5.3013e+11 1.5309e+12 30279
##
## Step: AIC=29617.66
## SalePrice ~ OverallQual + GrLivArea + Neighborhood + MSSubClass +
## RoofMatl + BsmtFinSF1 + BsmtQual + Condition2 + KitchenQual +
## BsmtExposure + OverallCond
##
## Df Sum of Sq RSS AIC
## + YearBuilt 1 3.7722e+10 9.2996e+11 29562
## + TotalBsmtSF 1 3.0509e+10 9.3718e+11 29573
## + SaleCondition 5 3.5626e+10 9.3206e+11 29573
## + GarageCars 1 2.7199e+10 9.4049e+11 29578
## + GarageArea 1 2.5728e+10 9.4196e+11 29581
## + SaleType 8 3.3771e+10 9.3391e+11 29582
## + LotArea 1 2.4544e+10 9.4314e+11 29582
## + ExterQual 3 2.6590e+10 9.4110e+11 29583
## + PoolQC 3 1.7405e+10 9.5028e+11 29597
## + BsmtUnfSF 1 1.4605e+10 9.5308e+11 29598
## + HouseStyle 7 2.1246e+10 9.4644e+11 29599
## + PoolArea 1 1.2480e+10 9.5520e+11 29601
## + MasVnrArea 1 1.1896e+10 9.5579e+11 29602
## + LotConfig 4 1.5619e+10 9.5207e+11 29602
## + Functional 6 1.8004e+10 9.4968e+11 29602
## + BedroomAbvGr 1 9.7143e+09 9.5797e+11 29605
## + Exterior1st 14 2.5216e+10 9.4247e+11 29607
## + Fireplaces 1 6.9235e+09 9.6076e+11 29609
## + GarageYrBlt 1 6.6441e+09 9.6104e+11 29610
## + LowQualFinSF 1 6.1275e+09 9.6156e+11 29610
## + HeatingQC 4 9.5410e+09 9.5814e+11 29611
## + LotShape 3 8.0620e+09 9.5962e+11 29612
## + GarageFinish 3 7.9730e+09 9.5971e+11 29612
## + GarageQual 3 7.9730e+09 9.5971e+11 29612
## + KitchenAbvGr 1 5.1956e+09 9.6249e+11 29612
## + `1stFlrSF` 1 4.7272e+09 9.6296e+11 29613
## + Foundation 5 9.9937e+09 9.5769e+11 29613
## + ScreenPorch 1 4.6917e+09 9.6299e+11 29613
## + Condition1 8 1.3454e+10 9.5423e+11 29613
## + YearRemodAdd 1 3.9315e+09 9.6375e+11 29614
## + LandContour 3 5.8025e+09 9.6188e+11 29615
## + BsmtCond 3 5.5192e+09 9.6217e+11 29615
## + Heating 5 7.9390e+09 9.5975e+11 29616
## + FullBath 1 2.2358e+09 9.6545e+11 29616
## + GarageCond 5 7.5188e+09 9.6017e+11 29616
## + LotFrontage 1 2.0765e+09 9.6561e+11 29617
## + MSZoning 4 5.9868e+09 9.6170e+11 29617
## + MoSold 1 1.9691e+09 9.6572e+11 29617
## + `2ndFlrSF` 1 1.9595e+09 9.6573e+11 29617
## + WoodDeckSF 1 1.8003e+09 9.6588e+11 29617
## + BsmtFinSF2 1 1.4398e+09 9.6625e+11 29618
## + CentralAir 1 1.4389e+09 9.6625e+11 29618
## + MasVnrType 3 4.0709e+09 9.6361e+11 29618
## <none> 9.6768e+11 29618
## + PavedDrive 2 2.5037e+09 9.6518e+11 29618
## + `3SsnPorch` 1 1.1538e+09 9.6653e+11 29618
## + BsmtFullBath 1 1.1470e+09 9.6654e+11 29618
## + Utilities 1 9.9459e+08 9.6669e+11 29618
## + GarageType 6 7.5037e+09 9.6018e+11 29618
## + EnclosedPorch 1 5.8820e+08 9.6710e+11 29619
## + BsmtFinType1 5 5.8479e+09 9.6184e+11 29619
## + TotRmsAbvGrd 1 4.2484e+08 9.6726e+11 29619
## + RoofStyle 5 5.7015e+09 9.6198e+11 29619
## + HalfBath 1 2.5046e+08 9.6743e+11 29619
## + OpenPorchSF 1 2.1984e+08 9.6746e+11 29619
## + MiscVal 1 1.6292e+08 9.6752e+11 29619
## + BsmtHalfBath 1 9.8871e+07 9.6759e+11 29620
## + YrSold 1 7.1700e+07 9.6761e+11 29620
## + Street 1 1.4848e+07 9.6767e+11 29620
## + Id 1 3.6830e+06 9.6768e+11 29620
## + BldgType 3 2.2809e+09 9.6540e+11 29620
## + LandSlope 2 1.3846e+08 9.6755e+11 29621
## + Alley 2 3.8268e+07 9.6765e+11 29622
## + Fence 4 2.0491e+09 9.6564e+11 29623
## + ExterCond 4 1.6880e+09 9.6600e+11 29623
## + FireplaceQu 5 2.8253e+09 9.6486e+11 29623
## + BsmtFinType2 6 4.0914e+09 9.6359e+11 29624
## + Exterior2nd 15 1.5273e+10 9.5241e+11 29625
## + Electrical 4 6.2293e+08 9.6706e+11 29625
## + MiscFeature 4 5.5720e+08 9.6713e+11 29625
## - OverallCond 1 3.3081e+10 1.0008e+12 29664
## - KitchenQual 3 6.3439e+10 1.0311e+12 29704
## - BsmtQual 4 6.6567e+10 1.0343e+12 29706
## - BsmtExposure 4 6.9824e+10 1.0375e+12 29711
## - Condition2 7 7.6023e+10 1.0437e+12 29713
## - BsmtFinSF1 1 8.6838e+10 1.0545e+12 29740
## - OverallQual 1 8.7263e+10 1.0549e+12 29741
## - MSSubClass 14 1.4238e+11 1.1101e+12 29789
## - Neighborhood 24 2.2947e+11 1.1972e+12 29878
## - RoofMatl 7 2.6233e+11 1.2300e+12 29952
## - GrLivArea 1 5.5492e+11 1.5226e+12 30273
##
## Step: AIC=29561.96
## SalePrice ~ OverallQual + GrLivArea + Neighborhood + MSSubClass +
## RoofMatl + BsmtFinSF1 + BsmtQual + Condition2 + KitchenQual +
## BsmtExposure + OverallCond + YearBuilt
##
## Df Sum of Sq RSS AIC
## + LotArea 1 2.9093e+10 9.0087e+11 29518
## + TotalBsmtSF 1 2.4286e+10 9.0568e+11 29526
## + SaleCondition 5 2.6800e+10 9.0316e+11 29530
## + GarageCars 1 2.0750e+10 9.0921e+11 29531
## + ExterQual 3 2.2233e+10 9.0773e+11 29533
## + GarageArea 1 1.9411e+10 9.1055e+11 29533
## + PoolQC 3 1.8767e+10 9.1120e+11 29538
## + SaleType 8 2.4583e+10 9.0538e+11 29539
## + PoolArea 1 1.3535e+10 9.1643e+11 29543
## + LotConfig 4 1.5642e+10 9.1432e+11 29545
## + Functional 6 1.7201e+10 9.1276e+11 29547
## + MasVnrArea 1 1.0186e+10 9.1978e+11 29548
## + BedroomAbvGr 1 9.9217e+09 9.2004e+11 29548
## + BsmtUnfSF 1 9.2800e+09 9.2068e+11 29549
## + Fireplaces 1 8.2724e+09 9.2169e+11 29551
## + HouseStyle 7 1.5854e+10 9.1411e+11 29551
## + Exterior1st 14 2.4006e+10 9.0596e+11 29552
## + ScreenPorch 1 6.7124e+09 9.2325e+11 29553
## + LotShape 3 8.8412e+09 9.2112e+11 29554
## + LowQualFinSF 1 6.2711e+09 9.2369e+11 29554
## + Condition1 8 1.4388e+10 9.1557e+11 29555
## + `1stFlrSF` 1 3.3085e+09 9.2665e+11 29559
## + LotFrontage 1 2.9754e+09 9.2699e+11 29559
## + KitchenAbvGr 1 2.7576e+09 9.2720e+11 29560
## + LandContour 3 5.1733e+09 9.2479e+11 29560
## + BsmtFinSF2 1 2.5954e+09 9.2737e+11 29560
## + MSZoning 4 6.3202e+09 9.2364e+11 29560
## + GarageFinish 3 4.5136e+09 9.2545e+11 29561
## + GarageQual 3 4.5136e+09 9.2545e+11 29561
## + Heating 5 6.9767e+09 9.2299e+11 29561
## + MoSold 1 1.8357e+09 9.2813e+11 29561
## + WoodDeckSF 1 1.5277e+09 9.2843e+11 29562
## + BsmtFullBath 1 1.5044e+09 9.2846e+11 29562
## <none> 9.2996e+11 29562
## + `2ndFlrSF` 1 1.0796e+09 9.2888e+11 29562
## + RoofStyle 5 6.1624e+09 9.2380e+11 29562
## + `3SsnPorch` 1 8.9436e+08 9.2907e+11 29563
## + GarageYrBlt 1 7.8776e+08 9.2917e+11 29563
## + FullBath 1 6.8709e+08 9.2928e+11 29563
## + HeatingQC 4 4.4354e+09 9.2553e+11 29563
## + YearRemodAdd 1 5.3547e+08 9.2943e+11 29563
## + Utilities 1 3.9273e+08 9.2957e+11 29563
## + TotRmsAbvGrd 1 3.5654e+08 9.2961e+11 29563
## + BsmtCond 3 2.8269e+09 9.2714e+11 29564
## + OpenPorchSF 1 1.6365e+08 9.2980e+11 29564
## + EnclosedPorch 1 1.3857e+08 9.2982e+11 29564
## + MiscVal 1 8.9972e+07 9.2987e+11 29564
## + Street 1 8.4852e+07 9.2988e+11 29564
## + BsmtHalfBath 1 4.5516e+07 9.2992e+11 29564
## + HalfBath 1 4.3389e+07 9.2992e+11 29564
## + YrSold 1 2.8509e+07 9.2993e+11 29564
## + CentralAir 1 9.5401e+06 9.2995e+11 29564
## + Id 1 6.4375e+06 9.2996e+11 29564
## + GarageType 6 6.2864e+09 9.2368e+11 29564
## + MasVnrType 3 2.3213e+09 9.2764e+11 29564
## + BldgType 3 1.9638e+09 9.2800e+11 29565
## + Foundation 5 4.5019e+09 9.2546e+11 29565
## + BsmtFinType1 5 4.4747e+09 9.2549e+11 29565
## + GarageCond 5 4.4429e+09 9.2552e+11 29565
## + Alley 2 4.0931e+08 9.2955e+11 29565
## + LandSlope 2 2.5509e+08 9.2971e+11 29566
## + PavedDrive 2 3.4750e+07 9.2993e+11 29566
## + BsmtFinType2 6 4.8615e+09 9.2510e+11 29566
## + FireplaceQu 5 3.2902e+09 9.2667e+11 29567
## + Fence 4 1.3332e+09 9.2863e+11 29568
## + ExterCond 4 1.2762e+09 9.2869e+11 29568
## + Electrical 4 5.3947e+08 9.2942e+11 29569
## + MiscFeature 4 4.5508e+08 9.2951e+11 29569
## + Exterior2nd 15 1.3948e+10 9.1601e+11 29570
## - YearBuilt 1 3.7722e+10 9.6768e+11 29618
## - BsmtQual 4 5.1880e+10 9.8184e+11 29633
## - OverallCond 1 4.9405e+10 9.7937e+11 29635
## - KitchenQual 3 6.0898e+10 9.9086e+11 29648
## - OverallQual 1 5.9771e+10 9.8973e+11 29650
## - BsmtExposure 4 6.8988e+10 9.9895e+11 29658
## - Condition2 7 8.0747e+10 1.0107e+12 29669
## - BsmtFinSF1 1 8.2604e+10 1.0126e+12 29683
## - MSSubClass 14 1.3839e+11 1.0684e+12 29735
## - Neighborhood 24 2.0153e+11 1.1315e+12 29799
## - RoofMatl 7 2.7615e+11 1.2061e+12 29925
## - GrLivArea 1 5.8770e+11 1.5177e+12 30271
##
## Step: AIC=29517.84
## SalePrice ~ OverallQual + GrLivArea + Neighborhood + MSSubClass +
## RoofMatl + BsmtFinSF1 + BsmtQual + Condition2 + KitchenQual +
## BsmtExposure + OverallCond + YearBuilt + LotArea
##
## Df Sum of Sq RSS AIC
## + SaleCondition 5 2.6682e+10 8.7419e+11 29484
## + TotalBsmtSF 1 2.1232e+10 8.7964e+11 29485
## + ExterQual 3 2.1918e+10 8.7895e+11 29488
## + GarageCars 1 1.7876e+10 8.8299e+11 29491
## + GarageArea 1 1.6719e+10 8.8415e+11 29493
## + SaleType 8 2.4697e+10 8.7617e+11 29494
## + PoolQC 3 1.7932e+10 8.8294e+11 29495
## + PoolArea 1 1.2798e+10 8.8807e+11 29499
## + Functional 6 1.6872e+10 8.8400e+11 29502
## + MasVnrArea 1 9.5987e+09 8.9127e+11 29504
## + BsmtUnfSF 1 9.1840e+09 8.9169e+11 29505
## + BedroomAbvGr 1 9.0492e+09 8.9182e+11 29505
## + LotConfig 4 1.1745e+10 8.8912e+11 29507
## + LandSlope 2 8.5265e+09 8.9234e+11 29508
## + ScreenPorch 1 7.1088e+09 8.9376e+11 29508
## + HouseStyle 7 1.3591e+10 8.8728e+11 29510
## + Exterior1st 14 2.2024e+10 8.7885e+11 29510
## + Condition1 8 1.4222e+10 8.8665e+11 29511
## + LowQualFinSF 1 5.5571e+09 8.9531e+11 29511
## + Fireplaces 1 5.0859e+09 8.9578e+11 29512
## + LandContour 3 7.4376e+09 8.9343e+11 29512
## + MSZoning 4 5.9832e+09 8.9489e+11 29516
## + Street 1 2.0738e+09 8.9880e+11 29517
## + MoSold 1 1.8299e+09 8.9904e+11 29517
## + `1stFlrSF` 1 1.7289e+09 8.9914e+11 29517
## + GarageYrBlt 1 1.7144e+09 8.9916e+11 29517
## + KitchenAbvGr 1 1.5636e+09 8.9931e+11 29517
## + BsmtFinSF2 1 1.5253e+09 8.9934e+11 29517
## + RoofStyle 5 6.2208e+09 8.9465e+11 29518
## <none> 9.0087e+11 29518
## + LotFrontage 1 1.2406e+09 8.9963e+11 29518
## + MasVnrType 3 3.6661e+09 8.9720e+11 29518
## + HeatingQC 4 4.7088e+09 8.9616e+11 29518
## + WoodDeckSF 1 8.7044e+08 9.0000e+11 29518
## + YearRemodAdd 1 8.6503e+08 9.0000e+11 29518
## + BsmtFullBath 1 8.2830e+08 9.0004e+11 29519
## + Heating 5 5.7665e+09 8.9510e+11 29519
## + GarageFinish 3 3.2393e+09 8.9763e+11 29519
## + GarageQual 3 3.2393e+09 8.9763e+11 29519
## + `3SsnPorch` 1 7.3072e+08 9.0014e+11 29519
## + FullBath 1 6.0853e+08 9.0026e+11 29519
## + `2ndFlrSF` 1 3.3898e+08 9.0053e+11 29519
## + EnclosedPorch 1 3.0056e+08 9.0057e+11 29519
## + Foundation 5 5.2480e+09 8.9562e+11 29519
## + Utilities 1 2.3813e+08 9.0063e+11 29520
## + TotRmsAbvGrd 1 1.4643e+08 9.0072e+11 29520
## + OpenPorchSF 1 1.1801e+08 9.0075e+11 29520
## + HalfBath 1 1.0890e+08 9.0076e+11 29520
## + BsmtHalfBath 1 1.0123e+08 9.0077e+11 29520
## + Id 1 7.2302e+07 9.0080e+11 29520
## + YrSold 1 4.1230e+07 9.0083e+11 29520
## + LotShape 3 2.5125e+09 8.9836e+11 29520
## + MiscVal 1 1.1183e+07 9.0086e+11 29520
## + CentralAir 1 1.0171e+07 9.0086e+11 29520
## + BsmtCond 3 2.1268e+09 8.9874e+11 29520
## + BsmtFinType1 5 4.4750e+09 8.9639e+11 29521
## + GarageType 6 5.6049e+09 8.9527e+11 29521
## + Alley 2 4.7947e+08 9.0039e+11 29521
## + BldgType 3 1.6318e+09 8.9924e+11 29521
## + PavedDrive 2 6.1063e+07 9.0081e+11 29522
## + GarageCond 5 3.2637e+09 8.9761e+11 29523
## + BsmtFinType2 6 4.2807e+09 8.9659e+11 29523
## + Fence 4 1.1341e+09 8.9974e+11 29524
## + FireplaceQu 5 2.2603e+09 8.9861e+11 29524
## + ExterCond 4 9.3269e+08 8.9994e+11 29524
## + Electrical 4 6.6309e+08 9.0021e+11 29525
## + MiscFeature 4 3.4373e+08 9.0053e+11 29525
## + Exterior2nd 15 1.2816e+10 8.8805e+11 29527
## - LotArea 1 2.9093e+10 9.2996e+11 29562
## - YearBuilt 1 4.2271e+10 9.4314e+11 29582
## - OverallCond 1 4.8526e+10 9.4940e+11 29592
## - BsmtExposure 4 5.3855e+10 9.5472e+11 29594
## - BsmtQual 4 5.6801e+10 9.5767e+11 29599
## - KitchenQual 3 6.1060e+10 9.6193e+11 29607
## - OverallQual 1 6.3535e+10 9.6440e+11 29615
## - Condition2 7 8.4666e+10 9.8554e+11 29634
## - BsmtFinSF1 1 7.8361e+10 9.7923e+11 29637
## - MSSubClass 14 1.1743e+11 1.0183e+12 29668
## - Neighborhood 24 2.0327e+11 1.1041e+12 29765
## - RoofMatl 7 2.8670e+11 1.1876e+12 29905
## - GrLivArea 1 5.3794e+11 1.4388e+12 30195
##
## Step: AIC=29484.22
## SalePrice ~ OverallQual + GrLivArea + Neighborhood + MSSubClass +
## RoofMatl + BsmtFinSF1 + BsmtQual + Condition2 + KitchenQual +
## BsmtExposure + OverallCond + YearBuilt + LotArea + SaleCondition
##
## Df Sum of Sq RSS AIC
## + TotalBsmtSF 1 2.1678e+10 8.5251e+11 29450
## + PoolQC 3 2.0594e+10 8.5359e+11 29456
## + ExterQual 3 1.8600e+10 8.5559e+11 29459
## + GarageCars 1 1.6153e+10 8.5804e+11 29459
## + GarageArea 1 1.4764e+10 8.5942e+11 29462
## + PoolArea 1 1.3885e+10 8.6030e+11 29463
## + Functional 6 1.5826e+10 8.5836e+11 29470
## + LotConfig 4 1.2334e+10 8.6185e+11 29472
## + MasVnrArea 1 8.6372e+09 8.6555e+11 29472
## + BsmtUnfSF 1 8.1716e+09 8.6602e+11 29473
## + BedroomAbvGr 1 8.1293e+09 8.6606e+11 29473
## + ScreenPorch 1 7.1065e+09 8.6708e+11 29474
## + LandSlope 2 7.7404e+09 8.6645e+11 29475
## + Condition1 8 1.4840e+10 8.5935e+11 29475
## + HouseStyle 7 1.3358e+10 8.6083e+11 29476
## + LowQualFinSF 1 4.8344e+09 8.6935e+11 29478
## + Fireplaces 1 4.3720e+09 8.6982e+11 29479
## + LandContour 3 6.7399e+09 8.6745e+11 29479
## + Exterior1st 14 1.8874e+10 8.5531e+11 29481
## + MoSold 1 2.6965e+09 8.7149e+11 29482
## + BsmtFinSF2 1 2.3489e+09 8.7184e+11 29482
## + Street 1 2.1684e+09 8.7202e+11 29483
## + MSZoning 4 5.7309e+09 8.6846e+11 29483
## + KitchenAbvGr 1 1.7519e+09 8.7244e+11 29483
## + `1stFlrSF` 1 1.6310e+09 8.7256e+11 29484
## + WoodDeckSF 1 1.5146e+09 8.7267e+11 29484
## + LotFrontage 1 1.4731e+09 8.7272e+11 29484
## + Heating 5 6.0644e+09 8.6812e+11 29484
## <none> 8.7419e+11 29484
## + GarageYrBlt 1 1.1130e+09 8.7308e+11 29484
## + HeatingQC 4 4.6904e+09 8.6950e+11 29484
## + GarageFinish 3 3.3290e+09 8.7086e+11 29485
## + GarageQual 3 3.3290e+09 8.7086e+11 29485
## + BsmtFullBath 1 8.9337e+08 8.7330e+11 29485
## + RoofStyle 5 5.4283e+09 8.6876e+11 29485
## + `3SsnPorch` 1 6.1928e+08 8.7357e+11 29485
## + LotShape 3 2.8687e+09 8.7132e+11 29485
## + FullBath 1 4.3588e+08 8.7375e+11 29486
## + EnclosedPorch 1 3.5867e+08 8.7383e+11 29486
## + `2ndFlrSF` 1 3.5184e+08 8.7384e+11 29486
## + TotRmsAbvGrd 1 3.2945e+08 8.7386e+11 29486
## + YearRemodAdd 1 2.1708e+08 8.7397e+11 29486
## + Foundation 5 4.9108e+09 8.6928e+11 29486
## + Id 1 9.4739e+07 8.7409e+11 29486
## + BsmtHalfBath 1 7.7313e+07 8.7411e+11 29486
## + OpenPorchSF 1 7.4528e+07 8.7411e+11 29486
## + BsmtCond 3 2.4790e+09 8.7171e+11 29486
## + YrSold 1 6.0752e+07 8.7413e+11 29486
## + Utilities 1 4.7471e+07 8.7414e+11 29486
## + MiscVal 1 7.4334e+06 8.7418e+11 29486
## + HalfBath 1 5.6639e+06 8.7418e+11 29486
## + CentralAir 1 2.4995e+06 8.7419e+11 29486
## + MasVnrType 3 2.2727e+09 8.7192e+11 29486
## + BsmtFinType1 5 4.1984e+09 8.6999e+11 29487
## + Alley 2 5.8195e+08 8.7361e+11 29487
## + GarageType 6 5.3527e+09 8.6884e+11 29487
## + BsmtFinType2 6 5.3302e+09 8.6886e+11 29487
## + PavedDrive 2 2.9404e+08 8.7389e+11 29488
## + SaleType 8 7.4552e+09 8.6673e+11 29488
## + BldgType 3 9.6477e+08 8.7322e+11 29489
## + GarageCond 5 2.9832e+09 8.7121e+11 29489
## + ExterCond 4 8.9657e+08 8.7329e+11 29491
## + Fence 4 8.7055e+08 8.7332e+11 29491
## + Electrical 4 5.2210e+08 8.7367e+11 29491
## + MiscFeature 4 3.6846e+08 8.7382e+11 29492
## + FireplaceQu 5 1.4329e+09 8.7276e+11 29492
## + Exterior2nd 15 1.1886e+10 8.6230e+11 29494
## - SaleCondition 5 2.6682e+10 9.0087e+11 29518
## - LotArea 1 2.8974e+10 9.0316e+11 29530
## - YearBuilt 1 3.2829e+10 9.0702e+11 29536
## - BsmtQual 4 4.5267e+10 9.1946e+11 29550
## - OverallCond 1 4.3392e+10 9.1758e+11 29553
## - BsmtExposure 4 5.1709e+10 9.2590e+11 29560
## - KitchenQual 3 5.9411e+10 9.3360e+11 29574
## - OverallQual 1 6.4636e+10 9.3882e+11 29586
## - Condition2 7 9.0864e+10 9.6505e+11 29614
## - BsmtFinSF1 1 8.4951e+10 9.5914e+11 29617
## - MSSubClass 14 1.0255e+11 9.7674e+11 29617
## - Neighborhood 24 1.8856e+11 1.0627e+12 29720
## - RoofMatl 7 2.9715e+11 1.1713e+12 29895
## - GrLivArea 1 5.2924e+11 1.4034e+12 30169
##
## Step: AIC=29449.78
## SalePrice ~ OverallQual + GrLivArea + Neighborhood + MSSubClass +
## RoofMatl + BsmtFinSF1 + BsmtQual + Condition2 + KitchenQual +
## BsmtExposure + OverallCond + YearBuilt + LotArea + SaleCondition +
## TotalBsmtSF
##
## Df Sum of Sq RSS AIC
## + PoolQC 3 2.1010e+10 8.3150e+11 29420
## + GarageCars 1 1.4634e+10 8.3788e+11 29427
## + PoolArea 1 1.4451e+10 8.3806e+11 29427
## + ExterQual 3 1.5675e+10 8.3684e+11 29429
## + GarageArea 1 1.3345e+10 8.3917e+11 29429
## + Functional 6 1.4615e+10 8.3790e+11 29437
## + LotConfig 4 1.1361e+10 8.4115e+11 29438
## + MasVnrArea 1 7.4371e+09 8.4507e+11 29439
## + BedroomAbvGr 1 7.2505e+09 8.4526e+11 29439
## + ScreenPorch 1 6.3425e+09 8.4617e+11 29441
## + LandSlope 2 7.2154e+09 8.4530e+11 29442
## + `2ndFlrSF` 1 4.7107e+09 8.4780e+11 29444
## + Condition1 8 1.2828e+10 8.3968e+11 29444
## + LowQualFinSF 1 3.9583e+09 8.4855e+11 29445
## + LandContour 3 5.9666e+09 8.4654e+11 29446
## + Fireplaces 1 3.6113e+09 8.4890e+11 29446
## + MoSold 1 2.3054e+09 8.5021e+11 29448
## + `1stFlrSF` 1 2.2695e+09 8.5024e+11 29448
## + MSZoning 4 5.6873e+09 8.4682e+11 29448
## + KitchenAbvGr 1 1.9603e+09 8.5055e+11 29448
## + LotFrontage 1 1.9277e+09 8.5058e+11 29449
## + Street 1 1.7571e+09 8.5075e+11 29449
## + WoodDeckSF 1 1.6463e+09 8.5086e+11 29449
## + GarageYrBlt 1 1.5014e+09 8.5101e+11 29449
## + HouseStyle 7 8.4426e+09 8.4407e+11 29449
## + GarageFinish 3 3.6915e+09 8.4882e+11 29450
## + GarageQual 3 3.6915e+09 8.4882e+11 29450
## + Exterior1st 14 1.6446e+10 8.3606e+11 29450
## <none> 8.5251e+11 29450
## + LotShape 3 3.3785e+09 8.4913e+11 29450
## + BsmtFullBath 1 7.2454e+08 8.5179e+11 29451
## + BsmtFinSF2 1 6.4594e+08 8.5186e+11 29451
## + BsmtUnfSF 1 6.4594e+08 8.5186e+11 29451
## + HeatingQC 4 4.0937e+09 8.4842e+11 29451
## + YearRemodAdd 1 5.3301e+08 8.5198e+11 29451
## + `3SsnPorch` 1 4.8577e+08 8.5202e+11 29451
## + FullBath 1 2.9048e+08 8.5222e+11 29451
## + BsmtFinType1 5 4.9635e+09 8.4755e+11 29451
## + Id 1 2.4533e+08 8.5227e+11 29451
## + HalfBath 1 2.3336e+08 8.5228e+11 29451
## + Heating 5 4.9127e+09 8.4760e+11 29451
## + EnclosedPorch 1 1.9362e+08 8.5232e+11 29452
## + TotRmsAbvGrd 1 1.7872e+08 8.5233e+11 29452
## + OpenPorchSF 1 6.4657e+07 8.5245e+11 29452
## + BsmtHalfBath 1 5.7835e+07 8.5245e+11 29452
## + YrSold 1 4.6583e+07 8.5246e+11 29452
## + CentralAir 1 2.3894e+07 8.5249e+11 29452
## + RoofStyle 5 4.7073e+09 8.4780e+11 29452
## + MiscVal 1 7.5577e+06 8.5250e+11 29452
## + Utilities 1 9.7762e+04 8.5251e+11 29452
## + MasVnrType 3 2.2477e+09 8.5026e+11 29452
## + BsmtCond 