library(RCurl)

## Loading required package: bitops

library(knitr)
library(ggplot2)

## Warning: package 'ggplot2' was built under R version 3.4.4

library(gridExtra)

## Warning: package 'gridExtra' was built under R version 3.4.4

library(MASS)

sc.data <- read.csv(text = getURL("https://raw.githubusercontent.com/AjayArora35/compmath/master/train.csv"), header = T, stringsAsFactors = F)
kable(sc.data[sample(nrow(sc.data), 10), ], align='l', caption = "Sample of 10 rows", row.names=FALSE)

Sample of 10 rows
Id	MSSubClass	MSZoning	LotFrontage	LotArea	Street	Alley	LotShape	LandContour	Utilities	LotConfig	LandSlope	Neighborhood	Condition1	Condition2	BldgType	HouseStyle	OverallQual	OverallCond	YearBuilt	YearRemodAdd	RoofStyle	RoofMatl	Exterior1st	Exterior2nd	MasVnrType	MasVnrArea	ExterQual	ExterCond	Foundation	BsmtQual	BsmtCond	BsmtExposure	BsmtFinType1	BsmtFinSF1	BsmtFinType2	BsmtFinSF2	BsmtUnfSF	TotalBsmtSF	Heating	HeatingQC	CentralAir	Electrical	X1stFlrSF	X2ndFlrSF	GrLivArea	BsmtFullBath	BsmtHalfBath	FullBath	HalfBath	BedroomAbvGr	KitchenAbvGr	KitchenQual	TotRmsAbvGrd	Functional	Fireplaces	FireplaceQu	GarageType	GarageYrBlt	GarageFinish	GarageCars	GarageArea	GarageQual	GarageCond	PavedDrive	WoodDeckSF	OpenPorchSF	PoolQC	Fence	MiscFeature	MiscVal	MoSold	YrSold	SaleType	SaleCondition	SalePrice
772	20	RL	67	8877	Pave	NA	Reg	Lvl	AllPub	Inside	Gtl	Edwards	Norm	Norm	1Fam	1Story	4	5	1951	1951	Gable	CompShg	Wd Sdng	Wd Sdng	None	0	TA	TA	CBlock	Fa	Fa	No	LwQ	836	Unf	0	0	836	GasA	TA	Y	FuseF	1220	0	1220	0	0	1	0	2	1	TA	6	Typ	0	NA	Detchd	1951	Unf	2	396	TA	TA	Y	0	0	NA	NA	NA	0	4	2006	COD	Normal	102000
1042	60	RL	NA	9130	Pave	NA	Reg	Lvl	AllPub	Inside	Gtl	NWAmes	Feedr	Norm	1Fam	2Story	6	8	1966	2000	Hip	CompShg	HdBoard	HdBoard	BrkFace	252	TA	TA	CBlock	TA	TA	No	GLQ	400	Rec	64	336	800	GasA	Gd	Y	SBrkr	800	832	1632	0	1	1	1	4	1	Gd	7	Typ	0	NA	Attchd	1966	Unf	2	484	TA	TA	Y	0	40	NA	NA	NA	0	7	2008	WD	Normal	173000
1436	20	RL	80	8400	Pave	NA	Reg	Lvl	AllPub	Inside	Gtl	NAmes	Norm	Norm	1Fam	1Story	6	9	1962	2005	Gable	CompShg	Wd Sdng	Wd Sdng	BrkFace	237	Gd	Gd	CBlock	TA	TA	No	Unf	0	Unf	0	1319	1319	GasA	TA	Y	SBrkr	1537	0	1537	1	0	1	1	3	1	Gd	7	Typ	1	Gd	Attchd	1962	RFn	2	462	TA	TA	Y	0	36	NA	GdPrv	NA	0	7	2008	COD	Abnorml	174000
798	20	RL	57	7677	Pave	NA	Reg	Lvl	AllPub	Inside	Gtl	NAmes	Norm	Norm	1Fam	1Story	5	5	1953	1953	Gable	CompShg	VinylSd	VinylSd	None	0	TA	TA	CBlock	TA	TA	No	BLQ	570	Unf	0	203	773	GasA	Gd	Y	SBrkr	773	0	773	0	0	1	0	2	1	TA	4	Typ	0	NA	Attchd	1953	Unf	1	240	TA	TA	Y	0	0	NA	NA	NA	0	4	2008	WD	Abnorml	110000
652	70	RL	60	9084	Pave	NA	Reg	Lvl	AllPub	Inside	Gtl	Edwards	Artery	Norm	1Fam	2Story	4	5	1940	1950	Gable	CompShg	MetalSd	MetalSd	None	0	TA	TA	CBlock	TA	TA	Mn	Unf	0	Unf	0	755	755	GasA	TA	Y	SBrkr	755	755	1510	1	0	1	0	4	1	TA	7	Typ	1	Gd	Detchd	1940	Unf	1	296	Fa	Po	P	120	0	NA	MnPrv	NA	0	10	2009	WD	Normal	108000
348	20	RL	NA	17600	Pave	NA	IR1	Lvl	AllPub	Inside	Gtl	NAmes	Norm	Norm	1Fam	1Story	6	5	1960	1960	Gable	CompShg	Wd Sdng	Wd Sdng	BrkFace	30	TA	TA	CBlock	TA	TA	No	BLQ	1270	Unf	0	208	1478	GasA	Ex	Y	FuseA	1478	0	1478	1	0	2	0	3	1	TA	6	Typ	2	Gd	Attchd	1960	Unf	2	498	TA	TA	Y	0	40	NA	NA	NA	0	12	2009	WD	Normal	157500
740	60	RL	65	9313	Pave	NA	IR1	Lvl	AllPub	Inside	Gtl	CollgCr	Norm	Norm	1Fam	2Story	7	5	2004	2004	Gable	CompShg	VinylSd	VinylSd	None	0	Gd	TA	PConc	Gd	TA	No	Unf	0	Unf	0	864	864	GasA	Ex	Y	SBrkr	864	864	1728	0	0	2	1	3	1	Gd	7	Typ	0	NA	Attchd	2004	RFn	2	572	TA	TA	Y	187	56	NA	NA	NA	0	4	2009	WD	Normal	190000
974	20	FV	95	11639	Pave	NA	Reg	Lvl	AllPub	Corner	Gtl	Somerst	Norm	Norm	1Fam	1Story	7	5	2007	2008	Gable	CompShg	CemntBd	CmentBd	NA	NA	Gd	TA	PConc	Gd	TA	No	Unf	0	Unf	0	1428	1428	GasA	Ex	Y	SBrkr	1428	0	1428	0	0	2	0	3	1	Gd	6	Typ	0	NA	Attchd	2007	Fin	2	480	TA	TA	Y	0	120	NA	NA	NA	0	12	2008	New	Partial	182000
1150	70	RM	50	9000	Pave	NA	Reg	Lvl	AllPub	Inside	Gtl	OldTown	Artery	Norm	1Fam	2Story	7	9	1920	1988	Hip	CompShg	VinylSd	VinylSd	None	0	TA	Gd	PConc	TA	TA	No	ALQ	624	Unf	0	26	650	GasA	Ex	Y	SBrkr	832	650	1482	0	1	1	0	3	1	TA	7	Typ	0	NA	Detchd	1930	Unf	2	324	TA	TA	Y	0	0	NA	NA	NA	0	7	2009	WD	Normal	143000
1253	20	RL	62	9858	Pave	NA	Reg	Lvl	AllPub	Inside	Gtl	Mitchel	Norm	Norm	1Fam	1Story	5	6	1968	1968	Gable	CompShg	HdBoard	HdBoard	None	0	TA	TA	CBlock	TA	TA	No	BLQ	510	Unf	0	354	864	GasA	TA	Y	SBrkr	874	0	874	1	0	1	0	3	1	TA	5	Typ	0	NA	Attchd	1968	RFn	1	288	TA	TA	Y	33	0	NA	GdWo	Shed	600	11	2009	WD	Normal	130000

Data fields

Here’s a brief version of what you’ll find in the data description file.

SalePrice - the property's sale price in dollars. This is the target variable that you're trying to predict.
MSSubClass: The building class
MSZoning: The general zoning classification
LotFrontage: Linear feet of street connected to property
LotArea: Lot size in square feet
Street: Type of road access
Alley: Type of alley access
LotShape: General shape of property
LandContour: Flatness of the property
Utilities: Type of utilities available
LotConfig: Lot configuration
LandSlope: Slope of property
Neighborhood: Physical locations within Ames city limits
Condition1: Proximity to main road or railroad
Condition2: Proximity to main road or railroad (if a second is present)
BldgType: Type of dwelling
HouseStyle: Style of dwelling
OverallQual: Overall material and finish quality
OverallCond: Overall condition rating
YearBuilt: Original construction date
YearRemodAdd: Remodel date
RoofStyle: Type of roof
RoofMatl: Roof material
Exterior1st: Exterior covering on house
Exterior2nd: Exterior covering on house (if more than one material)
MasVnrType: Masonry veneer type
MasVnrArea: Masonry veneer area in square feet
ExterQual: Exterior material quality
ExterCond: Present condition of the material on the exterior
Foundation: Type of foundation
BsmtQual: Height of the basement
BsmtCond: General condition of the basement
BsmtExposure: Walkout or garden level basement walls
BsmtFinType1: Quality of basement finished area
BsmtFinSF1: Type 1 finished square feet
BsmtFinType2: Quality of second finished area (if present)
BsmtFinSF2: Type 2 finished square feet
BsmtUnfSF: Unfinished square feet of basement area
TotalBsmtSF: Total square feet of basement area
Heating: Type of heating
HeatingQC: Heating quality and condition
CentralAir: Central air conditioning
Electrical: Electrical system
1stFlrSF: First Floor square feet
2ndFlrSF: Second floor square feet
LowQualFinSF: Low quality finished square feet (all floors)
GrLivArea: Above grade (ground) living area square feet
BsmtFullBath: Basement full bathrooms
BsmtHalfBath: Basement half bathrooms
FullBath: Full bathrooms above grade
HalfBath: Half baths above grade
Bedroom: Number of bedrooms above basement level
Kitchen: Number of kitchens
KitchenQual: Kitchen quality
TotRmsAbvGrd: Total rooms above grade (does not include bathrooms)
Functional: Home functionality rating
Fireplaces: Number of fireplaces
FireplaceQu: Fireplace quality
GarageType: Garage location
GarageYrBlt: Year garage was built
GarageFinish: Interior finish of the garage
GarageCars: Size of garage in car capacity
GarageArea: Size of garage in square feet
GarageQual: Garage quality
GarageCond: Garage condition
PavedDrive: Paved driveway
WoodDeckSF: Wood deck area in square feet
OpenPorchSF: Open porch area in square feet
EnclosedPorch: Enclosed porch area in square feet
3SsnPorch: Three season porch area in square feet
ScreenPorch: Screen porch area in square feet
PoolArea: Pool area in square feet
PoolQC: Pool quality
Fence: Fence quality
MiscFeature: Miscellaneous feature not covered in other categories
MiscVal: $Value of miscellaneous feature
MoSold: Month Sold
YrSold: Year Sold
SaleType: Type of sale
SaleCondition: Condition of sale

Choosing Variables:

Independent Variable: OverallQual: Overall material and finish quality
Dependent Variable: SalePrice - the property’s sale price in dollars. This is the target variable that you’re trying to predict.

X = OverallQual

Y = Sales price

hist(sc.data$OverallQual)

# X = OverallQual
# Y = SalesPrice

X <- sc.data$OverallQual
Y <- sc.data$SalePrice

The chosen independent variable (OverallQual) has skewed data to the right. (A “skewed right” distribution is one in which the tail is on the right side. )

Probability:

Definitions of Probablities:

P(X=x and Y=y) = P(x,y)

If X and Y are independent then

P(x,y) = P(x) P(y)

P(x | y) is the probability of x given y

P(x | y) = P(x,y) / P(y)
P(x,y) = P(x | y) P(y)

If X and Y are independent then
P(x | y) = P(x)

# Summary of X (OverallQual) and Y (SalesPrice)
quantile(X)

##   0%  25%  50%  75% 100% 
##    1    5    6    7   10

summary(X)

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   1.000   5.000   6.000   6.099   7.000  10.000

quantile(Y)

##     0%    25%    50%    75%   100% 
##  34900 129975 163000 214000 755000

summary(Y)

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   34900  129975  163000  180921  214000  755000

Total Rows:

#Length of X (OverallQual) and Y (SalesPrice)
length(X)

## [1] 1460

length(Y)

## [1] 1460

x <- 5.0
y <- 129975

1st quartile of “X”: x = 5.0

1st quartile of “Y”: y = 129975

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

Formula Conditional Probability (2 events): P(B|A) = P(A n B) / P(A)

P(X|Y) = P(Y n X) / P(Y)

# Count of Y (SalestPrice) greater than 129975
countofY <- sum(Y > y) 
countofY

## [1] 1095

# Count of X (OverallQual > 5.0)
countofX <- sum(X > x)
countofX

## [1] 922

# Count of both (Y > y and X > x)
countofBoth <- (sum(Y > y & X > x))
countofBoth

## [1] 848

# Probability

(countofBoth / length(X)) / (countofY / length(Y))

## [1] 0.7744292

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

# Count of both (X > x and Y > y)
countofBoth2 <- sum(X > x & Y > y)
countofBoth2

## [1] 848

# Probability

(countofBoth2 / length(X)) / (countofY / length(Y)) * (countofY / length(Y))

## [1] 0.5808219

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

# Count of both (X < x & Y > y)
countofBoth3 <- sum(Y > y & X < x)
countofBoth3

## [1] 23

# Probability 
countofBoth3 / length(X)

## [1] 0.01575342

Count Table (Professor, I have 2 count tables – the initial question and the amended question)

sum(X <= 7 & Y <= 163000)

sum(X <= 7 & Y > 163000)

sum(X > 7 & Y <= 163000)

sum(X > 7 & Y > 163000)

[1] 728 [1] 503 [1] 4 [1] 225 Count Table

x/y	<=1st Quartile	>1st Quartile	Total
<=1st Quartile	728	503	1231
>1st Quartile	4	225	229
Total	732	728	1460

#Verify Count Table

table(X > 7, Y > 163000)

##        
##         FALSE TRUE
##   FALSE   728  503
##   TRUE      4  225

# Summary of X (OverallQual) and Y (SalesPrice) shown here as reference
quantile(X)

##   0%  25%  50%  75% 100% 
##    1    5    6    7   10

summary(X)

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   1.000   5.000   6.000   6.099   7.000  10.000

quantile(Y)

##     0%    25%    50%    75%   100% 
##  34900 129975 163000 214000 755000

summary(Y)

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   34900  129975  163000  180921  214000  755000

sum(X <= 5 & Y <= 129975)

sum(X <= 5 & Y > 129975)

sum(X > 5 & Y <= 129975)

sum(X > 5 & Y > 129975)

[1] 291 [1] 247 [1] 74 [1] 848 Count Table

x/y	<=1st Quartile	>1st Quartile	Total
<=1st Quartile	291	247	538
>1st Quartile	74	848	922
Total	365	1095	1460

#Verify Count Table

table(X > 5, Y > 129975)

##        
##         FALSE TRUE
##   FALSE   291  247
##   TRUE     74  848

P(AB)=P(A)P(B) ?

ProbA <- sum(X > x)/length(X)
ProbA

## [1] 0.6315068

ProbB <- sum(Y > y)/length(Y)
ProbB

## [1] 0.75

ProbAnProbB <- ProbA * ProbB
ProbAnProbB

## [1] 0.4736301

P(AB)=P(B)P(A|B) Product Rule By Definition

Definitions

The conditional probability of A given B is the probability of event A, if event B

occurred. P(A|B)

A is independent of B if the conditional probability of A given B is the same as the

unconditional probability of A. P(A|B) = P(A), so we will use this test to determine

independence between variables.

#P(A|B) = P(A)
#P(X>x|Y>y) = P(X>x)

#P(X>x|Y>y)
(sum(Y > y & X > x) / length(X)) / (sum(Y > y) / length(Y))

## [1] 0.7744292

#P(X>x)
sum(X > x) / length(X)

## [1] 0.6315068

P(A|B) = 0.77 and P(A) = 0.63 are not equal,hence, the two variables are dependent. In addition, P(A|B) = 0.77 and ProbBnProbA = 0.47 are not equal.

Chi-Square

The Chi Square Test, tests the hypothesis of whether the Overall Quality is independent of the Sale Price.

tbl <- table(X > 5, Y > 129975)
tbl

##        
##         FALSE TRUE
##   FALSE   291  247
##   TRUE     74  848

chisq.test(tbl)

## 
##  Pearson's Chi-squared test with Yates' continuity correction
## 
## data:  tbl
## X-squared = 382.02, df = 1, p-value < 2.2e-16

NULL Hypothesis: Overall Quality has no impact on Sale price

Alternative Hypothesis: Overall Quality has an impact on Sale price

We can reject the NULL Hypothesis given the p-value (< 2.2e-16) is less than 0.05.

Descriptive and Inferential Statistics

Univariate Statistics

We will investigate the data for any missing values, structure, ect. We will initialize the missing data as necessary.

#What is the "structure" of the data.
dim(sc.data)

## [1] 1460   81

# Numeric types and categorical types
str(sc.data)

## 'data.frame':    1460 obs. of  81 variables:
##  $ Id           : int  1 2 3 4 5 6 7 8 9 10 ...
##  $ MSSubClass   : int  60 20 60 70 60 50 20 60 50 190 ...
##  $ MSZoning     : chr  "RL" "RL" "RL" "RL" ...
##  $ LotFrontage  : int  65 80 68 60 84 85 75 NA 51 50 ...
##  $ LotArea      : int  8450 9600 11250 9550 14260 14115 10084 10382 6120 7420 ...
##  $ Street       : chr  "Pave" "Pave" "Pave" "Pave" ...
##  $ Alley        : chr  NA NA NA NA ...
##  $ LotShape     : chr  "Reg" "Reg" "IR1" "IR1" ...
##  $ LandContour  : chr  "Lvl" "Lvl" "Lvl" "Lvl" ...
##  $ Utilities    : chr  "AllPub" "AllPub" "AllPub" "AllPub" ...
##  $ LotConfig    : chr  "Inside" "FR2" "Inside" "Corner" ...
##  $ LandSlope    : chr  "Gtl" "Gtl" "Gtl" "Gtl" ...
##  $ Neighborhood : chr  "CollgCr" "Veenker" "CollgCr" "Crawfor" ...
##  $ Condition1   : chr  "Norm" "Feedr" "Norm" "Norm" ...
##  $ Condition2   : chr  "Norm" "Norm" "Norm" "Norm" ...
##  $ BldgType     : chr  "1Fam" "1Fam" "1Fam" "1Fam" ...
##  $ HouseStyle   : chr  "2Story" "1Story" "2Story" "2Story" ...
##  $ OverallQual  : int  7 6 7 7 8 5 8 7 7 5 ...
##  $ OverallCond  : int  5 8 5 5 5 5 5 6 5 6 ...
##  $ YearBuilt    : int  2003 1976 2001 1915 2000 1993 2004 1973 1931 1939 ...
##  $ YearRemodAdd : int  2003 1976 2002 1970 2000 1995 2005 1973 1950 1950 ...
##  $ RoofStyle    : chr  "Gable" "Gable" "Gable" "Gable" ...
##  $ RoofMatl     : chr  "CompShg" "CompShg" "CompShg" "CompShg" ...
##  $ Exterior1st  : chr  "VinylSd" "MetalSd" "VinylSd" "Wd Sdng" ...
##  $ Exterior2nd  : chr  "VinylSd" "MetalSd" "VinylSd" "Wd Shng" ...
##  $ MasVnrType   : chr  "BrkFace" "None" "BrkFace" "None" ...
##  $ MasVnrArea   : int  196 0 162 0 350 0 186 240 0 0 ...
##  $ ExterQual    : chr  "Gd" "TA" "Gd" "TA" ...
##  $ ExterCond    : chr  "TA" "TA" "TA" "TA" ...
##  $ Foundation   : chr  "PConc" "CBlock" "PConc" "BrkTil" ...
##  $ BsmtQual     : chr  "Gd" "Gd" "Gd" "TA" ...
##  $ BsmtCond     : chr  "TA" "TA" "TA" "Gd" ...
##  $ BsmtExposure : chr  "No" "Gd" "Mn" "No" ...
##  $ BsmtFinType1 : chr  "GLQ" "ALQ" "GLQ" "ALQ" ...
##  $ BsmtFinSF1   : int  706 978 486 216 655 732 1369 859 0 851 ...
##  $ BsmtFinType2 : chr  "Unf" "Unf" "Unf" "Unf" ...
##  $ BsmtFinSF2   : int  0 0 0 0 0 0 0 32 0 0 ...
##  $ BsmtUnfSF    : int  150 284 434 540 490 64 317 216 952 140 ...
##  $ TotalBsmtSF  : int  856 1262 920 756 1145 796 1686 1107 952 991 ...
##  $ Heating      : chr  "GasA" "GasA" "GasA" "GasA" ...
##  $ HeatingQC    : chr  "Ex" "Ex" "Ex" "Gd" ...
##  $ CentralAir   : chr  "Y" "Y" "Y" "Y" ...
##  $ Electrical   : chr  "SBrkr" "SBrkr" "SBrkr" "SBrkr" ...
##  $ X1stFlrSF    : int  856 1262 920 961 1145 796 1694 1107 1022 1077 ...
##  $ X2ndFlrSF    : int  854 0 866 756 1053 566 0 983 752 0 ...
##  $ LowQualFinSF : int  0 0 0 0 0 0 0 0 0 0 ...
##  $ GrLivArea    : int  1710 1262 1786 1717 2198 1362 1694 2090 1774 1077 ...
##  $ BsmtFullBath : int  1 0 1 1 1 1 1 1 0 1 ...
##  $ BsmtHalfBath : int  0 1 0 0 0 0 0 0 0 0 ...
##  $ FullBath     : int  2 2 2 1 2 1 2 2 2 1 ...
##  $ HalfBath     : int  1 0 1 0 1 1 0 1 0 0 ...
##  $ BedroomAbvGr : int  3 3 3 3 4 1 3 3 2 2 ...
##  $ KitchenAbvGr : int  1 1 1 1 1 1 1 1 2 2 ...
##  $ KitchenQual  : chr  "Gd" "TA" "Gd" "Gd" ...
##  $ TotRmsAbvGrd : int  8 6 6 7 9 5 7 7 8 5 ...
##  $ Functional   : chr  "Typ" "Typ" "Typ" "Typ" ...
##  $ Fireplaces   : int  0 1 1 1 1 0 1 2 2 2 ...
##  $ FireplaceQu  : chr  NA "TA" "TA" "Gd" ...
##  $ GarageType   : chr  "Attchd" "Attchd" "Attchd" "Detchd" ...
##  $ GarageYrBlt  : int  2003 1976 2001 1998 2000 1993 2004 1973 1931 1939 ...
##  $ GarageFinish : chr  "RFn" "RFn" "RFn" "Unf" ...
##  $ GarageCars   : int  2 2 2 3 3 2 2 2 2 1 ...
##  $ GarageArea   : int  548 460 608 642 836 480 636 484 468 205 ...
##  $ GarageQual   : chr  "TA" "TA" "TA" "TA" ...
##  $ GarageCond   : chr  "TA" "TA" "TA" "TA" ...
##  $ PavedDrive   : chr  "Y" "Y" "Y" "Y" ...
##  $ WoodDeckSF   : int  0 298 0 0 192 40 255 235 90 0 ...
##  $ OpenPorchSF  : int  61 0 42 35 84 30 57 204 0 4 ...
##  $ EnclosedPorch: int  0 0 0 272 0 0 0 228 205 0 ...
##  $ X3SsnPorch   : int  0 0 0 0 0 320 0 0 0 0 ...
##  $ ScreenPorch  : int  0 0 0 0 0 0 0 0 0 0 ...
##  $ PoolArea     : int  0 0 0 0 0 0 0 0 0 0 ...
##  $ PoolQC       : chr  NA NA NA NA ...
##  $ Fence        : chr  NA NA NA NA ...
##  $ MiscFeature  : chr  NA NA NA NA ...
##  $ MiscVal      : int  0 0 0 0 0 700 0 350 0 0 ...
##  $ MoSold       : int  2 5 9 2 12 10 8 11 4 1 ...
##  $ YrSold       : int  2008 2007 2008 2006 2008 2009 2007 2009 2008 2008 ...
##  $ SaleType     : chr  "WD" "WD" "WD" "WD" ...
##  $ SaleCondition: chr  "Normal" "Normal" "Normal" "Abnorml" ...
##  $ SalePrice    : int  208500 181500 223500 140000 250000 143000 307000 200000 129900 118000 ...

# Summary of data 
head(sc.data)

##   Id MSSubClass MSZoning LotFrontage LotArea Street Alley LotShape
## 1  1         60       RL          65    8450   Pave  <NA>      Reg
## 2  2         20       RL          80    9600   Pave  <NA>      Reg
## 3  3         60       RL          68   11250   Pave  <NA>      IR1
## 4  4         70       RL          60    9550   Pave  <NA>      IR1
## 5  5         60       RL          84   14260   Pave  <NA>      IR1
## 6  6         50       RL          85   14115   Pave  <NA>      IR1
##   LandContour Utilities LotConfig LandSlope Neighborhood Condition1
## 1         Lvl    AllPub    Inside       Gtl      CollgCr       Norm
## 2         Lvl    AllPub       FR2       Gtl      Veenker      Feedr
## 3         Lvl    AllPub    Inside       Gtl      CollgCr       Norm
## 4         Lvl    AllPub    Corner       Gtl      Crawfor       Norm
## 5         Lvl    AllPub       FR2       Gtl      NoRidge       Norm
## 6         Lvl    AllPub    Inside       Gtl      Mitchel       Norm
##   Condition2 BldgType HouseStyle OverallQual OverallCond YearBuilt
## 1       Norm     1Fam     2Story           7           5      2003
## 2       Norm     1Fam     1Story           6           8      1976
## 3       Norm     1Fam     2Story           7           5      2001
## 4       Norm     1Fam     2Story           7           5      1915
## 5       Norm     1Fam     2Story           8           5      2000
## 6       Norm     1Fam     1.5Fin           5           5      1993
##   YearRemodAdd RoofStyle RoofMatl Exterior1st Exterior2nd MasVnrType
## 1         2003     Gable  CompShg     VinylSd     VinylSd    BrkFace
## 2         1976     Gable  CompShg     MetalSd     MetalSd       None
## 3         2002     Gable  CompShg     VinylSd     VinylSd    BrkFace
## 4         1970     Gable  CompShg     Wd Sdng     Wd Shng       None
## 5         2000     Gable  CompShg     VinylSd     VinylSd    BrkFace
## 6         1995     Gable  CompShg     VinylSd     VinylSd       None
##   MasVnrArea ExterQual ExterCond Foundation BsmtQual BsmtCond BsmtExposure
## 1        196        Gd        TA      PConc       Gd       TA           No
## 2          0        TA        TA     CBlock       Gd       TA           Gd
## 3        162        Gd        TA      PConc       Gd       TA           Mn
## 4          0        TA        TA     BrkTil       TA       Gd           No
## 5        350        Gd        TA      PConc       Gd       TA           Av
## 6          0        TA        TA       Wood       Gd       TA           No
##   BsmtFinType1 BsmtFinSF1 BsmtFinType2 BsmtFinSF2 BsmtUnfSF TotalBsmtSF
## 1          GLQ        706          Unf          0       150         856
## 2          ALQ        978          Unf          0       284        1262
## 3          GLQ        486          Unf          0       434         920
## 4          ALQ        216          Unf          0       540         756
## 5          GLQ        655          Unf          0       490        1145
## 6          GLQ        732          Unf          0        64         796
##   Heating HeatingQC CentralAir Electrical X1stFlrSF X2ndFlrSF LowQualFinSF
## 1    GasA        Ex          Y      SBrkr       856       854            0
## 2    GasA        Ex          Y      SBrkr      1262         0            0
## 3    GasA        Ex          Y      SBrkr       920       866            0
## 4    GasA        Gd          Y      SBrkr       961       756            0
## 5    GasA        Ex          Y      SBrkr      1145      1053            0
## 6    GasA        Ex          Y      SBrkr       796       566            0
##   GrLivArea BsmtFullBath BsmtHalfBath FullBath HalfBath BedroomAbvGr
## 1      1710            1            0        2        1            3
## 2      1262            0            1        2        0            3
## 3      1786            1            0        2        1            3
## 4      1717            1            0        1        0            3
## 5      2198            1            0        2        1            4
## 6      1362            1            0        1        1            1
##   KitchenAbvGr KitchenQual TotRmsAbvGrd Functional Fireplaces FireplaceQu
## 1            1          Gd            8        Typ          0        <NA>
## 2            1          TA            6        Typ          1          TA
## 3            1          Gd            6        Typ          1          TA
## 4            1          Gd            7        Typ          1          Gd
## 5            1          Gd            9        Typ          1          TA
## 6            1          TA            5        Typ          0        <NA>
##   GarageType GarageYrBlt GarageFinish GarageCars GarageArea GarageQual
## 1     Attchd        2003          RFn          2        548         TA
## 2     Attchd        1976          RFn          2        460         TA
## 3     Attchd        2001          RFn          2        608         TA
## 4     Detchd        1998          Unf          3        642         TA
## 5     Attchd        2000          RFn          3        836         TA
## 6     Attchd        1993          Unf          2        480         TA
##   GarageCond PavedDrive WoodDeckSF OpenPorchSF EnclosedPorch X3SsnPorch
## 1         TA          Y          0          61             0          0
## 2         TA          Y        298           0             0          0
## 3         TA          Y          0          42             0          0
## 4         TA          Y          0          35           272          0
## 5         TA          Y        192          84             0          0
## 6         TA          Y         40          30             0        320
##   ScreenPorch PoolArea PoolQC Fence MiscFeature MiscVal MoSold YrSold
## 1           0        0   <NA>  <NA>        <NA>       0      2   2008
## 2           0        0   <NA>  <NA>        <NA>       0      5   2007
## 3           0        0   <NA>  <NA>        <NA>       0      9   2008
## 4           0        0   <NA>  <NA>        <NA>       0      2   2006
## 5           0        0   <NA>  <NA>        <NA>       0     12   2008
## 6           0        0   <NA> MnPrv        Shed     700     10   2009
##   SaleType SaleCondition SalePrice
## 1       WD        Normal    208500
## 2       WD        Normal    181500
## 3       WD        Normal    223500
## 4       WD       Abnorml    140000
## 5       WD        Normal    250000
## 6       WD        Normal    143000

#Do we have missing data (add up fields with missing data)
colSums(sapply(sc.data, is.na))

##            Id    MSSubClass      MSZoning   LotFrontage       LotArea 
##             0             0             0           259             0 
##        Street         Alley      LotShape   LandContour     Utilities 
##             0          1369             0             0             0 
##     LotConfig     LandSlope  Neighborhood    Condition1    Condition2 
##             0             0             0             0             0 
##      BldgType    HouseStyle   OverallQual   OverallCond     YearBuilt 
##             0             0             0             0             0 
##  YearRemodAdd     RoofStyle      RoofMatl   Exterior1st   Exterior2nd 
##             0             0             0             0             0 
##    MasVnrType    MasVnrArea     ExterQual     ExterCond    Foundation 
##             8             8             0             0             0 
##      BsmtQual      BsmtCond  BsmtExposure  BsmtFinType1    BsmtFinSF1 
##            37            37            38            37             0 
##  BsmtFinType2    BsmtFinSF2     BsmtUnfSF   TotalBsmtSF       Heating 
##            38             0             0             0             0 
##     HeatingQC    CentralAir    Electrical     X1stFlrSF     X2ndFlrSF 
##             0             0             1             0             0 
##  LowQualFinSF     GrLivArea  BsmtFullBath  BsmtHalfBath      FullBath 
##             0             0             0             0             0 
##      HalfBath  BedroomAbvGr  KitchenAbvGr   KitchenQual  TotRmsAbvGrd 
##             0             0             0             0             0 
##    Functional    Fireplaces   FireplaceQu    GarageType   GarageYrBlt 
##             0             0           690            81            81 
##  GarageFinish    GarageCars    GarageArea    GarageQual    GarageCond 
##            81             0             0            81            81 
##    PavedDrive    WoodDeckSF   OpenPorchSF EnclosedPorch    X3SsnPorch 
##             0             0             0             0             0 
##   ScreenPorch      PoolArea        PoolQC         Fence   MiscFeature 
##             0             0          1453          1179          1406 
##       MiscVal        MoSold        YrSold      SaleType SaleCondition 
##             0             0             0             0             0 
##     SalePrice 
##             0

# What % of data is missing
sum(is.na(sc.data)) / (nrow(sc.data) * ncol(sc.data))

## [1] 0.05889565

#Fill in missing field data with defaults and zeros

sc.data$GarageYrBlt[is.na(sc.data$GarageYrBlt)] <- sc.data$YearBuilt[is.na(sc.data$GarageYrBlt)]
sc.data$SalePrice[is.na(sc.data$SalePrice)] <- 0
sc.data$LotFrontage[is.na(sc.data$LotFrontage)] <- 0
sc.data$MasVnrArea[is.na(sc.data$MasVnrArea)] <- 0
sc.data$BsmtFullBath[is.na(sc.data$BsmtFullBath)] <- 0
sc.data$BsmtHalfBath[is.na(sc.data$BsmtHalfBath)] <- 0
sc.data$BsmtFinSF1[is.na(sc.data$BsmtFinSF1)] <- 0
sc.data$BsmtFinSF2[is.na(sc.data$BsmtFinSF2)] <- 0
sc.data$BsmtUnfSF[is.na(sc.data$BsmtUnfSF)] <- 0
sc.data$TotalBsmtSF[is.na(sc.data$TotalBsmtSF)] <- 0
sc.data$GarageCars[is.na(sc.data$GarageCars)] <- 0
sc.data$GarageArea[is.na(sc.data$GarageArea)] <- 0
sc.data[is.na(sc.data)] <- 0

# What % of data is still missing
sum(is.na(sc.data)) / (nrow(sc.data) * ncol(sc.data))

## [1] 0

# Summary of all the numeric variables
sc.data2 <- sc.data[, sapply(sc.data, is.numeric)]
length(sc.data2)

## [1] 38

summary(sc.data2)

##        Id           MSSubClass     LotFrontage        LotArea      
##  Min.   :   1.0   Min.   : 20.0   Min.   :  0.00   Min.   :  1300  
##  1st Qu.: 365.8   1st Qu.: 20.0   1st Qu.: 42.00   1st Qu.:  7554  
##  Median : 730.5   Median : 50.0   Median : 63.00   Median :  9478  
##  Mean   : 730.5   Mean   : 56.9   Mean   : 57.62   Mean   : 10517  
##  3rd Qu.:1095.2   3rd Qu.: 70.0   3rd Qu.: 79.00   3rd Qu.: 11602  
##  Max.   :1460.0   Max.   :190.0   Max.   :313.00   Max.   :215245  
##   OverallQual      OverallCond      YearBuilt     YearRemodAdd 
##  Min.   : 1.000   Min.   :1.000   Min.   :1872   Min.   :1950  
##  1st Qu.: 5.000   1st Qu.:5.000   1st Qu.:1954   1st Qu.:1967  
##  Median : 6.000   Median :5.000   Median :1973   Median :1994  
##  Mean   : 6.099   Mean   :5.575   Mean   :1971   Mean   :1985  
##  3rd Qu.: 7.000   3rd Qu.:6.000   3rd Qu.:2000   3rd Qu.:2004  
##  Max.   :10.000   Max.   :9.000   Max.   :2010   Max.   :2010  
##    MasVnrArea       BsmtFinSF1       BsmtFinSF2        BsmtUnfSF     
##  Min.   :   0.0   Min.   :   0.0   Min.   :   0.00   Min.   :   0.0  
##  1st Qu.:   0.0   1st Qu.:   0.0   1st Qu.:   0.00   1st Qu.: 223.0  
##  Median :   0.0   Median : 383.5   Median :   0.00   Median : 477.5  
##  Mean   : 103.1   Mean   : 443.6   Mean   :  46.55   Mean   : 567.2  
##  3rd Qu.: 164.2   3rd Qu.: 712.2   3rd Qu.:   0.00   3rd Qu.: 808.0  
##  Max.   :1600.0   Max.   :5644.0   Max.   :1474.00   Max.   :2336.0  
##   TotalBsmtSF       X1stFlrSF      X2ndFlrSF     LowQualFinSF    
##  Min.   :   0.0   Min.   : 334   Min.   :   0   Min.   :  0.000  
##  1st Qu.: 795.8   1st Qu.: 882   1st Qu.:   0   1st Qu.:  0.000  
##  Median : 991.5   Median :1087   Median :   0   Median :  0.000  
##  Mean   :1057.4   Mean   :1163   Mean   : 347   Mean   :  5.845  
##  3rd Qu.:1298.2   3rd Qu.:1391   3rd Qu.: 728   3rd Qu.:  0.000  
##  Max.   :6110.0   Max.   :4692   Max.   :2065   Max.   :572.000  
##    GrLivArea     BsmtFullBath     BsmtHalfBath        FullBath    
##  Min.   : 334   Min.   :0.0000   Min.   :0.00000   Min.   :0.000  
##  1st Qu.:1130   1st Qu.:0.0000   1st Qu.:0.00000   1st Qu.:1.000  
##  Median :1464   Median :0.0000   Median :0.00000   Median :2.000  
##  Mean   :1515   Mean   :0.4253   Mean   :0.05753   Mean   :1.565  
##  3rd Qu.:1777   3rd Qu.:1.0000   3rd Qu.:0.00000   3rd Qu.:2.000  
##  Max.   :5642   Max.   :3.0000   Max.   :2.00000   Max.   :3.000  
##     HalfBath       BedroomAbvGr    KitchenAbvGr    TotRmsAbvGrd   
##  Min.   :0.0000   Min.   :0.000   Min.   :0.000   Min.   : 2.000  
##  1st Qu.:0.0000   1st Qu.:2.000   1st Qu.:1.000   1st Qu.: 5.000  
##  Median :0.0000   Median :3.000   Median :1.000   Median : 6.000  
##  Mean   :0.3829   Mean   :2.866   Mean   :1.047   Mean   : 6.518  
##  3rd Qu.:1.0000   3rd Qu.:3.000   3rd Qu.:1.000   3rd Qu.: 7.000  
##  Max.   :2.0000   Max.   :8.000   Max.   :3.000   Max.   :14.000  
##    Fireplaces     GarageYrBlt     GarageCars      GarageArea    
##  Min.   :0.000   Min.   :1872   Min.   :0.000   Min.   :   0.0  
##  1st Qu.:0.000   1st Qu.:1959   1st Qu.:1.000   1st Qu.: 334.5  
##  Median :1.000   Median :1978   Median :2.000   Median : 480.0  
##  Mean   :0.613   Mean   :1977   Mean   :1.767   Mean   : 473.0  
##  3rd Qu.:1.000   3rd Qu.:2001   3rd Qu.:2.000   3rd Qu.: 576.0  
##  Max.   :3.000   Max.   :2010   Max.   :4.000   Max.   :1418.0  
##    WoodDeckSF      OpenPorchSF     EnclosedPorch      X3SsnPorch    
##  Min.   :  0.00   Min.   :  0.00   Min.   :  0.00   Min.   :  0.00  
##  1st Qu.:  0.00   1st Qu.:  0.00   1st Qu.:  0.00   1st Qu.:  0.00  
##  Median :  0.00   Median : 25.00   Median :  0.00   Median :  0.00  
##  Mean   : 94.24   Mean   : 46.66   Mean   : 21.95   Mean   :  3.41  
##  3rd Qu.:168.00   3rd Qu.: 68.00   3rd Qu.:  0.00   3rd Qu.:  0.00  
##  Max.   :857.00   Max.   :547.00   Max.   :552.00   Max.   :508.00  
##   ScreenPorch        PoolArea          MiscVal             MoSold      
##  Min.   :  0.00   Min.   :  0.000   Min.   :    0.00   Min.   : 1.000  
##  1st Qu.:  0.00   1st Qu.:  0.000   1st Qu.:    0.00   1st Qu.: 5.000  
##  Median :  0.00   Median :  0.000   Median :    0.00   Median : 6.000  
##  Mean   : 15.06   Mean   :  2.759   Mean   :   43.49   Mean   : 6.322  
##  3rd Qu.:  0.00   3rd Qu.:  0.000   3rd Qu.:    0.00   3rd Qu.: 8.000  
##  Max.   :480.00   Max.   :738.000   Max.   :15500.00   Max.   :12.000  
##      YrSold       SalePrice     
##  Min.   :2006   Min.   : 34900  
##  1st Qu.:2007   1st Qu.:129975  
##  Median :2008   Median :163000  
##  Mean   :2008   Mean   :180921  
##  3rd Qu.:2009   3rd Qu.:214000  
##  Max.   :2010   Max.   :755000

The following density and histograms graphs depict skewness.
MSSubClass: The building class LotFrontage: Linear feet of street connected to property LotArea: Lot size in square feet OverallQual: Overall material and finish quality

# Sample Plots 
graphs_list <- list()

#for(index in 2:4){
  
graphs_list[[1]] <- ggplot(data = sc.data2) + geom_density(aes(x = sc.data2[[2]]),   size = 1, alpha = 1.0) + xlab(paste0((colnames(sc.data2)[2]) ))  

graphs_list[[2]] <- ggplot(data = sc.data2) + geom_density(aes(x = sc.data2[[3]]),   size = 1, alpha = 1.0) + xlab(paste0((colnames(sc.data2)[3]) ))  

graphs_list[[3]] <- ggplot(data = sc.data2) + geom_density(aes(x = sc.data2[[4]]),   size = 1, alpha = 1.0) + xlab(paste0((colnames(sc.data2)[4]) ))  

graphs_list[[4]] <- ggplot(data = sc.data2) + geom_density(aes(x = sc.data2[[5]]),   size = 1, alpha = 1.0) + xlab(paste0((colnames(sc.data2)[5]) ))  
#}

do.call("grid.arrange", c(graphs_list, ncol=2))

#Sample Histograms

graphs_list[[1]] <- ggplot(data = sc.data2) + aes(x = factor(sc.data2[[2]])) + stat_count() + xlab(colnames(sc.data2)[2]) + theme(axis.text.x = element_text(angle = 90, hjust =1))

graphs_list[[2]] <- ggplot(data = sc.data2) + aes(x = factor(sc.data2[[3]])) + stat_count() + xlab(colnames(sc.data2)[3]) + theme(axis.text.x = element_text(angle = 90, hjust =1))

graphs_list[[3]] <- ggplot(data = sc.data2) + aes(x = factor(sc.data2[[4]])) + stat_count() + xlab(colnames(sc.data2)[4]) + theme(axis.text.x = element_text(angle = 90, hjust =1))

graphs_list[[4]] <- ggplot(data = sc.data2) + aes(x = factor(sc.data2[[5]])) + stat_count() + xlab(colnames(sc.data2)[5]) + theme(axis.text.x = element_text(angle = 90, hjust =1))



do.call("grid.arrange", c(graphs_list, ncol=2))

Scatterplot of X and Y

ggplot(sc.data, aes(x = OverallQual, y = SalePrice)) + geom_point(color="red") + labs(x="Overall Quality", y = "Sale Price") + ggtitle("Overall Quality vs. Sales Price") + geom_smooth(method = "lm", se = TRUE)

Correlation Matrix for any 3 quantitative variables in dataset.

Pearson Correlation Test:

The Pearson correlation coefficient can take a range of values from +1 to -1. A value of 0 indicates that there is no association between the two variables. A value greater than 0 indicates a positive association.

# X = Overall Quality Y = Sale price Z = Year built
Z <- sc.data$YearBuilt
data <- data.frame(X, Y, Z)
cm <- cor(data)
cm

##           X         Y         Z
## X 1.0000000 0.7909816 0.5723228
## Y 0.7909816 1.0000000 0.5228973
## Z 0.5723228 0.5228973 1.0000000

# Correlation Test for Y and X
cor.test(Y, X, conf.level = 0.92)

## 
##  Pearson's product-moment correlation
## 
## data:  Y and X
## t = 49.364, df = 1458, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 92 percent confidence interval:
##  0.7731789 0.8075387
## sample estimates:
##       cor 
## 0.7909816

Discussion:

We see above a Pearson correlation of 0.7910 between Y and X. There exists a positive association between Sales price and Overall quality. If overall quality goes down or up, it will affect the sale price.

# Correlation Test for Y and Z
cor.test(Y, Z, conf.level = 0.92)

## 
##  Pearson's product-moment correlation
## 
## data:  Y and Z
## t = 23.424, df = 1458, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 92 percent confidence interval:
##  0.4887787 0.5554189
## sample estimates:
##       cor 
## 0.5228973

Discussion:

We see above a Pearson correlation of 0.5228973 between Y and Z. There exists a positive association between Sales price and Year built. If Year built is very old, or present date, sale price will be affected.

# Correlation Test for X and Z
cor.test(X, Z, conf.level = 0.92)

## 
##  Pearson's product-moment correlation
## 
## data:  X and Z
## t = 26.65, df = 1458, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 92 percent confidence interval:
##  0.5406726 0.6023549
## sample estimates:
##       cor 
## 0.5723228

Discussion:

We see above a Pearson correlation of 0.5228973 between X and Z. There exists a positive association between Overall quality and Year built. If Year built is very old, or present date, the quality of the home will be affected.

T-Test Definition:

In statistics, Welch’s t-test, or unequal variances t-test, is a two-sample location test which is used to test the hypothesis that two populations have equal means.

# Run the T test
t.test(Y, X, conf.level = 0.92)

## 
##  Welch Two Sample t-test
## 
## data:  Y and X
## t = 87.016, df = 1459, p-value < 2.2e-16
## alternative hypothesis: true difference in means is not equal to 0
## 92 percent confidence interval:
##  177272.7 184557.5
## sample estimates:
##    mean of x    mean of y 
## 1.809212e+05 6.099315e+00

Discussion:

The T-Test shows difference in the means between Overall Quality and Sale Price. The difference in means is not equal to 0.

Definition of Familywise Error:

The familywise error rate (FWE or FWER) is the probability of a coming to at least one false conclusion in a series of hypothesis tests . In other words, it’s the probability of making at least one Type I Error. The term “familywise” error rate comes from family of tests, which is the technical definition for a series of tests on data.

A Type I error (sometimes called a Type 1 error), is the incorrect rejection of a true null hypothesis. The alpha symbol, alpha, is usually used to denote a Type I error.

Would you be worried about familywise error? Yes.

Why or why not? It is entirely possible that the first series of tests were affected by personal bias or just got lucky. Another set of tests should be done as well, with choosing the same variables and data. The second and third set of tests would be a validation step with different people performing the tests.

Linear Algebra and Correlation

#3x3 Correlation matrix from above
cm

##           X         Y         Z
## X 1.0000000 0.7909816 0.5723228
## Y 0.7909816 1.0000000 0.5228973
## Z 0.5723228 0.5228973 1.0000000

Precision Matrix Detailed Steps (Rounded to 4 decimal places)

Augmented Matrix

\[A = \begin{pmatrix} 1.0000 & 0.7909 & 0.5723 | 1 & 0 & 0\\ 0.7909 & 1.0000 & 0.5228 | 0 & 1 & 0\\ 0.5723 & 0.5228 & 1.0000 | 0 & 0 & 1 \end{pmatrix}\]

R2 = R2 -0.7909 x R1

\[A = \begin{pmatrix} 1.0000 & 0.7909 & 0.5723 &| 1 & 0 & 0 \\ 0 & 0.3745 & 0.0702 &| -0.7909 & 1 & 0\\ 0.5723 & 0.5228 & 1.0000 &| 0 & 0 & 1 \end{pmatrix}\]

R3 = R3 -0.5723 x R1

\[A = \begin{pmatrix} 1.0000 & 0.7909 & 0.5723 &| 1 & 0 & 0 \\ 0 & 0.3745 & 0.0702 &| -0.7909 & 1 & 0\\ 0 & 0.0702 & 0.6724 &| -0.5723 & 0 & 1 \end{pmatrix}\]

R3 = R3 -0.1875 x R2

\[A = \begin{pmatrix} 1.0000 & 0.7909 & 0.5723 &| 1 & 0 & 0 \\ 0 & 0.3745 & 0.0702 &| -0.7909 & 1 & 0\\ 0 & 0 & 0.6592 &| -0.4239 & -0.1875 & 1 \end{pmatrix}\]

R3 = 1.5168 * R3

\[A = \begin{pmatrix} 1.0000 & 0.7909 & 0.5723 &| 1 & 0 & 0 \\ 0 & 0.3745 & 0.0702 &| -0.7909 & 1 & 0\\ 0 & 0 & 1 &| -0.6431 & -0.2844 & 1.5168 \end{pmatrix}\]

R2 = R2 -0.07020 * R3

\[A = \begin{pmatrix} 1.0000 & 0.7909 & 0.5723 &| 1 & 0 & 0 \\ 0 & 0.3745 & 0 &| -0.7458 & 1.0199 & -0.1064\\ 0 & 0 & 1 &| -0.6431 & -0.2844 & 1.5168 \end{pmatrix}\]

R1 = R1 -0.5723 * R3

\[A = \begin{pmatrix} 1.0000 & 0.7909 & 0 &| 1.3680 & 0.1627 & -0.8681 \\ 0 & 0.3745 & 0 &| -0.7458 & 1.0199 & -0.1064\\ 0 & 0 & 1 &| -0.6431 & -0.2844 & 1.5168 \end{pmatrix}\]

R2 = 2.6713 * R2

\[A = \begin{pmatrix} 1 & 0.7909 & 0 &| 1.3680 & 0.1627 & -0.8681 \\ 0 & 1 & 0 &| -1.9923 & 2.7246 & -0.2844\\ 0 & 0 & 1 &| -0.6431 & -0.2844 & 1.5168 \end{pmatrix}\]

R1 = R1 -0.7909 * R2

\[A = \begin{pmatrix} 1 & 0 & 0 &| 2.9439 & -1.9923 & -0.6434 \\ 0 & 1 & 0 &| -1.9923 & 2.7246 & -0.2844\\ 0 & 0 & 1 &| -0.6431 & -0.2844 & 1.5168 \end{pmatrix}\]

\[A = \begin{pmatrix} 2.9439 & -1.9923 & -0.6434 \\ -1.9923 & 2.7246 & -0.2844\\ -0.6431 & -0.2844 & 1.5168 \end{pmatrix}\]

Precision matrix or inverse (verify with R)

# Precision matrix (verify with R)
pm <- solve(cm)
pm

##            X          Y          Z
## X  2.9439846 -1.9923563 -0.6431116
## Y -1.9923563  2.7246511 -0.2844419
## Z -0.6431116 -0.2844419  1.5168013

#Multiply Correlation matrix by Precision matrix
round(cm %*% pm, digits = 0)

##   X Y Z
## X 1 0 0
## Y 0 1 0
## Z 0 0 1

#Multiply Precision matrix by Correlation matrix
round(pm %*% cm, digits = 0)

##   X Y Z
## X 1 0 0
## Y 0 1 0
## Z 0 0 1

#Conduct LU decomposition on the matrix.   

#Rounded to 4 decimal places

\[A = \begin{pmatrix} 1.0000 & 0.7909 & 0.5723 \\ 0.7909 & 1.0000 & 0.5228 \\ 0.5723 & 0.5228 & 1.0000 \end{pmatrix}\]

Using Gaussian Elimination method

R2 = R2 - 0.079 x R1

\[A = \begin{pmatrix} 1.0000 & 0.7909 & 0.5723 \\ 0.7909 & 0.3743 & 0.0702 \\ 0.5723 & 0.5228 & 1.0000 \end{pmatrix}\]

R3 = R3 - 0.5723 x R1

\[A = \begin{pmatrix} 1.0000 & 0.7909 & 0.5723 \\ 0.0000 & 0.3743 & 0.0702 \\ 0.0000 & 0.0702 & 0.6724 \end{pmatrix}\]

R3 = R3 = 0.1875 x R2

\[A = \begin{pmatrix} 1.0000 & 0.7909 & 0.5723 \\ 0.0000 & 0.3743 & 0.0702 \\ 0.0000 & 0.0000 & 0.6593 \end{pmatrix}\]

Let U =

\[U = \begin{pmatrix} 1.0000 & 0.7909 & 0.5723 \\ 0.0000 & 0.3743 & 0.0702 \\ 0.0000 & 0.0000 & 0.6593 \end{pmatrix}\]

r #L consists of the multipliers used in the Gaussian elimination with 1s on the diagonal. \[L = \begin{pmatrix} 1.0000 & 0.0000 & 0.0000 \\ 0.7909 & 1.0000 & 0.0000 \\ 0.5723 & 0.1875 & 1.0000 \end{pmatrix}\]

Hence, A = LU \[ \left[ \begin{array}{c} 1.0000 & 0.7909 & 0.5723 \\ 0.7909 & 1.0000 & 0.5228 \\ 0.5723 & 0.5228 & 1.0000 \end{array} \right] = \begin{bmatrix} 1.0000 & 0.0000 & 0.0000 \\ 0.7909 & 1.0000 & 0.0000 \\ 0.5723 & 0.1875 & 1.0000\end{bmatrix} \times \left[ \begin{array}{c} 1.0000 & 0.7909 & 0.5723 \\ 0.0000 & 0.3743 & 0.0702 \\ 0.0000 & 0.0000 & 0.6593 \end{array} \right] \]

Calculus-Based Probability & Statistics.

#Get minimun value (Since, X has a minimum value of 1, I did not shift X)
min(X)

## [1] 1

#nonZeroMin <- min(X[X!=0])

#Shift the variable above 0

#shiftedX <- X + nonZeroMin

#Find the optimal value

lambda <- fitdistr(X, densfun = "exponential")$estimate["rate"]
lambda

##      rate 
## 0.1639528

#Take samples
exponential_distribution_of_X <- rexp(1000, lambda)

par(mfrow = c(1, 2))
hist(X)
hist(exponential_distribution_of_X)

#Percentiles
percentiles5th95th <- quantile(exponential_distribution_of_X, c(0.05,0.95))
percentiles5th95th

##         5%        95% 
##  0.3295653 17.3578192

#Formula: normal distribution we calcualte the Confidence Interval as: CI = Sample Mean plus/minus standard error.

lower_left <- mean(X) - qnorm(0.95) * sd(X) / sqrt(length(X))
lower_left

## [1] 6.03978

upper_right <- mean(X) + qnorm(0.95) * sd(X) / sqrt(length(X))
upper_right

## [1] 6.15885

#Provide the empirical 5th percentile and 95th
quantile(X, c(0.05, 0.95))

##  5% 95% 
##   4   8

Definition:

Suppose p(x) is a density function for a quantity. The cumulative distribution function (cdf) for the quantity is de???ned as P(x) = integral from lower bound -infinity to upper bound x where p(t) dt. Gives: The proportion of population with value less than x The probability of having a value less than x.

https://www.quora.com/What-is-a-cumulative-distribution-function

Intuitive definition of CDF A CDF is a function that describes the probability of a random variable taking on a given value or less. A good example is rolling a single 6-sided die. Normally, we talk about the probability of a given number coming up–for example, the probability of rolling a 2 is 1 out of 6, 1/6, 0.166667. (That probability is described by the probability mass function, or PMF.) But what if you don’t just want 2; you are okay with a 2 or any number less than it? In this case, there is only one other number: 1. So now when you roll your die, you are looking for a 2 OR a 1. You are now looking for 2 outcomes out of 6, so the probability is 2/6 = 1/3. Similarly, if you want a 3 or less, the probability is 3/6 or 1/2. It’s called cumulative because you find the probability by adding up the individual probabilities of all the outcomes included. In the case of our die, when you want a 2 or less, you have 2 outcomes fulfilling this condition: 1 and 2, each with an individual probability of 1/6. 1/6 + 1/6 = 2/6 or 1/3, which is the cumulative probability of a 2. That’s what cumulative means–addition.

Discussion:

The variable X (Overall quality) does not have any zeros, and so we did not shift the data. Next, we generated 1000 samples. Comparing the histograms of the original data (X) versus exponential distribution (exponential_distribution_of_X), we can see there is a difference. The exponential distribution reduced much of the right-skew; coming closer to a normal distribution.

The 5th and 95th percentiles using the cumulative distribution function of 1000 samples provided 0.3481007 and 18.5301051 respectively.

The 5th and 95th percentiles of the original data is 4 and 8 respectively.

Modeling

#Using all the variables
First_mod = lm(sc.data$SalePrice ~ ., data = sc.data)
summary(First_mod)

## 
## Call:
## lm(formula = sc.data$SalePrice ~ ., data = sc.data)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -176695   -9164       0    9498  176695 
## 
## Coefficients: (8 not defined because of singularities)
##                        Estimate Std. Error t value Pr(>|t|)    
## (Intercept)          -2.845e+05  1.050e+06  -0.271 0.786553    
## Id                    1.130e+00  1.548e+00   0.730 0.465588    
## MSSubClass           -5.365e+01  8.273e+01  -0.649 0.516772    
## MSZoningFV            3.261e+04  1.200e+04   2.717 0.006675 ** 
## MSZoningRH            2.203e+04  1.190e+04   1.851 0.064350 .  
## MSZoningRL            2.486e+04  1.022e+04   2.433 0.015117 *  
## MSZoningRM            2.152e+04  9.584e+03   2.246 0.024910 *  
## LotFrontage           6.745e+00  2.300e+01   0.293 0.769395    
## LotArea               7.230e-01  1.086e-01   6.654 4.31e-11 ***
## StreetPave            3.303e+04  1.217e+04   2.714 0.006740 ** 
## AlleyGrvl             1.193e+03  4.213e+03   0.283 0.777034    
## AlleyPave             4.623e+02  4.737e+03   0.098 0.922276    
## LotShapeIR2           4.916e+03  4.212e+03   1.167 0.243385    
## LotShapeIR3           5.767e+03  8.824e+03   0.654 0.513508    
## LotShapeReg           1.692e+03  1.637e+03   1.033 0.301610    
## LandContourHLS        7.569e+03  5.126e+03   1.477 0.140060    
## LandContourLow       -1.131e+04  6.403e+03  -1.766 0.077614 .  
## LandContourLvl        5.453e+03  3.702e+03   1.473 0.140964    
## UtilitiesNoSeWa      -3.643e+04  2.636e+04  -1.382 0.167114    
## LotConfigCulDSac      7.803e+03  3.251e+03   2.401 0.016520 *  
## LotConfigFR2         -7.945e+03  4.002e+03  -1.986 0.047312 *  
## LotConfigFR3         -1.774e+04  1.255e+04  -1.413 0.157773    
## LotConfigInside      -1.681e+03  1.759e+03  -0.956 0.339470    
## LandSlopeMod          7.460e+03  3.971e+03   1.878 0.060567 .  
## LandSlopeSev         -4.229e+04  1.138e+04  -3.716 0.000211 ***
## NeighborhoodBlueste   7.291e+03  1.921e+04   0.380 0.704337    
## NeighborhoodBrDale   -2.675e+03  1.096e+04  -0.244 0.807238    
## NeighborhoodBrkSide  -5.667e+03  9.468e+03  -0.599 0.549559    
## NeighborhoodClearCr  -1.448e+04  9.199e+03  -1.574 0.115663    
## NeighborhoodCollgCr  -1.019e+04  7.252e+03  -1.404 0.160435    
## NeighborhoodCrawfor   1.179e+04  8.533e+03   1.381 0.167469    
## NeighborhoodEdwards  -2.147e+04  7.994e+03  -2.685 0.007342 ** 
## NeighborhoodGilbert  -1.118e+04  7.663e+03  -1.459 0.144919    
## NeighborhoodIDOTRR   -1.199e+04  1.073e+04  -1.117 0.264088    
## NeighborhoodMeadowV  -6.901e+03  1.116e+04  -0.618 0.536621    
## NeighborhoodMitchel  -2.094e+04  8.162e+03  -2.565 0.010434 *  
## NeighborhoodNAmes    -1.726e+04  7.835e+03  -2.203 0.027766 *  
## NeighborhoodNoRidge   2.532e+04  8.426e+03   3.005 0.002710 ** 
## NeighborhoodNPkVill   1.354e+04  1.401e+04   0.966 0.334205    
## NeighborhoodNridgHt   1.832e+04  7.513e+03   2.439 0.014883 *  
## NeighborhoodNWAmes   -1.747e+04  7.998e+03  -2.184 0.029160 *  
## NeighborhoodOldTown  -1.408e+04  9.661e+03  -1.458 0.145166    
## NeighborhoodSawyer   -1.101e+04  8.109e+03  -1.357 0.174879    
## NeighborhoodSawyerW  -2.794e+03  7.782e+03  -0.359 0.719602    
## NeighborhoodSomerst  -2.464e+03  9.004e+03  -0.274 0.784391    
## NeighborhoodStoneBr   3.919e+04  8.283e+03   4.731 2.50e-06 ***
## NeighborhoodSWISU    -8.965e+03  9.669e+03  -0.927 0.354022    
## NeighborhoodTimber   -1.025e+04  8.132e+03  -1.261 0.207633    
## NeighborhoodVeenker  -6.996e+01  1.048e+04  -0.007 0.994676    
## Condition1Feedr       7.108e+03  5.006e+03   1.420 0.155874    
## Condition1Norm        1.635e+04  4.181e+03   3.911 9.70e-05 ***
## Condition1PosA        1.022e+04  9.922e+03   1.030 0.303157    
## Condition1PosN        1.504e+04  7.462e+03   2.016 0.044036 *  
## Condition1RRAe       -1.578e+04  9.053e+03  -1.743 0.081512 .  
## Condition1RRAn        1.289e+04  6.937e+03   1.858 0.063385 .  
## Condition1RRNe       -3.359e+03  1.746e+04  -0.192 0.847484    
## Condition1RRNn        1.137e+04  1.283e+04   0.886 0.375730    
## Condition2Feedr      -4.714e+03  2.340e+04  -0.201 0.840388    
## Condition2Norm       -9.818e+03  2.027e+04  -0.484 0.628146    
## Condition2PosA        4.487e+04  3.695e+04   1.214 0.224851    
## Condition2PosN       -2.384e+05  2.760e+04  -8.636  < 2e-16 ***
## Condition2RRAe       -1.287e+05  6.503e+04  -1.980 0.047963 *  
## Condition2RRAn       -2.300e+04  3.148e+04  -0.731 0.465108    
## Condition2RRNn       -2.229e+03  2.707e+04  -0.082 0.934382    
## BldgType2fmCon       -3.473e+03  1.248e+04  -0.278 0.780909    
## BldgTypeDuplex       -7.484e+03  7.419e+03  -1.009 0.313305    
## BldgTypeTwnhs        -1.951e+04  9.962e+03  -1.958 0.050434 .  
## BldgTypeTwnhsE       -1.544e+04  9.002e+03  -1.715 0.086574 .  
## HouseStyle1.5Unf      1.195e+04  7.949e+03   1.503 0.133185    
## HouseStyle1Story      5.241e+03  4.380e+03   1.197 0.231717    
## HouseStyle2.5Fin     -1.647e+04  1.238e+04  -1.331 0.183492    
## HouseStyle2.5Unf     -9.690e+03  9.184e+03  -1.055 0.291594    
## HouseStyle2Story     -5.896e+03  3.494e+03  -1.687 0.091780 .  
## HouseStyleSFoyer      1.112e+03  6.257e+03   0.178 0.858987    
## HouseStyleSLvl        3.498e+03  5.582e+03   0.627 0.531014    
## OverallQual           6.840e+03  1.015e+03   6.741 2.43e-11 ***
## OverallCond           5.737e+03  8.708e+02   6.588 6.63e-11 ***
## YearBuilt             3.353e+02  8.044e+01   4.168 3.29e-05 ***
## YearRemodAdd          1.063e+02  5.550e+01   1.915 0.055790 .  
## RoofStyleGable        9.192e+03  1.844e+04   0.499 0.618178    
## RoofStyleGambrel      1.206e+04  2.018e+04   0.598 0.550255    
## RoofStyleHip          8.901e+03  1.851e+04   0.481 0.630779    
## RoofStyleMansard      2.024e+04  2.145e+04   0.944 0.345600    
## RoofStyleShed         9.980e+04  3.452e+04   2.891 0.003908 ** 
## RoofMatlCompShg       5.707e+05  5.242e+04  10.888  < 2e-16 ***
## RoofMatlMembran       6.664e+05  6.234e+04  10.690  < 2e-16 ***
## RoofMatlMetal         6.356e+05  6.200e+04  10.251  < 2e-16 ***
## RoofMatlRoll          5.582e+05  5.815e+04   9.599  < 2e-16 ***
## RoofMatlTar&Grv       5.724e+05  5.628e+04  10.171  < 2e-16 ***
## RoofMatlWdShake       5.624e+05  5.475e+04  10.271  < 2e-16 ***
## RoofMatlWdShngl       6.250e+05  5.329e+04  11.728  < 2e-16 ***
## Exterior1stAsphShn   -2.486e+04  3.296e+04  -0.754 0.450833    
## Exterior1stBrkComm   -3.437e+03  2.777e+04  -0.124 0.901505    
## Exterior1stBrkFace    7.164e+03  1.275e+04   0.562 0.574158    
## Exterior1stCBlock    -1.430e+04  2.724e+04  -0.525 0.599655    
## Exterior1stCemntBd   -1.241e+04  1.899e+04  -0.654 0.513550    
## Exterior1stHdBoard   -1.343e+04  1.293e+04  -1.039 0.299208    
## Exterior1stImStucc   -2.355e+04  2.814e+04  -0.837 0.402650    
## Exterior1stMetalSd   -6.437e+03  1.459e+04  -0.441 0.659108    
## Exterior1stPlywood   -1.439e+04  1.275e+04  -1.129 0.259271    
## Exterior1stStone     -2.525e+03  2.430e+04  -0.104 0.917266    
## Exterior1stStucco    -7.862e+03  1.406e+04  -0.559 0.576289    
## Exterior1stVinylSd   -1.441e+04  1.332e+04  -1.082 0.279539    
## Exterior1stWd Sdng   -1.424e+04  1.236e+04  -1.152 0.249541    
## Exterior1stWdShing   -1.014e+04  1.334e+04  -0.760 0.447277    
## Exterior2ndAsphShn    1.253e+04  2.217e+04   0.565 0.571966    
## Exterior2ndBrk Cmn    5.107e+03  2.005e+04   0.255 0.799003    
## Exterior2ndBrkFace    4.292e+03  1.320e+04   0.325 0.745178    
## Exterior2ndCBlock            NA         NA      NA       NA    
## Exterior2ndCmentBd    1.302e+04  1.867e+04   0.697 0.485746    
## Exterior2ndHdBoard    8.588e+03  1.241e+04   0.692 0.488940    
## Exterior2ndImStucc    1.748e+04  1.432e+04   1.221 0.222447    
## Exterior2ndMetalSd    6.117e+03  1.419e+04   0.431 0.666585    
## Exterior2ndOther     -1.813e+04  2.707e+04  -0.670 0.503059    
## Exterior2ndPlywood    6.974e+03  1.203e+04   0.580 0.562334    
## Exterior2ndStone     -1.016e+04  1.721e+04  -0.590 0.555130    
## Exterior2ndStucco     6.283e+03  1.358e+04   0.462 0.643814    
## Exterior2ndVinylSd    1.336e+04  1.279e+04   1.045 0.296154    
## Exterior2ndWd Sdng    1.232e+04  1.192e+04   1.034 0.301354    
## Exterior2ndWd Shng    5.715e+03  1.245e+04   0.459 0.646259    
## MasVnrTypeBrkCmn     -2.274e+03  1.091e+04  -0.208 0.834881    
## MasVnrTypeBrkFace     1.931e+03  8.750e+03   0.221 0.825393    
## MasVnrTypeNone        4.927e+03  8.588e+03   0.574 0.566251    
## MasVnrTypeStone       6.716e+03  8.823e+03   0.761 0.446683    
## MasVnrArea            2.075e+01  5.789e+00   3.584 0.000352 ***
## ExterQualFa          -7.382e+03  1.109e+04  -0.666 0.505680    
## ExterQualGd          -2.066e+04  4.786e+03  -4.317 1.72e-05 ***
## ExterQualTA          -1.992e+04  5.309e+03  -3.751 0.000184 ***
## ExterCondFa          -2.510e+03  1.805e+04  -0.139 0.889452    
## ExterCondGd          -7.126e+03  1.722e+04  -0.414 0.679095    
## ExterCondPo           7.638e+03  3.167e+04   0.241 0.809450    
## ExterCondTA          -4.068e+03  1.719e+04  -0.237 0.812932    
## FoundationCBlock      2.955e+03  3.167e+03   0.933 0.350925    
## FoundationPConc       3.969e+03  3.419e+03   1.161 0.245916    
## FoundationSlab       -7.323e+03  1.005e+04  -0.729 0.466178    
## FoundationStone       9.680e+03  1.141e+04   0.849 0.396262    
## FoundationWood       -2.664e+04  1.473e+04  -1.808 0.070792 .  
## BsmtQualEx           -3.222e+04  3.624e+04  -0.889 0.374052    
## BsmtQualFa           -4.403e+04  3.603e+04  -1.222 0.221842    
## BsmtQualGd           -5.038e+04  3.601e+04  -1.399 0.162098    
## BsmtQualTA           -4.677e+04  3.591e+04  -1.302 0.193061    
## BsmtCondFa           -2.870e+03  4.240e+03  -0.677 0.498590    
## BsmtCondGd           -2.725e+03  3.247e+03  -0.839 0.401431    
## BsmtCondPo            6.500e+04  3.002e+04   2.165 0.030581 *  
## BsmtCondTA                   NA         NA      NA       NA    
## BsmtExposureAv        1.132e+04  2.297e+04   0.493 0.622214    
## BsmtExposureGd        2.561e+04  2.307e+04   1.110 0.267224    
## BsmtExposureMn        7.765e+03  2.304e+04   0.337 0.736191    
## BsmtExposureNo        6.192e+03  2.293e+04   0.270 0.787177    
## BsmtFinType1ALQ      -2.617e+03  2.915e+03  -0.898 0.369482    
## BsmtFinType1BLQ       1.857e+02  3.121e+03   0.060 0.952561    
## BsmtFinType1GLQ       3.077e+03  2.710e+03   1.135 0.256446    
## BsmtFinType1LwQ      -6.004e+03  3.770e+03  -1.592 0.111542    
## BsmtFinType1Rec      -2.464e+03  3.171e+03  -0.777 0.437339    
## BsmtFinType1Unf              NA         NA      NA       NA    
## BsmtFinSF1            3.829e+01  5.338e+00   7.173 1.27e-12 ***
## BsmtFinType2ALQ       2.894e+04  2.496e+04   1.159 0.246600    
## BsmtFinType2BLQ       1.587e+04  2.470e+04   0.643 0.520558    
## BsmtFinType2GLQ       2.613e+04  2.548e+04   1.025 0.305423    
## BsmtFinType2LwQ       1.454e+04  2.474e+04   0.588 0.556776    
## BsmtFinType2Rec       1.853e+04  2.468e+04   0.751 0.452930    
## BsmtFinType2Unf       2.048e+04  2.461e+04   0.832 0.405494    
## BsmtFinSF2            3.136e+01  9.054e+00   3.464 0.000551 ***
## BsmtUnfSF             2.079e+01  4.897e+00   4.246 2.34e-05 ***
## TotalBsmtSF                  NA         NA      NA       NA    
## HeatingGasA           9.448e+03  2.557e+04   0.369 0.711888    
## HeatingGasW           6.832e+03  2.636e+04   0.259 0.795524    
## HeatingGrav           1.290e+03  2.805e+04   0.046 0.963342    
## HeatingOthW          -1.226e+04  3.142e+04  -0.390 0.696519    
## HeatingWall           2.289e+04  2.972e+04   0.770 0.441272    
## HeatingQCFa           4.379e+02  4.707e+03   0.093 0.925903    
## HeatingQCGd          -4.032e+03  2.073e+03  -1.945 0.052014 .  
## HeatingQCPo           2.419e+03  2.653e+04   0.091 0.927376    
## HeatingQCTA          -3.286e+03  2.069e+03  -1.588 0.112507    
## CentralAirY          -1.175e+02  3.867e+03  -0.030 0.975769    
## ElectricalFuseA      -1.023e+04  2.407e+04  -0.425 0.670873    
## ElectricalFuseF      -1.028e+04  2.447e+04  -0.420 0.674326    
## ElectricalFuseP      -1.831e+04  3.019e+04  -0.607 0.544251    
## ElectricalMix        -5.324e+04  5.057e+04  -1.053 0.292637    
## ElectricalSBrkr      -1.232e+04  2.387e+04  -0.516 0.605903    
## X1stFlrSF             4.476e+01  5.641e+00   7.936 4.75e-15 ***
## X2ndFlrSF             6.224e+01  5.684e+00  10.949  < 2e-16 ***
## LowQualFinSF         -3.508e+00  1.905e+01  -0.184 0.853924    
## GrLivArea                    NA         NA      NA       NA    
## BsmtFullBath          1.532e+03  1.978e+03   0.775 0.438767    
## BsmtHalfBath         -4.404e+02  3.024e+03  -0.146 0.884214    
## FullBath              3.644e+03  2.196e+03   1.660 0.097215 .  
## HalfBath              1.820e+03  2.096e+03   0.868 0.385358    
## BedroomAbvGr         -3.609e+03  1.362e+03  -2.649 0.008178 ** 
## KitchenAbvGr         -1.346e+04  5.689e+03  -2.366 0.018129 *  
## KitchenQualFa        -1.956e+04  6.193e+03  -3.159 0.001621 ** 
## KitchenQualGd        -2.352e+04  3.482e+03  -6.754 2.23e-11 ***
## KitchenQualTA        -2.250e+04  3.927e+03  -5.729 1.28e-08 ***
## TotRmsAbvGrd          1.763e+03  9.573e+02   1.842 0.065724 .  
## FunctionalMaj2       -1.657e+03  1.438e+04  -0.115 0.908303    
## FunctionalMin1        6.696e+03  8.610e+03   0.778 0.436937    
## FunctionalMin2        8.360e+03  8.655e+03   0.966 0.334259    
## FunctionalMod        -5.722e+03  1.056e+04  -0.542 0.587985    
## FunctionalSev        -4.167e+04  2.959e+04  -1.408 0.159259    
## FunctionalTyp         1.789e+04  7.484e+03   2.390 0.016980 *  
## Fireplaces            6.257e+03  2.563e+03   2.442 0.014763 *  
## FireplaceQuEx        -9.074e+03  6.233e+03  -1.456 0.145718    
## FireplaceQuFa        -9.649e+03  5.338e+03  -1.807 0.070940 .  
## FireplaceQuGd        -6.075e+03  3.421e+03  -1.776 0.076007 .  
## FireplaceQuPo         3.592e+03  6.385e+03   0.563 0.573812    
## FireplaceQuTA        -5.066e+03  3.577e+03  -1.416 0.157015    
## GarageType2Types     -2.870e+04  1.198e+04  -2.395 0.016774 *  
## GarageTypeAttchd     -8.849e+03  4.401e+03  -2.011 0.044568 *  
## GarageTypeBasment    -4.640e+03  7.554e+03  -0.614 0.539211    
## GarageTypeBuiltIn    -8.963e+03  5.403e+03  -1.659 0.097359 .  
## GarageTypeCarPort    -3.529e+03  1.051e+04  -0.336 0.737147    
## GarageTypeDetchd     -5.729e+03  4.438e+03  -1.291 0.197041    
## GarageYrBlt          -4.397e+01  5.926e+01  -0.742 0.458245    
## GarageFinishFin       6.233e+02  2.428e+03   0.257 0.797487    
## GarageFinishRFn      -1.775e+03  2.158e+03  -0.822 0.410968    
## GarageFinishUnf              NA         NA      NA       NA    
## GarageCars            3.948e+03  2.278e+03   1.733 0.083330 .  
## GarageArea            1.901e+01  7.862e+00   2.418 0.015735 *  
## GarageQualEx          1.209e+05  2.989e+04   4.045 5.56e-05 ***
## GarageQualFa         -6.385e+03  4.838e+03  -1.320 0.187124    
## GarageQualGd         -1.054e+03  7.697e+03  -0.137 0.891067    
## GarageQualPo         -2.371e+04  2.396e+04  -0.990 0.322469    
## GarageQualTA                 NA         NA      NA       NA    
## GarageCondEx         -1.150e+05  3.450e+04  -3.334 0.000881 ***
## GarageCondFa         -1.760e+03  5.398e+03  -0.326 0.744450    
## GarageCondGd         -2.432e+03  9.238e+03  -0.263 0.792392    
## GarageCondPo          4.195e+03  1.389e+04   0.302 0.762665    
## GarageCondTA                 NA         NA      NA       NA    
## PavedDriveP          -3.124e+03  5.560e+03  -0.562 0.574325    
## PavedDriveY          -1.515e+02  3.462e+03  -0.044 0.965103    
## WoodDeckSF            1.514e+01  5.870e+00   2.580 0.009994 ** 
## OpenPorchSF           3.456e-01  1.157e+01   0.030 0.976176    
## EnclosedPorch         3.417e+00  1.248e+01   0.274 0.784187    
## X3SsnPorch            3.462e+01  2.236e+01   1.548 0.121852    
## ScreenPorch           3.538e+01  1.249e+01   2.832 0.004701 ** 
## PoolArea              6.735e+02  2.267e+02   2.970 0.003034 ** 
## PoolQCEx             -2.482e+05  1.226e+05  -2.025 0.043131 *  
## PoolQCFa             -4.050e+05  1.494e+05  -2.712 0.006792 ** 
## PoolQCGd             -3.764e+05  1.469e+05  -2.562 0.010520 *  
## FenceGdPrv           -8.957e+03  3.671e+03  -2.440 0.014827 *  
## FenceGdWo            -9.422e+02  3.569e+03  -0.264 0.791835    
## FenceMnPrv            6.126e+02  2.268e+03   0.270 0.787082    
## FenceMnWw            -5.598e+03  7.466e+03  -0.750 0.453570    
## MiscFeatureGar2      -2.224e+03  9.716e+04  -0.023 0.981739    
## MiscFeatureOthr       1.415e+04  2.019e+04   0.701 0.483621    
## MiscFeatureShed       2.387e+03  5.692e+03   0.419 0.675009    
## MiscFeatureTenC       2.956e+04  4.727e+04   0.625 0.531800    
## MiscVal               1.975e-01  6.110e+00   0.032 0.974218    
## MoSold               -4.711e+02  2.450e+02  -1.923 0.054751 .  
## YrSold               -5.515e+02  5.146e+02  -1.072 0.284068    
## SaleTypeCon           2.527e+04  1.754e+04   1.440 0.150035    
## SaleTypeConLD         1.654e+04  9.672e+03   1.710 0.087443 .  
## SaleTypeConLI         4.933e+03  1.157e+04   0.426 0.669840    
## SaleTypeConLw         6.856e+02  1.214e+04   0.056 0.954977    
## SaleTypeCWD           1.467e+04  1.287e+04   1.140 0.254710    
## SaleTypeNew           2.154e+04  1.541e+04   1.398 0.162239    
## SaleTypeOth           7.591e+03  1.451e+04   0.523 0.600869    
## SaleTypeWD           -4.374e+02  4.177e+03  -0.105 0.916617    
## SaleConditionAdjLand  9.562e+03  1.459e+04   0.655 0.512345    
## SaleConditionAlloca   1.352e+03  8.887e+03   0.152 0.879122    
## SaleConditionFamily   8.849e+02  6.084e+03   0.145 0.884376    
## SaleConditionNormal   6.729e+03  2.903e+03   2.318 0.020639 *  
## SaleConditionPartial -4.704e+02  1.483e+04  -0.032 0.974696    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 22580 on 1205 degrees of freedom
## Multiple R-squared:  0.9333, Adjusted R-squared:  0.9192 
## F-statistic: 66.35 on 254 and 1205 DF,  p-value: < 2.2e-16

#Graphical Analysis of First model
layout(matrix(c(1,2,3,4),2,2)) # optional 4 graphs/page 
plot(First_mod)

## Warning: not plotting observations with leverage one:
##   121, 186, 251, 272, 333, 347, 376, 399, 584, 596, 667, 811, 945, 949, 1004, 1012, 1188, 1231, 1271, 1276, 1299, 1322, 1371, 1380, 1387

## Warning: not plotting observations with leverage one:
##   121, 186, 251, 272, 333, 347, 376, 399, 584, 596, 667, 811, 945, 949, 1004, 1012, 1188, 1231, 1271, 1276, 1299, 1322, 1371, 1380, 1387

## Warning in sqrt(crit * p * (1 - hh)/hh): NaNs produced

## Warning in sqrt(crit * p * (1 - hh)/hh): NaNs produced

The Residuals versus Fitted graph shows error Residuals versus fitted values. The dotted line at y = 0 indicates our fit line. Any point on the fit line has zero residual. Points above have positive residuals and points below have negative residuals.

The Normal Q-Q plot is close to a straight line. The closer the points are to falling directly on the diagonal line then the more we can interpret the residuals as normally distributed.

The Scale-Location Plot graph indicates the spread of points across predicted values range. One of the assumptions for Regression is Homoscedasticity . i.e variance should be reasonably equal across the predictor range. A horizontal red line is ideal and would indicate that residuals have uniform variance across the range. As residuals spread wider from each other the red spread line goes up.

Definitions:

Influence : The Influence of an observation can be thought of in terms of how much the predicted scores would change if the observation is excluded. Cook’s Distance is a pretty good measure of influence of an observation.

Leverage : The leverage of an observation is based on how much the observation’s value on the predictor variable differs from the mean of the predictor variable. The more the leverage of an observation , the greater potential that point has in terms of influence.

The Residuals versus Levarage Plot

In this plot the dotted red lines are Cook’s distance and the areas of interest for us are the ones outside dotted line on top right corner or bottom right corner. If any point falls in that region , we say that the observation has high leverage or potential for influencing our model is higher if we exclude that point.

The R-Squared is 93.32% This statistic indicates the percentage of the variance in the dependent variable that the independent variables explain collectively. R-squared measures the strength of the relationship between your model and the dependent variable on a convenient 0 - 100% scale.

0% represents a model that does not explain any of the variation in the response variable around its mean. The mean of the dependent variable predicts the dependent variable as well as the regression model.

100% represents a model that explains all of the variation in the response variable around its mean. Usually, the larger the R2, the better the regression model fits your observations.

So, in this instance, 91.92% is above 50%, which may indicate that the variables chosen above could be good indicators.

The Adjusted R-Squared is 91.92%. This value is slightly lower than R-Squared which adds evidence that the all predictors chosen do not necessarily improve the model. We may have to start eliminating variables to improve Adjusted R-Squared.

The P-value is less than 0.05.

Reference: http://r-statistics.co/Linear-Regression.html

How to know if the model is best fit for your data?

The most common metrics to look at while selecting the model are:

STATISTIC CRITERION

R-Squared Higher the better (> 0.70)

Adj R-Squared Higher the better

F-Statistic Higher the better

Std. Error Closer to zero the better

t-statistic Should be greater 1.96 for p-value to be less than 0.05

AIC Lower the better

BIC Lower the better

Mallows cp Should be close to the number of predictors in model

MAPE (Mean absolute percentage error) Lower the better

MSE (Mean squared error) Lower the better

Min_Max Accuracy => mean(min(actual, predicted)/max(actual, predicted)) Higher the better

#Starting Second variation
#Using only variables where the variable's p-value < 0.05

for (i in 2:length(sc.data)) {
  if(is.numeric(sc.data[,i])){
  a <- cor.test(sc.data$SalePrice, sc.data[,i])
  #print(paste(colnames(sc.data)[i], " est:", a$estimate, " p=value:", a$p.value))
  if (a$p.value < 0.05) {
    print(paste(colnames(sc.data)[i], " cor:", a$estimate, " p=value:", a$p.value))
  }  
  }
}

## [1] "MSSubClass  cor: -0.0842841351265952  p=value: 0.00126647168474946"
## [1] "LotFrontage  cor: 0.209623944799484  p=value: 5.82430315472025e-16"
## [1] "LotArea  cor: 0.263843353871406  p=value: 1.12313915491861e-24"
## [1] "OverallQual  cor: 0.790981600583805  p=value: 2.18567526799377e-313"
## [1] "OverallCond  cor: -0.077855894048678  p=value: 0.0029123512679155"
## [1] "YearBuilt  cor: 0.522897332879497  p=value: 2.99022909901342e-103"
## [1] "YearRemodAdd  cor: 0.507100967111386  p=value: 3.16494824191794e-96"
## [1] "MasVnrArea  cor: 0.472614499004574  p=value: 4.10046104453644e-82"
## [1] "BsmtFinSF1  cor: 0.386419806242153  p=value: 3.39410982928866e-53"
## [1] "BsmtUnfSF  cor: 0.214479105546969  p=value: 1.18297579635939e-16"
## [1] "TotalBsmtSF  cor: 0.613580551559196  p=value: 9.48422939149901e-152"
## [1] "X1stFlrSF  cor: 0.605852184691915  p=value: 5.3947106189684e-147"
## [1] "X2ndFlrSF  cor: 0.319333802832068  p=value: 5.76433511917945e-36"
## [1] "GrLivArea  cor: 0.708624477612652  p=value: 4.51803364677756e-223"
## [1] "BsmtFullBath  cor: 0.227122233131494  p=value: 1.55034413721333e-18"
## [1] "FullBath  cor: 0.560663762748446  p=value: 1.23647006675964e-121"
## [1] "HalfBath  cor: 0.284107675594783  p=value: 1.65047339557169e-28"
## [1] "BedroomAbvGr  cor: 0.16821315430074  p=value: 9.92749732617907e-11"
## [1] "KitchenAbvGr  cor: -0.135907370842141  p=value: 1.86042603207529e-07"
## [1] "TotRmsAbvGrd  cor: 0.533723155582028  p=value: 2.77228093295633e-108"
## [1] "Fireplaces  cor: 0.466928836751528  p=value: 6.14148746111509e-80"
## [1] "GarageYrBlt  cor: 0.508043287161517  p=value: 1.23482286114448e-96"
## [1] "GarageCars  cor: 0.640409197258352  p=value: 2.49864416717662e-169"
## [1] "GarageArea  cor: 0.623431438918362  p=value: 5.26503816797456e-158"
## [1] "WoodDeckSF  cor: 0.32441344456813  p=value: 3.97221653562712e-37"
## [1] "OpenPorchSF  cor: 0.315856227116055  p=value: 3.49337362309482e-35"
## [1] "EnclosedPorch  cor: -0.128577957925957  p=value: 8.25577047511324e-07"
## [1] "ScreenPorch  cor: 0.111446571142911  p=value: 1.97214001946891e-05"
## [1] "PoolArea  cor: 0.0924035494918732  p=value: 0.000407348960119616"
## [1] "SalePrice  cor: 1  p=value: 0"

#Second variation using variables where p-value < 0.05
Second_mod = lm(sc.data$SalePrice ~ MSSubClass + LotArea + OverallQual + OverallCond + YearBuilt + YearRemodAdd + BsmtFinSF1 + BsmtUnfSF + TotalBsmtSF + X1stFlrSF + X2ndFlrSF + GrLivArea + BsmtFullBath + FullBath + HalfBath + BedroomAbvGr + KitchenAbvGr + TotRmsAbvGrd + Fireplaces + GarageCars + GarageArea + WoodDeckSF + OpenPorchSF + EnclosedPorch + ScreenPorch + PoolArea, data = sc.data)
summary(Second_mod)

## 
## Call:
## lm(formula = sc.data$SalePrice ~ MSSubClass + LotArea + OverallQual + 
##     OverallCond + YearBuilt + YearRemodAdd + BsmtFinSF1 + BsmtUnfSF + 
##     TotalBsmtSF + X1stFlrSF + X2ndFlrSF + GrLivArea + BsmtFullBath + 
##     FullBath + HalfBath + BedroomAbvGr + KitchenAbvGr + TotRmsAbvGrd + 
##     Fireplaces + GarageCars + GarageArea + WoodDeckSF + OpenPorchSF + 
##     EnclosedPorch + ScreenPorch + PoolArea, data = sc.data)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -481876  -16926   -2280   13326  289614 
## 
## Coefficients:
##                 Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   -1.019e+06  1.356e+05  -7.515 9.97e-14 ***
## MSSubClass    -1.602e+02  2.631e+01  -6.086 1.48e-09 ***
## LotArea        3.995e-01  1.013e-01   3.943 8.43e-05 ***
## OverallQual    1.786e+04  1.190e+03  15.009  < 2e-16 ***
## OverallCond    4.441e+03  1.026e+03   4.329 1.60e-05 ***
## YearBuilt      3.482e+02  6.100e+01   5.708 1.39e-08 ***
## YearRemodAdd   1.354e+02  6.611e+01   2.049 0.040689 *  
## BsmtFinSF1     1.477e+01  6.075e+00   2.431 0.015173 *  
## BsmtUnfSF      3.231e+00  6.183e+00   0.523 0.601374    
## TotalBsmtSF    7.372e+00  7.067e+00   1.043 0.297078    
## X1stFlrSF      2.430e+01  2.029e+01   1.198 0.231134    
## X2ndFlrSF      2.409e+01  1.997e+01   1.206 0.227834    
## GrLivArea      2.653e+01  1.986e+01   1.336 0.181704    
## BsmtFullBath   7.935e+03  2.503e+03   3.170 0.001557 ** 
## FullBath       3.453e+03  2.829e+03   1.221 0.222451    
## HalfBath      -1.343e+03  2.681e+03  -0.501 0.616585    
## BedroomAbvGr  -1.042e+04  1.698e+03  -6.134 1.10e-09 ***
## KitchenAbvGr  -1.356e+04  5.216e+03  -2.599 0.009437 ** 
## TotRmsAbvGrd   5.111e+03  1.244e+03   4.109 4.19e-05 ***
## Fireplaces     3.601e+03  1.779e+03   2.024 0.043185 *  
## GarageCars     1.087e+04  2.873e+03   3.783 0.000161 ***
## GarageArea     1.000e+00  9.770e+00   0.102 0.918460    
## WoodDeckSF     2.604e+01  8.004e+00   3.253 0.001168 ** 
## OpenPorchSF   -5.109e+00  1.521e+01  -0.336 0.737048    
## EnclosedPorch  8.686e+00  1.698e+01   0.512 0.608975    
## ScreenPorch    5.677e+01  1.730e+01   3.282 0.001055 ** 
## PoolArea      -4.133e+01  2.367e+01  -1.746 0.081086 .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 35070 on 1433 degrees of freedom
## Multiple R-squared:  0.8086, Adjusted R-squared:  0.8051 
## F-statistic: 232.9 on 26 and 1433 DF,  p-value: < 2.2e-16

#Graphical Analysis of Second model
layout(matrix(c(1,2,3,4),2,2)) # optional 4 graphs/page 
plot(Second_mod)

Residual standard error: 35070 on 1433 degrees of freedom

Multiple R-squared: 0.8086, Adjusted R-squared: 0.8051

F-statistic: 232.9 on 26 and 1433 DF, p-value: < 2.2e-16

Discussion for 2nd submission:

The multiple R-squared of 80.86 > 70%. The Adjusted R-squared is 80.51 and higher the better. The F-statistic is 232.9 and higher the better. The p-value < 0.05.

#Starting third variation using variables where p-value < 0.01;  

Third_mod = lm(sc.data$SalePrice ~ MSSubClass + LotArea + OverallQual + OverallCond + YearBuilt + YearRemodAdd + BsmtFinSF1 + BsmtUnfSF + TotalBsmtSF + X1stFlrSF + X2ndFlrSF + GrLivArea + BsmtFullBath + FullBath + HalfBath + BedroomAbvGr + KitchenAbvGr + TotRmsAbvGrd + Fireplaces + GarageCars + GarageArea + WoodDeckSF + OpenPorchSF + EnclosedPorch + ScreenPorch + PoolArea, data = sc.data)

summary(Third_mod)

## 
## Call:
## lm(formula = sc.data$SalePrice ~ MSSubClass + LotArea + OverallQual + 
##     OverallCond + YearBuilt + YearRemodAdd + BsmtFinSF1 + BsmtUnfSF + 
##     TotalBsmtSF + X1stFlrSF + X2ndFlrSF + GrLivArea + BsmtFullBath + 
##     FullBath + HalfBath + BedroomAbvGr + KitchenAbvGr + TotRmsAbvGrd + 
##     Fireplaces + GarageCars + GarageArea + WoodDeckSF + OpenPorchSF + 
##     EnclosedPorch + ScreenPorch + PoolArea, data = sc.data)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -481876  -16926   -2280   13326  289614 
## 
## Coefficients:
##                 Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   -1.019e+06  1.356e+05  -7.515 9.97e-14 ***
## MSSubClass    -1.602e+02  2.631e+01  -6.086 1.48e-09 ***
## LotArea        3.995e-01  1.013e-01   3.943 8.43e-05 ***
## OverallQual    1.786e+04  1.190e+03  15.009  < 2e-16 ***
## OverallCond    4.441e+03  1.026e+03   4.329 1.60e-05 ***
## YearBuilt      3.482e+02  6.100e+01   5.708 1.39e-08 ***
## YearRemodAdd   1.354e+02  6.611e+01   2.049 0.040689 *  
## BsmtFinSF1     1.477e+01  6.075e+00   2.431 0.015173 *  
## BsmtUnfSF      3.231e+00  6.183e+00   0.523 0.601374    
## TotalBsmtSF    7.372e+00  7.067e+00   1.043 0.297078    
## X1stFlrSF      2.430e+01  2.029e+01   1.198 0.231134    
## X2ndFlrSF      2.409e+01  1.997e+01   1.206 0.227834    
## GrLivArea      2.653e+01  1.986e+01   1.336 0.181704    
## BsmtFullBath   7.935e+03  2.503e+03   3.170 0.001557 ** 
## FullBath       3.453e+03  2.829e+03   1.221 0.222451    
## HalfBath      -1.343e+03  2.681e+03  -0.501 0.616585    
## BedroomAbvGr  -1.042e+04  1.698e+03  -6.134 1.10e-09 ***
## KitchenAbvGr  -1.356e+04  5.216e+03  -2.599 0.009437 ** 
## TotRmsAbvGrd   5.111e+03  1.244e+03   4.109 4.19e-05 ***
## Fireplaces     3.601e+03  1.779e+03   2.024 0.043185 *  
## GarageCars     1.087e+04  2.873e+03   3.783 0.000161 ***
## GarageArea     1.000e+00  9.770e+00   0.102 0.918460    
## WoodDeckSF     2.604e+01  8.004e+00   3.253 0.001168 ** 
## OpenPorchSF   -5.109e+00  1.521e+01  -0.336 0.737048    
## EnclosedPorch  8.686e+00  1.698e+01   0.512 0.608975    
## ScreenPorch    5.677e+01  1.730e+01   3.282 0.001055 ** 
## PoolArea      -4.133e+01  2.367e+01  -1.746 0.081086 .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 35070 on 1433 degrees of freedom
## Multiple R-squared:  0.8086, Adjusted R-squared:  0.8051 
## F-statistic: 232.9 on 26 and 1433 DF,  p-value: < 2.2e-16

#Graphical Analysis of Third model
layout(matrix(c(1,2,3,4),2,2)) # optional 4 graphs/page 
plot(Third_mod)

Residual standard error: 22580 on 1205 degrees of freedom

Multiple R-squared: 0.9332, Adjusted R-squared: 0.9192

F-statistic: 66.33 on 254 and 1205 DF, p-value: < 2.2e-16

Discussion on 3rd submission:

The multiple R-squared of 93.32 > 70%. The Adjusted R-squared is 91.92 and higher the better. The F-statistic is 66.33 and higher the better. The p-value < 0.05.

#For the Fourth variation, we will narrow down the variables based on p-value and correlation test result value >0.50

#https://www.statisticssolutions.com/pearsons-correlation-coefficient/

#Perfect: If the value is near ± 1, then it said to be a perfect correlation: as one variable increases, the other variable tends to also increase (if positive) or decrease (if negative).
#High degree: If the coefficient value lies between ± 0.50 and ± 1, then it is said to be a strong correlation.
#Moderate degree: If the value lies between ± 0.30 and ± 0.49, then it is said to be a medium correlation.
#Low degree: When the value lies below + .29, then it is said to be a small correlation.
#No correlation: When the value is zero.

#Using only variables where the variable's p-value < 0.001 and correlation test value > 0.50

for (i in 2:length(sc.data)) {
  if(is.numeric(sc.data[,i])){
  a <- cor.test(sc.data$SalePrice, sc.data[,i])
  #print(paste(colnames(sc.data)[i], " est:", a$estimate, " p=value:", a$p.value))
  if (a$p.value < 0.001 && a$estimate > 0.50) {
    print(paste(colnames(sc.data)[i], " cor:", a$estimate, " p=value:", a$p.value))
  }  
  }
}

## [1] "OverallQual  cor: 0.790981600583805  p=value: 2.18567526799377e-313"
## [1] "YearBuilt  cor: 0.522897332879497  p=value: 2.99022909901342e-103"
## [1] "YearRemodAdd  cor: 0.507100967111386  p=value: 3.16494824191794e-96"
## [1] "TotalBsmtSF  cor: 0.613580551559196  p=value: 9.48422939149901e-152"
## [1] "X1stFlrSF  cor: 0.605852184691915  p=value: 5.3947106189684e-147"
## [1] "GrLivArea  cor: 0.708624477612652  p=value: 4.51803364677756e-223"
## [1] "FullBath  cor: 0.560663762748446  p=value: 1.23647006675964e-121"
## [1] "TotRmsAbvGrd  cor: 0.533723155582028  p=value: 2.77228093295633e-108"
## [1] "GarageYrBlt  cor: 0.508043287161517  p=value: 1.23482286114448e-96"
## [1] "GarageCars  cor: 0.640409197258352  p=value: 2.49864416717662e-169"
## [1] "GarageArea  cor: 0.623431438918362  p=value: 5.26503816797456e-158"
## [1] "SalePrice  cor: 1  p=value: 0"

#Fourth variation using variables where p-value < 0.001 and correlation > 0.50; Rather than add the numeric variables, we will multiply them




Fourth_mod = lm(sc.data$SalePrice ~   OverallQual *  YearBuilt * YearRemodAdd *  TotalBsmtSF * X1stFlrSF *  GrLivArea *  FullBath * TotRmsAbvGrd *  GarageCars * GarageArea , data = sc.data)

summary(Fourth_mod)