3 2.2084e+09 8.5030e+11 29452
## + SaleType 8 7.7387e+09 8.4477e+11 29453
## + Alley 2 6.6275e+08 8.5185e+11 29453
## + GarageType 6 5.3309e+09 8.4718e+11 29453
## + PavedDrive 2 4.9956e+08 8.5201e+11 29453
## + Foundation 5 3.5399e+09 8.4897e+11 29454
## + GarageCond 5 3.4552e+09 8.4906e+11 29454
## + BldgType 3 1.0747e+09 8.5144e+11 29454
## + BsmtFinType2 6 3.4065e+09 8.4910e+11 29456
## + Electrical 4 5.8333e+08 8.5193e+11 29457
## + ExterCond 4 5.3558e+08 8.5198e+11 29457
## + Fence 4 5.0698e+08 8.5200e+11 29457
## + MiscFeature 4 4.0452e+08 8.5211e+11 29457
## + FireplaceQu 5 1.1986e+09 8.5131e+11 29458
## + Exterior2nd 15 1.0111e+10 8.4240e+11 29463
## - TotalBsmtSF 1 2.1678e+10 8.7419e+11 29484
## - SaleCondition 5 2.7127e+10 8.7964e+11 29485
## - LotArea 1 2.5941e+10 8.7845e+11 29491
## - YearBuilt 1 2.6985e+10 8.7950e+11 29493
## - BsmtExposure 4 4.3582e+10 8.9609e+11 29514
## - BsmtQual 4 4.6427e+10 8.9894e+11 29519
## - OverallCond 1 5.2042e+10 9.0455e+11 29534
## - KitchenQual 3 5.5228e+10 9.0774e+11 29535
## - OverallQual 1 5.3347e+10 9.0586e+11 29536
## - MSSubClass 14 6.9782e+10 9.2229e+11 29536
## - BsmtFinSF1 1 6.6003e+10 9.1851e+11 29556
## - Condition2 7 9.4239e+10 9.4675e+11 29588
## - Neighborhood 24 1.7693e+11 1.0294e+12 29675
## - GrLivArea 1 2.8459e+11 1.1371e+12 29866
## - RoofMatl 7 3.1800e+11 1.1705e+12 29896
##
## Step: AIC=29419.58
## SalePrice ~ OverallQual + GrLivArea + Neighborhood + MSSubClass +
## RoofMatl + BsmtFinSF1 + BsmtQual + Condition2 + KitchenQual +
## BsmtExposure + OverallCond + YearBuilt + LotArea + SaleCondition +
## TotalBsmtSF + PoolQC
##
## Df Sum of Sq RSS AIC
## + GarageCars 1 1.6007e+10 8.1549e+11 29393
## + ExterQual 3 1.7044e+10 8.1446e+11 29396
## + GarageArea 1 1.3811e+10 8.1769e+11 29397
## + MasVnrArea 1 1.0408e+10 8.2109e+11 29403
## + LotConfig 4 1.0994e+10 8.2051e+11 29408
## + ScreenPorch 1 7.5259e+09 8.2397e+11 29408
## + Functional 6 1.2531e+10 8.1897e+11 29410
## + BedroomAbvGr 1 6.7886e+09 8.2471e+11 29410
## + PoolArea 1 6.7754e+09 8.2472e+11 29410
## + Condition1 8 1.4045e+10 8.1746e+11 29411
## + LowQualFinSF 1 5.4571e+09 8.2604e+11 29412
## + LandSlope 2 6.5384e+09 8.2496e+11 29412
## + Fireplaces 1 3.9584e+09 8.2754e+11 29415
## + `2ndFlrSF` 1 3.1089e+09 8.2839e+11 29416
## + LandContour 3 5.1353e+09 8.2636e+11 29417
## + GarageYrBlt 1 2.1055e+09 8.2939e+11 29418
## + MoSold 1 2.0581e+09 8.2944e+11 29418
## + MSZoning 4 5.2542e+09 8.2625e+11 29418
## + Street 1 1.8082e+09 8.2969e+11 29418
## + HeatingQC 4 5.1873e+09 8.2631e+11 29419
## + KitchenAbvGr 1 1.5562e+09 8.2994e+11 29419
## + Exterior1st 14 1.6211e+10 8.1529e+11 29419
## + WoodDeckSF 1 1.4673e+09 8.3003e+11 29419
## + LotShape 3 3.7379e+09 8.2776e+11 29419
## <none> 8.3150e+11 29420
## + GarageFinish 3 3.3816e+09 8.2812e+11 29420
## + GarageQual 3 3.3816e+09 8.2812e+11 29420
## + `1stFlrSF` 1 9.2625e+08 8.3057e+11 29420
## + BsmtFullBath 1 8.4684e+08 8.3065e+11 29420
## + LotFrontage 1 7.1381e+08 8.3079e+11 29420
## + BsmtFinSF2 1 6.5316e+08 8.3085e+11 29420
## + BsmtUnfSF 1 6.5316e+08 8.3085e+11 29420
## + YearRemodAdd 1 6.1074e+08 8.3089e+11 29421
## + `3SsnPorch` 1 5.4504e+08 8.3096e+11 29421
## + HalfBath 1 4.9951e+08 8.3100e+11 29421
## + FullBath 1 3.0655e+08 8.3119e+11 29421
## + BsmtHalfBath 1 1.7947e+08 8.3132e+11 29421
## + Id 1 1.6548e+08 8.3133e+11 29421
## + YrSold 1 1.6319e+08 8.3134e+11 29421
## + BsmtFinType1 5 4.6122e+09 8.2689e+11 29422
## + TotRmsAbvGrd 1 2.8995e+07 8.3147e+11 29422
## + EnclosedPorch 1 1.2576e+07 8.3149e+11 29422
## + OpenPorchSF 1 1.1939e+07 8.3149e+11 29422
## + CentralAir 1 5.8173e+06 8.3149e+11 29422
## + MiscVal 1 4.1540e+06 8.3150e+11 29422
## + Utilities 1 7.4147e+05 8.3150e+11 29422
## + RoofStyle 5 4.4333e+09 8.2707e+11 29422
## + MasVnrType 3 2.1148e+09 8.2939e+11 29422
## + SaleType 8 7.7908e+09 8.2371e+11 29422
## + Heating 5 4.3505e+09 8.2715e+11 29422
## + BsmtCond 3 1.8688e+09 8.2963e+11 29422
## + Alley 2 7.2417e+08 8.3078e+11 29422
## + PavedDrive 2 4.9624e+08 8.3100e+11 29423
## + GarageType 6 4.7230e+09 8.2678e+11 29423
## + BldgType 3 9.9829e+08 8.3050e+11 29424
## + GarageCond 5 3.2133e+09 8.2829e+11 29424
## + Foundation 5 3.1382e+09 8.2836e+11 29424
## + BsmtFinType2 6 4.0999e+09 8.2740e+11 29424
## + Fence 4 1.6598e+09 8.2984e+11 29425
## + HouseStyle 7 4.9925e+09 8.2651e+11 29425
## + MiscFeature 4 6.8716e+08 8.3081e+11 29426
## + ExterCond 4 6.7821e+08 8.3082e+11 29426
## + Electrical 4 6.1357e+08 8.3089e+11 29427
## + FireplaceQu 5 1.1992e+09 8.3030e+11 29428
## + Exterior2nd 15 8.1766e+09 8.2332e+11 29435
## - PoolQC 3 2.1010e+10 8.5251e+11 29450
## - TotalBsmtSF 1 2.2094e+10 8.5359e+11 29456
## - SaleCondition 5 2.9357e+10 8.6086e+11 29460
## - LotArea 1 2.4953e+10 8.5645e+11 29461
## - YearBuilt 1 2.8282e+10 8.5978e+11 29466
## - BsmtQual 4 4.4852e+10 8.7635e+11 29488
## - BsmtExposure 4 4.7168e+10 8.7867e+11 29492
## - OverallQual 1 5.1506e+10 8.8301e+11 29505
## - KitchenQual 3 5.4838e+10 8.8634e+11 29506
## - OverallCond 1 5.3277e+10 8.8478e+11 29508
## - MSSubClass 14 7.0321e+10 9.0182e+11 29509
## - BsmtFinSF1 1 6.0598e+10 8.9210e+11 29520
## - Condition2 7 9.2108e+10 9.2361e+11 29558
## - Neighborhood 24 1.7938e+11 1.0109e+12 29655
## - RoofMatl 7 2.6529e+11 1.0968e+12 29807
## - GrLivArea 1 2.6608e+11 1.0976e+12 29820
##
## Step: AIC=29393.37
## SalePrice ~ OverallQual + GrLivArea + Neighborhood + MSSubClass +
## RoofMatl + BsmtFinSF1 + BsmtQual + Condition2 + KitchenQual +
## BsmtExposure + OverallCond + YearBuilt + LotArea + SaleCondition +
## TotalBsmtSF + PoolQC + GarageCars
##
## Df Sum of Sq RSS AIC
## + ExterQual 3 1.7012e+10 7.9848e+11 29369
## + MasVnrArea 1 8.6261e+09 8.0687e+11 29380
## + LotConfig 4 1.1047e+10 8.0445e+11 29382
## + Condition1 8 1.4875e+10 8.0062e+11 29383
## + ScreenPorch 1 6.7626e+09 8.0873e+11 29383
## + Functional 6 1.2298e+10 8.0319e+11 29383
## + PoolArea 1 6.2120e+09 8.0928e+11 29384
## + BedroomAbvGr 1 5.7596e+09 8.0973e+11 29385
## + LandSlope 2 5.7725e+09 8.0972e+11 29387
## + LowQualFinSF 1 4.5437e+09 8.1095e+11 29387
## + MSZoning 4 7.7208e+09 8.0777e+11 29388
## + Fireplaces 1 3.7539e+09 8.1174e+11 29389
## + `2ndFlrSF` 1 3.6993e+09 8.1179e+11 29389
## + LandContour 3 5.2208e+09 8.1027e+11 29390
## + Street 1 2.5679e+09 8.1292e+11 29391
## + HeatingQC 4 5.6197e+09 8.0987e+11 29391
## + Exterior1st 14 1.6511e+10 7.9898e+11 29392
## + MoSold 1 1.9535e+09 8.1354e+11 29392
## + KitchenAbvGr 1 1.5731e+09 8.1392e+11 29393
## + `1stFlrSF` 1 1.4520e+09 8.1404e+11 29393
## + GarageFinish 3 3.6151e+09 8.1188e+11 29393
## + GarageQual 3 3.6151e+09 8.1188e+11 29393
## + GarageYrBlt 1 1.3555e+09 8.1414e+11 29393
## + WoodDeckSF 1 1.2631e+09 8.1423e+11 29393
## + LotShape 3 3.4801e+09 8.1201e+11 29393
## <none> 8.1549e+11 29393
## + BsmtFinSF2 1 8.9419e+08 8.1460e+11 29394
## + BsmtUnfSF 1 8.9419e+08 8.1460e+11 29394
## + YearRemodAdd 1 7.9188e+08 8.1470e+11 29394
## + GarageType 6 6.3604e+09 8.0913e+11 29394
## + BsmtFullBath 1 7.6289e+08 8.1473e+11 29394
## + GarageArea 1 6.3334e+08 8.1486e+11 29394
## + SaleType 8 8.4127e+09 8.0708e+11 29394
## + `3SsnPorch` 1 4.6944e+08 8.1502e+11 29395
## + FullBath 1 3.9434e+08 8.1510e+11 29395
## + HalfBath 1 3.8652e+08 8.1511e+11 29395
## + BsmtFinType1 5 4.8355e+09 8.1066e+11 29395
## + LotFrontage 1 2.5697e+08 8.1524e+11 29395
## + YrSold 1 2.4917e+08 8.1524e+11 29395
## + BsmtHalfBath 1 2.3650e+08 8.1526e+11 29395
## + Id 1 5.0962e+07 8.1544e+11 29395
## + MiscVal 1 4.2269e+07 8.1545e+11 29395
## + TotRmsAbvGrd 1 1.8202e+07 8.1547e+11 29395
## + EnclosedPorch 1 1.3992e+07 8.1548e+11 29395
## + Utilities 1 1.8754e+06 8.1549e+11 29395
## + CentralAir 1 8.4352e+05 8.1549e+11 29395
## + OpenPorchSF 1 7.3730e+03 8.1549e+11 29395
## + BsmtCond 3 1.9698e+09 8.1352e+11 29396
## + MasVnrType 3 1.9001e+09 8.1359e+11 29396
## + Alley 2 5.0339e+08 8.1499e+11 29397
## + PavedDrive 2 3.5328e+08 8.1514e+11 29397
## + RoofStyle 5 3.6829e+09 8.1181e+11 29397
## + GarageCond 5 3.3576e+09 8.1214e+11 29397
## + Heating 5 3.2345e+09 8.1226e+11 29398
## + Fence 4 1.8805e+09 8.1361e+11 29398
## + BsmtFinType2 6 4.0000e+09 8.1149e+11 29398
## + BldgType 3 5.7325e+08 8.1492e+11 29398
## + Foundation 5 2.7218e+09 8.1277e+11 29399
## + HouseStyle 7 4.1163e+09 8.1138e+11 29400
## + Electrical 4 7.3535e+08 8.1476e+11 29400
## + ExterCond 4 5.4911e+08 8.1494e+11 29400
## + MiscFeature 4 5.1034e+08 8.1498e+11 29401
## + FireplaceQu 5 8.3375e+08 8.1466e+11 29402
## + Exterior2nd 15 8.2509e+09 8.0724e+11 29409
## - GarageCars 1 1.6007e+10 8.3150e+11 29420
## - PoolQC 3 2.2384e+10 8.3788e+11 29427
## - TotalBsmtSF 1 2.0505e+10 8.3600e+11 29427
## - LotArea 1 2.2530e+10 8.3802e+11 29431
## - SaleCondition 5 2.7553e+10 8.4305e+11 29432
## - YearBuilt 1 2.4059e+10 8.3955e+11 29434
## - BsmtQual 4 4.2195e+10 8.5769e+11 29459
## - BsmtExposure 4 4.6068e+10 8.6156e+11 29465
## - OverallQual 1 4.5683e+10 8.6118e+11 29471
## - MSSubClass 14 6.7380e+10 8.8287e+11 29481
## - KitchenQual 3 5.4992e+10 8.7048e+11 29482
## - OverallCond 1 5.6568e+10 8.7206e+11 29489
## - BsmtFinSF1 1 5.8822e+10 8.7431e+11 29492
## - Condition2 7 9.0100e+10 9.0559e+11 29531
## - Neighborhood 24 1.7501e+11 9.9050e+11 29628
## - GrLivArea 1 2.4112e+11 1.0566e+12 29767
## - RoofMatl 7 2.5454e+11 1.0700e+12 29774
##
## Step: AIC=29368.78
## SalePrice ~ OverallQual + GrLivArea + Neighborhood + MSSubClass +
## RoofMatl + BsmtFinSF1 + BsmtQual + Condition2 + KitchenQual +
## BsmtExposure + OverallCond + YearBuilt + LotArea + SaleCondition +
## TotalBsmtSF + PoolQC + GarageCars + ExterQual
##
## Df Sum of Sq RSS AIC
## + Functional 6 1.3678e+10 7.8480e+11 29356
## + Condition1 8 1.4753e+10 7.8373e+11 29358
## + LotConfig 4 1.0243e+10 7.8824e+11 29358
## + PoolArea 1 6.2262e+09 7.9225e+11 29359
## + ScreenPorch 1 6.1291e+09 7.9235e+11 29360
## + MasVnrArea 1 5.7544e+09 7.9273e+11 29360
## + BedroomAbvGr 1 5.6721e+09 7.9281e+11 29360
## + MSZoning 4 7.6791e+09 7.9080e+11 29363
## + LandSlope 2 5.4204e+09 7.9306e+11 29363
## + LowQualFinSF 1 4.1423e+09 7.9434e+11 29363
## + Fireplaces 1 4.0594e+09 7.9442e+11 29363
## + `2ndFlrSF` 1 3.6120e+09 7.9487e+11 29364
## + Street 1 2.7777e+09 7.9570e+11 29366
## + LandContour 3 4.7943e+09 7.9369e+11 29366
## + HeatingQC 4 5.5134e+09 7.9297e+11 29367
## + MoSold 1 1.7396e+09 7.9674e+11 29368
## + KitchenAbvGr 1 1.6821e+09 7.9680e+11 29368
## + `1stFlrSF` 1 1.5035e+09 7.9698e+11 29368
## + Exterior1st 14 1.5571e+10 7.8291e+11 29368
## + GarageYrBlt 1 1.2336e+09 7.9725e+11 29369
## + WoodDeckSF 1 1.2153e+09 7.9727e+11 29369
## <none> 7.9848e+11 29369
## + BsmtFullBath 1 9.5775e+08 7.9752e+11 29369
## + BsmtFinSF2 1 9.1285e+08 7.9757e+11 29369
## + BsmtUnfSF 1 9.1285e+08 7.9757e+11 29369
## + GarageFinish 3 3.1071e+09 7.9537e+11 29369
## + GarageQual 3 3.1071e+09 7.9537e+11 29369
## + YearRemodAdd 1 7.7908e+08 7.9770e+11 29369
## + GarageArea 1 7.5054e+08 7.9773e+11 29369
## + LotFrontage 1 4.6182e+08 7.9802e+11 29370
## + BsmtHalfBath 1 3.8288e+08 7.9810e+11 29370
## + HalfBath 1 3.6793e+08 7.9811e+11 29370
## + FullBath 1 3.2651e+08 7.9815e+11 29370
## + `3SsnPorch` 1 3.0713e+08 7.9817e+11 29370
## + GarageType 6 5.7046e+09 7.9278e+11 29370
## + SaleType 8 7.8790e+09 7.9060e+11 29370
## + BsmtFinType1 5 4.4712e+09 7.9401e+11 29371
## + LotShape 3 2.2377e+09 7.9624e+11 29371
## + YrSold 1 3.6467e+07 7.9844e+11 29371
## + CentralAir 1 2.6621e+07 7.9845e+11 29371
## + Id 1 2.3667e+07 7.9846e+11 29371
## + TotRmsAbvGrd 1 2.2597e+07 7.9846e+11 29371
## + BsmtCond 3 2.2110e+09 7.9627e+11 29371
## + EnclosedPorch 1 9.6447e+06 7.9847e+11 29371
## + Utilities 1 6.7772e+06 7.9847e+11 29371
## + MiscVal 1 5.0886e+06 7.9848e+11 29371
## + OpenPorchSF 1 2.2660e+05 7.9848e+11 29371
## + MasVnrType 3 2.0504e+09 7.9643e+11 29371
## + Alley 2 5.8356e+08 7.9790e+11 29372
## + PavedDrive 2 3.4063e+08 7.9814e+11 29372
## + GarageCond 5 3.3621e+09 7.9512e+11 29373
## + Heating 5 3.1432e+09 7.9534e+11 29373
## + Fence 4 1.8119e+09 7.9667e+11 29374
## + RoofStyle 5 2.6728e+09 7.9581e+11 29374
## + Foundation 5 2.6668e+09 7.9581e+11 29374
## + BldgType 3 4.1161e+08 7.9807e+11 29374
## + BsmtFinType2 6 3.5330e+09 7.9495e+11 29374
## + ExterCond 4 7.5956e+08 7.9772e+11 29375
## + Electrical 4 6.9402e+08 7.9779e+11 29376
## + MiscFeature 4 6.0126e+08 7.9788e+11 29376
## + HouseStyle 7 3.7302e+09 7.9475e+11 29376
## + FireplaceQu 5 1.0194e+09 7.9746e+11 29377
## + Exterior2nd 15 7.5437e+09 7.9094e+11 29385
## - ExterQual 3 1.7012e+10 8.1549e+11 29393
## - GarageCars 1 1.5976e+10 8.1446e+11 29396
## - TotalBsmtSF 1 1.7815e+10 8.1630e+11 29399
## - SaleCondition 5 2.4652e+10 8.2313e+11 29403
## - PoolQC 3 2.3809e+10 8.2229e+11 29405
## - LotArea 1 2.2321e+10 8.2080e+11 29407
## - YearBuilt 1 2.2513e+10 8.2099e+11 29407
## - BsmtQual 4 2.8919e+10 8.2740e+11 29412
## - KitchenQual 3 3.3042e+10 8.3152e+11 29422
## - OverallQual 1 3.9846e+10 8.3833e+11 29437
## - BsmtExposure 4 4.3325e+10 8.4181e+11 29437
## - OverallCond 1 5.0830e+10 8.4931e+11 29456
## - MSSubClass 14 6.8339e+10 8.6682e+11 29460
## - BsmtFinSF1 1 5.9405e+10 8.5789e+11 29471
## - Condition2 7 9.4682e+10 8.9316e+11 29517
## - Neighborhood 24 1.6333e+11 9.6181e+11 29591
## - GrLivArea 1 2.4005e+11 1.0385e+12 29748
## - RoofMatl 7 2.5680e+11 1.0553e+12 29759
##
## Step: AIC=29355.71
## SalePrice ~ OverallQual + GrLivArea + Neighborhood + MSSubClass +
## RoofMatl + BsmtFinSF1 + BsmtQual + Condition2 + KitchenQual +
## BsmtExposure + OverallCond + YearBuilt + LotArea + SaleCondition +
## TotalBsmtSF + PoolQC + GarageCars + ExterQual + Functional
##
## Df Sum of Sq RSS AIC
## + Condition1 8 1.5715e+10 7.6909e+11 29342
## + BedroomAbvGr 1 7.2582e+09 7.7755e+11 29344
## + LotConfig 4 1.0147e+10 7.7466e+11 29345
## + ScreenPorch 1 5.9170e+09 7.7889e+11 29347
## + PoolArea 1 5.5757e+09 7.7923e+11 29347
## + MSZoning 4 7.9571e+09 7.7685e+11 29349
## + MasVnrArea 1 4.4743e+09 7.8033e+11 29349
## + LandSlope 2 5.4246e+09 7.7938e+11 29350
## + Fireplaces 1 4.2452e+09 7.8056e+11 29350
## + LowQualFinSF 1 3.6812e+09 7.8112e+11 29351
## + Street 1 2.8720e+09 7.8193e+11 29352
## + LandContour 3 4.8850e+09 7.7992e+11 29353
## + HeatingQC 4 5.2609e+09 7.7954e+11 29354
## + BsmtFinSF2 1 1.8977e+09 7.8291e+11 29354
## + BsmtUnfSF 1 1.8977e+09 7.8291e+11 29354
## + MoSold 1 1.8573e+09 7.8295e+11 29354
## + YearRemodAdd 1 1.7705e+09 7.8303e+11 29354
## + `2ndFlrSF` 1 1.7635e+09 7.8304e+11 29354
## + KitchenAbvGr 1 1.6124e+09 7.8319e+11 29355
## + WoodDeckSF 1 1.5989e+09 7.8320e+11 29355
## + SaleType 8 8.7186e+09 7.7608e+11 29356
## + BsmtFullBath 1 1.1666e+09 7.8364e+11 29356
## + Exterior1st 14 1.5077e+10 7.6973e+11 29356
## + GarageYrBlt 1 1.1472e+09 7.8366e+11 29356
## <none> 7.8480e+11 29356
## + GarageFinish 3 3.1101e+09 7.8169e+11 29356
## + GarageQual 3 3.1101e+09 7.8169e+11 29356
## + GarageArea 1 9.1228e+08 7.8389e+11 29356
## + `1stFlrSF` 1 4.4430e+08 7.8436e+11 29357
## + BsmtHalfBath 1 3.7176e+08 7.8443e+11 29357
## + BsmtCond 3 2.5001e+09 7.8230e+11 29357
## + FullBath 1 3.3446e+08 7.8447e+11 29357
## + LotFrontage 1 2.8022e+08 7.8452e+11 29357
## + `3SsnPorch` 1 2.1268e+08 7.8459e+11 29357
## + HalfBath 1 1.9768e+08 7.8461e+11 29357
## + YrSold 1 9.7058e+07 7.8471e+11 29358
## + MiscVal 1 6.2156e+07 7.8474e+11 29358
## + TotRmsAbvGrd 1 6.0257e+07 7.8474e+11 29358
## + CentralAir 1 3.7371e+07 7.8477e+11 29358
## + EnclosedPorch 1 3.3582e+07 7.8477e+11 29358
## + Id 1 1.1159e+07 7.8479e+11 29358
## + Utilities 1 6.5028e+06 7.8480e+11 29358
## + OpenPorchSF 1 5.5816e+05 7.8480e+11 29358
## + GarageType 6 5.1485e+09 7.7966e+11 29358
## + LotShape 3 1.8463e+09 7.8296e+11 29358
## + PavedDrive 2 5.2067e+08 7.8428e+11 29359
## + Alley 2 3.7282e+08 7.8443e+11 29359
## + Heating 5 3.5697e+09 7.8123e+11 29359
## + RoofStyle 5 3.4446e+09 7.8136e+11 29359
## + MasVnrType 3 1.1914e+09 7.8361e+11 29360
## + GarageCond 5 3.2931e+09 7.8151e+11 29360
## + BsmtFinType1 5 3.2637e+09 7.8154e+11 29360
## + BsmtFinType2 6 4.0669e+09 7.8074e+11 29360
## + Fence 4 1.8507e+09 7.8295e+11 29360
## + BldgType 3 5.9847e+08 7.8421e+11 29361
## + HouseStyle 7 4.6563e+09 7.8015e+11 29361
## + Foundation 5 2.3892e+09 7.8241e+11 29361
## + ExterCond 4 1.0390e+09 7.8376e+11 29362
## + Electrical 4 6.6168e+08 7.8414e+11 29363
## + MiscFeature 4 5.4639e+08 7.8426e+11 29363
## + FireplaceQu 5 1.2384e+09 7.8357e+11 29363
## - Functional 6 1.3678e+10 7.9848e+11 29369
## + Exterior2nd 15 6.3766e+09 7.7843e+11 29374
## - GarageCars 1 1.5749e+10 8.0055e+11 29383
## - ExterQual 3 1.8391e+10 8.0319e+11 29383
## - TotalBsmtSF 1 1.6613e+10 8.0142e+11 29384
## - SaleCondition 5 2.3386e+10 8.0819e+11 29388
## - PoolQC 3 2.1484e+10 8.0629e+11 29389
## - YearBuilt 1 2.1969e+10 8.0677e+11 29394
## - LotArea 1 2.2207e+10 8.0701e+11 29394
## - BsmtQual 4 2.8286e+10 8.1309e+11 29399
## - KitchenQual 3 3.1729e+10 8.1653e+11 29407
## - OverallQual 1 3.4790e+10 8.1959e+11 29417
## - BsmtExposure 4 4.0840e+10 8.2564e+11 29421
## - OverallCond 1 4.3310e+10 8.2811e+11 29432
## - MSSubClass 14 7.0581e+10 8.5538e+11 29453
## - BsmtFinSF1 1 5.9051e+10 8.4385e+11 29459
## - Condition2 7 9.7189e+10 8.8199e+11 29511
## - Neighborhood 24 1.5544e+11 9.4024e+11 29570
## - RoofMatl 7 2.5666e+11 1.0415e+12 29752
## - GrLivArea 1 2.4937e+11 1.0342e+12 29754
##
## Step: AIC=29342.36
## SalePrice ~ OverallQual + GrLivArea + Neighborhood + MSSubClass +
## RoofMatl + BsmtFinSF1 + BsmtQual + Condition2 + KitchenQual +
## BsmtExposure + OverallCond + YearBuilt + LotArea + SaleCondition +
## TotalBsmtSF + PoolQC + GarageCars + ExterQual + Functional +
## Condition1
##
## Df Sum of Sq RSS AIC
## + LotConfig 4 1.0177e+10 7.5891e+11 29331
## + BedroomAbvGr 1 5.7825e+09 7.6331e+11 29333
## + ScreenPorch 1 5.4792e+09 7.6361e+11 29334
## + PoolArea 1 5.4299e+09 7.6366e+11 29334
## + LandSlope 2 6.0820e+09 7.6301e+11 29335
## + MasVnrArea 1 4.9525e+09 7.6414e+11 29335
## + Fireplaces 1 4.7731e+09 7.6432e+11 29335
## + LandContour 3 6.0085e+09 7.6308e+11 29337
## + MSZoning 4 6.9451e+09 7.6214e+11 29337
## + LowQualFinSF 1 3.3683e+09 7.6572e+11 29338
## + Street 1 3.1990e+09 7.6589e+11 29338
## + MoSold 1 2.4894e+09 7.6660e+11 29340
## + Exterior1st 14 1.6057e+10 7.5303e+11 29340
## + HeatingQC 4 5.5565e+09 7.6353e+11 29340
## + `2ndFlrSF` 1 1.7562e+09 