## 
## Call:
## lm(formula = sc.data$SalePrice ~ OverallQual * YearBuilt * YearRemodAdd * 
##     TotalBsmtSF * X1stFlrSF * GrLivArea * FullBath * TotRmsAbvGrd * 
##     GarageCars * GarageArea, data = sc.data)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -152690   -5372      -2    5350  139933 
## 
## Coefficients: (239 not defined because of singularities)
##                                                                                                                  Estimate
## (Intercept)                                                                                                    -2.895e+10
## OverallQual                                                                                                     1.896e+09
## YearBuilt                                                                                                       1.692e+07
## YearRemodAdd                                                                                                    1.420e+07
## TotalBsmtSF                                                                                                     2.031e+06
## X1stFlrSF                                                                                                       1.773e+07
## GrLivArea                                                                                                      -1.774e+06
## FullBath                                                                                                        1.557e+10
## TotRmsAbvGrd                                                                                                    3.301e+09
## GarageCars                                                                                                      1.012e+10
## GarageArea                                                                                                      2.222e+07
## OverallQual:YearBuilt                                                                                          -1.184e+06
## OverallQual:YearRemodAdd                                                                                       -7.190e+05
## YearBuilt:YearRemodAdd                                                                                         -8.334e+03
## OverallQual:TotalBsmtSF                                                                                        -5.150e+05
## YearBuilt:TotalBsmtSF                                                                                          -4.180e+03
## YearRemodAdd:TotalBsmtSF                                                                                       -2.408e+03
## OverallQual:X1stFlrSF                                                                                          -1.400e+06
## YearBuilt:X1stFlrSF                                                                                            -8.332e+03
## YearRemodAdd:X1stFlrSF                                                                                         -6.533e+03
## TotalBsmtSF:X1stFlrSF                                                                                          -2.479e+03
## OverallQual:GrLivArea                                                                                           1.386e+06
## YearBuilt:GrLivArea                                                                                            -3.304e+02
## YearRemodAdd:GrLivArea                                                                                          4.442e+02
## TotalBsmtSF:GrLivArea                                                                                          -9.702e+03
## X1stFlrSF:GrLivArea                                                                                             1.125e+04
## OverallQual:FullBath                                                                                           -8.970e+08
## YearBuilt:FullBath                                                                                             -1.060e+07
## YearRemodAdd:FullBath                                                                                          -7.340e+06
## TotalBsmtSF:FullBath                                                                                            1.606e+07
## X1stFlrSF:FullBath                                                                                             -2.505e+07
## GrLivArea:FullBath                                                                                              1.161e+06
## OverallQual:TotRmsAbvGrd                                                                                       -2.597e+08
## YearBuilt:TotRmsAbvGrd                                                                                         -1.763e+06
## YearRemodAdd:TotRmsAbvGrd                                                                                      -1.690e+06
## TotalBsmtSF:TotRmsAbvGrd                                                                                       -1.798e+05
## X1stFlrSF:TotRmsAbvGrd                                                                                         -5.685e+05
## GrLivArea:TotRmsAbvGrd                                                                                         -1.075e+06
## FullBath:TotRmsAbvGrd                                                                                          -5.680e+08
## OverallQual:GarageCars                                                                                         -6.040e+07
## YearBuilt:GarageCars                                                                                           -6.291e+06
## YearRemodAdd:GarageCars                                                                                        -4.729e+06
## TotalBsmtSF:GarageCars                                                                                          9.177e+06
## X1stFlrSF:GarageCars                                                                                           -1.511e+07
## GrLivArea:GarageCars                                                                                            7.681e+06
## FullBath:GarageCars                                                                                            -5.536e+09
## TotRmsAbvGrd:GarageCars                                                                                        -2.401e+09
## OverallQual:GarageArea                                                                                         -2.454e+06
## YearBuilt:GarageArea                                                                                           -9.939e+03
## YearRemodAdd:GarageArea                                                                                        -1.639e+04
## TotalBsmtSF:GarageArea                                                                                         -1.428e+04
## X1stFlrSF:GarageArea                                                                                            2.765e+03
## GrLivArea:GarageArea                                                                                           -2.238e+04
## FullBath:GarageArea                                                                                             5.748e+06
## TotRmsAbvGrd:GarageArea                                                                                         1.500e+06
## GarageCars:GarageArea                                                                                          -5.614e+06
## OverallQual:YearBuilt:YearRemodAdd                                                                              4.743e+02
## OverallQual:YearBuilt:TotalBsmtSF                                                                               1.067e+03
## OverallQual:YearRemodAdd:TotalBsmtSF                                                                            1.441e+02
## YearBuilt:YearRemodAdd:TotalBsmtSF                                                                              2.846e+00
## OverallQual:YearBuilt:X1stFlrSF                                                                                 3.063e+02
## OverallQual:YearRemodAdd:X1stFlrSF                                                                              3.618e+02
## YearBuilt:YearRemodAdd:X1stFlrSF                                                                                2.907e+00
## OverallQual:TotalBsmtSF:X1stFlrSF                                                                               1.335e+03
## YearBuilt:TotalBsmtSF:X1stFlrSF                                                                                 1.907e+00
## YearRemodAdd:TotalBsmtSF:X1stFlrSF                                                                              9.067e-01
## OverallQual:YearBuilt:GrLivArea                                                                                -7.605e+02
## OverallQual:YearRemodAdd:GrLivArea                                                                             -5.404e+02
## YearBuilt:YearRemodAdd:GrLivArea                                                                                4.054e-01
## OverallQual:TotalBsmtSF:GrLivArea                                                                              -6.407e+02
## YearBuilt:TotalBsmtSF:GrLivArea                                                                                 4.584e+00
## YearRemodAdd:TotalBsmtSF:GrLivArea                                                                              6.963e+00
## OverallQual:X1stFlrSF:GrLivArea                                                                                -3.440e+02
## YearBuilt:X1stFlrSF:GrLivArea                                                                                  -4.247e+00
## YearRemodAdd:X1stFlrSF:GrLivArea                                                                               -8.498e+00
## TotalBsmtSF:X1stFlrSF:GrLivArea                                                                                -5.004e-01
## OverallQual:YearBuilt:FullBath                                                                                  8.187e+05
## OverallQual:YearRemodAdd:FullBath                                                                               1.164e+05
## YearBuilt:YearRemodAdd:FullBath                                                                                 5.100e+03
## OverallQual:TotalBsmtSF:FullBath                                                                               -1.111e+06
## YearBuilt:TotalBsmtSF:FullBath                                                                                 -5.317e+03
## YearRemodAdd:TotalBsmtSF:FullBath                                                                              -6.141e+03
## OverallQual:X1stFlrSF:FullBath                                                                                  1.449e+06
## YearBuilt:X1stFlrSF:FullBath                                                                                    1.326e+04
## YearRemodAdd:X1stFlrSF:FullBath                                                                                 1.033e+04
## TotalBsmtSF:X1stFlrSF:FullBath                                                                                 -6.777e+02
## OverallQual:GrLivArea:FullBath                                                                                 -3.807e+05
## YearBuilt:GrLivArea:FullBath                                                                                    4.379e+02
## YearRemodAdd:GrLivArea:FullBath                                                                                 2.443e+02
## TotalBsmtSF:GrLivArea:FullBath                                                                                 -3.183e+03
## X1stFlrSF:GrLivArea:FullBath                                                                                    4.120e+03
## OverallQual:YearBuilt:TotRmsAbvGrd                                                                              1.520e+05
## OverallQual:YearRemodAdd:TotRmsAbvGrd                                                                           9.892e+04
## YearBuilt:YearRemodAdd:TotRmsAbvGrd                                                                             9.043e+02
## OverallQual:TotalBsmtSF:TotRmsAbvGrd                                                                            1.623e+05
## YearBuilt:TotalBsmtSF:TotRmsAbvGrd                                                                              4.802e+02
## YearRemodAdd:TotalBsmtSF:TotRmsAbvGrd                                                                          -1.449e+02
## OverallQual:X1stFlrSF:TotRmsAbvGrd                                                                             -1.685e+05
## YearBuilt:X1stFlrSF:TotRmsAbvGrd                                                                                1.742e+01
## YearRemodAdd:X1stFlrSF:TotRmsAbvGrd                                                                             4.284e+02
## TotalBsmtSF:X1stFlrSF:TotRmsAbvGrd                                                                             -3.563e+02
## OverallQual:GrLivArea:TotRmsAbvGrd                                                                              6.403e+04
## YearBuilt:GrLivArea:TotRmsAbvGrd                                                                                5.444e+02
## YearRemodAdd:GrLivArea:TotRmsAbvGrd                                                                             6.855e+02
## TotalBsmtSF:GrLivArea:TotRmsAbvGrd                                                                              2.814e+02
## X1stFlrSF:GrLivArea:TotRmsAbvGrd                                                                                2.553e+02
## OverallQual:FullBath:TotRmsAbvGrd                                                                               6.600e+07
## YearBuilt:FullBath:TotRmsAbvGrd                                                                                 4.512e+05
## YearRemodAdd:FullBath:TotRmsAbvGrd                                                                              2.418e+05
## TotalBsmtSF:FullBath:TotRmsAbvGrd                                                                              -9.140e+05
## X1stFlrSF:FullBath:TotRmsAbvGrd                                                                                 6.405e+05
## GrLivArea:FullBath:TotRmsAbvGrd                                                                                -2.869e+05
## OverallQual:YearBuilt:GarageCars                                                                                1.148e+05
## OverallQual:YearRemodAdd:GarageCars                                                                            -1.518e+05
## YearBuilt:YearRemodAdd:GarageCars                                                                               3.006e+03
## OverallQual:TotalBsmtSF:GarageCars                                                                             -1.036e+06
## YearBuilt:TotalBsmtSF:GarageCars                                                                               -4.126e+03
## YearRemodAdd:TotalBsmtSF:GarageCars                                                                            -3.904e+03
## OverallQual:X1stFlrSF:GarageCars                                                                                1.030e+06
## YearBuilt:X1stFlrSF:GarageCars                                                                                  6.929e+03
## YearRemodAdd:X1stFlrSF:GarageCars                                                                               7.421e+03
## TotalBsmtSF:X1stFlrSF:GarageCars                                                                                7.215e+02
## OverallQual:GrLivArea:GarageCars                                                                               -8.838e+05
## YearBuilt:GrLivArea:GarageCars                                                                                 -1.742e+03
## YearRemodAdd:GrLivArea:GarageCars                                                                              -4.740e+03
## TotalBsmtSF:GrLivArea:GarageCars                                                                                4.112e+02
## X1stFlrSF:GrLivArea:GarageCars                                                                                 -3.962e+03
## OverallQual:FullBath:GarageCars                                                                                 4.490e+08
## YearBuilt:FullBath:GarageCars                                                                                   4.654e+06
## YearRemodAdd:FullBath:GarageCars                                                                                2.107e+06
## TotalBsmtSF:FullBath:GarageCars                                                                                -1.049e+07
## X1stFlrSF:FullBath:GarageCars                                                                                   9.537e+06
## GrLivArea:FullBath:GarageCars                                                                                  -2.935e+06
## OverallQual:TotRmsAbvGrd:GarageCars                                                                             1.560e+08
## YearBuilt:TotRmsAbvGrd:GarageCars                                                                               1.122e+06
## YearRemodAdd:TotRmsAbvGrd:GarageCars                                                                            1.320e+06
## TotalBsmtSF:TotRmsAbvGrd:GarageCars                                                                             5.697e+05
## X1stFlrSF:TotRmsAbvGrd:GarageCars                                                                               9.510e+05
## GrLivArea:TotRmsAbvGrd:GarageCars                                                                               1.177e+04
## FullBath:TotRmsAbvGrd:GarageCars                                                                                2.830e+08
## OverallQual:YearBuilt:GarageArea                                                                                7.737e+02
## OverallQual:YearRemodAdd:GarageArea                                                                             2.244e+03
## YearBuilt:YearRemodAdd:GarageArea                                                                               7.582e+00
## OverallQual:TotalBsmtSF:GarageArea                                                                             -9.673e+02
## YearBuilt:TotalBsmtSF:GarageArea                                                                                1.004e+01
## YearRemodAdd:TotalBsmtSF:GarageArea                                                                             1.096e+01
## OverallQual:X1stFlrSF:GarageArea                                                                                2.863e+03
## YearBuilt:X1stFlrSF:GarageArea                                                                                 -4.509e+00
## YearRemodAdd:X1stFlrSF:GarageArea                                                                              -2.406e+00
## TotalBsmtSF:X1stFlrSF:GarageArea                                                                               -5.388e+00
## OverallQual:GrLivArea:GarageArea                                                                                1.840e+03
## YearBuilt:GrLivArea:GarageArea                                                                                  9.697e+00
## YearRemodAdd:GrLivArea:GarageArea                                                                               1.480e+01
## TotalBsmtSF:GrLivArea:GarageArea                                                                                2.148e+01
## X1stFlrSF:GrLivArea:GarageArea                                                                                 -8.888e+00
## OverallQual:FullBath:GarageArea                                                                                -1.324e+06
## YearBuilt:FullBath:GarageArea                                                                                  -4.833e+03
## YearRemodAdd:FullBath:GarageArea                                                                                2.433e+03
## TotalBsmtSF:FullBath:GarageArea                                                                                 1.905e+02
## X1stFlrSF:FullBath:GarageArea                                                                                  -4.132e+03
## GrLivArea:FullBath:GarageArea                                                                                  -3.323e+03
## OverallQual:TotRmsAbvGrd:GarageArea                                                                            -2.579e+05
## YearBuilt:TotRmsAbvGrd:GarageArea                                                                              -6.548e+02
## YearRemodAdd:TotRmsAbvGrd:GarageArea                                                                           -5.712e+02
## TotalBsmtSF:TotRmsAbvGrd:GarageArea                                                                            -2.398e+03
## X1stFlrSF:TotRmsAbvGrd:GarageArea                                                                               1.106e+03
## GrLivArea:TotRmsAbvGrd:GarageArea                                                                               3.419e+02
## FullBath:TotRmsAbvGrd:GarageArea                                                                               -2.218e+05
## OverallQual:GarageCars:GarageArea                                                                              -3.530e+05
## YearBuilt:GarageCars:GarageArea                                                                                 2.879e+03
## YearRemodAdd:GarageCars:GarageArea                                                                              4.360e+03
## TotalBsmtSF:GarageCars:GarageArea                                                                              -5.180e+03
## X1stFlrSF:GarageCars:GarageArea                                                                                 7.972e+03
## GrLivArea:GarageCars:GarageArea                                                                                -1.812e+03
## FullBath:GarageCars:GarageArea                                                                                  1.320e+06
## TotRmsAbvGrd:GarageCars:GarageArea                                                                              1.407e+05
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF                                                                 -4.829e-01
## OverallQual:YearBuilt:YearRemodAdd:X1stFlrSF                                                                    3.447e-02
## OverallQual:YearBuilt:TotalBsmtSF:X1stFlrSF                                                                    -8.148e-01
## OverallQual:YearRemodAdd:TotalBsmtSF:X1stFlrSF                                                                 -4.681e-01
## YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF                                                                   -7.586e-04
## OverallQual:YearBuilt:YearRemodAdd:GrLivArea                                                                    3.035e-01
## OverallQual:YearBuilt:TotalBsmtSF:GrLivArea                                                                     3.380e-01
## OverallQual:YearRemodAdd:TotalBsmtSF:GrLivArea                                                                 -3.808e-02
## YearBuilt:YearRemodAdd:TotalBsmtSF:GrLivArea                                                                   -3.399e-03
## OverallQual:YearBuilt:X1stFlrSF:GrLivArea                                                                       3.177e-01
## OverallQual:YearRemodAdd:X1stFlrSF:GrLivArea                                                                    4.525e-01
## YearBuilt:YearRemodAdd:X1stFlrSF:GrLivArea                                                                      3.637e-03
## OverallQual:TotalBsmtSF:X1stFlrSF:GrLivArea                                                                    -3.439e-01
## YearBuilt:TotalBsmtSF:X1stFlrSF:GrLivArea                                                                      -6.919e-04
## YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea                                                                    1.850e-03
## OverallQual:YearBuilt:YearRemodAdd:FullBath                                                                    -2.411e+02
## OverallQual:YearBuilt:TotalBsmtSF:FullBath                                                                     -2.197e+02
## OverallQual:YearRemodAdd:TotalBsmtSF:FullBath                                                                   6.938e+02
## YearBuilt:YearRemodAdd:TotalBsmtSF:FullBath                                                                     1.649e+00
## OverallQual:YearBuilt:X1stFlrSF:FullBath                                                                       -6.072e+02
## OverallQual:YearRemodAdd:X1stFlrSF:FullBath                                                                    -3.753e+02
## YearBuilt:YearRemodAdd:X1stFlrSF:FullBath                                                                      -5.467e+00
## OverallQual:TotalBsmtSF:X1stFlrSF:FullBath                                                                      7.314e+01
## YearBuilt:TotalBsmtSF:X1stFlrSF:FullBath                                                                       -6.290e-01
## YearRemodAdd:TotalBsmtSF:X1stFlrSF:FullBath                                                                     3.573e-01
## OverallQual:YearBuilt:GrLivArea:FullBath                                                                        2.170e+02
## OverallQual:YearRemodAdd:GrLivArea:FullBath                                                                     3.085e+01
## YearBuilt:YearRemodAdd:GrLivArea:FullBath                                                                      -6.543e-01
## OverallQual:TotalBsmtSF:GrLivArea:FullBath                                                                      6.826e+02
## YearBuilt:TotalBsmtSF:GrLivArea:FullBath                                                                        2.541e+00
## YearRemodAdd:TotalBsmtSF:GrLivArea:FullBath                                                                    -1.469e+00
## OverallQual:X1stFlrSF:GrLivArea:FullBath                                                                       -3.260e+02
## YearBuilt:X1stFlrSF:GrLivArea:FullBath                                                                         -3.671e+00
## YearRemodAdd:X1stFlrSF:GrLivArea:FullBath                                                                      -3.169e-01
## TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath                                                                        5.668e-01
## OverallQual:YearBuilt:YearRemodAdd:TotRmsAbvGrd                                                                -6.040e+01
## OverallQual:YearBuilt:TotalBsmtSF:TotRmsAbvGrd                                                                 -1.823e+02
## OverallQual:YearRemodAdd:TotalBsmtSF:TotRmsAbvGrd                                                              -1.928e+01
## YearBuilt:YearRemodAdd:TotalBsmtSF:TotRmsAbvGrd                                                                -1.252e-01
## OverallQual:YearBuilt:X1stFlrSF:TotRmsAbvGrd                                                                    1.176e+02
## OverallQual:YearRemodAdd:X1stFlrSF:TotRmsAbvGrd                                                                 9.243e+01
## YearBuilt:YearRemodAdd:X1stFlrSF:TotRmsAbvGrd                                                                  -7.595e-02
## OverallQual:TotalBsmtSF:X1stFlrSF:TotRmsAbvGrd                                                                  1.945e+01
## YearBuilt:TotalBsmtSF:X1stFlrSF:TotRmsAbvGrd                                                                    2.339e-01
## YearRemodAdd:TotalBsmtSF:X1stFlrSF:TotRmsAbvGrd                                                                 8.031e-02
## OverallQual:YearBuilt:GrLivArea:TotRmsAbvGrd                                                                   -1.561e+01
## OverallQual:YearRemodAdd:GrLivArea:TotRmsAbvGrd                                                                -5.606e+01
## YearBuilt:YearRemodAdd:GrLivArea:TotRmsAbvGrd                                                                  -3.504e-01
## OverallQual:TotalBsmtSF:GrLivArea:TotRmsAbvGrd                                                                  3.048e+01
## YearBuilt:TotalBsmtSF:GrLivArea:TotRmsAbvGrd                                                                   -2.101e-01
## YearRemodAdd:TotalBsmtSF:GrLivArea:TotRmsAbvGrd                                                                -2.380e-02
## OverallQual:X1stFlrSF:GrLivArea:TotRmsAbvGrd                                                                   -4.979e+01
## YearBuilt:X1stFlrSF:GrLivArea:TotRmsAbvGrd                                                                     -6.348e-02
## YearRemodAdd:X1stFlrSF:GrLivArea:TotRmsAbvGrd                                                                  -1.702e-01
## TotalBsmtSF:X1stFlrSF:GrLivArea:TotRmsAbvGrd                                                                   -1.964e-01
## OverallQual:YearBuilt:FullBath:TotRmsAbvGrd                                                                    -7.196e+04
## OverallQual:YearRemodAdd:FullBath:TotRmsAbvGrd                                                                  2.608e+04
## YearBuilt:YearRemodAdd:FullBath:TotRmsAbvGrd                                                                   -2.087e+02
## OverallQual:TotalBsmtSF:FullBath:TotRmsAbvGrd                                                                   8.225e+04
## YearBuilt:TotalBsmtSF:FullBath:TotRmsAbvGrd                                                                     1.606e+02
## YearRemodAdd:TotalBsmtSF:FullBath:TotRmsAbvGrd                                                                  4.616e+02
## OverallQual:X1stFlrSF:FullBath:TotRmsAbvGrd                                                                    -7.475e+04
## YearBuilt:X1stFlrSF:FullBath:TotRmsAbvGrd                                                                      -2.814e+02
## YearRemodAdd:X1stFlrSF:FullBath:TotRmsAbvGrd                                                                   -2.632e+02
## TotalBsmtSF:X1stFlrSF:FullBath:TotRmsAbvGrd                                                                     2.357e+02
## OverallQual:GrLivArea:FullBath:TotRmsAbvGrd                                                                    -9.950e+03
## YearBuilt:GrLivArea:FullBath:TotRmsAbvGrd                                                                       1.974e+02
## YearRemodAdd:GrLivArea:FullBath:TotRmsAbvGrd                                                                    3.375e+00
## TotalBsmtSF:GrLivArea:FullBath:TotRmsAbvGrd                                                                     1.256e+02
## X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd                                                                      -4.999e+01
## OverallQual:YearBuilt:YearRemodAdd:GarageCars                                                                   3.196e+01
## OverallQual:YearBuilt:TotalBsmtSF:GarageCars                                                                    3.501e+02
## OverallQual:YearRemodAdd:TotalBsmtSF:GarageCars                                                                 7.438e+02
## YearBuilt:YearRemodAdd:TotalBsmtSF:GarageCars                                                                   1.684e+00
## OverallQual:YearBuilt:X1stFlrSF:GarageCars                                                                     -3.238e+02
## OverallQual:YearRemodAdd:X1stFlrSF:GarageCars                                                                  -5.891e+02
## YearBuilt:YearRemodAdd:X1stFlrSF:GarageCars                                                                    -3.385e+00
## OverallQual:TotalBsmtSF:X1stFlrSF:GarageCars                                                                   -2.039e+02
## YearBuilt:TotalBsmtSF:X1stFlrSF:GarageCars                                                                      9.641e-01
## YearRemodAdd:TotalBsmtSF:X1stFlrSF:GarageCars                                                                  -1.417e+00
## OverallQual:YearBuilt:GrLivArea:GarageCars                                                                      2.941e+02
## OverallQual:YearRemodAdd:GrLivArea:GarageCars                                                                   5.017e+02
## YearBuilt:YearRemodAdd:GrLivArea:GarageCars                                                                     1.305e+00
## OverallQual:TotalBsmtSF:GrLivArea:GarageCars                                                                    1.304e+02
## YearBuilt:TotalBsmtSF:GrLivArea:GarageCars                                                                     -9.232e-01
## YearRemodAdd:TotalBsmtSF:GrLivArea:GarageCars                                                                  -4.223e-01
## OverallQual:X1stFlrSF:GrLivArea:GarageCars                                                                     -2.262e+01
## YearBuilt:X1stFlrSF:GrLivArea:GarageCars                                                                        2.113e-01
## YearRemodAdd:X1stFlrSF:GrLivArea:GarageCars                                                                     3.798e+00
## TotalBsmtSF:X1stFlrSF:GrLivArea:GarageCars                                                                     -2.853e-01
## OverallQual:YearBuilt:FullBath:GarageCars                                                                      -4.869e+05
## OverallQual:YearRemodAdd:FullBath:GarageCars                                                                    8.995e+04
## YearBuilt:YearRemodAdd:FullBath:GarageCars                                                                     -2.020e+03
## OverallQual:TotalBsmtSF:FullBath:GarageCars                                                                     5.782e+05
## YearBuilt:TotalBsmtSF:FullBath:GarageCars                                                                       3.865e+03
## YearRemodAdd:TotalBsmtSF:FullBath:GarageCars                                                                    3.486e+03
## OverallQual:X1stFlrSF:FullBath:GarageCars                                                                      -5.827e+05
## YearBuilt:X1stFlrSF:FullBath:GarageCars                                                                        -4.661e+03
## YearRemodAdd:X1stFlrSF:FullBath:GarageCars                                                                     -3.398e+03
## TotalBsmtSF:X1stFlrSF:FullBath:GarageCars                                                                       8.478e+02
## OverallQual:GrLivArea:FullBath:GarageCars                                                                       1.012e+05
## YearBuilt:GrLivArea:FullBath:GarageCars                                                                        -3.489e+01
## YearRemodAdd:GrLivArea:FullBath:GarageCars                                                                      1.917e+03
## TotalBsmtSF:GrLivArea:FullBath:GarageCars                                                                       3.290e+03
## X1stFlrSF:GrLivArea:FullBath:GarageCars                                                                        -6.583e+02
## OverallQual:YearBuilt:TotRmsAbvGrd:GarageCars                                                                  -5.931e+04
## OverallQual:YearRemodAdd:TotRmsAbvGrd:GarageCars                                                               -7.350e+04
## YearBuilt:YearRemodAdd:TotRmsAbvGrd:GarageCars                                                                 -6.247e+02
## OverallQual:TotalBsmtSF:TotRmsAbvGrd:GarageCars                                                                -1.320e+05
## YearBuilt:TotalBsmtSF:TotRmsAbvGrd:GarageCars                                                                  -2.324e+02
## YearRemodAdd:TotalBsmtSF:TotRmsAbvGrd:GarageCars                                                               -1.133e+02
## OverallQual:X1stFlrSF:TotRmsAbvGrd:GarageCars                                                                   4.381e+04
## YearBuilt:X1stFlrSF:TotRmsAbvGrd:GarageCars                                                                    -2.211e+02
## YearRemodAdd:X1stFlrSF:TotRmsAbvGrd:GarageCars                                                                 -7.850e+02
## TotalBsmtSF:X1stFlrSF:TotRmsAbvGrd:GarageCars                                                                  -2.942e+02
## OverallQual:GrLivArea:TotRmsAbvGrd:GarageCars                                                                   1.471e+04
## YearBuilt:GrLivArea:TotRmsAbvGrd:GarageCars                                                                    -1.480e+02
## YearRemodAdd:GrLivArea:TotRmsAbvGrd:GarageCars                                                                  2.450e+00
## TotalBsmtSF:GrLivArea:TotRmsAbvGrd:GarageCars                                                                  -1.907e+02
## X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageCars                                                                     2.051e+02
## OverallQual:FullBath:TotRmsAbvGrd:GarageCars                                                                   -3.005e+07
## YearBuilt:FullBath:TotRmsAbvGrd:GarageCars                                                                     -1.795e+05
## YearRemodAdd:FullBath:TotRmsAbvGrd:GarageCars                                                                  -2.163e+05
## TotalBsmtSF:FullBath:TotRmsAbvGrd:GarageCars                                                                    4.602e+05
## X1stFlrSF:FullBath:TotRmsAbvGrd:GarageCars                                                                     -1.793e+05
## GrLivArea:FullBath:TotRmsAbvGrd:GarageCars                                                                      2.151e+05
## OverallQual:YearBuilt:YearRemodAdd:GarageArea                                                                  -8.816e-01
## OverallQual:YearBuilt:TotalBsmtSF:GarageArea                                                                   -3.820e-01
## OverallQual:YearRemodAdd:TotalBsmtSF:GarageArea                                                                -1.497e-01
## YearBuilt:YearRemodAdd:TotalBsmtSF:GarageArea                                                                  -7.118e-03
## OverallQual:YearBuilt:X1stFlrSF:GarageArea                                                                     -2.403e-01
## OverallQual:YearRemodAdd:X1stFlrSF:GarageArea                                                                  -1.332e+00
## YearBuilt:YearRemodAdd:X1stFlrSF:GarageArea                                                                     3.107e-03
## OverallQual:TotalBsmtSF:X1stFlrSF:GarageArea                                                                   -2.652e-02
## YearBuilt:TotalBsmtSF:X1stFlrSF:GarageArea                                                                      2.522e-05
## YearRemodAdd:TotalBsmtSF:X1stFlrSF:GarageArea                                                                   2.907e-03
## OverallQual:YearBuilt:GrLivArea:GarageArea                                                                     -7.619e-01
## OverallQual:YearRemodAdd:GrLivArea:GarageArea                                                                  -1.417e+00
## YearBuilt:YearRemodAdd:GrLivArea:GarageArea                                                                    -6.704e-03
## OverallQual:TotalBsmtSF:GrLivArea:GarageArea                                                                    1.303e+00
## YearBuilt:TotalBsmtSF:GrLivArea:GarageArea                                                                     -5.171e-03
## YearRemodAdd:TotalBsmtSF:GrLivArea:GarageArea                                                                  -1.541e-02
## OverallQual:X1stFlrSF:GrLivArea:GarageArea                                                                     -1.664e+00
## YearBuilt:X1stFlrSF:GrLivArea:GarageArea                                                                        2.830e-03
## YearRemodAdd:X1stFlrSF:GrLivArea:GarageArea                                                                     6.011e-03
## TotalBsmtSF:X1stFlrSF:GrLivArea:GarageArea                                                                      3.045e-04
## OverallQual:YearBuilt:FullBath:GarageArea                                                                       1.213e+03
## OverallQual:YearRemodAdd:FullBath:GarageArea                                                                   -3.672e+02
## YearBuilt:YearRemodAdd:FullBath:GarageArea                                                                     -2.458e-01
## OverallQual:TotalBsmtSF:FullBath:GarageArea                                                                     4.607e+02
## YearBuilt:TotalBsmtSF:FullBath:GarageArea                                                                      -1.953e+00
## YearRemodAdd:TotalBsmtSF:FullBath:GarageArea                                                                    1.210e+00
## OverallQual:X1stFlrSF:FullBath:GarageArea                                                                      -7.724e+01
## YearBuilt:X1stFlrSF:FullBath:GarageArea                                                                         6.075e+00
## YearRemodAdd:X1stFlrSF:FullBath:GarageArea                                                                     -3.132e+00
## TotalBsmtSF:X1stFlrSF:FullBath:GarageArea                                                                       1.225e+00
## OverallQual:GrLivArea:FullBath:GarageArea                                                                       7.918e+02
## YearBuilt:GrLivArea:FullBath:GarageArea                                                                         2.108e+00
## YearRemodAdd:GrLivArea:FullBath:GarageArea                                                                     -7.443e-01
## TotalBsmtSF:GrLivArea:FullBath:GarageArea                                                                      -5.181e+00
## X1stFlrSF:GrLivArea:FullBath:GarageArea                                                                         6.771e+00
## OverallQual:YearBuilt:TotRmsAbvGrd:GarageArea                                                                   1.604e+02
## OverallQual:YearRemodAdd:TotRmsAbvGrd:GarageArea                                                                4.373e+01
## YearBuilt:YearRemodAdd:TotRmsAbvGrd:GarageArea                                                                  2.407e-01
## OverallQual:TotalBsmtSF:TotRmsAbvGrd:GarageArea                                                                 3.350e+02
## YearBuilt:TotalBsmtSF:TotRmsAbvGrd:GarageArea                                                                   6.391e-01
## YearRemodAdd:TotalBsmtSF:TotRmsAbvGrd:GarageArea                                                                1.113e+00
## OverallQual:X1stFlrSF:TotRmsAbvGrd:GarageArea                                                                  -2.563e+02
## YearBuilt:X1stFlrSF:TotRmsAbvGrd:GarageArea                                                                    -5.033e-01
## YearRemodAdd:X1stFlrSF:TotRmsAbvGrd:GarageArea                                                                 -1.114e-01
## TotalBsmtSF:X1stFlrSF:TotRmsAbvGrd:GarageArea                                                                   7.630e-01
## OverallQual:GrLivArea:TotRmsAbvGrd:GarageArea                                                                   7.148e+01
## YearBuilt:GrLivArea:TotRmsAbvGrd:GarageArea                                                                     1.030e-01
## YearRemodAdd:GrLivArea:TotRmsAbvGrd:GarageArea                                                                 -6.035e-01
## TotalBsmtSF:GrLivArea:TotRmsAbvGrd:GarageArea                                                                  -2.035e-01
## X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageArea                                                                    -2.440e-02
## OverallQual:FullBath:TotRmsAbvGrd:GarageArea                                                                    4.848e+04
## YearBuilt:FullBath:TotRmsAbvGrd:GarageArea                                                                     -3.316e+01
## YearRemodAdd:FullBath:TotRmsAbvGrd:GarageArea                                                                   1.278e+02
## TotalBsmtSF:FullBath:TotRmsAbvGrd:GarageArea                                                                   -3.016e+01
## X1stFlrSF:FullBath:TotRmsAbvGrd:GarageArea                                                                     -2.075e+02
## GrLivArea:FullBath:TotRmsAbvGrd:GarageArea                                                                      3.688e+01
## OverallQual:YearBuilt:GarageCars:GarageArea                                                                     2.975e+02
## OverallQual:YearRemodAdd:GarageCars:GarageArea                                                                 -1.187e+02
## YearBuilt:YearRemodAdd:GarageCars:GarageArea                                                                   -2.231e+00
## OverallQual:TotalBsmtSF:GarageCars:GarageArea                                                                   7.276e+02
## YearBuilt:TotalBsmtSF:GarageCars:GarageArea                                                                     1.663e+00
## YearRemodAdd:TotalBsmtSF:GarageCars:GarageArea                                                                  9.205e-01
## OverallQual:X1stFlrSF:GarageCars:GarageArea                                                                    -5.487e+02
## YearBuilt:X1stFlrSF:GarageCars:GarageArea                                                                      -2.695e+00
## YearRemodAdd:X1stFlrSF:GarageCars:GarageArea                                                                   -3.726e+00
## TotalBsmtSF:X1stFlrSF:GarageCars:GarageArea                                                                     2.010e+00
## OverallQual:GrLivArea:GarageCars:GarageArea                                                                     4.201e+02
## YearBuilt:GrLivArea:GarageCars:GarageArea                                                                       9.127e-03
## YearRemodAdd:GrLivArea:GarageCars:GarageArea                                                                    6.010e-01
## TotalBsmtSF:GrLivArea:GarageCars:GarageArea                                                                     2.005e-01
## X1stFlrSF:GrLivArea:GarageCars:GarageArea                                                                       2.255e-01
## OverallQual:FullBath:GarageCars:GarageArea                                                                      2.311e+05
## YearBuilt:FullBath:GarageCars:GarageArea                                                                       -6.550e+02
## YearRemodAdd:FullBath:GarageCars:GarageArea                                                                    -2.135e+03
## TotalBsmtSF:FullBath:GarageCars:GarageArea                                                                      5.648e+03
## X1stFlrSF:FullBath:GarageCars:GarageArea                                                                       -3.255e+03
## GrLivArea:FullBath:GarageCars:GarageArea                                                                        1.710e+03
## OverallQual:TotRmsAbvGrd:GarageCars:GarageArea                                                                  2.098e+04
## YearBuilt:TotRmsAbvGrd:GarageCars:GarageArea                                                                    4.123e+00
## YearRemodAdd:TotRmsAbvGrd:GarageCars:GarageArea                                                                -2.247e+02
## TotalBsmtSF:TotRmsAbvGrd:GarageCars:GarageArea                                                                 -1.966e+01
## X1stFlrSF:TotRmsAbvGrd:GarageCars:GarageArea                                                                   -3.353e+02
## GrLivArea:TotRmsAbvGrd:GarageCars:GarageArea                                                                    3.503e+02
## FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                                                     2.289e+05
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF                                                        3.002e-04
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:GrLivArea                                                        1.654e-05
## OverallQual:YearBuilt:YearRemodAdd:X1stFlrSF:GrLivArea                                                         -3.132e-04
## OverallQual:YearBuilt:TotalBsmtSF:X1stFlrSF:GrLivArea                                                           1.932e-04
## OverallQual:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea                                                       -7.975e-06
## YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea                                                         -4.850e-07
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:FullBath                                                         4.633e-02
## OverallQual:YearBuilt:YearRemodAdd:X1stFlrSF:FullBath                                                           1.159e-01
## OverallQual:YearBuilt:TotalBsmtSF:X1stFlrSF:FullBath                                                            2.117e-01
## OverallQual:YearRemodAdd:TotalBsmtSF:X1stFlrSF:FullBath                                                        -2.398e-01
## YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:FullBath                                                           2.945e-04
## OverallQual:YearBuilt:YearRemodAdd:GrLivArea:FullBath                                                          -2.789e-02
## OverallQual:YearBuilt:TotalBsmtSF:GrLivArea:FullBath                                                           -4.335e-01
## OverallQual:YearRemodAdd:TotalBsmtSF:GrLivArea:FullBath                                                         8.144e-02
## YearBuilt:YearRemodAdd:TotalBsmtSF:GrLivArea:FullBath                                                           3.121e-04
## OverallQual:YearBuilt:X1stFlrSF:GrLivArea:FullBath                                                              1.058e-01
## OverallQual:YearRemodAdd:X1stFlrSF:GrLivArea:FullBath                                                           7.427e-02
## YearBuilt:YearRemodAdd:X1stFlrSF:GrLivArea:FullBath                                                             9.145e-04
## OverallQual:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath                                                           -1.489e-02
## YearBuilt:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath                                                              3.456e-04
## YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath                                                          -6.046e-04
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:TotRmsAbvGrd                                                     6.051e-02
## OverallQual:YearBuilt:YearRemodAdd:X1stFlrSF:TotRmsAbvGrd                                                      -6.438e-02
## OverallQual:YearBuilt:TotalBsmtSF:X1stFlrSF:TotRmsAbvGrd                                                        9.505e-03
## OverallQual:YearRemodAdd:TotalBsmtSF:X1stFlrSF:TotRmsAbvGrd                                                    -1.770e-02
## YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:TotRmsAbvGrd                                                      -7.109e-05
## OverallQual:YearBuilt:YearRemodAdd:GrLivArea:TotRmsAbvGrd                                                       2.013e-02
## OverallQual:YearBuilt:TotalBsmtSF:GrLivArea:TotRmsAbvGrd                                                        8.645e-03
## OverallQual:YearRemodAdd:TotalBsmtSF:GrLivArea:TotRmsAbvGrd                                                    -2.472e-02
## YearBuilt:YearRemodAdd:TotalBsmtSF:GrLivArea:TotRmsAbvGrd                                                       4.948e-05
## OverallQual:YearBuilt:X1stFlrSF:GrLivArea:TotRmsAbvGrd                                                         -6.665e-03
## OverallQual:YearRemodAdd:X1stFlrSF:GrLivArea:TotRmsAbvGrd                                                       3.370e-02
## YearBuilt:YearRemodAdd:X1stFlrSF:GrLivArea:TotRmsAbvGrd                                                         4.867e-05
## OverallQual:TotalBsmtSF:X1stFlrSF:GrLivArea:TotRmsAbvGrd                                                        2.250e-02
## YearBuilt:TotalBsmtSF:X1stFlrSF:GrLivArea:TotRmsAbvGrd                                                          1.572e-04
## YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:TotRmsAbvGrd                                                      -5.212e-05
## OverallQual:YearBuilt:YearRemodAdd:FullBath:TotRmsAbvGrd                                                        6.352e+00
## OverallQual:YearBuilt:TotalBsmtSF:FullBath:TotRmsAbvGrd                                                         4.198e+01
## OverallQual:YearRemodAdd:TotalBsmtSF:FullBath:TotRmsAbvGrd                                                     -8.426e+01
## YearBuilt:YearRemodAdd:TotalBsmtSF:FullBath:TotRmsAbvGrd                                                       -7.733e-02
## OverallQual:YearBuilt:X1stFlrSF:FullBath:TotRmsAbvGrd                                                           5.511e+01
## OverallQual:YearRemodAdd:X1stFlrSF:FullBath:TotRmsAbvGrd                                                       -1.530e+01
## YearBuilt:YearRemodAdd:X1stFlrSF:FullBath:TotRmsAbvGrd                                                          1.089e-01
## OverallQual:TotalBsmtSF:X1stFlrSF:FullBath:TotRmsAbvGrd                                                        -3.121e+01
## YearBuilt:TotalBsmtSF:X1stFlrSF:FullBath:TotRmsAbvGrd                                                          -1.219e-01
## YearRemodAdd:TotalBsmtSF:X1stFlrSF:FullBath:TotRmsAbvGrd                                                        5.531e-03
## OverallQual:YearBuilt:GrLivArea:FullBath:TotRmsAbvGrd                                                          -1.455e+01
## OverallQual:YearRemodAdd:GrLivArea:FullBath:TotRmsAbvGrd                                                        1.897e+01
## YearBuilt:YearRemodAdd:GrLivArea:FullBath:TotRmsAbvGrd                                                         -2.436e-02
## OverallQual:TotalBsmtSF:GrLivArea:FullBath:TotRmsAbvGrd                                                        -2.943e+01
## YearBuilt:TotalBsmtSF:GrLivArea:FullBath:TotRmsAbvGrd                                                          -1.436e-01
## YearRemodAdd:TotalBsmtSF:GrLivArea:FullBath:TotRmsAbvGrd                                                        7.165e-02
## OverallQual:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd                                                           3.369e+01
## YearBuilt:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd                                                            -3.404e-03
## YearRemodAdd:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd                                                          3.374e-02
## TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd                                                           1.425e-02
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:GarageCars                                                      -2.850e-01
## OverallQual:YearBuilt:YearRemodAdd:X1stFlrSF:GarageCars                                                         1.965e-01
## OverallQual:YearBuilt:TotalBsmtSF:X1stFlrSF:GarageCars                                                         -5.751e-02
## OverallQual:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GarageCars                                                       1.582e-01
## YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GarageCars                                                         5.819e-05
## OverallQual:YearBuilt:YearRemodAdd:GrLivArea:GarageCars                                                        -1.753e-01
## OverallQual:YearBuilt:TotalBsmtSF:GrLivArea:GarageCars                                                          1.301e-02
## OverallQual:YearRemodAdd:TotalBsmtSF:GrLivArea:GarageCars                                                      -8.332e-02
## YearBuilt:YearRemodAdd:TotalBsmtSF:GrLivArea:GarageCars                                                         5.941e-04
## OverallQual:YearBuilt:X1stFlrSF:GrLivArea:GarageCars                                                            8.048e-02
## OverallQual:YearRemodAdd:X1stFlrSF:GrLivArea:GarageCars                                                        -6.186e-02
## YearBuilt:YearRemodAdd:X1stFlrSF:GrLivArea:GarageCars                                                          -1.039e-03
## OverallQual:TotalBsmtSF:X1stFlrSF:GrLivArea:GarageCars                                                          9.064e-02
## YearBuilt:TotalBsmtSF:X1stFlrSF:GrLivArea:GarageCars                                                            7.035e-04
## YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:GarageCars                                                        -5.520e-04
## OverallQual:YearBuilt:YearRemodAdd:FullBath:GarageCars                                                          8.730e+01
## OverallQual:YearBuilt:TotalBsmtSF:FullBath:GarageCars                                                           7.341e+01
## OverallQual:YearRemodAdd:TotalBsmtSF:FullBath:GarageCars                                                       -3.705e+02
## YearBuilt:YearRemodAdd:TotalBsmtSF:FullBath:GarageCars                                                         -1.008e+00
## OverallQual:YearBuilt:X1stFlrSF:FullBath:GarageCars                                                             2.324e+02
## OverallQual:YearRemodAdd:X1stFlrSF:FullBath:GarageCars                                                          6.652e+01
## YearBuilt:YearRemodAdd:X1stFlrSF:FullBath:GarageCars                                                            1.625e+00
## OverallQual:TotalBsmtSF:X1stFlrSF:FullBath:GarageCars                                                           2.156e+01
## YearBuilt:TotalBsmtSF:X1stFlrSF:FullBath:GarageCars                                                            -7.982e-01
## YearRemodAdd:TotalBsmtSF:X1stFlrSF:FullBath:GarageCars                                                          3.588e-01
## OverallQual:YearBuilt:GrLivArea:FullBath:GarageCars                                                             6.015e+01
## OverallQual:YearRemodAdd:GrLivArea:FullBath:GarageCars                                                         -1.141e+02
## YearBuilt:YearRemodAdd:GrLivArea:FullBath:GarageCars                                                           -1.895e-01
## OverallQual:TotalBsmtSF:GrLivArea:FullBath:GarageCars                                                          -3.120e+02
## YearBuilt:TotalBsmtSF:GrLivArea:FullBath:GarageCars                                                            -1.514e+00
## YearRemodAdd:TotalBsmtSF:GrLivArea:FullBath:GarageCars                                                         -1.914e-01
## OverallQual:X1stFlrSF:GrLivArea:FullBath:GarageCars                                                             1.511e+02
## YearBuilt:X1stFlrSF:GrLivArea:FullBath:GarageCars                                                               1.702e+00
## YearRemodAdd:X1stFlrSF:GrLivArea:FullBath:GarageCars                                                           -1.334e+00
## TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:GarageCars                                                            -4.435e-01
## OverallQual:YearBuilt:YearRemodAdd:TotRmsAbvGrd:GarageCars                                                      2.771e+01
## OverallQual:YearBuilt:TotalBsmtSF:TotRmsAbvGrd:GarageCars                                                       6.094e+01
## OverallQual:YearRemodAdd:TotalBsmtSF:TotRmsAbvGrd:GarageCars                                                    5.032e+00
## YearBuilt:YearRemodAdd:TotalBsmtSF:TotRmsAbvGrd:GarageCars                                                      3.177e-02
## OverallQual:YearBuilt:X1stFlrSF:TotRmsAbvGrd:GarageCars                                                        -4.202e+01
## OverallQual:YearRemodAdd:X1stFlrSF:TotRmsAbvGrd:GarageCars                                                      1.993e+01
## YearBuilt:YearRemodAdd:X1stFlrSF:TotRmsAbvGrd:GarageCars                                                        2.666e-01
## OverallQual:TotalBsmtSF:X1stFlrSF:TotRmsAbvGrd:GarageCars                                                       4.187e+01
## YearBuilt:TotalBsmtSF:X1stFlrSF:TotRmsAbvGrd:GarageCars                                                        -1.490e-01
## YearRemodAdd:TotalBsmtSF:X1stFlrSF:TotRmsAbvGrd:GarageCars                                                      2.947e-01
## OverallQual:YearBuilt:GrLivArea:TotRmsAbvGrd:GarageCars                                                        -5.458e+00
## OverallQual:YearRemodAdd:GrLivArea:TotRmsAbvGrd:GarageCars                                                     -2.669e+00
## YearBuilt:YearRemodAdd:GrLivArea:TotRmsAbvGrd:GarageCars                                                        7.301e-02
## OverallQual:TotalBsmtSF:GrLivArea:TotRmsAbvGrd:GarageCars                                                       5.058e+01
## YearBuilt:TotalBsmtSF:GrLivArea:TotRmsAbvGrd:GarageCars                                                         2.062e-01
## YearRemodAdd:TotalBsmtSF:GrLivArea:TotRmsAbvGrd:GarageCars                                                     -1.139e-01
## OverallQual:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageCars                                                        -4.248e+01
## YearBuilt:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageCars                                                          -2.180e-02
## YearRemodAdd:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageCars                                                       -7.923e-02
## TotalBsmtSF:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageCars                                                         1.631e-01
## OverallQual:YearBuilt:FullBath:TotRmsAbvGrd:GarageCars                                                          2.513e+04
## OverallQual:YearRemodAdd:FullBath:TotRmsAbvGrd:GarageCars                                                      -1.052e+04
## YearBuilt:YearRemodAdd:FullBath:TotRmsAbvGrd:GarageCars                                                         1.308e+02
## OverallQual:TotalBsmtSF:FullBath:TotRmsAbvGrd:GarageCars                                                       -9.968e+03
## YearBuilt:TotalBsmtSF:FullBath:TotRmsAbvGrd:GarageCars                                                         -1.310e+02
## YearRemodAdd:TotalBsmtSF:FullBath:TotRmsAbvGrd:GarageCars                                                      -1.065e+02
## OverallQual:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageCars                                                          2.705e+04
## YearBuilt:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageCars                                                           -7.431e+01
## YearRemodAdd:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageCars                                                         1.649e+02
## TotalBsmtSF:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageCars                                                         -6.108e+01
## OverallQual:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars                                                          2.341e+03
## YearBuilt:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars                                                           -4.016e+01
## YearRemodAdd:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars                                                        -7.356e+01
## TotalBsmtSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars                                                         -1.768e+02
## X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars                                                           -1.399e+01
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:GarageArea                                                       5.389e-04
## OverallQual:YearBuilt:YearRemodAdd:X1stFlrSF:GarageArea                                                                NA
## OverallQual:YearBuilt:TotalBsmtSF:X1stFlrSF:GarageArea                                                          1.720e-04
## OverallQual:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GarageArea                                                      -1.083e-04
## YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GarageArea                                                        -2.254e-07
## OverallQual:YearBuilt:YearRemodAdd:GrLivArea:GarageArea                                                         6.333e-04
## OverallQual:YearBuilt:TotalBsmtSF:GrLivArea:GarageArea                                                         -1.127e-03
## OverallQual:YearRemodAdd:TotalBsmtSF:GrLivArea:GarageArea                                                       4.114e-04
## YearBuilt:YearRemodAdd:TotalBsmtSF:GrLivArea:GarageArea                                                         5.086e-06
## OverallQual:YearBuilt:X1stFlrSF:GrLivArea:GarageArea                                                            8.152e-04
## OverallQual:YearRemodAdd:X1stFlrSF:GrLivArea:GarageArea                                                         9.639e-05
## YearBuilt:YearRemodAdd:X1stFlrSF:GrLivArea:GarageArea                                                          -2.373e-06
## OverallQual:TotalBsmtSF:X1stFlrSF:GrLivArea:GarageArea                                                          3.523e-04
## YearBuilt:TotalBsmtSF:X1stFlrSF:GrLivArea:GarageArea                                                            2.167e-07
## YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:GarageArea                                                        -2.918e-07
## OverallQual:YearBuilt:YearRemodAdd:FullBath:GarageArea                                                         -9.967e-02
## OverallQual:YearBuilt:TotalBsmtSF:FullBath:GarageArea                                                           5.444e-01
## OverallQual:YearRemodAdd:TotalBsmtSF:FullBath:GarageArea                                                       -8.235e-01
## YearBuilt:YearRemodAdd:TotalBsmtSF:FullBath:GarageArea                                                          4.962e-04
## OverallQual:YearBuilt:X1stFlrSF:FullBath:GarageArea                                                            -1.267e+00
## OverallQual:YearRemodAdd:X1stFlrSF:FullBath:GarageArea                                                          1.395e+00
## YearBuilt:YearRemodAdd:X1stFlrSF:FullBath:GarageArea                                                           -6.558e-04
## OverallQual:TotalBsmtSF:X1stFlrSF:FullBath:GarageArea                                                           1.600e-01
## YearBuilt:TotalBsmtSF:X1stFlrSF:FullBath:GarageArea                                                            -3.680e-04
## YearRemodAdd:TotalBsmtSF:X1stFlrSF:FullBath:GarageArea                                                         -1.597e-04
## OverallQual:YearBuilt:GrLivArea:FullBath:GarageArea                                                            -3.008e-01
## OverallQual:YearRemodAdd:GrLivArea:FullBath:GarageArea                                                         -9.919e-02
## YearBuilt:YearRemodAdd:GrLivArea:FullBath:GarageArea                                                            1.895e-04
## OverallQual:TotalBsmtSF:GrLivArea:FullBath:GarageArea                                                          -7.142e-02
## YearBuilt:TotalBsmtSF:GrLivArea:FullBath:GarageArea                                                            -7.746e-04
## YearRemodAdd:TotalBsmtSF:GrLivArea:FullBath:GarageArea                                                          3.121e-03
## OverallQual:X1stFlrSF:GrLivArea:FullBath:GarageArea                                                            -4.439e-01
## YearBuilt:X1stFlrSF:GrLivArea:FullBath:GarageArea                                                              -2.049e-03
## YearRemodAdd:X1stFlrSF:GrLivArea:FullBath:GarageArea                                                           -1.121e-03
## TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:GarageArea                                                            -6.696e-04
## OverallQual:YearBuilt:YearRemodAdd:TotRmsAbvGrd:GarageArea                                                     -3.935e-02
## OverallQual:YearBuilt:TotalBsmtSF:TotRmsAbvGrd:GarageArea                                                      -1.113e-01
## OverallQual:YearRemodAdd:TotalBsmtSF:TotRmsAbvGrd:GarageArea                                                   -6.152e-02
## YearBuilt:YearRemodAdd:TotalBsmtSF:TotRmsAbvGrd:GarageArea                                                     -2.620e-04
## OverallQual:YearBuilt:X1stFlrSF:TotRmsAbvGrd:GarageArea                                                         8.021e-02
## OverallQual:YearRemodAdd:X1stFlrSF:TotRmsAbvGrd:GarageArea                                                      6.214e-02
## YearBuilt:YearRemodAdd:X1stFlrSF:TotRmsAbvGrd:GarageArea                                                               NA
## OverallQual:TotalBsmtSF:X1stFlrSF:TotRmsAbvGrd:GarageArea                                                      -5.979e-02
## YearBuilt:TotalBsmtSF:X1stFlrSF:TotRmsAbvGrd:GarageArea                                                         3.165e-05
## YearRemodAdd:TotalBsmtSF:X1stFlrSF:TotRmsAbvGrd:GarageArea                                                     -3.919e-04
## OverallQual:YearBuilt:GrLivArea:TotRmsAbvGrd:GarageArea                                                        -5.625e-02
## OverallQual:YearRemodAdd:GrLivArea:TotRmsAbvGrd:GarageArea                                                      1.963e-02
## YearBuilt:YearRemodAdd:GrLivArea:TotRmsAbvGrd:GarageArea                                                        1.725e-04
## OverallQual:TotalBsmtSF:GrLivArea:TotRmsAbvGrd:GarageArea                                                      -1.835e-01
## YearBuilt:TotalBsmtSF:GrLivArea:TotRmsAbvGrd:GarageArea                                                        -2.115e-04
## YearRemodAdd:TotalBsmtSF:GrLivArea:TotRmsAbvGrd:GarageArea                                                      2.868e-04
## OverallQual:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageArea                                                         1.809e-01
## YearBuilt:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageArea                                                          -1.598e-04
## YearRemodAdd:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageArea                                                        1.943e-04
## TotalBsmtSF:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageArea                                                        -2.704e-04
## OverallQual:YearBuilt:FullBath:TotRmsAbvGrd:GarageArea                                                         -5.241e+01
## OverallQual:YearRemodAdd:FullBath:TotRmsAbvGrd:GarageArea                                                       2.997e+01
## YearBuilt:YearRemodAdd:FullBath:TotRmsAbvGrd:GarageArea                                                         1.080e-02
## OverallQual:TotalBsmtSF:FullBath:TotRmsAbvGrd:GarageArea                                                        7.727e+00
## YearBuilt:TotalBsmtSF:FullBath:TotRmsAbvGrd:GarageArea                                                          3.786e-01
## YearRemodAdd:TotalBsmtSF:FullBath:TotRmsAbvGrd:GarageArea                                                      -4.014e-01
## OverallQual:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageArea                                                         -2.005e+01
## YearBuilt:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageArea                                                            3.234e-01
## YearRemodAdd:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageArea                                                        -1.772e-01
## TotalBsmtSF:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageArea                                                         -1.186e-01
## OverallQual:GrLivArea:FullBath:TotRmsAbvGrd:GarageArea                                                         -3.149e+01
## YearBuilt:GrLivArea:FullBath:TotRmsAbvGrd:GarageArea                                                           -1.380e-01
## YearRemodAdd:GrLivArea:FullBath:TotRmsAbvGrd:GarageArea                                                         1.067e-01
## TotalBsmtSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageArea                                                          7.273e-01
## X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageArea                                                           -3.354e-01
## OverallQual:YearBuilt:YearRemodAdd:GarageCars:GarageArea                                                       -2.743e-03
## OverallQual:YearBuilt:TotalBsmtSF:GarageCars:GarageArea                                                        -2.072e-02
## OverallQual:YearRemodAdd:TotalBsmtSF:GarageCars:GarageArea                                                     -3.728e-01
## YearBuilt:YearRemodAdd:TotalBsmtSF:GarageCars:GarageArea                                                        1.028e-04
## OverallQual:YearBuilt:X1stFlrSF:GarageCars:GarageArea                                                          -1.119e-01
## OverallQual:YearRemodAdd:X1stFlrSF:GarageCars:GarageArea                                                        4.343e-01
## YearBuilt:YearRemodAdd:X1stFlrSF:GarageCars:GarageArea                                                          1.096e-03
## OverallQual:TotalBsmtSF:X1stFlrSF:GarageCars:GarageArea                                                        -1.437e-01
## YearBuilt:TotalBsmtSF:X1stFlrSF:GarageCars:GarageArea                                                          -6.643e-04
## YearRemodAdd:TotalBsmtSF:X1stFlrSF:GarageCars:GarageArea                                                       -3.064e-04
## OverallQual:YearBuilt:GrLivArea:GarageCars:GarageArea                                                          -1.322e-01
## OverallQual:YearRemodAdd:GrLivArea:GarageCars:GarageArea                                                       -8.739e-02
## YearBuilt:YearRemodAdd:GrLivArea:GarageCars:GarageArea                                                          1.835e-04
## OverallQual:TotalBsmtSF:GrLivArea:GarageCars:GarageArea                                                        -4.584e-01
## YearBuilt:TotalBsmtSF:GrLivArea:GarageCars:GarageArea                                                          -1.671e-03
## YearRemodAdd:TotalBsmtSF:GrLivArea:GarageCars:GarageArea                                                        1.408e-03
## OverallQual:X1stFlrSF:GrLivArea:GarageCars:GarageArea                                                           3.293e-01
## YearBuilt:X1stFlrSF:GrLivArea:GarageCars:GarageArea                                                             1.774e-03
## YearRemodAdd:X1stFlrSF:GrLivArea:GarageCars:GarageArea                                                         -1.745e-03
## TotalBsmtSF:X1stFlrSF:GrLivArea:GarageCars:GarageArea                                                          -5.575e-04
## OverallQual:YearBuilt:FullBath:GarageCars:GarageArea                                                           -1.977e+02
## OverallQual:YearRemodAdd:FullBath:GarageCars:GarageArea                                                         8.276e+01
## YearBuilt:YearRemodAdd:FullBath:GarageCars:GarageArea                                                           1.090e+00
## OverallQual:TotalBsmtSF:FullBath:GarageCars:GarageArea                                                         -4.804e+02
## YearBuilt:TotalBsmtSF:FullBath:GarageCars:GarageArea                                                           -1.192e+00
## YearRemodAdd:TotalBsmtSF:FullBath:GarageCars:GarageArea                                                        -1.840e+00
## OverallQual:X1stFlrSF:FullBath:GarageCars:GarageArea                                                            3.321e+02
## YearBuilt:X1stFlrSF:FullBath:GarageCars:GarageArea                                                             -7.671e-01
## YearRemodAdd:X1stFlrSF:FullBath:GarageCars:GarageArea                                                           2.583e+00
## TotalBsmtSF:X1stFlrSF:FullBath:GarageCars:GarageArea                                                           -1.106e+00
## OverallQual:GrLivArea:FullBath:GarageCars:GarageArea                                                           -2.368e+02
## YearBuilt:GrLivArea:FullBath:GarageCars:GarageArea                                                             -2.471e-01
## YearRemodAdd:GrLivArea:FullBath:GarageCars:GarageArea                                                          -6.716e-01
## TotalBsmtSF:GrLivArea:FullBath:GarageCars:GarageArea                                                            5.163e-02
## X1stFlrSF:GrLivArea:FullBath:GarageCars:GarageArea                                                             -1.092e+00
## OverallQual:YearBuilt:TotRmsAbvGrd:GarageCars:GarageArea                                                       -4.610e+01
## OverallQual:YearRemodAdd:TotRmsAbvGrd:GarageCars:GarageArea                                                     3.634e+01
## YearBuilt:YearRemodAdd:TotRmsAbvGrd:GarageCars:GarageArea                                                       7.620e-02
## OverallQual:TotalBsmtSF:TotRmsAbvGrd:GarageCars:GarageArea                                                      4.220e+01
## YearBuilt:TotalBsmtSF:TotRmsAbvGrd:GarageCars:GarageArea                                                        7.061e-02
## YearRemodAdd:TotalBsmtSF:TotRmsAbvGrd:GarageCars:GarageArea                                                    -7.235e-02
## OverallQual:X1stFlrSF:TotRmsAbvGrd:GarageCars:GarageArea                                                       -2.736e+01
## YearBuilt:X1stFlrSF:TotRmsAbvGrd:GarageCars:GarageArea                                                          5.909e-02
## YearRemodAdd:X1stFlrSF:TotRmsAbvGrd:GarageCars:GarageArea                                                       1.304e-01
## TotalBsmtSF:X1stFlrSF:TotRmsAbvGrd:GarageCars:GarageArea                                                        9.631e-02
## OverallQual:GrLivArea:TotRmsAbvGrd:GarageCars:GarageArea                                                       -5.607e+01
## YearBuilt:GrLivArea:TotRmsAbvGrd:GarageCars:GarageArea                                                         -1.405e-01
## YearRemodAdd:GrLivArea:TotRmsAbvGrd:GarageCars:GarageArea                                                      -4.545e-02
## TotalBsmtSF:GrLivArea:TotRmsAbvGrd:GarageCars:GarageArea                                                        1.423e-01
## X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageCars:GarageArea                                                         -1.625e-01
## OverallQual:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                                        -1.020e+04
## YearBuilt:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                                          -1.232e+02
## YearRemodAdd:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                                        2.046e+00
## TotalBsmtSF:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                                        -4.871e+02
## X1stFlrSF:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                                           2.219e+02
## GrLivArea:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                                          -1.539e+02
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea                                                     NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:FullBath                                                      NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:GrLivArea:FullBath                                                      NA
## OverallQual:YearBuilt:YearRemodAdd:X1stFlrSF:GrLivArea:FullBath                                                        NA
## OverallQual:YearBuilt:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath                                                  4.953e-06
## OverallQual:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath                                              -4.070e-06
## YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath                                                        NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:TotRmsAbvGrd                                                  NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:GrLivArea:TotRmsAbvGrd                                                  NA
## OverallQual:YearBuilt:YearRemodAdd:X1stFlrSF:GrLivArea:TotRmsAbvGrd                                                    NA
## OverallQual:YearBuilt:TotalBsmtSF:X1stFlrSF:GrLivArea:TotRmsAbvGrd                                             -2.082e-05
## OverallQual:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:TotRmsAbvGrd                                           8.130e-06
## YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:TotRmsAbvGrd                                                    NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:FullBath:TotRmsAbvGrd                                                   NA
## OverallQual:YearBuilt:YearRemodAdd:X1stFlrSF:FullBath:TotRmsAbvGrd                                                     NA
## OverallQual:YearBuilt:TotalBsmtSF:X1stFlrSF:FullBath:TotRmsAbvGrd                                              -1.913e-02
## OverallQual:YearRemodAdd:TotalBsmtSF:X1stFlrSF:FullBath:TotRmsAbvGrd                                            3.388e-02
## YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:FullBath:TotRmsAbvGrd                                                     NA
## OverallQual:YearBuilt:YearRemodAdd:GrLivArea:FullBath:TotRmsAbvGrd                                                     NA
## OverallQual:YearBuilt:TotalBsmtSF:GrLivArea:FullBath:TotRmsAbvGrd                                               1.937e-02
## OverallQual:YearRemodAdd:TotalBsmtSF:GrLivArea:FullBath:TotRmsAbvGrd                                           -3.621e-03
## YearBuilt:YearRemodAdd:TotalBsmtSF:GrLivArea:FullBath:TotRmsAbvGrd                                                     NA
## OverallQual:YearBuilt:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd                                                 1.278e-04
## OverallQual:YearRemodAdd:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd                                             -1.838e-02
## YearBuilt:YearRemodAdd:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd                                                       NA
## OverallQual:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd                                               1.363e-03
## YearBuilt:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd                                                 3.111e-08
## YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd                                             -9.366e-06
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GarageCars                                                    NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:GrLivArea:GarageCars                                                    NA
## OverallQual:YearBuilt:YearRemodAdd:X1stFlrSF:GrLivArea:GarageCars                                                      NA
## OverallQual:YearBuilt:TotalBsmtSF:X1stFlrSF:GrLivArea:GarageCars                                               -4.386e-05
## OverallQual:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:GarageCars                                            -3.859e-06
## YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:GarageCars                                                      NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:FullBath:GarageCars                                                     NA
## OverallQual:YearBuilt:YearRemodAdd:X1stFlrSF:FullBath:GarageCars                                                       NA
## OverallQual:YearBuilt:TotalBsmtSF:X1stFlrSF:FullBath:GarageCars                                                -3.595e-02
## OverallQual:YearRemodAdd:TotalBsmtSF:X1stFlrSF:FullBath:GarageCars                                              2.529e-02
## YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:FullBath:GarageCars                                                       NA
## OverallQual:YearBuilt:YearRemodAdd:GrLivArea:FullBath:GarageCars                                                       NA
## OverallQual:YearBuilt:TotalBsmtSF:GrLivArea:FullBath:GarageCars                                                 1.459e-01
## OverallQual:YearRemodAdd:TotalBsmtSF:GrLivArea:FullBath:GarageCars                                              1.628e-02
## YearBuilt:YearRemodAdd:TotalBsmtSF:GrLivArea:FullBath:GarageCars                                                       NA
## OverallQual:YearBuilt:X1stFlrSF:GrLivArea:FullBath:GarageCars                                                  -1.312e-01
## OverallQual:YearRemodAdd:X1stFlrSF:GrLivArea:FullBath:GarageCars                                                5.011e-02
## YearBuilt:YearRemodAdd:X1stFlrSF:GrLivArea:FullBath:GarageCars                                                         NA
## OverallQual:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:GarageCars                                                 1.841e-03
## YearBuilt:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:GarageCars                                                  -1.810e-04
## YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:GarageCars                                                4.032e-04
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:TotRmsAbvGrd:GarageCars                                                 NA
## OverallQual:YearBuilt:YearRemodAdd:X1stFlrSF:TotRmsAbvGrd:GarageCars                                                   NA
## OverallQual:YearBuilt:TotalBsmtSF:X1stFlrSF:TotRmsAbvGrd:GarageCars                                             5.054e-03
## OverallQual:YearRemodAdd:TotalBsmtSF:X1stFlrSF:TotRmsAbvGrd:GarageCars                                         -2.594e-02
## YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:TotRmsAbvGrd:GarageCars                                                   NA
## OverallQual:YearBuilt:YearRemodAdd:GrLivArea:TotRmsAbvGrd:GarageCars                                                   NA
## OverallQual:YearBuilt:TotalBsmtSF:GrLivArea:TotRmsAbvGrd:GarageCars                                            -3.612e-02
## OverallQual:YearRemodAdd:TotalBsmtSF:GrLivArea:TotRmsAbvGrd:GarageCars                                          1.114e-02
## YearBuilt:YearRemodAdd:TotalBsmtSF:GrLivArea:TotRmsAbvGrd:GarageCars                                                   NA
## OverallQual:YearBuilt:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageCars                                               2.037e-02
## OverallQual:YearRemodAdd:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageCars                                            6.122e-04
## YearBuilt:YearRemodAdd:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageCars                                                     NA
## OverallQual:TotalBsmtSF:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageCars                                            -1.981e-02
## YearBuilt:TotalBsmtSF:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageCars                                              -1.017e-04
## YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageCars                                            1.874e-05
## OverallQual:YearBuilt:YearRemodAdd:FullBath:TotRmsAbvGrd:GarageCars                                                    NA
## OverallQual:YearBuilt:TotalBsmtSF:FullBath:TotRmsAbvGrd:GarageCars                                             -1.915e+01
## OverallQual:YearRemodAdd:TotalBsmtSF:FullBath:TotRmsAbvGrd:GarageCars                                           2.484e+01
## YearBuilt:YearRemodAdd:TotalBsmtSF:FullBath:TotRmsAbvGrd:GarageCars                                                    NA
## OverallQual:YearBuilt:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageCars                                               -1.411e+01
## OverallQual:YearRemodAdd:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageCars                                                    NA
## YearBuilt:YearRemodAdd:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageCars                                                      NA
## OverallQual:TotalBsmtSF:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageCars                                              4.596e-02
## YearBuilt:TotalBsmtSF:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageCars                                                1.820e-01
## YearRemodAdd:TotalBsmtSF:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageCars                                            -1.500e-01
## OverallQual:YearBuilt:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars                                                7.086e-01
## OverallQual:YearRemodAdd:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars                                            -1.251e+00
## YearBuilt:YearRemodAdd:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars                                                      NA
## OverallQual:TotalBsmtSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars                                             -1.266e+00
## YearBuilt:TotalBsmtSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars                                                5.905e-02
## YearRemodAdd:TotalBsmtSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars                                             3.525e-02
## OverallQual:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars                                                6.737e-01
## YearBuilt:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars                                                 -2.872e-02
## YearRemodAdd:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars                                               3.414e-02
## TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars                                               -2.446e-04
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GarageArea                                                    NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:GrLivArea:GarageArea                                                    NA
## OverallQual:YearBuilt:YearRemodAdd:X1stFlrSF:GrLivArea:GarageArea                                                      NA
## OverallQual:YearBuilt:TotalBsmtSF:X1stFlrSF:GrLivArea:GarageArea                                               -1.973e-07
## OverallQual:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:GarageArea                                                    NA
## YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:GarageArea                                                      NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:FullBath:GarageArea                                                     NA
## OverallQual:YearBuilt:YearRemodAdd:X1stFlrSF:FullBath:GarageArea                                                       NA
## OverallQual:YearBuilt:TotalBsmtSF:X1stFlrSF:FullBath:GarageArea                                                 4.404e-05
## OverallQual:YearRemodAdd:TotalBsmtSF:X1stFlrSF:FullBath:GarageArea                                             -1.495e-04
## YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:FullBath:GarageArea                                                       NA
## OverallQual:YearBuilt:YearRemodAdd:GrLivArea:FullBath:GarageArea                                                       NA
## OverallQual:YearBuilt:TotalBsmtSF:GrLivArea:FullBath:GarageArea                                                 7.508e-05
## OverallQual:YearRemodAdd:TotalBsmtSF:GrLivArea:FullBath:GarageArea                                                     NA
## YearBuilt:YearRemodAdd:TotalBsmtSF:GrLivArea:FullBath:GarageArea                                                       NA
## OverallQual:YearBuilt:X1stFlrSF:GrLivArea:FullBath:GarageArea                                                   2.679e-04
## OverallQual:YearRemodAdd:X1stFlrSF:GrLivArea:FullBath:GarageArea                                               -9.295e-05
## YearBuilt:YearRemodAdd:X1stFlrSF:GrLivArea:FullBath:GarageArea                                                         NA
## OverallQual:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:GarageArea                                                 2.135e-05
## YearBuilt:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:GarageArea                                                   3.059e-07
## YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:GarageArea                                                       NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:TotRmsAbvGrd:GarageArea                                                 NA
## OverallQual:YearBuilt:YearRemodAdd:X1stFlrSF:TotRmsAbvGrd:GarageArea                                                   NA
## OverallQual:YearBuilt:TotalBsmtSF:X1stFlrSF:TotRmsAbvGrd:GarageArea                                             2.464e-05
## OverallQual:YearRemodAdd:TotalBsmtSF:X1stFlrSF:TotRmsAbvGrd:GarageArea                                                 NA
## YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:TotRmsAbvGrd:GarageArea                                                   NA
## OverallQual:YearBuilt:YearRemodAdd:GrLivArea:TotRmsAbvGrd:GarageArea                                                   NA
## OverallQual:YearBuilt:TotalBsmtSF:GrLivArea:TotRmsAbvGrd:GarageArea                                             9.723e-05
## OverallQual:YearRemodAdd:TotalBsmtSF:GrLivArea:TotRmsAbvGrd:GarageArea                                                 NA
## YearBuilt:YearRemodAdd:TotalBsmtSF:GrLivArea:TotRmsAbvGrd:GarageArea                                                   NA
## OverallQual:YearBuilt:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageArea                                              -6.063e-05
## OverallQual:YearRemodAdd:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageArea                                           -3.684e-05
## YearBuilt:YearRemodAdd:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageArea                                                     NA
## OverallQual:TotalBsmtSF:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageArea                                             4.045e-06
## YearBuilt:TotalBsmtSF:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageArea                                               1.305e-07
## YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageArea                                                   NA
## OverallQual:YearBuilt:YearRemodAdd:FullBath:TotRmsAbvGrd:GarageArea                                                    NA
## OverallQual:YearBuilt:TotalBsmtSF:FullBath:TotRmsAbvGrd:GarageArea                                             -2.088e-02
## OverallQual:YearRemodAdd:TotalBsmtSF:FullBath:TotRmsAbvGrd:GarageArea                                           2.268e-02
## YearBuilt:YearRemodAdd:TotalBsmtSF:FullBath:TotRmsAbvGrd:GarageArea                                                    NA
## OverallQual:YearBuilt:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageArea                                                       NA
## OverallQual:YearRemodAdd:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageArea                                                    NA
## YearBuilt:YearRemodAdd:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageArea                                                      NA
## OverallQual:TotalBsmtSF:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageArea                                              5.132e-03
## YearBuilt:TotalBsmtSF:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageArea                                               -2.111e-04
## YearRemodAdd:TotalBsmtSF:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageArea                                             2.637e-04
## OverallQual:YearBuilt:GrLivArea:FullBath:TotRmsAbvGrd:GarageArea                                                1.422e-02
## OverallQual:YearRemodAdd:GrLivArea:FullBath:TotRmsAbvGrd:GarageArea                                             2.110e-03
## YearBuilt:YearRemodAdd:GrLivArea:FullBath:TotRmsAbvGrd:GarageArea                                                      NA
## OverallQual:TotalBsmtSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageArea                                             -8.070e-03
## YearBuilt:TotalBsmtSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageArea                                               -1.591e-04
## YearRemodAdd:TotalBsmtSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageArea                                            -1.800e-04
## OverallQual:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageArea                                                9.205e-03
## YearBuilt:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageArea                                                  1.520e-04
## YearRemodAdd:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageArea                                                      NA
## TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageArea                                                9.840e-07
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:GarageCars:GarageArea                                                   NA