7.6733e+11 29341
## + BsmtFinSF2 1 1.7346e+09 7.6735e+11 29341
## + BsmtUnfSF 1 1.7346e+09 7.6735e+11 29341
## + YearRemodAdd 1 1.6307e+09 7.6746e+11 29341
## + KitchenAbvGr 1 1.5339e+09 7.6755e+11 29342
## + BsmtFullBath 1 1.4923e+09 7.6760e+11 29342
## + WoodDeckSF 1 1.2409e+09 7.6785e+11 29342
## + GarageYrBlt 1 1.1571e+09 7.6793e+11 29342
## + GarageFinish 3 3.2608e+09 7.6583e+11 29342
## + GarageQual 3 3.2608e+09 7.6583e+11 29342
## <none> 7.6909e+11 29342
## + GarageArea 1 9.6417e+08 7.6812e+11 29343
## + SaleType 8 8.2766e+09 7.6081e+11 29343
## + GarageType 6 5.9591e+09 7.6313e+11 29343
## + `1stFlrSF` 1 4.8062e+08 7.6861e+11 29344
## + BsmtHalfBath 1 4.0494e+08 7.6868e+11 29344
## + `3SsnPorch` 1 3.6313e+08 7.6873e+11 29344
## + LotFrontage 1 3.3969e+08 7.6875e+11 29344
## + HalfBath 1 3.0649e+08 7.6878e+11 29344
## + FullBath 1 1.8039e+08 7.6891e+11 29344
## + YrSold 1 1.3279e+08 7.6896e+11 29344
## + BsmtCond 3 2.1795e+09 7.6691e+11 29344
## + CentralAir 1 4.1829e+07 7.6905e+11 29344
## + MiscVal 1 3.5542e+07 7.6905e+11 29344
## + TotRmsAbvGrd 1 1.5724e+07 7.6907e+11 29344
## + LotShape 3 2.1277e+09 7.6696e+11 29344
## + Id 1 9.6852e+06 7.6908e+11 29344
## + Utilities 1 9.6244e+06 7.6908e+11 29344
## + EnclosedPorch 1 6.3334e+06 7.6908e+11 29344
## + OpenPorchSF 1 3.7356e+06 7.6908e+11 29344
## + PavedDrive 2 5.1580e+08 7.6857e+11 29345
## + GarageCond 5 3.6259e+09 7.6546e+11 29346
## + BsmtFinType1 5 3.5411e+09 7.6555e+11 29346
## + Alley 2 2.4103e+08 7.6885e+11 29346
## + MasVnrType 3 1.2345e+09 7.6785e+11 29346
## + Fence 4 2.2045e+09 7.6688e+11 29346
## + Heating 5 3.2594e+09 7.6583e+11 29346
## + Foundation 5 3.1186e+09 7.6597e+11 29347
## + BsmtFinType2 6 4.1713e+09 7.6492e+11 29347
## + RoofStyle 5 3.0918e+09 7.6600e+11 29347
## + BldgType 3 4.5419e+08 7.6863e+11 29348
## + Electrical 4 8.8552e+08 7.6820e+11 29349
## + ExterCond 4 8.8348e+08 7.6820e+11 29349
## + MiscFeature 4 5.4582e+08 7.6854e+11 29349
## + FireplaceQu 5 1.5353e+09 7.6755e+11 29350
## + HouseStyle 7 3.6156e+09 7.6547e+11 29350
## - Condition1 8 1.5715e+10 7.8480e+11 29356
## - Functional 6 1.4640e+10 7.8373e+11 29358
## + Exterior2nd 15 6.9255e+09 7.6216e+11 29359
## - TotalBsmtSF 1 1.4745e+10 7.8383e+11 29368
## - ExterQual 3 1.8434e+10 7.8752e+11 29371
## - GarageCars 1 1.6556e+10 7.8564e+11 29371
## - SaleCondition 5 2.3897e+10 7.9299e+11 29377
## - PoolQC 3 2.3021e+10 7.9211e+11 29379
## - LotArea 1 2.1947e+10 7.9104e+11 29381
## - YearBuilt 1 2.3106e+10 7.9219e+11 29383
## - BsmtQual 4 2.7389e+10 7.9648e+11 29385
## - KitchenQual 3 3.0997e+10 8.0009e+11 29394
## - OverallQual 1 3.4758e+10 8.0385e+11 29405
## - BsmtExposure 4 4.0634e+10 8.0972e+11 29409
## - OverallCond 1 4.4422e+10 8.1351e+11 29422
## - MSSubClass 14 6.9640e+10 8.3873e+11 29440
## - BsmtFinSF1 1 6.1279e+10 8.3037e+11 29452
## - Condition2 7 8.8587e+10 8.5768e+11 29487
## - Neighborhood 24 1.4741e+11 9.1650e+11 29549
## - RoofMatl 7 2.5111e+11 1.0202e+12 29738
## - GrLivArea 1 2.5350e+11 1.0226e+12 29754
##
## Step: AIC=29331.03
## SalePrice ~ OverallQual + GrLivArea + Neighborhood + MSSubClass +
## RoofMatl + BsmtFinSF1 + BsmtQual + Condition2 + KitchenQual +
## BsmtExposure + OverallCond + YearBuilt + LotArea + SaleCondition +
## TotalBsmtSF + PoolQC + GarageCars + ExterQual + Functional +
## Condition1 + LotConfig
##
## Df Sum of Sq RSS AIC
## + ScreenPorch 1 5.0633e+09 7.5385e+11 29323
## + PoolArea 1 4.8479e+09 7.5406e+11 29324
## + LandSlope 2 5.8713e+09 7.5304e+11 29324
## + BedroomAbvGr 1 4.6782e+09 7.5423e+11 29324
## + MasVnrArea 1 4.5049e+09 7.5441e+11 29324
## + Fireplaces 1 4.3467e+09 7.5456e+11 29325
## + LandContour 3 5.8489e+09 7.5306e+11 29326
## + MSZoning 4 6.6346e+09 7.5228e+11 29326
## + LowQualFinSF 1 3.5132e+09 7.5540e+11 29326
## + Street 1 2.9727e+09 7.5594e+11 29327
## + HeatingQC 4 5.9336e+09 7.5298e+11 29328
## + Exterior1st 14 1.6110e+10 7.4280e+11 29328
## + MoSold 1 2.4220e+09 7.5649e+11 29328
## + `2ndFlrSF` 1 2.0822e+09 7.5683e+11 29329
## + BsmtFinSF2 1 1.8831e+09 7.5703e+11 29329
## + BsmtUnfSF 1 1.8831e+09 7.5703e+11 29329
## + YearRemodAdd 1 1.6900e+09 7.5722e+11 29330
## + BsmtFullBath 1 1.5367e+09 7.5737e+11 29330
## + GarageFinish 3 3.5528e+09 7.5536e+11 29330
## + GarageQual 3 3.5528e+09 7.5536e+11 29330
## + KitchenAbvGr 1 1.3033e+09 7.5761e+11 29331
## + WoodDeckSF 1 1.1818e+09 7.5773e+11 29331
## + GarageYrBlt 1 1.1080e+09 7.5780e+11 29331
## + GarageType 6 6.3040e+09 7.5261e+11 29331
## <none> 7.5891e+11 29331
## + GarageArea 1 8.0023e+08 7.5811e+11 29332
## + LotFrontage 1 7.7241e+08 7.5814e+11 29332
## + `1stFlrSF` 1 6.4113e+08 7.5827e+11 29332
## + FullBath 1 5.6918e+08 7.5834e+11 29332
## + BsmtHalfBath 1 4.4271e+08 7.5847e+11 29332
## + `3SsnPorch` 1 3.8332e+08 7.5853e+11 29332
## + BsmtCond 3 2.3646e+09 7.5655e+11 29333
## + HalfBath 1 2.4129e+08 7.5867e+11 29333
## + YrSold 1 1.3334e+08 7.5878e+11 29333
## + Utilities 1 1.3199e+08 7.5878e+11 29333
## + CentralAir 1 1.0726e+08 7.5880e+11 29333
## + Id 1 3.1713e+07 7.5888e+11 29333
## + OpenPorchSF 1 2.2151e+07 7.5889e+11 29333
## + EnclosedPorch 1 6.3326e+06 7.5890e+11 29333
## + MiscVal 1 1.0980e+06 7.5891e+11 29333
## + TotRmsAbvGrd 1 1.7186e+05 7.5891e+11 29333
## + LotShape 3 1.9238e+09 7.5699e+11 29333
## + GarageCond 5 3.8931e+09 7.5502e+11 29334
## + BsmtFinType1 5 3.6965e+09 7.5521e+11 29334
## + PavedDrive 2 5.1377e+08 7.5840e+11 29334
## + SaleType 8 6.7288e+09 7.5218e+11 29334
## + Foundation 5 3.4780e+09 7.5543e+11 29334
## + MasVnrType 3 1.3732e+09 7.5754e+11 29334
## + Alley 2 2.1539e+08 7.5870e+11 29335
## + RoofStyle 5 3.3135e+09 7.5560e+11 29335
## + Fence 4 2.2680e+09 7.5664e+11 29335
## + Heating 5 3.1580e+09 7.5575e+11 29335
## + BsmtFinType2 6 3.9990e+09 7.5491e+11 29335
## + BldgType 3 3.8850e+08 7.5852e+11 29336
## + ExterCond 4 9.7837e+08 7.5793e+11 29337
## + Electrical 4 7.8987e+08 7.5812e+11 29338
## + MiscFeature 4 4.5969e+08 7.5845e+11 29338
## + FireplaceQu 5 1.5028e+09 7.5741e+11 29338
## + HouseStyle 7 3.2104e+09 7.5570e+11 29339
## - LotConfig 4 1.0177e+10 7.6909e+11 29342
## - Condition1 8 1.5745e+10 7.7466e+11 29345
## - Functional 6 1.4425e+10 7.7334e+11 29346
## + Exterior2nd 15 7.5417e+09 7.5137e+11 29347
## - TotalBsmtSF 1 1.4125e+10 7.7304e+11 29356
## - ExterQual 3 1.7389e+10 7.7630e+11 29358
## - GarageCars 1 1.6588e+10 7.7550e+11 29360
## - LotArea 1 1.8441e+10 7.7735e+11 29364
## - SaleCondition 5 2.4651e+10 7.8356e+11 29367
## - PoolQC 3 2.2775e+10 7.8169e+11 29368
## - YearBuilt 1 2.3120e+10 7.8203e+11 29373
## - BsmtQual 4 2.6871e+10 7.8578e+11 29374
## - KitchenQual 3 3.2655e+10 7.9157e+11 29386
## - OverallQual 1 3.4119e+10 7.9303e+11 29393
## - BsmtExposure 4 4.1046e+10 7.9996e+11 29400
## - OverallCond 1 4.2589e+10 8.0150e+11 29408
## - MSSubClass 14 6.6713e+10 8.2562e+11 29425
## - BsmtFinSF1 1 6.1523e+10 8.2043e+11 29442
## - Condition2 7 8.5964e+10 8.4487e+11 29473
## - Neighborhood 24 1.4706e+11 9.0597e+11 29540
## - RoofMatl 7 2.4793e+11 1.0068e+12 29727
## - GrLivArea 1 2.5071e+11 1.0096e+12 29743
##
## Step: AIC=29323.32
## SalePrice ~ OverallQual + GrLivArea + Neighborhood + MSSubClass +
## RoofMatl + BsmtFinSF1 + BsmtQual + Condition2 + KitchenQual +
## BsmtExposure + OverallCond + YearBuilt + LotArea + SaleCondition +
## TotalBsmtSF + PoolQC + GarageCars + ExterQual + Functional +
## Condition1 + LotConfig + ScreenPorch
##
## Df Sum of Sq RSS AIC
## + PoolArea 1 6.0473e+09 7.4780e+11 29314
## + LandSlope 2 5.8860e+09 7.4796e+11 29316
## + BedroomAbvGr 1 4.7963e+09 7.4905e+11 29316
## + LandContour 3 6.2690e+09 7.4758e+11 29317
## + MasVnrArea 1 4.1802e+09 7.4967e+11 29317
## + LowQualFinSF 1 3.7200e+09 7.5013e+11 29318
## + Street 1 3.4977e+09 7.5035e+11 29319
## + MSZoning 4 6.5274e+09 7.4732e+11 29319
## + Fireplaces 1 3.3884e+09 7.5046e+11 29319
## + HeatingQC 4 6.4046e+09 7.4744e+11 29319
## + MoSold 1 2.5174e+09 7.5133e+11 29321
## + Exterior1st 14 1.5521e+10 7.3833e+11 29321
## + WoodDeckSF 1 1.9390e+09 7.5191e+11 29322
## + `2ndFlrSF` 1 1.9200e+09 7.5193e+11 29322
## + YearRemodAdd 1 1.8477e+09 7.5200e+11 29322
## + BsmtFullBath 1 1.6456e+09 7.5220e+11 29322
## + BsmtFinSF2 1 1.6366e+09 7.5221e+11 29322
## + BsmtUnfSF 1 1.6366e+09 7.5221e+11 29322
## + GarageType 6 6.7727e+09 7.4708e+11 29322
## + GarageFinish 3 3.6106e+09 7.5024e+11 29322
## + GarageQual 3 3.6106e+09 7.5024e+11 29322
## + GarageYrBlt 1 1.3353e+09 7.5251e+11 29323
## + KitchenAbvGr 1 1.1698e+09 7.5268e+11 29323
## <none> 7.5385e+11 29323
## + LotFrontage 1 8.2013e+08 7.5303e+11 29324
## + GarageArea 1 7.7168e+08 7.5308e+11 29324
## + FullBath 1 6.9557e+08 7.5315e+11 29324
## + `1stFlrSF` 1 5.1976e+08 7.5333e+11 29324
## + `3SsnPorch` 1 4.9323e+08 7.5335e+11 29324
## + BsmtHalfBath 1 4.4556e+08 7.5340e+11 29325
## + Utilities 1 3.8621e+08 7.5346e+11 29325
## + HalfBath 1 1.1436e+08 7.5373e+11 29325
## + YrSold 1 1.0197e+08 7.5375e+11 29325
## + BsmtCond 3 2.1468e+09 7.5170e+11 29325
## + CentralAir 1 5.8012e+07 7.5379e+11 29325
## + EnclosedPorch 1 3.6778e+07 7.5381e+11 29325
## + Id 1 3.4014e+07 7.5381e+11 29325
## + TotRmsAbvGrd 1 8.2138e+06 7.5384e+11 29325
## + MiscVal 1 5.5558e+06 7.5384e+11 29325
## + OpenPorchSF 1 1.7058e+06 7.5385e+11 29325
## + BsmtFinType1 5 4.1438e+09 7.4970e+11 29325
## + SaleType 8 7.0545e+09 7.4679e+11 29326
## + GarageCond 5 3.8152e+09 7.5003e+11 29326
## + LotShape 3 1.7190e+09 7.5213e+11 29326
## + PavedDrive 2 5.7283e+08 7.5328e+11 29326
## + Foundation 5 3.4618e+09 7.5039e+11 29327
## + MasVnrType 3 1.3585e+09 7.5249e+11 29327
## + Alley 2 2.2798e+08 7.5362e+11 29327
## + Fence 4 2.1258e+09 7.5172e+11 29327
## + RoofStyle 5 3.1366e+09 7.5071e+11 29327
## + Heating 5 2.9888e+09 7.5086e+11 29328
## + BsmtFinType2 6 3.8470e+09 7.5000e+11 29328
## + BldgType 3 3.8135e+08 7.5347e+11 29329
## + ExterCond 4 1.0168e+09 7.5283e+11 29329
## + MiscFeature 4 1.0086e+09 7.5284e+11 29329
## + Electrical 4 8.2496e+08 7.5302e+11 29330
## - ScreenPorch 1 5.0633e+09 7.5891e+11 29331
## + HouseStyle 7 3.2112e+09 7.5064e+11 29331
## + FireplaceQu 5 1.0906e+09 7.5276e+11 29331
## - LotConfig 4 9.7612e+09 7.6361e+11 29334
## - Condition1 8 1.5337e+10 7.6919e+11 29337
## - Functional 6 1.4226e+10 7.6807e+11 29338
## + Exterior2nd 15 7.6292e+09 7.4622e+11 29339
## - TotalBsmtSF 1 1.3682e+10 7.6753e+11 29347
## - ExterQual 3 1.6830e+10 7.7068e+11 29349
## - GarageCars 1 1.5888e+10 7.6974e+11 29352
## - LotArea 1 1.8808e+10 7.7266e+11 29357
## - SaleCondition 5 2.4850e+10 7.7870e+11 29360
## - PoolQC 3 2.3708e+10 7.7756e+11 29362
## - BsmtQual 4 2.7363e+10 7.8121e+11 29367
## - YearBuilt 1 2.4701e+10 7.7855e+11 29368
## - KitchenQual 3 3.1950e+10 7.8580e+11 29378
## - OverallQual 1 3.3036e+10 7.8688e+11 29384
## - BsmtExposure 4 4.0617e+10 7.9447e+11 29392
## - OverallCond 1 4.2381e+10 7.9623e+11 29401
## - MSSubClass 14 6.6603e+10 8.2045e+11 29418
## - BsmtFinSF1 1 6.1330e+10 8.1518e+11 29435
## - Condition2 7 8.5422e+10 8.3927e+11 29465
## - Neighborhood 24 1.4772e+11 9.0157e+11 29535
## - RoofMatl 7 2.4569e+11 9.9954e+11 29719
## - GrLivArea 1 2.4877e+11 1.0026e+12 29735
##
## Step: AIC=29313.63
## SalePrice ~ OverallQual + GrLivArea + Neighborhood + MSSubClass +
## RoofMatl + BsmtFinSF1 + BsmtQual + Condition2 + KitchenQual +
## BsmtExposure + OverallCond + YearBuilt + LotArea + SaleCondition +
## TotalBsmtSF + PoolQC + GarageCars + ExterQual + Functional +
## Condition1 + LotConfig + ScreenPorch + PoolArea
##
## Df Sum of Sq RSS AIC
## + BedroomAbvGr 1 4.7761e+09 7.4302e+11 29306
## + LandSlope 2 5.5368e+09 7.4226e+11 29307
## + MasVnrArea 1 4.2684e+09 7.4353e+11 29307
## + LandContour 3 6.1540e+09 7.4165e+11 29308
## + LowQualFinSF 1 3.4729e+09 7.4433e+11 29309
## + Street 1 3.4164e+09 7.4438e+11 29309
## + Fireplaces 1 3.3944e+09 7.4441e+11 29309
## + HeatingQC 4 6.2282e+09 7.4157e+11 29310
## + MSZoning 4 6.2074e+09 7.4159e+11 29310
## + MoSold 1 2.4003e+09 7.4540e+11 29311
## + YearRemodAdd 1 2.0725e+09 7.4573e+11 29312
## + `2ndFlrSF` 1 2.0309e+09 7.4577e+11 29312
## + Exterior1st 14 1.5250e+10 7.3255e+11 29312
## + BsmtFullBath 1 1.9365e+09 7.4586e+11 29312
## + GarageType 6 6.7608e+09 7.4104e+11 29313
## + BsmtFinSF2 1 1.6359e+09 7.4616e+11 29313
## + BsmtUnfSF 1 1.6359e+09 7.4616e+11 29313
## + WoodDeckSF 1 1.5319e+09 7.4627e+11 29313
## + GarageFinish 3 3.5410e+09 7.4426e+11 29313
## + GarageQual 3 3.5410e+09 7.4426e+11 29313
## + GarageYrBlt 1 1.3405e+09 7.4646e+11 29313
## + KitchenAbvGr 1 1.2448e+09 7.4656e+11 29313
## <none> 7.4780e+11 29314
## + LotFrontage 1 9.5929e+08 7.4684e+11 29314
## + GarageArea 1 9.4229e+08 7.4686e+11 29314
## + FullBath 1 7.6677e+08 7.4703e+11 29314
## + `1stFlrSF` 1 6.1884e+08 7.4718e+11 29314
## + `3SsnPorch` 1 5.1286e+08 7.4729e+11 29315
## + Utilities 1 3.9316e+08 7.4741e+11 29315
## + BsmtFinType1 5 4.4486e+09 7.4335e+11 29315
## + BsmtHalfBath 1 3.2938e+08 7.4747e+11 29315
## + GarageCond 5 4.2819e+09 7.4352e+11 29315
## + YrSold 1 1.6363e+08 7.4764e+11 29315
## + EnclosedPorch 1 8.2922e+07 7.4772e+11 29316
## + HalfBath 1 8.0549e+07 7.4772e+11 29316
## + CentralAir 1 6.9835e+07 7.4773e+11 29316
## + TotRmsAbvGrd 1 5.6804e+07 7.4774e+11 29316
## + Id 1 3.8298e+07 7.4776e+11 29316
## + OpenPorchSF 1 9.5009e+06 7.4779e+11 29316
## + MiscVal 1 2.6644e+06 7.4780e+11 29316
## + BsmtCond 3 1.9029e+09 7.4590e+11 29316
## + LotShape 3 1.7650e+09 7.4604e+11 29316
## + PavedDrive 2 6.0141e+08 7.4720e+11 29317
## + SaleType 8 6.7441e+09 7.4106e+11 29317
## + Foundation 5 3.5253e+09 7.4428e+11 29317
## + Fence 4 2.4887e+09 7.4531e+11 29317
## + MasVnrType 3 1.3339e+09 7.4647e+11 29317
## + Alley 2 2.3582e+08 7.4756e+11 29317
## + Heating 5 2.9543e+09 7.4485e+11 29318
## + BsmtFinType2 6 3.8054e+09 7.4400e+11 29318
## + RoofStyle 5 2.6792e+09 7.4512e+11 29318
## + BldgType 3 3.7889e+08 7.4742e+11 29319
## + ExterCond 4 1.0938e+09 7.4671e+11 29320
## + Electrical 4 8.4698e+08 7.4695e+11 29320
## + FireplaceQu 5 1.6501e+09 7.4615e+11 29320
## + MiscFeature 4 5.7121e+08 7.4723e+11 29321
## + HouseStyle 7 3.4303e+09 7.4437e+11 29321
## - LotConfig 4 9.0694e+09 7.5687e+11 29323
## - PoolArea 1 6.0473e+09 7.5385e+11 29323
## - ScreenPorch 1 6.2627e+09 7.5406e+11 29324
## - Condition1 8 1.5009e+10 7.6281e+11 29327
## - Functional 6 1.3686e+10 7.6149e+11 29328
## + Exterior2nd 15 7.3452e+09 7.4046e+11 29329
## - PoolQC 3 1.5567e+10 7.6337e+11 29338
## - TotalBsmtSF 1 1.4570e+10 7.6237e+11 29340
## - ExterQual 3 1.6881e+10 7.6468e+11 29340
## - GarageCars 1 1.5211e+10 7.6301e+11 29341
## - LotArea 1 1.8736e+10 7.6654e+11 29348
## - SaleCondition 5 2.5662e+10 7.7346e+11 29353
## - BsmtQual 4 2.6687e+10 7.7449e+11 29357
## - YearBuilt 1 2.4764e+10 7.7256e+11 29359
## - KitchenQual 3 3.1459e+10 7.7926e+11 29367
## - OverallQual 1 3.3686e+10 7.8149e+11 29376
## - BsmtExposure 4 4.1529e+10 7.8933e+11 29384
## - OverallCond 1 4.1852e+10 7.8965e+11 29391
## - MSSubClass 14 6.5942e+10 8.1374e+11 29408
## - BsmtFinSF1 1 6.1824e+10 8.0962e+11 29427
## - Condition2 7 8.5537e+10 8.3334e+11 29457
## - Neighborhood 24 1.4720e+11 8.9500e+11 29526
## - RoofMatl 7 1.2915e+11 8.7696e+11 29531
## - GrLivArea 1 2.4578e+11 9.9358e+11 29724
##
## Step: AIC=29306.33
## SalePrice ~ OverallQual + GrLivArea + Neighborhood + MSSubClass +
## RoofMatl + BsmtFinSF1 + BsmtQual + Condition2 + KitchenQual +
## BsmtExposure + OverallCond + YearBuilt + LotArea + SaleCondition +
## TotalBsmtSF + PoolQC + GarageCars + ExterQual + Functional +
## Condition1 + LotConfig + ScreenPorch + PoolArea + BedroomAbvGr
##
## Df Sum of Sq RSS AIC
## + LandSlope 2 6.0850e+09 7.3694e+11 29298
## + LandContour 3 6.2311e+09 7.3679e+11 29300
## + MasVnrArea 1 4.1275e+09 7.3890e+11 29300
## + Street 1 3.4323e+09 7.3959e+11 29302
## + LowQualFinSF 1 3.3562e+09 7.3967e+11 29302
## + MSZoning 4 6.2054e+09 7.3682e+11 29302
## + `2ndFlrSF` 1 2.7270e+09 7.4030e+11 29303
## + Fireplaces 1 2.6001e+09 7.4042e+11 29303
## + HeatingQC 4 5.6015e+09 7.3742e+11 29303
## + MoSold 1 2.1412e+09 7.4088e+11 29304
## + GarageFinish 3 3.9094e+09 7.3912e+11 29305
## + GarageQual 3 3.9094e+09 7.3912e+11 29305
## + YearRemodAdd 1 1.8027e+09 7.4122e+11 29305
## + BsmtFullBath 1 1.6962e+09 7.4133e+11 29305
## + Exterior1st 14 1.4778e+10 7.2825e+11 29305
## + GarageType 6 6.6683e+09 7.3636e+11 29305
## + FullBath 1 1.5554e+09 7.4147e+11 29305
## + TotRmsAbvGrd 1 1.5455e+09 7.4148e+11 29305
## + WoodDeckSF 1 1.4212e+09 7.4160e+11 29306
## + KitchenAbvGr 1 1.3842e+09 7.4164e+11 29306
## + BsmtFinSF2 1 1.3673e+09 7.4166e+11 29306
## + BsmtUnfSF 1 1.3673e+09 7.4166e+11 29306
## + GarageYrBlt 1 1.2756e+09 7.4175e+11 29306
## + LotFrontage 1 1.1569e+09 7.4187e+11 29306
## + `1stFlrSF` 1 1.0644e+09 7.4196e+11 29306
## <none> 7.4302e+11 29306
## + GarageArea 1 5.5797e+08 7.4247e+11 29307
## + `3SsnPorch` 1 3.9492e+08 7.4263e+11 29308
## + Utilities 1 3.9471e+08 7.4263e+11 29308
## + GarageCond 5 4.3758e+09 7.3865e+11 29308
## + BsmtHalfBath 1 1.9260e+08 7.4283e+11 29308
## + SaleType 8 7.2599e+09 7.3576e+11 29308
## + CentralAir 1 1.1559e+08 7.4291e+11 29308
## + EnclosedPorch 1 9.8748e+07 7.4293e+11 29308
## + YrSold 1 8.8706e+07 7.4294e+11 29308
## + Id 1 6.0308e+07 7.4296e+11 29308
## + OpenPorchSF 1 1.6728e+07 7.4301e+11 29308
## + HalfBath 1 9.5221e+06 7.4301e+11 29308
## + MiscVal 1 8.8974e+05 7.4302e+11 29308
## + BsmtCond 3 1.8944e+09 7.4113e+11 29309
## + BsmtFinType1 5 3.7975e+09 7.3923e+11 29309
## + Fence 4 2.7444e+09 7.4028e+11 29309
## + PavedDrive 2 6.8374e+08 7.4234e+11 29309
## + LotShape 3 1.6574e+09 7.4137e+11 29309
## + Foundation 5 3.6447e+09 7.3938e+11 29309
## + Alley 2 3.5135e+08 7.4267e+11 29310
## + MasVnrType 3 1.2990e+09 7.4173e+11 29310
## + Heating 5 2.7844e+09 7.4024e+11 29311
## + BldgType 3 4.1262e+08 7.4261e+11 29312
## + RoofStyle 5 2.3663e+09 7.4066e+11 29312
## + BsmtFinType2 6 3.2581e+09 7.3977e+11 29312
## + ExterCond 4 1.0281e+09 7.4200e+11 29312
## + Electrical 4 8.1525e+08 7.4221e+11 29313
## + MiscFeature 4 6.2942e+08 7.4240e+11 29313
## + FireplaceQu 5 1.5506e+09 7.4147e+11 29313
## - BedroomAbvGr 1 4.7761e+09 7.4780e+11 29314
## - LotConfig 4 8.0195e+09 7.5104e+11 29314
## + HouseStyle 7 2.3915e+09 7.4063e+11 29316
## - PoolArea 1 6.0271e+09 7.4905e+11 29316
## - ScreenPorch 1 6.3907e+09 7.4942e+11 29317
## - Condition1 8 1.3708e+10 7.5673e+11 29317
## - Functional 6 1.4754e+10 7.5778e+11 29323
## + Exterior2nd 15 6.8068e+09 7.3622e+11 29323
## - PoolQC 3 1.4753e+10 7.5778e+11 29329
## - TotalBsmtSF 1 1.4024e+10 7.5705e+11 29332
## - GarageCars 1 1.4187e+10 7.5721e+11 29332
## - ExterQual 3 1.6837e+10 7.5986e+11 29333
## - LotArea 1 1.8431e+10 7.6146e+11 29340
## - SaleCondition 5 2.5072e+10 7.6810e+11 29345
## - BsmtQual 4 2.5235e+10 7.6826e+11 29347
## - YearBuilt 1 2.5177e+10 7.6820e+11 29353
## - KitchenQual 3 2.8972e+10 7.7200e+11 29356
## - OverallQual 1 3.3438e+10 7.7646e+11 29368
## - BsmtExposure 4 3.9572e+10 7.8260e+11 29374
## - OverallCond 1 4.1888e+10 7.8491e+11 29384
## - MSSubClass 14 6.7091e+10 8.1012e+11 29404
## - BsmtFinSF1 1 5.4896e+10 7.9792e+11 29408
## - Condition2 7 8.8204e+10 8.3123e+11 29455
## - Neighborhood 24 1.4284e+11 8.8586e+11 29514
## - RoofMatl 7 1.3021e+11 8.7324e+11 29527
## - GrLivArea 1 2.2930e+11 9.7232e+11 29695
##
## Step: AIC=29298.4
## SalePrice ~ OverallQual + GrLivArea + Neighborhood + MSSubClass +
## RoofMatl + BsmtFinSF1 + BsmtQual + Condition2 + KitchenQual +
## BsmtExposure + OverallCond + YearBuilt + LotArea + SaleCondition +
## TotalBsmtSF + PoolQC + GarageCars + ExterQual + Functional +
## Condition1 + LotConfig + ScreenPorch + PoolArea + BedroomAbvGr +
## LandSlope
##
## Df Sum of Sq RSS AIC
## + LandContour 3 6.2169e+09 7.3072e+11 29292
## + MasVnrArea 1 4.1454e+09 7.3279e+11 29292
## + Street 1 3.8822e+09 7.3306e+11 29293
## + MSZoning 4 6.7657e+09 7.3017e+11 29293
## + LowQualFinSF 1 3.7271e+09 7.3321e+11 29293
## + `2ndFlrSF` 1 3.0002e+09 7.3394e+11 29295
## + Fireplaces 1 2.7963e+09 7.3414e+11 29295
## + HeatingQC 4 5.5319e+09 7.3141e+11 29296
## + BsmtFullBath 1 2.0568e+09 7.3488e+11 29296
## + MoSold 1 2.0538e+09 7.3489e+11 29296
## + GarageType 6 7.0305e+09 7.2991e+11 29297
## + YearRemodAdd 1 1.9017e+09 7.3504e+11 29297
## + GarageFinish 3 3.9152e+09 7.3302e+11 29297
## + GarageQual 3 3.9152e+09 7.3302e+11 29297
## + GarageYrBlt 1 1.5600e+09 7.3538e+11 29297
## + Exterior1st 14 1.4582e+10 7.2236e+11 29297
## + BsmtFinSF2 1 1.4590e+09 7.3548e+11 29298
## + BsmtUnfSF 1 1.4590e+09 7.3548e+11 29298
## + WoodDeckSF 1 1.3769e+09 7.3556e+11 29298
## + TotRmsAbvGrd 1 1.2849e+09 7.3565e+11 29298
## + KitchenAbvGr 1 1.2023e+09 7.3574e+11 29298
## + `1stFlrSF` 1 1.1631e+09 7.3578e+11 29298
## + FullBath 1 1.0894e+09 7.3585e+11 29298
## <none> 7.3694e+11 29298
## + BsmtCond 3 3.0190e+09 7.3392e+11 29298
## + LotFrontage 1 6.5970e+08 7.3628e+11 29299
## + GarageArea 1 5.8294e+08 7.3636e+11 29299
## + Utilities 1 4.4314e+08 7.3650e+11 29300
## + GarageCond 5 4.4257e+09 7.3251e+11 29300
## + `3SsnPorch` 1 3.7369e+08 7.3657e+11 29300
## + YrSold 1 1.8243e+08 7.3676e+11 29300
## + Foundation 5 4.2134e+09 7.3273e+11 29300
## + CentralAir 1 1.2991e+08 7.3681e+11 29300
## + BsmtHalfBath 1 1.0484e+08 7.3683e+11 29300
## + EnclosedPorch 1 8.8672e+07 7.3685e+11 29300
## + HalfBath 1 7.9913e+07 7.3686e+11 29300
## + RoofStyle 5 4.1236e+09 7.3282e+11 29300
## + OpenPorchSF 1 7.1966e+07 7.3687e+11 29300
## + Id 1 6.4523e+07 7.3688e+11 29300
## + MiscVal 1 3.8867e+05 7.3694e+11 29300
## + BsmtFinType1 5 4.0073e+09 7.3293e+11 29301
## + PavedDrive 2 7.8436e+08 7.3616e+11 29301
## + Fence 4 2.6509e+09 7.3429e+11 29301
## + LotShape 3 1.4612e+09 7.3548e+11 29302
## + MasVnrType 3 1.3029e+09 7.3564e+11 29302
## + Alley 2 2.5522e+08 7.3668e+11 29302
## + SaleType 8 5.9448e+09 7.3099e+11 29303
## + BsmtFinType2 6 3.7038e+09 7.3324e+11 29303
## + Heating 5 2.6817e+09 7.3426e+11 29303
## + BldgType 3 3.8732e+08 7.3655e+11 29304
## + ExterCond 4 1.2243e+09 7.3572e+11 29304
## + Electrical 4 7.4685e+08 7.3619e+11 29305
## + MiscFeature 4 6.0712e+08 7.3633e+11 29305
## + FireplaceQu 5 1.4900e+09 7.3545e+11 29306
## - LotConfig 4 7.7848e+09 7.4472e+11 29306
## - LandSlope 2 6.0850e+09 7.4302e+11 29306
## - BedroomAbvGr 1 5.3243e+09 7.4226e+11 29307
## - PoolArea 1 5.6610e+09 7.4260e+11 29308
## + HouseStyle 7 2.0394e+09 7.3490e+11 29308
## - ScreenPorch 1 6.3679e+09 7.4331e+11 29309
## - Condition1 8 1.4244e+10 7.5118e+11 29310
## - Functional 6 1.4713e+10 7.5165e+11 29315
## + Exterior2nd 15 6.7153e+09 7.3022e+11 29315
## - PoolQC 3 1.4210e+10 7.5115e+11 29320
## - GarageCars 1 1.3494e+10 7.5043e+11 29323
## - TotalBsmtSF 1 1.3814e+10 7.5075e+11 29323
## - ExterQual 3 1.6469e+10 7.5341e+11 29325
## - SaleCondition 5 2.4232e+10 7.6117e+11 29335
## - BsmtQual 4 2.5081e+10 7.6202e+11 29339
## - LotArea 1 2.3863e+10 7.6080e+11 29343
## - YearBuilt 1 2.5712e+10 7.6265e+11 29346
## - KitchenQual 3 2.9759e+10 7.6670e+11 29350
## - OverallQual 1 3.2419e+10 7.6936e+11 29359
## - BsmtExposure 4 3.8192e+10 7.7513e+11 29364
## - OverallCond 1 4.2275e+10 7.7921e+11 29377
## - MSSubClass 14 6.5456e+10 8.0240e+11 29394
## - BsmtFinSF1 1 5.4872e+10 7.9181e+11 29401
## - Condition2 7 8.9895e+10 8.2683e+11 29451
## - Neighborhood 24 1.4116e+11 8.7810e+11 29505
## - RoofMatl 7 1.3154e+11 8.6848e+11 29523
## - GrLivArea 1 2.2660e+11 9.6354e+11 29685
##
## Step: AIC=29292.11
## SalePrice ~ OverallQual + GrLivArea + Neighborhood + MSSubClass +
## RoofMatl + BsmtFinSF1 + BsmtQual + Condition2 + KitchenQual +
## BsmtExposure + OverallCond + YearBuilt + LotArea + SaleCondition +
## TotalBsmtSF + PoolQC + GarageCars + ExterQual + Functional +
## Condition1 + LotConfig + ScreenPorch + PoolArea + BedroomAbvGr +
## LandSlope + LandContour
##
## Df Sum of Sq RSS AIC
## + Street 1 4.4728e+09 7.2625e+11 29285
## + LowQualFinSF 1 4.0714e+09 7.2665e+11 29286
## + MSZoning 4 7.0158e+09 7.2371e+11 29286
## + MasVnrArea 1 3.8695e+09 7.2685e+11 29286
## + `2ndFlrSF` 1 3.0560e+09 7.2767e+11 29288
## + Fireplaces 1 2.7162e+09 7.2801e+11 29289
## + GarageFinish 3 4.2598e+09 7.2646e+11 29290
## + GarageQual 3 4.2598e+09 7.2646e+11 29290
## + GarageType 6 7.2557e+09 7.2347e+11 29290
## + MoSold 1 2.1629e+09 7.2856e+11 29290
## + HeatingQC 4 5.1675e+09 7.2556e+11 29290
## + YearRemodAdd 1 1.9245e+09 7.2880e+11 29290
## + BsmtFullBath 1 1.8272e+09 7.2890e+11 29291
## + Exterior1st 14 1.4687e+10 7.1604e+11 29291
## + GarageYrBlt 1 1.7101e+09 7.2901e+11 29291
## + BsmtFinSF2 1 1.4064e+09 7.2932e+11 29291
## + BsmtUnfSF 1 1.4064e+09 7.2932e+11 29291
## + TotRmsAbvGrd 1 1.3161e+09 7.2941e+11 29292
## + WoodDeckSF 1 1.2331e+09 7.2949e+11 29292
## + KitchenAbvGr 1 1.2283e+09 7.2949e+11 29292
## + BsmtCond 3 3.1788e+09 7.2754e+11 29292
## + `1stFlrSF` 1 1.1233e+09 7.2960e+11 29292
## <none> 7.3072e+11 29292
## + FullBath 1 7.2646e+08 7.3000e+11 29293
## + GarageArea 1 6.6627e+08 7.3006e+11 29293
## + LotFrontage 1 6.3317e+08 7.3009e+11 29293
## + RoofStyle 5 4.6259e+09 7.2610e+11 29293
## + GarageCond 5 4.5122e+09 7.2621e+11 29293
## + Utilities 1 4.2371e+08 7.3030e+11 29293
## + `3SsnPorch` 1 4.0627e+08 7.3032e+11 29293
## + HalfBath 1 2.0539e+08 7.3052e+11 29294
## + BsmtHalfBath 1 1.8927e+08 7.3053e+11 29294
## + CentralAir 1 1.3452e+08 7.3059e+11 29294
## + YrSold 1 1.2859e+08 7.3059e+11 29294
## + EnclosedPorch 1 8.8815e+07 7.3063e+11 29294
## + Id 1 7.6426e+07 7.3065e+11 29294
## + OpenPorchSF 1 4.8442e+07 7.3067e+11 29294
## + MiscVal 1 1.5732e+04 7.3072e+11 29294
## + PavedDrive 2 7.5752e+08 7.2997e+11 29295
## + BsmtFinType1 5 3.7545e+09 7.2697e+11 29295
## + Foundation 5 3.6956e+09 7.2703e+11 29295
## + Fence 4 2.5095e+09 7.2821e+11 29295
## + LotShape 3 1.4890e+09 7.2923e+11 29295
## + Alley 2 3.0668e+08 7.3042e+11 29296
## + MasVnrType 3 1.0994e+09 7.2962e+11 29296
## + BsmtFinType2 6 3.9214e+09 7.2680e+11 29296
## + SaleType 8 5.8747e+09 7.2485e+11 29296
## + Heating 5 2.6532e+09 7.2807e+11 29297
## + BldgType 3 3.4666e+08 7.3038e+11 29297
## + ExterCond 4 1.0630e+09 7.2966e+11 29298
## - LandContour 3 6.2169e+09 7.3694e+11 29298
## + MiscFeature 4 7.0136e+08 7.3002e+11 29299
## + Electrical 4 6.1009e+08 7.3011e+11 29299
## + FireplaceQu 5 1.4463e+09 7.2928e+11 29299
## - LotConfig 4 7.6958e+09 7.3842e+11 29299
## - LandSlope 2 6.0708e+09 7.3679e+11 29300
## - BedroomAbvGr 1 5.3195e+09 7.3604e+11 29301
## - PoolArea 1 5.6064e+09 7.3633e+11 29301
## + HouseStyle 7 2.0918e+09 7.2863e+11 29302
## - ScreenPorch 1 6.7201e+09 7.3744e+11 29303
## - Condition1 8 1.5313e+10 7.4604e+11 29306
## + Exterior2nd 15 7.0355e+09 7.2369e+11 29308
## - Functional 6 1.5140e+10 7.4586e+11 29310
## - PoolQC 3 1.4169e+10 7.4489e+11 29314
## - GarageCars 1 1.3665e+10 7.4439e+11 29317
## - TotalBsmtSF 1 1.3822e+10 7.4454e+11 29317
## - ExterQual 3 1.6100e+10 7.4682e+11 29318
## - SaleCondition 5 2.3363e+10 7.5409e+11 29328
## - BsmtQual 4 2.5247e+10 7.5597e+11 29333
## - YearBuilt 1 2.4821e+10 7.5554e+11 29339
## - LotArea 1 2.6365e+10 7.5709e+11 29342
## - KitchenQual 3 2.9736e+10 7.6046e+11 29344
## - OverallQual 1 3.1586e+10 7.6231e+11 29352
## - BsmtExposure 4 3.6913e+10 7.6764e+11 29356
## - OverallCond 1 4.2026e+10 7.7275e+11 29371
## - MSSubClass 14 6.5269e+10 7.9599e+11 29388
## - BsmtFinSF1 1 5.6552e+10 7.8728e+11 29398
## - Condition2 7 8.7201e+10 8.1792e+11 29442
## - Neighborhood 24 1.4149e+11 8.7221e+11 29501
## - RoofMatl 7 1.3014e+11 8.6086e+11 29516
## - GrLivArea 1 2.2333e+11 9.5405e+11 29677
##
## Step: AIC=29285.2
## SalePrice ~ OverallQual + GrLivArea + Neighborhood + MSSubClass +
## RoofMatl + BsmtFinSF1 + BsmtQual + Condition2 + KitchenQual +
## BsmtExposure + OverallCond + YearBuilt + LotArea + SaleCondition +
## TotalBsmtSF + PoolQC + GarageCars + ExterQual + Functional +
## Condition1 + LotConfig + ScreenPorch + PoolArea + BedroomAbvGr +
## LandSlope + LandContour + Street
##
## Df Sum of Sq RSS AIC
## + LowQualFinSF 1 4.4593e+09 7.2179e+11 29278
## + MasVnrArea 1 3.6539e+09 7.2260e+11 29280
## + `2ndFlrSF` 1 2.9517e+09 7.2330e+11 29281
## + MSZoning 4 5.9294e+09 7.2032e+11 29281
## + Fireplaces 1 2.8367e+09 7.2341e+11 29282
## + GarageFinish 3 4.2590e+09 7.2199e+11 29283
## + GarageQual 3 4.2590e+09 7.2199e+11 29283
## + HeatingQC 4 5.0814e+09 7.2117e+11 29283
## + KitchenAbvGr 1 2.0398e+09 7.2421e+11 29283
## + MoSold 1 2.0290e+09 7.2422e+11 29283
## + BsmtFullBath 1 1.9491e+09 7.2430e+11 29283
## + YearRemodAdd 1 1.8423e+09 7.2441e+11 29284
## + GarageYrBlt 1 1.6054e+09 7.2464e+11 29284
## + Exterior1st 14 1.4426e+10 7.1182e+11 29284
## + BsmtFinSF2 1 1.5120e+09 7.2474e+11 29284
## + BsmtUnfSF 1 1.5120e+09 7.2474e+11 29284
## + WoodDeckSF 1 1.3624e+09 7.2489e+11 29285
## + GarageType 6 6.2934e+09 7.1996e+11 29285
## + BsmtCond 3 3.1912e+09 7.2306e+11 29285
## + TotRmsAbvGrd 1 1.1068e+09 7.2514e+11 29285
## <none> 7.2625e+11 29285
## + GarageArea 1 9.9677e+08 7.2525e+11 29285
## + `1stFlrSF` 1 9.8853e+08 7.2526e+11 29285
## + RoofStyle 5 4.7106e+09 7.2154e+11 29286
## + LotFrontage 1 6.4764e+08 7.2560e+11 29286
## + FullBath 1 6.4482e+08 7.2561e+11 29286
## + GarageCond 5 4.6068e+09 7.2164e+11 29286
## + Utilities 1 4.8206e+08 7.2577e+11 29286
## + `3SsnPorch` 1 4.0242e+08 7.2585e+11 29286
## + BsmtHalfBath 1 2.1505e+08 7.2603e+11 29287
## + HalfBath 1 2.0792e+08 7.2604e+11 29287
## + CentralAir 1 1.4348e+08 7.2611e+11 29287
## + YrSold 1 1.3711e+08 7.2611e+11 29287
## + Id 1 7.1280e+07 7.2618e+11 29287
## + EnclosedPorch 1 5.4934e+07 7.2619e+11 29287
## + OpenPorchSF 1 1.5759e+07 7.2623e+11 29287
## + MiscVal 1 3.2733e+05 7.2625e+11 29287
## + PavedDrive 2 7.1600e+08 7.2553e+11 29288
## + Foundation 5 3.6896e+09 7.2256e+11 29288
## + BsmtFinType1 5 3.6301e+09 7.2262e+11 29288
## + Fence 4 2.4802e+09 7.2377e+11 29288
## + LotShape 3 1.4348e+09 7.2482e+11 29288
## + Alley 2 2.5447e+08 7.2600e+11 29289
## + SaleType 8 6.2226e+09 7.2003e+11 29289
## + MasVnrType 3 1.0430e+09 7.2521e+11 29289
## + BsmtFinType2 6 3.9212e+09 7.2233e+11 29289
## + Heating 5 2.5387e+09 7.2371e+11 29290
## + BldgType 3 3.0768e+08 7.2594e+11 29291
## + ExterCond 4 7.6835e+08 7.2548e+11 29292
## + MiscFeature 4 7.1718e+08 7.2553e+11 29292
## - LotConfig 4 7.4664e+09 7.3372e+11 29292
## - Street 1 4.4728e+09 7.3072e+11 29292
## + Electrical 4 4.9882e+08 7.2575e+11 29292
## + FireplaceQu 5 1.4129e+09 7.2484e+11 29292
## - LandContour 3 6.8075e+09 7.3306e+11 29293
## - BedroomAbvGr 1 5.3683e+09 7.3162e+11 29294
## - PoolArea 1 5.5192e+09 7.3177e+11 29294
## + HouseStyle 7 2.4645e+09 7.2379e+11 29294
## - LandSlope 2 6.7889e+09 7.3304e+11 29295
## - ScreenPorch 1 7.3635e+09 7.3361e+11 29298
## - Condition1 8 1.5890e+10 7.4214e+11 29301
## + Exterior2nd 15 6.9055e+09 7.1934e+11 29301
## - Functional 6 1.5419e+10 7.4167e+11 29304
## - PoolQC 3 1.4346e+10 7.4060e+11 29308
## - TotalBsmtSF 1 1.3450e+10 7.3970e+11 29310
## - GarageCars 1 1.4749e+10 7.4100e+11 29312
## - ExterQual 3 1.7041e+10 7.4329e+11 29313
## - SaleCondition 5 2.3374e+10 7.4962e+11 29321
## - BsmtQual 4 2.4578e+10 7.5083e+11 29326
## - YearBuilt 1 2.5748e+10 7.5200e+11 29334
## - KitchenQual 3 2.9733e+10 7.5598e+11 29337
## - LotArea 1 2.9865e+10 7.5612e+11 29342
## - OverallQual 1 3.1626e+10 7.5788e+11 29345
## - BsmtExposure 4 3.7638e+10 7.6389e+11 29351
## - OverallCond 1 4.2419e+10 7.6867e+11 29366
## - MSSubClass 14 6.2166e+10 7.8842e+11 29376
## - BsmtFinSF1 1 5.6303e+10 7.8255e+11 29392
## - Condition2 7 8.7915e+10 8.1416e+11 29437
## - Neighborhood 24 1.4111e+11 8.6736e+11 29495
## - RoofMatl 7 1.3021e+11 8.5646e+11 29511
## - GrLivArea 1 2.1985e+11 9.4610e+11 29667
##
## Step: AIC=29278.26
## SalePrice ~ OverallQual + GrLivArea + Neighborhood + MSSubClass +
## RoofMatl + BsmtFinSF1 + BsmtQual + Condition2 + KitchenQual +
## BsmtExposure + OverallCond + YearBuilt + LotArea + SaleCondition +
## TotalBsmtSF + PoolQC + GarageCars + ExterQual + Functional +
## Condition1 + LotConfig + ScreenPorch + PoolArea + BedroomAbvGr +
## LandSlope + LandContour + Street + LowQualFinSF
##
## Df Sum of Sq RSS AIC
## + MasVnrArea 1 3.4240e+09 7.1837e+11 29273
## + GarageFinish 3 5.0029e+09 7.1679e+11 29274
## + GarageQual 3 5.0029e+09 7.1679e+11 29274
## + MSZoning 4 5.7262e+09 7.1606e+11 29275
## + GarageYrBlt 1 2.6547e+09 7.1914e+11 29275
## + KitchenAbvGr 1 2.5947e+09 7.1920e+11 29275
## + Fireplaces 1 2.4042e+09 7.1939e+11 29275
## + HeatingQC 4 5.2959e+09 7.1649e+11 29276
## + GarageType 6 7.1208e+09 7.1467e+11 29276
## + MoSold 1 2.1467e+09 7.1964e+11 29276
## + BsmtFullBath 1 2.0986e+09 7.1969e+11 29276
## + YearRemodAdd 1 1.9528e+09 7.1984e+11 29276
## + BsmtFinSF2 1 1.6768e+09 7.2011e+11 29277
## + BsmtUnfSF 1 1.6768e+09 7.2011e+11 29277
## + `1stFlrSF` 1 1.3429e+09 7.2045e+11 29278
## + `2ndFlrSF` 1 1.3429e+09 7.2045e+11 29278
## + WoodDeckSF 1 1.3417e+09 7.2045e+11 29278
## + TotRmsAbvGrd 1 1.2831e+09 7.2051e+11 29278
## + GarageCond 5 5.2395e+09 7.1655e+11 29278
## + Exterior1st 14 1.4047e+10 7.0774e+11 29278
## + GarageArea 1 1.1116e+09 7.2068e+11 29278
## <none> 7.2179e+11 29278
## + BsmtCond 3 2.8039e+09 7.1899e+11 29279
## + LotFrontage 1 8.0574e+08 7.2098e+11 29279
## + Utilities 1 5.1745e+08 7.2127e+11 29279
## + FullBath 1 5.1358e+08 7.2128e+11 29279
## + RoofStyle 5 4.4777e+09 7.1731e+11 29279
## + `3SsnPorch` 1 4.3834e+08 7.2135e+11 29279
## + CentralAir 1 3.0290e+08 7.2149e+11 29280
## + BsmtHalfBath 1 2.2467e+08 7.2157e+11 29280
## + HalfBath 1 1.7416e+08 7.2162e+11 29280
## + YrSold 1 8.4558e+07 7.2171e+11 29280
## + Id 1 3.3166e+07 7.2176e+11 29280
## + OpenPorchSF 1 1.5486e+07 7.2178e+11 29280
## + EnclosedPorch 1 4.1866e+06 7.2179e+11 29280
## + MiscVal 1 1.4059e+04 7.2179e+11 29280
## + Foundation 5 3.8729e+09 7.1792e+11 29281
## + BsmtFinType1 5 3.7020e+09 7.1809e+11 29281
## + PavedDrive 2 5.7710e+08 7.2121e+11 29281
## + LotShape 3 1.5092e+09 7.2028e+11 29281
## + SaleType 8 6.4120e+09 7.1538e+11 29281
## + Fence 4 2.2955e+09 7.1950e+11 29282
## + BsmtFinType2 6 4.1894e+09 7.1760e+11 29282
## + Alley 2 2.1439e+08 7.2158e+11 29282
## + MasVnrType 3 1.1105e+09 7.2068e+11 29282
## + Heating 5 2.4613e+09 7.1933e+11 29283
## + BldgType 3 3.4645e+08 7.2144e+11 29284
## + ExterCond 4 8.7489e+08 7.2092e+11 29285
## + MiscFeature 4 5.8098e+08 7.2121e+11 29285
## - LowQualFinSF 1 4.4593e+09 7.2625e+11 29285
## - LotConfig 4 7.6160e+09 7.2941e+11 29286
## + Electrical 4 3.6649e+08 7.2142e+11 29286
## + FireplaceQu 5 1.2852e+09 7.2051e+11 29286
## - Street 1 4.8607e+09 7.2665e+11 29286
## + HouseStyle 7 2.7578e+09 7.1903e+11 29287
## - LandContour 3 7.2336e+09 7.2902e+11 29287
## - PoolArea 1 5.2389e+09 7.2703e+11 29287
## - BedroomAbvGr 1 5.2497e+09 7.2704e+11 29287
## - LandSlope 2 7.2806e+09 7.2907e+11 29289
## - ScreenPorch 1 7.6256e+09 7.2942e+11 29292
## - Condition1 8 1.5537e+10 7.3733e+11 29293
## + Exterior2nd 15 7.0006e+09 7.1479e+11 29294
## - Functional 6 1.4928e+10 7.3672e+11 29296
## - PoolQC 3 1.4914e+10 7.3670e+11 29302
## - TotalBsmtSF 1 1.2909e+10 7.3470e+11 29302
## - GarageCars 1 1.4078e+10 7.3587e+11 29304
## - ExterQual 3 1.7216e+10 7.3901e+11 29307
## - SaleCondition 5 2.2884e+10 7.4467e+11 29314
## - BsmtQual 4 2.4648e+10 7.4644e+11 29319
## - YearBuilt 1 2.6120e+10 7.4791e+11 29328
## - KitchenQual 3 3.0716e+10 7.5251e+11 29333
## - LotArea 1 3.0291e+10 7.5208e+11 29336
## - OverallQual 1 3.0742e+10 7.5253e+11 29337
## - BsmtExposure 4 3.7341e+10 7.5913e+11 29344
## - OverallCond 1 4.3047e+10 7.6484e+11 29360
## - MSSubClass 14 5.9766e+10 7.8156e+11 29366
## - BsmtFinSF1 1 5.6061e+10 7.7785e+11 29385
## - Condition2 7 8.6726e+10 8.0852e+11 29429
## - Neighborhood 24 1.3998e+11 8.6177e+11 29488
## - RoofMatl 7 1.3302e+11 8.5481e+11 29510
## - GrLivArea 1 2.2389e+11 9.4569e+11 29668
##
## Step: AIC=29273.36
## SalePrice ~ OverallQual + GrLivArea + Neighborhood + MSSubClass +
## RoofMatl + BsmtFinSF1 + BsmtQual + Condition2 + KitchenQual +
## BsmtExposure + OverallCond + YearBuilt + LotArea + SaleCondition +
## TotalBsmtSF + PoolQC + GarageCars + ExterQual + Functional +
## Condition1 + LotConfig + ScreenPorch + PoolArea + BedroomAbvGr +
## LandSlope + LandContour + Street + LowQualFinSF + MasVnrArea
##
## Df Sum of Sq RSS AIC
## + Exterior1st 14 1.6009e+10 7.0236e+11 29269
## + MSZoning 4 6.1161e+09 7.1225e+11 29269
## + MasVnrType 3 5.0693e+09 7.1330e+11 29269
## + GarageYrBlt 1 2.7122e+09 7.1565e+11 29270
## + GarageFinish 3 4.6318e+09 7.1373e+11 29270
## + GarageQual 3 4.6318e+09 7.1373e+11 29270
## + BsmtFullBath 1 2.4949e+09 7.1587e+11 29270
## + KitchenAbvGr 1 2.4098e+09 7.1596e+11 29271
## + HeatingQC 4 5.3011e+09 7.1307e+11 29271
## + Fireplaces 1 2.1629e+09 7.1620e+11 29271
## + YearRemodAdd 1 2.1222e+09 