## OverallQual:YearBuilt:YearRemodAdd:X1stFlrSF:GarageCars:GarageArea                                                     NA
## OverallQual:YearBuilt:TotalBsmtSF:X1stFlrSF:GarageCars:GarageArea                                               1.860e-06
## OverallQual:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GarageCars:GarageArea                                            5.830e-05
## YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GarageCars:GarageArea                                                     NA
## OverallQual:YearBuilt:YearRemodAdd:GrLivArea:GarageCars:GarageArea                                                     NA
## OverallQual:YearBuilt:TotalBsmtSF:GrLivArea:GarageCars:GarageArea                                               3.326e-04
## OverallQual:YearRemodAdd:TotalBsmtSF:GrLivArea:GarageCars:GarageArea                                           -7.294e-05
## YearBuilt:YearRemodAdd:TotalBsmtSF:GrLivArea:GarageCars:GarageArea                                                     NA
## OverallQual:YearBuilt:X1stFlrSF:GrLivArea:GarageCars:GarageArea                                                -2.572e-04
## OverallQual:YearRemodAdd:X1stFlrSF:GrLivArea:GarageCars:GarageArea                                              6.356e-05
## YearBuilt:YearRemodAdd:X1stFlrSF:GrLivArea:GarageCars:GarageArea                                                       NA
## OverallQual:TotalBsmtSF:X1stFlrSF:GrLivArea:GarageCars:GarageArea                                               7.979e-06
## YearBuilt:TotalBsmtSF:X1stFlrSF:GrLivArea:GarageCars:GarageArea                                                -3.309e-08
## YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:GarageCars:GarageArea                                              3.009e-07
## OverallQual:YearBuilt:YearRemodAdd:FullBath:GarageCars:GarageArea                                                      NA
## OverallQual:YearBuilt:TotalBsmtSF:FullBath:GarageCars:GarageArea                                               -2.568e-01
## OverallQual:YearRemodAdd:TotalBsmtSF:FullBath:GarageCars:GarageArea                                             5.248e-01
## YearBuilt:YearRemodAdd:TotalBsmtSF:FullBath:GarageCars:GarageArea                                                      NA
## OverallQual:YearBuilt:X1stFlrSF:FullBath:GarageCars:GarageArea                                                  3.782e-01
## OverallQual:YearRemodAdd:X1stFlrSF:FullBath:GarageCars:GarageArea                                              -5.806e-01
## YearBuilt:YearRemodAdd:X1stFlrSF:FullBath:GarageCars:GarageArea                                                        NA
## OverallQual:TotalBsmtSF:X1stFlrSF:FullBath:GarageCars:GarageArea                                                3.129e-02
## YearBuilt:TotalBsmtSF:X1stFlrSF:FullBath:GarageCars:GarageArea                                                  7.604e-04
## YearRemodAdd:TotalBsmtSF:X1stFlrSF:FullBath:GarageCars:GarageArea                                              -2.138e-04
## OverallQual:YearBuilt:GrLivArea:FullBath:GarageCars:GarageArea                                                  3.167e-03
## OverallQual:YearRemodAdd:GrLivArea:FullBath:GarageCars:GarageArea                                               1.220e-01
## YearBuilt:YearRemodAdd:GrLivArea:FullBath:GarageCars:GarageArea                                                        NA
## OverallQual:TotalBsmtSF:GrLivArea:FullBath:GarageCars:GarageArea                                                4.035e-02
## YearBuilt:TotalBsmtSF:GrLivArea:FullBath:GarageCars:GarageArea                                                  1.024e-03
## YearRemodAdd:TotalBsmtSF:GrLivArea:FullBath:GarageCars:GarageArea                                              -9.105e-04
## OverallQual:X1stFlrSF:GrLivArea:FullBath:GarageCars:GarageArea                                                  3.727e-02
## YearBuilt:X1stFlrSF:GrLivArea:FullBath:GarageCars:GarageArea                                                   -4.854e-04
## YearRemodAdd:X1stFlrSF:GrLivArea:FullBath:GarageCars:GarageArea                                                 9.363e-04
## TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:GarageCars:GarageArea                                                  2.312e-04
## OverallQual:YearBuilt:YearRemodAdd:TotRmsAbvGrd:GarageCars:GarageArea                                                  NA
## OverallQual:YearBuilt:TotalBsmtSF:TotRmsAbvGrd:GarageCars:GarageArea                                           -1.661e-03
## OverallQual:YearRemodAdd:TotalBsmtSF:TotRmsAbvGrd:GarageCars:GarageArea                                        -1.771e-02
## YearBuilt:YearRemodAdd:TotalBsmtSF:TotRmsAbvGrd:GarageCars:GarageArea                                                  NA
## OverallQual:YearBuilt:X1stFlrSF:TotRmsAbvGrd:GarageCars:GarageArea                                              9.065e-03
## OverallQual:YearRemodAdd:X1stFlrSF:TotRmsAbvGrd:GarageCars:GarageArea                                                  NA
## YearBuilt:YearRemodAdd:X1stFlrSF:TotRmsAbvGrd:GarageCars:GarageArea                                                    NA
## OverallQual:TotalBsmtSF:X1stFlrSF:TotRmsAbvGrd:GarageCars:GarageArea                                           -6.863e-03
## YearBuilt:TotalBsmtSF:X1stFlrSF:TotRmsAbvGrd:GarageCars:GarageArea                                             -3.237e-05
## YearRemodAdd:TotalBsmtSF:X1stFlrSF:TotRmsAbvGrd:GarageCars:GarageArea                                          -2.272e-05
## OverallQual:YearBuilt:GrLivArea:TotRmsAbvGrd:GarageCars:GarageArea                                              2.959e-02
## OverallQual:YearRemodAdd:GrLivArea:TotRmsAbvGrd:GarageCars:GarageArea                                          -2.923e-04
## YearBuilt:YearRemodAdd:GrLivArea:TotRmsAbvGrd:GarageCars:GarageArea                                                    NA
## OverallQual:TotalBsmtSF:GrLivArea:TotRmsAbvGrd:GarageCars:GarageArea                                            9.624e-03
## YearBuilt:TotalBsmtSF:GrLivArea:TotRmsAbvGrd:GarageCars:GarageArea                                             -7.572e-05
## YearRemodAdd:TotalBsmtSF:GrLivArea:TotRmsAbvGrd:GarageCars:GarageArea                                           1.758e-05
## OverallQual:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageCars:GarageArea                                              4.652e-03
## YearBuilt:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageCars:GarageArea                                                5.309e-05
## YearRemodAdd:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageCars:GarageArea                                             1.957e-05
## TotalBsmtSF:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageCars:GarageArea                                              1.830e-06
## OverallQual:YearBuilt:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                               2.802e+01
## OverallQual:YearRemodAdd:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                           -2.308e+01
## YearBuilt:YearRemodAdd:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                                     NA
## OverallQual:TotalBsmtSF:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                            -5.812e+00
## YearBuilt:TotalBsmtSF:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                               7.825e-02
## YearRemodAdd:TotalBsmtSF:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                            1.867e-01
## OverallQual:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                               8.255e+00
## YearBuilt:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                                        NA
## YearRemodAdd:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                                     NA
## TotalBsmtSF:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                               3.013e-03
## OverallQual:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                               1.532e+01
## YearBuilt:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                                 7.612e-02
## YearRemodAdd:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                              1.047e-02
## TotalBsmtSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                              -2.924e-02
## X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                                 2.386e-02
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath                                            NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:TotRmsAbvGrd                                        NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:FullBath:TotRmsAbvGrd                                         NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:GrLivArea:FullBath:TotRmsAbvGrd                                         NA
## OverallQual:YearBuilt:YearRemodAdd:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd                                           NA
## OverallQual:YearBuilt:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd                                            NA
## OverallQual:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd                                         NA
## YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd                                           NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:GarageCars                                          NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:FullBath:GarageCars                                           NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:GrLivArea:FullBath:GarageCars                                           NA
## OverallQual:YearBuilt:YearRemodAdd:X1stFlrSF:GrLivArea:FullBath:GarageCars                                             NA
## OverallQual:YearBuilt:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:GarageCars                                              NA
## OverallQual:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:GarageCars                                           NA
## YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:GarageCars                                             NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:TotRmsAbvGrd:GarageCars                                       NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:GrLivArea:TotRmsAbvGrd:GarageCars                                       NA
## OverallQual:YearBuilt:YearRemodAdd:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageCars                                         NA
## OverallQual:YearBuilt:TotalBsmtSF:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageCars                                   1.018e-05
## OverallQual:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageCars                                       NA
## YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageCars                                         NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:FullBath:TotRmsAbvGrd:GarageCars                                        NA
## OverallQual:YearBuilt:YearRemodAdd:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageCars                                          NA
## OverallQual:YearBuilt:TotalBsmtSF:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageCars                                           NA
## OverallQual:YearRemodAdd:TotalBsmtSF:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageCars                                        NA
## YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageCars                                          NA
## OverallQual:YearBuilt:YearRemodAdd:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars                                          NA
## OverallQual:YearBuilt:TotalBsmtSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars                                           NA
## OverallQual:YearRemodAdd:TotalBsmtSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars                                        NA
## YearBuilt:YearRemodAdd:TotalBsmtSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars                                          NA
## OverallQual:YearBuilt:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars                                             NA
## OverallQual:YearRemodAdd:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars                                          NA
## YearBuilt:YearRemodAdd:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars                                            NA
## OverallQual:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars                                    1.593e-03
## YearBuilt:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars                                             NA
## YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars                                          NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:GarageArea                                          NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:FullBath:GarageArea                                           NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:GrLivArea:FullBath:GarageArea                                           NA
## OverallQual:YearBuilt:YearRemodAdd:X1stFlrSF:GrLivArea:FullBath:GarageArea                                             NA
## OverallQual:YearBuilt:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:GarageArea                                              NA
## OverallQual:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:GarageArea                                           NA
## YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:GarageArea                                             NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:TotRmsAbvGrd:GarageArea                                       NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:GrLivArea:TotRmsAbvGrd:GarageArea                                       NA
## OverallQual:YearBuilt:YearRemodAdd:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageArea                                         NA
## OverallQual:YearBuilt:TotalBsmtSF:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageArea                                          NA
## OverallQual:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageArea                                       NA
## YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageArea                                         NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:FullBath:TotRmsAbvGrd:GarageArea                                        NA
## OverallQual:YearBuilt:YearRemodAdd:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageArea                                          NA
## OverallQual:YearBuilt:TotalBsmtSF:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageArea                                           NA
## OverallQual:YearRemodAdd:TotalBsmtSF:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageArea                                        NA
## YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageArea                                          NA
## OverallQual:YearBuilt:YearRemodAdd:GrLivArea:FullBath:TotRmsAbvGrd:GarageArea                                          NA
## OverallQual:YearBuilt:TotalBsmtSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageArea                                           NA
## OverallQual:YearRemodAdd:TotalBsmtSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageArea                                        NA
## YearBuilt:YearRemodAdd:TotalBsmtSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageArea                                          NA
## OverallQual:YearBuilt:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageArea                                             NA
## OverallQual:YearRemodAdd:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageArea                                          NA
## YearBuilt:YearRemodAdd:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageArea                                            NA
## OverallQual:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageArea                                   -1.946e-06
## YearBuilt:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageArea                                             NA
## YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageArea                                          NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GarageCars:GarageArea                                         NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:GrLivArea:GarageCars:GarageArea                                         NA
## OverallQual:YearBuilt:YearRemodAdd:X1stFlrSF:GrLivArea:GarageCars:GarageArea                                           NA
## OverallQual:YearBuilt:TotalBsmtSF:X1stFlrSF:GrLivArea:GarageCars:GarageArea                                            NA
## OverallQual:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:GarageCars:GarageArea                                         NA
## YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:GarageCars:GarageArea                                           NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:FullBath:GarageCars:GarageArea                                          NA
## OverallQual:YearBuilt:YearRemodAdd:X1stFlrSF:FullBath:GarageCars:GarageArea                                            NA
## OverallQual:YearBuilt:TotalBsmtSF:X1stFlrSF:FullBath:GarageCars:GarageArea                                     -9.652e-06
## OverallQual:YearRemodAdd:TotalBsmtSF:X1stFlrSF:FullBath:GarageCars:GarageArea                                          NA
## YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:FullBath:GarageCars:GarageArea                                            NA
## OverallQual:YearBuilt:YearRemodAdd:GrLivArea:FullBath:GarageCars:GarageArea                                            NA
## OverallQual:YearBuilt:TotalBsmtSF:GrLivArea:FullBath:GarageCars:GarageArea                                             NA
## OverallQual:YearRemodAdd:TotalBsmtSF:GrLivArea:FullBath:GarageCars:GarageArea                                          NA
## YearBuilt:YearRemodAdd:TotalBsmtSF:GrLivArea:FullBath:GarageCars:GarageArea                                            NA
## OverallQual:YearBuilt:X1stFlrSF:GrLivArea:FullBath:GarageCars:GarageArea                                               NA
## OverallQual:YearRemodAdd:X1stFlrSF:GrLivArea:FullBath:GarageCars:GarageArea                                            NA
## YearBuilt:YearRemodAdd:X1stFlrSF:GrLivArea:FullBath:GarageCars:GarageArea                                              NA
## OverallQual:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:GarageCars:GarageArea                                     -1.503e-05
## YearBuilt:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:GarageCars:GarageArea                                               NA
## YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:GarageCars:GarageArea                                            NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:TotRmsAbvGrd:GarageCars:GarageArea                                      NA
## OverallQual:YearBuilt:YearRemodAdd:X1stFlrSF:TotRmsAbvGrd:GarageCars:GarageArea                                        NA
## OverallQual:YearBuilt:TotalBsmtSF:X1stFlrSF:TotRmsAbvGrd:GarageCars:GarageArea                                         NA
## OverallQual:YearRemodAdd:TotalBsmtSF:X1stFlrSF:TotRmsAbvGrd:GarageCars:GarageArea                               5.105e-06
## YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:TotRmsAbvGrd:GarageCars:GarageArea                                        NA
## OverallQual:YearBuilt:YearRemodAdd:GrLivArea:TotRmsAbvGrd:GarageCars:GarageArea                                        NA
## OverallQual:YearBuilt:TotalBsmtSF:GrLivArea:TotRmsAbvGrd:GarageCars:GarageArea                                         NA
## OverallQual:YearRemodAdd:TotalBsmtSF:GrLivArea:TotRmsAbvGrd:GarageCars:GarageArea                                      NA
## YearBuilt:YearRemodAdd:TotalBsmtSF:GrLivArea:TotRmsAbvGrd:GarageCars:GarageArea                                        NA
## OverallQual:YearBuilt:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageCars:GarageArea                                           NA
## OverallQual:YearRemodAdd:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageCars:GarageArea                                        NA
## YearBuilt:YearRemodAdd:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageCars:GarageArea                                          NA
## OverallQual:TotalBsmtSF:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageCars:GarageArea                                 -8.721e-07
## YearBuilt:TotalBsmtSF:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageCars:GarageArea                                           NA
## YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageCars:GarageArea                                        NA
## OverallQual:YearBuilt:YearRemodAdd:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                         NA
## OverallQual:YearBuilt:TotalBsmtSF:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                          NA
## OverallQual:YearRemodAdd:TotalBsmtSF:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                       NA
## YearBuilt:YearRemodAdd:TotalBsmtSF:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                         NA
## OverallQual:YearBuilt:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                            NA
## OverallQual:YearRemodAdd:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                         NA
## YearBuilt:YearRemodAdd:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                   -6.513e-05
## OverallQual:TotalBsmtSF:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                  -1.589e-03
## YearBuilt:TotalBsmtSF:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                            NA
## YearRemodAdd:TotalBsmtSF:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                         NA
## OverallQual:YearBuilt:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                    -8.597e-03
## OverallQual:YearRemodAdd:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                         NA
## YearBuilt:YearRemodAdd:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                           NA
## OverallQual:TotalBsmtSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                   4.542e-03
## YearBuilt:TotalBsmtSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                            NA
## YearRemodAdd:TotalBsmtSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                         NA
## OverallQual:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                    -1.140e-02
## YearBuilt:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                              NA
## YearRemodAdd:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                           NA
## TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                     1.810e-06
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd                               NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:GarageCars                                 NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageCars                             NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageCars                              NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars                              NA
## OverallQual:YearBuilt:YearRemodAdd:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars                                NA
## OverallQual:YearBuilt:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars                                 NA
## OverallQual:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars                              NA
## YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars                                NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:GarageArea                                 NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageArea                             NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageArea                              NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageArea                              NA
## OverallQual:YearBuilt:YearRemodAdd:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageArea                                NA
## OverallQual:YearBuilt:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageArea                                 NA
## OverallQual:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageArea                              NA
## YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageArea                                NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:GarageCars:GarageArea                               NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:FullBath:GarageCars:GarageArea                                NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:GrLivArea:FullBath:GarageCars:GarageArea                        -2.088e-08
## OverallQual:YearBuilt:YearRemodAdd:X1stFlrSF:GrLivArea:FullBath:GarageCars:GarageArea                                  NA
## OverallQual:YearBuilt:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:GarageCars:GarageArea                                   NA
## OverallQual:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:GarageCars:GarageArea                                NA
## YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:GarageCars:GarageArea                          -5.911e-11
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:TotRmsAbvGrd:GarageCars:GarageArea                            NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:GrLivArea:TotRmsAbvGrd:GarageCars:GarageArea                    -3.693e-09
## OverallQual:YearBuilt:YearRemodAdd:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageCars:GarageArea                              NA
## OverallQual:YearBuilt:TotalBsmtSF:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageCars:GarageArea                               NA
## OverallQual:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageCars:GarageArea                            NA
## YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageCars:GarageArea                              NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                             NA
## OverallQual:YearBuilt:YearRemodAdd:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                               NA
## OverallQual:YearBuilt:TotalBsmtSF:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                NA
## OverallQual:YearRemodAdd:TotalBsmtSF:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                             NA
## YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                               NA
## OverallQual:YearBuilt:YearRemodAdd:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                               NA
## OverallQual:YearBuilt:TotalBsmtSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                NA
## OverallQual:YearRemodAdd:TotalBsmtSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                             NA
## YearBuilt:YearRemodAdd:TotalBsmtSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                               NA
## OverallQual:YearBuilt:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                  NA
## OverallQual:YearRemodAdd:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                        3.920e-06
## YearBuilt:YearRemodAdd:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                         -2.415e-09
## OverallQual:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                         2.811e-07
## YearBuilt:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                  NA
## YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                               NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars            -4.426e-10
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageArea                    NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:GarageCars:GarageArea               2.967e-12
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageCars:GarageArea                  NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageCars:GarageArea           -1.049e-11
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                   NA
## OverallQual:YearBuilt:YearRemodAdd:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                     NA
## OverallQual:YearBuilt:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                      NA
## OverallQual:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                   NA
## YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                     NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars:GarageArea         NA
##                                                                                                                Std. Error
## (Intercept)                                                                                                     1.086e+10
## OverallQual                                                                                                     1.163e+09
## YearBuilt                                                                                                       5.855e+06
## YearRemodAdd                                                                                                    6.019e+06
## TotalBsmtSF                                                                                                     1.268e+07
## X1stFlrSF                                                                                                       1.266e+07
## GrLivArea                                                                                                       5.573e+06
## FullBath                                                                                                        1.119e+10
## TotRmsAbvGrd                                                                                                    1.348e+09
## GarageCars                                                                                                      5.280e+09
## GarageArea                                                                                                      1.477e+07
## OverallQual:YearBuilt                                                                                           6.231e+05
## OverallQual:YearRemodAdd                                                                                        6.538e+05
## YearBuilt:YearRemodAdd                                                                                          3.008e+03
## OverallQual:TotalBsmtSF                                                                                         1.645e+06
## YearBuilt:TotalBsmtSF                                                                                           6.388e+03
## YearRemodAdd:TotalBsmtSF                                                                                        6.679e+03
## OverallQual:X1stFlrSF                                                                                           1.667e+06
## YearBuilt:X1stFlrSF                                                                                             6.406e+03
## YearRemodAdd:X1stFlrSF                                                                                          6.828e+03
## TotalBsmtSF:X1stFlrSF                                                                                           3.812e+03
## OverallQual:GrLivArea                                                                                           7.450e+05
## YearBuilt:GrLivArea                                                                                             3.098e+03
## YearRemodAdd:GrLivArea                                                                                          3.110e+03
## TotalBsmtSF:GrLivArea                                                                                           6.824e+03
## X1stFlrSF:GrLivArea                                                                                             6.638e+03
## OverallQual:FullBath                                                                                            1.237e+09
## YearBuilt:FullBath                                                                                              5.893e+06
## YearRemodAdd:FullBath                                                                                           6.102e+06
## TotalBsmtSF:FullBath                                                                                            1.028e+07
## X1stFlrSF:FullBath                                                                                              1.148e+07
## GrLivArea:FullBath                                                                                              5.482e+06
## OverallQual:TotRmsAbvGrd                                                                                        1.731e+08
## YearBuilt:TotRmsAbvGrd                                                                                          7.449e+05
## YearRemodAdd:TotRmsAbvGrd                                                                                       7.098e+05
## TotalBsmtSF:TotRmsAbvGrd                                                                                        1.922e+06
## X1stFlrSF:TotRmsAbvGrd                                                                                          1.789e+06
## GrLivArea:TotRmsAbvGrd                                                                                          6.904e+05
## FullBath:TotRmsAbvGrd                                                                                           1.348e+09
## OverallQual:GarageCars                                                                                          7.354e+08
## YearBuilt:GarageCars                                                                                            2.784e+06
## YearRemodAdd:GarageCars                                                                                         2.988e+06
## TotalBsmtSF:GarageCars                                                                                          7.136e+06
## X1stFlrSF:GarageCars                                                                                            7.029e+06
## GrLivArea:GarageCars                                                                                            3.814e+06
## FullBath:GarageCars                                                                                             4.938e+09
## TotRmsAbvGrd:GarageCars                                                                                         9.385e+08
## OverallQual:GarageArea                                                                                          2.135e+06
## YearBuilt:GarageArea                                                                                            7.497e+03
## YearRemodAdd:GarageArea                                                                                         8.452e+03
## TotalBsmtSF:GarageArea                                                                                          1.623e+04
## X1stFlrSF:GarageArea                                                                                            1.797e+04
## GrLivArea:GarageArea                                                                                            1.334e+04
## FullBath:GarageArea                                                                                             1.411e+07
## TotRmsAbvGrd:GarageArea                                                                                         2.728e+06
## GarageCars:GarageArea                                                                                           3.668e+06
## OverallQual:YearBuilt:YearRemodAdd                                                                              2.917e+02
## OverallQual:YearBuilt:TotalBsmtSF                                                                               8.715e+02
## OverallQual:YearRemodAdd:TotalBsmtSF                                                                            9.335e+02
## YearBuilt:YearRemodAdd:TotalBsmtSF                                                                              3.265e+00
## OverallQual:YearBuilt:X1stFlrSF                                                                                 8.367e+02
## OverallQual:YearRemodAdd:X1stFlrSF                                                                              9.531e+02
## YearBuilt:YearRemodAdd:X1stFlrSF                                                                                3.246e+00
## OverallQual:TotalBsmtSF:X1stFlrSF                                                                               5.591e+02
## YearBuilt:TotalBsmtSF:X1stFlrSF                                                                                 2.063e+00
## YearRemodAdd:TotalBsmtSF:X1stFlrSF                                                                              2.047e+00
## OverallQual:YearBuilt:GrLivArea                                                                                 4.206e+02
## OverallQual:YearRemodAdd:GrLivArea                                                                              4.157e+02
## YearBuilt:YearRemodAdd:GrLivArea                                                                                1.506e+00
## OverallQual:TotalBsmtSF:GrLivArea                                                                               1.079e+03
## YearBuilt:TotalBsmtSF:GrLivArea                                                                                 3.527e+00
## YearRemodAdd:TotalBsmtSF:GrLivArea                                                                              3.619e+00
## OverallQual:X1stFlrSF:GrLivArea                                                                                 1.099e+03
## YearBuilt:X1stFlrSF:GrLivArea                                                                                   3.461e+00
## YearRemodAdd:X1stFlrSF:GrLivArea                                                                                3.667e+00
## TotalBsmtSF:X1stFlrSF:GrLivArea                                                                                 2.103e+00
## OverallQual:YearBuilt:FullBath                                                                                  6.564e+05
## OverallQual:YearRemodAdd:FullBath                                                                               6.909e+05
## YearBuilt:YearRemodAdd:FullBath                                                                                 2.986e+03
## OverallQual:TotalBsmtSF:FullBath                                                                                1.077e+06
## YearBuilt:TotalBsmtSF:FullBath                                                                                  4.821e+03
## YearRemodAdd:TotalBsmtSF:FullBath                                                                               5.193e+03
## OverallQual:X1stFlrSF:FullBath                                                                                  1.171e+06
## YearBuilt:X1stFlrSF:FullBath                                                                                    5.452e+03
## YearRemodAdd:X1stFlrSF:FullBath                                                                                 5.783e+03
## TotalBsmtSF:X1stFlrSF:FullBath                                                                                  2.682e+03
## OverallQual:GrLivArea:FullBath                                                                                  5.144e+05
## YearBuilt:GrLivArea:FullBath                                                                                    3.144e+03
## YearRemodAdd:GrLivArea:FullBath                                                                                 3.070e+03
## TotalBsmtSF:GrLivArea:FullBath                                                                                  3.847e+03
## X1stFlrSF:GrLivArea:FullBath                                                                                    3.818e+03
## OverallQual:YearBuilt:TotRmsAbvGrd                                                                              9.583e+04
## OverallQual:YearRemodAdd:TotRmsAbvGrd                                                                           8.903e+04
## YearBuilt:YearRemodAdd:TotRmsAbvGrd                                                                             3.739e+02
## OverallQual:TotalBsmtSF:TotRmsAbvGrd                                                                            2.998e+05
## YearBuilt:TotalBsmtSF:TotRmsAbvGrd                                                                              9.898e+02
## YearRemodAdd:TotalBsmtSF:TotRmsAbvGrd                                                                           1.019e+03
## OverallQual:X1stFlrSF:TotRmsAbvGrd                                                                              3.065e+05
## YearBuilt:X1stFlrSF:TotRmsAbvGrd                                                                                9.124e+02
## YearRemodAdd:X1stFlrSF:TotRmsAbvGrd                                                                             9.643e+02
## TotalBsmtSF:X1stFlrSF:TotRmsAbvGrd                                                                              6.276e+02
## OverallQual:GrLivArea:TotRmsAbvGrd                                                                              1.009e+05
## YearBuilt:GrLivArea:TotRmsAbvGrd                                                                                3.519e+02
## YearRemodAdd:GrLivArea:TotRmsAbvGrd                                                                             3.622e+02
## TotalBsmtSF:GrLivArea:TotRmsAbvGrd                                                                              6.318e+02
## X1stFlrSF:GrLivArea:TotRmsAbvGrd                                                                                6.456e+02
## OverallQual:FullBath:TotRmsAbvGrd                                                                               1.313e+08
## YearBuilt:FullBath:TotRmsAbvGrd                                                                                 7.262e+05
## YearRemodAdd:FullBath:TotRmsAbvGrd                                                                              6.930e+05
## TotalBsmtSF:FullBath:TotRmsAbvGrd                                                                               9.281e+05
## X1stFlrSF:FullBath:TotRmsAbvGrd                                                                                 1.088e+06
## GrLivArea:FullBath:TotRmsAbvGrd                                                                                 4.240e+05
## OverallQual:YearBuilt:GarageCars                                                                                3.760e+05
## OverallQual:YearRemodAdd:GarageCars                                                                             3.990e+05
## YearBuilt:YearRemodAdd:GarageCars                                                                               1.409e+03
## OverallQual:TotalBsmtSF:GarageCars                                                                              9.713e+05
## YearBuilt:TotalBsmtSF:GarageCars                                                                                3.631e+03
## YearRemodAdd:TotalBsmtSF:GarageCars                                                                             3.459e+03
## OverallQual:X1stFlrSF:GarageCars                                                                                8.808e+05
## YearBuilt:X1stFlrSF:GarageCars                                                                                  3.750e+03
## YearRemodAdd:X1stFlrSF:GarageCars                                                                               3.564e+03
## TotalBsmtSF:X1stFlrSF:GarageCars                                                                                2.695e+03
## OverallQual:GrLivArea:GarageCars                                                                                5.329e+05
## YearBuilt:GrLivArea:GarageCars                                                                                  2.110e+03
## YearRemodAdd:GrLivArea:GarageCars                                                                               1.976e+03
## TotalBsmtSF:GrLivArea:GarageCars                                                                                3.947e+03
## X1stFlrSF:GrLivArea:GarageCars                                                                                  3.993e+03
## OverallQual:FullBath:GarageCars                                                                                 4.930e+08
## YearBuilt:FullBath:GarageCars                                                                                   2.603e+06
## YearRemodAdd:FullBath:GarageCars                                                                                2.915e+06
## TotalBsmtSF:FullBath:GarageCars                                                                                 4.455e+06
## X1stFlrSF:FullBath:GarageCars                                                                                   4.536e+06
## GrLivArea:FullBath:GarageCars                                                                                   2.313e+06
## OverallQual:TotRmsAbvGrd:GarageCars                                                                             1.430e+08
## YearBuilt:TotRmsAbvGrd:GarageCars                                                                               4.695e+05
## YearRemodAdd:TotRmsAbvGrd:GarageCars                                                                            5.096e+05
## TotalBsmtSF:TotRmsAbvGrd:GarageCars                                                                             1.058e+06
## X1stFlrSF:TotRmsAbvGrd:GarageCars                                                                               9.352e+05
## GrLivArea:TotRmsAbvGrd:GarageCars                                                                               3.884e+05
## FullBath:TotRmsAbvGrd:GarageCars                                                                                5.255e+08
## OverallQual:YearBuilt:GarageArea                                                                                1.178e+03
## OverallQual:YearRemodAdd:GarageArea                                                                             1.210e+03
## YearBuilt:YearRemodAdd:GarageArea                                                                               3.861e+00
## OverallQual:TotalBsmtSF:GarageArea                                                                              1.785e+03
## YearBuilt:TotalBsmtSF:GarageArea                                                                                8.469e+00
## YearRemodAdd:TotalBsmtSF:GarageArea                                                                             8.212e+00
## OverallQual:X1stFlrSF:GarageArea                                                                                1.279e+03
## YearBuilt:X1stFlrSF:GarageArea                                                                                  8.666e+00
## YearRemodAdd:X1stFlrSF:GarageArea                                                                               9.393e+00
## TotalBsmtSF:X1stFlrSF:GarageArea                                                                                7.228e+00
## OverallQual:GrLivArea:GarageArea                                                                                1.872e+03
## YearBuilt:GrLivArea:GarageArea                                                                                  7.222e+00
## YearRemodAdd:GrLivArea:GarageArea                                                                               7.379e+00
## TotalBsmtSF:GrLivArea:GarageArea                                                                                1.037e+01
## X1stFlrSF:GrLivArea:GarageArea                                                                                  1.149e+01
## OverallQual:FullBath:GarageArea                                                                                 1.439e+06
## YearBuilt:FullBath:GarageArea                                                                                   7.237e+03
## YearRemodAdd:FullBath:GarageArea                                                                                7.486e+03
## TotalBsmtSF:FullBath:GarageArea                                                                                 9.997e+03
## X1stFlrSF:FullBath:GarageArea                                                                                   1.063e+04
## GrLivArea:FullBath:GarageArea                                                                                   6.441e+03
## OverallQual:TotRmsAbvGrd:GarageArea                                                                             4.242e+05
## YearBuilt:TotRmsAbvGrd:GarageArea                                                                               1.392e+03
## YearRemodAdd:TotRmsAbvGrd:GarageArea                                                                            1.457e+03
## TotalBsmtSF:TotRmsAbvGrd:GarageArea                                                                             2.249e+03
## X1stFlrSF:TotRmsAbvGrd:GarageArea                                                                               1.099e+03
## GrLivArea:TotRmsAbvGrd:GarageArea                                                                               1.162e+03
## FullBath:TotRmsAbvGrd:GarageArea                                                                                1.670e+06
## OverallQual:GarageCars:GarageArea                                                                               4.952e+05
## YearBuilt:GarageCars:GarageArea                                                                                 1.948e+03
## YearRemodAdd:GarageCars:GarageArea                                                                              2.139e+03
## TotalBsmtSF:GarageCars:GarageArea                                                                               4.877e+03
## X1stFlrSF:GarageCars:GarageArea                                                                                 5.933e+03
## GrLivArea:GarageCars:GarageArea                                                                                 2.457e+03
## FullBath:GarageCars:GarageArea                                                                                  2.767e+06
## TotRmsAbvGrd:GarageCars:GarageArea                                                                              5.262e+05
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF                                                                  4.430e-01
## OverallQual:YearBuilt:YearRemodAdd:X1stFlrSF                                                                    4.483e-01
## OverallQual:YearBuilt:TotalBsmtSF:X1stFlrSF                                                                     2.807e-01
## OverallQual:YearRemodAdd:TotalBsmtSF:X1stFlrSF                                                                  3.034e-01
## YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF                                                                    9.752e-04
## OverallQual:YearBuilt:YearRemodAdd:GrLivArea                                                                    1.952e-01
## OverallQual:YearBuilt:TotalBsmtSF:GrLivArea                                                                     5.561e-01
## OverallQual:YearRemodAdd:TotalBsmtSF:GrLivArea                                                                  5.771e-01
## YearBuilt:YearRemodAdd:TotalBsmtSF:GrLivArea                                                                    1.775e-03
## OverallQual:YearBuilt:X1stFlrSF:GrLivArea                                                                       5.618e-01
## OverallQual:YearRemodAdd:X1stFlrSF:GrLivArea                                                                    5.780e-01
## YearBuilt:YearRemodAdd:X1stFlrSF:GrLivArea                                                                      1.653e-03
## OverallQual:TotalBsmtSF:X1stFlrSF:GrLivArea                                                                     1.844e-01
## YearBuilt:TotalBsmtSF:X1stFlrSF:GrLivArea                                                                       1.177e-03
## YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea                                                                    1.118e-03
## OverallQual:YearBuilt:YearRemodAdd:FullBath                                                                     3.072e+02
## OverallQual:YearBuilt:TotalBsmtSF:FullBath                                                                      5.681e+02
## OverallQual:YearRemodAdd:TotalBsmtSF:FullBath                                                                   5.927e+02
## YearBuilt:YearRemodAdd:TotalBsmtSF:FullBath                                                                     2.297e+00
## OverallQual:YearBuilt:X1stFlrSF:FullBath                                                                        5.900e+02
## OverallQual:YearRemodAdd:X1stFlrSF:FullBath                                                                     5.753e+02
## YearBuilt:YearRemodAdd:X1stFlrSF:FullBath                                                                       2.471e+00
## OverallQual:TotalBsmtSF:X1stFlrSF:FullBath                                                                      2.576e+02
## YearBuilt:TotalBsmtSF:X1stFlrSF:FullBath                                                                        1.345e+00
## YearRemodAdd:TotalBsmtSF:X1stFlrSF:FullBath                                                                     1.458e+00
## OverallQual:YearBuilt:GrLivArea:FullBath                                                                        2.969e+02
## OverallQual:YearRemodAdd:GrLivArea:FullBath                                                                     3.595e+02
## YearBuilt:YearRemodAdd:GrLivArea:FullBath                                                                       1.450e+00
## OverallQual:TotalBsmtSF:GrLivArea:FullBath                                                                      4.406e+02
## YearBuilt:TotalBsmtSF:GrLivArea:FullBath                                                                        1.829e+00
## YearRemodAdd:TotalBsmtSF:GrLivArea:FullBath                                                                     1.933e+00
## OverallQual:X1stFlrSF:GrLivArea:FullBath                                                                        3.984e+02
## YearBuilt:X1stFlrSF:GrLivArea:FullBath                                                                          2.290e+00
## YearRemodAdd:X1stFlrSF:GrLivArea:FullBath                                                                       2.110e+00
## TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath                                                                        8.085e-01
## OverallQual:YearBuilt:YearRemodAdd:TotRmsAbvGrd                                                                 4.100e+01
## OverallQual:YearBuilt:TotalBsmtSF:TotRmsAbvGrd                                                                  1.530e+02
## OverallQual:YearRemodAdd:TotalBsmtSF:TotRmsAbvGrd                                                               1.680e+02
## YearBuilt:YearRemodAdd:TotalBsmtSF:TotRmsAbvGrd                                                                 4.958e-01
## OverallQual:YearBuilt:X1stFlrSF:TotRmsAbvGrd                                                                    1.575e+02
## OverallQual:YearRemodAdd:X1stFlrSF:TotRmsAbvGrd                                                                 1.639e+02
## YearBuilt:YearRemodAdd:X1stFlrSF:TotRmsAbvGrd                                                                   4.613e-01
## OverallQual:TotalBsmtSF:X1stFlrSF:TotRmsAbvGrd                                                                  5.164e+01
## YearBuilt:TotalBsmtSF:X1stFlrSF:TotRmsAbvGrd                                                                    3.436e-01
## YearRemodAdd:TotalBsmtSF:X1stFlrSF:TotRmsAbvGrd                                                                 3.293e-01
## OverallQual:YearBuilt:GrLivArea:TotRmsAbvGrd                                                                    5.103e+01
## OverallQual:YearRemodAdd:GrLivArea:TotRmsAbvGrd                                                                 5.428e+01
## YearBuilt:YearRemodAdd:GrLivArea:TotRmsAbvGrd                                                                   1.708e-01
## OverallQual:TotalBsmtSF:GrLivArea:TotRmsAbvGrd                                                                  5.211e+01
## YearBuilt:TotalBsmtSF:GrLivArea:TotRmsAbvGrd                                                                    3.052e-01
## YearRemodAdd:TotalBsmtSF:GrLivArea:TotRmsAbvGrd                                                                 3.143e-01
## OverallQual:X1stFlrSF:GrLivArea:TotRmsAbvGrd                                                                    5.110e+01
## YearBuilt:X1stFlrSF:GrLivArea:TotRmsAbvGrd                                                                      3.159e-01
## YearRemodAdd:X1stFlrSF:GrLivArea:TotRmsAbvGrd                                                                   3.548e-01
## TotalBsmtSF:X1stFlrSF:GrLivArea:TotRmsAbvGrd                                                                    1.698e-01
## OverallQual:YearBuilt:FullBath:TotRmsAbvGrd                                                                     7.457e+04
## OverallQual:YearRemodAdd:FullBath:TotRmsAbvGrd                                                                  7.118e+04
## YearBuilt:YearRemodAdd:FullBath:TotRmsAbvGrd                                                                    3.540e+02
## OverallQual:TotalBsmtSF:FullBath:TotRmsAbvGrd                                                                   6.695e+04
## YearBuilt:TotalBsmtSF:FullBath:TotRmsAbvGrd                                                                     5.101e+02
## YearRemodAdd:TotalBsmtSF:FullBath:TotRmsAbvGrd                                                                  5.007e+02
## OverallQual:X1stFlrSF:FullBath:TotRmsAbvGrd                                                                     8.468e+04
## YearBuilt:X1stFlrSF:FullBath:TotRmsAbvGrd                                                                       5.318e+02
## YearRemodAdd:X1stFlrSF:FullBath:TotRmsAbvGrd                                                                    5.170e+02
## TotalBsmtSF:X1stFlrSF:FullBath:TotRmsAbvGrd                                                                     2.422e+02
## OverallQual:GrLivArea:FullBath:TotRmsAbvGrd                                                                     3.158e+04
## YearBuilt:GrLivArea:FullBath:TotRmsAbvGrd                                                                       2.204e+02
## YearRemodAdd:GrLivArea:FullBath:TotRmsAbvGrd                                                                    2.321e+02
## TotalBsmtSF:GrLivArea:FullBath:TotRmsAbvGrd                                                                     2.535e+02
## X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd                                                                       2.227e+02
## OverallQual:YearBuilt:YearRemodAdd:GarageCars                                                                   1.731e+02
## OverallQual:YearBuilt:TotalBsmtSF:GarageCars                                                                    5.174e+02
## OverallQual:YearRemodAdd:TotalBsmtSF:GarageCars                                                                 4.812e+02
## YearBuilt:YearRemodAdd:TotalBsmtSF:GarageCars                                                                   1.706e+00
## OverallQual:YearBuilt:X1stFlrSF:GarageCars                                                                      4.722e+02
## OverallQual:YearRemodAdd:X1stFlrSF:GarageCars                                                                   4.425e+02
## YearBuilt:YearRemodAdd:X1stFlrSF:GarageCars                                                                     1.744e+00
## OverallQual:TotalBsmtSF:X1stFlrSF:GarageCars                                                                    2.618e+02
## YearBuilt:TotalBsmtSF:X1stFlrSF:GarageCars                                                                      1.346e+00
## YearRemodAdd:TotalBsmtSF:X1stFlrSF:GarageCars                                                                   1.411e+00
## OverallQual:YearBuilt:GrLivArea:GarageCars                                                                      2.853e+02
## OverallQual:YearRemodAdd:GrLivArea:GarageCars                                                                   2.819e+02
## YearBuilt:YearRemodAdd:GrLivArea:GarageCars                                                                     1.014e+00
## OverallQual:TotalBsmtSF:GrLivArea:GarageCars                                                                    2.679e+02
## YearBuilt:TotalBsmtSF:GrLivArea:GarageCars                                                                      2.116e+00
## YearRemodAdd:TotalBsmtSF:GrLivArea:GarageCars                                                                   1.999e+00
## OverallQual:X1stFlrSF:GrLivArea:GarageCars                                                                      2.747e+02
## YearBuilt:X1stFlrSF:GrLivArea:GarageCars                                                                        2.022e+00
## YearRemodAdd:X1stFlrSF:GrLivArea:GarageCars                                                                     2.190e+00
## TotalBsmtSF:X1stFlrSF:GrLivArea:GarageCars                                                                      6.687e-01
## OverallQual:YearBuilt:FullBath:GarageCars                                                                       2.738e+05
## OverallQual:YearRemodAdd:FullBath:GarageCars                                                                    2.973e+05
## YearBuilt:YearRemodAdd:FullBath:GarageCars                                                                      1.323e+03
## OverallQual:TotalBsmtSF:FullBath:GarageCars                                                                     3.501e+05
## YearBuilt:TotalBsmtSF:FullBath:GarageCars                                                                       2.108e+03
## YearRemodAdd:TotalBsmtSF:FullBath:GarageCars                                                                    2.195e+03
## OverallQual:X1stFlrSF:FullBath:GarageCars                                                                       3.609e+05
## YearBuilt:X1stFlrSF:FullBath:GarageCars                                                                         2.120e+03
## YearRemodAdd:X1stFlrSF:FullBath:GarageCars                                                                      2.489e+03
## TotalBsmtSF:X1stFlrSF:FullBath:GarageCars                                                                       9.118e+02
## OverallQual:GrLivArea:FullBath:GarageCars                                                                       1.525e+05
## YearBuilt:GrLivArea:FullBath:GarageCars                                                                         1.330e+03
## YearRemodAdd:GrLivArea:FullBath:GarageCars                                                                      1.290e+03
## TotalBsmtSF:GrLivArea:FullBath:GarageCars                                                                       1.433e+03
## X1stFlrSF:GrLivArea:FullBath:GarageCars                                                                         1.283e+03
## OverallQual:YearBuilt:TotRmsAbvGrd:GarageCars                                                                   7.355e+04
## OverallQual:YearRemodAdd:TotRmsAbvGrd:GarageCars                                                                7.677e+04
## YearBuilt:YearRemodAdd:TotRmsAbvGrd:GarageCars                                                                  2.397e+02
## OverallQual:TotalBsmtSF:TotRmsAbvGrd:GarageCars                                                                 6.358e+04
## YearBuilt:TotalBsmtSF:TotRmsAbvGrd:GarageCars                                                                   5.401e+02
## YearRemodAdd:TotalBsmtSF:TotRmsAbvGrd:GarageCars                                                                5.175e+02
## OverallQual:X1stFlrSF:TotRmsAbvGrd:GarageCars                                                                   5.662e+04
## YearBuilt:X1stFlrSF:TotRmsAbvGrd:GarageCars                                                                     5.037e+02
## YearRemodAdd:X1stFlrSF:TotRmsAbvGrd:GarageCars                                                                  4.900e+02
## TotalBsmtSF:X1stFlrSF:TotRmsAbvGrd:GarageCars                                                                   2.237e+02
## OverallQual:GrLivArea:TotRmsAbvGrd:GarageCars                                                                   2.505e+04
## YearBuilt:GrLivArea:TotRmsAbvGrd:GarageCars                                                                     2.157e+02
## YearRemodAdd:GrLivArea:TotRmsAbvGrd:GarageCars                                                                  1.869e+02
## TotalBsmtSF:GrLivArea:TotRmsAbvGrd:GarageCars                                                                   2.446e+02
## X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageCars                                                                     2.061e+02
## OverallQual:FullBath:TotRmsAbvGrd:GarageCars                                                                    3.536e+07
## YearBuilt:FullBath:TotRmsAbvGrd:GarageCars                                                                      2.948e+05
## YearRemodAdd:FullBath:TotRmsAbvGrd:GarageCars                                                                   3.046e+05
## TotalBsmtSF:FullBath:TotRmsAbvGrd:GarageCars                                                                    2.862e+05
## X1stFlrSF:FullBath:TotRmsAbvGrd:GarageCars                                                                      3.553e+05
## GrLivArea:FullBath:TotRmsAbvGrd:GarageCars                                                                      1.631e+05
## OverallQual:YearBuilt:YearRemodAdd:GarageArea                                                                   5.508e-01
## OverallQual:YearBuilt:TotalBsmtSF:GarageArea                                                                    9.981e-01
## OverallQual:YearRemodAdd:TotalBsmtSF:GarageArea                                                                 8.781e-01
## YearBuilt:YearRemodAdd:TotalBsmtSF:GarageArea                                                                   4.099e-03
## OverallQual:YearBuilt:X1stFlrSF:GarageArea                                                                      6.743e-01
## OverallQual:YearRemodAdd:X1stFlrSF:GarageArea                                                                   5.610e-01
## YearBuilt:YearRemodAdd:X1stFlrSF:GarageArea                                                                     4.303e-03
## OverallQual:TotalBsmtSF:X1stFlrSF:GarageArea                                                                    5.969e-01
## YearBuilt:TotalBsmtSF:X1stFlrSF:GarageArea                                                                      3.522e-03
## YearRemodAdd:TotalBsmtSF:X1stFlrSF:GarageArea                                                                   3.438e-03
## OverallQual:YearBuilt:GrLivArea:GarageArea                                                                      1.019e+00
## OverallQual:YearRemodAdd:GrLivArea:GarageArea                                                                   9.850e-01
## YearBuilt:YearRemodAdd:GrLivArea:GarageArea                                                                     3.676e-03
## OverallQual:TotalBsmtSF:GrLivArea:GarageArea                                                                    8.096e-01
## YearBuilt:TotalBsmtSF:GrLivArea:GarageArea                                                                      5.365e-03
## YearRemodAdd:TotalBsmtSF:GrLivArea:GarageArea                                                                   5.238e-03
## OverallQual:X1stFlrSF:GrLivArea:GarageArea                                                                      8.614e-01
## YearBuilt:X1stFlrSF:GrLivArea:GarageArea                                                                        5.530e-03
## YearRemodAdd:X1stFlrSF:GrLivArea:GarageArea                                                                     6.223e-03
## TotalBsmtSF:X1stFlrSF:GrLivArea:GarageArea                                                                      1.713e-03
## OverallQual:YearBuilt:FullBath:GarageArea                                                                       8.175e+02
## OverallQual:YearRemodAdd:FullBath:GarageArea                                                                    8.616e+02
## YearBuilt:YearRemodAdd:FullBath:GarageArea                                                                      3.346e+00
## OverallQual:TotalBsmtSF:FullBath:GarageArea                                                                     8.614e+02
## YearBuilt:TotalBsmtSF:FullBath:GarageArea                                                                       5.116e+00
## YearRemodAdd:TotalBsmtSF:FullBath:GarageArea                                                                    4.570e+00
## OverallQual:X1stFlrSF:FullBath:GarageArea                                                                       7.443e+02
## YearBuilt:X1stFlrSF:FullBath:GarageArea                                                                         5.775e+00
## YearRemodAdd:X1stFlrSF:FullBath:GarageArea                                                                      4.744e+00
## TotalBsmtSF:X1stFlrSF:FullBath:GarageArea                                                                       2.718e+00
## OverallQual:GrLivArea:FullBath:GarageArea                                                                       5.541e+02
## YearBuilt:GrLivArea:FullBath:GarageArea                                                                         3.372e+00
## YearRemodAdd:GrLivArea:FullBath:GarageArea                                                                      3.737e+00
## TotalBsmtSF:GrLivArea:FullBath:GarageArea                                                                       3.412e+00
## X1stFlrSF:GrLivArea:FullBath:GarageArea                                                                         2.927e+00
## OverallQual:YearBuilt:TotRmsAbvGrd:GarageArea                                                                   2.227e+02
## OverallQual:YearRemodAdd:TotRmsAbvGrd:GarageArea                                                                2.389e+02
## YearBuilt:YearRemodAdd:TotRmsAbvGrd:GarageArea                                                                  7.204e-01
## OverallQual:TotalBsmtSF:TotRmsAbvGrd:GarageArea                                                                 2.155e+02
## YearBuilt:TotalBsmtSF:TotRmsAbvGrd:GarageArea                                                                   1.164e+00
## YearRemodAdd:TotalBsmtSF:TotRmsAbvGrd:GarageArea                                                                1.126e+00
## OverallQual:X1stFlrSF:TotRmsAbvGrd:GarageArea                                                                   1.912e+02
## YearBuilt:X1stFlrSF:TotRmsAbvGrd:GarageArea                                                                     5.304e-01
## YearRemodAdd:X1stFlrSF:TotRmsAbvGrd:GarageArea                                                                  4.390e-01
## TotalBsmtSF:X1stFlrSF:TotRmsAbvGrd:GarageArea                                                                   6.536e-01
## OverallQual:GrLivArea:TotRmsAbvGrd:GarageArea                                                                   7.619e+01
## YearBuilt:GrLivArea:TotRmsAbvGrd:GarageArea                                                                     5.932e-01
## YearRemodAdd:GrLivArea:TotRmsAbvGrd:GarageArea                                                                  6.482e-01
## TotalBsmtSF:GrLivArea:TotRmsAbvGrd:GarageArea                                                                   6.546e-01
## X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageArea                                                                     5.168e-01
## OverallQual:FullBath:TotRmsAbvGrd:GarageArea                                                                    1.296e+05
## YearBuilt:FullBath:TotRmsAbvGrd:GarageArea                                                                      8.248e+02
## YearRemodAdd:FullBath:TotRmsAbvGrd:GarageArea                                                                   7.420e+02
## TotalBsmtSF:FullBath:TotRmsAbvGrd:GarageArea                                                                    8.194e+02
## X1stFlrSF:FullBath:TotRmsAbvGrd:GarageArea                                                                      8.671e+02
## GrLivArea:FullBath:TotRmsAbvGrd:GarageArea                                                                      3.745e+02
## OverallQual:YearBuilt:GarageCars:GarageArea                                                                     2.861e+02
## OverallQual:YearRemodAdd:GarageCars:GarageArea                                                                  2.659e+02
## YearBuilt:YearRemodAdd:GarageCars:GarageArea                                                                    9.967e-01
## OverallQual:TotalBsmtSF:GarageCars:GarageArea                                                                   4.491e+02
## YearBuilt:TotalBsmtSF:GarageCars:GarageArea                                                                     2.347e+00
## YearRemodAdd:TotalBsmtSF:GarageCars:GarageArea                                                                  2.248e+00
## OverallQual:X1stFlrSF:GarageCars:GarageArea                                                                     4.248e+02
## YearBuilt:X1stFlrSF:GarageCars:GarageArea                                                                       2.810e+00
## YearRemodAdd:X1stFlrSF:GarageCars:GarageArea                                                                    2.901e+00
## TotalBsmtSF:X1stFlrSF:GarageCars:GarageArea                                                                     2.180e+00
## OverallQual:GrLivArea:GarageCars:GarageArea                                                                     2.304e+02
## YearBuilt:GrLivArea:GarageCars:GarageArea                                                                       1.463e+00
## YearRemodAdd:GrLivArea:GarageCars:GarageArea                                                                    1.470e+00
## TotalBsmtSF:GrLivArea:GarageCars:GarageArea                                                                     2.263e+00
## X1stFlrSF:GrLivArea:GarageCars:GarageArea                                                                       1.655e+00
## OverallQual:FullBath:GarageCars:GarageArea                                                                      3.690e+05
## YearBuilt:FullBath:GarageCars:GarageArea                                                                        1.241e+03
## YearRemodAdd:FullBath:GarageCars:GarageArea                                                                     1.516e+03
## TotalBsmtSF:FullBath:GarageCars:GarageArea                                                                      2.712e+03
## X1stFlrSF:FullBath:GarageCars:GarageArea                                                                        2.299e+03
## GrLivArea:FullBath:GarageCars:GarageArea                                                                        1.577e+03
## OverallQual:TotRmsAbvGrd:GarageCars:GarageArea                                                                  4.584e+04
## YearBuilt:TotRmsAbvGrd:GarageCars:GarageArea                                                                    2.616e+02
## YearRemodAdd:TotRmsAbvGrd:GarageCars:GarageArea                                                                 2.612e+02
## TotalBsmtSF:TotRmsAbvGrd:GarageCars:GarageArea                                                                  4.354e+02
## X1stFlrSF:TotRmsAbvGrd:GarageCars:GarageArea                                                                    4.200e+02
## GrLivArea:TotRmsAbvGrd:GarageCars:GarageArea                                                                    2.915e+02
## FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                                                     3.445e+05
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF                                                        1.295e-04
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:GrLivArea                                                        2.667e-04
## OverallQual:YearBuilt:YearRemodAdd:X1stFlrSF:GrLivArea                                                          2.748e-04
## OverallQual:YearBuilt:TotalBsmtSF:X1stFlrSF:GrLivArea                                                           9.623e-05
## OverallQual:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea                                                        7.701e-05
## YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea                                                          4.753e-07
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:FullBath                                                         2.131e-01
## OverallQual:YearBuilt:YearRemodAdd:X1stFlrSF:FullBath                                                           2.318e-01
## OverallQual:YearBuilt:TotalBsmtSF:X1stFlrSF:FullBath                                                            1.329e-01
## OverallQual:YearRemodAdd:TotalBsmtSF:X1stFlrSF:FullBath                                                         1.611e-01
## YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:FullBath                                                           4.691e-04
## OverallQual:YearBuilt:YearRemodAdd:GrLivArea:FullBath                                                           1.167e-01
## OverallQual:YearBuilt:TotalBsmtSF:GrLivArea:FullBath                                                            2.077e-01
## OverallQual:YearRemodAdd:TotalBsmtSF:GrLivArea:FullBath                                                         2.872e-01
## YearBuilt:YearRemodAdd:TotalBsmtSF:GrLivArea:FullBath                                                           6.651e-04
## OverallQual:YearBuilt:X1stFlrSF:GrLivArea:FullBath                                                              1.969e-01
## OverallQual:YearRemodAdd:X1stFlrSF:GrLivArea:FullBath                                                           2.523e-01
## YearBuilt:YearRemodAdd:X1stFlrSF:GrLivArea:FullBath                                                             6.993e-04
## OverallQual:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath                                                            5.672e-02
## YearBuilt:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath                                                              5.563e-04
## YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath                                                           6.234e-04
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:TotRmsAbvGrd                                                     7.893e-02
## OverallQual:YearBuilt:YearRemodAdd:X1stFlrSF:TotRmsAbvGrd                                                       8.160e-02
## OverallQual:YearBuilt:TotalBsmtSF:X1stFlrSF:TotRmsAbvGrd                                                        2.475e-02
## OverallQual:YearRemodAdd:TotalBsmtSF:X1stFlrSF:TotRmsAbvGrd                                                     3.297e-02
## YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:TotRmsAbvGrd                                                       1.422e-04
## OverallQual:YearBuilt:YearRemodAdd:GrLivArea:TotRmsAbvGrd                                                       2.454e-02
## OverallQual:YearBuilt:TotalBsmtSF:GrLivArea:TotRmsAbvGrd                                                        2.079e-02
## OverallQual:YearRemodAdd:TotalBsmtSF:GrLivArea:TotRmsAbvGrd                                                     2.151e-02
## YearBuilt:YearRemodAdd:TotalBsmtSF:GrLivArea:TotRmsAbvGrd                                                       1.355e-04
## OverallQual:YearBuilt:X1stFlrSF:GrLivArea:TotRmsAbvGrd                                                          2.124e-02
## OverallQual:YearRemodAdd:X1stFlrSF:GrLivArea:TotRmsAbvGrd                                                       2.338e-02
## YearBuilt:YearRemodAdd:X1stFlrSF:GrLivArea:TotRmsAbvGrd                                                         1.412e-04
## OverallQual:TotalBsmtSF:X1stFlrSF:GrLivArea:TotRmsAbvGrd                                                        2.344e-02
## YearBuilt:TotalBsmtSF:X1stFlrSF:GrLivArea:TotRmsAbvGrd                                                          8.929e-05
## YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:TotRmsAbvGrd                                                       4.224e-05
## OverallQual:YearBuilt:YearRemodAdd:FullBath:TotRmsAbvGrd                                                        2.899e+01
## OverallQual:YearBuilt:TotalBsmtSF:FullBath:TotRmsAbvGrd                                                         5.406e+01
## OverallQual:YearRemodAdd:TotalBsmtSF:FullBath:TotRmsAbvGrd                                                      5.026e+01
## YearBuilt:YearRemodAdd:TotalBsmtSF:FullBath:TotRmsAbvGrd                                                        1.991e-01
## OverallQual:YearBuilt:X1stFlrSF:FullBath:TotRmsAbvGrd                                                           3.732e+01
## OverallQual:YearRemodAdd:X1stFlrSF:FullBath:TotRmsAbvGrd                                                        1.966e+01
## YearBuilt:YearRemodAdd:X1stFlrSF:FullBath:TotRmsAbvGrd                                                          2.216e-01
## OverallQual:TotalBsmtSF:X1stFlrSF:FullBath:TotRmsAbvGrd                                                         2.681e+01
## YearBuilt:TotalBsmtSF:X1stFlrSF:FullBath:TotRmsAbvGrd                                                           1.491e-01
## YearRemodAdd:TotalBsmtSF:X1stFlrSF:FullBath:TotRmsAbvGrd                                                        1.725e-01
## OverallQual:YearBuilt:GrLivArea:FullBath:TotRmsAbvGrd                                                           2.407e+01
## OverallQual:YearRemodAdd:GrLivArea:FullBath:TotRmsAbvGrd                                                        2.396e+01
## YearBuilt:YearRemodAdd:GrLivArea:FullBath:TotRmsAbvGrd                                                          8.707e-02
## OverallQual:TotalBsmtSF:GrLivArea:FullBath:TotRmsAbvGrd                                                         2.385e+01
## YearBuilt:TotalBsmtSF:GrLivArea:FullBath:TotRmsAbvGrd                                                           1.256e-01
## YearRemodAdd:TotalBsmtSF:GrLivArea:FullBath:TotRmsAbvGrd                                                        1.444e-01
## OverallQual:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd                                                           2.108e+01
## YearBuilt:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd                                                             1.445e-01
## YearRemodAdd:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd                                                          1.824e-01
## TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd                                                           5.472e-02
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:GarageCars                                                       2.311e-01
## OverallQual:YearBuilt:YearRemodAdd:X1stFlrSF:GarageCars                                                         2.083e-01
## OverallQual:YearBuilt:TotalBsmtSF:X1stFlrSF:GarageCars                                                          1.107e-01
## OverallQual:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GarageCars                                                       1.374e-01
## YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GarageCars                                                         6.187e-04
## OverallQual:YearBuilt:YearRemodAdd:GrLivArea:GarageCars                                                         1.395e-01
## OverallQual:YearBuilt:TotalBsmtSF:GrLivArea:GarageCars                                                          1.378e-01
## OverallQual:YearRemodAdd:TotalBsmtSF:GrLivArea:GarageCars                                                       1.290e-01
## YearBuilt:YearRemodAdd:TotalBsmtSF:GrLivArea:GarageCars                                                         1.011e-03
## OverallQual:YearBuilt:X1stFlrSF:GrLivArea:GarageCars                                                            1.473e-01
## OverallQual:YearRemodAdd:X1stFlrSF:GrLivArea:GarageCars                                                         1.432e-01
## YearBuilt:YearRemodAdd:X1stFlrSF:GrLivArea:GarageCars                                                           9.740e-04
## OverallQual:TotalBsmtSF:X1stFlrSF:GrLivArea:GarageCars                                                          1.040e-01
## YearBuilt:TotalBsmtSF:X1stFlrSF:GrLivArea:GarageCars                                                            4.141e-04
## YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:GarageCars                                                         3.285e-04
## OverallQual:YearBuilt:YearRemodAdd:FullBath:GarageCars                                                          1.119e+02
## OverallQual:YearBuilt:TotalBsmtSF:FullBath:GarageCars                                                           1.891e+02
## OverallQual:YearRemodAdd:TotalBsmtSF:FullBath:GarageCars                                                        2.167e+02
## YearBuilt:YearRemodAdd:TotalBsmtSF:FullBath:GarageCars                                                          9.632e-01
## OverallQual:YearBuilt:X1stFlrSF:FullBath:GarageCars                                                             1.652e+02
## OverallQual:YearRemodAdd:X1stFlrSF:FullBath:GarageCars                                                          1.854e+02
## YearBuilt:YearRemodAdd:X1stFlrSF:FullBath:GarageCars                                                            9.775e-01
## OverallQual:TotalBsmtSF:X1stFlrSF:FullBath:GarageCars                                                           1.021e+02
## YearBuilt:TotalBsmtSF:X1stFlrSF:FullBath:GarageCars                                                             5.194e-01
## YearRemodAdd:TotalBsmtSF:X1stFlrSF:FullBath:GarageCars                                                          5.265e-01
## OverallQual:YearBuilt:GrLivArea:FullBath:GarageCars                                                             1.013e+02
## OverallQual:YearRemodAdd:GrLivArea:FullBath:GarageCars                                                          1.135e+02
## YearBuilt:YearRemodAdd:GrLivArea:FullBath:GarageCars                                                            5.463e-01
## OverallQual:TotalBsmtSF:GrLivArea:FullBath:GarageCars                                                           2.059e+02
## YearBuilt:TotalBsmtSF:GrLivArea:FullBath:GarageCars                                                             7.335e-01
## YearRemodAdd:TotalBsmtSF:GrLivArea:FullBath:GarageCars                                                          7.152e-01
## OverallQual:X1stFlrSF:GrLivArea:FullBath:GarageCars                                                             1.981e+02
## YearBuilt:X1stFlrSF:GrLivArea:FullBath:GarageCars                                                               8.566e-01
## YearRemodAdd:X1stFlrSF:GrLivArea:FullBath:GarageCars                                                            7.770e-01
## TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:GarageCars                                                             3.197e-01
## OverallQual:YearBuilt:YearRemodAdd:TotRmsAbvGrd:GarageCars                                                      3.497e+01
## OverallQual:YearBuilt:TotalBsmtSF:TotRmsAbvGrd:GarageCars                                                       3.675e+01
## OverallQual:YearRemodAdd:TotalBsmtSF:TotRmsAbvGrd:GarageCars                                                    3.225e+01
## YearBuilt:YearRemodAdd:TotalBsmtSF:TotRmsAbvGrd:GarageCars                                                      2.516e-01
## OverallQual:YearBuilt:X1stFlrSF:TotRmsAbvGrd:GarageCars                                                         3.721e+01
## OverallQual:YearRemodAdd:X1stFlrSF:TotRmsAbvGrd:GarageCars                                                      3.070e+01
## YearBuilt:YearRemodAdd:X1stFlrSF:TotRmsAbvGrd:GarageCars                                                        2.261e-01
## OverallQual:TotalBsmtSF:X1stFlrSF:TotRmsAbvGrd:GarageCars                                                       3.613e+01
## YearBuilt:TotalBsmtSF:X1stFlrSF:TotRmsAbvGrd:GarageCars                                                         1.247e-01
## YearRemodAdd:TotalBsmtSF:X1stFlrSF:TotRmsAbvGrd:GarageCars                                                      1.573e-01
## OverallQual:YearBuilt:GrLivArea:TotRmsAbvGrd:GarageCars                                                         1.571e+01
## OverallQual:YearRemodAdd:GrLivArea:TotRmsAbvGrd:GarageCars                                                      1.538e+01
## YearBuilt:YearRemodAdd:GrLivArea:TotRmsAbvGrd:GarageCars                                                        9.104e-02
## OverallQual:TotalBsmtSF:GrLivArea:TotRmsAbvGrd:GarageCars                                                       3.670e+01
## YearBuilt:TotalBsmtSF:GrLivArea:TotRmsAbvGrd:GarageCars                                                         9.985e-02
## YearRemodAdd:TotalBsmtSF:GrLivArea:TotRmsAbvGrd:GarageCars                                                      1.267e-01
## OverallQual:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageCars                                                         3.256e+01
## YearBuilt:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageCars                                                           8.952e-02
## YearRemodAdd:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageCars                                                        1.098e-01
## TotalBsmtSF:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageCars                                                         1.048e-01
## OverallQual:YearBuilt:FullBath:TotRmsAbvGrd:GarageCars                                                          2.608e+04
## OverallQual:YearRemodAdd:FullBath:TotRmsAbvGrd:GarageCars                                                       2.656e+04
## YearBuilt:YearRemodAdd:FullBath:TotRmsAbvGrd:GarageCars                                                         1.434e+02
## OverallQual:TotalBsmtSF:FullBath:TotRmsAbvGrd:GarageCars                                                        3.092e+04
## YearBuilt:TotalBsmtSF:FullBath:TotRmsAbvGrd:GarageCars                                                          1.654e+02
## YearRemodAdd:TotalBsmtSF:FullBath:TotRmsAbvGrd:GarageCars                                                       1.420e+02
## OverallQual:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageCars                                                          3.428e+04
## YearBuilt:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageCars                                                            1.606e+02
## YearRemodAdd:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageCars                                                         1.728e+02
## TotalBsmtSF:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageCars                                                          8.048e+01
## OverallQual:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars                                                          1.665e+04
## YearBuilt:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars                                                            8.243e+01
## YearRemodAdd:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars                                                         9.338e+01
## TotalBsmtSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars                                                          9.147e+01
## X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars                                                            9.630e+01
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:GarageArea                                                       3.799e-04
## OverallQual:YearBuilt:YearRemodAdd:X1stFlrSF:GarageArea                                                                NA
## OverallQual:YearBuilt:TotalBsmtSF:X1stFlrSF:GarageArea                                                          2.959e-04
## OverallQual:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GarageArea                                                       2.192e-04
## YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GarageArea                                                         1.667e-06
## OverallQual:YearBuilt:YearRemodAdd:GrLivArea:GarageArea                                                         4.823e-04
## OverallQual:YearBuilt:TotalBsmtSF:GrLivArea:GarageArea                                                          3.770e-04
## OverallQual:YearRemodAdd:TotalBsmtSF:GrLivArea:GarageArea                                                       1.698e-04
## YearBuilt:YearRemodAdd:TotalBsmtSF:GrLivArea:GarageArea                                                         2.661e-06
## OverallQual:YearBuilt:X1stFlrSF:GrLivArea:GarageArea                                                            3.939e-04
## OverallQual:YearRemodAdd:X1stFlrSF:GrLivArea:GarageArea                                                         3.588e-04
## YearBuilt:YearRemodAdd:X1stFlrSF:GrLivArea:GarageArea                                                           2.869e-06
## OverallQual:TotalBsmtSF:X1stFlrSF:GrLivArea:GarageArea                                                          1.974e-04
## YearBuilt:TotalBsmtSF:X1stFlrSF:GrLivArea:GarageArea                                                            8.821e-07
## YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:GarageArea                                                         3.402e-07
## OverallQual:YearBuilt:YearRemodAdd:FullBath:GarageArea                                                          3.097e-01
## OverallQual:YearBuilt:TotalBsmtSF:FullBath:GarageArea                                                           4.975e-01
## OverallQual:YearRemodAdd:TotalBsmtSF:FullBath:GarageArea                                                        4.586e-01
## YearBuilt:YearRemodAdd:TotalBsmtSF:FullBath:GarageArea                                                          2.047e-03
## OverallQual:YearBuilt:X1stFlrSF:FullBath:GarageArea                                                             4.131e-01
## OverallQual:YearRemodAdd:X1stFlrSF:FullBath:GarageArea                                                          4.172e-01
## YearBuilt:YearRemodAdd:X1stFlrSF:FullBath:GarageArea                                                            2.221e-03
## OverallQual:TotalBsmtSF:X1stFlrSF:FullBath:GarageArea                                                           2.923e-01
## YearBuilt:TotalBsmtSF:X1stFlrSF:FullBath:GarageArea                                                             1.402e-03
## YearRemodAdd:TotalBsmtSF:X1stFlrSF:FullBath:GarageArea                                                          1.176e-03
## OverallQual:YearBuilt:GrLivArea:FullBath:GarageArea                                                             3.246e-01
## OverallQual:YearRemodAdd:GrLivArea:FullBath:GarageArea                                                          3.046e-01
## YearBuilt:YearRemodAdd:GrLivArea:FullBath:GarageArea                                                            1.387e-03
## OverallQual:TotalBsmtSF:GrLivArea:FullBath:GarageArea                                                           3.807e-01
## YearBuilt:TotalBsmtSF:GrLivArea:FullBath:GarageArea                                                             1.721e-03
## YearRemodAdd:TotalBsmtSF:GrLivArea:FullBath:GarageArea                                                          1.491e-03
## OverallQual:X1stFlrSF:GrLivArea:FullBath:GarageArea                                                             4.091e-01
## YearBuilt:X1stFlrSF:GrLivArea:FullBath:GarageArea                                                               1.563e-03
## YearRemodAdd:X1stFlrSF:GrLivArea:FullBath:GarageArea                                                            1.413e-03
## TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:GarageArea                                                             8.050e-04
## OverallQual:YearBuilt:YearRemodAdd:TotRmsAbvGrd:GarageArea                                                      1.169e-01
## OverallQual:YearBuilt:TotalBsmtSF:TotRmsAbvGrd:GarageArea                                                       1.107e-01
## OverallQual:YearRemodAdd:TotalBsmtSF:TotRmsAbvGrd:GarageArea                                                    7.301e-02
## YearBuilt:YearRemodAdd:TotalBsmtSF:TotRmsAbvGrd:GarageArea                                                      5.499e-04
## OverallQual:YearBuilt:X1stFlrSF:TotRmsAbvGrd:GarageArea                                                         1.022e-01
## OverallQual:YearRemodAdd:X1stFlrSF:TotRmsAbvGrd:GarageArea                                                      6.476e-02
## YearBuilt:YearRemodAdd:X1stFlrSF:TotRmsAbvGrd:GarageArea                                                               NA
## OverallQual:TotalBsmtSF:X1stFlrSF:TotRmsAbvGrd:GarageArea                                                       7.687e-02
## YearBuilt:TotalBsmtSF:X1stFlrSF:TotRmsAbvGrd:GarageArea                                                         3.038e-04
## YearRemodAdd:TotalBsmtSF:X1stFlrSF:TotRmsAbvGrd:GarageArea                                                      1.968e-04
## OverallQual:YearBuilt:GrLivArea:TotRmsAbvGrd:GarageArea                                                         4.667e-02
## OverallQual:YearRemodAdd:GrLivArea:TotRmsAbvGrd:GarageArea                                                      4.151e-02
## YearBuilt:YearRemodAdd:GrLivArea:TotRmsAbvGrd:GarageArea                                                        2.964e-04
## OverallQual:TotalBsmtSF:GrLivArea:TotRmsAbvGrd:GarageArea                                                       9.228e-02
## YearBuilt:TotalBsmtSF:GrLivArea:TotRmsAbvGrd:GarageArea                                                         2.944e-04
## YearRemodAdd:TotalBsmtSF:GrLivArea:TotRmsAbvGrd:GarageArea                                                      2.250e-04
## OverallQual:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageArea                                                         7.552e-02
## YearBuilt:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageArea                                                           2.408e-04
## YearRemodAdd:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageArea                                                        2.207e-04
## TotalBsmtSF:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageArea                                                         1.259e-04
## OverallQual:YearBuilt:FullBath:TotRmsAbvGrd:GarageArea                                                          7.327e+01
## OverallQual:YearRemodAdd:FullBath:TotRmsAbvGrd:GarageArea                                                       7.677e+01
## YearBuilt:YearRemodAdd:FullBath:TotRmsAbvGrd:GarageArea                                                         3.011e-01
## OverallQual:TotalBsmtSF:FullBath:TotRmsAbvGrd:GarageArea                                                        7.186e+01
## YearBuilt:TotalBsmtSF:FullBath:TotRmsAbvGrd:GarageArea                                                          3.582e-01
## YearRemodAdd:TotalBsmtSF:FullBath:TotRmsAbvGrd:GarageArea                                                       3.059e-01
## OverallQual:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageArea                                                          1.035e+01
## YearBuilt:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageArea                                                            3.220e-01
## YearRemodAdd:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageArea                                                         1.963e-01
## TotalBsmtSF:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageArea                                                          2.655e-01
## OverallQual:GrLivArea:FullBath:TotRmsAbvGrd:GarageArea                                                          5.318e+01
## YearBuilt:GrLivArea:FullBath:TotRmsAbvGrd:GarageArea                                                            1.969e-01
## YearRemodAdd:GrLivArea:FullBath:TotRmsAbvGrd:GarageArea                                                         1.861e-01
## TotalBsmtSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageArea                                                          2.350e-01
## X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageArea                                                            2.399e-01
## OverallQual:YearBuilt:YearRemodAdd:GarageCars:GarageArea                                                        1.003e-01
## OverallQual:YearBuilt:TotalBsmtSF:GarageCars:GarageArea                                                         2.195e-01
## OverallQual:YearRemodAdd:TotalBsmtSF:GarageCars:GarageArea                                                      2.159e-01
## YearBuilt:YearRemodAdd:TotalBsmtSF:GarageCars:GarageArea                                                        9.659e-04
## OverallQual:YearBuilt:X1stFlrSF:GarageCars:GarageArea                                                           2.205e-01
## OverallQual:YearRemodAdd:X1stFlrSF:GarageCars:GarageArea                                                        1.738e-01
## YearBuilt:YearRemodAdd:X1stFlrSF:GarageCars:GarageArea                                                          1.278e-03
## OverallQual:TotalBsmtSF:X1stFlrSF:GarageCars:GarageArea                                                         3.403e-01
## YearBuilt:TotalBsmtSF:X1stFlrSF:GarageCars:GarageArea                                                           7.962e-04
## YearRemodAdd:TotalBsmtSF:X1stFlrSF:GarageCars:GarageArea                                                        8.661e-04
## OverallQual:YearBuilt:GrLivArea:GarageCars:GarageArea                                                           1.508e-01
## OverallQual:YearRemodAdd:GrLivArea:GarageCars:GarageArea                                                        1.363e-01
## YearBuilt:YearRemodAdd:GrLivArea:GarageCars:GarageArea                                                          6.083e-04
## OverallQual:TotalBsmtSF:GrLivArea:GarageCars:GarageArea                                                         2.794e-01
## YearBuilt:TotalBsmtSF:GrLivArea:GarageCars:GarageArea                                                           8.314e-04
## YearRemodAdd:TotalBsmtSF:GrLivArea:GarageCars:GarageArea                                                        8.878e-04
## OverallQual:X1stFlrSF:GrLivArea:GarageCars:GarageArea                                                           2.279e-01
## YearBuilt:X1stFlrSF:GrLivArea:GarageCars:GarageArea                                                             8.342e-04
## YearRemodAdd:X1stFlrSF:GrLivArea:GarageCars:GarageArea                                                          6.947e-04
## TotalBsmtSF:X1stFlrSF:GrLivArea:GarageCars:GarageArea                                                           7.471e-04
## OverallQual:YearBuilt:FullBath:GarageCars:GarageArea                                                            2.146e+02
## OverallQual:YearRemodAdd:FullBath:GarageCars:GarageArea                                                         2.000e+02
## YearBuilt:YearRemodAdd:FullBath:GarageCars:GarageArea                                                           4.615e-01
## OverallQual:TotalBsmtSF:FullBath:GarageCars:GarageArea                                                          3.074e+02
## YearBuilt:TotalBsmtSF:FullBath:GarageCars:GarageArea                                                            1.175e+00
## YearRemodAdd:TotalBsmtSF:FullBath:GarageCars:GarageArea                                                         1.254e+00
## OverallQual:X1stFlrSF:FullBath:GarageCars:GarageArea                                                            2.767e+02
## YearBuilt:X1stFlrSF:FullBath:GarageCars:GarageArea                                                              1.089e+00
## YearRemodAdd:X1stFlrSF:FullBath:GarageCars:GarageArea                                                           1.132e+00
## TotalBsmtSF:X1stFlrSF:FullBath:GarageCars:GarageArea                                                            1.101e+00
## OverallQual:GrLivArea:FullBath:GarageCars:GarageArea                                                            2.319e+02
## YearBuilt:GrLivArea:FullBath:GarageCars:GarageArea                                                              9.936e-01
## YearRemodAdd:GrLivArea:FullBath:GarageCars:GarageArea                                                           8.595e-01
## TotalBsmtSF:GrLivArea:FullBath:GarageCars:GarageArea                                                            1.535e+00
## X1stFlrSF:GrLivArea:FullBath:GarageCars:GarageArea                                                              1.015e+00
## OverallQual:YearBuilt:TotRmsAbvGrd:GarageCars:GarageArea                                                        2.723e+01
## OverallQual:YearRemodAdd:TotRmsAbvGrd:GarageCars:GarageArea                                                     2.983e+01
## YearBuilt:YearRemodAdd:TotRmsAbvGrd:GarageCars:GarageArea                                                       1.189e-01
## OverallQual:TotalBsmtSF:TotRmsAbvGrd:GarageCars:GarageArea                                                      7.532e+01
## YearBuilt:TotalBsmtSF:TotRmsAbvGrd:GarageCars:GarageArea                                                        1.822e-01
## YearRemodAdd:TotalBsmtSF:TotRmsAbvGrd:GarageCars:GarageArea                                                     2.049e-01
## OverallQual:X1stFlrSF:TotRmsAbvGrd:GarageCars:GarageArea                                                        6.532e+01
## YearBuilt:X1stFlrSF:TotRmsAbvGrd:GarageCars:GarageArea                                                          1.547e-01
## YearRemodAdd:X1stFlrSF:TotRmsAbvGrd:GarageCars:GarageArea                                                       1.347e-01
## TotalBsmtSF:X1stFlrSF:TotRmsAbvGrd:GarageCars:GarageArea                                                        2.024e-01
## OverallQual:GrLivArea:TotRmsAbvGrd:GarageCars:GarageArea                                                        3.700e+01
## YearBuilt:GrLivArea:TotRmsAbvGrd:GarageCars:GarageArea                                                          1.280e-01
## YearRemodAdd:GrLivArea:TotRmsAbvGrd:GarageCars:GarageArea                                                       9.776e-02
## TotalBsmtSF:GrLivArea:TotRmsAbvGrd:GarageCars:GarageArea                                                        2.432e-01
## X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageCars:GarageArea                                                          2.197e-01
## OverallQual:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                                         3.972e+04
## YearBuilt:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                                           1.356e+02
## YearRemodAdd:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                                        1.486e+02
## TotalBsmtSF:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                                         3.330e+02
## X1stFlrSF:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                                           2.051e+02
## GrLivArea:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                                           1.686e+02
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea                                                     NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:FullBath                                                      NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:GrLivArea:FullBath                                                      NA
## OverallQual:YearBuilt:YearRemodAdd:X1stFlrSF:GrLivArea:FullBath                                                        NA
## OverallQual:YearBuilt:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath                                                  3.270e-05
## OverallQual:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath                                               4.082e-05
## YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath                                                        NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:TotRmsAbvGrd                                                  NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:GrLivArea:TotRmsAbvGrd                                                  NA
## OverallQual:YearBuilt:YearRemodAdd:X1stFlrSF:GrLivArea:TotRmsAbvGrd                                                    NA
## OverallQual:YearBuilt:TotalBsmtSF:X1stFlrSF:GrLivArea:TotRmsAbvGrd                                              1.300e-05
## OverallQual:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:TotRmsAbvGrd                                           7.780e-06
## YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:TotRmsAbvGrd                                                    NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:FullBath:TotRmsAbvGrd                                                   NA
## OverallQual:YearBuilt:YearRemodAdd:X1stFlrSF:FullBath:TotRmsAbvGrd                                                     NA
## OverallQual:YearBuilt:TotalBsmtSF:X1stFlrSF:FullBath:TotRmsAbvGrd                                               1.208e-02
## OverallQual:YearRemodAdd:TotalBsmtSF:X1stFlrSF:FullBath:TotRmsAbvGrd                                            1.491e-02
## YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:FullBath:TotRmsAbvGrd                                                     NA
## OverallQual:YearBuilt:YearRemodAdd:GrLivArea:FullBath:TotRmsAbvGrd                                                     NA
## OverallQual:YearBuilt:TotalBsmtSF:GrLivArea:FullBath:TotRmsAbvGrd                                               1.073e-02
## OverallQual:YearRemodAdd:TotalBsmtSF:GrLivArea:FullBath:TotRmsAbvGrd                                            1.098e-02
## YearBuilt:YearRemodAdd:TotalBsmtSF:GrLivArea:FullBath:TotRmsAbvGrd                                                     NA
## OverallQual:YearBuilt:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd                                                 8.855e-03
## OverallQual:YearRemodAdd:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd                                              9.973e-03
## YearBuilt:YearRemodAdd:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd                                                       NA
## OverallQual:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd                                               1.389e-03
## YearBuilt:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd                                                 2.043e-05
## YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd                                              2.535e-05
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GarageCars                                                    NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:GrLivArea:GarageCars                                                    NA
## OverallQual:YearBuilt:YearRemodAdd:X1stFlrSF:GrLivArea:GarageCars                                                      NA
## OverallQual:YearBuilt:TotalBsmtSF:X1stFlrSF:GrLivArea:GarageCars                                                5.880e-05
## OverallQual:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:GarageCars                                             4.107e-05
## YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:GarageCars                                                      NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:FullBath:GarageCars                                                     NA
## OverallQual:YearBuilt:YearRemodAdd:X1stFlrSF:FullBath:GarageCars                                                       NA
## OverallQual:YearBuilt:TotalBsmtSF:X1stFlrSF:FullBath:GarageCars                                                 5.967e-02
## OverallQual:YearRemodAdd:TotalBsmtSF:X1stFlrSF:FullBath:GarageCars                                              6.312e-02
## YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:FullBath:GarageCars                                                       NA
## OverallQual:YearBuilt:YearRemodAdd:GrLivArea:FullBath:GarageCars                                                       NA
## OverallQual:YearBuilt:TotalBsmtSF:GrLivArea:FullBath:GarageCars                                                 1.042e-01
## OverallQual:YearRemodAdd:TotalBsmtSF:GrLivArea:FullBath:GarageCars                                              1.280e-01
## YearBuilt:YearRemodAdd:TotalBsmtSF:GrLivArea:FullBath:GarageCars                                                       NA
## OverallQual:YearBuilt:X1stFlrSF:GrLivArea:FullBath:GarageCars                                                   9.491e-02
## OverallQual:YearRemodAdd:X1stFlrSF:GrLivArea:FullBath:GarageCars                                                1.173e-01
## YearBuilt:YearRemodAdd:X1stFlrSF:GrLivArea:FullBath:GarageCars                                                         NA
## OverallQual:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:GarageCars                                                 4.545e-03
## YearBuilt:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:GarageCars                                                   2.641e-04
## YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:GarageCars                                                2.973e-04
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:TotRmsAbvGrd:GarageCars                                                 NA
## OverallQual:YearBuilt:YearRemodAdd:X1stFlrSF:TotRmsAbvGrd:GarageCars                                                   NA
## OverallQual:YearBuilt:TotalBsmtSF:X1stFlrSF:TotRmsAbvGrd:GarageCars                                             1.796e-02
## OverallQual:YearRemodAdd:TotalBsmtSF:X1stFlrSF:TotRmsAbvGrd:GarageCars                                          2.637e-02
## YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:TotRmsAbvGrd:GarageCars                                                   NA
## OverallQual:YearBuilt:YearRemodAdd:GrLivArea:TotRmsAbvGrd:GarageCars                                                   NA
## OverallQual:YearBuilt:TotalBsmtSF:GrLivArea:TotRmsAbvGrd:GarageCars                                             1.525e-02
## OverallQual:YearRemodAdd:TotalBsmtSF:GrLivArea:TotRmsAbvGrd:GarageCars                                          1.580e-02
## YearBuilt:YearRemodAdd:TotalBsmtSF:GrLivArea:TotRmsAbvGrd:GarageCars                                                   NA
## OverallQual:YearBuilt:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageCars                                               1.420e-02
## OverallQual:YearRemodAdd:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageCars                                            1.465e-02
## YearBuilt:YearRemodAdd:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageCars                                                     NA
## OverallQual:TotalBsmtSF:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageCars                                             1.482e-02
## YearBuilt:TotalBsmtSF:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageCars                                               5.491e-05
## YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageCars                                            2.573e-05
## OverallQual:YearBuilt:YearRemodAdd:FullBath:TotRmsAbvGrd:GarageCars                                                    NA
## OverallQual:YearBuilt:TotalBsmtSF:FullBath:TotRmsAbvGrd:GarageCars                                              2.766e+01
## OverallQual:YearRemodAdd:TotalBsmtSF:FullBath:TotRmsAbvGrd:GarageCars                                           2.351e+01
## YearBuilt:YearRemodAdd:TotalBsmtSF:FullBath:TotRmsAbvGrd:GarageCars                                                    NA
## OverallQual:YearBuilt:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageCars                                                1.775e+01
## OverallQual:YearRemodAdd:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageCars                                                    NA
## YearBuilt:YearRemodAdd:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageCars                                                      NA
## OverallQual:TotalBsmtSF:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageCars                                              1.524e+00
## YearBuilt:TotalBsmtSF:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageCars                                                7.517e-02
## YearRemodAdd:TotalBsmtSF:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageCars                                             7.983e-02
## OverallQual:YearBuilt:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars                                                1.164e+01
## OverallQual:YearRemodAdd:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars                                             1.055e+01
## YearBuilt:YearRemodAdd:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars                                                      NA
## OverallQual:TotalBsmtSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars                                              1.480e+00
## YearBuilt:TotalBsmtSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars                                                5.730e-02
## YearRemodAdd:TotalBsmtSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars                                             6.913e-02
## OverallQual:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars                                                1.638e+00
## YearBuilt:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars                                                  6.527e-02
## YearRemodAdd:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars                                               8.789e-02
## TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars                                                4.780e-03
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GarageArea                                                    NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:GrLivArea:GarageArea                                                    NA
## OverallQual:YearBuilt:YearRemodAdd:X1stFlrSF:GrLivArea:GarageArea                                                      NA
## OverallQual:YearBuilt:TotalBsmtSF:X1stFlrSF:GrLivArea:GarageArea                                                1.013e-07
## OverallQual:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:GarageArea                                                    NA
## YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:GarageArea                                                      NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:FullBath:GarageArea                                                     NA
## OverallQual:YearBuilt:YearRemodAdd:X1stFlrSF:FullBath:GarageArea                                                       NA
## OverallQual:YearBuilt:TotalBsmtSF:X1stFlrSF:FullBath:GarageArea                                                 1.965e-04
## OverallQual:YearRemodAdd:TotalBsmtSF:X1stFlrSF:FullBath:GarageArea                                              1.404e-04
## YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:FullBath:GarageArea                                                       NA
## OverallQual:YearBuilt:YearRemodAdd:GrLivArea:FullBath:GarageArea                                                       NA
## OverallQual:YearBuilt:TotalBsmtSF:GrLivArea:FullBath:GarageArea                                                 1.906e-04
## OverallQual:YearRemodAdd:TotalBsmtSF:GrLivArea:FullBath:GarageArea                                                     NA
## YearBuilt:YearRemodAdd:TotalBsmtSF:GrLivArea:FullBath:GarageArea                                                       NA
## OverallQual:YearBuilt:X1stFlrSF:GrLivArea:FullBath:GarageArea                                                   1.508e-04
## OverallQual:YearRemodAdd:X1stFlrSF:GrLivArea:FullBath:GarageArea                                                1.709e-04
## YearBuilt:YearRemodAdd:X1stFlrSF:GrLivArea:FullBath:GarageArea                                                         NA
## OverallQual:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:GarageArea                                                 1.990e-05
## YearBuilt:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:GarageArea                                                   4.072e-07
## YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:GarageArea                                                       NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:TotRmsAbvGrd:GarageArea                                                 NA
## OverallQual:YearBuilt:YearRemodAdd:X1stFlrSF:TotRmsAbvGrd:GarageArea                                                   NA
## OverallQual:YearBuilt:TotalBsmtSF:X1stFlrSF:TotRmsAbvGrd:GarageArea                                             3.916e-05
## OverallQual:YearRemodAdd:TotalBsmtSF:X1stFlrSF:TotRmsAbvGrd:GarageArea                                                 NA
## YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:TotRmsAbvGrd:GarageArea                                                   NA
## OverallQual:YearBuilt:YearRemodAdd:GrLivArea:TotRmsAbvGrd:GarageArea                                                   NA
## OverallQual:YearBuilt:TotalBsmtSF:GrLivArea:TotRmsAbvGrd:GarageArea                                             4.750e-05
## OverallQual:YearRemodAdd:TotalBsmtSF:GrLivArea:TotRmsAbvGrd:GarageArea                                                 NA
## YearBuilt:YearRemodAdd:TotalBsmtSF:GrLivArea:TotRmsAbvGrd:GarageArea                                                   NA
## OverallQual:YearBuilt:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageArea                                               3.045e-05
## OverallQual:YearRemodAdd:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageArea                                            3.267e-05
## YearBuilt:YearRemodAdd:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageArea                                                     NA
## OverallQual:TotalBsmtSF:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageArea                                             4.587e-06
## YearBuilt:TotalBsmtSF:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageArea                                               6.516e-08
## YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageArea                                                   NA
## OverallQual:YearBuilt:YearRemodAdd:FullBath:TotRmsAbvGrd:GarageArea                                                    NA
## OverallQual:YearBuilt:TotalBsmtSF:FullBath:TotRmsAbvGrd:GarageArea                                              4.394e-02
## OverallQual:YearRemodAdd:TotalBsmtSF:FullBath:TotRmsAbvGrd:GarageArea                                           3.691e-02
## YearBuilt:YearRemodAdd:TotalBsmtSF:FullBath:TotRmsAbvGrd:GarageArea                                                    NA
## OverallQual:YearBuilt:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageArea                                                       NA
## OverallQual:YearRemodAdd:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageArea                                                    NA
## YearBuilt:YearRemodAdd:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageArea                                                      NA
## OverallQual:TotalBsmtSF:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageArea                                              5.057e-03
## YearBuilt:TotalBsmtSF:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageArea                                                1.164e-04
## YearRemodAdd:TotalBsmtSF:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageArea                                             1.170e-04
## OverallQual:YearBuilt:GrLivArea:FullBath:TotRmsAbvGrd:GarageArea                                                2.713e-02
## OverallQual:YearRemodAdd:GrLivArea:FullBath:TotRmsAbvGrd:GarageArea                                             2.399e-02
## YearBuilt:YearRemodAdd:GrLivArea:FullBath:TotRmsAbvGrd:GarageArea                                                      NA
## OverallQual:TotalBsmtSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageArea                                              5.809e-03
## YearBuilt:TotalBsmtSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageArea                                                1.052e-04
## YearRemodAdd:TotalBsmtSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageArea                                             1.090e-04
## OverallQual:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageArea                                                5.649e-03
## YearBuilt:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageArea                                                  1.189e-04
## YearRemodAdd:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageArea                                                      NA
## TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageArea                                                1.969e-05
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:GarageCars:GarageArea                                                   NA
## OverallQual:YearBuilt:YearRemodAdd:X1stFlrSF:GarageCars:GarageArea                                                     NA
## OverallQual:YearBuilt:TotalBsmtSF:X1stFlrSF:GarageCars:GarageArea                                               1.268e-04
## OverallQual:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GarageCars:GarageArea                                            1.376e-04
## YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GarageCars:GarageArea                                                     NA
## OverallQual:YearBuilt:YearRemodAdd:GrLivArea:GarageCars:GarageArea                                                     NA
## OverallQual:YearBuilt:TotalBsmtSF:GrLivArea:GarageCars:GarageArea                                               1.107e-04
## OverallQual:YearRemodAdd:TotalBsmtSF:GrLivArea:GarageCars:GarageArea                                            9.636e-05
## YearBuilt:YearRemodAdd:TotalBsmtSF:GrLivArea:GarageCars:GarageArea                                                     NA
## OverallQual:YearBuilt:X1stFlrSF:GrLivArea:GarageCars:GarageArea                                                 1.081e-04
## OverallQual:YearRemodAdd:X1stFlrSF:GrLivArea:GarageCars:GarageArea                                              9.819e-05
## YearBuilt:YearRemodAdd:X1stFlrSF:GrLivArea:GarageCars:GarageArea                                                       NA
## OverallQual:TotalBsmtSF:X1stFlrSF:GrLivArea:GarageCars:GarageArea                                               1.035e-05
## YearBuilt:TotalBsmtSF:X1stFlrSF:GrLivArea:GarageCars:GarageArea                                                 2.062e-07
## YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:GarageCars:GarageArea                                              2.575e-07
## OverallQual:YearBuilt:YearRemodAdd:FullBath:GarageCars:GarageArea                                                      NA
## OverallQual:YearBuilt:TotalBsmtSF:FullBath:GarageCars:GarageArea                                                1.688e-01
## OverallQual:YearRemodAdd:TotalBsmtSF:FullBath:GarageCars:GarageArea                                             1.590e-01
## YearBuilt:YearRemodAdd:TotalBsmtSF:FullBath:GarageCars:GarageArea                                                      NA
## OverallQual:YearBuilt:X1stFlrSF:FullBath:GarageCars:GarageArea                                                  1.587e-01
## OverallQual:YearRemodAdd:X1stFlrSF:FullBath:GarageCars:GarageArea                                               1.735e-01
## YearBuilt:YearRemodAdd:X1stFlrSF:FullBath:GarageCars:GarageArea                                                        NA
## OverallQual:TotalBsmtSF:X1stFlrSF:FullBath:GarageCars:GarageArea                                                1.741e-01
## YearBuilt:TotalBsmtSF:X1stFlrSF:FullBath:GarageCars:GarageArea                                                  5.367e-04
## YearRemodAdd:TotalBsmtSF:X1stFlrSF:FullBath:GarageCars:GarageArea                                               2.810e-04
## OverallQual:YearBuilt:GrLivArea:FullBath:GarageCars:GarageArea                                                  1.356e-01
## OverallQual:YearRemodAdd:GrLivArea:FullBath:GarageCars:GarageArea                                               9.667e-02
## YearBuilt:YearRemodAdd:GrLivArea:FullBath:GarageCars:GarageArea                                                        NA
## OverallQual:TotalBsmtSF:GrLivArea:FullBath:GarageCars:GarageArea                                                8.768e-02
## YearBuilt:TotalBsmtSF:GrLivArea:FullBath:GarageCars:GarageArea                                                  5.509e-04
## YearRemodAdd:TotalBsmtSF:GrLivArea:FullBath:GarageCars:GarageArea                                               7.112e-04
## OverallQual:X1stFlrSF:GrLivArea:FullBath:GarageCars:GarageArea                                                  1.921e-02
## YearBuilt:X1stFlrSF:GrLivArea:FullBath:GarageCars:GarageArea                                                    5.477e-04
## YearRemodAdd:X1stFlrSF:GrLivArea:FullBath:GarageCars:GarageArea                                                 5.732e-04
## TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:GarageCars:GarageArea                                                  2.345e-04
## OverallQual:YearBuilt:YearRemodAdd:TotRmsAbvGrd:GarageCars:GarageArea                                                  NA
## OverallQual:YearBuilt:TotalBsmtSF:TotRmsAbvGrd:GarageCars:GarageArea                                            3.770e-02
## OverallQual:YearRemodAdd:TotalBsmtSF:TotRmsAbvGrd:GarageCars:GarageArea                                         3.544e-02
## YearBuilt:YearRemodAdd:TotalBsmtSF:TotRmsAbvGrd:GarageCars:GarageArea                                                  NA
## OverallQual:YearBuilt:X1stFlrSF:TotRmsAbvGrd:GarageCars:GarageArea                                              3.444e-02
## OverallQual:YearRemodAdd:X1stFlrSF:TotRmsAbvGrd:GarageCars:GarageArea                                                  NA
## YearBuilt:YearRemodAdd:X1stFlrSF:TotRmsAbvGrd:GarageCars:GarageArea                                                    NA
## OverallQual:TotalBsmtSF:X1stFlrSF:TotRmsAbvGrd:GarageCars:GarageArea                                            4.140e-02
## YearBuilt:TotalBsmtSF:X1stFlrSF:TotRmsAbvGrd:GarageCars:GarageArea                                              6.810e-05
## YearRemodAdd:TotalBsmtSF:X1stFlrSF:TotRmsAbvGrd:GarageCars:GarageArea                                           1.281e-04
## OverallQual:YearBuilt:GrLivArea:TotRmsAbvGrd:GarageCars:GarageArea                                              1.922e-02
## OverallQual:YearRemodAdd:GrLivArea:TotRmsAbvGrd:GarageCars:GarageArea                                           1.702e-02
## YearBuilt:YearRemodAdd:GrLivArea:TotRmsAbvGrd:GarageCars:GarageArea                                                    NA
## OverallQual:TotalBsmtSF:GrLivArea:TotRmsAbvGrd:GarageCars:GarageArea                                            1.221e-02
## YearBuilt:TotalBsmtSF:GrLivArea:TotRmsAbvGrd:GarageCars:GarageArea                                              8.702e-05
## YearRemodAdd:TotalBsmtSF:GrLivArea:TotRmsAbvGrd:GarageCars:GarageArea                                           1.052e-04
## OverallQual:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageCars:GarageArea                                              3.387e-03
## YearBuilt:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageCars:GarageArea                                                8.776e-05
## YearRemodAdd:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageCars:GarageArea                                             8.779e-05
## TotalBsmtSF:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageCars:GarageArea                                              1.021e-05
## OverallQual:YearBuilt:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                               2.478e+01
## OverallQual:YearRemodAdd:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                            2.431e+01
## YearBuilt:YearRemodAdd:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                                     NA
## OverallQual:TotalBsmtSF:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                             5.222e+00
## YearBuilt:TotalBsmtSF:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                               1.231e-01
## YearRemodAdd:TotalBsmtSF:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                            1.177e-01
## OverallQual:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                               4.364e+00
## YearBuilt:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                                        NA
## YearRemodAdd:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                                     NA
## TotalBsmtSF:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                               1.538e-02
## OverallQual:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                               2.282e+01
## YearBuilt:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                                 8.358e-02
## YearRemodAdd:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                              4.559e-02
## TotalBsmtSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                               1.590e-02
## X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                                 5.822e-02
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath                                            NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:TotRmsAbvGrd                                        NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:FullBath:TotRmsAbvGrd                                         NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:GrLivArea:FullBath:TotRmsAbvGrd                                         NA
## OverallQual:YearBuilt:YearRemodAdd:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd                                           NA
## OverallQual:YearBuilt:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd                                            NA
## OverallQual:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd                                         NA
## YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd                                           NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:GarageCars                                          NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:FullBath:GarageCars                                           NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:GrLivArea:FullBath:GarageCars                                           NA
## OverallQual:YearBuilt:YearRemodAdd:X1stFlrSF:GrLivArea:FullBath:GarageCars                                             NA
## OverallQual:YearBuilt:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:GarageCars                                              NA
## OverallQual:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:GarageCars                                           NA
## YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:GarageCars                                             NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:TotRmsAbvGrd:GarageCars                                       NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:GrLivArea:TotRmsAbvGrd:GarageCars                                       NA
## OverallQual:YearBuilt:YearRemodAdd:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageCars                                         NA
## OverallQual:YearBuilt:TotalBsmtSF:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageCars                                   7.568e-06
## OverallQual:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageCars                                       NA
## YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageCars                                         NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:FullBath:TotRmsAbvGrd:GarageCars                                        NA
## OverallQual:YearBuilt:YearRemodAdd:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageCars                                          NA
## OverallQual:YearBuilt:TotalBsmtSF:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageCars                                           NA
## OverallQual:YearRemodAdd:TotalBsmtSF:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageCars                                        NA
## YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageCars                                          NA
## OverallQual:YearBuilt:YearRemodAdd:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars                                          NA
## OverallQual:YearBuilt:TotalBsmtSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars                                           NA
## OverallQual:YearRemodAdd:TotalBsmtSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars                                        NA
## YearBuilt:YearRemodAdd:TotalBsmtSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars                                          NA
## OverallQual:YearBuilt:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars                                             NA
## OverallQual:YearRemodAdd:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars                                          NA
## YearBuilt:YearRemodAdd:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars                                            NA
## OverallQual:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars                                    2.000e-03
## YearBuilt:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars                                             NA
## YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars                                          NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:GarageArea                                          NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:FullBath:GarageArea                                           NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:GrLivArea:FullBath:GarageArea                                           NA
## OverallQual:YearBuilt:YearRemodAdd:X1stFlrSF:GrLivArea:FullBath:GarageArea                                             NA
## OverallQual:YearBuilt:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:GarageArea                                              NA
## OverallQual:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:GarageArea                                           NA
## YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:GarageArea                                             NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:TotRmsAbvGrd:GarageArea                                       NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:GrLivArea:TotRmsAbvGrd:GarageArea                                       NA
## OverallQual:YearBuilt:YearRemodAdd:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageArea                                         NA
## OverallQual:YearBuilt:TotalBsmtSF:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageArea                                          NA
## OverallQual:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageArea                                       NA
## YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageArea                                         NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:FullBath:TotRmsAbvGrd:GarageArea                                        NA
## OverallQual:YearBuilt:YearRemodAdd:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageArea                                          NA
## OverallQual:YearBuilt:TotalBsmtSF:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageArea                                           NA
## OverallQual:YearRemodAdd:TotalBsmtSF:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageArea                                        NA
## YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageArea                                          NA
## OverallQual:YearBuilt:YearRemodAdd:GrLivArea:FullBath:TotRmsAbvGrd:GarageArea                                          NA
## OverallQual:YearBuilt:TotalBsmtSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageArea                                           NA
## OverallQual:YearRemodAdd:TotalBsmtSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageArea                                        NA
## YearBuilt:YearRemodAdd:TotalBsmtSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageArea                                          NA
## OverallQual:YearBuilt:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageArea                                             NA
## OverallQual:YearRemodAdd:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageArea                                          NA
## YearBuilt:YearRemodAdd:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageArea                                            NA
## OverallQual:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageArea                                    2.652e-06
## YearBuilt:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageArea                                             NA
## YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageArea                                          NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GarageCars:GarageArea                                         NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:GrLivArea:GarageCars:GarageArea                                         NA
## OverallQual:YearBuilt:YearRemodAdd:X1stFlrSF:GrLivArea:GarageCars:GarageArea                                           NA
## OverallQual:YearBuilt:TotalBsmtSF:X1stFlrSF:GrLivArea:GarageCars:GarageArea                                            NA
## OverallQual:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:GarageCars:GarageArea                                         NA
## YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:GarageCars:GarageArea                                           NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:FullBath:GarageCars:GarageArea                                          NA
## OverallQual:YearBuilt:YearRemodAdd:X1stFlrSF:FullBath:GarageCars:GarageArea                                            NA
## OverallQual:YearBuilt:TotalBsmtSF:X1stFlrSF:FullBath:GarageCars:GarageArea                                      8.826e-05
## OverallQual:YearRemodAdd:TotalBsmtSF:X1stFlrSF:FullBath:GarageCars:GarageArea                                          NA
## YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:FullBath:GarageCars:GarageArea                                            NA
## OverallQual:YearBuilt:YearRemodAdd:GrLivArea:FullBath:GarageCars:GarageArea                                            NA
## OverallQual:YearBuilt:TotalBsmtSF:GrLivArea:FullBath:GarageCars:GarageArea                                             NA
## OverallQual:YearRemodAdd:TotalBsmtSF:GrLivArea:FullBath:GarageCars:GarageArea                                          NA
## YearBuilt:YearRemodAdd:TotalBsmtSF:GrLivArea:FullBath:GarageCars:GarageArea                                            NA
## OverallQual:YearBuilt:X1stFlrSF:GrLivArea:FullBath:GarageCars:GarageArea                                               NA
## OverallQual:YearRemodAdd:X1stFlrSF:GrLivArea:FullBath:GarageCars:GarageArea                                            NA
## YearBuilt:YearRemodAdd:X1stFlrSF:GrLivArea:FullBath:GarageCars:GarageArea                                              NA
## OverallQual:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:GarageCars:GarageArea                                      2.052e-05
## YearBuilt:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:GarageCars:GarageArea                                               NA
## YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:GarageCars:GarageArea                                            NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:TotRmsAbvGrd:GarageCars:GarageArea                                      NA
## OverallQual:YearBuilt:YearRemodAdd:X1stFlrSF:TotRmsAbvGrd:GarageCars:GarageArea                                        NA
## OverallQual:YearBuilt:TotalBsmtSF:X1stFlrSF:TotRmsAbvGrd:GarageCars:GarageArea                                         NA
## OverallQual:YearRemodAdd:TotalBsmtSF:X1stFlrSF:TotRmsAbvGrd:GarageCars:GarageArea                               2.125e-05
## YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:TotRmsAbvGrd:GarageCars:GarageArea                                        NA
## OverallQual:YearBuilt:YearRemodAdd:GrLivArea:TotRmsAbvGrd:GarageCars:GarageArea                                        NA
## OverallQual:YearBuilt:TotalBsmtSF:GrLivArea:TotRmsAbvGrd:GarageCars:GarageArea                                         NA
## OverallQual:YearRemodAdd:TotalBsmtSF:GrLivArea:TotRmsAbvGrd:GarageCars:GarageArea                                      NA
## YearBuilt:YearRemodAdd:TotalBsmtSF:GrLivArea:TotRmsAbvGrd:GarageCars:GarageArea                                        NA
## OverallQual:YearBuilt:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageCars:GarageArea                                           NA
## OverallQual:YearRemodAdd:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageCars:GarageArea                                        NA
## YearBuilt:YearRemodAdd:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageCars:GarageArea                                          NA
## OverallQual:TotalBsmtSF:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageCars:GarageArea                                  1.454e-06
## YearBuilt:TotalBsmtSF:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageCars:GarageArea                                           NA
## YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageCars:GarageArea                                        NA
## OverallQual:YearBuilt:YearRemodAdd:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                         NA
## OverallQual:YearBuilt:TotalBsmtSF:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                          NA
## OverallQual:YearRemodAdd:TotalBsmtSF:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                       NA
## YearBuilt:YearRemodAdd:TotalBsmtSF:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                         NA
## OverallQual:YearBuilt:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                            NA
## OverallQual:YearRemodAdd:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                         NA
## YearBuilt:YearRemodAdd:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                    5.200e-05
## OverallQual:TotalBsmtSF:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                   6.590e-03
## YearBuilt:TotalBsmtSF:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                            NA
## YearRemodAdd:TotalBsmtSF:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                         NA
## OverallQual:YearBuilt:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                     1.159e-02
## OverallQual:YearRemodAdd:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                         NA
## YearBuilt:YearRemodAdd:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                           NA
## OverallQual:TotalBsmtSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                   2.141e-03
## YearBuilt:TotalBsmtSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                            NA
## YearRemodAdd:TotalBsmtSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                         NA
## OverallQual:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                     7.128e-03
## YearBuilt:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                              NA
## YearRemodAdd:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                           NA
## TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                     7.772e-06
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd                               NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:GarageCars                                 NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageCars                             NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageCars                              NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars                              NA
## OverallQual:YearBuilt:YearRemodAdd:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars                                NA
## OverallQual:YearBuilt:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars                                 NA
## OverallQual:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars                              NA
## YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars                                NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:GarageArea                                 NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageArea                             NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageArea                              NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageArea                              NA
## OverallQual:YearBuilt:YearRemodAdd:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageArea                                NA
## OverallQual:YearBuilt:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageArea                                 NA
## OverallQual:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageArea                              NA
## YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageArea                                NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:GarageCars:GarageArea                               NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:FullBath:GarageCars:GarageArea                                NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:GrLivArea:FullBath:GarageCars:GarageArea                         2.200e-08
## OverallQual:YearBuilt:YearRemodAdd:X1stFlrSF:GrLivArea:FullBath:GarageCars:GarageArea                                  NA
## OverallQual:YearBuilt:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:GarageCars:GarageArea                                   NA
## OverallQual:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:GarageCars:GarageArea                                NA
## YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:GarageCars:GarageArea                           5.926e-11
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:TotRmsAbvGrd:GarageCars:GarageArea                            NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:GrLivArea:TotRmsAbvGrd:GarageCars:GarageArea                     3.129e-09
## OverallQual:YearBuilt:YearRemodAdd:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageCars:GarageArea                              NA
## OverallQual:YearBuilt:TotalBsmtSF:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageCars:GarageArea                               NA
## OverallQual:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageCars:GarageArea                            NA
## YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageCars:GarageArea                              NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                             NA
## OverallQual:YearBuilt:YearRemodAdd:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                               NA
## OverallQual:YearBuilt:TotalBsmtSF:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                NA
## OverallQual:YearRemodAdd:TotalBsmtSF:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                             NA
## YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                               NA
## OverallQual:YearBuilt:YearRemodAdd:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                               NA
## OverallQual:YearBuilt:TotalBsmtSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                NA
## OverallQual:YearRemodAdd:TotalBsmtSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                             NA
## YearBuilt:YearRemodAdd:TotalBsmtSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                               NA
## OverallQual:YearBuilt:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                  NA
## OverallQual:YearRemodAdd:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                        3.145e-06
## YearBuilt:YearRemodAdd:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                          1.498e-08
## OverallQual:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                         9.391e-07
## YearBuilt:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                  NA
## YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                               NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars             4.251e-10
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageArea                    NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:GarageCars:GarageArea               4.692e-12
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageCars:GarageArea                  NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageCars:GarageArea            1.508e-09
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                   NA
## OverallQual:YearBuilt:YearRemodAdd:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                     NA
## OverallQual:YearBuilt:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                      NA
## OverallQual:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                   NA
## YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                     NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars:GarageArea         NA
##                                                                                                                t value
## (Intercept)                                                                                                     -2.666
## OverallQual                                                                                                      1.630
## YearBuilt                                                                                                        2.889
## YearRemodAdd                                                                                                     2.360
## TotalBsmtSF                                                                                                      0.160
## X1stFlrSF                                                                                                        1.401
## GrLivArea                                                                                                       -0.318
## FullBath                                                                                                         1.391
## TotRmsAbvGrd                                                                                                     2.448
## GarageCars                                                                                                       1.916
## GarageArea                                                                                                       1.505
## OverallQual:YearBuilt                                                                                           -1.901
## OverallQual:YearRemodAdd                                                                                        -1.100
## YearBuilt:YearRemodAdd                                                                                          -2.771
## OverallQual:TotalBsmtSF                                                                                         -0.313
## YearBuilt:TotalBsmtSF                                                                                           -0.654
## YearRemodAdd:TotalBsmtSF                                                                                        -0.361
## OverallQual:X1stFlrSF                                                                                           -0.840
## YearBuilt:X1stFlrSF                                                                                             -1.301
## YearRemodAdd:X1stFlrSF                                                                                          -0.957
## TotalBsmtSF:X1stFlrSF                                                                                           -0.650
## OverallQual:GrLivArea                                                                                            1.861
## YearBuilt:GrLivArea                                                                                             -0.107
## YearRemodAdd:GrLivArea                                                                                           0.143
## TotalBsmtSF:GrLivArea                                                                                           -1.422
## X1stFlrSF:GrLivArea                                                                                              1.695
## OverallQual:FullBath                                                                                            -0.725
## YearBuilt:FullBath                                                                                              -1.799
## YearRemodAdd:FullBath                                                                                           -1.203
## TotalBsmtSF:FullBath                                                                                             1.562
## X1stFlrSF:FullBath                                                                                              -2.182
## GrLivArea:FullBath                                                                                               0.212
## OverallQual:TotRmsAbvGrd                                                                                        -1.501
## YearBuilt:TotRmsAbvGrd                                                                                          -2.367
## YearRemodAdd:TotRmsAbvGrd                                                                                       -2.380
## TotalBsmtSF:TotRmsAbvGrd                                                                                        -0.094
## X1stFlrSF:TotRmsAbvGrd                                                                                          -0.318
## GrLivArea:TotRmsAbvGrd                                                                                          -1.557
## FullBath:TotRmsAbvGrd                                                                                           -0.421
## OverallQual:GarageCars                                                                                          -0.082
## YearBuilt:GarageCars                                                                                            -2.259
## YearRemodAdd:GarageCars                                                                                         -1.583
## TotalBsmtSF:GarageCars                                                                                           1.286
## X1stFlrSF:GarageCars                                                                                            -2.149
## GrLivArea:GarageCars                                                                                             2.014
## FullBath:GarageCars                                                                                             -1.121
## TotRmsAbvGrd:GarageCars                                                                                         -2.558
## OverallQual:GarageArea                                                                                          -1.149
## YearBuilt:GarageArea                                                                                            -1.326
## YearRemodAdd:GarageArea                                                                                         -1.939
## TotalBsmtSF:GarageArea                                                                                          -0.880
## X1stFlrSF:GarageArea                                                                                             0.154
## GrLivArea:GarageArea                                                                                            -1.678
## FullBath:GarageArea                                                                                              0.407
## TotRmsAbvGrd:GarageArea                                                                                          0.550
## GarageCars:GarageArea                                                                                           -1.530
## OverallQual:YearBuilt:YearRemodAdd                                                                               1.626
## OverallQual:YearBuilt:TotalBsmtSF                                                                                1.224
## OverallQual:YearRemodAdd:TotalBsmtSF                                                                             0.154
## YearBuilt:YearRemodAdd:TotalBsmtSF                                                                               0.872
## OverallQual:YearBuilt:X1stFlrSF                                                                                  0.366
## OverallQual:YearRemodAdd:X1stFlrSF                                                                               0.380
## YearBuilt:YearRemodAdd:X1stFlrSF                                                                                 0.895
## OverallQual:TotalBsmtSF:X1stFlrSF                                                                                2.387
## YearBuilt:TotalBsmtSF:X1stFlrSF                                                                                  0.924
## YearRemodAdd:TotalBsmtSF:X1stFlrSF                                                                               0.443
## OverallQual:YearBuilt:GrLivArea                                                                                 -1.808
## OverallQual:YearRemodAdd:GrLivArea                                                                              -1.300
## YearBuilt:YearRemodAdd:GrLivArea                                                                                 0.269
## OverallQual:TotalBsmtSF:GrLivArea                                                                               -0.594
## YearBuilt:TotalBsmtSF:GrLivArea                                                                                  1.300
## YearRemodAdd:TotalBsmtSF:GrLivArea                                                                               1.924
## OverallQual:X1stFlrSF:GrLivArea                                                                                 -0.313
## YearBuilt:X1stFlrSF:GrLivArea                                                                                   -1.227
## YearRemodAdd:X1stFlrSF:GrLivArea                                                                                -2.318
## TotalBsmtSF:X1stFlrSF:GrLivArea                                                                                 -0.238
## OverallQual:YearBuilt:FullBath                                                                                   1.247
## OverallQual:YearRemodAdd:FullBath                                                                                0.168
## YearBuilt:YearRemodAdd:FullBath                                                                                  1.708
## OverallQual:TotalBsmtSF:FullBath                                                                                -1.031
## YearBuilt:TotalBsmtSF:FullBath                                                                                  -1.103
## YearRemodAdd:TotalBsmtSF:FullBath                                                                               -1.183
## OverallQual:X1stFlrSF:FullBath                                                                                   1.238
## YearBuilt:X1stFlrSF:FullBath                                                                                     2.432
## YearRemodAdd:X1stFlrSF:FullBath                                                                                  1.786
## TotalBsmtSF:X1stFlrSF:FullBath                                                                                  -0.253
## OverallQual:GrLivArea:FullBath                                                                                  -0.740
## YearBuilt:GrLivArea:FullBath                                                                                     0.139
## YearRemodAdd:GrLivArea:FullBath                                                                                  0.080
## TotalBsmtSF:GrLivArea:FullBath                                                                                  -0.828
## X1stFlrSF:GrLivArea:FullBath                                                                                     1.079
## OverallQual:YearBuilt:TotRmsAbvGrd                                                                               1.587
## OverallQual:YearRemodAdd:TotRmsAbvGrd                                                                            1.111
## YearBuilt:YearRemodAdd:TotRmsAbvGrd                                                                              2.418
## OverallQual:TotalBsmtSF:TotRmsAbvGrd                                                                             0.541
## YearBuilt:TotalBsmtSF:TotRmsAbvGrd                                                                               0.485
## YearRemodAdd:TotalBsmtSF:TotRmsAbvGrd                                                                           -0.142
## OverallQual:X1stFlrSF:TotRmsAbvGrd                                                                              -0.550
## YearBuilt:X1stFlrSF:TotRmsAbvGrd                                                                                 0.019
## YearRemodAdd:X1stFlrSF:TotRmsAbvGrd                                                                              0.444
## TotalBsmtSF:X1stFlrSF:TotRmsAbvGrd                                                                              -0.568
## OverallQual:GrLivArea:TotRmsAbvGrd                                                                               0.635
## YearBuilt:GrLivArea:TotRmsAbvGrd                                                                                 1.547
## YearRemodAdd:GrLivArea:TotRmsAbvGrd                                                                              1.893
## TotalBsmtSF:GrLivArea:TotRmsAbvGrd                                                                               0.445
## X1stFlrSF:GrLivArea:TotRmsAbvGrd                                                                                 0.395
## OverallQual:FullBath:TotRmsAbvGrd                                                                                0.503
## YearBuilt:FullBath:TotRmsAbvGrd                                                                                  0.621
## YearRemodAdd:FullBath:TotRmsAbvGrd                                                                               0.349
## TotalBsmtSF:FullBath:TotRmsAbvGrd                                                                               -0.985
## X1stFlrSF:FullBath:TotRmsAbvGrd                                                                                  0.589
## GrLivArea:FullBath:TotRmsAbvGrd                                                                                 -0.677
## OverallQual:YearBuilt:GarageCars                                                                                 0.305
## OverallQual:YearRemodAdd:GarageCars                                                                             -0.380
## YearBuilt:YearRemodAdd:GarageCars                                                                                2.133
## OverallQual:TotalBsmtSF:GarageCars                                                                              -1.067
## YearBuilt:TotalBsmtSF:GarageCars                                                                                -1.136
## YearRemodAdd:TotalBsmtSF:GarageCars                                                                             -1.129
## OverallQual:X1stFlrSF:GarageCars                                                                                 1.170
## YearBuilt:X1stFlrSF:GarageCars                                                                                   1.848
## YearRemodAdd:X1stFlrSF:GarageCars                                                                                2.082
## TotalBsmtSF:X1stFlrSF:GarageCars                                                                                 0.268
## OverallQual:GrLivArea:GarageCars                                                                                -1.659
## YearBuilt:GrLivArea:GarageCars                                                                                  -0.825
## YearRemodAdd:GrLivArea:GarageCars                                                                               -2.399
## TotalBsmtSF:GrLivArea:GarageCars                                                                                 0.104
## X1stFlrSF:GrLivArea:GarageCars                                                                                  -0.992
## OverallQual:FullBath:GarageCars                                                                                  0.911
## YearBuilt:FullBath:GarageCars                                                                                    1.788
## YearRemodAdd:FullBath:GarageCars                                                                                 0.723
## TotalBsmtSF:FullBath:GarageCars                                                                                 -2.356
## X1stFlrSF:FullBath:GarageCars                                                                                    2.103
## GrLivArea:FullBath:GarageCars                                                                                   -1.269
## OverallQual:TotRmsAbvGrd:GarageCars                                                                              1.091
## YearBuilt:TotRmsAbvGrd:GarageCars                                                                                2.389
## YearRemodAdd:TotRmsAbvGrd:GarageCars                                                                             2.591
## TotalBsmtSF:TotRmsAbvGrd:GarageCars                                                                              0.539
## X1stFlrSF:TotRmsAbvGrd:GarageCars                                                                                1.017
## GrLivArea:TotRmsAbvGrd:GarageCars                                                                                0.030
## FullBath:TotRmsAbvGrd:GarageCars                                                                                 0.538
## OverallQual:YearBuilt:GarageArea                                                                                 0.657
## OverallQual:YearRemodAdd:GarageArea                                                                              1.855
## YearBuilt:YearRemodAdd:GarageArea                                                                                1.963
## OverallQual:TotalBsmtSF:GarageArea                                                                              -0.542
## YearBuilt:TotalBsmtSF:GarageArea                                                                                 1.185
## YearRemodAdd:TotalBsmtSF:GarageArea                                                                              1.335
## OverallQual:X1stFlrSF:GarageArea                                                                                 2.238
## YearBuilt:X1stFlrSF:GarageArea                                                                                  -0.520
## YearRemodAdd:X1stFlrSF:GarageArea                                                                               -0.256
## TotalBsmtSF:X1stFlrSF:GarageArea                                                                                -0.746
## OverallQual:GrLivArea:GarageArea                                                                                 0.983
## YearBuilt:GrLivArea:GarageArea                                                                                   1.343
## YearRemodAdd:GrLivArea:GarageArea                                                                                2.006
## TotalBsmtSF:GrLivArea:GarageArea                                                                                 2.071
## X1stFlrSF:GrLivArea:GarageArea                                                                                  -0.773
## OverallQual:FullBath:GarageArea                                                                                 -0.920
## YearBuilt:FullBath:GarageArea                                                                                   -0.668
## YearRemodAdd:FullBath:GarageArea                                                                                 0.325
## TotalBsmtSF:FullBath:GarageArea                                                                                  0.019
## X1stFlrSF:FullBath:GarageArea                                                                                   -0.389
## GrLivArea:FullBath:GarageArea                                                                                   -0.516
## OverallQual:TotRmsAbvGrd:GarageArea                                                                             -0.608
## YearBuilt:TotRmsAbvGrd:GarageArea                                                                               -0.470
## YearRemodAdd:TotRmsAbvGrd:GarageArea                                                                            -0.392
## TotalBsmtSF:TotRmsAbvGrd:GarageArea                                                                             -1.066
## X1stFlrSF:TotRmsAbvGrd:GarageArea                                                                                1.006
## GrLivArea:TotRmsAbvGrd:GarageArea                                                                                0.294
## FullBath:TotRmsAbvGrd:GarageArea                                                                                -0.133
## OverallQual:GarageCars:GarageArea                                                                               -0.713
## YearBuilt:GarageCars:GarageArea                                                                                  1.478
## YearRemodAdd:GarageCars:GarageArea                                                                               2.039
## TotalBsmtSF:GarageCars:GarageArea                                                                               -1.062
## X1stFlrSF:GarageCars:GarageArea                                                                                  1.344
## GrLivArea:GarageCars:GarageArea                                                                                 -0.737
## FullBath:GarageCars:GarageArea                                                                                   0.477
## TotRmsAbvGrd:GarageCars:GarageArea                                                                               0.267
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF                                                                  -1.090
## OverallQual:YearBuilt:YearRemodAdd:X1stFlrSF                                                                     0.077
## OverallQual:YearBuilt:TotalBsmtSF:X1stFlrSF                                                                     -2.902
## OverallQual:YearRemodAdd:TotalBsmtSF:X1stFlrSF                                                                  -1.543
## YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF                                                                    -0.778
## OverallQual:YearBuilt:YearRemodAdd:GrLivArea                                                                     1.555
## OverallQual:YearBuilt:TotalBsmtSF:GrLivArea                                                                      0.608
## OverallQual:YearRemodAdd:TotalBsmtSF:GrLivArea                                                                  -0.066
## YearBuilt:YearRemodAdd:TotalBsmtSF:GrLivArea                                                                    -1.915
## OverallQual:YearBuilt:X1stFlrSF:GrLivArea                                                                        0.565
## OverallQual:YearRemodAdd:X1stFlrSF:GrLivArea                                                                     0.783
## YearBuilt:YearRemodAdd:X1stFlrSF:GrLivArea                                                                       2.201
## OverallQual:TotalBsmtSF:X1stFlrSF:GrLivArea                                                                     -1.864
## YearBuilt:TotalBsmtSF:X1stFlrSF:GrLivArea                                                                       -0.588
## YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea                                                                     1.655
## OverallQual:YearBuilt:YearRemodAdd:FullBath                                                                     -0.785
## OverallQual:YearBuilt:TotalBsmtSF:FullBath                                                                      -0.387
## OverallQual:YearRemodAdd:TotalBsmtSF:FullBath                                                                    1.171
## YearBuilt:YearRemodAdd:TotalBsmtSF:FullBath                                                                      0.718
## OverallQual:YearBuilt:X1stFlrSF:FullBath                                                                        -1.029
## OverallQual:YearRemodAdd:X1stFlrSF:FullBath                                                                     -0.652
## YearBuilt:YearRemodAdd:X1stFlrSF:FullBath                                                                       -2.212
## OverallQual:TotalBsmtSF:X1stFlrSF:FullBath                                                                       0.284
## YearBuilt:TotalBsmtSF:X1stFlrSF:FullBath                                                                        -0.468
## YearRemodAdd:TotalBsmtSF:X1stFlrSF:FullBath                                                                      0.245
## OverallQual:YearBuilt:GrLivArea:FullBath                                                                         0.731
## OverallQual:YearRemodAdd:GrLivArea:FullBath                                                                      0.086
## YearBuilt:YearRemodAdd:GrLivArea:FullBath                                                                       -0.451
## OverallQual:TotalBsmtSF:GrLivArea:FullBath                                                                       1.549
## YearBuilt:TotalBsmtSF:GrLivArea:FullBath                                                                         1.389
## YearRemodAdd:TotalBsmtSF:GrLivArea:FullBath                                                                     -0.760
## OverallQual:X1stFlrSF:GrLivArea:FullBath                                                                        -0.818
## YearBuilt:X1stFlrSF:GrLivArea:FullBath                                                                          -1.604
## YearRemodAdd:X1stFlrSF:GrLivArea:FullBath                                                                       -0.150
## TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath                                                                         0.701
## OverallQual:YearBuilt:YearRemodAdd:TotRmsAbvGrd                                                                 -1.473
## OverallQual:YearBuilt:TotalBsmtSF:TotRmsAbvGrd                                                                  -1.191
## OverallQual:YearRemodAdd:TotalBsmtSF:TotRmsAbvGrd                                                               -0.115
## YearBuilt:YearRemodAdd:TotalBsmtSF:TotRmsAbvGrd                                                                 -0.252
## OverallQual:YearBuilt:X1stFlrSF:TotRmsAbvGrd                                                                     0.747
## OverallQual:YearRemodAdd:X1stFlrSF:TotRmsAbvGrd                                                                  0.564
## YearBuilt:YearRemodAdd:X1stFlrSF:TotRmsAbvGrd                                                                   -0.165
## OverallQual:TotalBsmtSF:X1stFlrSF:TotRmsAbvGrd                                                                   0.377
## YearBuilt:TotalBsmtSF:X1stFlrSF:TotRmsAbvGrd                                                                     0.681
## YearRemodAdd:TotalBsmtSF:X1stFlrSF:TotRmsAbvGrd                                                                  0.244
## OverallQual:YearBuilt:GrLivArea:TotRmsAbvGrd                                                                    -0.306
## OverallQual:YearRemodAdd:GrLivArea:TotRmsAbvGrd                                                                 -1.033
## YearBuilt:YearRemodAdd:GrLivArea:TotRmsAbvGrd                                                                   -2.052
## OverallQual:TotalBsmtSF:GrLivArea:TotRmsAbvGrd                                                                   0.585
## YearBuilt:TotalBsmtSF:GrLivArea:TotRmsAbvGrd                                                                    -0.688
## YearRemodAdd:TotalBsmtSF:GrLivArea:TotRmsAbvGrd                                                                 -0.076
## OverallQual:X1stFlrSF:GrLivArea:TotRmsAbvGrd                                                                    -0.974
## YearBuilt:X1stFlrSF:GrLivArea:TotRmsAbvGrd                                                                      -0.201
## YearRemodAdd:X1stFlrSF:GrLivArea:TotRmsAbvGrd                                                                   -0.480
## TotalBsmtSF:X1stFlrSF:GrLivArea:TotRmsAbvGrd                                                                    -1.157
## OverallQual:YearBuilt:FullBath:TotRmsAbvGrd                                                                     -0.965
## OverallQual:YearRemodAdd:FullBath:TotRmsAbvGrd                                                                   0.366
## YearBuilt:YearRemodAdd:FullBath:TotRmsAbvGrd                                                                    -0.590
## OverallQual:TotalBsmtSF:FullBath:TotRmsAbvGrd                                                                    1.228
## YearBuilt:TotalBsmtSF:FullBath:TotRmsAbvGrd                                                                      0.315
## YearRemodAdd:TotalBsmtSF:FullBath:TotRmsAbvGrd                                                                   0.922
## OverallQual:X1stFlrSF:FullBath:TotRmsAbvGrd                                                                     -0.883
## YearBuilt:X1stFlrSF:FullBath:TotRmsAbvGrd                                                                       -0.529
## YearRemodAdd:X1stFlrSF:FullBath:TotRmsAbvGrd                                                                    -0.509
## TotalBsmtSF:X1stFlrSF:FullBath:TotRmsAbvGrd                                                                      0.973
## OverallQual:GrLivArea:FullBath:TotRmsAbvGrd                                                                     -0.315
## YearBuilt:GrLivArea:FullBath:TotRmsAbvGrd                                                                        0.895
## YearRemodAdd:GrLivArea:FullBath:TotRmsAbvGrd                                                                     0.015
## TotalBsmtSF:GrLivArea:FullBath:TotRmsAbvGrd                                                                      0.495
## X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd                                                                       -0.225
## OverallQual:YearBuilt:YearRemodAdd:GarageCars                                                                    0.185
## OverallQual:YearBuilt:TotalBsmtSF:GarageCars                                                                     0.677
## OverallQual:YearRemodAdd:TotalBsmtSF:GarageCars                                                                  1.546
## YearBuilt:YearRemodAdd:TotalBsmtSF:GarageCars                                                                    0.987
## OverallQual:YearBuilt:X1stFlrSF:GarageCars                                                                      -0.686
## OverallQual:YearRemodAdd:X1stFlrSF:GarageCars                                                                   -1.331
## YearBuilt:YearRemodAdd:X1stFlrSF:GarageCars                                                                     -1.941
## OverallQual:TotalBsmtSF:X1stFlrSF:GarageCars                                                                    -0.779
## YearBuilt:TotalBsmtSF:X1stFlrSF:GarageCars                                                                       0.716
## YearRemodAdd:TotalBsmtSF:X1stFlrSF:GarageCars                                                                   -1.005
## OverallQual:YearBuilt:GrLivArea:GarageCars                                                                       1.031
## OverallQual:YearRemodAdd:GrLivArea:GarageCars                                                                    1.780
## YearBuilt:YearRemodAdd:GrLivArea:GarageCars                                                                      1.287
## OverallQual:TotalBsmtSF:GrLivArea:GarageCars                                                                     0.487
## YearBuilt:TotalBsmtSF:GrLivArea:GarageCars                                                                      -0.436
## YearRemodAdd:TotalBsmtSF:GrLivArea:GarageCars                                                                   -0.211
## OverallQual:X1stFlrSF:GrLivArea:GarageCars                                                                      -0.082
## YearBuilt:X1stFlrSF:GrLivArea:GarageCars                                                                         0.104
## YearRemodAdd:X1stFlrSF:GrLivArea:GarageCars                                                                      1.734
## TotalBsmtSF:X1stFlrSF:GrLivArea:GarageCars                                                                      -0.427
## OverallQual:YearBuilt:FullBath:GarageCars                                                                       -1.778
## OverallQual:YearRemodAdd:FullBath:GarageCars                                                                     0.303
## YearBuilt:YearRemodAdd:FullBath:GarageCars                                                                      -1.527
## OverallQual:TotalBsmtSF:FullBath:GarageCars                                                                      1.651
## YearBuilt:TotalBsmtSF:FullBath:GarageCars                                                                        1.833
## YearRemodAdd:TotalBsmtSF:FullBath:GarageCars                                                                     1.588
## OverallQual:X1stFlrSF:FullBath:GarageCars                                                                       -1.615
## YearBuilt:X1stFlrSF:FullBath:GarageCars                                                                         -2.198
## YearRemodAdd:X1stFlrSF:FullBath:GarageCars                                                                      -1.365
## TotalBsmtSF:X1stFlrSF:FullBath:GarageCars                                                                        0.930
## OverallQual:GrLivArea:FullBath:GarageCars                                                                        0.664
## YearBuilt:GrLivArea:FullBath:GarageCars                                                                         -0.026
## YearRemodAdd:GrLivArea:FullBath:GarageCars                                                                       1.486
## TotalBsmtSF:GrLivArea:FullBath:GarageCars                                                                        2.296
## X1stFlrSF:GrLivArea:FullBath:GarageCars                                                                         -0.513
## OverallQual:YearBuilt:TotRmsAbvGrd:GarageCars                                                                   -0.806
## OverallQual:YearRemodAdd:TotRmsAbvGrd:GarageCars                                                                -0.957
## YearBuilt:YearRemodAdd:TotRmsAbvGrd:GarageCars                                                                  -2.606
## OverallQual:TotalBsmtSF:TotRmsAbvGrd:GarageCars                                                                 -2.075
## YearBuilt:TotalBsmtSF:TotRmsAbvGrd:GarageCars                                                                   -0.430
## YearRemodAdd:TotalBsmtSF:TotRmsAbvGrd:GarageCars                                                                -0.219
## OverallQual:X1stFlrSF:TotRmsAbvGrd:GarageCars                                                                    0.774
## YearBuilt:X1stFlrSF:TotRmsAbvGrd:GarageCars                                                                     -0.439
## YearRemodAdd:X1stFlrSF:TotRmsAbvGrd:GarageCars                                                                  -1.602
## TotalBsmtSF:X1stFlrSF:TotRmsAbvGrd:GarageCars                                                                   -1.315
## OverallQual:GrLivArea:TotRmsAbvGrd:GarageCars                                                                    0.587
## YearBuilt:GrLivArea:TotRmsAbvGrd:GarageCars                                                                     -0.686
## YearRemodAdd:GrLivArea:TotRmsAbvGrd:GarageCars                                                                   0.013
## TotalBsmtSF:GrLivArea:TotRmsAbvGrd:GarageCars                                                                   -0.779
## X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageCars                                                                      0.995
## OverallQual:FullBath:TotRmsAbvGrd:GarageCars                                                                    -0.850
## YearBuilt:FullBath:TotRmsAbvGrd:GarageCars                                                                      -0.609
## YearRemodAdd:FullBath:TotRmsAbvGrd:GarageCars                                                                   -0.710
## TotalBsmtSF:FullBath:TotRmsAbvGrd:GarageCars                                                                     1.608
## X1stFlrSF:FullBath:TotRmsAbvGrd:GarageCars                                                                      -0.505
## GrLivArea:FullBath:TotRmsAbvGrd:GarageCars                                                                       1.319
## OverallQual:YearBuilt:YearRemodAdd:GarageArea                                                                   -1.601
## OverallQual:YearBuilt:TotalBsmtSF:GarageArea                                                                    -0.383
## OverallQual:YearRemodAdd:TotalBsmtSF:GarageArea                                                                 -0.170
## YearBuilt:YearRemodAdd:TotalBsmtSF:GarageArea                                                                   -1.736
## OverallQual:YearBuilt:X1stFlrSF:GarageArea                                                                      -0.356
## OverallQual:YearRemodAdd:X1stFlrSF:GarageArea                                                                   -2.374
## YearBuilt:YearRemodAdd:X1stFlrSF:GarageArea                                                                      0.722
## OverallQual:TotalBsmtSF:X1stFlrSF:GarageArea                                                                    -0.044
## YearBuilt:TotalBsmtSF:X1stFlrSF:GarageArea                                                                       0.007
## YearRemodAdd:TotalBsmtSF:X1stFlrSF:GarageArea                                                                    0.846
## OverallQual:YearBuilt:GrLivArea:GarageArea                                                                      -0.748
## OverallQual:YearRemodAdd:GrLivArea:GarageArea                                                                   -1.439
## YearBuilt:YearRemodAdd:GrLivArea:GarageArea                                                                     -1.824
## OverallQual:TotalBsmtSF:GrLivArea:GarageArea                                                                     1.610
## YearBuilt:TotalBsmtSF:GrLivArea:GarageArea                                                                      -0.964
## YearRemodAdd:TotalBsmtSF:GrLivArea:GarageArea                                                                   -2.942
## OverallQual:X1stFlrSF:GrLivArea:GarageArea                                                                      -1.932
## YearBuilt:X1stFlrSF:GrLivArea:GarageArea                                                                         0.512
## YearRemodAdd:X1stFlrSF:GrLivArea:GarageArea                                                                      0.966
## TotalBsmtSF:X1stFlrSF:GrLivArea:GarageArea                                                                       0.178
## OverallQual:YearBuilt:FullBath:GarageArea                                                                        1.484
## OverallQual:YearRemodAdd:FullBath:GarageArea                                                                    -0.426
## YearBuilt:YearRemodAdd:FullBath:GarageArea                                                                      -0.073
## OverallQual:TotalBsmtSF:FullBath:GarageArea                                                                      0.535
## YearBuilt:TotalBsmtSF:FullBath:GarageArea                                                                       -0.382
## YearRemodAdd:TotalBsmtSF:FullBath:GarageArea                                                                     0.265
## OverallQual:X1stFlrSF:FullBath:GarageArea                                                                       -0.104
## YearBuilt:X1stFlrSF:FullBath:GarageArea                                                                          1.052
## YearRemodAdd:X1stFlrSF:FullBath:GarageArea                                                                      -0.660
## TotalBsmtSF:X1stFlrSF:FullBath:GarageArea                                                                        0.451
## OverallQual:GrLivArea:FullBath:GarageArea                                                                        1.429
## YearBuilt:GrLivArea:FullBath:GarageArea                                                                          0.625
## YearRemodAdd:GrLivArea:FullBath:GarageArea                                                                      -0.199
## TotalBsmtSF:GrLivArea:FullBath:GarageArea                                                                       -1.518
## X1stFlrSF:GrLivArea:FullBath:GarageArea                                                                          2.313
## OverallQual:YearBuilt:TotRmsAbvGrd:GarageArea                                                                    0.720
## OverallQual:YearRemodAdd:TotRmsAbvGrd:GarageArea                                                                 0.183
## YearBuilt:YearRemodAdd:TotRmsAbvGrd:GarageArea                                                                   0.334
## OverallQual:TotalBsmtSF:TotRmsAbvGrd:GarageArea                                                                  1.555
## YearBuilt:TotalBsmtSF:TotRmsAbvGrd:GarageArea                                                                    0.549
## YearRemodAdd:TotalBsmtSF:TotRmsAbvGrd:GarageArea                                                                 0.988
## OverallQual:X1stFlrSF:TotRmsAbvGrd:GarageArea                                                                   -1.341
## YearBuilt:X1stFlrSF:TotRmsAbvGrd:GarageArea                                                                     -0.949
## YearRemodAdd:X1stFlrSF:TotRmsAbvGrd:GarageArea                                                                  -0.254
## TotalBsmtSF:X1stFlrSF:TotRmsAbvGrd:GarageArea                                                                    1.167
## OverallQual:GrLivArea:TotRmsAbvGrd:GarageArea                                                                    0.938
## YearBuilt:GrLivArea:TotRmsAbvGrd:GarageArea                                                                      0.174
## YearRemodAdd:GrLivArea:TotRmsAbvGrd:GarageArea                                                                  -0.931
## TotalBsmtSF:GrLivArea:TotRmsAbvGrd:GarageArea                                                                   -0.311
## X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageArea                                                                     -0.047
## OverallQual:FullBath:TotRmsAbvGrd:GarageArea                                                                     0.374
## YearBuilt:FullBath:TotRmsAbvGrd:GarageArea                                                                      -0.040
## YearRemodAdd:FullBath:TotRmsAbvGrd:GarageArea                                                                    0.172
## TotalBsmtSF:FullBath:TotRmsAbvGrd:GarageArea                                                                    -0.037
## X1stFlrSF:FullBath:TotRmsAbvGrd:GarageArea                                                                      -0.239
## GrLivArea:FullBath:TotRmsAbvGrd:GarageArea                                                                       0.098
## OverallQual:YearBuilt:GarageCars:GarageArea                                                                      1.040
## OverallQual:YearRemodAdd:GarageCars:GarageArea                                                                  -0.446
## YearBuilt:YearRemodAdd:GarageCars:GarageArea                                                                    -2.238
## OverallQual:TotalBsmtSF:GarageCars:GarageArea                                                                    1.620
## YearBuilt:TotalBsmtSF:GarageCars:GarageArea                                                                      0.708
## YearRemodAdd:TotalBsmtSF:GarageCars:GarageArea                                                                   0.409
## OverallQual:X1stFlrSF:GarageCars:GarageArea                                                                     -1.292
## YearBuilt:X1stFlrSF:GarageCars:GarageArea                                                                       -0.959
## YearRemodAdd:X1stFlrSF:GarageCars:GarageArea                                                                    -1.284
## TotalBsmtSF:X1stFlrSF:GarageCars:GarageArea                                                                      0.922
## OverallQual:GrLivArea:GarageCars:GarageArea                                                                      1.824
## YearBuilt:GrLivArea:GarageCars:GarageArea                                                                        0.006
## YearRemodAdd:GrLivArea:GarageCars:GarageArea                                                                     0.409
## TotalBsmtSF:GrLivArea:GarageCars:GarageArea                                                                      0.089
## X1stFlrSF:GrLivArea:GarageCars:GarageArea                                                                        0.136
## OverallQual:FullBath:GarageCars:GarageArea                                                                       0.626
## YearBuilt:FullBath:GarageCars:GarageArea                                                                        -0.528
## YearRemodAdd:FullBath:GarageCars:GarageArea                                                                     -1.408
## TotalBsmtSF:FullBath:GarageCars:GarageArea                                                                       2.083
## X1stFlrSF:FullBath:GarageCars:GarageArea                                                                        -1.416
## GrLivArea:FullBath:GarageCars:GarageArea                                                                         1.084
## OverallQual:TotRmsAbvGrd:GarageCars:GarageArea                                                                   0.458
## YearBuilt:TotRmsAbvGrd:GarageCars:GarageArea                                                                     0.016
## YearRemodAdd:TotRmsAbvGrd:GarageCars:GarageArea                                                                 -0.860
## TotalBsmtSF:TotRmsAbvGrd:GarageCars:GarageArea                                                                  -0.045
## X1stFlrSF:TotRmsAbvGrd:GarageCars:GarageArea                                                                    -0.798
## GrLivArea:TotRmsAbvGrd:GarageCars:GarageArea                                                                     1.202
## FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                                                      0.664
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF                                                         2.319