7.1624e+11 29271
## + BsmtFinSF2 1 2.0974e+09 7.1627e+11 29271
## + BsmtUnfSF 1 2.0974e+09 7.1627e+11 29271
## + MoSold 1 2.0073e+09 7.1636e+11 29271
## + GarageType 6 6.8069e+09 7.1156e+11 29272
## + TotRmsAbvGrd 1 1.4071e+09 7.1696e+11 29273
## + WoodDeckSF 1 1.2632e+09 7.1710e+11 29273
## + GarageArea 1 1.1343e+09 7.1723e+11 29273
## + `1stFlrSF` 1 1.1310e+09 7.1724e+11 29273
## + `2ndFlrSF` 1 1.1310e+09 7.1724e+11 29273
## + GarageCond 5 4.9961e+09 7.1337e+11 29273
## <none> 7.1837e+11 29273
## + Utilities 1 7.9754e+08 7.1757e+11 29274
## + LotFrontage 1 7.8071e+08 7.1759e+11 29274
## + BsmtCond 3 2.6441e+09 7.1572e+11 29274
## + FullBath 1 5.6795e+08 7.1780e+11 29274
## + RoofStyle 5 4.4698e+09 7.1390e+11 29274
## + `3SsnPorch` 1 4.0605e+08 7.1796e+11 29275
## + CentralAir 1 3.3243e+08 7.1803e+11 29275
## + BsmtHalfBath 1 3.0295e+08 7.1806e+11 29275
## + HalfBath 1 1.3657e+08 7.1823e+11 29275
## + YrSold 1 9.7362e+07 7.1827e+11 29275
## + Id 1 8.9230e+07 7.1828e+11 29275
## + Foundation 5 4.0003e+09 7.1437e+11 29275
## + EnclosedPorch 1 5.8930e+06 7.1836e+11 29275
## + MiscVal 1 5.8462e+05 7.1837e+11 29275
## + OpenPorchSF 1 2.4230e+04 7.1837e+11 29275
## + BsmtFinType1 5 3.8843e+09 7.1448e+11 29276
## + LotShape 3 1.7056e+09 7.1666e+11 29276
## + SaleType 8 6.6167e+09 7.1175e+11 29276
## + BsmtFinType2 6 4.5266e+09 7.1384e+11 29276
## + PavedDrive 2 5.3551e+08 7.1783e+11 29276
## + Fence 4 2.2896e+09 7.1608e+11 29277
## + Alley 2 1.4661e+08 7.1822e+11 29277
## - MasVnrArea 1 3.4240e+09 7.2179e+11 29278
## + Heating 5 2.3884e+09 7.1598e+11 29279
## + BldgType 3 3.1755e+08 7.1805e+11 29279
## + ExterCond 4 8.7642e+08 7.1749e+11 29280
## - LowQualFinSF 1 4.2294e+09 7.2260e+11 29280
## - LotConfig 4 7.2872e+09 7.2565e+11 29280
## + MiscFeature 4 6.3978e+08 7.1773e+11 29280
## - Street 1 4.6323e+09 7.2300e+11 29281
## + Electrical 4 3.1383e+08 7.1805e+11 29281
## + FireplaceQu 5 1.2337e+09 7.1713e+11 29281
## - LandContour 3 6.9049e+09 7.2527e+11 29281
## - BedroomAbvGr 1 5.1190e+09 7.2349e+11 29282
## + HouseStyle 7 2.6951e+09 7.1567e+11 29282
## - PoolArea 1 5.3236e+09 7.2369e+11 29282
## - LandSlope 2 7.2754e+09 7.2564e+11 29284
## - ScreenPorch 1 7.2452e+09 7.2561e+11 29286
## + Exterior2nd 15 8.0783e+09 7.1029e+11 29287
## - Functional 6 1.3790e+10 7.3216e+11 29289
## - Condition1 8 1.5858e+10 7.3422e+11 29289
## - TotalBsmtSF 1 1.2550e+10 7.3092e+11 29297
## - GarageCars 1 1.2957e+10 7.3132e+11 29297
## - ExterQual 3 1.5109e+10 7.3348e+11 29298
## - PoolQC 3 1.5705e+10 7.3407e+11 29299
## - SaleCondition 5 2.2615e+10 7.4098e+11 29308
## - BsmtQual 4 2.3611e+10 7.4198e+11 29312
## - YearBuilt 1 2.5494e+10 7.4386e+11 29322
## - KitchenQual 3 3.1682e+10 7.5005e+11 29330
## - OverallQual 1 2.9851e+10 7.4822e+11 29330
## - LotArea 1 2.9872e+10 7.4824e+11 29331
## - BsmtExposure 4 3.6223e+10 7.5459e+11 29337
## - OverallCond 1 4.3824e+10 7.6219e+11 29357
## - MSSubClass 14 6.0611e+10 7.7898e+11 29363
## - BsmtFinSF1 1 5.4388e+10 7.7275e+11 29377
## - Condition2 7 8.8678e+10 8.0704e+11 29428
## - Neighborhood 24 1.3091e+11 8.4928e+11 29468
## - RoofMatl 7 1.3302e+11 8.5138e+11 29506
## - GrLivArea 1 2.1398e+11 9.3235e+11 29650
##
## Step: AIC=29268.66
## SalePrice ~ OverallQual + GrLivArea + Neighborhood + MSSubClass +
## RoofMatl + BsmtFinSF1 + BsmtQual + Condition2 + KitchenQual +
## BsmtExposure + OverallCond + YearBuilt + LotArea + SaleCondition +
## TotalBsmtSF + PoolQC + GarageCars + ExterQual + Functional +
## Condition1 + LotConfig + ScreenPorch + PoolArea + BedroomAbvGr +
## LandSlope + LandContour + Street + LowQualFinSF + MasVnrArea +
## Exterior1st
##
## Df Sum of Sq RSS AIC
## + MSZoning 4 7.0095e+09 6.9535e+11 29262
## + GarageYrBlt 1 3.3331e+09 6.9902e+11 29264
## + BsmtFullBath 1 2.8724e+09 6.9949e+11 29265
## + YearRemodAdd 1 2.8661e+09 6.9949e+11 29265
## + GarageFinish 3 4.2804e+09 6.9808e+11 29266
## + GarageQual 3 4.2804e+09 6.9808e+11 29266
## + Fireplaces 1 2.2299e+09 7.0013e+11 29266
## + KitchenAbvGr 1 2.2241e+09 7.0013e+11 29266
## + MoSold 1 2.1328e+09 7.0023e+11 29266
## + BsmtFinSF2 1 2.0312e+09 7.0033e+11 29267
## + BsmtUnfSF 1 2.0312e+09 7.0033e+11 29267
## + WoodDeckSF 1 1.6407e+09 7.0072e+11 29267
## + GarageArea 1 1.6308e+09 7.0073e+11 29267
## + MasVnrType 3 3.4695e+09 6.9889e+11 29268
## + TotRmsAbvGrd 1 1.3923e+09 7.0097e+11 29268
## + GarageType 6 6.2061e+09 6.9615e+11 29268
## + HeatingQC 4 4.1645e+09 6.9819e+11 29268
## + LotFrontage 1 1.0525e+09 7.0131e+11 29269
## <none> 7.0236e+11 29269
## + GarageCond 5 4.7167e+09 6.9764e+11 29269
## + Utilities 1 7.5866e+08 7.0160e+11 29269
## + `1stFlrSF` 1 7.5478e+08 7.0160e+11 29269
## + `2ndFlrSF` 1 7.5478e+08 7.0160e+11 29269
## + BsmtCond 3 2.4300e+09 6.9993e+11 29270
## + `3SsnPorch` 1 4.3431e+08 7.0192e+11 29270
## + BsmtHalfBath 1 4.3314e+08 7.0192e+11 29270
## + FullBath 1 3.7731e+08 7.0198e+11 29270
## + CentralAir 1 2.7365e+08 7.0208e+11 29270
## + BsmtFinType1 5 4.1022e+09 6.9826e+11 29270
## + Id 1 1.0814e+08 7.0225e+11 29270
## + HalfBath 1 1.0244e+08 7.0226e+11 29271
## + YrSold 1 6.8189e+07 7.0229e+11 29271
## + OpenPorchSF 1 2.0370e+07 7.0234e+11 29271
## + EnclosedPorch 1 6.1711e+06 7.0235e+11 29271
## + MiscVal 1 4.5124e+04 7.0236e+11 29271
## + RoofStyle 5 3.7362e+09 6.9862e+11 29271
## + Foundation 5 3.7217e+09 6.9864e+11 29271
## + Fence 4 2.5447e+09 6.9981e+11 29271
## + BsmtFinType2 6 4.4564e+09 6.9790e+11 29271
## + PavedDrive 2 5.8026e+08 7.0178e+11 29272
## + LotShape 3 1.4413e+09 7.0092e+11 29272
## + Alley 2 1.9603e+08 7.0216e+11 29272
## + SaleType 8 5.8350e+09 6.9652e+11 29273
## - Exterior1st 14 1.6009e+10 7.1837e+11 29273
## + BldgType 3 4.2136e+08 7.0194e+11 29274
## - LowQualFinSF 1 3.6959e+09 7.0605e+11 29274
## + ExterCond 4 8.2257e+08 7.0154e+11 29275
## + FireplaceQu 5 1.6980e+09 7.0066e+11 29275
## + Heating 5 1.6586e+09 7.0070e+11 29275
## + MiscFeature 4 6.4716e+08 7.0171e+11 29275
## - Street 1 4.3180e+09 7.0668e+11 29276
## - LotConfig 4 7.2725e+09 7.0963e+11 29276
## - BedroomAbvGr 1 4.5833e+09 7.0694e+11 29276
## + Electrical 4 1.1166e+08 7.0225e+11 29276
## - PoolArea 1 4.9931e+09 7.0735e+11 29277
## + HouseStyle 7 2.7274e+09 6.9963e+11 29277
## - LandContour 3 7.0579e+09 7.0942e+11 29277
## - MasVnrArea 1 5.3853e+09 7.0774e+11 29278
## - LandSlope 2 6.6928e+09 7.0905e+11 29278
## - ScreenPorch 1 6.2564e+09 7.0861e+11 29280
## - Functional 6 1.3316e+10 7.1567e+11 29284
## - Condition1 8 1.7156e+10 7.1951e+11 29288
## - TotalBsmtSF 1 1.0729e+10 7.1309e+11 29289
## + Exterior2nd 14 3.2161e+09 6.9914e+11 29290
## - ExterQual 3 1.3801e+10 7.1616e+11 29291
## - GarageCars 1 1.2871e+10 7.1523e+11 29293
## - PoolQC 3 1.4897e+10 7.1725e+11 29293
## - SaleCondition 5 2.0274e+10 7.2263e+11 29300
## - BsmtQual 4 2.3391e+10 7.2575e+11 29308
## - YearBuilt 1 2.4661e+10 7.2702e+11 29317
## - OverallQual 1 2.7217e+10 7.2957e+11 29322
## - KitchenQual 3 2.9842e+10 7.3220e+11 29323
## - LotArea 1 2.8344e+10 7.3070e+11 29324
## - BsmtExposure 4 3.8128e+10 7.4049e+11 29337
## - OverallCond 1 4.4311e+10 7.4667e+11 29355
## - MSSubClass 14 5.8179e+10 7.6054e+11 29356
## - BsmtFinSF1 1 5.5102e+10 7.5746e+11 29376
## - Condition2 7 8.6201e+10 7.8856e+11 29423
## - Neighborhood 24 1.2940e+11 8.3176e+11 29466
## - RoofMatl 7 1.2973e+11 8.3209e+11 29501
## - GrLivArea 1 2.0309e+11 9.0545e+11 29635
##
## Step: AIC=29262.11
## SalePrice ~ OverallQual + GrLivArea + Neighborhood + MSSubClass +
## RoofMatl + BsmtFinSF1 + BsmtQual + Condition2 + KitchenQual +
## BsmtExposure + OverallCond + YearBuilt + LotArea + SaleCondition +
## TotalBsmtSF + PoolQC + GarageCars + ExterQual + Functional +
## Condition1 + LotConfig + ScreenPorch + PoolArea + BedroomAbvGr +
## LandSlope + LandContour + Street + LowQualFinSF + MasVnrArea +
## Exterior1st + MSZoning
##
## Df Sum of Sq RSS AIC
## + GarageYrBlt 1 3.5359e+09 6.9181e+11 29257
## + YearRemodAdd 1 2.9687e+09 6.9238e+11 29258
## + BsmtFullBath 1 2.5054e+09 6.9284e+11 29259
## + GarageFinish 3 4.1231e+09 6.9123e+11 29260
## + GarageQual 3 4.1231e+09 6.9123e+11 29260
## + Fireplaces 1 2.1952e+09 6.9315e+11 29260
## + MoSold 1 1.7834e+09 6.9357e+11 29260
## + KitchenAbvGr 1 1.7350e+09 6.9361e+11 29261
## + BsmtFinSF2 1 1.7164e+09 6.9363e+11 29261
## + BsmtUnfSF 1 1.7164e+09 6.9363e+11 29261
## + MasVnrType 3 3.5420e+09 6.9181e+11 29261
## + TotRmsAbvGrd 1 1.6265e+09 6.9372e+11 29261
## + GarageArea 1 1.5678e+09 6.9378e+11 29261
## + GarageType 6 6.2184e+09 6.8913e+11 29261
## + WoodDeckSF 1 1.4393e+09 6.9391e+11 29261
## + HeatingQC 4 4.1372e+09 6.9121e+11 29262
## + GarageCond 5 4.8231e+09 6.9053e+11 29262
## + LotFrontage 1 1.0038e+09 6.9434e+11 29262
## <none> 6.9535e+11 29262
## + Utilities 1 7.8077e+08 6.9457e+11 29263
## + `1stFlrSF` 1 7.3910e+08 6.9461e+11 29263
## + `2ndFlrSF` 1 7.3910e+08 6.9461e+11 29263
## + BsmtFinType1 5 4.1988e+09 6.9115e+11 29263
## + `3SsnPorch` 1 3.5088e+08 6.9500e+11 29263
## + BsmtHalfBath 1 3.3463e+08 6.9501e+11 29263
## + FullBath 1 3.1149e+08 6.9504e+11 29264
## + Id 1 1.3892e+08 6.9521e+11 29264
## + BsmtCond 3 2.0171e+09 6.9333e+11 29264
## + CentralAir 1 8.8534e+07 6.9526e+11 29264
## + YrSold 1 8.6897e+07 6.9526e+11 29264
## + RoofStyle 5 3.8985e+09 6.9145e+11 29264
## + OpenPorchSF 1 3.8665e+07 6.9531e+11 29264
## + EnclosedPorch 1 2.6271e+07 6.9532e+11 29264
## + HalfBath 1 5.9827e+06 6.9534e+11 29264
## + MiscVal 1 1.1137e+06 6.9535e+11 29264
## + Fence 4 2.7904e+09 6.9256e+11 29264
## + PavedDrive 2 6.9622e+08 6.9465e+11 29265
## + Foundation 5 3.5589e+09 6.9179e+11 29265
## + LotShape 3 1.4599e+09 6.9389e+11 29265
## + BsmtFinType2 6 4.1507e+09 6.9120e+11 29265
## + SaleType 8 5.9347e+09 6.8941e+11 29266
## + Alley 2 1.1245e+08 6.9524e+11 29266
## - Street 1 3.2674e+09 6.9862e+11 29267
## - LowQualFinSF 1 3.4689e+09 6.9882e+11 29267
## + BldgType 3 3.7167e+08 6.9498e+11 29267
## + ExterCond 4 8.3673e+08 6.9451e+11 29268
## + MiscFeature 4 7.6691e+08 6.9458e+11 29269
## + Heating 5 1.7000e+09 6.9365e+11 29269
## + FireplaceQu 5 1.6559e+09 6.9369e+11 29269
## - LotConfig 4 7.0035e+09 7.0235e+11 29269
## - MSZoning 4 7.0095e+09 7.0236e+11 29269
## - Exterior1st 14 1.6902e+10 7.1225e+11 29269
## - BedroomAbvGr 1 4.4643e+09 6.9981e+11 29269
## - PoolArea 1 4.6364e+09 6.9998e+11 29270
## + Electrical 4 4.5401e+07 6.9530e+11 29270
## - LandContour 3 7.2708e+09 7.0262e+11 29271
## + HouseStyle 7 2.2504e+09 6.9310e+11 29271
## - MasVnrArea 1 5.9359e+09 7.0128e+11 29272
## - ScreenPorch 1 5.9451e+09 7.0129e+11 29273
## - LandSlope 2 7.2879e+09 7.0264e+11 29273
## - Functional 6 1.3901e+10 7.0925e+11 29279
## - Condition1 8 1.6352e+10 7.1170e+11 29280
## - TotalBsmtSF 1 1.0582e+10 7.0593e+11 29282
## + Exterior2nd 14 3.1350e+09 6.9221e+11 29284
## - ExterQual 3 1.4299e+10 7.0965e+11 29286
## - PoolQC 3 1.4422e+10 7.0977e+11 29286
## - GarageCars 1 1.4679e+10 7.1003e+11 29290
## - SaleCondition 5 1.9202e+10 7.1455e+11 29292
## - BsmtQual 4 2.3878e+10 7.1923e+11 29303
## - YearBuilt 1 2.3818e+10 7.1917e+11 29309
## - OverallQual 1 2.6216e+10 7.2156e+11 29314
## - KitchenQual 3 2.9777e+10 7.2513e+11 29317
## - LotArea 1 2.8075e+10 7.2342e+11 29318
## - BsmtExposure 4 3.8623e+10 7.3397e+11 29333
## - MSSubClass 14 4.9861e+10 7.4521e+11 29335
## - OverallCond 1 4.2687e+10 7.3804e+11 29347
## - BsmtFinSF1 1 5.3868e+10 7.4922e+11 29368
## - Condition2 7 8.6773e+10 7.8212e+11 29419
## - Neighborhood 24 1.2188e+11 8.1723e+11 29449
## - RoofMatl 7 1.3027e+11 8.2562e+11 29497
## - GrLivArea 1 2.0385e+11 8.9920e+11 29633
##
## Step: AIC=29256.71
## SalePrice ~ OverallQual + GrLivArea + Neighborhood + MSSubClass +
## RoofMatl + BsmtFinSF1 + BsmtQual + Condition2 + KitchenQual +
## BsmtExposure + OverallCond + YearBuilt + LotArea + SaleCondition +
## TotalBsmtSF + PoolQC + GarageCars + ExterQual + Functional +
## Condition1 + LotConfig + ScreenPorch + PoolArea + BedroomAbvGr +
## LandSlope + LandContour + Street + LowQualFinSF + MasVnrArea +
## Exterior1st + MSZoning + GarageYrBlt
##
## Df Sum of Sq RSS AIC
## + Fireplaces 1 2.7663e+09 6.8905e+11 29253
## + BsmtFullBath 1 2.4785e+09 6.8933e+11 29254
## + YearRemodAdd 1 1.9448e+09 6.8987e+11 29255
## + KitchenAbvGr 1 1.7775e+09 6.9004e+11 29255
## + MoSold 1 1.7529e+09 6.9006e+11 29255
## + BsmtFinSF2 1 1.6897e+09 6.9012e+11 29255
## + BsmtUnfSF 1 1.6897e+09 6.9012e+11 29255
## + MasVnrType 3 3.5012e+09 6.8831e+11 29255
## + TotRmsAbvGrd 1 1.5367e+09 6.9028e+11 29256
## + LotFrontage 1 1.2986e+09 6.9051e+11 29256
## + WoodDeckSF 1 1.1963e+09 6.9062e+11 29256
## + HeatingQC 4 3.9061e+09 6.8791e+11 29257
## <none> 6.9181e+11 29257
## + `1stFlrSF` 1 8.5656e+08 6.9096e+11 29257
## + `2ndFlrSF` 1 8.5656e+08 6.9096e+11 29257
## + GarageArea 1 7.7990e+08 6.9103e+11 29257
## + Utilities 1 6.8901e+08 6.9112e+11 29257
## + GarageFinish 3 2.3175e+09 6.8950e+11 29258
## + GarageQual 3 2.3175e+09 6.8950e+11 29258
## + `3SsnPorch` 1 3.0183e+08 6.9151e+11 29258
## + BsmtHalfBath 1 2.7353e+08 6.9154e+11 29258
## + BsmtCond 3 2.0644e+09 6.8975e+11 29258
## + FullBath 1 1.5050e+08 6.9166e+11 29258
## + RoofStyle 5 3.9084e+09 6.8790e+11 29259
## + Id 1 1.0087e+08 6.9171e+11 29259
## + BsmtFinType1 5 3.8833e+09 6.8793e+11 29259
## + YrSold 1 5.9554e+07 6.9175e+11 29259
## + CentralAir 1 3.0784e+07 6.9178e+11 29259
## + EnclosedPorch 1 2.2198e+07 6.9179e+11 29259
## + OpenPorchSF 1 2.1324e+07 6.9179e+11 29259
## + HalfBath 1 1.6801e+07 6.9180e+11 29259
## + MiscVal 1 4.7427e+06 6.9181e+11 29259
## + Fence 4 2.7359e+09 6.8908e+11 29259
## + PavedDrive 2 6.2556e+08 6.9119e+11 29259
## + LotShape 3 1.4580e+09 6.9035e+11 29260
## + BsmtFinType2 6 4.2483e+09 6.8756e+11 29260
## + GarageType 6 4.2115e+09 6.8760e+11 29260
## + Foundation 5 3.1257e+09 6.8869e+11 29260
## + Alley 2 1.1909e+08 6.9169e+11 29261
## + SaleType 8 5.6896e+09 6.8612e+11 29261
## - Street 1 3.2069e+09 6.9502e+11 29261
## + GarageCond 5 2.4928e+09 6.8932e+11 29262
## + BldgType 3 3.8991e+08 6.9142e+11 29262
## - GarageYrBlt 1 3.5359e+09 6.9535e+11 29262
## + Heating 5 1.9865e+09 6.8983e+11 29263
## + ExterCond 4 8.7585e+08 6.9094e+11 29263
## - LotConfig 4 6.8723e+09 6.9868e+11 29263
## + MiscFeature 4 7.5382e+08 6.9106e+11 29263
## + FireplaceQu 5 1.5421e+09 6.9027e+11 29264
## - MSZoning 4 7.2123e+09 6.9902e+11 29264
## - BedroomAbvGr 1 4.3408e+09 6.9615e+11 29264
## - PoolArea 1 4.5884e+09 6.9640e+11 29264
## - LowQualFinSF 1 4.5909e+09 6.9640e+11 29264
## + Electrical 4 4.3385e+07 6.9177e+11 29265
## - Exterior1st 14 1.7494e+10 7.0931e+11 29265
## + HouseStyle 7 1.9918e+09 6.8982e+11 29267
## - LandContour 3 7.6118e+09 6.9942e+11 29267
## - MasVnrArea 1 6.1239e+09 6.9794e+11 29268
## - ScreenPorch 1 6.3516e+09 6.9816e+11 29268
## - LandSlope 2 7.7286e+09 6.9954e+11 29269
## - Functional 6 1.3731e+10 7.0554e+11 29273
## - Condition1 8 1.6280e+10 7.0809e+11 29275
## - TotalBsmtSF 1 1.0967e+10 7.0278e+11 29278
## + Exterior2nd 14 3.0724e+09 6.8874e+11 29278
## - ExterQual 3 1.3835e+10 7.0565e+11 29279
## - PoolQC 3 1.4985e+10 7.0680e+11 29282
## - GarageCars 1 1.3492e+10 7.0530e+11 29283
## - SaleCondition 5 1.8418e+10 7.1023e+11 29285
## - YearBuilt 1 1.8693e+10 7.1051e+11 29293
## - BsmtQual 4 2.3241e+10 7.1505e+11 29297
## - OverallQual 1 2.6292e+10 7.1810e+11 29309
## - KitchenQual 3 2.9856e+10 7.2167e+11 29312
## - LotArea 1 2.9740e+10 7.2155e+11 29316
## - BsmtExposure 4 3.8557e+10 7.3037e+11 29327
## - MSSubClass 14 5.1637e+10 7.4345e+11 29333
## - OverallCond 1 4.2460e+10 7.3427e+11 29341
## - BsmtFinSF1 1 5.4557e+10 7.4637e+11 29365
## - Condition2 7 8.6436e+10 7.7825e+11 29414
## - Neighborhood 24 1.2313e+11 8.1494e+11 29446
## - RoofMatl 7 1.3100e+11 8.2282e+11 29494
## - GrLivArea 1 2.0135e+11 8.9316e+11 29625
##
## Step: AIC=29252.9
## SalePrice ~ OverallQual + GrLivArea + Neighborhood + MSSubClass +
## RoofMatl + BsmtFinSF1 + BsmtQual + Condition2 + KitchenQual +
## BsmtExposure + OverallCond + YearBuilt + LotArea + SaleCondition +
## TotalBsmtSF + PoolQC + GarageCars + ExterQual + Functional +
## Condition1 + LotConfig + ScreenPorch + PoolArea + BedroomAbvGr +
## LandSlope + LandContour + Street + LowQualFinSF + MasVnrArea +
## Exterior1st + MSZoning + GarageYrBlt + Fireplaces
##
## Df Sum of Sq RSS AIC
## + BsmtFullBath 1 2.4203e+09 6.8663e+11 29250
## + YearRemodAdd 1 2.1436e+09 6.8690e+11 29250
## + MoSold 1 1.9111e+09 6.8714e+11 29251
## + BsmtFinSF2 1 1.7864e+09 6.8726e+11 29251
## + BsmtUnfSF 1 1.7864e+09 6.8726e+11 29251
## + KitchenAbvGr 1 1.6239e+09 6.8742e+11 29252
## + MasVnrType 3 3.4812e+09 6.8557e+11 29252
## + TotRmsAbvGrd 1 1.5165e+09 6.8753e+11 29252
## + `1stFlrSF` 1 1.2958e+09 6.8775e+11 29252
## + `2ndFlrSF` 1 1.2958e+09 6.8775e+11 29252
## + LotFrontage 1 1.2777e+09 6.8777e+11 29252
## + WoodDeckSF 1 1.0241e+09 6.8802e+11 29253
## <none> 6.8905e+11 29253
## + GarageArea 1 8.7994e+08 6.8817e+11 29253
## + Utilities 1 7.1056e+08 6.8834e+11 29253
## + HeatingQC 4 3.5171e+09 6.8553e+11 29254
## + `3SsnPorch` 1 3.8409e+08 6.8866e+11 29254
## + RoofStyle 5 4.0809e+09 6.8497e+11 29254
## + GarageFinish 3 2.1634e+09 6.8688e+11 29254
## + GarageQual 3 2.1634e+09 6.8688e+11 29254
## + BsmtHalfBath 1 2.6693e+08 6.8878e+11 29254
## + BsmtCond 3 2.1404e+09 6.8691e+11 29254
## + FullBath 1 2.2107e+08 6.8883e+11 29254
## + BsmtFinType1 5 3.9065e+09 6.8514e+11 29255
## + Id 1 1.1248e+08 6.8893e+11 29255
## + YrSold 1 7.0735e+07 6.8898e+11 29255
## + EnclosedPorch 1 2.4460e+07 6.8902e+11 29255
## + OpenPorchSF 1 8.8103e+06 6.8904e+11 29255
## + HalfBath 1 7.0756e+06 6.8904e+11 29255
## + MiscVal 1 3.9688e+06 6.8904e+11 29255
## + CentralAir 1 1.1147e+05 6.8905e+11 29255
## + FireplaceQu 5 3.7360e+09 6.8531e+11 29255
## + PavedDrive 2 8.5861e+08 6.8819e+11 29255
## + Fence 4 2.5529e+09 6.8649e+11 29256
## + LotShape 3 1.6035e+09 6.8744e+11 29256
## + GarageType 6 4.3620e+09 6.8468e+11 29256
## + BsmtFinType2 6 4.2264e+09 6.8482e+11 29256
## + Alley 2 1.0833e+08 6.8894e+11 29257
## + Foundation 5 2.9501e+09 6.8610e+11 29257
## - Fireplaces 1 2.7663e+09 6.9181e+11 29257
## + SaleType 8 5.6284e+09 6.8342e+11 29257
## - Street 1 3.2792e+09 6.9233e+11 29258
## + BldgType 3 3.5611e+08 6.8869e+11 29258
## - BedroomAbvGr 1 3.5437e+09 6.9259e+11 29258
## + GarageCond 5 2.1604e+09 6.8689e+11 29258
## + Heating 5 1.9853e+09 6.8706e+11 29259
## - LotConfig 4 6.7708e+09 6.9582e+11 29259
## + ExterCond 4 8.2022e+08 6.8823e+11 29259
## + MiscFeature 4 7.9862e+08 6.8825e+11 29259
## - GarageYrBlt 1 4.1070e+09 6.9315e+11 29260
## - LowQualFinSF 1 4.2314e+09 6.9328e+11 29260
## - MSZoning 4 7.1847e+09 6.9623e+11 29260
## - PoolArea 1 4.5432e+09 6.9359e+11 29260
## + Electrical 4 7.1869e+07 6.8897e+11 29261
## - Exterior1st 14 1.7566e+10 7.0661e+11 29261
## - ScreenPorch 1 5.4011e+09 6.9445e+11 29262
## - LandContour 3 7.5314e+09 6.9658e+11 29263
## - MasVnrArea 1 5.7498e+09 6.9480e+11 29263
## + HouseStyle 7 1.6634e+09 6.8738e+11 29263
## - LandSlope 2 7.9377e+09 6.9698e+11 29266
## - Functional 6 1.3735e+10 7.0278e+11 29270
## - Condition1 8 1.6846e+10 7.0589e+11 29272
## - TotalBsmtSF 1 1.0688e+10 6.9973e+11 29273
## + Exterior2nd 14 3.0103e+09 6.8604e+11 29275
## - ExterQual 3 1.4000e+10 7.0305e+11 29276
## - GarageCars 1 1.3484e+10 7.0253e+11 29279
## - PoolQC 3 1.5482e+10 7.0453e+11 29279
## - SaleCondition 5 1.8111e+10 7.0716e+11 29281
## - YearBuilt 1 1.8488e+10 7.0753e+11 29289
## - BsmtQual 4 2.3925e+10 7.1297e+11 29294
## - OverallQual 1 2.3829e+10 7.1288e+11 29300
## - KitchenQual 3 2.9187e+10 7.1823e+11 29307
## - LotArea 1 2.8275e+10 7.1732e+11 29309
## - BsmtExposure 4 3.7638e+10 7.2668e+11 29322
## - MSSubClass 14 4.9232e+10 7.3828e+11 29325
## - OverallCond 1 4.3334e+10 7.3238e+11 29339
## - BsmtFinSF1 1 5.2143e+10 7.4119e+11 29357
## - Condition2 7 8.3546e+10 7.7259e+11 29405
## - Neighborhood 24 1.2315e+11 8.1219e+11 29444
## - RoofMatl 7 1.3020e+11 8.1925e+11 29490
## - GrLivArea 1 1.8556e+11 8.7461e+11 29597
##
## Step: AIC=29249.79
## SalePrice ~ OverallQual + GrLivArea + Neighborhood + MSSubClass +
## RoofMatl + BsmtFinSF1 + BsmtQual + Condition2 + KitchenQual +
## BsmtExposure + OverallCond + YearBuilt + LotArea + SaleCondition +
## TotalBsmtSF + PoolQC + GarageCars + ExterQual + Functional +
## Condition1 + LotConfig + ScreenPorch + PoolArea + BedroomAbvGr +
## LandSlope + LandContour + Street + LowQualFinSF + MasVnrArea +
## Exterior1st + MSZoning + GarageYrBlt + Fireplaces + BsmtFullBath
##
## Df Sum of Sq RSS AIC
## + YearRemodAdd 1 1.9604e+09 6.8467e+11 29248
## + MoSold 1 1.8228e+09 6.8480e+11 29248
## + MasVnrType 3 3.4799e+09 6.8315e+11 29248
## + KitchenAbvGr 1 1.5185e+09 6.8511e+11 29249
## + TotRmsAbvGrd 1 1.3708e+09 6.8526e+11 29249
## + `1stFlrSF` 1 1.3103e+09 6.8532e+11 29249
## + `2ndFlrSF` 1 1.3103e+09 6.8532e+11 29249
## + LotFrontage 1 1.2945e+09 6.8533e+11 29249
## <none> 6.8663e+11 29250
## + BsmtFinSF2 1 9.3625e+08 6.8569e+11 29250
## + BsmtUnfSF 1 9.3625e+08 6.8569e+11 29250
## + WoodDeckSF 1 8.6817e+08 6.8576e+11 29250
## + GarageArea 1 7.6265e+08 6.8586e+11 29250
## + Utilities 1 7.2118e+08 6.8590e+11 29250
## + FullBath 1 4.4518e+08 6.8618e+11 29251
## + `3SsnPorch` 1 3.9366e+08 6.8623e+11 29251
## + HeatingQC 4 3.1838e+09 6.8344e+11 29251
## + BsmtCond 3 2.2035e+09 6.8442e+11 29251
## + GarageFinish 3 2.1003e+09 6.8453e+11 29251
## + GarageQual 3 2.1003e+09 6.8453e+11 29251
## + RoofStyle 5 3.8786e+09 6.8275e+11 29252
## + Id 1 1.0141e+08 6.8652e+11 29252
## + YrSold 1 2.1630e+07 6.8660e+11 29252
## + EnclosedPorch 1 5.0834e+06 6.8662e+11 29252
## + BsmtHalfBath 1 5.0458e+06 6.8662e+11 29252
## + CentralAir 1 1.2033e+06 6.8662e+11 29252
## + MiscVal 1 1.0628e+06 6.8662e+11 29252
## + HalfBath 1 1.0110e+06 6.8662e+11 29252
## + OpenPorchSF 1 3.4537e+05 6.8663e+11 29252
## + FireplaceQu 5 3.7169e+09 6.8291e+11 29252
## + Fence 4 2.6974e+09 6.8393e+11 29252
## + LotShape 3 1.7356e+09 6.8489e+11 29252
## + PavedDrive 2 7.8443e+08 6.8584e+11 29252
## + BsmtFinType1 5 3.2776e+09 6.8335e+11 29253
## - BsmtFullBath 1 2.4203e+09 6.8905e+11 29253
## + GarageType 6 4.1486e+09 6.8248e+11 29253
## - Fireplaces 1 2.7082e+09 6.8933e+11 29254
## + SaleType 8 5.7568e+09 6.8087e+11 29254
## + Alley 2 9.2175e+07 6.8653e+11 29254
## + Foundation 5 2.8801e+09 6.8375e+11 29254
## + BsmtFinType2 6 3.5402e+09 6.8309e+11 29254
## - BedroomAbvGr 1 3.3102e+09 6.8994e+11 29255
## + GarageCond 5 2.2893e+09 6.8434e+11 29255
## + BldgType 3 3.9864e+08 6.8623e+11 29255
## - Street 1 3.4150e+09 6.9004e+11 29255
## + Heating 5 1.8884e+09 6.8474e+11 29256
## + ExterCond 4 9.2770e+08 6.8570e+11 29256
## + MiscFeature 4 8.6061e+08 6.8577e+11 29256
## - MSZoning 4 6.8193e+09 6.9345e+11 29256
## - LotConfig 4 6.8409e+09 6.9347e+11 29256
## - GarageYrBlt 1 4.0719e+09 6.9070e+11 29256
## - LowQualFinSF 1 4.3810e+09 6.9101e+11 29257
## + Electrical 4 9.3750e+07 6.8653e+11 29258
## - PoolArea 1 4.8264e+09 6.9145e+11 29258
## - LandContour 3 7.2439e+09 6.9387e+11 29259
## - Exterior1st 14 1.7886e+10 7.0451e+11 29259
## - ScreenPorch 1 5.5649e+09 6.9219e+11 29260
## + HouseStyle 7 1.5936e+09 6.8503e+11 29260
## - MasVnrArea 1 6.3044e+09 6.9293e+11 29261
## - LandSlope 2 8.3836e+09 6.9501e+11 29263
## - Functional 6 1.3892e+10 7.0052e+11 29267
## - TotalBsmtSF 1 1.0405e+10 6.9703e+11 29270
## - Condition1 8 1.7391e+10 7.0402e+11 29270
## + Exterior2nd 14 3.1269e+09 6.8350e+11 29271
## - ExterQual 3 1.4188e+10 7.0081e+11 29274
## - GarageCars 1 1.3258e+10 6.9988e+11 29276
## - PoolQC 3 1.6301e+10 7.0293e+11 29278
## - SaleCondition 5 1.8521e+10 7.0515e+11 29278
## - YearBuilt 1 1.8867e+10 7.0549e+11 29287
## - BsmtQual 4 2.3702e+10 7.1033e+11 29291
## - OverallQual 1 2.4157e+10 7.1078e+11 29298
## - BsmtFinSF1 1 2.6768e+10 7.1339e+11 29303
## - KitchenQual 3 2.9053e+10 7.1568e+11 29304
## - LotArea 1 2.7793e+10 7.1442e+11 29305
## - BsmtExposure 4 3.6764e+10 7.2339e+11 29318
## - MSSubClass 14 5.0888e+10 7.3751e+11 29326
## - OverallCond 1 4.4171e+10 7.3080e+11 29338
## - Condition2 7 8.2474e+10 7.6910e+11 29400
## - Neighborhood 24 1.2282e+11 8.0945e+11 29441
## - RoofMatl 7 1.2538e+11 8.1201e+11 29479
## - GrLivArea 1 1.8739e+11 8.7402e+11 29598
##
## Step: AIC=29247.64
## SalePrice ~ OverallQual + GrLivArea + Neighborhood + MSSubClass +
## RoofMatl + BsmtFinSF1 + BsmtQual + Condition2 + KitchenQual +
## BsmtExposure + OverallCond + YearBuilt + LotArea + SaleCondition +
## TotalBsmtSF + PoolQC + GarageCars + ExterQual + Functional +
## Condition1 + LotConfig + ScreenPorch + PoolArea + BedroomAbvGr +
## LandSlope + LandContour + Street + LowQualFinSF + MasVnrArea +
## Exterior1st + MSZoning + GarageYrBlt + Fireplaces + BsmtFullBath +
## YearRemodAdd
##
## Df Sum of Sq RSS AIC
## + MoSold 1 1.8130e+09 6.8285e+11 29246
## + MasVnrType 3 3.5034e+09 6.8116e+11 29246
## + KitchenAbvGr 1 1.5847e+09 6.8308e+11 29246
## + `1stFlrSF` 1 1.5591e+09 6.8311e+11 29246
## + `2ndFlrSF` 1 1.5591e+09 6.8311e+11 29246
## + LotFrontage 1 1.3217e+09 6.8334e+11 29247
## + TotRmsAbvGrd 1 1.2561e+09 6.8341e+11 29247
## + GarageArea 1 1.0137e+09 6.8365e+11 29248
## + BsmtFinSF2 1 9.8724e+08 6.8368e+11 29248
## + BsmtUnfSF 1 9.8724e+08 6.8368e+11 29248
## <none> 6.8467e+11 29248
## + WoodDeckSF 1 8.5613e+08 6.8381e+11 29248
## + Utilities 1 6.1045e+08 6.8406e+11 29248
## + BsmtCond 3 2.4052e+09 6.8226e+11 29249
## + FullBath 1 3.6213e+08 6.8430e+11 29249
## + `3SsnPorch` 1 3.3314e+08 6.8433e+11 29249
## + Id 1 1.3387e+08 6.8453e+11 29249
## + HeatingQC 4 2.9332e+09 6.8173e+11 29249
## + Fence 4 2.8786e+09 6.8179e+11 29250
## + RoofStyle 5 3.7985e+09 6.8087e+11 29250
## + BsmtHalfBath 1 1.5892e+07 6.8465e+11 29250
## + FireplaceQu 5 3.7748e+09 6.8089e+11 29250
## + CentralAir 1 7.5066e+06 6.8466e+11 29250
## + EnclosedPorch 1 3.8811e+06 6.8466e+11 29250
## + YrSold 1 3.8230e+06 6.8466e+11 29250
## + MiscVal 1 3.4580e+06 6.8466e+11 29250
## + OpenPorchSF 1 7.4770e+05 6.8466e+11 29250
## + HalfBath 1 3.5639e+05 6.8467e+11 29250
## + GarageFinish 3 1.8840e+09 6.8278e+11 29250
## + GarageQual 3 1.8840e+09 6.8278e+11 29250
## - YearRemodAdd 1 1.9604e+09 6.8663e+11 29250
## - BsmtFullBath 1 2.2371e+09 6.8690e+11 29250
## + LotShape 3 1.5155e+09 6.8315e+11 29250
## + PavedDrive 2 5.5505e+08 6.8411e+11 29251
## + GarageType 6 4.0986e+09 6.8057e+11 29251
## + BsmtFinType1 5 2.9702e+09 6.8170e+11 29251
## + Alley 2 8.8469e+07 6.8458e+11 29252
## + Foundation 5 2.8506e+09 6.8181e+11 29252
## - Fireplaces 1 2.8982e+09 6.8756e+11 29252
## - GarageYrBlt 1 2.9812e+09 6.8765e+11 29252
## + SaleType 8 5.4285e+09 6.7924e+11 29252
## + BsmtFinType2 6 3.5465e+09 6.8112e+11 29252
## - BedroomAbvGr 1 3.0805e+09 6.8775e+11 29252
## - Street 1 3.3315e+09 6.8800e+11 29253
## + BldgType 3 3.7468e+08 6.8429e+11 29253
## + GarageCond 5 2.2317e+09 6.8243e+11 29253
## + MiscFeature 4 9.6939e+08 6.8370e+11 29254
## + ExterCond 4 9.1071e+08 6.8375e+11 29254
## + Heating 5 1.8418e+09 6.8282e+11 29254
## - LotConfig 4 6.8119e+09 6.9148e+11 29254
## - MSZoning 4 6.8800e+09 6.9155e+11 29254
## - LowQualFinSF 1 4.2435e+09 6.8891e+11 29255
## + Electrical 4 1.7427e+08 6.8449e+11 29255
## - PoolArea 1 5.0258e+09 6.8969e+11 29256
## - LandContour 3 7.2126e+09 6.9188e+11 29257
## - ScreenPorch 1 5.5956e+09 6.9026e+11 29258
## - Exterior1st 14 1.8391e+10 7.0306e+11 29258
## + HouseStyle 7 1.5719e+09 6.8309e+11 29258
## - MasVnrArea 1 6.5839e+09 6.9125e+11 29260
## - LandSlope 2 8.4607e+09 6.9313e+11 29262
## - Functional 6 1.4893e+10 6.9956e+11 29267
## - Condition1 8 1.7160e+10 7.0183e+11 29268
## - TotalBsmtSF 1 1.0830e+10 6.9550e+11 29268
## + Exterior2nd 14 3.2723e+09 6.8139e+11 29269
## - ExterQual 3 1.4289e+10 6.9895e+11 29272
## - SaleCondition 5 1.7433e+10 7.0210e+11 29274
## - GarageCars 1 1.3710e+10 6.9838e+11 29274
## - PoolQC 3 1.6152e+10 7.0082e+11 29276
## - YearBuilt 1 1.7185e+10 7.0185e+11 29282
## - BsmtQual 4 2.3726e+10 7.0839e+11 29289
## - OverallQual 1 2.4027e+10 7.0869e+11 29296
## - KitchenQual 3 2.8428e+10 7.1309e+11 29301
## - BsmtFinSF1 1 2.7314e+10 7.1198e+11 29302
## - LotArea 1 2.7887e+10 7.1255e+11 29304
## - OverallCond 1 3.1837e+10 7.1650e+11 29312
## - BsmtExposure 4 3.6395e+10 7.2106e+11 29315
## - MSSubClass 14 5.1485e+10 7.3615e+11 29325
## - Condition2 7 8.2344e+10 7.6701e+11 29398
## - Neighborhood 24 1.2370e+11 8.0837e+11 29441
## - RoofMatl 7 1.2607e+11 8.1074e+11 29479
## - GrLivArea 1 1.8027e+11 8.6493e+11 29585
##
## Step: AIC=29245.8
## SalePrice ~ OverallQual + GrLivArea + Neighborhood + MSSubClass +
## RoofMatl + BsmtFinSF1 + BsmtQual + Condition2 + KitchenQual +
## BsmtExposure + OverallCond + YearBuilt + LotArea + SaleCondition +
## TotalBsmtSF + PoolQC + GarageCars + ExterQual + Functional +
## Condition1 + LotConfig + ScreenPorch + PoolArea + BedroomAbvGr +
## LandSlope + LandContour + Street + LowQualFinSF + MasVnrArea +
## Exterior1st + MSZoning + GarageYrBlt + Fireplaces + BsmtFullBath +
## YearRemodAdd + MoSold
##
## Df Sum of Sq RSS AIC
## + MasVnrType 3 3.4212e+09 6.7943e+11 29245
## + `1stFlrSF` 1 1.5111e+09 6.8134e+11 29245
## + `2ndFlrSF` 1 1.5111e+09 6.8134e+11 29245
## + KitchenAbvGr 1 1.4937e+09 6.8136e+11 29245
## + LotFrontage 1 1.2594e+09 6.8159e+11 29245
## + TotRmsAbvGrd 1 1.1073e+09 6.8175e+11 29245
## + BsmtFinSF2 1 1.0120e+09 6.8184e+11 29246
## + BsmtUnfSF 1 1.0120e+09 6.8184e+11 29246
## + GarageArea 1 9.4825e+08 6.8190e+11 29246
## <none> 6.8285e+11 29246
## + WoodDeckSF 1 9.1997e+08 6.8193e+11 29246
## + Utilities 1 7.3025e+08 6.8212e+11 29246
## + BsmtCond 3 2.3737e+09 6.8048e+11 29247
## + FullBath 1 4.1027e+08 6.8244e+11 29247
## + `3SsnPorch` 1 3.7778e+08 6.8247e+11 29247
## + Id 1 1.4982e+08 6.8270e+11 29248
## + Fence 4 2.9240e+09 6.7993e+11 29248
## - MoSold 1 1.8130e+09 6.8467e+11 29248
## + GarageFinish 3 1.9423e+09 6.8091e+11 29248
## + GarageQual 3 1.9423e+09 6.8091e+11 29248
## + HeatingQC 4 2.8726e+09 6.7998e+11 29248
## + FireplaceQu 5 3.7972e+09 6.7906e+11 29248
## + YrSold 1 1.5396e+07 6.8284e+11 29248
## + OpenPorchSF 1 1.3972e+07 6.8284e+11 29248
## + CentralAir 1 9.9384e+06 6.8284e+11 29248
## + BsmtHalfBath 1 8.6026e+06 6.8284e+11 29248
## + MiscVal 1 5.1581e+06 6.8285e+11 29248
## + HalfBath 1 4.8122e+06 6.8285e+11 29248
## + EnclosedPorch 1 5.7432e+04 6.8285e+11 29248
## - YearRemodAdd 1 1.9506e+09 6.8480e+11 29248
## + RoofStyle 5 3.6505e+09 6.7920e+11 29248
## - BsmtFullBath 1 2.1530e+09 6.8501e+11 29248
## + GarageType 6 4.4098e+09 6.7844e+11 29248
## + LotShape 3 1.5029e+09 6.8135e+11 29249
## + PavedDrive 2 5.5182e+08 6.8230e+11 29249
## + Alley 2 1.0035e+08 6.8275e+11 29250
## + BsmtFinType1 5 2.8837e+09 6.7997e+11 29250
## + SaleType 8 5.6547e+09 6.7720e+11 29250
## + Foundation 5 2.7874e+09 6.8007e+11 29250
## - BedroomAbvGr 1 2.8859e+09 6.8574e+11 29250
## - GarageYrBlt 1 2.9708e+09 6.8582e+11 29250
## - Fireplaces 1 3.0562e+09 6.8591e+11 29250
## + BsmtFinType2 6 3.5097e+09 6.7934e+11 29250
## - Street 1 3.2589e+09 6.8611e+11 29251
## + BldgType 3 4.1542e+08 6.8244e+11 29251
## + GarageCond 5 2.1856e+09 6.8067e+11 29251
## + MiscFeature 4 1.0318e+09 6.8182e+11 29252
## - MSZoning 4 6.5453e+09 6.8940e+11 29252
## + ExterCond 4 9.3477e+08 6.8192e+11 29252
## + Heating 5 1.7840e+09 6.8107e+11 29252
## - LotConfig 4 6.7960e+09 6.8965e+11 29252
## - LowQualFinSF 1 4.3249e+09 6.8718e+11 29253
## + Electrical 4 2.2372e+08 6.8263e+11 29253
## - PoolArea 1 4.8929e+09 6.8775e+11 29254
## - LandContour 3 7.3474e+09 6.9020e+11 29255
## - ScreenPorch 1 5.6752e+09 6.8853e+11 29256
## + HouseStyle 7 1.7178e+09 6.8113e+11 29256
## - Exterior1st 14 1.8463e+10 7.0132e+11 29257
## - MasVnrArea 1 6.3913e+09 6.8924e+11 29257
## - LandSlope 2 8.2661e+09 6.9112e+11 29259
## - Functional 6 1.4849e+10 6.9770e+11 29265
## - TotalBsmtSF 1 1.0631e+10 6.9348e+11 29266
## + Exterior2nd 14 3.2599e+09 6.7959e+11 29267
## - Condition1 8 1.7749e+10 7.0060e+11 29267
## - ExterQual 3 1.3854e+10 6.9671e+11 29269
## - GarageCars 1 1.3639e+10 6.9649e+11 29273
## - PoolQC 3 1.6120e+10 6.9897e+11 29274
## - SaleCondition 5 1.8065e+10 7.0092e+11 29274
## - YearBuilt 1 1.7178e+10 7.0003e+11 29280
## - BsmtQual 4 2.3213e+10 7.0607e+11 29286
## - OverallQual 1 2.4629e+10 7.0748e+11 29295
## - KitchenQual 3 2.8228e+10 7.1108e+11 29299
## - BsmtFinSF1 1 2.7613e+10 7.1047e+11 29301
## - LotArea 1 2.7796e+10 7.1065e+11 29302
## - OverallCond 1 3.1433e+10 7.1429e+11 29309
## - BsmtExposure 4 3.6071e+10 7.1892e+11 29313
## - MSSubClass 14 5.1695e+10 7.3455e+11 29324
## - Condition2 7 8.2071e+10 7.6492e+11 29397
## - Neighborhood 24 1.2473e+11 8.0758e+11 29441
## - RoofMatl 7 1.2699e+11 8.0985e+11 29479
## - GrLivArea 1 1.8065e+11 8.6350e+11 29584
##
## Step: AIC=29244.51
## SalePrice ~ OverallQual + GrLivArea + Neighborhood + MSSubClass +
## RoofMatl + BsmtFinSF1 + BsmtQual + Condition2 + KitchenQual +
## BsmtExposure + OverallCond + YearBuilt + LotArea + SaleCondition +
## TotalBsmtSF + PoolQC + GarageCars + ExterQual + Functional +
## Condition1 + LotConfig + ScreenPorch + PoolArea + BedroomAbvGr +
## LandSlope + LandContour + Street + LowQualFinSF + MasVnrArea +
## Exterior1st + MSZoning + GarageYrBlt + Fireplaces + BsmtFullBath +
## YearRemodAdd + MoSold + MasVnrType
##
## Df Sum of Sq RSS AIC
## + KitchenAbvGr 1 1.6867e+09 6.7774e+11 29243
## + LotFrontage 1 1.3597e+09 6.7807e+11 29244
## + `1stFlrSF` 1 1.2582e+09 6.7817e+11 29244
## + `2ndFlrSF` 1 1.2582e+09 6.7817e+11 29244
## + TotRmsAbvGrd 1 1.0539e+09 6.7838e+11 29244
## + BsmtFinSF2 1 9.8949e+08 6.7844e+11 29244
## + BsmtUnfSF 1 9.8949e+08 6.7844e+11 29244
## <none> 6.7943e+11 29245
## + WoodDeckSF 1 9.0357e+08 6.7853e+11 29245
## + GarageArea 1 8.7935e+08 6.7855e+11 29245
## + Utilities 1 8.1983e+08 6.7861e+11 29245
## + BsmtCond 3 2.3536e+09 6.7708e+11 29246
## + FullBath 1 4.6390e+08 6.7897e+11 29246
## + `3SsnPorch` 1 4.4602e+08 6.7899e+11 29246
## - MasVnrType 3 3.4212e+09 6.8285e+11 29246
## - MoSold 1 1.7308e+09 6.8116e+11 29246
## + Id 1 8.3717e+07 6.7935e+11 29246
## + FireplaceQu 5 3.8007e+09 6.7563e+11 29246
## + YrSold 1 4.1621e+07 6.7939e+11 29246
## + OpenPorchSF 1 3.5707e+07 6.7940e+11 29246
## + CentralAir 1 7.8519e+06 6.7942e+11 29247
## + MiscVal 1 5.0049e+06 6.7943e+11 29247
## + HalfBath 1 1.4173e+06 6.7943e+11 29247
## + BsmtHalfBath 1 6.4265e+05 6.7943e+11 29247
## + EnclosedPorch 1 3.8445e+05 6.7943e+11 29247
## + RoofStyle 5 3.7246e+09 6.7571e+11 29247
## - YearRemodAdd 1 1.9766e+09 6.8141e+11 29247
## + GarageFinish 3 1.6902e+09 6.7774e+11 29247
## + GarageQual 3 1.6902e+09 6.7774e+11 29247
## + Fence 4 2.6078e+09 6.7682e+11 29247
## + HeatingQC 4 2.5933e+09 6.7684e+11 29247
## - BsmtFullBath 1 2.1515e+09 6.8158e+11 29247
## + PavedDrive 2 5.6684e+08 6.7886e+11 29247
## + LotShape 3 1.4409e+09 6.7799e+11 29247
## + SaleType 8 5.7966e+09 6.7363e+11 29248
## + GarageType 6 3.8914e+09 6.7554e+11 29248
## + Alley 2 1.1290e+08 6.7932e+11 29248
## - BedroomAbvGr 1 2.7101e+09 6.8214e+11 29248
## + BsmtFinType1 5 2.8567e+09 6.7657e+11 29248
## + Foundation 5 2.8411e+09 6.7659e+11 29248
## - GarageYrBlt 1 2.9262e+09 6.8236e+11 29249
## - Fireplaces 1 3.0375e+09 6.8247e+11 29249
## + BsmtFinType2 6 3.4374e+09 6.7599e+11 29249
## - Street 1 3.1387e+09 6.8257e+11 29249
## + BldgType 3 3.6758e+08 6.7906e+11 29250
## + GarageCond 5 2.1116e+09 6.7732e+11 29250
## + MiscFeature 4 1.0331e+09 6.7840e+11 29250
## + ExterCond 4 9.6229e+08 6.7847e+11 29251
## - MSZoning 4 6.5741e+09 6.8601e+11 29251
## + Heating 5 1.7751e+09 6.7766e+11 29251
## - LotConfig 4 6.9096e+09 6.8634e+11 29251
## - LowQualFinSF 1 4.4257e+09 6.8386e+11 29252
## + Electrical 4 1.8992e+08 6.7924e+11 29252
## - Exterior1st 14 1.6970e+10 6.9640e+11 29252
## - PoolArea 1 4.8953e+09 6.8433e+11 29253
## - LandContour 3 6.9340e+09 6.8637e+11 29253
## - ScreenPorch 1 5.5561e+09 6.8499e+11 29254
## + HouseStyle 7 1.9447e+09 6.7749e+11 29254
## - LandSlope 2 8.1245e+09 6.8756e+11 29258
## - MasVnrArea 1 8.1259e+09 6.8756e+11 29260
## - Functional 6 1.3891e+10 6.9332e+11 29262
## - TotalBsmtSF 1 1.0571e+10 6.9000e+11 29265
## + Exterior2nd 14 3.3377e+09 6.7609e+11 29265
## - Condition1 8 1.7870e+10 6.9730e+11 29266
## - ExterQual 3 1.3187e+10 6.9262e+11 29266
## - SaleCondition 5 1.6663e+10 6.9609e+11 29270
## - GarageCars 1 1.3749e+10 6.9318e+11 29272
## - PoolQC 3 1.5664e+10 6.9510e+11 29272
## - YearBuilt 1 1.7623e+10 6.9705e+11 29280
## - BsmtQual 4 2.2201e+10 7.0163e+11 29283
## - OverallQual 1 2.4559e+10 7.0399e+11 29294
## - KitchenQual 3 2.7821e+10 7.0725e+11 29297
## - BsmtFinSF1 1 2.6987e+10 7.0642e+11 29299
## - LotArea 1 2.7825e+10 7.0726e+11 29301
## - OverallCond 1 3.0714e+10 7.1015e+11 29307
## - BsmtExposure 4 3.4839e+10 7.1427e+11 29309
## - MSSubClass 14 5.1084e+10 7.3052e+11 