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:GrLivArea                                                         0.062
## OverallQual:YearBuilt:YearRemodAdd:X1stFlrSF:GrLivArea                                                          -1.140
## OverallQual:YearBuilt:TotalBsmtSF:X1stFlrSF:GrLivArea                                                            2.008
## OverallQual:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea                                                        -0.104
## YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea                                                          -1.020
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:FullBath                                                          0.217
## OverallQual:YearBuilt:YearRemodAdd:X1stFlrSF:FullBath                                                            0.500
## OverallQual:YearBuilt:TotalBsmtSF:X1stFlrSF:FullBath                                                             1.593
## OverallQual:YearRemodAdd:TotalBsmtSF:X1stFlrSF:FullBath                                                         -1.489
## YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:FullBath                                                            0.628
## OverallQual:YearBuilt:YearRemodAdd:GrLivArea:FullBath                                                           -0.239
## OverallQual:YearBuilt:TotalBsmtSF:GrLivArea:FullBath                                                            -2.087
## OverallQual:YearRemodAdd:TotalBsmtSF:GrLivArea:FullBath                                                          0.284
## YearBuilt:YearRemodAdd:TotalBsmtSF:GrLivArea:FullBath                                                            0.469
## OverallQual:YearBuilt:X1stFlrSF:GrLivArea:FullBath                                                               0.537
## OverallQual:YearRemodAdd:X1stFlrSF:GrLivArea:FullBath                                                            0.294
## YearBuilt:YearRemodAdd:X1stFlrSF:GrLivArea:FullBath                                                              1.308
## OverallQual:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath                                                            -0.263
## YearBuilt:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath                                                               0.621
## YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath                                                           -0.970
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:TotRmsAbvGrd                                                      0.767
## OverallQual:YearBuilt:YearRemodAdd:X1stFlrSF:TotRmsAbvGrd                                                       -0.789
## OverallQual:YearBuilt:TotalBsmtSF:X1stFlrSF:TotRmsAbvGrd                                                         0.384
## OverallQual:YearRemodAdd:TotalBsmtSF:X1stFlrSF:TotRmsAbvGrd                                                     -0.537
## YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:TotRmsAbvGrd                                                       -0.500
## OverallQual:YearBuilt:YearRemodAdd:GrLivArea:TotRmsAbvGrd                                                        0.820
## OverallQual:YearBuilt:TotalBsmtSF:GrLivArea:TotRmsAbvGrd                                                         0.416
## OverallQual:YearRemodAdd:TotalBsmtSF:GrLivArea:TotRmsAbvGrd                                                     -1.149
## YearBuilt:YearRemodAdd:TotalBsmtSF:GrLivArea:TotRmsAbvGrd                                                        0.365
## OverallQual:YearBuilt:X1stFlrSF:GrLivArea:TotRmsAbvGrd                                                          -0.314
## OverallQual:YearRemodAdd:X1stFlrSF:GrLivArea:TotRmsAbvGrd                                                        1.441
## YearBuilt:YearRemodAdd:X1stFlrSF:GrLivArea:TotRmsAbvGrd                                                          0.345
## OverallQual:TotalBsmtSF:X1stFlrSF:GrLivArea:TotRmsAbvGrd                                                         0.960
## YearBuilt:TotalBsmtSF:X1stFlrSF:GrLivArea:TotRmsAbvGrd                                                           1.760
## YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:TotRmsAbvGrd                                                       -1.234
## OverallQual:YearBuilt:YearRemodAdd:FullBath:TotRmsAbvGrd                                                         0.219
## OverallQual:YearBuilt:TotalBsmtSF:FullBath:TotRmsAbvGrd                                                          0.776
## OverallQual:YearRemodAdd:TotalBsmtSF:FullBath:TotRmsAbvGrd                                                      -1.677
## YearBuilt:YearRemodAdd:TotalBsmtSF:FullBath:TotRmsAbvGrd                                                        -0.388
## OverallQual:YearBuilt:X1stFlrSF:FullBath:TotRmsAbvGrd                                                            1.477
## OverallQual:YearRemodAdd:X1stFlrSF:FullBath:TotRmsAbvGrd                                                        -0.778
## YearBuilt:YearRemodAdd:X1stFlrSF:FullBath:TotRmsAbvGrd                                                           0.491
## OverallQual:TotalBsmtSF:X1stFlrSF:FullBath:TotRmsAbvGrd                                                         -1.164
## YearBuilt:TotalBsmtSF:X1stFlrSF:FullBath:TotRmsAbvGrd                                                           -0.818
## YearRemodAdd:TotalBsmtSF:X1stFlrSF:FullBath:TotRmsAbvGrd                                                         0.032
## OverallQual:YearBuilt:GrLivArea:FullBath:TotRmsAbvGrd                                                           -0.604
## OverallQual:YearRemodAdd:GrLivArea:FullBath:TotRmsAbvGrd                                                         0.792
## YearBuilt:YearRemodAdd:GrLivArea:FullBath:TotRmsAbvGrd                                                          -0.280
## OverallQual:TotalBsmtSF:GrLivArea:FullBath:TotRmsAbvGrd                                                         -1.234
## YearBuilt:TotalBsmtSF:GrLivArea:FullBath:TotRmsAbvGrd                                                           -1.143
## YearRemodAdd:TotalBsmtSF:GrLivArea:FullBath:TotRmsAbvGrd                                                         0.496
## OverallQual:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd                                                            1.598
## YearBuilt:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd                                                             -0.024
## YearRemodAdd:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd                                                           0.185
## TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd                                                            0.260
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:GarageCars                                                       -1.233
## OverallQual:YearBuilt:YearRemodAdd:X1stFlrSF:GarageCars                                                          0.943
## OverallQual:YearBuilt:TotalBsmtSF:X1stFlrSF:GarageCars                                                          -0.520
## OverallQual:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GarageCars                                                        1.152
## YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GarageCars                                                          0.094
## OverallQual:YearBuilt:YearRemodAdd:GrLivArea:GarageCars                                                         -1.256
## OverallQual:YearBuilt:TotalBsmtSF:GrLivArea:GarageCars                                                           0.094
## OverallQual:YearRemodAdd:TotalBsmtSF:GrLivArea:GarageCars                                                       -0.646
## YearBuilt:YearRemodAdd:TotalBsmtSF:GrLivArea:GarageCars                                                          0.587
## OverallQual:YearBuilt:X1stFlrSF:GrLivArea:GarageCars                                                             0.547
## OverallQual:YearRemodAdd:X1stFlrSF:GrLivArea:GarageCars                                                         -0.432
## YearBuilt:YearRemodAdd:X1stFlrSF:GrLivArea:GarageCars                                                           -1.067
## OverallQual:TotalBsmtSF:X1stFlrSF:GrLivArea:GarageCars                                                           0.872
## YearBuilt:TotalBsmtSF:X1stFlrSF:GrLivArea:GarageCars                                                             1.699
## YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:GarageCars                                                         -1.680
## OverallQual:YearBuilt:YearRemodAdd:FullBath:GarageCars                                                           0.780
## OverallQual:YearBuilt:TotalBsmtSF:FullBath:GarageCars                                                            0.388
## OverallQual:YearRemodAdd:TotalBsmtSF:FullBath:GarageCars                                                        -1.710
## YearBuilt:YearRemodAdd:TotalBsmtSF:FullBath:GarageCars                                                          -1.047
## OverallQual:YearBuilt:X1stFlrSF:FullBath:GarageCars                                                              1.407
## OverallQual:YearRemodAdd:X1stFlrSF:FullBath:GarageCars                                                           0.359
## YearBuilt:YearRemodAdd:X1stFlrSF:FullBath:GarageCars                                                             1.662
## OverallQual:TotalBsmtSF:X1stFlrSF:FullBath:GarageCars                                                            0.211
## YearBuilt:TotalBsmtSF:X1stFlrSF:FullBath:GarageCars                                                             -1.537
## YearRemodAdd:TotalBsmtSF:X1stFlrSF:FullBath:GarageCars                                                           0.682
## OverallQual:YearBuilt:GrLivArea:FullBath:GarageCars                                                              0.594
## OverallQual:YearRemodAdd:GrLivArea:FullBath:GarageCars                                                          -1.005
## YearBuilt:YearRemodAdd:GrLivArea:FullBath:GarageCars                                                            -0.347
## OverallQual:TotalBsmtSF:GrLivArea:FullBath:GarageCars                                                           -1.515
## YearBuilt:TotalBsmtSF:GrLivArea:FullBath:GarageCars                                                             -2.065
## YearRemodAdd:TotalBsmtSF:GrLivArea:FullBath:GarageCars                                                          -0.268
## OverallQual:X1stFlrSF:GrLivArea:FullBath:GarageCars                                                              0.763
## YearBuilt:X1stFlrSF:GrLivArea:FullBath:GarageCars                                                                1.987
## YearRemodAdd:X1stFlrSF:GrLivArea:FullBath:GarageCars                                                            -1.717
## TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:GarageCars                                                             -1.387
## OverallQual:YearBuilt:YearRemodAdd:TotRmsAbvGrd:GarageCars                                                       0.793
## OverallQual:YearBuilt:TotalBsmtSF:TotRmsAbvGrd:GarageCars                                                        1.658
## OverallQual:YearRemodAdd:TotalBsmtSF:TotRmsAbvGrd:GarageCars                                                     0.156
## YearBuilt:YearRemodAdd:TotalBsmtSF:TotRmsAbvGrd:GarageCars                                                       0.126
## OverallQual:YearBuilt:X1stFlrSF:TotRmsAbvGrd:GarageCars                                                         -1.129
## OverallQual:YearRemodAdd:X1stFlrSF:TotRmsAbvGrd:GarageCars                                                       0.649
## YearBuilt:YearRemodAdd:X1stFlrSF:TotRmsAbvGrd:GarageCars                                                         1.179
## OverallQual:TotalBsmtSF:X1stFlrSF:TotRmsAbvGrd:GarageCars                                                        1.159
## YearBuilt:TotalBsmtSF:X1stFlrSF:TotRmsAbvGrd:GarageCars                                                         -1.195
## YearRemodAdd:TotalBsmtSF:X1stFlrSF:TotRmsAbvGrd:GarageCars                                                       1.873
## OverallQual:YearBuilt:GrLivArea:TotRmsAbvGrd:GarageCars                                                         -0.347
## OverallQual:YearRemodAdd:GrLivArea:TotRmsAbvGrd:GarageCars                                                      -0.174
## YearBuilt:YearRemodAdd:GrLivArea:TotRmsAbvGrd:GarageCars                                                         0.802
## OverallQual:TotalBsmtSF:GrLivArea:TotRmsAbvGrd:GarageCars                                                        1.378
## YearBuilt:TotalBsmtSF:GrLivArea:TotRmsAbvGrd:GarageCars                                                          2.066
## YearRemodAdd:TotalBsmtSF:GrLivArea:TotRmsAbvGrd:GarageCars                                                      -0.898
## OverallQual:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageCars                                                         -1.305
## YearBuilt:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageCars                                                           -0.243
## YearRemodAdd:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageCars                                                        -0.721
## TotalBsmtSF:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageCars                                                          1.557
## OverallQual:YearBuilt:FullBath:TotRmsAbvGrd:GarageCars                                                           0.963
## OverallQual:YearRemodAdd:FullBath:TotRmsAbvGrd:GarageCars                                                       -0.396
## YearBuilt:YearRemodAdd:FullBath:TotRmsAbvGrd:GarageCars                                                          0.912
## OverallQual:TotalBsmtSF:FullBath:TotRmsAbvGrd:GarageCars                                                        -0.322
## YearBuilt:TotalBsmtSF:FullBath:TotRmsAbvGrd:GarageCars                                                          -0.792
## YearRemodAdd:TotalBsmtSF:FullBath:TotRmsAbvGrd:GarageCars                                                       -0.750
## OverallQual:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageCars                                                           0.789
## YearBuilt:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageCars                                                            -0.463
## YearRemodAdd:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageCars                                                          0.955
## TotalBsmtSF:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageCars                                                          -0.759
## OverallQual:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars                                                           0.141
## YearBuilt:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars                                                            -0.487
## YearRemodAdd:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars                                                         -0.788
## TotalBsmtSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars                                                          -1.933
## X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars                                                            -0.145
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:GarageArea                                                        1.419
## OverallQual:YearBuilt:YearRemodAdd:X1stFlrSF:GarageArea                                                             NA
## OverallQual:YearBuilt:TotalBsmtSF:X1stFlrSF:GarageArea                                                           0.581
## OverallQual:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GarageArea                                                       -0.494
## YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GarageArea                                                         -0.135
## OverallQual:YearBuilt:YearRemodAdd:GrLivArea:GarageArea                                                          1.313
## OverallQual:YearBuilt:TotalBsmtSF:GrLivArea:GarageArea                                                          -2.990
## OverallQual:YearRemodAdd:TotalBsmtSF:GrLivArea:GarageArea                                                        2.422
## YearBuilt:YearRemodAdd:TotalBsmtSF:GrLivArea:GarageArea                                                          1.911
## OverallQual:YearBuilt:X1stFlrSF:GrLivArea:GarageArea                                                             2.069
## OverallQual:YearRemodAdd:X1stFlrSF:GrLivArea:GarageArea                                                          0.269
## YearBuilt:YearRemodAdd:X1stFlrSF:GrLivArea:GarageArea                                                           -0.827
## OverallQual:TotalBsmtSF:X1stFlrSF:GrLivArea:GarageArea                                                           1.785
## YearBuilt:TotalBsmtSF:X1stFlrSF:GrLivArea:GarageArea                                                             0.246
## YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:GarageArea                                                         -0.858
## OverallQual:YearBuilt:YearRemodAdd:FullBath:GarageArea                                                          -0.322
## OverallQual:YearBuilt:TotalBsmtSF:FullBath:GarageArea                                                            1.094
## OverallQual:YearRemodAdd:TotalBsmtSF:FullBath:GarageArea                                                        -1.796
## YearBuilt:YearRemodAdd:TotalBsmtSF:FullBath:GarageArea                                                           0.242
## OverallQual:YearBuilt:X1stFlrSF:FullBath:GarageArea                                                             -3.066
## OverallQual:YearRemodAdd:X1stFlrSF:FullBath:GarageArea                                                           3.343
## YearBuilt:YearRemodAdd:X1stFlrSF:FullBath:GarageArea                                                            -0.295
## OverallQual:TotalBsmtSF:X1stFlrSF:FullBath:GarageArea                                                            0.547
## YearBuilt:TotalBsmtSF:X1stFlrSF:FullBath:GarageArea                                                             -0.262
## YearRemodAdd:TotalBsmtSF:X1stFlrSF:FullBath:GarageArea                                                          -0.136
## OverallQual:YearBuilt:GrLivArea:FullBath:GarageArea                                                             -0.926
## OverallQual:YearRemodAdd:GrLivArea:FullBath:GarageArea                                                          -0.326
## YearBuilt:YearRemodAdd:GrLivArea:FullBath:GarageArea                                                             0.137
## OverallQual:TotalBsmtSF:GrLivArea:FullBath:GarageArea                                                           -0.188
## YearBuilt:TotalBsmtSF:GrLivArea:FullBath:GarageArea                                                             -0.450
## YearRemodAdd:TotalBsmtSF:GrLivArea:FullBath:GarageArea                                                           2.093
## OverallQual:X1stFlrSF:GrLivArea:FullBath:GarageArea                                                             -1.085
## YearBuilt:X1stFlrSF:GrLivArea:FullBath:GarageArea                                                               -1.311
## YearRemodAdd:X1stFlrSF:GrLivArea:FullBath:GarageArea                                                            -0.794
## TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:GarageArea                                                             -0.832
## OverallQual:YearBuilt:YearRemodAdd:TotRmsAbvGrd:GarageArea                                                      -0.336
## OverallQual:YearBuilt:TotalBsmtSF:TotRmsAbvGrd:GarageArea                                                       -1.005
## OverallQual:YearRemodAdd:TotalBsmtSF:TotRmsAbvGrd:GarageArea                                                    -0.843
## YearBuilt:YearRemodAdd:TotalBsmtSF:TotRmsAbvGrd:GarageArea                                                      -0.476
## OverallQual:YearBuilt:X1stFlrSF:TotRmsAbvGrd:GarageArea                                                          0.785
## OverallQual:YearRemodAdd:X1stFlrSF:TotRmsAbvGrd:GarageArea                                                       0.959
## YearBuilt:YearRemodAdd:X1stFlrSF:TotRmsAbvGrd:GarageArea                                                            NA
## OverallQual:TotalBsmtSF:X1stFlrSF:TotRmsAbvGrd:GarageArea                                                       -0.778
## YearBuilt:TotalBsmtSF:X1stFlrSF:TotRmsAbvGrd:GarageArea                                                          0.104
## YearRemodAdd:TotalBsmtSF:X1stFlrSF:TotRmsAbvGrd:GarageArea                                                      -1.991
## OverallQual:YearBuilt:GrLivArea:TotRmsAbvGrd:GarageArea                                                         -1.205
## OverallQual:YearRemodAdd:GrLivArea:TotRmsAbvGrd:GarageArea                                                       0.473
## YearBuilt:YearRemodAdd:GrLivArea:TotRmsAbvGrd:GarageArea                                                         0.582
## OverallQual:TotalBsmtSF:GrLivArea:TotRmsAbvGrd:GarageArea                                                       -1.989
## YearBuilt:TotalBsmtSF:GrLivArea:TotRmsAbvGrd:GarageArea                                                         -0.718
## YearRemodAdd:TotalBsmtSF:GrLivArea:TotRmsAbvGrd:GarageArea                                                       1.275
## OverallQual:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageArea                                                          2.396
## YearBuilt:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageArea                                                           -0.663
## YearRemodAdd:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageArea                                                         0.880
## TotalBsmtSF:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageArea                                                         -2.148
## OverallQual:YearBuilt:FullBath:TotRmsAbvGrd:GarageArea                                                          -0.715
## OverallQual:YearRemodAdd:FullBath:TotRmsAbvGrd:GarageArea                                                        0.390
## YearBuilt:YearRemodAdd:FullBath:TotRmsAbvGrd:GarageArea                                                          0.036
## OverallQual:TotalBsmtSF:FullBath:TotRmsAbvGrd:GarageArea                                                         0.108
## YearBuilt:TotalBsmtSF:FullBath:TotRmsAbvGrd:GarageArea                                                           1.057
## YearRemodAdd:TotalBsmtSF:FullBath:TotRmsAbvGrd:GarageArea                                                       -1.312
## OverallQual:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageArea                                                          -1.937
## YearBuilt:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageArea                                                             1.005
## YearRemodAdd:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageArea                                                         -0.903
## TotalBsmtSF:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageArea                                                          -0.447
## OverallQual:GrLivArea:FullBath:TotRmsAbvGrd:GarageArea                                                          -0.592
## YearBuilt:GrLivArea:FullBath:TotRmsAbvGrd:GarageArea                                                            -0.701
## YearRemodAdd:GrLivArea:FullBath:TotRmsAbvGrd:GarageArea                                                          0.574
## TotalBsmtSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageArea                                                           3.094
## X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageArea                                                            -1.398
## OverallQual:YearBuilt:YearRemodAdd:GarageCars:GarageArea                                                        -0.027
## OverallQual:YearBuilt:TotalBsmtSF:GarageCars:GarageArea                                                         -0.094
## OverallQual:YearRemodAdd:TotalBsmtSF:GarageCars:GarageArea                                                      -1.727
## YearBuilt:YearRemodAdd:TotalBsmtSF:GarageCars:GarageArea                                                         0.106
## OverallQual:YearBuilt:X1stFlrSF:GarageCars:GarageArea                                                           -0.508
## OverallQual:YearRemodAdd:X1stFlrSF:GarageCars:GarageArea                                                         2.499
## YearBuilt:YearRemodAdd:X1stFlrSF:GarageCars:GarageArea                                                           0.857
## OverallQual:TotalBsmtSF:X1stFlrSF:GarageCars:GarageArea                                                         -0.422
## YearBuilt:TotalBsmtSF:X1stFlrSF:GarageCars:GarageArea                                                           -0.834
## YearRemodAdd:TotalBsmtSF:X1stFlrSF:GarageCars:GarageArea                                                        -0.354
## OverallQual:YearBuilt:GrLivArea:GarageCars:GarageArea                                                           -0.877
## OverallQual:YearRemodAdd:GrLivArea:GarageCars:GarageArea                                                        -0.641
## YearBuilt:YearRemodAdd:GrLivArea:GarageCars:GarageArea                                                           0.302
## OverallQual:TotalBsmtSF:GrLivArea:GarageCars:GarageArea                                                         -1.641
## YearBuilt:TotalBsmtSF:GrLivArea:GarageCars:GarageArea                                                           -2.010
## YearRemodAdd:TotalBsmtSF:GrLivArea:GarageCars:GarageArea                                                         1.586
## OverallQual:X1stFlrSF:GrLivArea:GarageCars:GarageArea                                                            1.445
## YearBuilt:X1stFlrSF:GrLivArea:GarageCars:GarageArea                                                              2.126
## YearRemodAdd:X1stFlrSF:GrLivArea:GarageCars:GarageArea                                                          -2.512
## TotalBsmtSF:X1stFlrSF:GrLivArea:GarageCars:GarageArea                                                           -0.746
## OverallQual:YearBuilt:FullBath:GarageCars:GarageArea                                                            -0.921
## OverallQual:YearRemodAdd:FullBath:GarageCars:GarageArea                                                          0.414
## YearBuilt:YearRemodAdd:FullBath:GarageCars:GarageArea                                                            2.362
## OverallQual:TotalBsmtSF:FullBath:GarageCars:GarageArea                                                          -1.563
## YearBuilt:TotalBsmtSF:FullBath:GarageCars:GarageArea                                                            -1.015
## YearRemodAdd:TotalBsmtSF:FullBath:GarageCars:GarageArea                                                         -1.467
## OverallQual:X1stFlrSF:FullBath:GarageCars:GarageArea                                                             1.200
## YearBuilt:X1stFlrSF:FullBath:GarageCars:GarageArea                                                              -0.704
## YearRemodAdd:X1stFlrSF:FullBath:GarageCars:GarageArea                                                            2.281
## TotalBsmtSF:X1stFlrSF:FullBath:GarageCars:GarageArea                                                            -1.004
## OverallQual:GrLivArea:FullBath:GarageCars:GarageArea                                                            -1.021
## YearBuilt:GrLivArea:FullBath:GarageCars:GarageArea                                                              -0.249
## YearRemodAdd:GrLivArea:FullBath:GarageCars:GarageArea                                                           -0.781
## TotalBsmtSF:GrLivArea:FullBath:GarageCars:GarageArea                                                             0.034
## X1stFlrSF:GrLivArea:FullBath:GarageCars:GarageArea                                                              -1.076
## OverallQual:YearBuilt:TotRmsAbvGrd:GarageCars:GarageArea                                                        -1.693
## OverallQual:YearRemodAdd:TotRmsAbvGrd:GarageCars:GarageArea                                                      1.218
## YearBuilt:YearRemodAdd:TotRmsAbvGrd:GarageCars:GarageArea                                                        0.641
## OverallQual:TotalBsmtSF:TotRmsAbvGrd:GarageCars:GarageArea                                                       0.560
## YearBuilt:TotalBsmtSF:TotRmsAbvGrd:GarageCars:GarageArea                                                         0.387
## YearRemodAdd:TotalBsmtSF:TotRmsAbvGrd:GarageCars:GarageArea                                                     -0.353
## OverallQual:X1stFlrSF:TotRmsAbvGrd:GarageCars:GarageArea                                                        -0.419
## YearBuilt:X1stFlrSF:TotRmsAbvGrd:GarageCars:GarageArea                                                           0.382
## YearRemodAdd:X1stFlrSF:TotRmsAbvGrd:GarageCars:GarageArea                                                        0.968
## TotalBsmtSF:X1stFlrSF:TotRmsAbvGrd:GarageCars:GarageArea                                                         0.476
## OverallQual:GrLivArea:TotRmsAbvGrd:GarageCars:GarageArea                                                        -1.516
## YearBuilt:GrLivArea:TotRmsAbvGrd:GarageCars:GarageArea                                                          -1.097
## YearRemodAdd:GrLivArea:TotRmsAbvGrd:GarageCars:GarageArea                                                       -0.465
## TotalBsmtSF:GrLivArea:TotRmsAbvGrd:GarageCars:GarageArea                                                         0.585
## X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageCars:GarageArea                                                          -0.740
## OverallQual:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                                         -0.257
## YearBuilt:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                                           -0.909
## YearRemodAdd:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                                         0.014
## TotalBsmtSF:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                                         -1.463
## X1stFlrSF:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                                            1.082
## GrLivArea:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                                           -0.913
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea                                                  NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:FullBath                                                   NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:GrLivArea:FullBath                                                   NA
## OverallQual:YearBuilt:YearRemodAdd:X1stFlrSF:GrLivArea:FullBath                                                     NA
## OverallQual:YearBuilt:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath                                                   0.151
## OverallQual:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath                                               -0.100
## YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath                                                     NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:TotRmsAbvGrd                                               NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:GrLivArea:TotRmsAbvGrd                                               NA
## OverallQual:YearBuilt:YearRemodAdd:X1stFlrSF:GrLivArea:TotRmsAbvGrd                                                 NA
## OverallQual:YearBuilt:TotalBsmtSF:X1stFlrSF:GrLivArea:TotRmsAbvGrd                                              -1.602
## OverallQual:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:TotRmsAbvGrd                                            1.045
## YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:TotRmsAbvGrd                                                 NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:FullBath:TotRmsAbvGrd                                                NA
## OverallQual:YearBuilt:YearRemodAdd:X1stFlrSF:FullBath:TotRmsAbvGrd                                                  NA
## OverallQual:YearBuilt:TotalBsmtSF:X1stFlrSF:FullBath:TotRmsAbvGrd                                               -1.584
## OverallQual:YearRemodAdd:TotalBsmtSF:X1stFlrSF:FullBath:TotRmsAbvGrd                                             2.272
## YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:FullBath:TotRmsAbvGrd                                                  NA
## OverallQual:YearBuilt:YearRemodAdd:GrLivArea:FullBath:TotRmsAbvGrd                                                  NA
## OverallQual:YearBuilt:TotalBsmtSF:GrLivArea:FullBath:TotRmsAbvGrd                                                1.805
## OverallQual:YearRemodAdd:TotalBsmtSF:GrLivArea:FullBath:TotRmsAbvGrd                                            -0.330
## YearBuilt:YearRemodAdd:TotalBsmtSF:GrLivArea:FullBath:TotRmsAbvGrd                                                  NA
## OverallQual:YearBuilt:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd                                                  0.014
## OverallQual:YearRemodAdd:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd                                              -1.843
## YearBuilt:YearRemodAdd:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd                                                    NA
## OverallQual:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd                                                0.981
## YearBuilt:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd                                                  0.002
## YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd                                              -0.370
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GarageCars                                                 NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:GrLivArea:GarageCars                                                 NA
## OverallQual:YearBuilt:YearRemodAdd:X1stFlrSF:GrLivArea:GarageCars                                                   NA
## OverallQual:YearBuilt:TotalBsmtSF:X1stFlrSF:GrLivArea:GarageCars                                                -0.746
## OverallQual:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:GarageCars                                             -0.094
## YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:GarageCars                                                   NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:FullBath:GarageCars                                                  NA
## OverallQual:YearBuilt:YearRemodAdd:X1stFlrSF:FullBath:GarageCars                                                    NA
## OverallQual:YearBuilt:TotalBsmtSF:X1stFlrSF:FullBath:GarageCars                                                 -0.602
## OverallQual:YearRemodAdd:TotalBsmtSF:X1stFlrSF:FullBath:GarageCars                                               0.401
## YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:FullBath:GarageCars                                                    NA
## OverallQual:YearBuilt:YearRemodAdd:GrLivArea:FullBath:GarageCars                                                    NA
## OverallQual:YearBuilt:TotalBsmtSF:GrLivArea:FullBath:GarageCars                                                  1.400
## OverallQual:YearRemodAdd:TotalBsmtSF:GrLivArea:FullBath:GarageCars                                               0.127
## YearBuilt:YearRemodAdd:TotalBsmtSF:GrLivArea:FullBath:GarageCars                                                    NA
## OverallQual:YearBuilt:X1stFlrSF:GrLivArea:FullBath:GarageCars                                                   -1.382
## OverallQual:YearRemodAdd:X1stFlrSF:GrLivArea:FullBath:GarageCars                                                 0.427
## YearBuilt:YearRemodAdd:X1stFlrSF:GrLivArea:FullBath:GarageCars                                                      NA
## OverallQual:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:GarageCars                                                  0.405
## YearBuilt:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:GarageCars                                                   -0.685
## YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:GarageCars                                                 1.356
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:TotRmsAbvGrd:GarageCars                                              NA
## OverallQual:YearBuilt:YearRemodAdd:X1stFlrSF:TotRmsAbvGrd:GarageCars                                                NA
## OverallQual:YearBuilt:TotalBsmtSF:X1stFlrSF:TotRmsAbvGrd:GarageCars                                              0.281
## OverallQual:YearRemodAdd:TotalBsmtSF:X1stFlrSF:TotRmsAbvGrd:GarageCars                                          -0.984
## YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:TotRmsAbvGrd:GarageCars                                                NA
## OverallQual:YearBuilt:YearRemodAdd:GrLivArea:TotRmsAbvGrd:GarageCars                                                NA
## OverallQual:YearBuilt:TotalBsmtSF:GrLivArea:TotRmsAbvGrd:GarageCars                                             -2.368
## OverallQual:YearRemodAdd:TotalBsmtSF:GrLivArea:TotRmsAbvGrd:GarageCars                                           0.705
## YearBuilt:YearRemodAdd:TotalBsmtSF:GrLivArea:TotRmsAbvGrd:GarageCars                                                NA
## OverallQual:YearBuilt:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageCars                                                1.434
## OverallQual:YearRemodAdd:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageCars                                             0.042
## YearBuilt:YearRemodAdd:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageCars                                                  NA
## OverallQual:TotalBsmtSF:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageCars                                             -1.336
## YearBuilt:TotalBsmtSF:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageCars                                               -1.852
## YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageCars                                             0.728
## OverallQual:YearBuilt:YearRemodAdd:FullBath:TotRmsAbvGrd:GarageCars                                                 NA
## OverallQual:YearBuilt:TotalBsmtSF:FullBath:TotRmsAbvGrd:GarageCars                                              -0.692
## OverallQual:YearRemodAdd:TotalBsmtSF:FullBath:TotRmsAbvGrd:GarageCars                                            1.056
## YearBuilt:YearRemodAdd:TotalBsmtSF:FullBath:TotRmsAbvGrd:GarageCars                                                 NA
## OverallQual:YearBuilt:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageCars                                                -0.795
## OverallQual:YearRemodAdd:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageCars                                                 NA
## YearBuilt:YearRemodAdd:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageCars                                                   NA
## OverallQual:TotalBsmtSF:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageCars                                               0.030
## YearBuilt:TotalBsmtSF:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageCars                                                 2.422
## YearRemodAdd:TotalBsmtSF:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageCars                                             -1.879
## OverallQual:YearBuilt:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars                                                 0.061
## OverallQual:YearRemodAdd:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars                                             -0.119
## YearBuilt:YearRemodAdd:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars                                                   NA
## OverallQual:TotalBsmtSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars                                              -0.855
## YearBuilt:TotalBsmtSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars                                                 1.031
## YearRemodAdd:TotalBsmtSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars                                              0.510
## OverallQual:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars                                                 0.411
## YearBuilt:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars                                                  -0.440
## YearRemodAdd:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars                                                0.388
## TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars                                                -0.051
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GarageArea                                                 NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:GrLivArea:GarageArea                                                 NA
## OverallQual:YearBuilt:YearRemodAdd:X1stFlrSF:GrLivArea:GarageArea                                                   NA
## OverallQual:YearBuilt:TotalBsmtSF:X1stFlrSF:GrLivArea:GarageArea                                                -1.948
## OverallQual:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:GarageArea                                                 NA
## YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:GarageArea                                                   NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:FullBath:GarageArea                                                  NA
## OverallQual:YearBuilt:YearRemodAdd:X1stFlrSF:FullBath:GarageArea                                                    NA
## OverallQual:YearBuilt:TotalBsmtSF:X1stFlrSF:FullBath:GarageArea                                                  0.224
## OverallQual:YearRemodAdd:TotalBsmtSF:X1stFlrSF:FullBath:GarageArea                                              -1.065
## YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:FullBath:GarageArea                                                    NA
## OverallQual:YearBuilt:YearRemodAdd:GrLivArea:FullBath:GarageArea                                                    NA
## OverallQual:YearBuilt:TotalBsmtSF:GrLivArea:FullBath:GarageArea                                                  0.394
## OverallQual:YearRemodAdd:TotalBsmtSF:GrLivArea:FullBath:GarageArea                                                  NA
## YearBuilt:YearRemodAdd:TotalBsmtSF:GrLivArea:FullBath:GarageArea                                                    NA
## OverallQual:YearBuilt:X1stFlrSF:GrLivArea:FullBath:GarageArea                                                    1.777
## OverallQual:YearRemodAdd:X1stFlrSF:GrLivArea:FullBath:GarageArea                                                -0.544
## YearBuilt:YearRemodAdd:X1stFlrSF:GrLivArea:FullBath:GarageArea                                                      NA
## OverallQual:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:GarageArea                                                  1.072
## YearBuilt:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:GarageArea                                                    0.751
## YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:GarageArea                                                    NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:TotRmsAbvGrd:GarageArea                                              NA
## OverallQual:YearBuilt:YearRemodAdd:X1stFlrSF:TotRmsAbvGrd:GarageArea                                                NA
## OverallQual:YearBuilt:TotalBsmtSF:X1stFlrSF:TotRmsAbvGrd:GarageArea                                              0.629
## OverallQual:YearRemodAdd:TotalBsmtSF:X1stFlrSF:TotRmsAbvGrd:GarageArea                                              NA
## YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:TotRmsAbvGrd:GarageArea                                                NA
## OverallQual:YearBuilt:YearRemodAdd:GrLivArea:TotRmsAbvGrd:GarageArea                                                NA
## OverallQual:YearBuilt:TotalBsmtSF:GrLivArea:TotRmsAbvGrd:GarageArea                                              2.047
## OverallQual:YearRemodAdd:TotalBsmtSF:GrLivArea:TotRmsAbvGrd:GarageArea                                              NA
## YearBuilt:YearRemodAdd:TotalBsmtSF:GrLivArea:TotRmsAbvGrd:GarageArea                                                NA
## OverallQual:YearBuilt:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageArea                                               -1.991
## OverallQual:YearRemodAdd:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageArea                                            -1.128
## YearBuilt:YearRemodAdd:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageArea                                                  NA
## OverallQual:TotalBsmtSF:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageArea                                              0.882
## YearBuilt:TotalBsmtSF:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageArea                                                2.003
## YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageArea                                                NA
## OverallQual:YearBuilt:YearRemodAdd:FullBath:TotRmsAbvGrd:GarageArea                                                 NA
## OverallQual:YearBuilt:TotalBsmtSF:FullBath:TotRmsAbvGrd:GarageArea                                              -0.475
## OverallQual:YearRemodAdd:TotalBsmtSF:FullBath:TotRmsAbvGrd:GarageArea                                            0.614
## YearBuilt:YearRemodAdd:TotalBsmtSF:FullBath:TotRmsAbvGrd:GarageArea                                                 NA
## OverallQual:YearBuilt:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageArea                                                    NA
## OverallQual:YearRemodAdd:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageArea                                                 NA
## YearBuilt:YearRemodAdd:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageArea                                                   NA
## OverallQual:TotalBsmtSF:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageArea                                               1.015
## YearBuilt:TotalBsmtSF:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageArea                                                -1.813
## YearRemodAdd:TotalBsmtSF:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageArea                                              2.254
## OverallQual:YearBuilt:GrLivArea:FullBath:TotRmsAbvGrd:GarageArea                                                 0.524
## OverallQual:YearRemodAdd:GrLivArea:FullBath:TotRmsAbvGrd:GarageArea                                              0.088
## YearBuilt:YearRemodAdd:GrLivArea:FullBath:TotRmsAbvGrd:GarageArea                                                   NA
## OverallQual:TotalBsmtSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageArea                                              -1.389
## YearBuilt:TotalBsmtSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageArea                                                -1.512
## YearRemodAdd:TotalBsmtSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageArea                                             -1.651
## OverallQual:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageArea                                                 1.629
## YearBuilt:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageArea                                                   1.278
## YearRemodAdd:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageArea                                                   NA
## TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageArea                                                 0.050
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:GarageCars:GarageArea                                                NA
## OverallQual:YearBuilt:YearRemodAdd:X1stFlrSF:GarageCars:GarageArea                                                  NA
## OverallQual:YearBuilt:TotalBsmtSF:X1stFlrSF:GarageCars:GarageArea                                                0.015
## OverallQual:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GarageCars:GarageArea                                             0.424
## YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GarageCars:GarageArea                                                  NA
## OverallQual:YearBuilt:YearRemodAdd:GrLivArea:GarageCars:GarageArea                                                  NA
## OverallQual:YearBuilt:TotalBsmtSF:GrLivArea:GarageCars:GarageArea                                                3.004
## OverallQual:YearRemodAdd:TotalBsmtSF:GrLivArea:GarageCars:GarageArea                                            -0.757
## YearBuilt:YearRemodAdd:TotalBsmtSF:GrLivArea:GarageCars:GarageArea                                                  NA
## OverallQual:YearBuilt:X1stFlrSF:GrLivArea:GarageCars:GarageArea                                                 -2.378
## OverallQual:YearRemodAdd:X1stFlrSF:GrLivArea:GarageCars:GarageArea                                               0.647
## YearBuilt:YearRemodAdd:X1stFlrSF:GrLivArea:GarageCars:GarageArea                                                    NA
## OverallQual:TotalBsmtSF:X1stFlrSF:GrLivArea:GarageCars:GarageArea                                                0.771
## YearBuilt:TotalBsmtSF:X1stFlrSF:GrLivArea:GarageCars:GarageArea                                                 -0.160
## YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:GarageCars:GarageArea                                               1.168
## OverallQual:YearBuilt:YearRemodAdd:FullBath:GarageCars:GarageArea                                                   NA
## OverallQual:YearBuilt:TotalBsmtSF:FullBath:GarageCars:GarageArea                                                -1.521
## OverallQual:YearRemodAdd:TotalBsmtSF:FullBath:GarageCars:GarageArea                                              3.300
## YearBuilt:YearRemodAdd:TotalBsmtSF:FullBath:GarageCars:GarageArea                                                   NA
## OverallQual:YearBuilt:X1stFlrSF:FullBath:GarageCars:GarageArea                                                   2.382
## OverallQual:YearRemodAdd:X1stFlrSF:FullBath:GarageCars:GarageArea                                               -3.347
## YearBuilt:YearRemodAdd:X1stFlrSF:FullBath:GarageCars:GarageArea                                                     NA
## OverallQual:TotalBsmtSF:X1stFlrSF:FullBath:GarageCars:GarageArea                                                 0.180
## YearBuilt:TotalBsmtSF:X1stFlrSF:FullBath:GarageCars:GarageArea                                                   1.417
## YearRemodAdd:TotalBsmtSF:X1stFlrSF:FullBath:GarageCars:GarageArea                                               -0.761
## OverallQual:YearBuilt:GrLivArea:FullBath:GarageCars:GarageArea                                                   0.023
## OverallQual:YearRemodAdd:GrLivArea:FullBath:GarageCars:GarageArea                                                1.262
## YearBuilt:YearRemodAdd:GrLivArea:FullBath:GarageCars:GarageArea                                                     NA
## OverallQual:TotalBsmtSF:GrLivArea:FullBath:GarageCars:GarageArea                                                 0.460
## YearBuilt:TotalBsmtSF:GrLivArea:FullBath:GarageCars:GarageArea                                                   1.859
## YearRemodAdd:TotalBsmtSF:GrLivArea:FullBath:GarageCars:GarageArea                                               -1.280
## OverallQual:X1stFlrSF:GrLivArea:FullBath:GarageCars:GarageArea                                                   1.940
## YearBuilt:X1stFlrSF:GrLivArea:FullBath:GarageCars:GarageArea                                                    -0.886
## YearRemodAdd:X1stFlrSF:GrLivArea:FullBath:GarageCars:GarageArea                                                  1.633
## TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:GarageCars:GarageArea                                                   0.986
## OverallQual:YearBuilt:YearRemodAdd:TotRmsAbvGrd:GarageCars:GarageArea                                               NA
## OverallQual:YearBuilt:TotalBsmtSF:TotRmsAbvGrd:GarageCars:GarageArea                                            -0.044
## OverallQual:YearRemodAdd:TotalBsmtSF:TotRmsAbvGrd:GarageCars:GarageArea                                         -0.500
## YearBuilt:YearRemodAdd:TotalBsmtSF:TotRmsAbvGrd:GarageCars:GarageArea                                               NA
## OverallQual:YearBuilt:X1stFlrSF:TotRmsAbvGrd:GarageCars:GarageArea                                               0.263
## OverallQual:YearRemodAdd:X1stFlrSF:TotRmsAbvGrd:GarageCars:GarageArea                                               NA
## YearBuilt:YearRemodAdd:X1stFlrSF:TotRmsAbvGrd:GarageCars:GarageArea                                                 NA
## OverallQual:TotalBsmtSF:X1stFlrSF:TotRmsAbvGrd:GarageCars:GarageArea                                            -0.166
## YearBuilt:TotalBsmtSF:X1stFlrSF:TotRmsAbvGrd:GarageCars:GarageArea                                              -0.475
## YearRemodAdd:TotalBsmtSF:X1stFlrSF:TotRmsAbvGrd:GarageCars:GarageArea                                           -0.177
## OverallQual:YearBuilt:GrLivArea:TotRmsAbvGrd:GarageCars:GarageArea                                               1.539
## OverallQual:YearRemodAdd:GrLivArea:TotRmsAbvGrd:GarageCars:GarageArea                                           -0.017
## YearBuilt:YearRemodAdd:GrLivArea:TotRmsAbvGrd:GarageCars:GarageArea                                                 NA
## OverallQual:TotalBsmtSF:GrLivArea:TotRmsAbvGrd:GarageCars:GarageArea                                             0.788
## YearBuilt:TotalBsmtSF:GrLivArea:TotRmsAbvGrd:GarageCars:GarageArea                                              -0.870
## YearRemodAdd:TotalBsmtSF:GrLivArea:TotRmsAbvGrd:GarageCars:GarageArea                                            0.167
## OverallQual:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageCars:GarageArea                                               1.374
## YearBuilt:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageCars:GarageArea                                                 0.605
## YearRemodAdd:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageCars:GarageArea                                              0.223
## TotalBsmtSF:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageCars:GarageArea                                               0.179
## OverallQual:YearBuilt:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                                1.131
## OverallQual:YearRemodAdd:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                            -0.949
## YearBuilt:YearRemodAdd:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                                  NA
## OverallQual:TotalBsmtSF:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                             -1.113
## YearBuilt:TotalBsmtSF:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                                0.636
## YearRemodAdd:TotalBsmtSF:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                             1.586
## OverallQual:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                                1.892
## YearBuilt:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                                     NA
## YearRemodAdd:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                                  NA
## TotalBsmtSF:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                                0.196
## OverallQual:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                                0.671
## YearBuilt:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                                  0.911
## YearRemodAdd:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                               0.230
## TotalBsmtSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                               -1.839
## X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                                  0.410
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath                                         NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:TotRmsAbvGrd                                     NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:FullBath:TotRmsAbvGrd                                      NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:GrLivArea:FullBath:TotRmsAbvGrd                                      NA
## OverallQual:YearBuilt:YearRemodAdd:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd                                        NA
## OverallQual:YearBuilt:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd                                         NA
## OverallQual:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd                                      NA
## YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd                                        NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:GarageCars                                       NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:FullBath:GarageCars                                        NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:GrLivArea:FullBath:GarageCars                                        NA
## OverallQual:YearBuilt:YearRemodAdd:X1stFlrSF:GrLivArea:FullBath:GarageCars                                          NA
## OverallQual:YearBuilt:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:GarageCars                                           NA
## OverallQual:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:GarageCars                                        NA
## YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:GarageCars                                          NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:TotRmsAbvGrd:GarageCars                                    NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:GrLivArea:TotRmsAbvGrd:GarageCars                                    NA
## OverallQual:YearBuilt:YearRemodAdd:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageCars                                      NA
## OverallQual:YearBuilt:TotalBsmtSF:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageCars                                    1.345
## OverallQual:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageCars                                    NA
## YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageCars                                      NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:FullBath:TotRmsAbvGrd:GarageCars                                     NA
## OverallQual:YearBuilt:YearRemodAdd:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageCars                                       NA
## OverallQual:YearBuilt:TotalBsmtSF:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageCars                                        NA
## OverallQual:YearRemodAdd:TotalBsmtSF:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageCars                                     NA
## YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageCars                                       NA
## OverallQual:YearBuilt:YearRemodAdd:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars                                       NA
## OverallQual:YearBuilt:TotalBsmtSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars                                        NA
## OverallQual:YearRemodAdd:TotalBsmtSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars                                     NA
## YearBuilt:YearRemodAdd:TotalBsmtSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars                                       NA
## OverallQual:YearBuilt:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars                                          NA
## OverallQual:YearRemodAdd:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars                                       NA
## YearBuilt:YearRemodAdd:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars                                         NA
## OverallQual:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars                                     0.796
## YearBuilt:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars                                          NA
## YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars                                       NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:GarageArea                                       NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:FullBath:GarageArea                                        NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:GrLivArea:FullBath:GarageArea                                        NA
## OverallQual:YearBuilt:YearRemodAdd:X1stFlrSF:GrLivArea:FullBath:GarageArea                                          NA
## OverallQual:YearBuilt:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:GarageArea                                           NA
## OverallQual:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:GarageArea                                        NA
## YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:GarageArea                                          NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:TotRmsAbvGrd:GarageArea                                    NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:GrLivArea:TotRmsAbvGrd:GarageArea                                    NA
## OverallQual:YearBuilt:YearRemodAdd:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageArea                                      NA
## OverallQual:YearBuilt:TotalBsmtSF:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageArea                                       NA
## OverallQual:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageArea                                    NA
## YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageArea                                      NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:FullBath:TotRmsAbvGrd:GarageArea                                     NA
## OverallQual:YearBuilt:YearRemodAdd:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageArea                                       NA
## OverallQual:YearBuilt:TotalBsmtSF:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageArea                                        NA
## OverallQual:YearRemodAdd:TotalBsmtSF:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageArea                                     NA
## YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageArea                                       NA
## OverallQual:YearBuilt:YearRemodAdd:GrLivArea:FullBath:TotRmsAbvGrd:GarageArea                                       NA
## OverallQual:YearBuilt:TotalBsmtSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageArea                                        NA
## OverallQual:YearRemodAdd:TotalBsmtSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageArea                                     NA
## YearBuilt:YearRemodAdd:TotalBsmtSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageArea                                       NA
## OverallQual:YearBuilt:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageArea                                          NA
## OverallQual:YearRemodAdd:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageArea                                       NA
## YearBuilt:YearRemodAdd:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageArea                                         NA
## OverallQual:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageArea                                    -0.734
## YearBuilt:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageArea                                          NA
## YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageArea                                       NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GarageCars:GarageArea                                      NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:GrLivArea:GarageCars:GarageArea                                      NA
## OverallQual:YearBuilt:YearRemodAdd:X1stFlrSF:GrLivArea:GarageCars:GarageArea                                        NA
## OverallQual:YearBuilt:TotalBsmtSF:X1stFlrSF:GrLivArea:GarageCars:GarageArea                                         NA
## OverallQual:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:GarageCars:GarageArea                                      NA
## YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:GarageCars:GarageArea                                        NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:FullBath:GarageCars:GarageArea                                       NA
## OverallQual:YearBuilt:YearRemodAdd:X1stFlrSF:FullBath:GarageCars:GarageArea                                         NA
## OverallQual:YearBuilt:TotalBsmtSF:X1stFlrSF:FullBath:GarageCars:GarageArea                                      -0.109
## OverallQual:YearRemodAdd:TotalBsmtSF:X1stFlrSF:FullBath:GarageCars:GarageArea                                       NA
## YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:FullBath:GarageCars:GarageArea                                         NA
## OverallQual:YearBuilt:YearRemodAdd:GrLivArea:FullBath:GarageCars:GarageArea                                         NA
## OverallQual:YearBuilt:TotalBsmtSF:GrLivArea:FullBath:GarageCars:GarageArea                                          NA
## OverallQual:YearRemodAdd:TotalBsmtSF:GrLivArea:FullBath:GarageCars:GarageArea                                       NA
## YearBuilt:YearRemodAdd:TotalBsmtSF:GrLivArea:FullBath:GarageCars:GarageArea                                         NA
## OverallQual:YearBuilt:X1stFlrSF:GrLivArea:FullBath:GarageCars:GarageArea                                            NA
## OverallQual:YearRemodAdd:X1stFlrSF:GrLivArea:FullBath:GarageCars:GarageArea                                         NA
## YearBuilt:YearRemodAdd:X1stFlrSF:GrLivArea:FullBath:GarageCars:GarageArea                                           NA
## OverallQual:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:GarageCars:GarageArea                                      -0.733
## YearBuilt:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:GarageCars:GarageArea                                            NA
## YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:GarageCars:GarageArea                                         NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:TotRmsAbvGrd:GarageCars:GarageArea                                   NA
## OverallQual:YearBuilt:YearRemodAdd:X1stFlrSF:TotRmsAbvGrd:GarageCars:GarageArea                                     NA
## OverallQual:YearBuilt:TotalBsmtSF:X1stFlrSF:TotRmsAbvGrd:GarageCars:GarageArea                                      NA
## OverallQual:YearRemodAdd:TotalBsmtSF:X1stFlrSF:TotRmsAbvGrd:GarageCars:GarageArea                                0.240
## YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:TotRmsAbvGrd:GarageCars:GarageArea                                     NA
## OverallQual:YearBuilt:YearRemodAdd:GrLivArea:TotRmsAbvGrd:GarageCars:GarageArea                                     NA
## OverallQual:YearBuilt:TotalBsmtSF:GrLivArea:TotRmsAbvGrd:GarageCars:GarageArea                                      NA
## OverallQual:YearRemodAdd:TotalBsmtSF:GrLivArea:TotRmsAbvGrd:GarageCars:GarageArea                                   NA
## YearBuilt:YearRemodAdd:TotalBsmtSF:GrLivArea:TotRmsAbvGrd:GarageCars:GarageArea                                     NA
## OverallQual:YearBuilt:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageCars:GarageArea                                        NA
## OverallQual:YearRemodAdd:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageCars:GarageArea                                     NA
## YearBuilt:YearRemodAdd:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageCars:GarageArea                                       NA
## OverallQual:TotalBsmtSF:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageCars:GarageArea                                  -0.600
## YearBuilt:TotalBsmtSF:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageCars:GarageArea                                        NA
## YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageCars:GarageArea                                     NA
## OverallQual:YearBuilt:YearRemodAdd:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                      NA
## OverallQual:YearBuilt:TotalBsmtSF:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                       NA
## OverallQual:YearRemodAdd:TotalBsmtSF:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                    NA
## YearBuilt:YearRemodAdd:TotalBsmtSF:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                      NA
## OverallQual:YearBuilt:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                         NA
## OverallQual:YearRemodAdd:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                      NA
## YearBuilt:YearRemodAdd:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                    -1.253
## OverallQual:TotalBsmtSF:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                   -0.241
## YearBuilt:TotalBsmtSF:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                         NA
## YearRemodAdd:TotalBsmtSF:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                      NA
## OverallQual:YearBuilt:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                     -0.742
## OverallQual:YearRemodAdd:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                      NA
## YearBuilt:YearRemodAdd:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                        NA
## OverallQual:TotalBsmtSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                    2.121
## YearBuilt:TotalBsmtSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                         NA
## YearRemodAdd:TotalBsmtSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                      NA
## OverallQual:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                     -1.599
## YearBuilt:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                           NA
## YearRemodAdd:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                        NA
## TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                      0.233
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd                            NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:GarageCars                              NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageCars                          NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageCars                           NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars                           NA
## OverallQual:YearBuilt:YearRemodAdd:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars                             NA
## OverallQual:YearBuilt:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars                              NA
## OverallQual:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars                           NA
## YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars                             NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:GarageArea                              NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageArea                          NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageArea                           NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageArea                           NA
## OverallQual:YearBuilt:YearRemodAdd:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageArea                             NA
## OverallQual:YearBuilt:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageArea                              NA
## OverallQual:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageArea                           NA
## YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageArea                             NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:GarageCars:GarageArea                            NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:FullBath:GarageCars:GarageArea                             NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:GrLivArea:FullBath:GarageCars:GarageArea                         -0.949
## OverallQual:YearBuilt:YearRemodAdd:X1stFlrSF:GrLivArea:FullBath:GarageCars:GarageArea                               NA
## OverallQual:YearBuilt:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:GarageCars:GarageArea                                NA
## OverallQual:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:GarageCars:GarageArea                             NA
## YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:GarageCars:GarageArea                           -0.997
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:TotRmsAbvGrd:GarageCars:GarageArea                         NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:GrLivArea:TotRmsAbvGrd:GarageCars:GarageArea                     -1.180
## OverallQual:YearBuilt:YearRemodAdd:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageCars:GarageArea                           NA
## OverallQual:YearBuilt:TotalBsmtSF:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageCars:GarageArea                            NA
## OverallQual:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageCars:GarageArea                         NA
## YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageCars:GarageArea                           NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                          NA
## OverallQual:YearBuilt:YearRemodAdd:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                            NA
## OverallQual:YearBuilt:TotalBsmtSF:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                             NA
## OverallQual:YearRemodAdd:TotalBsmtSF:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                          NA
## YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                            NA
## OverallQual:YearBuilt:YearRemodAdd:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                            NA
## OverallQual:YearBuilt:TotalBsmtSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                             NA
## OverallQual:YearRemodAdd:TotalBsmtSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                          NA
## YearBuilt:YearRemodAdd:TotalBsmtSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                            NA
## OverallQual:YearBuilt:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                               NA
## OverallQual:YearRemodAdd:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                         1.246
## YearBuilt:YearRemodAdd:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                          -0.161
## OverallQual:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                          0.299
## YearBuilt:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                               NA
## YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                            NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars             -1.041
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageArea                 NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:GarageCars:GarageArea                0.632
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageCars:GarageArea               NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageCars:GarageArea            -0.007
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                NA
## OverallQual:YearBuilt:YearRemodAdd:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                  NA
## OverallQual:YearBuilt:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                   NA
## OverallQual:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                NA
## YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                  NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars:GarageArea      NA
##                                                                                                                Pr(>|t|)
## (Intercept)                                                                                                    0.007860
## OverallQual                                                                                                    0.103627
## YearBuilt                                                                                                      0.003982
## YearRemodAdd                                                                                                   0.018583
## TotalBsmtSF                                                                                                    0.872848
## X1stFlrSF                                                                                                      0.161812
## GrLivArea                                                                                                      0.750289
## FullBath                                                                                                       0.164599
## TotRmsAbvGrd                                                                                                   0.014602
## GarageCars                                                                                                     0.055745
## GarageArea                                                                                                     0.132909
## OverallQual:YearBuilt                                                                                          0.057769
## OverallQual:YearRemodAdd                                                                                       0.271821
## YearBuilt:YearRemodAdd                                                                                         0.005749
## OverallQual:TotalBsmtSF                                                                                        0.754281
## YearBuilt:TotalBsmtSF                                                                                          0.513106
## YearRemodAdd:TotalBsmtSF                                                                                       0.718584
## OverallQual:X1stFlrSF                                                                                          0.401172
## YearBuilt:X1stFlrSF                                                                                            0.193828
## YearRemodAdd:X1stFlrSF                                                                                         0.338974
## TotalBsmtSF:X1stFlrSF                                                                                          0.515620
## OverallQual:GrLivArea                                                                                          0.063188
## YearBuilt:GrLivArea                                                                                            0.915105
## YearRemodAdd:GrLivArea                                                                                         0.886467
## TotalBsmtSF:GrLivArea                                                                                          0.155592
## X1stFlrSF:GrLivArea                                                                                            0.090528
## OverallQual:FullBath                                                                                           0.468631
## YearBuilt:FullBath                                                                                             0.072450
## YearRemodAdd:FullBath                                                                                          0.229450
## TotalBsmtSF:FullBath                                                                                           0.118655
## X1stFlrSF:FullBath                                                                                             0.029421
## GrLivArea:FullBath                                                                                             0.832307
## OverallQual:TotRmsAbvGrd                                                                                       0.133900
## YearBuilt:TotRmsAbvGrd                                                                                         0.018220
## YearRemodAdd:TotRmsAbvGrd                                                                                      0.017578
## TotalBsmtSF:TotRmsAbvGrd                                                                                       0.925490
## X1stFlrSF:TotRmsAbvGrd                                                                                         0.750802
## GrLivArea:TotRmsAbvGrd                                                                                         0.119883
## FullBath:TotRmsAbvGrd                                                                                          0.673604
## OverallQual:GarageCars                                                                                         0.934572
## YearBuilt:GarageCars                                                                                           0.024175
## YearRemodAdd:GarageCars                                                                                        0.113990
## TotalBsmtSF:GarageCars                                                                                         0.198883
## X1stFlrSF:GarageCars                                                                                           0.031964
## GrLivArea:GarageCars                                                                                           0.044414
## FullBath:GarageCars                                                                                            0.262616
## TotRmsAbvGrd:GarageCars                                                                                        0.010730
## OverallQual:GarageArea                                                                                         0.250784
## YearBuilt:GarageArea                                                                                           0.185411
## YearRemodAdd:GarageArea                                                                                        0.052917
## TotalBsmtSF:GarageArea                                                                                         0.379186
## X1stFlrSF:GarageArea                                                                                           0.877764
## GrLivArea:GarageArea                                                                                           0.093823
## FullBath:GarageArea                                                                                            0.683800
## TotRmsAbvGrd:GarageArea                                                                                        0.582638
## GarageCars:GarageArea                                                                                          0.126421
## OverallQual:YearBuilt:YearRemodAdd                                                                             0.104377
## OverallQual:YearBuilt:TotalBsmtSF                                                                              0.221210
## OverallQual:YearRemodAdd:TotalBsmtSF                                                                           0.877371
## YearBuilt:YearRemodAdd:TotalBsmtSF                                                                             0.383709
## OverallQual:YearBuilt:X1stFlrSF                                                                                0.714401
## OverallQual:YearRemodAdd:X1stFlrSF                                                                             0.704352
## YearBuilt:YearRemodAdd:X1stFlrSF                                                                               0.370848
## OverallQual:TotalBsmtSF:X1stFlrSF                                                                              0.017244
## YearBuilt:TotalBsmtSF:X1stFlrSF                                                                                0.355738
## YearRemodAdd:TotalBsmtSF:X1stFlrSF                                                                             0.657952
## OverallQual:YearBuilt:GrLivArea                                                                                0.071055
## OverallQual:YearRemodAdd:GrLivArea                                                                             0.194053
## YearBuilt:YearRemodAdd:GrLivArea                                                                               0.787942
## OverallQual:TotalBsmtSF:GrLivArea                                                                              0.552734
## YearBuilt:TotalBsmtSF:GrLivArea                                                                                0.194062
## YearRemodAdd:TotalBsmtSF:GrLivArea                                                                             0.054785
## OverallQual:X1stFlrSF:GrLivArea                                                                                0.754419
## YearBuilt:X1stFlrSF:GrLivArea                                                                                  0.220215
## YearRemodAdd:X1stFlrSF:GrLivArea                                                                               0.020756
## TotalBsmtSF:X1stFlrSF:GrLivArea                                                                                0.811978
## OverallQual:YearBuilt:FullBath                                                                                 0.212756
## OverallQual:YearRemodAdd:FullBath                                                                              0.866250
## YearBuilt:YearRemodAdd:FullBath                                                                                0.088064
## OverallQual:TotalBsmtSF:FullBath                                                                               0.302718
## YearBuilt:TotalBsmtSF:FullBath                                                                                 0.270498
## YearRemodAdd:TotalBsmtSF:FullBath                                                                              0.237417
## OverallQual:X1stFlrSF:FullBath                                                                                 0.216241
## YearBuilt:X1stFlrSF:FullBath                                                                                   0.015282
## YearRemodAdd:X1stFlrSF:FullBath                                                                                0.074566
## TotalBsmtSF:X1stFlrSF:FullBath                                                                                 0.800601
## OverallQual:GrLivArea:FullBath                                                                                 0.459514
## YearBuilt:GrLivArea:FullBath                                                                                   0.889278
## YearRemodAdd:GrLivArea:FullBath                                                                                0.936597
## TotalBsmtSF:GrLivArea:FullBath                                                                                 0.408245
## X1stFlrSF:GrLivArea:FullBath                                                                                   0.280927
## OverallQual:YearBuilt:TotRmsAbvGrd                                                                             0.113075
## OverallQual:YearRemodAdd:TotRmsAbvGrd                                                                          0.266947
## YearBuilt:YearRemodAdd:TotRmsAbvGrd                                                                            0.015859
## OverallQual:TotalBsmtSF:TotRmsAbvGrd                                                                           0.588406
## YearBuilt:TotalBsmtSF:TotRmsAbvGrd                                                                             0.627708
## YearRemodAdd:TotalBsmtSF:TotRmsAbvGrd                                                                          0.886983
## OverallQual:X1stFlrSF:TotRmsAbvGrd                                                                             0.582680
## YearBuilt:X1stFlrSF:TotRmsAbvGrd                                                                               0.984773
## YearRemodAdd:X1stFlrSF:TotRmsAbvGrd                                                                            0.656988
## TotalBsmtSF:X1stFlrSF:TotRmsAbvGrd                                                                             0.570401
## OverallQual:GrLivArea:TotRmsAbvGrd                                                                             0.525932
## YearBuilt:GrLivArea:TotRmsAbvGrd                                                                               0.122332
## YearRemodAdd:GrLivArea:TotRmsAbvGrd                                                                            0.058835
## TotalBsmtSF:GrLivArea:TotRmsAbvGrd                                                                             0.656190
## X1stFlrSF:GrLivArea:TotRmsAbvGrd                                                                               0.692634
## OverallQual:FullBath:TotRmsAbvGrd                                                                              0.615287
## YearBuilt:FullBath:TotRmsAbvGrd                                                                                0.534584
## YearRemodAdd:FullBath:TotRmsAbvGrd                                                                             0.727256
## TotalBsmtSF:FullBath:TotRmsAbvGrd                                                                              0.325073
## X1stFlrSF:FullBath:TotRmsAbvGrd                                                                                0.556071
## GrLivArea:FullBath:TotRmsAbvGrd                                                                                0.498835
## OverallQual:YearBuilt:GarageCars                                                                               0.760229
## OverallQual:YearRemodAdd:GarageCars                                                                            0.703844
## YearBuilt:YearRemodAdd:GarageCars                                                                              0.033271
## OverallQual:TotalBsmtSF:GarageCars                                                                             0.286434
## YearBuilt:TotalBsmtSF:GarageCars                                                                               0.256236
## YearRemodAdd:TotalBsmtSF:GarageCars                                                                            0.259441
## OverallQual:X1stFlrSF:GarageCars                                                                               0.242525
## YearBuilt:X1stFlrSF:GarageCars                                                                                 0.065048
## YearRemodAdd:X1stFlrSF:GarageCars                                                                              0.037702
## TotalBsmtSF:X1stFlrSF:GarageCars                                                                               0.789024
## OverallQual:GrLivArea:GarageCars                                                                               0.097663
## YearBuilt:GrLivArea:GarageCars                                                                                 0.409505
## YearRemodAdd:GrLivArea:GarageCars                                                                              0.016723
## TotalBsmtSF:GrLivArea:GarageCars                                                                               0.917054
## X1stFlrSF:GrLivArea:GarageCars                                                                                 0.321431
## OverallQual:FullBath:GarageCars                                                                                0.362721
## YearBuilt:FullBath:GarageCars                                                                                  0.074215
## YearRemodAdd:FullBath:GarageCars                                                                               0.470200
## TotalBsmtSF:FullBath:GarageCars                                                                                0.018777
## X1stFlrSF:FullBath:GarageCars                                                                                  0.035867
## GrLivArea:FullBath:GarageCars                                                                                  0.204835
## OverallQual:TotRmsAbvGrd:GarageCars                                                                            0.275516
## YearBuilt:TotRmsAbvGrd:GarageCars                                                                              0.017156
## YearRemodAdd:TotRmsAbvGrd:GarageCars                                                                           0.009786
## TotalBsmtSF:TotRmsAbvGrd:GarageCars                                                                            0.590407
## X1stFlrSF:TotRmsAbvGrd:GarageCars                                                                              0.309548
## GrLivArea:TotRmsAbvGrd:GarageCars                                                                              0.975833
## FullBath:TotRmsAbvGrd:GarageCars                                                                               0.590418
## OverallQual:YearBuilt:GarageArea                                                                               0.511470
## OverallQual:YearRemodAdd:GarageArea                                                                            0.064064
## YearBuilt:YearRemodAdd:GarageArea                                                                              0.049998
## OverallQual:TotalBsmtSF:GarageArea                                                                             0.588065
## YearBuilt:TotalBsmtSF:GarageArea                                                                               0.236401
## YearRemodAdd:TotalBsmtSF:GarageArea                                                                            0.182313
## OverallQual:X1stFlrSF:GarageArea                                                                               0.025559
## YearBuilt:X1stFlrSF:GarageArea                                                                                 0.602995
## YearRemodAdd:X1stFlrSF:GarageArea                                                                              0.797902
## TotalBsmtSF:X1stFlrSF:GarageArea                                                                               0.456212
## OverallQual:GrLivArea:GarageArea                                                                               0.325919
## YearBuilt:GrLivArea:GarageArea                                                                                 0.179810
## YearRemodAdd:GrLivArea:GarageArea                                                                              0.045284
## TotalBsmtSF:GrLivArea:GarageArea                                                                               0.038785
## X1stFlrSF:GrLivArea:GarageArea                                                                                 0.439631
## OverallQual:FullBath:GarageArea                                                                                0.357970
## YearBuilt:FullBath:GarageArea                                                                                  0.504458
## YearRemodAdd:FullBath:GarageArea                                                                               0.745316
## TotalBsmtSF:FullBath:GarageArea                                                                                0.984800
## X1stFlrSF:FullBath:GarageArea                                                                                  0.697533
## GrLivArea:FullBath:GarageArea                                                                                  0.606107
## OverallQual:TotRmsAbvGrd:GarageArea                                                                            0.543447
## YearBuilt:TotRmsAbvGrd:GarageArea                                                                              0.638281
## YearRemodAdd:TotRmsAbvGrd:GarageArea                                                                           0.695062
## TotalBsmtSF:TotRmsAbvGrd:GarageArea                                                                            0.286676
## X1stFlrSF:TotRmsAbvGrd:GarageArea                                                                              0.314763
## GrLivArea:TotRmsAbvGrd:GarageArea                                                                              0.768603
## FullBath:TotRmsAbvGrd:GarageArea                                                                               0.894374
## OverallQual:GarageCars:GarageArea                                                                              0.476207
## YearBuilt:GarageCars:GarageArea                                                                                0.139905
## YearRemodAdd:GarageCars:GarageArea                                                                             0.041884
## TotalBsmtSF:GarageCars:GarageArea                                                                              0.288640
## X1stFlrSF:GarageCars:GarageArea                                                                                0.179534
## GrLivArea:GarageCars:GarageArea                                                                                0.461077
## FullBath:GarageCars:GarageArea                                                                                 0.633583
## TotRmsAbvGrd:GarageCars:GarageArea                                                                             0.789315
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF                                                                 0.276136