29322
## - Condition2 7 8.2714e+10 7.6215e+11 29397
## - Neighborhood 24 1.1812e+11 7.9755e+11 29429
## - RoofMatl 7 1.2715e+11 8.0658e+11 29479
## - GrLivArea 1 1.8037e+11 8.5980e+11 29584
##
## Step: AIC=29242.9
## SalePrice ~ OverallQual + GrLivArea + Neighborhood + MSSubClass +
## RoofMatl + BsmtFinSF1 + BsmtQual + Condition2 + KitchenQual +
## BsmtExposure + OverallCond + YearBuilt + LotArea + SaleCondition +
## TotalBsmtSF + PoolQC + GarageCars + ExterQual + Functional +
## Condition1 + LotConfig + ScreenPorch + PoolArea + BedroomAbvGr +
## LandSlope + LandContour + Street + LowQualFinSF + MasVnrArea +
## Exterior1st + MSZoning + GarageYrBlt + Fireplaces + BsmtFullBath +
## YearRemodAdd + MoSold + MasVnrType + KitchenAbvGr
##
## Df Sum of Sq RSS AIC
## + TotRmsAbvGrd 1 1.8986e+09 6.7585e+11 29241
## + `1stFlrSF` 1 1.5459e+09 6.7620e+11 29242
## + `2ndFlrSF` 1 1.5459e+09 6.7620e+11 29242
## + LotFrontage 1 1.3487e+09 6.7640e+11 29242
## + BsmtFinSF2 1 9.3981e+08 6.7680e+11 29243
## + BsmtUnfSF 1 9.3981e+08 6.7680e+11 29243
## <none> 6.7774e+11 29243
## + WoodDeckSF 1 9.3038e+08 6.7681e+11 29243
## + Utilities 1 8.4811e+08 6.7690e+11 29243
## + GarageArea 1 8.0565e+08 6.7694e+11 29243
## + FullBath 1 7.0272e+08 6.7704e+11 29243
## + BsmtCond 3 2.4718e+09 6.7527e+11 29244
## + `3SsnPorch` 1 4.3505e+08 6.7731e+11 29244
## - MoSold 1 1.6313e+09 6.7938e+11 29244
## - KitchenAbvGr 1 1.6867e+09 6.7943e+11 29245
## + FireplaceQu 5 3.8957e+09 6.7385e+11 29245
## - MasVnrType 3 3.6142e+09 6.8136e+11 29245
## + RoofStyle 5 3.7880e+09 6.7396e+11 29245
## + Id 1 5.6736e+07 6.7769e+11 29245
## + OpenPorchSF 1 3.6434e+07 6.7771e+11 29245
## + CentralAir 1 2.3081e+07 6.7772e+11 29245
## + YrSold 1 1.3326e+07 6.7773e+11 29245
## + BsmtHalfBath 1 5.2278e+06 6.7774e+11 29245
## + HalfBath 1 1.0642e+06 6.7774e+11 29245
## + MiscVal 1 9.1751e+05 6.7774e+11 29245
## + EnclosedPorch 1 7.7247e+04 6.7774e+11 29245
## - YearRemodAdd 1 2.0418e+09 6.7979e+11 29245
## - BsmtFullBath 1 2.0475e+09 6.7979e+11 29245
## + GarageFinish 3 1.6843e+09 6.7606e+11 29245
## + GarageQual 3 1.6843e+09 6.7606e+11 29245
## + Fence 4 2.6034e+09 6.7514e+11 29245
## + PavedDrive 2 6.1440e+08 6.7713e+11 29246
## + HeatingQC 4 2.4755e+09 6.7527e+11 29246
## + LotShape 3 1.3832e+09 6.7636e+11 29246
## + Foundation 5 3.0945e+09 6.7465e+11 29246
## + SaleType 8 5.7263e+09 6.7202e+11 29247
## + BsmtFinType1 5 2.9349e+09 6.7481e+11 29247
## + Alley 2 9.0706e+07 6.7765e+11 29247
## - BedroomAbvGr 1 2.8291e+09 6.8057e+11 29247
## - Fireplaces 1 2.8755e+09 6.8062e+11 29247
## + GarageType 6 3.6333e+09 6.7411e+11 29247
## - GarageYrBlt 1 2.9333e+09 6.8068e+11 29247
## + BsmtFinType2 6 3.4676e+09 6.7428e+11 29248
## - MSZoning 4 6.1275e+09 6.8387e+11 29248
## + BldgType 3 3.9476e+08 6.7735e+11 29248
## + Heating 5 2.1754e+09 6.7557e+11 29248
## + GarageCond 5 2.0637e+09 6.7568e+11 29249
## + MiscFeature 4 9.6756e+08 6.7678e+11 29249
## + ExterCond 4 9.5011e+08 6.7679e+11 29249
## - Street 1 3.7829e+09 6.8153e+11 29249
## - LotConfig 4 6.6943e+09 6.8444e+11 29249
## - Exterior1st 14 1.6686e+10 6.9443e+11 29250
## + Electrical 4 2.6234e+08 6.7748e+11 29250
## - LowQualFinSF 1 4.8308e+09 6.8258e+11 29251
## - PoolArea 1 4.9500e+09 6.8269e+11 29252
## - LandContour 3 6.9893e+09 6.8473e+11 29252
## - ScreenPorch 1 5.4863e+09 6.8323e+11 29253
## + HouseStyle 7 1.1803e+09 6.7656e+11 29254
## - LandSlope 2 7.9676e+09 6.8571e+11 29256
## - MasVnrArea 1 8.1350e+09 6.8588e+11 29258
## - Functional 6 1.3759e+10 6.9150e+11 29260
## - TotalBsmtSF 1 1.0695e+10 6.8844e+11 29264
## - Condition1 8 1.7586e+10 6.9533e+11 29264
## + Exterior2nd 14 3.1086e+09 6.7464e+11 29264
## - ExterQual 3 1.3474e+10 6.9122e+11 29266
## - SaleCondition 5 1.6627e+10 6.9437e+11 29268
## - PoolQC 3 1.5450e+10 6.9319e+11 29270
## - GarageCars 1 1.3814e+10 6.9156e+11 29270
## - YearBuilt 1 1.6006e+10 6.9375e+11 29275
## - BsmtQual 4 2.2537e+10 7.0028e+11 29282
## - MSSubClass 14 3.5578e+10 7.1332e+11 29289
## - OverallQual 1 2.4200e+10 7.0194e+11 29292
## - KitchenQual 3 2.7517e+10 7.0526e+11 29295
## - BsmtFinSF1 1 2.6437e+10 7.0418e+11 29296
## - LotArea 1 2.7028e+10 7.0477e+11 29298
## - OverallCond 1 2.9707e+10 7.0745e+11 29303
## - BsmtExposure 4 3.2803e+10 7.1055e+11 29304
## - Condition2 7 8.2364e+10 7.6011e+11 29395
## - Neighborhood 24 1.1655e+11 7.9430e+11 29425
## - RoofMatl 7 1.2744e+11 8.0519e+11 29479
## - GrLivArea 1 1.8135e+11 8.5909e+11 29585
##
## Step: AIC=29240.83
## SalePrice ~ OverallQual + GrLivArea + Neighborhood + MSSubClass +
## RoofMatl + BsmtFinSF1 + BsmtQual + Condition2 + KitchenQual +
## BsmtExposure + OverallCond + YearBuilt + LotArea + SaleCondition +
## TotalBsmtSF + PoolQC + GarageCars + ExterQual + Functional +
## Condition1 + LotConfig + ScreenPorch + PoolArea + BedroomAbvGr +
## LandSlope + LandContour + Street + LowQualFinSF + MasVnrArea +
## Exterior1st + MSZoning + GarageYrBlt + Fireplaces + BsmtFullBath +
## YearRemodAdd + MoSold + MasVnrType + KitchenAbvGr + TotRmsAbvGrd
##
## Df Sum of Sq RSS AIC
## + `1stFlrSF` 1 1.7779e+09 6.7407e+11 29239
## + `2ndFlrSF` 1 1.7779e+09 6.7407e+11 29239
## + LotFrontage 1 1.3016e+09 6.7454e+11 29240
## + BsmtFinSF2 1 9.7897e+08 6.7487e+11 29241
## + BsmtUnfSF 1 9.7897e+08 6.7487e+11 29241
## + Utilities 1 9.3571e+08 6.7491e+11 29241
## <none> 6.7585e+11 29241
## + WoodDeckSF 1 9.2973e+08 6.7492e+11 29241
## + GarageArea 1 9.0901e+08 6.7494e+11 29241
## + FullBath 1 7.1802e+08 6.7513e+11 29241
## + `3SsnPorch` 1 4.9915e+08 6.7535e+11 29242
## + BsmtCond 3 2.3318e+09 6.7351e+11 29242
## - MoSold 1 1.4170e+09 6.7726e+11 29242
## + FireplaceQu 5 4.0337e+09 6.7181e+11 29242
## - MasVnrType 3 3.5966e+09 6.7944e+11 29243
## + Fence 4 2.8900e+09 6.7296e+11 29243
## + RoofStyle 5 3.8123e+09 6.7203e+11 29243
## + OpenPorchSF 1 3.4544e+07 6.7581e+11 29243
## + CentralAir 1 3.2929e+07 6.7581e+11 29243
## + Id 1 3.0462e+07 6.7582e+11 29243
## + YrSold 1 8.2653e+06 6.7584e+11 29243
## + EnclosedPorch 1 6.2885e+06 6.7584e+11 29243
## + BsmtHalfBath 1 2.0876e+06 6.7584e+11 29243
## + HalfBath 1 1.9052e+06 6.7584e+11 29243
## + MiscVal 1 1.6626e+06 6.7584e+11 29243
## - BsmtFullBath 1 1.8747e+09 6.7772e+11 29243
## - TotRmsAbvGrd 1 1.8986e+09 6.7774e+11 29243
## - YearRemodAdd 1 1.9172e+09 6.7776e+11 29243
## + GarageFinish 3 1.6269e+09 6.7422e+11 29243
## + GarageQual 3 1.6269e+09 6.7422e+11 29243
## + HeatingQC 4 2.4281e+09 6.7342e+11 29244
## + PavedDrive 2 5.5554e+08 6.7529e+11 29244
## + LotShape 3 1.4647e+09 6.7438e+11 29244
## - KitchenAbvGr 1 2.5314e+09 6.7838e+11 29244
## + Foundation 5 2.8985e+09 6.7295e+11 29245
## + SaleType 8 5.6579e+09 6.7019e+11 29245
## + Alley 2 5.3265e+07 6.7579e+11 29245
## - Fireplaces 1 2.8115e+09 6.7866e+11 29245
## + BsmtFinType1 5 2.7223e+09 6.7312e+11 29245
## - GarageYrBlt 1 2.8744e+09 6.7872e+11 29245
## + GarageType 6 3.4065e+09 6.7244e+11 29246
## + BsmtFinType2 6 3.3307e+09 6.7252e+11 29246
## + BldgType 3 4.1230e+08 6.7543e+11 29246
## + GarageCond 5 2.2534e+09 6.7359e+11 29246
## - MSZoning 4 6.2363e+09 6.8208e+11 29246
## + Heating 5 2.0460e+09 6.7380e+11 29246
## + ExterCond 4 9.4308e+08 6.7490e+11 29247
## - Street 1 3.7497e+09 6.7960e+11 29247
## + MiscFeature 4 8.7764e+08 6.7497e+11 29247
## - LotConfig 4 6.6859e+09 6.8253e+11 29247
## - Exterior1st 14 1.6563e+10 6.9241e+11 29248
## - BedroomAbvGr 1 4.4365e+09 6.8028e+11 29248
## + Electrical 4 2.2245e+08 6.7562e+11 29248
## - LandContour 3 7.0211e+09 6.8287e+11 29250
## - LowQualFinSF 1 5.1446e+09 6.8099e+11 29250
## - PoolArea 1 5.3811e+09 6.8123e+11 29250
## - ScreenPorch 1 5.7475e+09 6.8159e+11 29251
## + HouseStyle 7 1.2175e+09 6.7463e+11 29252
## - LandSlope 2 7.6780e+09 6.8352e+11 29253
## - MasVnrArea 1 8.4096e+09 6.8426e+11 29257
## - Functional 6 1.3544e+10 6.8939e+11 29258
## - Condition1 8 1.7352e+10 6.9320e+11 29262
## + Exterior2nd 14 3.1927e+09 6.7265e+11 29262
## - ExterQual 3 1.2755e+10 6.8860e+11 29262
## - TotalBsmtSF 1 1.1039e+10 6.8689e+11 29262
## - SaleCondition 5 1.6442e+10 6.9229e+11 29266
## - GarageCars 1 1.3425e+10 6.8927e+11 29267
## - PoolQC 3 1.6657e+10 6.9250e+11 29270
## - YearBuilt 1 1.6322e+10 6.9217e+11 29274
## - MSSubClass 14 3.1788e+10 7.0763e+11 29280
## - BsmtQual 4 2.2112e+10 6.9796e+11 29280
## - OverallQual 1 2.3931e+10 6.9978e+11 29289
## - KitchenQual 3 2.6896e+10 7.0274e+11 29292
## - LotArea 1 2.6544e+10 7.0239e+11 29295
## - BsmtFinSF1 1 2.6952e+10 7.0280e+11 29296
## - OverallCond 1 3.0039e+10 7.0588e+11 29302
## - BsmtExposure 4 3.3236e+10 7.0908e+11 29303
## - Condition2 7 7.9570e+10 7.5542e+11 29388
## - Neighborhood 24 1.1617e+11 7.9202e+11 29423
## - RoofMatl 7 1.2536e+11 8.0121e+11 29474
## - GrLivArea 1 1.2381e+11 7.9965e+11 29483
##
## Step: AIC=29239.01
## SalePrice ~ OverallQual + GrLivArea + Neighborhood + MSSubClass +
## RoofMatl + BsmtFinSF1 + BsmtQual + Condition2 + KitchenQual +
## BsmtExposure + OverallCond + YearBuilt + LotArea + SaleCondition +
## TotalBsmtSF + PoolQC + GarageCars + ExterQual + Functional +
## Condition1 + LotConfig + ScreenPorch + PoolArea + BedroomAbvGr +
## LandSlope + LandContour + Street + LowQualFinSF + MasVnrArea +
## Exterior1st + MSZoning + GarageYrBlt + Fireplaces + BsmtFullBath +
## YearRemodAdd + MoSold + MasVnrType + KitchenAbvGr + TotRmsAbvGrd +
## `1stFlrSF`
##
## Df Sum of Sq RSS AIC
## + LotFrontage 1 1.4978e+09 6.7257e+11 29238
## + GarageArea 1 1.0419e+09 6.7303e+11 29239
## + WoodDeckSF 1 9.4753e+08 6.7312e+11 29239
## <none> 6.7407e+11 29239
## + BsmtFinSF2 1 9.0072e+08 6.7317e+11 29239
## + BsmtUnfSF 1 9.0072e+08 6.7317e+11 29239
## + Utilities 1 7.8641e+08 6.7328e+11 29239
## + FullBath 1 6.7159e+08 6.7340e+11 29240
## + `3SsnPorch` 1 5.6094e+08 6.7351e+11 29240
## + BsmtCond 3 2.3901e+09 6.7168e+11 29240
## - MoSold 1 1.3576e+09 6.7543e+11 29240
## - MasVnrType 3 3.2861e+09 6.7735e+11 29240
## + Fence 4 3.1303e+09 6.7094e+11 29240
## + FireplaceQu 5 4.0433e+09 6.7002e+11 29240
## - `1stFlrSF` 1 1.7779e+09 6.7585e+11 29241
## + Id 1 4.2442e+07 6.7403e+11 29241
## + HalfBath 1 3.4907e+07 6.7403e+11 29241
## + OpenPorchSF 1 3.3020e+07 6.7404e+11 29241
## + CentralAir 1 1.8541e+07 6.7405e+11 29241
## + YrSold 1 1.8110e+07 6.7405e+11 29241
## + MiscVal 1 8.3609e+06 6.7406e+11 29241
## + EnclosedPorch 1 6.5311e+06 6.7406e+11 29241
## + BsmtHalfBath 1 5.0387e+06 6.7406e+11 29241
## - BsmtFullBath 1 1.8561e+09 6.7592e+11 29241
## + RoofStyle 5 3.6909e+09 6.7038e+11 29241
## - TotRmsAbvGrd 1 2.1306e+09 6.7620e+11 29242
## - YearRemodAdd 1 2.1803e+09 6.7625e+11 29242
## + LotShape 3 1.5010e+09 6.7257e+11 29242
## + GarageFinish 3 1.4268e+09 6.7264e+11 29242
## + GarageQual 3 1.4268e+09 6.7264e+11 29242
## + HeatingQC 4 2.3281e+09 6.7174e+11 29242
## + PavedDrive 2 4.5521e+08 6.7361e+11 29242
## + SaleType 8 5.8596e+09 6.6821e+11 29242
## + Foundation 5 2.9121e+09 6.7116e+11 29243
## + BsmtFinType1 5 2.8806e+09 6.7119e+11 29243
## + Alley 2 7.4751e+07 6.7399e+11 29243
## - KitchenAbvGr 1 2.9556e+09 6.7702e+11 29243
## - GarageYrBlt 1 3.0213e+09 6.7709e+11 29244
## + BsmtFinType2 6 3.3469e+09 6.7072e+11 29244
## + BldgType 3 4.8967e+08 6.7358e+11 29244
## - Fireplaces 1 3.3277e+09 6.7740e+11 29244
## + GarageCond 5 2.1865e+09 6.7188e+11 29244
## - MSZoning 4 6.2226e+09 6.8029e+11 29244
## + Heating 5 2.1377e+09 6.7193e+11 29244
## - Street 1 3.6612e+09 6.7773e+11 29245
## + GarageType 6 2.7841e+09 6.7128e+11 29245
## + ExterCond 4 8.9018e+08 6.7318e+11 29245
## + MiscFeature 4 8.6105e+08 6.7321e+11 29245
## - Exterior1st 14 1.6214e+10 6.9028e+11 29246
## - LotConfig 4 6.8346e+09 6.8090e+11 29246
## + Electrical 4 1.9325e+08 6.7387e+11 29247
## + HouseStyle 7 2.7623e+09 6.7131e+11 29247
## - BedroomAbvGr 1 5.0333e+09 6.7910e+11 29248
## - LandContour 3 6.9400e+09 6.8101e+11 29248
## - ScreenPorch 1 5.4533e+09 6.7952e+11 29249
## - LowQualFinSF 1 5.5955e+09 6.7966e+11 29249
## - PoolArea 1 5.6168e+09 6.7968e+11 29249
## - LandSlope 2 7.8433e+09 6.8191e+11 29252
## - Functional 6 1.2012e+10 6.8608e+11 29253
## - MasVnrArea 1 7.7761e+09 6.8184e+11 29254
## - Condition1 8 1.6957e+10 6.9103e+11 29259
## - ExterQual 3 1.2442e+10 6.8651e+11 29260
## + Exterior2nd 14 3.1506e+09 6.7092e+11 29260
## - TotalBsmtSF 1 1.2090e+10 6.8616e+11 29263
## - SaleCondition 5 1.6259e+10 6.9033e+11 29264
## - GarageCars 1 1.3942e+10 6.8801e+11 29267
## - PoolQC 3 1.6240e+10 6.9031e+11 29268
## - YearBuilt 1 1.6181e+10 6.9025e+11 29271
## - BsmtQual 4 2.2570e+10 6.9664e+11 29279
## - MSSubClass 14 3.3146e+10 7.0721e+11 29281
## - OverallQual 1 2.4265e+10 6.9833e+11 29288
## - KitchenQual 3 2.6307e+10 7.0038e+11 29289
## - BsmtFinSF1 1 2.7035e+10 7.0110e+11 29294
## - LotArea 1 2.7088e+10 7.0116e+11 29294
## - OverallCond 1 2.9200e+10 7.0327e+11 29299
## - BsmtExposure 4 3.3771e+10 7.0784e+11 29302
## - Condition2 7 8.0060e+10 7.5413e+11 29388
## - Neighborhood 24 1.1581e+11 7.8988e+11 29421
## - GrLivArea 1 9.9289e+10 7.7336e+11 29436
## - RoofMatl 7 1.2470e+11 7.9876e+11 29471
##
## Step: AIC=29237.78
## SalePrice ~ OverallQual + GrLivArea + Neighborhood + MSSubClass +
## RoofMatl + BsmtFinSF1 + BsmtQual + Condition2 + KitchenQual +
## BsmtExposure + OverallCond + YearBuilt + LotArea + SaleCondition +
## TotalBsmtSF + PoolQC + GarageCars + ExterQual + Functional +
## Condition1 + LotConfig + ScreenPorch + PoolArea + BedroomAbvGr +
## LandSlope + LandContour + Street + LowQualFinSF + MasVnrArea +
## Exterior1st + MSZoning + GarageYrBlt + Fireplaces + BsmtFullBath +
## YearRemodAdd + MoSold + MasVnrType + KitchenAbvGr + TotRmsAbvGrd +
## `1stFlrSF` + LotFrontage
##
## Df Sum of Sq RSS AIC
## + WoodDeckSF 1 1.1293e+09 6.7144e+11 29237
## + GarageArea 1 9.9366e+08 6.7158e+11 29238
## <none> 6.7257e+11 29238
## + BsmtFinSF2 1 8.7961e+08 6.7169e+11 29238
## + BsmtUnfSF 1 8.7961e+08 6.7169e+11 29238
## + Utilities 1 8.1242e+08 6.7176e+11 29238
## + FullBath 1 7.3774e+08 6.7183e+11 29238
## - MoSold 1 1.2989e+09 6.7387e+11 29239
## + `3SsnPorch` 1 4.4035e+08 6.7213e+11 29239
## + FireplaceQu 5 4.1202e+09 6.6845e+11 29239
## - LotFrontage 1 1.4978e+09 6.7407e+11 29239
## - MasVnrType 3 3.3723e+09 6.7594e+11 29239
## + Fence 4 3.0877e+09 6.6948e+11 29239
## + BsmtCond 3 2.1521e+09 6.7042e+11 29239
## + Id 1 4.7205e+07 6.7252e+11 29240
## + HalfBath 1 4.1407e+07 6.7253e+11 29240
## + YrSold 1 3.6950e+07 6.7253e+11 29240
## + OpenPorchSF 1 3.3175e+07 6.7254e+11 29240
## + CentralAir 1 2.3810e+07 6.7255e+11 29240
## + MiscVal 1 1.3528e+07 6.7256e+11 29240
## + EnclosedPorch 1 2.0694e+06 6.7257e+11 29240
## + BsmtHalfBath 1 2.4297e+05 6.7257e+11 29240
## - BsmtFullBath 1 1.8713e+09 6.7444e+11 29240
## - `1stFlrSF` 1 1.9741e+09 6.7454e+11 29240
## - TotRmsAbvGrd 1 2.0909e+09 6.7466e+11 29240
## + Foundation 5 3.4044e+09 6.6917e+11 29240
## + RoofStyle 5 3.3480e+09 6.6922e+11 29241
## + LotShape 3 1.4977e+09 6.7107e+11 29241
## - YearRemodAdd 1 2.2240e+09 6.7479e+11 29241
## + GarageFinish 3 1.4498e+09 6.7112e+11 29241
## + GarageQual 3 1.4498e+09 6.7112e+11 29241
## + PavedDrive 2 5.0766e+08 6.7206e+11 29241
## + HeatingQC 4 2.2340e+09 6.7034e+11 29241
## + SaleType 8 5.7469e+09 6.6682e+11 29241
## + BsmtFinType1 5 2.8119e+09 6.6976e+11 29242
## + Alley 2 2.8951e+07 6.7254e+11 29242
## - KitchenAbvGr 1 2.9520e+09 6.7552e+11 29242
## + BsmtFinType2 6 3.4023e+09 6.6917e+11 29242
## - GarageYrBlt 1 3.3133e+09 6.7588e+11 29243
## - Fireplaces 1 3.3249e+09 6.7590e+11 29243
## + BldgType 3 3.5488e+08 6.7222e+11 29243
## + Heating 5 2.1442e+09 6.7043e+11 29243
## - MSZoning 4 6.2283e+09 6.7880e+11 29243
## - Street 1 3.6668e+09 6.7624e+11 29244
## + GarageCond 5 1.8885e+09 6.7068e+11 29244
## + MiscFeature 4 9.3417e+08 6.7164e+11 29244
## + GarageType 6 2.7585e+09 6.6981e+11 29244
## + ExterCond 4 8.3297e+08 6.7174e+11 29244
## - Exterior1st 14 1.6520e+10 6.8909e+11 29245
## + Electrical 4 2.1731e+08 6.7235e+11 29245
## + HouseStyle 7 2.8950e+09 6.6968e+11 29246
## - LotConfig 4 7.5711e+09 6.8014e+11 29246
## - LandContour 3 6.9027e+09 6.7947e+11 29247
## - BedroomAbvGr 1 5.2061e+09 6.7778e+11 29247
## - ScreenPorch 1 5.5657e+09 6.7814e+11 29248
## - PoolArea 1 5.8361e+09 6.7841e+11 29248
## - LowQualFinSF 1 5.9075e+09 6.7848e+11 29249
## - LandSlope 2 7.1112e+09 6.7968e+11 29249
## - Functional 6 1.1771e+10 6.8434e+11 29251
## - MasVnrArea 1 7.7102e+09 6.8028e+11 29252
## - Condition1 8 1.7049e+10 6.8962e+11 29258
## - ExterQual 3 1.2611e+10 6.8518e+11 29259
## + Exterior2nd 14 3.0166e+09 6.6955e+11 29259
## - SaleCondition 5 1.6247e+10 6.8882e+11 29262
## - TotalBsmtSF 1 1.2533e+10 6.8510e+11 29263
## - GarageCars 1 1.2963e+10 6.8553e+11 29264
## - PoolQC 3 1.5532e+10 6.8810e+11 29265
## - MSSubClass 14 2.8394e+10 7.0096e+11 29270
## - YearBuilt 1 1.6161e+10 6.8873e+11 29270
## - BsmtQual 4 2.1813e+10 6.9438e+11 29276
## - OverallQual 1 2.4047e+10 6.9662e+11 29287
## - KitchenQual 3 2.6056e+10 6.9863e+11 29287
## - LotArea 1 2.4531e+10 6.9710e+11 29288
## - BsmtFinSF1 1 2.7296e+10 6.9987e+11 29294
## - OverallCond 1 2.9440e+10 7.0201e+11 29298
## - BsmtExposure 4 3.2975e+10 7.0555e+11 29299
## - Condition2 7 8.1154e+10 7.5372e+11 29389
## - Neighborhood 24 1.1512e+11 7.8769e+11 29419
## - GrLivArea 1 9.8961e+10 7.7153e+11 29435
## - RoofMatl 7 1.2548e+11 7.9805e+11 29472
##
## Step: AIC=29237.34
## SalePrice ~ OverallQual + GrLivArea + Neighborhood + MSSubClass +
## RoofMatl + BsmtFinSF1 + BsmtQual + Condition2 + KitchenQual +
## BsmtExposure + OverallCond + YearBuilt + LotArea + SaleCondition +
## TotalBsmtSF + PoolQC + GarageCars + ExterQual + Functional +
## Condition1 + LotConfig + ScreenPorch + PoolArea + BedroomAbvGr +
## LandSlope + LandContour + Street + LowQualFinSF + MasVnrArea +
## Exterior1st + MSZoning + GarageYrBlt + Fireplaces + BsmtFullBath +
## YearRemodAdd + MoSold + MasVnrType + KitchenAbvGr + TotRmsAbvGrd +
## `1stFlrSF` + LotFrontage + WoodDeckSF
##
## Df Sum of Sq RSS AIC
## + GarageArea 1 9.9023e+08 6.7045e+11 29237
## <none> 6.7144e+11 29237
## + Utilities 1 8.0644e+08 6.7063e+11 29238
## + BsmtFinSF2 1 7.4924e+08 6.7069e+11 29238
## + BsmtUnfSF 1 7.4924e+08 6.7069e+11 29238
## + FullBath 1 7.4159e+08 6.7070e+11 29238
## + FireplaceQu 5 4.4234e+09 6.6702e+11 29238
## - WoodDeckSF 1 1.1293e+09 6.7257e+11 29238
## + `3SsnPorch` 1 5.3214e+08 6.7091e+11 29238
## + Fence 4 3.2833e+09 6.6816e+11 29238
## - MoSold 1 1.3545e+09 6.7280e+11 29238
## + BsmtCond 3 2.2237e+09 6.6922e+11 29239
## - MasVnrType 3 3.3618e+09 6.7480e+11 29239
## - LotFrontage 1 1.6796e+09 6.7312e+11 29239
## - BsmtFullBath 1 1.7159e+09 6.7316e+11 29239
## + OpenPorchSF 1 6.4767e+07 6.7138e+11 29239
## + Id 1 5.7234e+07 6.7138e+11 29239
## + YrSold 1 4.4768e+07 6.7140e+11 29239
## + HalfBath 1 4.4221e+07 6.7140e+11 29239
## + CentralAir 1 3.1797e+07 6.7141e+11 29239
## + MiscVal 1 1.2161e+07 6.7143e+11 29239
## + EnclosedPorch 1 1.1692e+07 6.7143e+11 29239
## + BsmtHalfBath 1 3.4465e+06 6.7144e+11 29239
## - `1stFlrSF` 1 2.0073e+09 6.7345e+11 29240
## - TotRmsAbvGrd 1 2.0891e+09 6.7353e+11 29240
## + GarageFinish 3 1.5768e+09 6.6986e+11 29240
## + GarageQual 3 1.5768e+09 6.6986e+11 29240
## + LotShape 3 1.5508e+09 6.6989e+11 29240
## + Foundation 5 3.3723e+09 6.6807e+11 29240
## - YearRemodAdd 1 2.2118e+09 6.7365e+11 29240
## + PavedDrive 2 5.3151e+08 6.7091e+11 29240
## + HeatingQC 4 2.3685e+09 6.6907e+11 29240
## + RoofStyle 5 3.2874e+09 6.6815e+11 29240
## + SaleType 8 5.7173e+09 6.6572e+11 29241
## + BsmtFinType1 5 2.7917e+09 6.6865e+11 29241
## + Alley 2 1.7083e+07 6.7142e+11 29241
## - KitchenAbvGr 1 2.9919e+09 6.7443e+11 29242
## - GarageYrBlt 1 3.0969e+09 6.7454e+11 29242
## - Fireplaces 1 3.1325e+09 6.7457e+11 29242
## + BsmtFinType2 6 3.3184e+09 6.6812e+11 29242
## - MSZoning 4 6.0722e+09 6.7751e+11 29242
## + BldgType 3 3.1026e+08 6.7113e+11 29243
## + Heating 5 2.0954e+09 6.6935e+11 29243
## + GarageCond 5 2.0203e+09 6.6942e+11 29243
## + GarageType 6 2.9223e+09 6.6852e+11 29243
## + ExterCond 4 9.1767e+08 6.7052e+11 29243
## + MiscFeature 4 8.9423e+08 6.7055e+11 29243
## - Street 1 3.7748e+09 6.7522e+11 29244
## + Electrical 4 2.2335e+08 6.7122e+11 29245
## + HouseStyle 7 2.8858e+09 6.6856e+11 29245
## - Exterior1st 14 1.6842e+10 6.8828e+11 29245
## - LotConfig 4 7.6155e+09 6.7906e+11 29246
## - LandContour 3 6.7481e+09 6.7819e+11 29246
## - BedroomAbvGr 1 5.1128e+09 6.7655e+11 29246
## - PoolArea 1 5.4970e+09 6.7694e+11 29247
## - LowQualFinSF 1 5.8623e+09 6.7730e+11 29248
## - LandSlope 2 6.8791e+09 6.7832e+11 29248
## - ScreenPorch 1 6.1466e+09 6.7759e+11 29249
## - Functional 6 1.2090e+10 6.8353e+11 29251
## - MasVnrArea 1 7.6339e+09 6.7907e+11 29252
## - Condition1 8 1.6648e+10 6.8809e+11 29257
## - ExterQual 3 1.2674e+10 6.8412e+11 29259
## + Exterior2nd 14 3.0932e+09 6.6835e+11 29259
## - TotalBsmtSF 1 1.2642e+10 6.8408e+11 29262
## - GarageCars 1 1.2770e+10 6.8421e+11 29263
## - SaleCondition 5 1.6801e+10 6.8824e+11 29263
## - PoolQC 3 1.5519e+10 6.8696e+11 29265
## - MSSubClass 14 2.7950e+10 6.9939e+11 29269
## - YearBuilt 1 1.5966e+10 6.8741e+11 29269
## - BsmtQual 4 2.1591e+10 6.9303e+11 29275
## - LotArea 1 2.3903e+10 6.9534e+11 29286
## - OverallQual 1 2.4289e+10 6.9573e+11 29287
## - KitchenQual 3 2.6288e+10 6.9773e+11 29287
## - BsmtFinSF1 1 2.7311e+10 6.9875e+11 29293
## - OverallCond 1 2.8521e+10 6.9996e+11 29296
## - BsmtExposure 4 3.1649e+10 7.0309e+11 29296
## - Condition2 7 8.0438e+10 7.5188e+11 29388
## - Neighborhood 24 1.1415e+11 7.8559e+11 29417
## - GrLivArea 1 9.7754e+10 7.6919e+11 29433
## - RoofMatl 7 1.2467e+11 7.9611e+11 29471
##
## Step: AIC=29237.2
## SalePrice ~ OverallQual + GrLivArea + Neighborhood + MSSubClass +
## RoofMatl + BsmtFinSF1 + BsmtQual + Condition2 + KitchenQual +
## BsmtExposure + OverallCond + YearBuilt + LotArea + SaleCondition +
## TotalBsmtSF + PoolQC + GarageCars + ExterQual + Functional +
## Condition1 + LotConfig + ScreenPorch + PoolArea + BedroomAbvGr +
## LandSlope + LandContour + Street + LowQualFinSF + MasVnrArea +
## Exterior1st + MSZoning + GarageYrBlt + Fireplaces + BsmtFullBath +
## YearRemodAdd + MoSold + MasVnrType + KitchenAbvGr + TotRmsAbvGrd +
## `1stFlrSF` + LotFrontage + WoodDeckSF + GarageArea
##
## Df Sum of Sq RSS AIC
## <none> 6.7045e+11 29237
## + FireplaceQu 5 4.5531e+09 6.6590e+11 29237
## - GarageArea 1 9.9023e+08 6.7144e+11 29237
## + Utilities 1 8.1273e+08 6.6964e+11 29237
## + FullBath 1 7.9303e+08 6.6966e+11 29238
## + BsmtFinSF2 1 7.4268e+08 6.6971e+11 29238
## + BsmtUnfSF 1 7.4268e+08 6.6971e+11 29238
## - WoodDeckSF 1 1.1259e+09 6.7158e+11 29238
## - MoSold 1 1.2946e+09 6.7175e+11 29238
## + Fence 4 3.2745e+09 6.6718e+11 29238
## + `3SsnPorch` 1 5.0507e+08 6.6995e+11 29238
## - MasVnrType 3 3.2752e+09 6.7373e+11 29238
## + GarageFinish 3 2.2733e+09 6.6818e+11 29238
## + GarageQual 3 2.2733e+09 6.6818e+11 29238
## + BsmtCond 3 2.2062e+09 6.6824e+11 29238
## - BsmtFullBath 1 1.5904e+09 6.7204e+11 29239
## - LotFrontage 1 1.6284e+09 6.7208e+11 29239
## - GarageCars 1 1.6438e+09 6.7209e+11 29239
## + OpenPorchSF 1 6.3800e+07 6.7039e+11 29239
## + Id 1 5.2349e+07 6.7040e+11 29239
## + CentralAir 1 4.4274e+07 6.7041e+11 29239
## + YrSold 1 4.1176e+07 6.7041e+11 29239
## + HalfBath 1 2.3594e+07 6.7043e+11 29239
## + MiscVal 1 1.1944e+07 6.7044e+11 29239
## + BsmtHalfBath 1 6.6202e+06 6.7044e+11 29239
## + EnclosedPorch 1 5.3909e+06 6.7045e+11 29239
## + Foundation 5 3.4556e+09 6.6700e+11 29240
## + LotShape 3 1.5836e+09 6.6887e+11 29240
## + RoofStyle 5 3.4020e+09 6.6705e+11 29240
## - `1stFlrSF` 1 2.1408e+09 6.7259e+11 29240
## + PavedDrive 2 6.3059e+08 6.6982e+11 29240
## - TotRmsAbvGrd 1 2.2115e+09 6.7266e+11 29240
## + HeatingQC 4 2.4065e+09 6.6804e+11 29240
## - GarageYrBlt 1 2.2604e+09 6.7271e+11 29240
## - YearRemodAdd 1 2.4766e+09 6.7293e+11 29241
## + SaleType 8 5.7895e+09 6.6466e+11 29241
## + GarageType 6 3.7731e+09 6.6668e+11 29241
## + Alley 2 7.2266e+06 6.7044e+11 29241
## + BsmtFinType1 5 2.7309e+09 6.6772e+11 29241
## - KitchenAbvGr 1 2.9375e+09 6.7339e+11 29242
## + BsmtFinType2 6 3.3658e+09 6.6709e+11 29242
## + GarageCond 5 2.4054e+09 6.6805e+11 29242
## - Fireplaces 1 3.2727e+09 6.7372e+11 29242
## - MSZoning 4 6.0701e+09 6.7652e+11 29242
## + BldgType 3 3.1476e+08 6.7014e+11 29243
## + Heating 5 2.0388e+09 6.6841e+11 29243
## + ExterCond 4 1.0188e+09 6.6943e+11 29243
## + MiscFeature 4 8.9507e+08 6.6956e+11 29243
## - Street 1 4.0496e+09 6.7450e+11 29244
## + Electrical 4 2.3983e+08 6.7021e+11 29245
## + HouseStyle 7 2.8407e+09 6.6761e+11 29245
## - BedroomAbvGr 1 4.7696e+09 6.7522e+11 29246
## - LotConfig 4 7.5733e+09 6.7802e+11 29246
## - LandContour 3 6.8372e+09 6.7729e+11 29246
## - Exterior1st 14 1.7220e+10 6.8767e+11 29246
## - PoolArea 1 5.6933e+09 6.7614e+11 29248
## - LowQualFinSF 1 5.7949e+09 6.7625e+11 29248
## - LandSlope 2 6.8931e+09 6.7734e+11 29248
## - ScreenPorch 1 6.0533e+09 6.7650e+11 29248
## - MasVnrArea 1 7.5511e+09 6.7800e+11 29252
## - Functional 6 1.2291e+10 6.8274e+11 29252
## - Condition1 8 1.6836e+10 6.8729e+11 29257
## - ExterQual 3 1.2826e+10 6.8328e+11 29259
## + Exterior2nd 14 2.9163e+09 6.6753e+11 29259
## - SaleCondition 5 1.6390e+10 6.8684e+11 29262
## - TotalBsmtSF 1 1.2769e+10 6.8322e+11 29263
## - PoolQC 3 1.5454e+10 6.8590e+11 29264
## - MSSubClass 14 2.6914e+10 6.9737e+11 29266
## - YearBuilt 1 1.5975e+10 6.8643e+11 29269
## - BsmtQual 4 2.1213e+10 6.9166e+11 29274
## - LotArea 1 2.3885e+10 6.9434e+11 29286
## - OverallQual 1 2.4148e+10 6.9460e+11 29287
## - KitchenQual 3 2.6463e+10 6.9691e+11 29287
## - BsmtFinSF1 1 2.6887e+10 6.9734e+11 29292
## - OverallCond 1 2.7858e+10 6.9831e+11 29294
## - BsmtExposure 4 3.2065e+10 7.0252e+11 29297
## - Condition2 7 8.1084e+10 7.5154e+11 29389
## - Neighborhood 24 1.1252e+11 7.8298e+11 29414
## - GrLivArea 1 9.5740e+10 7.6619e+11 29429
## - RoofMatl 7 1.2563e+11 7.9608e+11 29472##
## Call:
## lm(formula = SalePrice ~ OverallQual + GrLivArea + Neighborhood +
## MSSubClass + RoofMatl + BsmtFinSF1 + BsmtQual + Condition2 +
## KitchenQual + BsmtExposure + OverallCond + YearBuilt + LotArea +
## SaleCondition + TotalBsmtSF + PoolQC + GarageCars + ExterQual +
## Functional + Condition1 + LotConfig + ScreenPorch + PoolArea +
## BedroomAbvGr + LandSlope + LandContour + Street + LowQualFinSF +
## MasVnrArea + Exterior1st + MSZoning + GarageYrBlt + Fireplaces +
## BsmtFullBath + YearRemodAdd + MoSold + MasVnrType + KitchenAbvGr +
## TotRmsAbvGrd + `1stFlrSF` + LotFrontage + WoodDeckSF + GarageArea,
## data = data_train_clean[complete.cases(data_train_clean),
## ])
##
## Coefficients:
## (Intercept) OverallQual GrLivArea
## -2.064e+06 6.507e+03 5.996e+01
## NeighborhoodBlueste NeighborhoodBrDale NeighborhoodBrkSide
## 4.151e+03 5.130e+03 -1.753e+03
## NeighborhoodClearCr NeighborhoodCollgCr NeighborhoodCrawfor
## -1.035e+04 -7.886e+03 1.233e+04
## NeighborhoodEdwards NeighborhoodGilbert NeighborhoodIDOTRR
## -1.782e+04 -1.155e+04 -3.461e+03
## NeighborhoodMeadowV NeighborhoodMitchel NeighborhoodNAmes
## -7.233e+03 -2.007e+04 -1.534e+04
## NeighborhoodNoRidge NeighborhoodNPkVill NeighborhoodNridgHt
## 2.772e+04 1.132e+04 1.636e+04
## NeighborhoodNWAmes NeighborhoodOldTown NeighborhoodSawyer
## -1.659e+04 -9.149e+03 -9.029e+03
## NeighborhoodSawyerW NeighborhoodSomerst NeighborhoodStoneBr
## -2.815e+03 -1.597e+03 3.666e+04
## NeighborhoodSWISU NeighborhoodTimber NeighborhoodVeenker
## -4.344e+03 -1.419e+04 -4.871e+02
## MSSubClass30 MSSubClass40 MSSubClass45
## 5.454e+03 1.487e+04 8.699e+03
## MSSubClass50 MSSubClass60 MSSubClass70
## -2.245e+03 -7.095e+03 -3.315e+03
## MSSubClass75 MSSubClass80 MSSubClass85
## -1.143e+04 -5.335e+03 -1.044e+04
## MSSubClass90 MSSubClass120 MSSubClass160
## -1.131e+04 -1.865e+04 -3.043e+04
## MSSubClass180 MSSubClass190 RoofMatlCompShg
## -1.666e+04 -1.169e+04 5.879e+05
## RoofMatlMembran RoofMatlMetal RoofMatlRoll
## 6.660e+05 6.298e+05 5.780e+05
## RoofMatlTar&Grv RoofMatlWdShake RoofMatlWdShngl
## 5.756e+05 5.990e+05 6.589e+05
## BsmtFinSF1 BsmtQual.L BsmtQual.Q
## 1.598e+01 -1.054e+04 2.354e+04
## BsmtQual.C BsmtQual^4 Condition2Feedr
## 8.556e+02 4.872e+03 -1.269e+04
## Condition2Norm Condition2PosA Condition2PosN
## -8.783e+03 5.154e+04 -2.352e+05
## Condition2RRAe Condition2RRAn Condition2RRNn
## -2.985e+04 -1.193e+04 -8.212e+02
## KitchenQual.L KitchenQual.Q KitchenQual.C
## 1.378e+04 1.310e+04 4.953e+03
## BsmtExposure.L BsmtExposure.Q BsmtExposure.C
## 2.178e+04 3.439e+03 5.799e+03
## BsmtExposure^4 OverallCond YearBuilt
## 1.166e+03 5.581e+03 3.923e+02
## LotArea SaleConditionAdjLand SaleConditionAlloca
## 6.440e-01 1.683e+04 3.354e+03
## SaleConditionFamily SaleConditionNormal SaleConditionPartial
## -1.615e+02 5.881e+03 1.900e+04
## TotalBsmtSF PoolQC.L PoolQC.Q
## 2.120e+01 -1.159e+05 2.196e+05
## PoolQC.C GarageCars ExterQual.L
## -5.454e+04 3.722e+03 2.772e+03
## ExterQual.Q ExterQual.C Functional.L
## 1.905e+04 4.896e+02 2.740e+04
## Functional.Q Functional.C Functional^4
## -6.279e+03 1.100e+04 -2.045e+03
## Functional^5 Functional^6 Condition1Feedr
## -2.728e+02 6.140e+03 3.627e+03
## Condition1Norm Condition1PosA Condition1PosN
## 1.273e+04 4.407e+03 9.849e+03
## Condition1RRAe Condition1RRAn Condition1RRNe
## -1.484e+04 1.143e+04 -4.940e+01
## Condition1RRNn LotConfigCulDSac LotConfigFR2
## 7.015e+03 9.193e+03 -4.312e+03
## LotConfigFR3 LotConfigInside ScreenPorch
## -9.551e+03 -4.590e+02 4.013e+01
## PoolArea BedroomAbvGr LandSlopeMod
## 5.433e+02 -3.918e+03 5.373e+03
## LandSlopeSev LandContourHLS LandContourLow
## -2.896e+04 1.138e+04 -6.284e+03
## LandContourLvl StreetPave LowQualFinSF
## 7.698e+03 3.175e+04 -5.085e+01
## MasVnrArea Exterior1stAsphShn Exterior1stBrkComm
## 2.137e+01 -6.982e+03 1.381e+03
## Exterior1stBrkFace Exterior1stCBlock Exterior1stCemntBd
## 1.675e+04 -1.933e+04 3.818e+03
## Exterior1stHdBoard Exterior1stImStucc Exterior1stMetalSd
## -3.584e+03 -1.282e+04 1.716e+03
## Exterior1stPlywood Exterior1stStone Exterior1stStucco
## -6.064e+03 -7.901e+03 6.290e+02
## Exterior1stVinylSd Exterior1stWd Sdng Exterior1stWdShing
## -2.310e+02 -2.148e+02 -1.549e+03
## MSZoningFV MSZoningRH MSZoningRL
## 3.736e+04 2.169e+04 2.652e+04
## MSZoningRM GarageYrBlt Fireplaces
## 2.075e+04 1.029e+02 3.224e+03
## BsmtFullBath YearRemodAdd MoSold
## 2.934e+03 1.122e+02 -3.701e+02
## MasVnrTypeBrkFace MasVnrTypeNone MasVnrTypeStone
## 8.500e+03 1.192e+04 1.278e+04
## KitchenAbvGr TotRmsAbvGrd `1stFlrSF`
## -1.283e+04 1.899e+03 -1.189e+01
## LotFrontage WoodDeckSF GarageArea
## 7.274e+01 8.276e+00 1.003e+01Final Model & Summary
To reduce the model complexity in this project, some the variables with large P-value are removed from the result using StepAIC above.
In the final model: The Residual standard error is 26340 on 1379 degrees of freedom The Multiple R-squared is 0.8951, and adjusted R-squared: 0.8897, means that the model has high explainability on the variance of the training dataset. F-statistic: 165.7 on 71 and 1379 DF, p-value: < 2.2e-16, means that the final model has better performance the the null model.
data_lm_final <- lm(formula = SalePrice ~ OverallQual + GrLivArea +
RoofMatl + BsmtFinSF1 + Condition2 +
BsmtExposure + OverallCond + YearBuilt + LotArea +
SaleCondition + TotalBsmtSF + PoolQC + GarageCars + ExterQual +
Condition1 + LotConfig + ScreenPorch + PoolArea +
BedroomAbvGr + LandSlope + LandContour + Street + LowQualFinSF +
MasVnrArea + GarageYrBlt + Fireplaces +
BsmtFullBath + YearRemodAdd + MoSold + KitchenAbvGr +
TotRmsAbvGrd + `1stFlrSF` + LotFrontage + WoodDeckSF + GarageArea,
data = data_train_clean[complete.cases(data_train_clean),
])
summary(data_lm_final)##
## Call:
## lm(formula = SalePrice ~ OverallQual + GrLivArea + RoofMatl +
## BsmtFinSF1 + Condition2 + BsmtExposure + OverallCond + YearBuilt +
## LotArea + SaleCondition + TotalBsmtSF + PoolQC + GarageCars +
## ExterQual + Condition1 + LotConfig + ScreenPorch + PoolArea +
## BedroomAbvGr + LandSlope + LandContour + Street + LowQualFinSF +
## MasVnrArea + GarageYrBlt + Fireplaces + BsmtFullBath + YearRemodAdd +
## MoSold + KitchenAbvGr + TotRmsAbvGrd + `1stFlrSF` + LotFrontage +
## WoodDeckSF + GarageArea, data = data_train_clean[complete.cases(data_train_clean),
## ])
##
## Residuals:
## Min 1Q Median 3Q Max
## -204952 -13111 -22 12524 204952
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -1.722e+06 1.298e+05 -13.270 < 2e-16 ***
## OverallQual 1.084e+04 9.726e+02 11.142 < 2e-16 ***
## GrLivArea 5.884e+01 3.337e+00 17.636 < 2e-16 ***
## RoofMatlCompShg 6.793e+05 4.884e+04 13.910 < 2e-16 ***
## RoofMatlMembran 7.233e+05 5.692e+04 12.708 < 2e-16 ***
## RoofMatlMetal 7.075e+05 5.701e+04 12.411 < 2e-16 ***
## RoofMatlRoll 6.715e+05 5.571e+04 12.052 < 2e-16 ***
## RoofMatlTar&Grv 6.481e+05 4.986e+04 12.999 < 2e-16 ***
## RoofMatlWdShake 6.710e+05 5.058e+04 13.266 < 2e-16 ***
## RoofMatlWdShngl 7.424e+05 4.981e+04 14.905 < 2e-16 ***
## BsmtFinSF1 1.923e+01 2.464e+00 7.806 1.16e-14 ***
## Condition2Feedr -2.035e+04 2.336e+04 -0.871 0.383891
## Condition2Norm -1.587e+04 1.976e+04 -0.803 0.422143
## Condition2PosA -3.794e+04 3.359e+04 -1.130 0.258867
## Condition2PosN -2.709e+05 2.862e+04 -9.465 < 2e-16 ***
## Condition2RRAe -3.747e+04 3.318e+04 -1.129 0.258983
## Condition2RRAn -1.972e+04 3.304e+04 -0.597 0.550671
## Condition2RRNn 3.492e+03 2.760e+04 0.127 0.899327
## BsmtExposure.L -1.133e+04 4.511e+03 -2.511 0.012152 *
## BsmtExposure.Q 2.599e+04 3.896e+03 6.671 3.68e-11 ***
## BsmtExposure.C -9.457e+03 2.542e+03 -3.721 0.000206 ***
## BsmtExposure^4 6.457e+03 2.188e+03 2.951 0.003223 **
## OverallCond 5.659e+03 7.949e+02 7.119 1.74e-12 ***
## YearBuilt 1.840e+02 4.955e+01 3.713 0.000213 ***
## LotArea 5.505e-01 1.028e-01 5.352 1.02e-07 ***
## SaleConditionAdjLand 1.746e+04 1.388e+04 1.258 0.208633
## SaleConditionAlloca 7.355e+03 9.339e+03 0.788 0.431107
## SaleConditionFamily -5.060e+03 6.580e+03 -0.769 0.442010
## SaleConditionNormal 6.871e+03 2.836e+03 2.423 0.015521 *
## SaleConditionPartial 3.123e+04 3.986e+03 7.835 9.34e-15 ***
## TotalBsmtSF 3.465e+01 4.378e+00 7.913 5.11e-15 ***
## PoolQC.L -1.923e+05 7.070e+04 -2.720 0.006617 **
## PoolQC.Q 2.964e+05 6.726e+04 4.407 1.13e-05 ***
## PoolQC.C -7.591e+04 2.408e+04 -3.153 0.001653 **
## GarageCars 7.276e+02 2.240e+03 0.325 0.745327
## ExterQual.L 2.591e+04 6.764e+03 3.830 0.000134 ***
## ExterQual.Q 3.385e+04 4.602e+03 7.357 3.22e-13 ***
## ExterQual.C 2.767e+03 2.314e+03 1.196 0.232013
## Condition1Feedr 4.872e+03 5.123e+03 0.951 0.341742
## Condition1Norm 1.448e+04 4.193e+03 3.452 0.000572 ***
## Condition1PosA -1.896e+03 1.058e+04 -0.179 0.857826
## Condition1PosN 8.878e+03 7.753e+03 1.145 0.252408
## Condition1RRAe -6.582e+03 9.115e+03 -0.722 0.470346
## Condition1RRAn 1.407e+04 7.029e+03 2.002 0.045482 *
## Condition1RRNe -4.156e+03 1.931e+04 -0.215 0.829598
## Condition1RRNn 5.503e+03 1.337e+04 0.412 0.680730
## LotConfigCulDSac 9.688e+03 3.465e+03 2.796 0.005243 **
## LotConfigFR2 -1.508e+03 4.320e+03 -0.349 0.727003
## LotConfigFR3 3.884e+01 1.394e+04 0.003 0.997778
## LotConfigInside -7.034e+02 1.931e+03 -0.364 0.715657
## ScreenPorch 3.653e+01 1.319e+01 2.769 0.005693 **
## PoolArea 7.404e+02 1.859e+02 3.982 7.19e-05 ***
## BedroomAbvGr -7.390e+03 1.337e+03 -5.529 3.84e-08 ***
## LandSlopeMod 7.003e+03 4.156e+03 1.685 0.092215 .
## LandSlopeSev -2.265e+04 1.084e+04 -2.089 0.036901 *
## LandContourHLS 8.910e+03 5.345e+03 1.667 0.095751 .
## LandContourLow -1.008e+04 6.580e+03 -1.532 0.125755
## LandContourLvl 1.642e+03 3.810e+03 0.431 0.666650
## StreetPave 4.286e+04 1.231e+04 3.483 0.000511 ***
## LowQualFinSF -6.527e+01 1.563e+01 -4.177 3.13e-05 ***
## MasVnrArea 2.003e+01 4.662e+00 4.296 1.86e-05 ***
## GarageYrBlt 7.682e+01 5.407e+01 1.421 0.155676
## Fireplaces 2.836e+03 1.381e+03 2.053 0.040263 *
## BsmtFullBath 2.497e+03 1.867e+03 1.337 0.181322
## YearRemodAdd 8.410e+01 5.363e+01 1.568 0.117088
## MoSold -2.121e+02 2.631e+02 -0.806 0.420467
## KitchenAbvGr -2.530e+04 3.939e+03 -6.423 1.84e-10 ***
## TotRmsAbvGrd 3.072e+03 9.823e+02 3.127 0.001803 **
## `1stFlrSF` -1.426e+01 4.529e+00 -3.148 0.001680 **
## LotFrontage 1.972e+02 4.059e+01 4.859 1.32e-06 ***
## WoodDeckSF 9.125e+00 6.221e+00 1.467 0.142667
## GarageArea 2.171e+01 7.703e+00 2.819 0.004885 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 26340 on 1379 degrees of freedom
## Multiple R-squared: 0.8951, Adjusted R-squared: 0.8897
## F-statistic: 165.7 on 71 and 1379 DF, p-value: < 2.2e-16Prediction & Submissions
data_pred <- predict(data_lm_final, data_test_clean)
submission <- data_test_clean %>%
cbind ('SalePrice' = data_pred) %>%
dplyr::select(Id, SalePrice)
submission Kaggle Submission & Score 