## OverallQual:YearBuilt:YearRemodAdd:X1stFlrSF                                                                   0.938726
## OverallQual:YearBuilt:TotalBsmtSF:X1stFlrSF                                                                    0.003823
## OverallQual:YearRemodAdd:TotalBsmtSF:X1stFlrSF                                                                 0.123356
## YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF                                                                   0.436873
## OverallQual:YearBuilt:YearRemodAdd:GrLivArea                                                                   0.120415
## OverallQual:YearBuilt:TotalBsmtSF:GrLivArea                                                                    0.543542
## OverallQual:YearRemodAdd:TotalBsmtSF:GrLivArea                                                                 0.947403
## YearBuilt:YearRemodAdd:TotalBsmtSF:GrLivArea                                                                   0.055898
## OverallQual:YearBuilt:X1stFlrSF:GrLivArea                                                                      0.571927
## OverallQual:YearRemodAdd:X1stFlrSF:GrLivArea                                                                   0.433968
## YearBuilt:YearRemodAdd:X1stFlrSF:GrLivArea                                                                     0.028099
## OverallQual:TotalBsmtSF:X1stFlrSF:GrLivArea                                                                    0.062688
## YearBuilt:TotalBsmtSF:X1stFlrSF:GrLivArea                                                                      0.556986
## YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea                                                                   0.098333
## OverallQual:YearBuilt:YearRemodAdd:FullBath                                                                    0.432746
## OverallQual:YearBuilt:TotalBsmtSF:FullBath                                                                     0.699106
## OverallQual:YearRemodAdd:TotalBsmtSF:FullBath                                                                  0.242118
## YearBuilt:YearRemodAdd:TotalBsmtSF:FullBath                                                                    0.473051
## OverallQual:YearBuilt:X1stFlrSF:FullBath                                                                       0.303759
## OverallQual:YearRemodAdd:X1stFlrSF:FullBath                                                                    0.514436
## YearBuilt:YearRemodAdd:X1stFlrSF:FullBath                                                                      0.027272
## OverallQual:TotalBsmtSF:X1stFlrSF:FullBath                                                                     0.776555
## YearBuilt:TotalBsmtSF:X1stFlrSF:FullBath                                                                       0.640237
## YearRemodAdd:TotalBsmtSF:X1stFlrSF:FullBath                                                                    0.806455
## OverallQual:YearBuilt:GrLivArea:FullBath                                                                       0.465167
## OverallQual:YearRemodAdd:GrLivArea:FullBath                                                                    0.931635
## YearBuilt:YearRemodAdd:GrLivArea:FullBath                                                                      0.652018
## OverallQual:TotalBsmtSF:GrLivArea:FullBath                                                                     0.121765
## YearBuilt:TotalBsmtSF:GrLivArea:FullBath                                                                       0.165239
## YearRemodAdd:TotalBsmtSF:GrLivArea:FullBath                                                                    0.447428
## OverallQual:X1stFlrSF:GrLivArea:FullBath                                                                       0.413507
## YearBuilt:X1stFlrSF:GrLivArea:FullBath                                                                         0.109274
## YearRemodAdd:X1stFlrSF:GrLivArea:FullBath                                                                      0.880665
## TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath                                                                       0.483541
## OverallQual:YearBuilt:YearRemodAdd:TotRmsAbvGrd                                                                0.141203
## OverallQual:YearBuilt:TotalBsmtSF:TotRmsAbvGrd                                                                 0.233904
## OverallQual:YearRemodAdd:TotalBsmtSF:TotRmsAbvGrd                                                              0.908656
## YearBuilt:YearRemodAdd:TotalBsmtSF:TotRmsAbvGrd                                                                0.800754
## OverallQual:YearBuilt:X1stFlrSF:TotRmsAbvGrd                                                                   0.455392
## OverallQual:YearRemodAdd:X1stFlrSF:TotRmsAbvGrd                                                                0.572888
## YearBuilt:YearRemodAdd:X1stFlrSF:TotRmsAbvGrd                                                                  0.869277
## OverallQual:TotalBsmtSF:X1stFlrSF:TotRmsAbvGrd                                                                 0.706543
## YearBuilt:TotalBsmtSF:X1stFlrSF:TotRmsAbvGrd                                                                   0.496341
## YearRemodAdd:TotalBsmtSF:X1stFlrSF:TotRmsAbvGrd                                                                0.807372
## OverallQual:YearBuilt:GrLivArea:TotRmsAbvGrd                                                                   0.759824
## OverallQual:YearRemodAdd:GrLivArea:TotRmsAbvGrd                                                                0.302119
## YearBuilt:YearRemodAdd:GrLivArea:TotRmsAbvGrd                                                                  0.040591
## OverallQual:TotalBsmtSF:GrLivArea:TotRmsAbvGrd                                                                 0.558788
## YearBuilt:TotalBsmtSF:GrLivArea:TotRmsAbvGrd                                                                   0.491580
## YearRemodAdd:TotalBsmtSF:GrLivArea:TotRmsAbvGrd                                                                0.939662
## OverallQual:X1stFlrSF:GrLivArea:TotRmsAbvGrd                                                                   0.330260
## YearBuilt:X1stFlrSF:GrLivArea:TotRmsAbvGrd                                                                     0.840786
## YearRemodAdd:X1stFlrSF:GrLivArea:TotRmsAbvGrd                                                                  0.631506
## TotalBsmtSF:X1stFlrSF:GrLivArea:TotRmsAbvGrd                                                                   0.247623
## OverallQual:YearBuilt:FullBath:TotRmsAbvGrd                                                                    0.334873
## OverallQual:YearRemodAdd:FullBath:TotRmsAbvGrd                                                                 0.714200
## YearBuilt:YearRemodAdd:FullBath:TotRmsAbvGrd                                                                   0.555654
## OverallQual:TotalBsmtSF:FullBath:TotRmsAbvGrd                                                                  0.219711
## YearBuilt:TotalBsmtSF:FullBath:TotRmsAbvGrd                                                                    0.753006
## YearRemodAdd:TotalBsmtSF:FullBath:TotRmsAbvGrd                                                                 0.356924
## OverallQual:X1stFlrSF:FullBath:TotRmsAbvGrd                                                                    0.377673
## YearBuilt:X1stFlrSF:FullBath:TotRmsAbvGrd                                                                      0.596920
## YearRemodAdd:X1stFlrSF:FullBath:TotRmsAbvGrd                                                                   0.610794
## TotalBsmtSF:X1stFlrSF:FullBath:TotRmsAbvGrd                                                                    0.330853
## OverallQual:GrLivArea:FullBath:TotRmsAbvGrd                                                                    0.752796
## YearBuilt:GrLivArea:FullBath:TotRmsAbvGrd                                                                      0.370886
## YearRemodAdd:GrLivArea:FullBath:TotRmsAbvGrd                                                                   0.988400
## TotalBsmtSF:GrLivArea:FullBath:TotRmsAbvGrd                                                                    0.620520
## X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd                                                                      0.822435
## OverallQual:YearBuilt:YearRemodAdd:GarageCars                                                                  0.853614
## OverallQual:YearBuilt:TotalBsmtSF:GarageCars                                                                   0.498796
## OverallQual:YearRemodAdd:TotalBsmtSF:GarageCars                                                                0.122673
## YearBuilt:YearRemodAdd:TotalBsmtSF:GarageCars                                                                  0.323812
## OverallQual:YearBuilt:X1stFlrSF:GarageCars                                                                     0.493040
## OverallQual:YearRemodAdd:X1stFlrSF:GarageCars                                                                  0.183499
## YearBuilt:YearRemodAdd:X1stFlrSF:GarageCars                                                                    0.052725
## OverallQual:TotalBsmtSF:X1stFlrSF:GarageCars                                                                   0.436348
## YearBuilt:TotalBsmtSF:X1stFlrSF:GarageCars                                                                     0.474033
## YearRemodAdd:TotalBsmtSF:X1stFlrSF:GarageCars                                                                  0.315369
## OverallQual:YearBuilt:GrLivArea:GarageCars                                                                     0.302986
## OverallQual:YearRemodAdd:GrLivArea:GarageCars                                                                  0.075559
## YearBuilt:YearRemodAdd:GrLivArea:GarageCars                                                                    0.198699
## OverallQual:TotalBsmtSF:GrLivArea:GarageCars                                                                   0.626676
## YearBuilt:TotalBsmtSF:GrLivArea:GarageCars                                                                     0.662825
## YearRemodAdd:TotalBsmtSF:GrLivArea:GarageCars                                                                  0.832782
## OverallQual:X1stFlrSF:GrLivArea:GarageCars                                                                     0.934421
## YearBuilt:X1stFlrSF:GrLivArea:GarageCars                                                                       0.916820
## YearRemodAdd:X1stFlrSF:GrLivArea:GarageCars                                                                    0.083300
## TotalBsmtSF:X1stFlrSF:GrLivArea:GarageCars                                                                     0.669782
## OverallQual:YearBuilt:FullBath:GarageCars                                                                      0.075847
## OverallQual:YearRemodAdd:FullBath:GarageCars                                                                   0.762344
## YearBuilt:YearRemodAdd:FullBath:GarageCars                                                                     0.127256
## OverallQual:TotalBsmtSF:FullBath:GarageCars                                                                    0.099111
## YearBuilt:TotalBsmtSF:FullBath:GarageCars                                                                      0.067185
## YearRemodAdd:TotalBsmtSF:FullBath:GarageCars                                                                   0.112808
## OverallQual:X1stFlrSF:FullBath:GarageCars                                                                      0.106826
## YearBuilt:X1stFlrSF:FullBath:GarageCars                                                                        0.028285
## YearRemodAdd:X1stFlrSF:FullBath:GarageCars                                                                     0.172559
## TotalBsmtSF:X1stFlrSF:FullBath:GarageCars                                                                      0.352795
## OverallQual:GrLivArea:FullBath:GarageCars                                                                      0.507177
## YearBuilt:GrLivArea:FullBath:GarageCars                                                                        0.979084
## YearRemodAdd:GrLivArea:FullBath:GarageCars                                                                     0.137725
## TotalBsmtSF:GrLivArea:FullBath:GarageCars                                                                      0.021972
## X1stFlrSF:GrLivArea:FullBath:GarageCars                                                                        0.607988
## OverallQual:YearBuilt:TotRmsAbvGrd:GarageCars                                                                  0.420273
## OverallQual:YearRemodAdd:TotRmsAbvGrd:GarageCars                                                               0.338761
## YearBuilt:YearRemodAdd:TotRmsAbvGrd:GarageCars                                                                 0.009370
## OverallQual:TotalBsmtSF:TotRmsAbvGrd:GarageCars                                                                0.038320
## YearBuilt:TotalBsmtSF:TotRmsAbvGrd:GarageCars                                                                  0.667070
## YearRemodAdd:TotalBsmtSF:TotRmsAbvGrd:GarageCars                                                               0.826715
## OverallQual:X1stFlrSF:TotRmsAbvGrd:GarageCars                                                                  0.439373
## YearBuilt:X1stFlrSF:TotRmsAbvGrd:GarageCars                                                                    0.660868
## YearRemodAdd:X1stFlrSF:TotRmsAbvGrd:GarageCars                                                                 0.109619
## TotalBsmtSF:X1stFlrSF:TotRmsAbvGrd:GarageCars                                                                  0.188984
## OverallQual:GrLivArea:TotRmsAbvGrd:GarageCars                                                                  0.557300
## YearBuilt:GrLivArea:TotRmsAbvGrd:GarageCars                                                                    0.492914
## YearRemodAdd:GrLivArea:TotRmsAbvGrd:GarageCars                                                                 0.989547
## TotalBsmtSF:GrLivArea:TotRmsAbvGrd:GarageCars                                                                  0.435986
## X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageCars                                                                    0.320000
## OverallQual:FullBath:TotRmsAbvGrd:GarageCars                                                                   0.395749
## YearBuilt:FullBath:TotRmsAbvGrd:GarageCars                                                                     0.542789
## YearRemodAdd:FullBath:TotRmsAbvGrd:GarageCars                                                                  0.477798
## TotalBsmtSF:FullBath:TotRmsAbvGrd:GarageCars                                                                   0.108211
## X1stFlrSF:FullBath:TotRmsAbvGrd:GarageCars                                                                     0.614053
## GrLivArea:FullBath:TotRmsAbvGrd:GarageCars                                                                     0.187644
## OverallQual:YearBuilt:YearRemodAdd:GarageArea                                                                  0.109952
## OverallQual:YearBuilt:TotalBsmtSF:GarageArea                                                                   0.702066
## OverallQual:YearRemodAdd:TotalBsmtSF:GarageArea                                                                0.864676
## YearBuilt:YearRemodAdd:TotalBsmtSF:GarageArea                                                                  0.082968
## OverallQual:YearBuilt:X1stFlrSF:GarageArea                                                                     0.721656
## OverallQual:YearRemodAdd:X1stFlrSF:GarageArea                                                                  0.017884
## YearBuilt:YearRemodAdd:X1stFlrSF:GarageArea                                                                    0.470437
## OverallQual:TotalBsmtSF:X1stFlrSF:GarageArea                                                                   0.964583
## YearBuilt:TotalBsmtSF:X1stFlrSF:GarageArea                                                                     0.994289
## YearRemodAdd:TotalBsmtSF:X1stFlrSF:GarageArea                                                                  0.398030
## OverallQual:YearBuilt:GrLivArea:GarageArea                                                                     0.454801
## OverallQual:YearRemodAdd:GrLivArea:GarageArea                                                                  0.150648
## YearBuilt:YearRemodAdd:GrLivArea:GarageArea                                                                    0.068608
## OverallQual:TotalBsmtSF:GrLivArea:GarageArea                                                                   0.107932
## YearBuilt:TotalBsmtSF:GrLivArea:GarageArea                                                                     0.335488
## YearRemodAdd:TotalBsmtSF:GrLivArea:GarageArea                                                                  0.003377
## OverallQual:X1stFlrSF:GrLivArea:GarageArea                                                                     0.053757
## YearBuilt:X1stFlrSF:GrLivArea:GarageArea                                                                       0.609028
## YearRemodAdd:X1stFlrSF:GrLivArea:GarageArea                                                                    0.334405
## TotalBsmtSF:X1stFlrSF:GrLivArea:GarageArea                                                                     0.858967
## OverallQual:YearBuilt:FullBath:GarageArea                                                                      0.138404
## OverallQual:YearRemodAdd:FullBath:GarageArea                                                                   0.670154
## YearBuilt:YearRemodAdd:FullBath:GarageArea                                                                     0.941468
## OverallQual:TotalBsmtSF:FullBath:GarageArea                                                                    0.592967
## YearBuilt:TotalBsmtSF:FullBath:GarageArea                                                                      0.702833
## YearRemodAdd:TotalBsmtSF:FullBath:GarageArea                                                                   0.791198
## OverallQual:X1stFlrSF:FullBath:GarageArea                                                                      0.917380
## YearBuilt:X1stFlrSF:FullBath:GarageArea                                                                        0.293162
## YearRemodAdd:X1stFlrSF:FullBath:GarageArea                                                                     0.509332
## TotalBsmtSF:X1stFlrSF:FullBath:GarageArea                                                                      0.652310
## OverallQual:GrLivArea:FullBath:GarageArea                                                                      0.153444
## YearBuilt:GrLivArea:FullBath:GarageArea                                                                        0.532047
## YearRemodAdd:GrLivArea:FullBath:GarageArea                                                                     0.842213
## TotalBsmtSF:GrLivArea:FullBath:GarageArea                                                                      0.129362
## X1stFlrSF:GrLivArea:FullBath:GarageArea                                                                        0.021009
## OverallQual:YearBuilt:TotRmsAbvGrd:GarageArea                                                                  0.471570
## OverallQual:YearRemodAdd:TotRmsAbvGrd:GarageArea                                                               0.854824
## YearBuilt:YearRemodAdd:TotRmsAbvGrd:GarageArea                                                                 0.738422
## OverallQual:TotalBsmtSF:TotRmsAbvGrd:GarageArea                                                                0.120448
## YearBuilt:TotalBsmtSF:TotRmsAbvGrd:GarageArea                                                                  0.583270
## YearRemodAdd:TotalBsmtSF:TotRmsAbvGrd:GarageArea                                                               0.323486
## OverallQual:X1stFlrSF:TotRmsAbvGrd:GarageArea                                                                  0.180472
## YearBuilt:X1stFlrSF:TotRmsAbvGrd:GarageArea                                                                    0.342981
## YearRemodAdd:X1stFlrSF:TotRmsAbvGrd:GarageArea                                                                 0.799684
## TotalBsmtSF:X1stFlrSF:TotRmsAbvGrd:GarageArea                                                                  0.243460
## OverallQual:GrLivArea:TotRmsAbvGrd:GarageArea                                                                  0.348534
## YearBuilt:GrLivArea:TotRmsAbvGrd:GarageArea                                                                    0.862249
## YearRemodAdd:GrLivArea:TotRmsAbvGrd:GarageArea                                                                 0.352108
## TotalBsmtSF:GrLivArea:TotRmsAbvGrd:GarageArea                                                                  0.756048
## X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageArea                                                                    0.962353
## OverallQual:FullBath:TotRmsAbvGrd:GarageArea                                                                   0.708396
## YearBuilt:FullBath:TotRmsAbvGrd:GarageArea                                                                     0.967943
## YearRemodAdd:FullBath:TotRmsAbvGrd:GarageArea                                                                  0.863329
## TotalBsmtSF:FullBath:TotRmsAbvGrd:GarageArea                                                                   0.970647
## X1stFlrSF:FullBath:TotRmsAbvGrd:GarageArea                                                                     0.810901
## GrLivArea:FullBath:TotRmsAbvGrd:GarageArea                                                                     0.921583
## OverallQual:YearBuilt:GarageCars:GarageArea                                                                    0.298740
## OverallQual:YearRemodAdd:GarageCars:GarageArea                                                                 0.655445
## YearBuilt:YearRemodAdd:GarageCars:GarageArea                                                                   0.025551
## OverallQual:TotalBsmtSF:GarageCars:GarageArea                                                                  0.105683
## YearBuilt:TotalBsmtSF:GarageCars:GarageArea                                                                    0.479034
## YearRemodAdd:TotalBsmtSF:GarageCars:GarageArea                                                                 0.682373
## OverallQual:X1stFlrSF:GarageCars:GarageArea                                                                    0.196971
## YearBuilt:X1stFlrSF:GarageCars:GarageArea                                                                      0.337823
## YearRemodAdd:X1stFlrSF:GarageCars:GarageArea                                                                   0.199479
## TotalBsmtSF:X1stFlrSF:GarageCars:GarageArea                                                                    0.356782
## OverallQual:GrLivArea:GarageCars:GarageArea                                                                    0.068620
## YearBuilt:GrLivArea:GarageCars:GarageArea                                                                      0.995024
## YearRemodAdd:GrLivArea:GarageCars:GarageArea                                                                   0.682826
## TotalBsmtSF:GrLivArea:GarageCars:GarageArea                                                                    0.929431
## X1stFlrSF:GrLivArea:GarageCars:GarageArea                                                                      0.891685
## OverallQual:FullBath:GarageCars:GarageArea                                                                     0.531317
## YearBuilt:FullBath:GarageCars:GarageArea                                                                       0.597811
## YearRemodAdd:FullBath:GarageCars:GarageArea                                                                    0.159546
## TotalBsmtSF:FullBath:GarageCars:GarageArea                                                                     0.037649
## X1stFlrSF:FullBath:GarageCars:GarageArea                                                                       0.157253
## GrLivArea:FullBath:GarageCars:GarageArea                                                                       0.278771
## OverallQual:TotRmsAbvGrd:GarageCars:GarageArea                                                                 0.647252
## YearBuilt:TotRmsAbvGrd:GarageCars:GarageArea                                                                   0.987431
## YearRemodAdd:TotRmsAbvGrd:GarageCars:GarageArea                                                                0.389962
## TotalBsmtSF:TotRmsAbvGrd:GarageCars:GarageArea                                                                 0.964004
## X1stFlrSF:TotRmsAbvGrd:GarageCars:GarageArea                                                                   0.424941
## GrLivArea:TotRmsAbvGrd:GarageCars:GarageArea                                                                   0.229898
## FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                                                    0.506724
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF                                                       0.020714
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:GrLivArea                                                       0.950547
## OverallQual:YearBuilt:YearRemodAdd:X1stFlrSF:GrLivArea                                                         0.254828
## OverallQual:YearBuilt:TotalBsmtSF:X1stFlrSF:GrLivArea                                                          0.045063
## OverallQual:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea                                                       0.917555
## YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea                                                         0.307908
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:FullBath                                                        0.827995
## OverallQual:YearBuilt:YearRemodAdd:X1stFlrSF:FullBath                                                          0.617171
## OverallQual:YearBuilt:TotalBsmtSF:X1stFlrSF:FullBath                                                           0.111633
## OverallQual:YearRemodAdd:TotalBsmtSF:X1stFlrSF:FullBath                                                        0.137029
## YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:FullBath                                                          0.530341
## OverallQual:YearBuilt:YearRemodAdd:GrLivArea:FullBath                                                          0.811245
## OverallQual:YearBuilt:TotalBsmtSF:GrLivArea:FullBath                                                           0.037258
## OverallQual:YearRemodAdd:TotalBsmtSF:GrLivArea:FullBath                                                        0.776828
## YearBuilt:YearRemodAdd:TotalBsmtSF:GrLivArea:FullBath                                                          0.638999
## OverallQual:YearBuilt:X1stFlrSF:GrLivArea:FullBath                                                             0.591117
## OverallQual:YearRemodAdd:X1stFlrSF:GrLivArea:FullBath                                                          0.768575
## YearBuilt:YearRemodAdd:X1stFlrSF:GrLivArea:FullBath                                                            0.191403
## OverallQual:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath                                                           0.792944
## YearBuilt:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath                                                             0.534701
## YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath                                                          0.332464
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:TotRmsAbvGrd                                                    0.443626
## OverallQual:YearBuilt:YearRemodAdd:X1stFlrSF:TotRmsAbvGrd                                                      0.430412
## OverallQual:YearBuilt:TotalBsmtSF:X1stFlrSF:TotRmsAbvGrd                                                       0.701027
## OverallQual:YearRemodAdd:TotalBsmtSF:X1stFlrSF:TotRmsAbvGrd                                                    0.591464
## YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:TotRmsAbvGrd                                                      0.617309
## OverallQual:YearBuilt:YearRemodAdd:GrLivArea:TotRmsAbvGrd                                                      0.412344
## OverallQual:YearBuilt:TotalBsmtSF:GrLivArea:TotRmsAbvGrd                                                       0.677622
## OverallQual:YearRemodAdd:TotalBsmtSF:GrLivArea:TotRmsAbvGrd                                                    0.250884
## YearBuilt:YearRemodAdd:TotalBsmtSF:GrLivArea:TotRmsAbvGrd                                                      0.715090
## OverallQual:YearBuilt:X1stFlrSF:GrLivArea:TotRmsAbvGrd                                                         0.753716
## OverallQual:YearRemodAdd:X1stFlrSF:GrLivArea:TotRmsAbvGrd                                                      0.149990
## YearBuilt:YearRemodAdd:X1stFlrSF:GrLivArea:TotRmsAbvGrd                                                        0.730461
## OverallQual:TotalBsmtSF:X1stFlrSF:GrLivArea:TotRmsAbvGrd                                                       0.337353
## YearBuilt:TotalBsmtSF:X1stFlrSF:GrLivArea:TotRmsAbvGrd                                                         0.078786
## YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:TotRmsAbvGrd                                                      0.217682
## OverallQual:YearBuilt:YearRemodAdd:FullBath:TotRmsAbvGrd                                                       0.826614
## OverallQual:YearBuilt:TotalBsmtSF:FullBath:TotRmsAbvGrd                                                        0.437735
## OverallQual:YearRemodAdd:TotalBsmtSF:FullBath:TotRmsAbvGrd                                                     0.094091
## YearBuilt:YearRemodAdd:TotalBsmtSF:FullBath:TotRmsAbvGrd                                                       0.697789
## OverallQual:YearBuilt:X1stFlrSF:FullBath:TotRmsAbvGrd                                                          0.140268
## OverallQual:YearRemodAdd:X1stFlrSF:FullBath:TotRmsAbvGrd                                                       0.436729
## YearBuilt:YearRemodAdd:X1stFlrSF:FullBath:TotRmsAbvGrd                                                         0.623364
## OverallQual:TotalBsmtSF:X1stFlrSF:FullBath:TotRmsAbvGrd                                                        0.244733
## YearBuilt:TotalBsmtSF:X1stFlrSF:FullBath:TotRmsAbvGrd                                                          0.413918
## YearRemodAdd:TotalBsmtSF:X1stFlrSF:FullBath:TotRmsAbvGrd                                                       0.974437
## OverallQual:YearBuilt:GrLivArea:FullBath:TotRmsAbvGrd                                                          0.545911
## OverallQual:YearRemodAdd:GrLivArea:FullBath:TotRmsAbvGrd                                                       0.428868
## YearBuilt:YearRemodAdd:GrLivArea:FullBath:TotRmsAbvGrd                                                         0.779737
## OverallQual:TotalBsmtSF:GrLivArea:FullBath:TotRmsAbvGrd                                                        0.217747
## YearBuilt:TotalBsmtSF:GrLivArea:FullBath:TotRmsAbvGrd                                                          0.253566
## YearRemodAdd:TotalBsmtSF:GrLivArea:FullBath:TotRmsAbvGrd                                                       0.619843
## OverallQual:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd                                                          0.110457
## YearBuilt:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd                                                            0.981220
## YearRemodAdd:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd                                                         0.853324
## TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd                                                          0.794684
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:GarageCars                                                      0.217943
## OverallQual:YearBuilt:YearRemodAdd:X1stFlrSF:GarageCars                                                        0.345900
## OverallQual:YearBuilt:TotalBsmtSF:X1stFlrSF:GarageCars                                                         0.603408
## OverallQual:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GarageCars                                                      0.249775
## YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GarageCars                                                        0.925099
## OverallQual:YearBuilt:YearRemodAdd:GrLivArea:GarageCars                                                        0.209370
## OverallQual:YearBuilt:TotalBsmtSF:GrLivArea:GarageCars                                                         0.924784
## OverallQual:YearRemodAdd:TotalBsmtSF:GrLivArea:GarageCars                                                      0.518461
## YearBuilt:YearRemodAdd:TotalBsmtSF:GrLivArea:GarageCars                                                        0.557151
## OverallQual:YearBuilt:X1stFlrSF:GrLivArea:GarageCars                                                           0.584879
## OverallQual:YearRemodAdd:X1stFlrSF:GrLivArea:GarageCars                                                        0.665927
## YearBuilt:YearRemodAdd:X1stFlrSF:GrLivArea:GarageCars                                                          0.286445
## OverallQual:TotalBsmtSF:X1stFlrSF:GrLivArea:GarageCars                                                         0.383639
## YearBuilt:TotalBsmtSF:X1stFlrSF:GrLivArea:GarageCars                                                           0.089795
## YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:GarageCars                                                        0.093331
## OverallQual:YearBuilt:YearRemodAdd:FullBath:GarageCars                                                         0.435418
## OverallQual:YearBuilt:TotalBsmtSF:FullBath:GarageCars                                                          0.697902
## OverallQual:YearRemodAdd:TotalBsmtSF:FullBath:GarageCars                                                       0.087792
## YearBuilt:YearRemodAdd:TotalBsmtSF:FullBath:GarageCars                                                         0.295559
## OverallQual:YearBuilt:X1stFlrSF:FullBath:GarageCars                                                            0.159798
## OverallQual:YearRemodAdd:X1stFlrSF:FullBath:GarageCars                                                         0.719950
## YearBuilt:YearRemodAdd:X1stFlrSF:FullBath:GarageCars                                                           0.096987
## OverallQual:TotalBsmtSF:X1stFlrSF:FullBath:GarageCars                                                          0.832719
## YearBuilt:TotalBsmtSF:X1stFlrSF:FullBath:GarageCars                                                            0.124771
## YearRemodAdd:TotalBsmtSF:X1stFlrSF:FullBath:GarageCars                                                         0.495778
## OverallQual:YearBuilt:GrLivArea:FullBath:GarageCars                                                            0.552753
## OverallQual:YearRemodAdd:GrLivArea:FullBath:GarageCars                                                         0.315194
## YearBuilt:YearRemodAdd:GrLivArea:FullBath:GarageCars                                                           0.728817
## OverallQual:TotalBsmtSF:GrLivArea:FullBath:GarageCars                                                          0.130146
## YearBuilt:TotalBsmtSF:GrLivArea:FullBath:GarageCars                                                            0.039345
## YearRemodAdd:TotalBsmtSF:GrLivArea:FullBath:GarageCars                                                         0.789083
## OverallQual:X1stFlrSF:GrLivArea:FullBath:GarageCars                                                            0.445812
## YearBuilt:X1stFlrSF:GrLivArea:FullBath:GarageCars                                                              0.047305
## YearRemodAdd:X1stFlrSF:GrLivArea:FullBath:GarageCars                                                           0.086404
## TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:GarageCars                                                            0.165862
## OverallQual:YearBuilt:YearRemodAdd:TotRmsAbvGrd:GarageCars                                                     0.428318
## OverallQual:YearBuilt:TotalBsmtSF:TotRmsAbvGrd:GarageCars                                                      0.097769
## OverallQual:YearRemodAdd:TotalBsmtSF:TotRmsAbvGrd:GarageCars                                                   0.876047
## YearBuilt:YearRemodAdd:TotalBsmtSF:TotRmsAbvGrd:GarageCars                                                     0.899549
## OverallQual:YearBuilt:X1stFlrSF:TotRmsAbvGrd:GarageCars                                                        0.259231
## OverallQual:YearRemodAdd:X1stFlrSF:TotRmsAbvGrd:GarageCars                                                     0.516390
## YearBuilt:YearRemodAdd:X1stFlrSF:TotRmsAbvGrd:GarageCars                                                       0.238776
## OverallQual:TotalBsmtSF:X1stFlrSF:TotRmsAbvGrd:GarageCars                                                      0.246952
## YearBuilt:TotalBsmtSF:X1stFlrSF:TotRmsAbvGrd:GarageCars                                                        0.232505
## YearRemodAdd:TotalBsmtSF:X1stFlrSF:TotRmsAbvGrd:GarageCars                                                     0.061480
## OverallQual:YearBuilt:GrLivArea:TotRmsAbvGrd:GarageCars                                                        0.728405
## OverallQual:YearRemodAdd:GrLivArea:TotRmsAbvGrd:GarageCars                                                     0.862246
## YearBuilt:YearRemodAdd:GrLivArea:TotRmsAbvGrd:GarageCars                                                       0.422896
## OverallQual:TotalBsmtSF:GrLivArea:TotRmsAbvGrd:GarageCars                                                      0.168544
## YearBuilt:TotalBsmtSF:GrLivArea:TotRmsAbvGrd:GarageCars                                                        0.039252
## YearRemodAdd:TotalBsmtSF:GrLivArea:TotRmsAbvGrd:GarageCars                                                     0.369253
## OverallQual:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageCars                                                        0.192423
## YearBuilt:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageCars                                                          0.807724
## YearRemodAdd:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageCars                                                       0.470945
## TotalBsmtSF:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageCars                                                        0.119933
## OverallQual:YearBuilt:FullBath:TotRmsAbvGrd:GarageCars                                                         0.335743
## OverallQual:YearRemodAdd:FullBath:TotRmsAbvGrd:GarageCars                                                      0.692249
## YearBuilt:YearRemodAdd:FullBath:TotRmsAbvGrd:GarageCars                                                        0.362132
## OverallQual:TotalBsmtSF:FullBath:TotRmsAbvGrd:GarageCars                                                       0.747252
## YearBuilt:TotalBsmtSF:FullBath:TotRmsAbvGrd:GarageCars                                                         0.428352
## YearRemodAdd:TotalBsmtSF:FullBath:TotRmsAbvGrd:GarageCars                                                      0.453592
## OverallQual:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageCars                                                         0.430256
## YearBuilt:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageCars                                                           0.643821
## YearRemodAdd:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageCars                                                        0.340100
## TotalBsmtSF:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageCars                                                         0.448125
## OverallQual:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars                                                         0.888246
## YearBuilt:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars                                                           0.626278
## YearRemodAdd:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars                                                        0.431094
## TotalBsmtSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars                                                         0.053613
## X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars                                                           0.884514
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:GarageArea                                                      0.156484
## OverallQual:YearBuilt:YearRemodAdd:X1stFlrSF:GarageArea                                                              NA
## OverallQual:YearBuilt:TotalBsmtSF:X1stFlrSF:GarageArea                                                         0.561277
## OverallQual:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GarageArea                                                      0.621520
## YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GarageArea                                                        0.892493
## OverallQual:YearBuilt:YearRemodAdd:GrLivArea:GarageArea                                                        0.189588
## OverallQual:YearBuilt:TotalBsmtSF:GrLivArea:GarageArea                                                         0.002895
## OverallQual:YearRemodAdd:TotalBsmtSF:GrLivArea:GarageArea                                                      0.015682
## YearBuilt:YearRemodAdd:TotalBsmtSF:GrLivArea:GarageArea                                                        0.056376
## OverallQual:YearBuilt:X1stFlrSF:GrLivArea:GarageArea                                                           0.038899
## OverallQual:YearRemodAdd:X1stFlrSF:GrLivArea:GarageArea                                                        0.788309
## YearBuilt:YearRemodAdd:X1stFlrSF:GrLivArea:GarageArea                                                          0.408431
## OverallQual:TotalBsmtSF:X1stFlrSF:GrLivArea:GarageArea                                                         0.074698
## YearBuilt:TotalBsmtSF:X1stFlrSF:GrLivArea:GarageArea                                                           0.806011
## YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:GarageArea                                                        0.391312
## OverallQual:YearBuilt:YearRemodAdd:FullBath:GarageArea                                                         0.747656
## OverallQual:YearBuilt:TotalBsmtSF:FullBath:GarageArea                                                          0.274259
## OverallQual:YearRemodAdd:TotalBsmtSF:FullBath:GarageArea                                                       0.072994
## YearBuilt:YearRemodAdd:TotalBsmtSF:FullBath:GarageArea                                                         0.808557
## OverallQual:YearBuilt:X1stFlrSF:FullBath:GarageArea                                                            0.002256
## OverallQual:YearRemodAdd:X1stFlrSF:FullBath:GarageArea                                                         0.000873
## YearBuilt:YearRemodAdd:X1stFlrSF:FullBath:GarageArea                                                           0.767835
## OverallQual:TotalBsmtSF:X1stFlrSF:FullBath:GarageArea                                                          0.584301
## YearBuilt:TotalBsmtSF:X1stFlrSF:FullBath:GarageArea                                                            0.793040
## YearRemodAdd:TotalBsmtSF:X1stFlrSF:FullBath:GarageArea                                                         0.892044
## OverallQual:YearBuilt:GrLivArea:FullBath:GarageArea                                                            0.354552
## OverallQual:YearRemodAdd:GrLivArea:FullBath:GarageArea                                                         0.744762
## YearBuilt:YearRemodAdd:GrLivArea:FullBath:GarageArea                                                           0.891379
## OverallQual:TotalBsmtSF:GrLivArea:FullBath:GarageArea                                                          0.851247
## YearBuilt:TotalBsmtSF:GrLivArea:FullBath:GarageArea                                                            0.652865
## YearRemodAdd:TotalBsmtSF:GrLivArea:FullBath:GarageArea                                                         0.036735
## OverallQual:X1stFlrSF:GrLivArea:FullBath:GarageArea                                                            0.278258
## YearBuilt:X1stFlrSF:GrLivArea:FullBath:GarageArea                                                              0.190362
## YearRemodAdd:X1stFlrSF:GrLivArea:FullBath:GarageArea                                                           0.427737
## TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:GarageArea                                                            0.405830
## OverallQual:YearBuilt:YearRemodAdd:TotRmsAbvGrd:GarageArea                                                     0.736609
## OverallQual:YearBuilt:TotalBsmtSF:TotRmsAbvGrd:GarageArea                                                      0.315326
## OverallQual:YearRemodAdd:TotalBsmtSF:TotRmsAbvGrd:GarageArea                                                   0.399731
## YearBuilt:YearRemodAdd:TotalBsmtSF:TotRmsAbvGrd:GarageArea                                                     0.633980
## OverallQual:YearBuilt:X1stFlrSF:TotRmsAbvGrd:GarageArea                                                        0.432661
## OverallQual:YearRemodAdd:X1stFlrSF:TotRmsAbvGrd:GarageArea                                                     0.337677
## YearBuilt:YearRemodAdd:X1stFlrSF:TotRmsAbvGrd:GarageArea                                                             NA
## OverallQual:TotalBsmtSF:X1stFlrSF:TotRmsAbvGrd:GarageArea                                                      0.436954
## YearBuilt:TotalBsmtSF:X1stFlrSF:TotRmsAbvGrd:GarageArea                                                        0.917066
## YearRemodAdd:TotalBsmtSF:X1stFlrSF:TotRmsAbvGrd:GarageArea                                                     0.046850
## OverallQual:YearBuilt:GrLivArea:TotRmsAbvGrd:GarageArea                                                        0.228536
## OverallQual:YearRemodAdd:GrLivArea:TotRmsAbvGrd:GarageArea                                                     0.636427
## YearBuilt:YearRemodAdd:GrLivArea:TotRmsAbvGrd:GarageArea                                                       0.560872
## OverallQual:TotalBsmtSF:GrLivArea:TotRmsAbvGrd:GarageArea                                                      0.047115
## YearBuilt:TotalBsmtSF:GrLivArea:TotRmsAbvGrd:GarageArea                                                        0.472803
## YearRemodAdd:TotalBsmtSF:GrLivArea:TotRmsAbvGrd:GarageArea                                                     0.202916
## OverallQual:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageArea                                                        0.016840
## YearBuilt:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageArea                                                          0.507267
## YearRemodAdd:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageArea                                                       0.378968
## TotalBsmtSF:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageArea                                                        0.032077
## OverallQual:YearBuilt:FullBath:TotRmsAbvGrd:GarageArea                                                         0.474699
## OverallQual:YearRemodAdd:FullBath:TotRmsAbvGrd:GarageArea                                                      0.696324
## YearBuilt:YearRemodAdd:FullBath:TotRmsAbvGrd:GarageArea                                                        0.971394
## OverallQual:TotalBsmtSF:FullBath:TotRmsAbvGrd:GarageArea                                                       0.914401
## YearBuilt:TotalBsmtSF:FullBath:TotRmsAbvGrd:GarageArea                                                         0.290936
## YearRemodAdd:TotalBsmtSF:FullBath:TotRmsAbvGrd:GarageArea                                                      0.189971
## OverallQual:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageArea                                                         0.053222
## YearBuilt:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageArea                                                           0.315478
## YearRemodAdd:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageArea                                                        0.366972
## TotalBsmtSF:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageArea                                                         0.655121
## OverallQual:GrLivArea:FullBath:TotRmsAbvGrd:GarageArea                                                         0.554002
## YearBuilt:GrLivArea:FullBath:TotRmsAbvGrd:GarageArea                                                           0.483392
## YearRemodAdd:GrLivArea:FullBath:TotRmsAbvGrd:GarageArea                                                        0.566414
## TotalBsmtSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageArea                                                         0.002054
## X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageArea                                                           0.162553
## OverallQual:YearBuilt:YearRemodAdd:GarageCars:GarageArea                                                       0.978190
## OverallQual:YearBuilt:TotalBsmtSF:GarageCars:GarageArea                                                        0.924848
## OverallQual:YearRemodAdd:TotalBsmtSF:GarageCars:GarageArea                                                     0.084701
## YearBuilt:YearRemodAdd:TotalBsmtSF:GarageCars:GarageArea                                                       0.915301
## OverallQual:YearBuilt:X1stFlrSF:GarageCars:GarageArea                                                          0.611862
## OverallQual:YearRemodAdd:X1stFlrSF:GarageCars:GarageArea                                                       0.012700
## YearBuilt:YearRemodAdd:X1stFlrSF:GarageCars:GarageArea                                                         0.391656
## OverallQual:TotalBsmtSF:X1stFlrSF:GarageCars:GarageArea                                                        0.672926
## YearBuilt:TotalBsmtSF:X1stFlrSF:GarageCars:GarageArea                                                          0.404389
## YearRemodAdd:TotalBsmtSF:X1stFlrSF:GarageCars:GarageArea                                                       0.723589
## OverallQual:YearBuilt:GrLivArea:GarageCars:GarageArea                                                          0.381015
## OverallQual:YearRemodAdd:GrLivArea:GarageCars:GarageArea                                                       0.521680
## YearBuilt:YearRemodAdd:GrLivArea:GarageCars:GarageArea                                                         0.762949
## OverallQual:TotalBsmtSF:GrLivArea:GarageCars:GarageArea                                                        0.101347
## YearBuilt:TotalBsmtSF:GrLivArea:GarageCars:GarageArea                                                          0.044819
## YearRemodAdd:TotalBsmtSF:GrLivArea:GarageCars:GarageArea                                                       0.113127
## OverallQual:X1stFlrSF:GrLivArea:GarageCars:GarageArea                                                          0.148935
## YearBuilt:X1stFlrSF:GrLivArea:GarageCars:GarageArea                                                            0.033857
## YearRemodAdd:X1stFlrSF:GrLivArea:GarageCars:GarageArea                                                         0.012238
## TotalBsmtSF:X1stFlrSF:GrLivArea:GarageCars:GarageArea                                                          0.455799
## OverallQual:YearBuilt:FullBath:GarageCars:GarageArea                                                           0.357193
## OverallQual:YearRemodAdd:FullBath:GarageCars:GarageArea                                                        0.679143
## YearBuilt:YearRemodAdd:FullBath:GarageCars:GarageArea                                                          0.018454
## OverallQual:TotalBsmtSF:FullBath:GarageCars:GarageArea                                                         0.118553
## YearBuilt:TotalBsmtSF:FullBath:GarageCars:GarageArea                                                           0.310658
## YearRemodAdd:TotalBsmtSF:FullBath:GarageCars:GarageArea                                                        0.142809
## OverallQual:X1stFlrSF:FullBath:GarageCars:GarageArea                                                           0.230534
## YearBuilt:X1stFlrSF:FullBath:GarageCars:GarageArea                                                             0.481583
## YearRemodAdd:X1stFlrSF:FullBath:GarageCars:GarageArea                                                          0.022843
## TotalBsmtSF:X1stFlrSF:FullBath:GarageCars:GarageArea                                                           0.315574
## OverallQual:GrLivArea:FullBath:GarageCars:GarageArea                                                           0.307558
## YearBuilt:GrLivArea:FullBath:GarageCars:GarageArea                                                             0.803634
## YearRemodAdd:GrLivArea:FullBath:GarageCars:GarageArea                                                          0.434839
## TotalBsmtSF:GrLivArea:FullBath:GarageCars:GarageArea                                                           0.973181
## X1stFlrSF:GrLivArea:FullBath:GarageCars:GarageArea                                                             0.282195
## OverallQual:YearBuilt:TotRmsAbvGrd:GarageCars:GarageArea                                                       0.090936
## OverallQual:YearRemodAdd:TotRmsAbvGrd:GarageCars:GarageArea                                                    0.223581
## YearBuilt:YearRemodAdd:TotRmsAbvGrd:GarageCars:GarageArea                                                      0.521660
## OverallQual:TotalBsmtSF:TotRmsAbvGrd:GarageCars:GarageArea                                                     0.575429
## YearBuilt:TotalBsmtSF:TotRmsAbvGrd:GarageCars:GarageArea                                                       0.698525
## YearRemodAdd:TotalBsmtSF:TotRmsAbvGrd:GarageCars:GarageArea                                                    0.724132
## OverallQual:X1stFlrSF:TotRmsAbvGrd:GarageCars:GarageArea                                                       0.675490
## YearBuilt:X1stFlrSF:TotRmsAbvGrd:GarageCars:GarageArea                                                         0.702636
## YearRemodAdd:X1stFlrSF:TotRmsAbvGrd:GarageCars:GarageArea                                                      0.333486
## TotalBsmtSF:X1stFlrSF:TotRmsAbvGrd:GarageCars:GarageArea                                                       0.634282
## OverallQual:GrLivArea:TotRmsAbvGrd:GarageCars:GarageArea                                                       0.130106
## YearBuilt:GrLivArea:TotRmsAbvGrd:GarageCars:GarageArea                                                         0.272876
## YearRemodAdd:GrLivArea:TotRmsAbvGrd:GarageCars:GarageArea                                                      0.642127
## TotalBsmtSF:GrLivArea:TotRmsAbvGrd:GarageCars:GarageArea                                                       0.558532
## X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageCars:GarageArea                                                         0.459836
## OverallQual:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                                        0.797454
## YearBuilt:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                                          0.363772
## YearRemodAdd:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                                       0.989016
## TotalBsmtSF:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                                        0.144001
## X1stFlrSF:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                                          0.279680
## GrLivArea:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                                          0.361747
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea                                                   NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:FullBath                                                    NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:GrLivArea:FullBath                                                    NA
## OverallQual:YearBuilt:YearRemodAdd:X1stFlrSF:GrLivArea:FullBath                                                      NA
## OverallQual:YearBuilt:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath                                                 0.879679
## OverallQual:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath                                              0.920617
## YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath                                                      NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:TotRmsAbvGrd                                                NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:GrLivArea:TotRmsAbvGrd                                                NA
## OverallQual:YearBuilt:YearRemodAdd:X1stFlrSF:GrLivArea:TotRmsAbvGrd                                                  NA
## OverallQual:YearBuilt:TotalBsmtSF:X1stFlrSF:GrLivArea:TotRmsAbvGrd                                             0.109702
## OverallQual:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:TotRmsAbvGrd                                          0.296409
## YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:TotRmsAbvGrd                                                  NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:FullBath:TotRmsAbvGrd                                                 NA
## OverallQual:YearBuilt:YearRemodAdd:X1stFlrSF:FullBath:TotRmsAbvGrd                                                   NA
## OverallQual:YearBuilt:TotalBsmtSF:X1stFlrSF:FullBath:TotRmsAbvGrd                                              0.113773
## OverallQual:YearRemodAdd:TotalBsmtSF:X1stFlrSF:FullBath:TotRmsAbvGrd                                           0.023429
## YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:FullBath:TotRmsAbvGrd                                                   NA
## OverallQual:YearBuilt:YearRemodAdd:GrLivArea:FullBath:TotRmsAbvGrd                                                   NA
## OverallQual:YearBuilt:TotalBsmtSF:GrLivArea:FullBath:TotRmsAbvGrd                                              0.071467
## OverallQual:YearRemodAdd:TotalBsmtSF:GrLivArea:FullBath:TotRmsAbvGrd                                           0.741666
## YearBuilt:YearRemodAdd:TotalBsmtSF:GrLivArea:FullBath:TotRmsAbvGrd                                                   NA
## OverallQual:YearBuilt:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd                                                0.988492
## OverallQual:YearRemodAdd:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd                                             0.065786
## YearBuilt:YearRemodAdd:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd                                                     NA
## OverallQual:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd                                              0.326844
## YearBuilt:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd                                                0.998786
## YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd                                             0.711850
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GarageCars                                                  NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:GrLivArea:GarageCars                                                  NA
## OverallQual:YearBuilt:YearRemodAdd:X1stFlrSF:GrLivArea:GarageCars                                                    NA
## OverallQual:YearBuilt:TotalBsmtSF:X1stFlrSF:GrLivArea:GarageCars                                               0.455957
## OverallQual:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:GarageCars                                            0.925151
## YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:GarageCars                                                    NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:FullBath:GarageCars                                                   NA
## OverallQual:YearBuilt:YearRemodAdd:X1stFlrSF:FullBath:GarageCars                                                     NA
## OverallQual:YearBuilt:TotalBsmtSF:X1stFlrSF:FullBath:GarageCars                                                0.547103
## OverallQual:YearRemodAdd:TotalBsmtSF:X1stFlrSF:FullBath:GarageCars                                             0.688835
## YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:FullBath:GarageCars                                                     NA
## OverallQual:YearBuilt:YearRemodAdd:GrLivArea:FullBath:GarageCars                                                     NA
## OverallQual:YearBuilt:TotalBsmtSF:GrLivArea:FullBath:GarageCars                                                0.162008
## OverallQual:YearRemodAdd:TotalBsmtSF:GrLivArea:FullBath:GarageCars                                             0.898851
## YearBuilt:YearRemodAdd:TotalBsmtSF:GrLivArea:FullBath:GarageCars                                                     NA
## OverallQual:YearBuilt:X1stFlrSF:GrLivArea:FullBath:GarageCars                                                  0.167426
## OverallQual:YearRemodAdd:X1stFlrSF:GrLivArea:FullBath:GarageCars                                               0.669472
## YearBuilt:YearRemodAdd:X1stFlrSF:GrLivArea:FullBath:GarageCars                                                       NA
## OverallQual:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:GarageCars                                                0.685537
## YearBuilt:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:GarageCars                                                  0.493326
## YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:GarageCars                                               0.175435
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:TotRmsAbvGrd:GarageCars                                               NA
## OverallQual:YearBuilt:YearRemodAdd:X1stFlrSF:TotRmsAbvGrd:GarageCars                                                 NA
## OverallQual:YearBuilt:TotalBsmtSF:X1stFlrSF:TotRmsAbvGrd:GarageCars                                            0.778474
## OverallQual:YearRemodAdd:TotalBsmtSF:X1stFlrSF:TotRmsAbvGrd:GarageCars                                         0.325702
## YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:TotRmsAbvGrd:GarageCars                                                 NA
## OverallQual:YearBuilt:YearRemodAdd:GrLivArea:TotRmsAbvGrd:GarageCars                                                 NA
## OverallQual:YearBuilt:TotalBsmtSF:GrLivArea:TotRmsAbvGrd:GarageCars                                            0.018162
## OverallQual:YearRemodAdd:TotalBsmtSF:GrLivArea:TotRmsAbvGrd:GarageCars                                         0.481060
## YearBuilt:YearRemodAdd:TotalBsmtSF:GrLivArea:TotRmsAbvGrd:GarageCars                                                 NA
## OverallQual:YearBuilt:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageCars                                              0.151940
## OverallQual:YearRemodAdd:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageCars                                           0.966679
## YearBuilt:YearRemodAdd:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageCars                                                   NA
## OverallQual:TotalBsmtSF:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageCars                                            0.181895
## YearBuilt:TotalBsmtSF:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageCars                                              0.064432
## YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageCars                                           0.466594
## OverallQual:YearBuilt:YearRemodAdd:FullBath:TotRmsAbvGrd:GarageCars                                                  NA
## OverallQual:YearBuilt:TotalBsmtSF:FullBath:TotRmsAbvGrd:GarageCars                                             0.489007
## OverallQual:YearRemodAdd:TotalBsmtSF:FullBath:TotRmsAbvGrd:GarageCars                                          0.291119
## YearBuilt:YearRemodAdd:TotalBsmtSF:FullBath:TotRmsAbvGrd:GarageCars                                                  NA
## OverallQual:YearBuilt:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageCars                                               0.427129
## OverallQual:YearRemodAdd:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageCars                                                  NA
## YearBuilt:YearRemodAdd:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageCars                                                    NA
## OverallQual:TotalBsmtSF:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageCars                                             0.975947
## YearBuilt:TotalBsmtSF:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageCars                                               0.015707
## YearRemodAdd:TotalBsmtSF:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageCars                                            0.060697
## OverallQual:YearBuilt:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars                                               0.951477
## OverallQual:YearRemodAdd:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars                                            0.905640
## YearBuilt:YearRemodAdd:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars                                                    NA
## OverallQual:TotalBsmtSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars                                             0.392893
## YearBuilt:TotalBsmtSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars                                               0.303093
## YearRemodAdd:TotalBsmtSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars                                            0.610322
## OverallQual:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars                                               0.681029
## YearBuilt:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars                                                 0.660024
## YearRemodAdd:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars                                              0.697818
## TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars                                               0.959211
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GarageArea                                                  NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:GrLivArea:GarageArea                                                  NA
## OverallQual:YearBuilt:YearRemodAdd:X1stFlrSF:GrLivArea:GarageArea                                                    NA
## OverallQual:YearBuilt:TotalBsmtSF:X1stFlrSF:GrLivArea:GarageArea                                               0.051836
## OverallQual:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:GarageArea                                                  NA
## YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:GarageArea                                                    NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:FullBath:GarageArea                                                   NA
## OverallQual:YearBuilt:YearRemodAdd:X1stFlrSF:FullBath:GarageArea                                                     NA
## OverallQual:YearBuilt:TotalBsmtSF:X1stFlrSF:FullBath:GarageArea                                                0.822738
## OverallQual:YearRemodAdd:TotalBsmtSF:X1stFlrSF:FullBath:GarageArea                                             0.287213
## YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:FullBath:GarageArea                                                     NA
## OverallQual:YearBuilt:YearRemodAdd:GrLivArea:FullBath:GarageArea                                                     NA
## OverallQual:YearBuilt:TotalBsmtSF:GrLivArea:FullBath:GarageArea                                                0.693704
## OverallQual:YearRemodAdd:TotalBsmtSF:GrLivArea:FullBath:GarageArea                                                   NA
## YearBuilt:YearRemodAdd:TotalBsmtSF:GrLivArea:FullBath:GarageArea                                                     NA
## OverallQual:YearBuilt:X1stFlrSF:GrLivArea:FullBath:GarageArea                                                  0.076046
## OverallQual:YearRemodAdd:X1stFlrSF:GrLivArea:FullBath:GarageArea                                               0.586621
## YearBuilt:YearRemodAdd:X1stFlrSF:GrLivArea:FullBath:GarageArea                                                       NA
## OverallQual:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:GarageArea                                                0.283898
## YearBuilt:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:GarageArea                                                  0.452710
## YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:GarageArea                                                     NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:TotRmsAbvGrd:GarageArea                                               NA
## OverallQual:YearBuilt:YearRemodAdd:X1stFlrSF:TotRmsAbvGrd:GarageArea                                                 NA
## OverallQual:YearBuilt:TotalBsmtSF:X1stFlrSF:TotRmsAbvGrd:GarageArea                                            0.529388
## OverallQual:YearRemodAdd:TotalBsmtSF:X1stFlrSF:TotRmsAbvGrd:GarageArea                                               NA
## YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:TotRmsAbvGrd:GarageArea                                                 NA
## OverallQual:YearBuilt:YearRemodAdd:GrLivArea:TotRmsAbvGrd:GarageArea                                                 NA
## OverallQual:YearBuilt:TotalBsmtSF:GrLivArea:TotRmsAbvGrd:GarageArea                                            0.041052
## OverallQual:YearRemodAdd:TotalBsmtSF:GrLivArea:TotRmsAbvGrd:GarageArea                                               NA
## YearBuilt:YearRemodAdd:TotalBsmtSF:GrLivArea:TotRmsAbvGrd:GarageArea                                                 NA
## OverallQual:YearBuilt:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageArea                                              0.046831
## OverallQual:YearRemodAdd:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageArea                                           0.259854
## YearBuilt:YearRemodAdd:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageArea                                                   NA
## OverallQual:TotalBsmtSF:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageArea                                            0.378131
## YearBuilt:TotalBsmtSF:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageArea                                              0.045558
## YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageArea                                                 NA
## OverallQual:YearBuilt:YearRemodAdd:FullBath:TotRmsAbvGrd:GarageArea                                                  NA
## OverallQual:YearBuilt:TotalBsmtSF:FullBath:TotRmsAbvGrd:GarageArea                                             0.634813
## OverallQual:YearRemodAdd:TotalBsmtSF:FullBath:TotRmsAbvGrd:GarageArea                                          0.539108
## YearBuilt:YearRemodAdd:TotalBsmtSF:FullBath:TotRmsAbvGrd:GarageArea                                                  NA
## OverallQual:YearBuilt:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageArea                                                     NA
## OverallQual:YearRemodAdd:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageArea                                                  NA
## YearBuilt:YearRemodAdd:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageArea                                                    NA
## OverallQual:TotalBsmtSF:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageArea                                             0.310540
## YearBuilt:TotalBsmtSF:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageArea                                               0.070221
## YearRemodAdd:TotalBsmtSF:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageArea                                            0.024487
## OverallQual:YearBuilt:GrLivArea:FullBath:TotRmsAbvGrd:GarageArea                                               0.600310
## OverallQual:YearRemodAdd:GrLivArea:FullBath:TotRmsAbvGrd:GarageArea                                            0.929914
## YearBuilt:YearRemodAdd:GrLivArea:FullBath:TotRmsAbvGrd:GarageArea                                                    NA
## OverallQual:TotalBsmtSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageArea                                             0.165215
## YearBuilt:TotalBsmtSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageArea                                               0.130978
## YearRemodAdd:TotalBsmtSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageArea                                            0.099190
## OverallQual:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageArea                                               0.103696
## YearBuilt:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageArea                                                 0.201646
## YearRemodAdd:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageArea                                                    NA
## TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageArea                                               0.960158
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:GarageCars:GarageArea                                                 NA
## OverallQual:YearBuilt:YearRemodAdd:X1stFlrSF:GarageCars:GarageArea                                                   NA
## OverallQual:YearBuilt:TotalBsmtSF:X1stFlrSF:GarageCars:GarageArea                                              0.988297
## OverallQual:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GarageCars:GarageArea                                           0.671824
## YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GarageCars:GarageArea                                                   NA
## OverallQual:YearBuilt:YearRemodAdd:GrLivArea:GarageCars:GarageArea                                                   NA
## OverallQual:YearBuilt:TotalBsmtSF:GrLivArea:GarageCars:GarageArea                                              0.002766
## OverallQual:YearRemodAdd:TotalBsmtSF:GrLivArea:GarageCars:GarageArea                                           0.449346
## YearBuilt:YearRemodAdd:TotalBsmtSF:GrLivArea:GarageCars:GarageArea                                                   NA
## OverallQual:YearBuilt:X1stFlrSF:GrLivArea:GarageCars:GarageArea                                                0.017672
## OverallQual:YearRemodAdd:X1stFlrSF:GrLivArea:GarageCars:GarageArea                                             0.517619
## YearBuilt:YearRemodAdd:X1stFlrSF:GrLivArea:GarageCars:GarageArea                                                     NA
## OverallQual:TotalBsmtSF:X1stFlrSF:GrLivArea:GarageCars:GarageArea                                              0.440935
## YearBuilt:TotalBsmtSF:X1stFlrSF:GrLivArea:GarageCars:GarageArea                                                0.872560
## YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:GarageCars:GarageArea                                             0.243115
## OverallQual:YearBuilt:YearRemodAdd:FullBath:GarageCars:GarageArea                                                    NA
## OverallQual:YearBuilt:TotalBsmtSF:FullBath:GarageCars:GarageArea                                               0.128671
## OverallQual:YearRemodAdd:TotalBsmtSF:FullBath:GarageCars:GarageArea                                            0.001017
## YearBuilt:YearRemodAdd:TotalBsmtSF:FullBath:GarageCars:GarageArea                                                    NA
## OverallQual:YearBuilt:X1stFlrSF:FullBath:GarageCars:GarageArea                                                 0.017484
## OverallQual:YearRemodAdd:X1stFlrSF:FullBath:GarageCars:GarageArea                                              0.000863
## YearBuilt:YearRemodAdd:X1stFlrSF:FullBath:GarageCars:GarageArea                                                      NA
## OverallQual:TotalBsmtSF:X1stFlrSF:FullBath:GarageCars:GarageArea                                               0.857377
## YearBuilt:TotalBsmtSF:X1stFlrSF:FullBath:GarageCars:GarageArea                                                 0.156989
## YearRemodAdd:TotalBsmtSF:X1stFlrSF:FullBath:GarageCars:GarageArea                                              0.446883
## OverallQual:YearBuilt:GrLivArea:FullBath:GarageCars:GarageArea                                                 0.981373
## OverallQual:YearRemodAdd:GrLivArea:FullBath:GarageCars:GarageArea                                              0.207347
## YearBuilt:YearRemodAdd:GrLivArea:FullBath:GarageCars:GarageArea                                                      NA
## OverallQual:TotalBsmtSF:GrLivArea:FullBath:GarageCars:GarageArea                                               0.645531
## YearBuilt:TotalBsmtSF:GrLivArea:FullBath:GarageCars:GarageArea                                                 0.063496
## YearRemodAdd:TotalBsmtSF:GrLivArea:FullBath:GarageCars:GarageArea                                              0.200894
## OverallQual:X1stFlrSF:GrLivArea:FullBath:GarageCars:GarageArea                                                 0.052806
## YearBuilt:X1stFlrSF:GrLivArea:FullBath:GarageCars:GarageArea                                                   0.375718
## YearRemodAdd:X1stFlrSF:GrLivArea:FullBath:GarageCars:GarageArea                                                0.102858
## TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:GarageCars:GarageArea                                                 0.324573
## OverallQual:YearBuilt:YearRemodAdd:TotRmsAbvGrd:GarageCars:GarageArea                                                NA
## OverallQual:YearBuilt:TotalBsmtSF:TotRmsAbvGrd:GarageCars:GarageArea                                           0.964862
## OverallQual:YearRemodAdd:TotalBsmtSF:TotRmsAbvGrd:GarageCars:GarageArea                                        0.617466
## YearBuilt:YearRemodAdd:TotalBsmtSF:TotRmsAbvGrd:GarageCars:GarageArea                                                NA
## OverallQual:YearBuilt:X1stFlrSF:TotRmsAbvGrd:GarageCars:GarageArea                                             0.792454
## OverallQual:YearRemodAdd:X1stFlrSF:TotRmsAbvGrd:GarageCars:GarageArea                                                NA
## YearBuilt:YearRemodAdd:X1stFlrSF:TotRmsAbvGrd:GarageCars:GarageArea                                                  NA
## OverallQual:TotalBsmtSF:X1stFlrSF:TotRmsAbvGrd:GarageCars:GarageArea                                           0.868367
## YearBuilt:TotalBsmtSF:X1stFlrSF:TotRmsAbvGrd:GarageCars:GarageArea                                             0.634680
## YearRemodAdd:TotalBsmtSF:X1stFlrSF:TotRmsAbvGrd:GarageCars:GarageArea                                          0.859242
## OverallQual:YearBuilt:GrLivArea:TotRmsAbvGrd:GarageCars:GarageArea                                             0.124220
## OverallQual:YearRemodAdd:GrLivArea:TotRmsAbvGrd:GarageCars:GarageArea                                          0.986305
## YearBuilt:YearRemodAdd:GrLivArea:TotRmsAbvGrd:GarageCars:GarageArea                                                  NA
## OverallQual:TotalBsmtSF:GrLivArea:TotRmsAbvGrd:GarageCars:GarageArea                                           0.430992
## YearBuilt:TotalBsmtSF:GrLivArea:TotRmsAbvGrd:GarageCars:GarageArea                                             0.384561
## YearRemodAdd:TotalBsmtSF:GrLivArea:TotRmsAbvGrd:GarageCars:GarageArea                                          0.867264
## OverallQual:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageCars:GarageArea                                             0.170050
## YearBuilt:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageCars:GarageArea                                               0.545431
## YearRemodAdd:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageCars:GarageArea                                            0.823667
## TotalBsmtSF:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageCars:GarageArea                                             0.857863
## OverallQual:YearBuilt:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                              0.258555
## OverallQual:YearRemodAdd:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                           0.342759
## YearBuilt:YearRemodAdd:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                                   NA
## OverallQual:TotalBsmtSF:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                            0.266122
## YearBuilt:TotalBsmtSF:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                              0.525119
## YearRemodAdd:TotalBsmtSF:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                           0.113096
## OverallQual:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                              0.058938
## YearBuilt:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                                      NA
## YearRemodAdd:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                                   NA
## TotalBsmtSF:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                              0.844799
## OverallQual:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                              0.502396
## YearBuilt:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                                0.362743
## YearRemodAdd:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                             0.818483
## TotalBsmtSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                              0.066319
## X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                                0.682125
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath                                          NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:TotRmsAbvGrd                                      NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:FullBath:TotRmsAbvGrd                                       NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:GrLivArea:FullBath:TotRmsAbvGrd                                       NA
## OverallQual:YearBuilt:YearRemodAdd:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd                                         NA
## OverallQual:YearBuilt:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd                                          NA
## OverallQual:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd                                       NA
## YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd                                         NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:GarageCars                                        NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:FullBath:GarageCars                                         NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:GrLivArea:FullBath:GarageCars                                         NA
## OverallQual:YearBuilt:YearRemodAdd:X1stFlrSF:GrLivArea:FullBath:GarageCars                                           NA
## OverallQual:YearBuilt:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:GarageCars                                            NA
## OverallQual:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:GarageCars                                         NA
## YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:GarageCars                                           NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:TotRmsAbvGrd:GarageCars                                     NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:GrLivArea:TotRmsAbvGrd:GarageCars                                     NA
## OverallQual:YearBuilt:YearRemodAdd:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageCars                                       NA
## OverallQual:YearBuilt:TotalBsmtSF:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageCars                                  0.179214
## OverallQual:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageCars                                     NA
## YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageCars                                       NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:FullBath:TotRmsAbvGrd:GarageCars                                      NA
## OverallQual:YearBuilt:YearRemodAdd:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageCars                                        NA
## OverallQual:YearBuilt:TotalBsmtSF:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageCars                                         NA
## OverallQual:YearRemodAdd:TotalBsmtSF:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageCars                                      NA
## YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageCars                                        NA
## OverallQual:YearBuilt:YearRemodAdd:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars                                        NA
## OverallQual:YearBuilt:TotalBsmtSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars                                         NA
## OverallQual:YearRemodAdd:TotalBsmtSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars                                      NA
## YearBuilt:YearRemodAdd:TotalBsmtSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars                                        NA
## OverallQual:YearBuilt:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars                                           NA
## OverallQual:YearRemodAdd:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars                                        NA
## YearBuilt:YearRemodAdd:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars                                          NA
## OverallQual:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars                                   0.426119
## YearBuilt:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars                                           NA
## YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars                                        NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:GarageArea                                        NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:FullBath:GarageArea                                         NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:GrLivArea:FullBath:GarageArea                                         NA
## OverallQual:YearBuilt:YearRemodAdd:X1stFlrSF:GrLivArea:FullBath:GarageArea                                           NA
## OverallQual:YearBuilt:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:GarageArea                                            NA
## OverallQual:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:GarageArea                                         NA
## YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:GarageArea                                           NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:TotRmsAbvGrd:GarageArea                                     NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:GrLivArea:TotRmsAbvGrd:GarageArea                                     NA
## OverallQual:YearBuilt:YearRemodAdd:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageArea                                       NA
## OverallQual:YearBuilt:TotalBsmtSF:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageArea                                        NA
## OverallQual:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageArea                                     NA
## YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageArea                                       NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:FullBath:TotRmsAbvGrd:GarageArea                                      NA
## OverallQual:YearBuilt:YearRemodAdd:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageArea                                        NA
## OverallQual:YearBuilt:TotalBsmtSF:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageArea                                         NA
## OverallQual:YearRemodAdd:TotalBsmtSF:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageArea                                      NA
## YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageArea                                        NA
## OverallQual:YearBuilt:YearRemodAdd:GrLivArea:FullBath:TotRmsAbvGrd:GarageArea                                        NA
## OverallQual:YearBuilt:TotalBsmtSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageArea                                         NA
## OverallQual:YearRemodAdd:TotalBsmtSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageArea                                      NA
## YearBuilt:YearRemodAdd:TotalBsmtSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageArea                                        NA
## OverallQual:YearBuilt:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageArea                                           NA
## OverallQual:YearRemodAdd:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageArea                                        NA
## YearBuilt:YearRemodAdd:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageArea                                          NA
## OverallQual:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageArea                                   0.463239
## YearBuilt:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageArea                                           NA
## YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageArea                                        NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GarageCars:GarageArea                                       NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:GrLivArea:GarageCars:GarageArea                                       NA
## OverallQual:YearBuilt:YearRemodAdd:X1stFlrSF:GrLivArea:GarageCars:GarageArea                                         NA
## OverallQual:YearBuilt:TotalBsmtSF:X1stFlrSF:GrLivArea:GarageCars:GarageArea                                          NA
## OverallQual:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:GarageCars:GarageArea                                       NA
## YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:GarageCars:GarageArea                                         NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:FullBath:GarageCars:GarageArea                                        NA
## OverallQual:YearBuilt:YearRemodAdd:X1stFlrSF:FullBath:GarageCars:GarageArea                                          NA
## OverallQual:YearBuilt:TotalBsmtSF:X1stFlrSF:FullBath:GarageCars:GarageArea                                     0.912948
## OverallQual:YearRemodAdd:TotalBsmtSF:X1stFlrSF:FullBath:GarageCars:GarageArea                                        NA
## YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:FullBath:GarageCars:GarageArea                                          NA
## OverallQual:YearBuilt:YearRemodAdd:GrLivArea:FullBath:GarageCars:GarageArea                                          NA
## OverallQual:YearBuilt:TotalBsmtSF:GrLivArea:FullBath:GarageCars:GarageArea                                           NA
## OverallQual:YearRemodAdd:TotalBsmtSF:GrLivArea:FullBath:GarageCars:GarageArea                                        NA
## YearBuilt:YearRemodAdd:TotalBsmtSF:GrLivArea:FullBath:GarageCars:GarageArea                                          NA
## OverallQual:YearBuilt:X1stFlrSF:GrLivArea:FullBath:GarageCars:GarageArea                                             NA
## OverallQual:YearRemodAdd:X1stFlrSF:GrLivArea:FullBath:GarageCars:GarageArea                                          NA
## YearBuilt:YearRemodAdd:X1stFlrSF:GrLivArea:FullBath:GarageCars:GarageArea                                            NA
## OverallQual:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:GarageCars:GarageArea                                     0.464081
## YearBuilt:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:GarageCars:GarageArea                                             NA
## YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:GarageCars:GarageArea                                          NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:TotRmsAbvGrd:GarageCars:GarageArea                                    NA
## OverallQual:YearBuilt:YearRemodAdd:X1stFlrSF:TotRmsAbvGrd:GarageCars:GarageArea                                      NA
## OverallQual:YearBuilt:TotalBsmtSF:X1stFlrSF:TotRmsAbvGrd:GarageCars:GarageArea                                       NA
## OverallQual:YearRemodAdd:TotalBsmtSF:X1stFlrSF:TotRmsAbvGrd:GarageCars:GarageArea                              0.810219
## YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:TotRmsAbvGrd:GarageCars:GarageArea                                      NA
## OverallQual:YearBuilt:YearRemodAdd:GrLivArea:TotRmsAbvGrd:GarageCars:GarageArea                                      NA
## OverallQual:YearBuilt:TotalBsmtSF:GrLivArea:TotRmsAbvGrd:GarageCars:GarageArea                                       NA
## OverallQual:YearRemodAdd:TotalBsmtSF:GrLivArea:TotRmsAbvGrd:GarageCars:GarageArea                                    NA
## YearBuilt:YearRemodAdd:TotalBsmtSF:GrLivArea:TotRmsAbvGrd:GarageCars:GarageArea                                      NA
## OverallQual:YearBuilt:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageCars:GarageArea                                         NA
## OverallQual:YearRemodAdd:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageCars:GarageArea                                      NA
## YearBuilt:YearRemodAdd:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageCars:GarageArea                                        NA
## OverallQual:TotalBsmtSF:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageCars:GarageArea                                 0.548782
## YearBuilt:TotalBsmtSF:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageCars:GarageArea                                         NA
## YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageCars:GarageArea                                      NA
## OverallQual:YearBuilt:YearRemodAdd:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                       NA
## OverallQual:YearBuilt:TotalBsmtSF:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                        NA
## OverallQual:YearRemodAdd:TotalBsmtSF:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                     NA
## YearBuilt:YearRemodAdd:TotalBsmtSF:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                       NA
## OverallQual:YearBuilt:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                          NA
## OverallQual:YearRemodAdd:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                       NA
## YearBuilt:YearRemodAdd:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                   0.210788
## OverallQual:TotalBsmtSF:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                  0.809568
## YearBuilt:TotalBsmtSF:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                          NA
## YearRemodAdd:TotalBsmtSF:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                       NA
## OverallQual:YearBuilt:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                    0.458341
## OverallQual:YearRemodAdd:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                       NA
## YearBuilt:YearRemodAdd:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                         NA
## OverallQual:TotalBsmtSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                  0.034262
## YearBuilt:TotalBsmtSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                          NA
## YearRemodAdd:TotalBsmtSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                       NA
## OverallQual:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                    0.110331
## YearBuilt:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                            NA
## YearRemodAdd:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                         NA
## TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                    0.815931
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd                             NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:GarageCars                               NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageCars                           NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageCars                            NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars                            NA
## OverallQual:YearBuilt:YearRemodAdd:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars                              NA
## OverallQual:YearBuilt:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars                               NA
## OverallQual:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars                            NA
## YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars                              NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:GarageArea                               NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageArea                           NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageArea                            NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageArea                            NA
## OverallQual:YearBuilt:YearRemodAdd:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageArea                              NA
## OverallQual:YearBuilt:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageArea                               NA
## OverallQual:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageArea                            NA
## YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageArea                              NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:GarageCars:GarageArea                             NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:FullBath:GarageCars:GarageArea                              NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:GrLivArea:FullBath:GarageCars:GarageArea                        0.342840
## OverallQual:YearBuilt:YearRemodAdd:X1stFlrSF:GrLivArea:FullBath:GarageCars:GarageArea                                NA
## OverallQual:YearBuilt:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:GarageCars:GarageArea                                 NA
## OverallQual:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:GarageCars:GarageArea                              NA
## YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:GarageCars:GarageArea                          0.318910
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:TotRmsAbvGrd:GarageCars:GarageArea                          NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:GrLivArea:TotRmsAbvGrd:GarageCars:GarageArea                    0.238324
## OverallQual:YearBuilt:YearRemodAdd:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageCars:GarageArea                            NA
## OverallQual:YearBuilt:TotalBsmtSF:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageCars:GarageArea                             NA
## OverallQual:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageCars:GarageArea                          NA
## YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageCars:GarageArea                            NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                           NA
## OverallQual:YearBuilt:YearRemodAdd:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                             NA
## OverallQual:YearBuilt:TotalBsmtSF:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                              NA
## OverallQual:YearRemodAdd:TotalBsmtSF:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                           NA
## YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                             NA
## OverallQual:YearBuilt:YearRemodAdd:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                             NA
## OverallQual:YearBuilt:TotalBsmtSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                              NA
## OverallQual:YearRemodAdd:TotalBsmtSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                           NA
## YearBuilt:YearRemodAdd:TotalBsmtSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                             NA
## OverallQual:YearBuilt:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                NA
## OverallQual:YearRemodAdd:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                       0.213017
## YearBuilt:YearRemodAdd:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                         0.871951
## OverallQual:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                        0.764802
## YearBuilt:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                NA
## YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                             NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars            0.298243
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageArea                  NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:GarageCars:GarageArea              0.527324
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageCars:GarageArea                NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageCars:GarageArea           0.994453
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                 NA
## OverallQual:YearBuilt:YearRemodAdd:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                   NA
## OverallQual:YearBuilt:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                    NA
## OverallQual:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                 NA
## YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                   NA
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars:GarageArea       NA
##                                                                                                                   
## (Intercept)                                                                                                    ** 
## OverallQual                                                                                                       
## YearBuilt                                                                                                      ** 
## YearRemodAdd                                                                                                   *  
## TotalBsmtSF                                                                                                       
## X1stFlrSF                                                                                                         
## GrLivArea                                                                                                         
## FullBath                                                                                                          
## TotRmsAbvGrd                                                                                                   *  
## GarageCars                                                                                                     .  
## GarageArea                                                                                                        
## OverallQual:YearBuilt                                                                                          .  
## OverallQual:YearRemodAdd                                                                                          
## YearBuilt:YearRemodAdd                                                                                         ** 
## OverallQual:TotalBsmtSF                                                                                           
## YearBuilt:TotalBsmtSF                                                                                             
## YearRemodAdd:TotalBsmtSF                                                                                          
## OverallQual:X1stFlrSF                                                                                             
## YearBuilt:X1stFlrSF                                                                                               
## YearRemodAdd:X1stFlrSF                                                                                            
## TotalBsmtSF:X1stFlrSF                                                                                             
## OverallQual:GrLivArea                                                                                          .  
## YearBuilt:GrLivArea                                                                                               
## YearRemodAdd:GrLivArea                                                                                            
## TotalBsmtSF:GrLivArea                                                                                             
## X1stFlrSF:GrLivArea                                                                                            .  
## OverallQual:FullBath                                                                                              
## YearBuilt:FullBath                                                                                             .  
## YearRemodAdd:FullBath                                                                                             
## TotalBsmtSF:FullBath                                                                                              
## X1stFlrSF:FullBath                                                                                             *  
## GrLivArea:FullBath                                                                                                
## OverallQual:TotRmsAbvGrd                                                                                          
## YearBuilt:TotRmsAbvGrd                                                                                         *  
## YearRemodAdd:TotRmsAbvGrd                                                                                      *  
## TotalBsmtSF:TotRmsAbvGrd                                                                                          
## X1stFlrSF:TotRmsAbvGrd                                                                                            
## GrLivArea:TotRmsAbvGrd                                                                                            
## FullBath:TotRmsAbvGrd                                                                                             
## OverallQual:GarageCars                                                                                            
## YearBuilt:GarageCars                                                                                           *  
## YearRemodAdd:GarageCars                                                                                           
## TotalBsmtSF:GarageCars                                                                                            
## X1stFlrSF:GarageCars                                                                                           *  
## GrLivArea:GarageCars                                                                                           *  
## FullBath:GarageCars                                                                                               
## TotRmsAbvGrd:GarageCars                                                                                        *  
## OverallQual:GarageArea                                                                                            
## YearBuilt:GarageArea                                                                                              
## YearRemodAdd:GarageArea                                                                                        .  
## TotalBsmtSF:GarageArea                                                                                            
## X1stFlrSF:GarageArea                                                                                              
## GrLivArea:GarageArea                                                                                           .  
## FullBath:GarageArea                                                                                               
## TotRmsAbvGrd:GarageArea                                                                                           
## GarageCars:GarageArea                                                                                             
## OverallQual:YearBuilt:YearRemodAdd                                                                                
## OverallQual:YearBuilt:TotalBsmtSF                                                                                 
## OverallQual:YearRemodAdd:TotalBsmtSF                                                                              
## YearBuilt:YearRemodAdd:TotalBsmtSF                                                                                
## OverallQual:YearBuilt:X1stFlrSF                                                                                   
## OverallQual:YearRemodAdd:X1stFlrSF                                                                                
## YearBuilt:YearRemodAdd:X1stFlrSF                                                                                  
## OverallQual:TotalBsmtSF:X1stFlrSF                                                                              *  
## YearBuilt:TotalBsmtSF:X1stFlrSF                                                                                   
## YearRemodAdd:TotalBsmtSF:X1stFlrSF                                                                                
## OverallQual:YearBuilt:GrLivArea                                                                                .  
## OverallQual:YearRemodAdd:GrLivArea                                                                                
## YearBuilt:YearRemodAdd:GrLivArea                                                                                  
## OverallQual:TotalBsmtSF:GrLivArea                                                                                 
## YearBuilt:TotalBsmtSF:GrLivArea                                                                                   
## YearRemodAdd:TotalBsmtSF:GrLivArea                                                                             .  
## OverallQual:X1stFlrSF:GrLivArea                                                                                   
## YearBuilt:X1stFlrSF:GrLivArea                                                                                     
## YearRemodAdd:X1stFlrSF:GrLivArea                                                                               *  
## TotalBsmtSF:X1stFlrSF:GrLivArea                                                                                   
## OverallQual:YearBuilt:FullBath                                                                                    
## OverallQual:YearRemodAdd:FullBath                                                                                 
## YearBuilt:YearRemodAdd:FullBath                                                                                .  
## OverallQual:TotalBsmtSF:FullBath                                                                                  
## YearBuilt:TotalBsmtSF:FullBath                                                                                    
## YearRemodAdd:TotalBsmtSF:FullBath                                                                                 
## OverallQual:X1stFlrSF:FullBath                                                                                    
## YearBuilt:X1stFlrSF:FullBath                                                                                   *  
## YearRemodAdd:X1stFlrSF:FullBath                                                                                .  
## TotalBsmtSF:X1stFlrSF:FullBath                                                                                    
## OverallQual:GrLivArea:FullBath                                                                                    
## YearBuilt:GrLivArea:FullBath                                                                                      
## YearRemodAdd:GrLivArea:FullBath                                                                                   
## TotalBsmtSF:GrLivArea:FullBath                                                                                    
## X1stFlrSF:GrLivArea:FullBath                                                                                      
## OverallQual:YearBuilt:TotRmsAbvGrd                                                                                
## OverallQual:YearRemodAdd:TotRmsAbvGrd                                                                             
## YearBuilt:YearRemodAdd:TotRmsAbvGrd                                                                            *  
## OverallQual:TotalBsmtSF:TotRmsAbvGrd                                                                              
## YearBuilt:TotalBsmtSF:TotRmsAbvGrd                                                                                
## YearRemodAdd:TotalBsmtSF:TotRmsAbvGrd                                                                             
## OverallQual:X1stFlrSF:TotRmsAbvGrd                                                                                
## YearBuilt:X1stFlrSF:TotRmsAbvGrd                                                                                  
## YearRemodAdd:X1stFlrSF:TotRmsAbvGrd                                                                               
## TotalBsmtSF:X1stFlrSF:TotRmsAbvGrd                                                                                
## OverallQual:GrLivArea:TotRmsAbvGrd                                                                                
## YearBuilt:GrLivArea:TotRmsAbvGrd                                                                                  
## YearRemodAdd:GrLivArea:TotRmsAbvGrd                                                                            .  
## TotalBsmtSF:GrLivArea:TotRmsAbvGrd                                                                                
## X1stFlrSF:GrLivArea:TotRmsAbvGrd                                                                                  
## OverallQual:FullBath:TotRmsAbvGrd                                                                                 
## YearBuilt:FullBath:TotRmsAbvGrd                                                                                   
## YearRemodAdd:FullBath:TotRmsAbvGrd                                                                                
## TotalBsmtSF:FullBath:TotRmsAbvGrd                                                                                 
## X1stFlrSF:FullBath:TotRmsAbvGrd                                                                                   
## GrLivArea:FullBath:TotRmsAbvGrd                                                                                   
## OverallQual:YearBuilt:GarageCars                                                                                  
## OverallQual:YearRemodAdd:GarageCars                                                                               
## YearBuilt:YearRemodAdd:GarageCars                                                                              *  
## OverallQual:TotalBsmtSF:GarageCars                                                                                
## YearBuilt:TotalBsmtSF:GarageCars                                                                                  
## YearRemodAdd:TotalBsmtSF:GarageCars                                                                               
## OverallQual:X1stFlrSF:GarageCars                                                                                  
## YearBuilt:X1stFlrSF:GarageCars                                                                                 .  
## YearRemodAdd:X1stFlrSF:GarageCars                                                                              *  
## TotalBsmtSF:X1stFlrSF:GarageCars                                                                                  
## OverallQual:GrLivArea:GarageCars                                                                               .  
## YearBuilt:GrLivArea:GarageCars                                                                                    
## YearRemodAdd:GrLivArea:GarageCars                                                                              *  
## TotalBsmtSF:GrLivArea:GarageCars                                                                                  
## X1stFlrSF:GrLivArea:GarageCars                                                                                    
## OverallQual:FullBath:GarageCars                                                                                   
## YearBuilt:FullBath:GarageCars                                                                                  .  
## YearRemodAdd:FullBath:GarageCars                                                                                  
## TotalBsmtSF:FullBath:GarageCars                                                                                *  
## X1stFlrSF:FullBath:GarageCars                                                                                  *  
## GrLivArea:FullBath:GarageCars                                                                                     
## OverallQual:TotRmsAbvGrd:GarageCars                                                                               
## YearBuilt:TotRmsAbvGrd:GarageCars                                                                              *  
## YearRemodAdd:TotRmsAbvGrd:GarageCars                                                                           ** 
## TotalBsmtSF:TotRmsAbvGrd:GarageCars                                                                               
## X1stFlrSF:TotRmsAbvGrd:GarageCars                                                                                 
## GrLivArea:TotRmsAbvGrd:GarageCars                                                                                 
## FullBath:TotRmsAbvGrd:GarageCars                                                                                  
## OverallQual:YearBuilt:GarageArea                                                                                  
## OverallQual:YearRemodAdd:GarageArea                                                                            .  
## YearBuilt:YearRemodAdd:GarageArea                                                                              *  
## OverallQual:TotalBsmtSF:GarageArea                                                                                
## YearBuilt:TotalBsmtSF:GarageArea                                                                                  
## YearRemodAdd:TotalBsmtSF:GarageArea                                                                               
## OverallQual:X1stFlrSF:GarageArea                                                                               *  
## YearBuilt:X1stFlrSF:GarageArea                                                                                    
## YearRemodAdd:X1stFlrSF:GarageArea                                                                                 
## TotalBsmtSF:X1stFlrSF:GarageArea                                                                                  
## OverallQual:GrLivArea:GarageArea                                                                                  
## YearBuilt:GrLivArea:GarageArea                                                                                    
## YearRemodAdd:GrLivArea:GarageArea                                                                              *  
## TotalBsmtSF:GrLivArea:GarageArea                                                                               *  
## X1stFlrSF:GrLivArea:GarageArea                                                                                    
## OverallQual:FullBath:GarageArea                                                                                   
## YearBuilt:FullBath:GarageArea                                                                                     
## YearRemodAdd:FullBath:GarageArea                                                                                  
## TotalBsmtSF:FullBath:GarageArea                                                                                   
## X1stFlrSF:FullBath:GarageArea                                                                                     
## GrLivArea:FullBath:GarageArea                                                                                     
## OverallQual:TotRmsAbvGrd:GarageArea                                                                               
## YearBuilt:TotRmsAbvGrd:GarageArea                                                                                 
## YearRemodAdd:TotRmsAbvGrd:GarageArea                                                                              
## TotalBsmtSF:TotRmsAbvGrd:GarageArea                                                                               
## X1stFlrSF:TotRmsAbvGrd:GarageArea                                                                                 
## GrLivArea:TotRmsAbvGrd:GarageArea                                                                                 
## FullBath:TotRmsAbvGrd:GarageArea                                                                                  
## OverallQual:GarageCars:GarageArea                                                                                 
## YearBuilt:GarageCars:GarageArea                                                                                   
## YearRemodAdd:GarageCars:GarageArea                                                                             *  
## TotalBsmtSF:GarageCars:GarageArea                                                                                 
## X1stFlrSF:GarageCars:GarageArea                                                                                   
## GrLivArea:GarageCars:GarageArea                                                                                   
## FullBath:GarageCars:GarageArea                                                                                    
## TotRmsAbvGrd:GarageCars:GarageArea                                                                                
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF                                                                    
## OverallQual:YearBuilt:YearRemodAdd:X1stFlrSF                                                                      
## OverallQual:YearBuilt:TotalBsmtSF:X1stFlrSF                                                                    ** 
## OverallQual:YearRemodAdd:TotalBsmtSF:X1stFlrSF                                                                    
## YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF                                                                      
## OverallQual:YearBuilt:YearRemodAdd:GrLivArea                                                                      
## OverallQual:YearBuilt:TotalBsmtSF:GrLivArea                                                                       
## OverallQual:YearRemodAdd:TotalBsmtSF:GrLivArea                                                                    
## YearBuilt:YearRemodAdd:TotalBsmtSF:GrLivArea                                                                   .  
## OverallQual:YearBuilt:X1stFlrSF:GrLivArea                                                                         
## OverallQual:YearRemodAdd:X1stFlrSF:GrLivArea                                                                      
## YearBuilt:YearRemodAdd:X1stFlrSF:GrLivArea                                                                     *  
## OverallQual:TotalBsmtSF:X1stFlrSF:GrLivArea                                                                    .  
## YearBuilt:TotalBsmtSF:X1stFlrSF:GrLivArea                                                                         
## YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea                                                                   .  
## OverallQual:YearBuilt:YearRemodAdd:FullBath                                                                       
## OverallQual:YearBuilt:TotalBsmtSF:FullBath                                                                        
## OverallQual:YearRemodAdd:TotalBsmtSF:FullBath                                                                     
## YearBuilt:YearRemodAdd:TotalBsmtSF:FullBath                                                                       
## OverallQual:YearBuilt:X1stFlrSF:FullBath                                                                          
## OverallQual:YearRemodAdd:X1stFlrSF:FullBath                                                                       
## YearBuilt:YearRemodAdd:X1stFlrSF:FullBath                                                                      *  
## OverallQual:TotalBsmtSF:X1stFlrSF:FullBath                                                                        
## YearBuilt:TotalBsmtSF:X1stFlrSF:FullBath                                                                          
## YearRemodAdd:TotalBsmtSF:X1stFlrSF:FullBath                                                                       
## OverallQual:YearBuilt:GrLivArea:FullBath                                                                          
## OverallQual:YearRemodAdd:GrLivArea:FullBath                                                                       
## YearBuilt:YearRemodAdd:GrLivArea:FullBath                                                                         
## OverallQual:TotalBsmtSF:GrLivArea:FullBath                                                                        
## YearBuilt:TotalBsmtSF:GrLivArea:FullBath                                                                          
## YearRemodAdd:TotalBsmtSF:GrLivArea:FullBath                                                                       
## OverallQual:X1stFlrSF:GrLivArea:FullBath                                                                          
## YearBuilt:X1stFlrSF:GrLivArea:FullBath                                                                            
## YearRemodAdd:X1stFlrSF:GrLivArea:FullBath                                                                         
## TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath                                                                          
## OverallQual:YearBuilt:YearRemodAdd:TotRmsAbvGrd                                                                   
## OverallQual:YearBuilt:TotalBsmtSF:TotRmsAbvGrd                                                                    
## OverallQual:YearRemodAdd:TotalBsmtSF:TotRmsAbvGrd                                                                 
## YearBuilt:YearRemodAdd:TotalBsmtSF:TotRmsAbvGrd                                                                   
## OverallQual:YearBuilt:X1stFlrSF:TotRmsAbvGrd                                                                      
## OverallQual:YearRemodAdd:X1stFlrSF:TotRmsAbvGrd                                                                   
## YearBuilt:YearRemodAdd:X1stFlrSF:TotRmsAbvGrd                                                                     
## OverallQual:TotalBsmtSF:X1stFlrSF:TotRmsAbvGrd                                                                    
## YearBuilt:TotalBsmtSF:X1stFlrSF:TotRmsAbvGrd                                                                      
## YearRemodAdd:TotalBsmtSF:X1stFlrSF:TotRmsAbvGrd                                                                   
## OverallQual:YearBuilt:GrLivArea:TotRmsAbvGrd                                                                      
## OverallQual:YearRemodAdd:GrLivArea:TotRmsAbvGrd                                                                   
## YearBuilt:YearRemodAdd:GrLivArea:TotRmsAbvGrd                                                                  *  
## OverallQual:TotalBsmtSF:GrLivArea:TotRmsAbvGrd                                                                    
## YearBuilt:TotalBsmtSF:GrLivArea:TotRmsAbvGrd                                                                      
## YearRemodAdd:TotalBsmtSF:GrLivArea:TotRmsAbvGrd                                                                   
## OverallQual:X1stFlrSF:GrLivArea:TotRmsAbvGrd                                                                      
## YearBuilt:X1stFlrSF:GrLivArea:TotRmsAbvGrd                                                                        
## YearRemodAdd:X1stFlrSF:GrLivArea:TotRmsAbvGrd                                                                     
## TotalBsmtSF:X1stFlrSF:GrLivArea:TotRmsAbvGrd                                                                      
## OverallQual:YearBuilt:FullBath:TotRmsAbvGrd                                                                       
## OverallQual:YearRemodAdd:FullBath:TotRmsAbvGrd                                                                    
## YearBuilt:YearRemodAdd:FullBath:TotRmsAbvGrd                                                                      
## OverallQual:TotalBsmtSF:FullBath:TotRmsAbvGrd                                                                     
## YearBuilt:TotalBsmtSF:FullBath:TotRmsAbvGrd                                                                       
## YearRemodAdd:TotalBsmtSF:FullBath:TotRmsAbvGrd                                                                    
## OverallQual:X1stFlrSF:FullBath:TotRmsAbvGrd                                                                       
## YearBuilt:X1stFlrSF:FullBath:TotRmsAbvGrd                                                                         
## YearRemodAdd:X1stFlrSF:FullBath:TotRmsAbvGrd                                                                      
## TotalBsmtSF:X1stFlrSF:FullBath:TotRmsAbvGrd                                                                       
## OverallQual:GrLivArea:FullBath:TotRmsAbvGrd                                                                       
## YearBuilt:GrLivArea:FullBath:TotRmsAbvGrd                                                                         
## YearRemodAdd:GrLivArea:FullBath:TotRmsAbvGrd                                                                      
## TotalBsmtSF:GrLivArea:FullBath:TotRmsAbvGrd                                                                       
## X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd                                                                         
## OverallQual:YearBuilt:YearRemodAdd:GarageCars                                                                     
## OverallQual:YearBuilt:TotalBsmtSF:GarageCars                                                                      
## OverallQual:YearRemodAdd:TotalBsmtSF:GarageCars                                                                   
## YearBuilt:YearRemodAdd:TotalBsmtSF:GarageCars                                                                     
## OverallQual:YearBuilt:X1stFlrSF:GarageCars                                                                        
## OverallQual:YearRemodAdd:X1stFlrSF:GarageCars                                                                     
## YearBuilt:YearRemodAdd:X1stFlrSF:GarageCars                                                                    .  
## OverallQual:TotalBsmtSF:X1stFlrSF:GarageCars                                                                      
## YearBuilt:TotalBsmtSF:X1stFlrSF:GarageCars                                                                        
## YearRemodAdd:TotalBsmtSF:X1stFlrSF:GarageCars                                                                     
## OverallQual:YearBuilt:GrLivArea:GarageCars                                                                        
## OverallQual:YearRemodAdd:GrLivArea:GarageCars                                                                  .  
## YearBuilt:YearRemodAdd:GrLivArea:GarageCars                                                                       
## OverallQual:TotalBsmtSF:GrLivArea:GarageCars                                                                      
## YearBuilt:TotalBsmtSF:GrLivArea:GarageCars                                                                        
## YearRemodAdd:TotalBsmtSF:GrLivArea:GarageCars                                                                     
## OverallQual:X1stFlrSF:GrLivArea:GarageCars                                                                        
## YearBuilt:X1stFlrSF:GrLivArea:GarageCars                                                                          
## YearRemodAdd:X1stFlrSF:GrLivArea:GarageCars                                                                    .  
## TotalBsmtSF:X1stFlrSF:GrLivArea:GarageCars                                                                        
## OverallQual:YearBuilt:FullBath:GarageCars                                                                      .  
## OverallQual:YearRemodAdd:FullBath:GarageCars                                                                      
## YearBuilt:YearRemodAdd:FullBath:GarageCars                                                                        
## OverallQual:TotalBsmtSF:FullBath:GarageCars                                                                    .  
## YearBuilt:TotalBsmtSF:FullBath:GarageCars                                                                      .  
## YearRemodAdd:TotalBsmtSF:FullBath:GarageCars                                                                      
## OverallQual:X1stFlrSF:FullBath:GarageCars                                                                         
## YearBuilt:X1stFlrSF:FullBath:GarageCars                                                                        *  
## YearRemodAdd:X1stFlrSF:FullBath:GarageCars                                                                        
## TotalBsmtSF:X1stFlrSF:FullBath:GarageCars                                                                         
## OverallQual:GrLivArea:FullBath:GarageCars                                                                         
## YearBuilt:GrLivArea:FullBath:GarageCars                                                                           
## YearRemodAdd:GrLivArea:FullBath:GarageCars                                                                        
## TotalBsmtSF:GrLivArea:FullBath:GarageCars                                                                      *  
## X1stFlrSF:GrLivArea:FullBath:GarageCars                                                                           
## OverallQual:YearBuilt:TotRmsAbvGrd:GarageCars                                                                     
## OverallQual:YearRemodAdd:TotRmsAbvGrd:GarageCars                                                                  
## YearBuilt:YearRemodAdd:TotRmsAbvGrd:GarageCars                                                                 ** 
## OverallQual:TotalBsmtSF:TotRmsAbvGrd:GarageCars                                                                *  
## YearBuilt:TotalBsmtSF:TotRmsAbvGrd:GarageCars                                                                     
## YearRemodAdd:TotalBsmtSF:TotRmsAbvGrd:GarageCars                                                                  
## OverallQual:X1stFlrSF:TotRmsAbvGrd:GarageCars                                                                     
## YearBuilt:X1stFlrSF:TotRmsAbvGrd:GarageCars                                                                       
## YearRemodAdd:X1stFlrSF:TotRmsAbvGrd:GarageCars                                                                    
## TotalBsmtSF:X1stFlrSF:TotRmsAbvGrd:GarageCars                                                                     
## OverallQual:GrLivArea:TotRmsAbvGrd:GarageCars                                                                     
## YearBuilt:GrLivArea:TotRmsAbvGrd:GarageCars                                                                       
## YearRemodAdd:GrLivArea:TotRmsAbvGrd:GarageCars                                                                    
## TotalBsmtSF:GrLivArea:TotRmsAbvGrd:GarageCars                                                                     
## X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageCars                                                                       
## OverallQual:FullBath:TotRmsAbvGrd:GarageCars                                                                      
## YearBuilt:FullBath:TotRmsAbvGrd:GarageCars                                                                        
## YearRemodAdd:FullBath:TotRmsAbvGrd:GarageCars                                                                     
## TotalBsmtSF:FullBath:TotRmsAbvGrd:GarageCars                                                                      
## X1stFlrSF:FullBath:TotRmsAbvGrd:GarageCars                                                                        
## GrLivArea:FullBath:TotRmsAbvGrd:GarageCars                                                                        
## OverallQual:YearBuilt:YearRemodAdd:GarageArea                                                                     
## OverallQual:YearBuilt:TotalBsmtSF:GarageArea                                                                      
## OverallQual:YearRemodAdd:TotalBsmtSF:GarageArea                                                                   
## YearBuilt:YearRemodAdd:TotalBsmtSF:GarageArea                                                                  .  
## OverallQual:YearBuilt:X1stFlrSF:GarageArea                                                                        
## OverallQual:YearRemodAdd:X1stFlrSF:GarageArea                                                                  *  
## YearBuilt:YearRemodAdd:X1stFlrSF:GarageArea                                                                       
## OverallQual:TotalBsmtSF:X1stFlrSF:GarageArea                                                                      
## YearBuilt:TotalBsmtSF:X1stFlrSF:GarageArea                                                                        
## YearRemodAdd:TotalBsmtSF:X1stFlrSF:GarageArea                                                                     
## OverallQual:YearBuilt:GrLivArea:GarageArea                                                                        
## OverallQual:YearRemodAdd:GrLivArea:GarageArea                                                                     
## YearBuilt:YearRemodAdd:GrLivArea:GarageArea                                                                    .  
## OverallQual:TotalBsmtSF:GrLivArea:GarageArea                                                                      
## YearBuilt:TotalBsmtSF:GrLivArea:GarageArea                                                                        
## YearRemodAdd:TotalBsmtSF:GrLivArea:GarageArea                                                                  ** 
## OverallQual:X1stFlrSF:GrLivArea:GarageArea                                                                     .  
## YearBuilt:X1stFlrSF:GrLivArea:GarageArea                                                                          
## YearRemodAdd:X1stFlrSF:GrLivArea:GarageArea                                                                       
## TotalBsmtSF:X1stFlrSF:GrLivArea:GarageArea                                                                        
## OverallQual:YearBuilt:FullBath:GarageArea                                                                         
## OverallQual:YearRemodAdd:FullBath:GarageArea                                                                      
## YearBuilt:YearRemodAdd:FullBath:GarageArea                                                                        
## OverallQual:TotalBsmtSF:FullBath:GarageArea                                                                       
## YearBuilt:TotalBsmtSF:FullBath:GarageArea                                                                         
## YearRemodAdd:TotalBsmtSF:FullBath:GarageArea                                                                      
## OverallQual:X1stFlrSF:FullBath:GarageArea                                                                         
## YearBuilt:X1stFlrSF:FullBath:GarageArea                                                                           
## YearRemodAdd:X1stFlrSF:FullBath:GarageArea                                                                        
## TotalBsmtSF:X1stFlrSF:FullBath:GarageArea                                                                         
## OverallQual:GrLivArea:FullBath:GarageArea                                                                         
## YearBuilt:GrLivArea:FullBath:GarageArea                                                                           
## YearRemodAdd:GrLivArea:FullBath:GarageArea                                                                        
## TotalBsmtSF:GrLivArea:FullBath:GarageArea                                                                         
## X1stFlrSF:GrLivArea:FullBath:GarageArea                                                                        *  
## OverallQual:YearBuilt:TotRmsAbvGrd:GarageArea                                                                     
## OverallQual:YearRemodAdd:TotRmsAbvGrd:GarageArea                                                                  
## YearBuilt:YearRemodAdd:TotRmsAbvGrd:GarageArea                                                                    
## OverallQual:TotalBsmtSF:TotRmsAbvGrd:GarageArea                                                                   
## YearBuilt:TotalBsmtSF:TotRmsAbvGrd:GarageArea                                                                     
## YearRemodAdd:TotalBsmtSF:TotRmsAbvGrd:GarageArea                                                                  
## OverallQual:X1stFlrSF:TotRmsAbvGrd:GarageArea                                                                     
## YearBuilt:X1stFlrSF:TotRmsAbvGrd:GarageArea                                                                       
## YearRemodAdd:X1stFlrSF:TotRmsAbvGrd:GarageArea                                                                    
## TotalBsmtSF:X1stFlrSF:TotRmsAbvGrd:GarageArea                                                                     
## OverallQual:GrLivArea:TotRmsAbvGrd:GarageArea                                                                     
## YearBuilt:GrLivArea:TotRmsAbvGrd:GarageArea                                                                       
## YearRemodAdd:GrLivArea:TotRmsAbvGrd:GarageArea                                                                    
## TotalBsmtSF:GrLivArea:TotRmsAbvGrd:GarageArea                                                                     
## X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageArea                                                                       
## OverallQual:FullBath:TotRmsAbvGrd:GarageArea                                                                      
## YearBuilt:FullBath:TotRmsAbvGrd:GarageArea                                                                        
## YearRemodAdd:FullBath:TotRmsAbvGrd:GarageArea                                                                     
## TotalBsmtSF:FullBath:TotRmsAbvGrd:GarageArea                                                                      
## X1stFlrSF:FullBath:TotRmsAbvGrd:GarageArea                                                                        
## GrLivArea:FullBath:TotRmsAbvGrd:GarageArea                                                                        
## OverallQual:YearBuilt:GarageCars:GarageArea                                                                       
## OverallQual:YearRemodAdd:GarageCars:GarageArea                                                                    
## YearBuilt:YearRemodAdd:GarageCars:GarageArea                                                                   *  
## OverallQual:TotalBsmtSF:GarageCars:GarageArea                                                                     
## YearBuilt:TotalBsmtSF:GarageCars:GarageArea                                                                       
## YearRemodAdd:TotalBsmtSF:GarageCars:GarageArea                                                                    
## OverallQual:X1stFlrSF:GarageCars:GarageArea                                                                       
## YearBuilt:X1stFlrSF:GarageCars:GarageArea                                                                         
## YearRemodAdd:X1stFlrSF:GarageCars:GarageArea                                                                      
## TotalBsmtSF:X1stFlrSF:GarageCars:GarageArea                                                                       
## OverallQual:GrLivArea:GarageCars:GarageArea                                                                    .  
## YearBuilt:GrLivArea:GarageCars:GarageArea                                                                         
## YearRemodAdd:GrLivArea:GarageCars:GarageArea                                                                      
## TotalBsmtSF:GrLivArea:GarageCars:GarageArea                                                                       
## X1stFlrSF:GrLivArea:GarageCars:GarageArea                                                                         
## OverallQual:FullBath:GarageCars:GarageArea                                                                        
## YearBuilt:FullBath:GarageCars:GarageArea                                                                          
## YearRemodAdd:FullBath:GarageCars:GarageArea                                                                       
## TotalBsmtSF:FullBath:GarageCars:GarageArea                                                                     *  
## X1stFlrSF:FullBath:GarageCars:GarageArea                                                                          
## GrLivArea:FullBath:GarageCars:GarageArea                                                                          
## OverallQual:TotRmsAbvGrd:GarageCars:GarageArea                                                                    
## YearBuilt:TotRmsAbvGrd:GarageCars:GarageArea                                                                      
## YearRemodAdd:TotRmsAbvGrd:GarageCars:GarageArea                                                                   
## TotalBsmtSF:TotRmsAbvGrd:GarageCars:GarageArea                                                                    
## X1stFlrSF:TotRmsAbvGrd:GarageCars:GarageArea                                                                      
## GrLivArea:TotRmsAbvGrd:GarageCars:GarageArea                                                                      
## FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                                                       
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF                                                       *  
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:GrLivArea                                                          
## OverallQual:YearBuilt:YearRemodAdd:X1stFlrSF:GrLivArea                                                            
## OverallQual:YearBuilt:TotalBsmtSF:X1stFlrSF:GrLivArea                                                          *  
## OverallQual:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea                                                          
## YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea                                                            
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:FullBath                                                           
## OverallQual:YearBuilt:YearRemodAdd:X1stFlrSF:FullBath                                                             
## OverallQual:YearBuilt:TotalBsmtSF:X1stFlrSF:FullBath                                                              
## OverallQual:YearRemodAdd:TotalBsmtSF:X1stFlrSF:FullBath                                                           
## YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:FullBath                                                             
## OverallQual:YearBuilt:YearRemodAdd:GrLivArea:FullBath                                                             
## OverallQual:YearBuilt:TotalBsmtSF:GrLivArea:FullBath                                                           *  
## OverallQual:YearRemodAdd:TotalBsmtSF:GrLivArea:FullBath                                                           
## YearBuilt:YearRemodAdd:TotalBsmtSF:GrLivArea:FullBath                                                             
## OverallQual:YearBuilt:X1stFlrSF:GrLivArea:FullBath                                                                
## OverallQual:YearRemodAdd:X1stFlrSF:GrLivArea:FullBath                                                             
## YearBuilt:YearRemodAdd:X1stFlrSF:GrLivArea:FullBath                                                               
## OverallQual:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath                                                              
## YearBuilt:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath                                                                
## YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath                                                             
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:TotRmsAbvGrd                                                       
## OverallQual:YearBuilt:YearRemodAdd:X1stFlrSF:TotRmsAbvGrd                                                         
## OverallQual:YearBuilt:TotalBsmtSF:X1stFlrSF:TotRmsAbvGrd                                                          
## OverallQual:YearRemodAdd:TotalBsmtSF:X1stFlrSF:TotRmsAbvGrd                                                       
## YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:TotRmsAbvGrd                                                         
## OverallQual:YearBuilt:YearRemodAdd:GrLivArea:TotRmsAbvGrd                                                         
## OverallQual:YearBuilt:TotalBsmtSF:GrLivArea:TotRmsAbvGrd                                                          
## OverallQual:YearRemodAdd:TotalBsmtSF:GrLivArea:TotRmsAbvGrd                                                       
## YearBuilt:YearRemodAdd:TotalBsmtSF:GrLivArea:TotRmsAbvGrd                                                         
## OverallQual:YearBuilt:X1stFlrSF:GrLivArea:TotRmsAbvGrd                                                            
## OverallQual:YearRemodAdd:X1stFlrSF:GrLivArea:TotRmsAbvGrd                                                         
## YearBuilt:YearRemodAdd:X1stFlrSF:GrLivArea:TotRmsAbvGrd                                                           
## OverallQual:TotalBsmtSF:X1stFlrSF:GrLivArea:TotRmsAbvGrd                                                          
## YearBuilt:TotalBsmtSF:X1stFlrSF:GrLivArea:TotRmsAbvGrd                                                         .  
## YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:TotRmsAbvGrd                                                         
## OverallQual:YearBuilt:YearRemodAdd:FullBath:TotRmsAbvGrd                                                          
## OverallQual:YearBuilt:TotalBsmtSF:FullBath:TotRmsAbvGrd                                                           
## OverallQual:YearRemodAdd:TotalBsmtSF:FullBath:TotRmsAbvGrd                                                     .  
## YearBuilt:YearRemodAdd:TotalBsmtSF:FullBath:TotRmsAbvGrd                                                          
## OverallQual:YearBuilt:X1stFlrSF:FullBath:TotRmsAbvGrd                                                             
## OverallQual:YearRemodAdd:X1stFlrSF:FullBath:TotRmsAbvGrd                                                          
## YearBuilt:YearRemodAdd:X1stFlrSF:FullBath:TotRmsAbvGrd                                                            
## OverallQual:TotalBsmtSF:X1stFlrSF:FullBath:TotRmsAbvGrd                                                           
## YearBuilt:TotalBsmtSF:X1stFlrSF:FullBath:TotRmsAbvGrd                                                             
## YearRemodAdd:TotalBsmtSF:X1stFlrSF:FullBath:TotRmsAbvGrd                                                          
## OverallQual:YearBuilt:GrLivArea:FullBath:TotRmsAbvGrd                                                             
## OverallQual:YearRemodAdd:GrLivArea:FullBath:TotRmsAbvGrd                                                          
## YearBuilt:YearRemodAdd:GrLivArea:FullBath:TotRmsAbvGrd                                                            
## OverallQual:TotalBsmtSF:GrLivArea:FullBath:TotRmsAbvGrd                                                           
## YearBuilt:TotalBsmtSF:GrLivArea:FullBath:TotRmsAbvGrd                                                             
## YearRemodAdd:TotalBsmtSF:GrLivArea:FullBath:TotRmsAbvGrd                                                          
## OverallQual:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd                                                             
## YearBuilt:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd                                                               
## YearRemodAdd:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd                                                            
## TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd                                                             
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:GarageCars                                                         
## OverallQual:YearBuilt:YearRemodAdd:X1stFlrSF:GarageCars                                                           
## OverallQual:YearBuilt:TotalBsmtSF:X1stFlrSF:GarageCars                                                            
## OverallQual:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GarageCars                                                         
## YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GarageCars                                                           
## OverallQual:YearBuilt:YearRemodAdd:GrLivArea:GarageCars                                                           
## OverallQual:YearBuilt:TotalBsmtSF:GrLivArea:GarageCars                                                            
## OverallQual:YearRemodAdd:TotalBsmtSF:GrLivArea:GarageCars                                                         
## YearBuilt:YearRemodAdd:TotalBsmtSF:GrLivArea:GarageCars                                                           
## OverallQual:YearBuilt:X1stFlrSF:GrLivArea:GarageCars                                                              
## OverallQual:YearRemodAdd:X1stFlrSF:GrLivArea:GarageCars                                                           
## YearBuilt:YearRemodAdd:X1stFlrSF:GrLivArea:GarageCars                                                             
## OverallQual:TotalBsmtSF:X1stFlrSF:GrLivArea:GarageCars                                                            
## YearBuilt:TotalBsmtSF:X1stFlrSF:GrLivArea:GarageCars                                                           .  
## YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:GarageCars                                                        .  
## OverallQual:YearBuilt:YearRemodAdd:FullBath:GarageCars                                                            
## OverallQual:YearBuilt:TotalBsmtSF:FullBath:GarageCars                                                             
## OverallQual:YearRemodAdd:TotalBsmtSF:FullBath:GarageCars                                                       .  
## YearBuilt:YearRemodAdd:TotalBsmtSF:FullBath:GarageCars                                                            
## OverallQual:YearBuilt:X1stFlrSF:FullBath:GarageCars                                                               
## OverallQual:YearRemodAdd:X1stFlrSF:FullBath:GarageCars                                                            
## YearBuilt:YearRemodAdd:X1stFlrSF:FullBath:GarageCars                                                           .  
## OverallQual:TotalBsmtSF:X1stFlrSF:FullBath:GarageCars                                                             
## YearBuilt:TotalBsmtSF:X1stFlrSF:FullBath:GarageCars                                                               
## YearRemodAdd:TotalBsmtSF:X1stFlrSF:FullBath:GarageCars                                                            
## OverallQual:YearBuilt:GrLivArea:FullBath:GarageCars                                                               
## OverallQual:YearRemodAdd:GrLivArea:FullBath:GarageCars                                                            
## YearBuilt:YearRemodAdd:GrLivArea:FullBath:GarageCars                                                              
## OverallQual:TotalBsmtSF:GrLivArea:FullBath:GarageCars                                                             
## YearBuilt:TotalBsmtSF:GrLivArea:FullBath:GarageCars                                                            *  
## YearRemodAdd:TotalBsmtSF:GrLivArea:FullBath:GarageCars                                                            
## OverallQual:X1stFlrSF:GrLivArea:FullBath:GarageCars                                                               
## YearBuilt:X1stFlrSF:GrLivArea:FullBath:GarageCars                                                              *  
## YearRemodAdd:X1stFlrSF:GrLivArea:FullBath:GarageCars                                                           .  
## TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:GarageCars                                                               
## OverallQual:YearBuilt:YearRemodAdd:TotRmsAbvGrd:GarageCars                                                        
## OverallQual:YearBuilt:TotalBsmtSF:TotRmsAbvGrd:GarageCars                                                      .  
## OverallQual:YearRemodAdd:TotalBsmtSF:TotRmsAbvGrd:GarageCars                                                      
## YearBuilt:YearRemodAdd:TotalBsmtSF:TotRmsAbvGrd:GarageCars                                                        
## OverallQual:YearBuilt:X1stFlrSF:TotRmsAbvGrd:GarageCars                                                           
## OverallQual:YearRemodAdd:X1stFlrSF:TotRmsAbvGrd:GarageCars                                                        
## YearBuilt:YearRemodAdd:X1stFlrSF:TotRmsAbvGrd:GarageCars                                                          
## OverallQual:TotalBsmtSF:X1stFlrSF:TotRmsAbvGrd:GarageCars                                                         
## YearBuilt:TotalBsmtSF:X1stFlrSF:TotRmsAbvGrd:GarageCars                                                           
## YearRemodAdd:TotalBsmtSF:X1stFlrSF:TotRmsAbvGrd:GarageCars                                                     .  
## OverallQual:YearBuilt:GrLivArea:TotRmsAbvGrd:GarageCars                                                           
## OverallQual:YearRemodAdd:GrLivArea:TotRmsAbvGrd:GarageCars                                                        
## YearBuilt:YearRemodAdd:GrLivArea:TotRmsAbvGrd:GarageCars                                                          
## OverallQual:TotalBsmtSF:GrLivArea:TotRmsAbvGrd:GarageCars                                                         
## YearBuilt:TotalBsmtSF:GrLivArea:TotRmsAbvGrd:GarageCars                                                        *  
## YearRemodAdd:TotalBsmtSF:GrLivArea:TotRmsAbvGrd:GarageCars                                                        
## OverallQual:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageCars                                                           
## YearBuilt:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageCars                                                             
## YearRemodAdd:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageCars                                                          
## TotalBsmtSF:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageCars                                                           
## OverallQual:YearBuilt:FullBath:TotRmsAbvGrd:GarageCars                                                            
## OverallQual:YearRemodAdd:FullBath:TotRmsAbvGrd:GarageCars                                                         
## YearBuilt:YearRemodAdd:FullBath:TotRmsAbvGrd:GarageCars                                                           
## OverallQual:TotalBsmtSF:FullBath:TotRmsAbvGrd:GarageCars                                                          
## YearBuilt:TotalBsmtSF:FullBath:TotRmsAbvGrd:GarageCars                                                            
## YearRemodAdd:TotalBsmtSF:FullBath:TotRmsAbvGrd:GarageCars                                                         
## OverallQual:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageCars                                                            
## YearBuilt:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageCars                                                              
## YearRemodAdd:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageCars                                                           
## TotalBsmtSF:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageCars                                                            
## OverallQual:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars                                                            
## YearBuilt:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars                                                              
## YearRemodAdd:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars                                                           
## TotalBsmtSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars                                                         .  
## X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars                                                              
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:GarageArea                                                         
## OverallQual:YearBuilt:YearRemodAdd:X1stFlrSF:GarageArea                                                           
## OverallQual:YearBuilt:TotalBsmtSF:X1stFlrSF:GarageArea                                                            
## OverallQual:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GarageArea                                                         
## YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GarageArea                                                           
## OverallQual:YearBuilt:YearRemodAdd:GrLivArea:GarageArea                                                           
## OverallQual:YearBuilt:TotalBsmtSF:GrLivArea:GarageArea                                                         ** 
## OverallQual:YearRemodAdd:TotalBsmtSF:GrLivArea:GarageArea                                                      *  
## YearBuilt:YearRemodAdd:TotalBsmtSF:GrLivArea:GarageArea                                                        .  
## OverallQual:YearBuilt:X1stFlrSF:GrLivArea:GarageArea                                                           *  
## OverallQual:YearRemodAdd:X1stFlrSF:GrLivArea:GarageArea                                                           
## YearBuilt:YearRemodAdd:X1stFlrSF:GrLivArea:GarageArea                                                             
## OverallQual:TotalBsmtSF:X1stFlrSF:GrLivArea:GarageArea                                                         .  
## YearBuilt:TotalBsmtSF:X1stFlrSF:GrLivArea:GarageArea                                                              
## YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:GarageArea                                                           
## OverallQual:YearBuilt:YearRemodAdd:FullBath:GarageArea                                                            
## OverallQual:YearBuilt:TotalBsmtSF:FullBath:GarageArea                                                             
## OverallQual:YearRemodAdd:TotalBsmtSF:FullBath:GarageArea                                                       .  
## YearBuilt:YearRemodAdd:TotalBsmtSF:FullBath:GarageArea                                                            
## OverallQual:YearBuilt:X1stFlrSF:FullBath:GarageArea                                                            ** 
## OverallQual:YearRemodAdd:X1stFlrSF:FullBath:GarageArea                                                         ***
## YearBuilt:YearRemodAdd:X1stFlrSF:FullBath:GarageArea                                                              
## OverallQual:TotalBsmtSF:X1stFlrSF:FullBath:GarageArea                                                             
## YearBuilt:TotalBsmtSF:X1stFlrSF:FullBath:GarageArea                                                               
## YearRemodAdd:TotalBsmtSF:X1stFlrSF:FullBath:GarageArea                                                            
## OverallQual:YearBuilt:GrLivArea:FullBath:GarageArea                                                               
## OverallQual:YearRemodAdd:GrLivArea:FullBath:GarageArea                                                            
## YearBuilt:YearRemodAdd:GrLivArea:FullBath:GarageArea                                                              
## OverallQual:TotalBsmtSF:GrLivArea:FullBath:GarageArea                                                             
## YearBuilt:TotalBsmtSF:GrLivArea:FullBath:GarageArea                                                               
## YearRemodAdd:TotalBsmtSF:GrLivArea:FullBath:GarageArea                                                         *  
## OverallQual:X1stFlrSF:GrLivArea:FullBath:GarageArea                                                               
## YearBuilt:X1stFlrSF:GrLivArea:FullBath:GarageArea                                                                 
## YearRemodAdd:X1stFlrSF:GrLivArea:FullBath:GarageArea                                                              
## TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:GarageArea                                                               
## OverallQual:YearBuilt:YearRemodAdd:TotRmsAbvGrd:GarageArea                                                        
## OverallQual:YearBuilt:TotalBsmtSF:TotRmsAbvGrd:GarageArea                                                         
## OverallQual:YearRemodAdd:TotalBsmtSF:TotRmsAbvGrd:GarageArea                                                      
## YearBuilt:YearRemodAdd:TotalBsmtSF:TotRmsAbvGrd:GarageArea                                                        
## OverallQual:YearBuilt:X1stFlrSF:TotRmsAbvGrd:GarageArea                                                           
## OverallQual:YearRemodAdd:X1stFlrSF:TotRmsAbvGrd:GarageArea                                                        
## YearBuilt:YearRemodAdd:X1stFlrSF:TotRmsAbvGrd:GarageArea                                                          
## OverallQual:TotalBsmtSF:X1stFlrSF:TotRmsAbvGrd:GarageArea                                                         
## YearBuilt:TotalBsmtSF:X1stFlrSF:TotRmsAbvGrd:GarageArea                                                           
## YearRemodAdd:TotalBsmtSF:X1stFlrSF:TotRmsAbvGrd:GarageArea                                                     *  
## OverallQual:YearBuilt:GrLivArea:TotRmsAbvGrd:GarageArea                                                           
## OverallQual:YearRemodAdd:GrLivArea:TotRmsAbvGrd:GarageArea                                                        
## YearBuilt:YearRemodAdd:GrLivArea:TotRmsAbvGrd:GarageArea                                                          
## OverallQual:TotalBsmtSF:GrLivArea:TotRmsAbvGrd:GarageArea                                                      *  
## YearBuilt:TotalBsmtSF:GrLivArea:TotRmsAbvGrd:GarageArea                                                           
## YearRemodAdd:TotalBsmtSF:GrLivArea:TotRmsAbvGrd:GarageArea                                                        
## OverallQual:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageArea                                                        *  
## YearBuilt:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageArea                                                             
## YearRemodAdd:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageArea                                                          
## TotalBsmtSF:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageArea                                                        *  
## OverallQual:YearBuilt:FullBath:TotRmsAbvGrd:GarageArea                                                            
## OverallQual:YearRemodAdd:FullBath:TotRmsAbvGrd:GarageArea                                                         
## YearBuilt:YearRemodAdd:FullBath:TotRmsAbvGrd:GarageArea                                                           
## OverallQual:TotalBsmtSF:FullBath:TotRmsAbvGrd:GarageArea                                                          
## YearBuilt:TotalBsmtSF:FullBath:TotRmsAbvGrd:GarageArea                                                            
## YearRemodAdd:TotalBsmtSF:FullBath:TotRmsAbvGrd:GarageArea                                                         
## OverallQual:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageArea                                                         .  
## YearBuilt:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageArea                                                              
## YearRemodAdd:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageArea                                                           
## TotalBsmtSF:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageArea                                                            
## OverallQual:GrLivArea:FullBath:TotRmsAbvGrd:GarageArea                                                            
## YearBuilt:GrLivArea:FullBath:TotRmsAbvGrd:GarageArea                                                              
## YearRemodAdd:GrLivArea:FullBath:TotRmsAbvGrd:GarageArea                                                           
## TotalBsmtSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageArea                                                         ** 
## X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageArea                                                              
## OverallQual:YearBuilt:YearRemodAdd:GarageCars:GarageArea                                                          
## OverallQual:YearBuilt:TotalBsmtSF:GarageCars:GarageArea                                                           
## OverallQual:YearRemodAdd:TotalBsmtSF:GarageCars:GarageArea                                                     .  
## YearBuilt:YearRemodAdd:TotalBsmtSF:GarageCars:GarageArea                                                          
## OverallQual:YearBuilt:X1stFlrSF:GarageCars:GarageArea                                                             
## OverallQual:YearRemodAdd:X1stFlrSF:GarageCars:GarageArea                                                       *  
## YearBuilt:YearRemodAdd:X1stFlrSF:GarageCars:GarageArea                                                            
## OverallQual:TotalBsmtSF:X1stFlrSF:GarageCars:GarageArea                                                           
## YearBuilt:TotalBsmtSF:X1stFlrSF:GarageCars:GarageArea                                                             
## YearRemodAdd:TotalBsmtSF:X1stFlrSF:GarageCars:GarageArea                                                          
## OverallQual:YearBuilt:GrLivArea:GarageCars:GarageArea                                                             
## OverallQual:YearRemodAdd:GrLivArea:GarageCars:GarageArea                                                          
## YearBuilt:YearRemodAdd:GrLivArea:GarageCars:GarageArea                                                            
## OverallQual:TotalBsmtSF:GrLivArea:GarageCars:GarageArea                                                           
## YearBuilt:TotalBsmtSF:GrLivArea:GarageCars:GarageArea                                                          *  
## YearRemodAdd:TotalBsmtSF:GrLivArea:GarageCars:GarageArea                                                          
## OverallQual:X1stFlrSF:GrLivArea:GarageCars:GarageArea                                                             
## YearBuilt:X1stFlrSF:GrLivArea:GarageCars:GarageArea                                                            *  
## YearRemodAdd:X1stFlrSF:GrLivArea:GarageCars:GarageArea                                                         *  
## TotalBsmtSF:X1stFlrSF:GrLivArea:GarageCars:GarageArea                                                             
## OverallQual:YearBuilt:FullBath:GarageCars:GarageArea                                                              
## OverallQual:YearRemodAdd:FullBath:GarageCars:GarageArea                                                           
## YearBuilt:YearRemodAdd:FullBath:GarageCars:GarageArea                                                          *  
## OverallQual:TotalBsmtSF:FullBath:GarageCars:GarageArea                                                            
## YearBuilt:TotalBsmtSF:FullBath:GarageCars:GarageArea                                                              
## YearRemodAdd:TotalBsmtSF:FullBath:GarageCars:GarageArea                                                           
## OverallQual:X1stFlrSF:FullBath:GarageCars:GarageArea                                                              
## YearBuilt:X1stFlrSF:FullBath:GarageCars:GarageArea                                                                
## YearRemodAdd:X1stFlrSF:FullBath:GarageCars:GarageArea                                                          *  
## TotalBsmtSF:X1stFlrSF:FullBath:GarageCars:GarageArea                                                              
## OverallQual:GrLivArea:FullBath:GarageCars:GarageArea                                                              
## YearBuilt:GrLivArea:FullBath:GarageCars:GarageArea                                                                
## YearRemodAdd:GrLivArea:FullBath:GarageCars:GarageArea                                                             
## TotalBsmtSF:GrLivArea:FullBath:GarageCars:GarageArea                                                              
## X1stFlrSF:GrLivArea:FullBath:GarageCars:GarageArea                                                                
## OverallQual:YearBuilt:TotRmsAbvGrd:GarageCars:GarageArea                                                       .  
## OverallQual:YearRemodAdd:TotRmsAbvGrd:GarageCars:GarageArea                                                       
## YearBuilt:YearRemodAdd:TotRmsAbvGrd:GarageCars:GarageArea                                                         
## OverallQual:TotalBsmtSF:TotRmsAbvGrd:GarageCars:GarageArea                                                        
## YearBuilt:TotalBsmtSF:TotRmsAbvGrd:GarageCars:GarageArea                                                          
## YearRemodAdd:TotalBsmtSF:TotRmsAbvGrd:GarageCars:GarageArea                                                       
## OverallQual:X1stFlrSF:TotRmsAbvGrd:GarageCars:GarageArea                                                          
## YearBuilt:X1stFlrSF:TotRmsAbvGrd:GarageCars:GarageArea                                                            
## YearRemodAdd:X1stFlrSF:TotRmsAbvGrd:GarageCars:GarageArea                                                         
## TotalBsmtSF:X1stFlrSF:TotRmsAbvGrd:GarageCars:GarageArea                                                          
## OverallQual:GrLivArea:TotRmsAbvGrd:GarageCars:GarageArea                                                          
## YearBuilt:GrLivArea:TotRmsAbvGrd:GarageCars:GarageArea                                                            
## YearRemodAdd:GrLivArea:TotRmsAbvGrd:GarageCars:GarageArea                                                         
## TotalBsmtSF:GrLivArea:TotRmsAbvGrd:GarageCars:GarageArea                                                          
## X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageCars:GarageArea                                                            
## OverallQual:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                                           
## YearBuilt:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                                             
## YearRemodAdd:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                                          
## TotalBsmtSF:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                                           
## X1stFlrSF:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                                             
## GrLivArea:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                                             
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea                                                
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:FullBath                                                 
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:GrLivArea:FullBath                                                 
## OverallQual:YearBuilt:YearRemodAdd:X1stFlrSF:GrLivArea:FullBath                                                   
## OverallQual:YearBuilt:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath                                                    
## OverallQual:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath                                                 
## YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath                                                   
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:TotRmsAbvGrd                                             
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:GrLivArea:TotRmsAbvGrd                                             
## OverallQual:YearBuilt:YearRemodAdd:X1stFlrSF:GrLivArea:TotRmsAbvGrd                                               
## OverallQual:YearBuilt:TotalBsmtSF:X1stFlrSF:GrLivArea:TotRmsAbvGrd                                                
## OverallQual:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:TotRmsAbvGrd                                             
## YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:TotRmsAbvGrd                                               
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:FullBath:TotRmsAbvGrd                                              
## OverallQual:YearBuilt:YearRemodAdd:X1stFlrSF:FullBath:TotRmsAbvGrd                                                
## OverallQual:YearBuilt:TotalBsmtSF:X1stFlrSF:FullBath:TotRmsAbvGrd                                                 
## OverallQual:YearRemodAdd:TotalBsmtSF:X1stFlrSF:FullBath:TotRmsAbvGrd                                           *  
## YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:FullBath:TotRmsAbvGrd                                                
## OverallQual:YearBuilt:YearRemodAdd:GrLivArea:FullBath:TotRmsAbvGrd                                                
## OverallQual:YearBuilt:TotalBsmtSF:GrLivArea:FullBath:TotRmsAbvGrd                                              .  
## OverallQual:YearRemodAdd:TotalBsmtSF:GrLivArea:FullBath:TotRmsAbvGrd                                              
## YearBuilt:YearRemodAdd:TotalBsmtSF:GrLivArea:FullBath:TotRmsAbvGrd                                                
## OverallQual:YearBuilt:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd                                                   
## OverallQual:YearRemodAdd:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd                                             .  
## YearBuilt:YearRemodAdd:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd                                                  
## OverallQual:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd                                                 
## YearBuilt:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd                                                   
## YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd                                                
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GarageCars                                               
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:GrLivArea:GarageCars                                               
## OverallQual:YearBuilt:YearRemodAdd:X1stFlrSF:GrLivArea:GarageCars                                                 
## OverallQual:YearBuilt:TotalBsmtSF:X1stFlrSF:GrLivArea:GarageCars                                                  
## OverallQual:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:GarageCars                                               
## YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:GarageCars                                                 
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:FullBath:GarageCars                                                
## OverallQual:YearBuilt:YearRemodAdd:X1stFlrSF:FullBath:GarageCars                                                  
## OverallQual:YearBuilt:TotalBsmtSF:X1stFlrSF:FullBath:GarageCars                                                   
## OverallQual:YearRemodAdd:TotalBsmtSF:X1stFlrSF:FullBath:GarageCars                                                
## YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:FullBath:GarageCars                                                  
## OverallQual:YearBuilt:YearRemodAdd:GrLivArea:FullBath:GarageCars                                                  
## OverallQual:YearBuilt:TotalBsmtSF:GrLivArea:FullBath:GarageCars                                                   
## OverallQual:YearRemodAdd:TotalBsmtSF:GrLivArea:FullBath:GarageCars                                                
## YearBuilt:YearRemodAdd:TotalBsmtSF:GrLivArea:FullBath:GarageCars                                                  
## OverallQual:YearBuilt:X1stFlrSF:GrLivArea:FullBath:GarageCars                                                     
## OverallQual:YearRemodAdd:X1stFlrSF:GrLivArea:FullBath:GarageCars                                                  
## YearBuilt:YearRemodAdd:X1stFlrSF:GrLivArea:FullBath:GarageCars                                                    
## OverallQual:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:GarageCars                                                   
## YearBuilt:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:GarageCars                                                     
## YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:GarageCars                                                  
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:TotRmsAbvGrd:GarageCars                                            
## OverallQual:YearBuilt:YearRemodAdd:X1stFlrSF:TotRmsAbvGrd:GarageCars                                              
## OverallQual:YearBuilt:TotalBsmtSF:X1stFlrSF:TotRmsAbvGrd:GarageCars                                               
## OverallQual:YearRemodAdd:TotalBsmtSF:X1stFlrSF:TotRmsAbvGrd:GarageCars                                            
## YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:TotRmsAbvGrd:GarageCars                                              
## OverallQual:YearBuilt:YearRemodAdd:GrLivArea:TotRmsAbvGrd:GarageCars                                              
## OverallQual:YearBuilt:TotalBsmtSF:GrLivArea:TotRmsAbvGrd:GarageCars                                            *  
## OverallQual:YearRemodAdd:TotalBsmtSF:GrLivArea:TotRmsAbvGrd:GarageCars                                            
## YearBuilt:YearRemodAdd:TotalBsmtSF:GrLivArea:TotRmsAbvGrd:GarageCars                                              
## OverallQual:YearBuilt:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageCars                                                 
## OverallQual:YearRemodAdd:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageCars                                              
## YearBuilt:YearRemodAdd:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageCars                                                
## OverallQual:TotalBsmtSF:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageCars                                               
## YearBuilt:TotalBsmtSF:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageCars                                              .  
## YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageCars                                              
## OverallQual:YearBuilt:YearRemodAdd:FullBath:TotRmsAbvGrd:GarageCars                                               
## OverallQual:YearBuilt:TotalBsmtSF:FullBath:TotRmsAbvGrd:GarageCars                                                
## OverallQual:YearRemodAdd:TotalBsmtSF:FullBath:TotRmsAbvGrd:GarageCars                                             
## YearBuilt:YearRemodAdd:TotalBsmtSF:FullBath:TotRmsAbvGrd:GarageCars                                               
## OverallQual:YearBuilt:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageCars                                                  
## OverallQual:YearRemodAdd:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageCars                                               
## YearBuilt:YearRemodAdd:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageCars                                                 
## OverallQual:TotalBsmtSF:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageCars                                                
## YearBuilt:TotalBsmtSF:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageCars                                               *  
## YearRemodAdd:TotalBsmtSF:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageCars                                            .  
## OverallQual:YearBuilt:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars                                                  
## OverallQual:YearRemodAdd:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars                                               
## YearBuilt:YearRemodAdd:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars                                                 
## OverallQual:TotalBsmtSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars                                                
## YearBuilt:TotalBsmtSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars                                                  
## YearRemodAdd:TotalBsmtSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars                                               
## OverallQual:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars                                                  
## YearBuilt:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars                                                    
## YearRemodAdd:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars                                                 
## TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars                                                  
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GarageArea                                               
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:GrLivArea:GarageArea                                               
## OverallQual:YearBuilt:YearRemodAdd:X1stFlrSF:GrLivArea:GarageArea                                                 
## OverallQual:YearBuilt:TotalBsmtSF:X1stFlrSF:GrLivArea:GarageArea                                               .  
## OverallQual:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:GarageArea                                               
## YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:GarageArea                                                 
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:FullBath:GarageArea                                                
## OverallQual:YearBuilt:YearRemodAdd:X1stFlrSF:FullBath:GarageArea                                                  
## OverallQual:YearBuilt:TotalBsmtSF:X1stFlrSF:FullBath:GarageArea                                                   
## OverallQual:YearRemodAdd:TotalBsmtSF:X1stFlrSF:FullBath:GarageArea                                                
## YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:FullBath:GarageArea                                                  
## OverallQual:YearBuilt:YearRemodAdd:GrLivArea:FullBath:GarageArea                                                  
## OverallQual:YearBuilt:TotalBsmtSF:GrLivArea:FullBath:GarageArea                                                   
## OverallQual:YearRemodAdd:TotalBsmtSF:GrLivArea:FullBath:GarageArea                                                
## YearBuilt:YearRemodAdd:TotalBsmtSF:GrLivArea:FullBath:GarageArea                                                  
## OverallQual:YearBuilt:X1stFlrSF:GrLivArea:FullBath:GarageArea                                                  .  
## OverallQual:YearRemodAdd:X1stFlrSF:GrLivArea:FullBath:GarageArea                                                  
## YearBuilt:YearRemodAdd:X1stFlrSF:GrLivArea:FullBath:GarageArea                                                    
## OverallQual:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:GarageArea                                                   
## YearBuilt:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:GarageArea                                                     
## YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:GarageArea                                                  
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:TotRmsAbvGrd:GarageArea                                            
## OverallQual:YearBuilt:YearRemodAdd:X1stFlrSF:TotRmsAbvGrd:GarageArea                                              
## OverallQual:YearBuilt:TotalBsmtSF:X1stFlrSF:TotRmsAbvGrd:GarageArea                                               
## OverallQual:YearRemodAdd:TotalBsmtSF:X1stFlrSF:TotRmsAbvGrd:GarageArea                                            
## YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:TotRmsAbvGrd:GarageArea                                              
## OverallQual:YearBuilt:YearRemodAdd:GrLivArea:TotRmsAbvGrd:GarageArea                                              
## OverallQual:YearBuilt:TotalBsmtSF:GrLivArea:TotRmsAbvGrd:GarageArea                                            *  
## OverallQual:YearRemodAdd:TotalBsmtSF:GrLivArea:TotRmsAbvGrd:GarageArea                                            
## YearBuilt:YearRemodAdd:TotalBsmtSF:GrLivArea:TotRmsAbvGrd:GarageArea                                              
## OverallQual:YearBuilt:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageArea                                              *  
## OverallQual:YearRemodAdd:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageArea                                              
## YearBuilt:YearRemodAdd:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageArea                                                
## OverallQual:TotalBsmtSF:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageArea                                               
## YearBuilt:TotalBsmtSF:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageArea                                              *  
## YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageArea                                              
## OverallQual:YearBuilt:YearRemodAdd:FullBath:TotRmsAbvGrd:GarageArea                                               
## OverallQual:YearBuilt:TotalBsmtSF:FullBath:TotRmsAbvGrd:GarageArea                                                
## OverallQual:YearRemodAdd:TotalBsmtSF:FullBath:TotRmsAbvGrd:GarageArea                                             
## YearBuilt:YearRemodAdd:TotalBsmtSF:FullBath:TotRmsAbvGrd:GarageArea                                               
## OverallQual:YearBuilt:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageArea                                                  
## OverallQual:YearRemodAdd:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageArea                                               
## YearBuilt:YearRemodAdd:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageArea                                                 
## OverallQual:TotalBsmtSF:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageArea                                                
## YearBuilt:TotalBsmtSF:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageArea                                               .  
## YearRemodAdd:TotalBsmtSF:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageArea                                            *  
## OverallQual:YearBuilt:GrLivArea:FullBath:TotRmsAbvGrd:GarageArea                                                  
## OverallQual:YearRemodAdd:GrLivArea:FullBath:TotRmsAbvGrd:GarageArea                                               
## YearBuilt:YearRemodAdd:GrLivArea:FullBath:TotRmsAbvGrd:GarageArea                                                 
## OverallQual:TotalBsmtSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageArea                                                
## YearBuilt:TotalBsmtSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageArea                                                  
## YearRemodAdd:TotalBsmtSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageArea                                            .  
## OverallQual:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageArea                                                  
## YearBuilt:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageArea                                                    
## YearRemodAdd:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageArea                                                 
## TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageArea                                                  
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:GarageCars:GarageArea                                              
## OverallQual:YearBuilt:YearRemodAdd:X1stFlrSF:GarageCars:GarageArea                                                
## OverallQual:YearBuilt:TotalBsmtSF:X1stFlrSF:GarageCars:GarageArea                                                 
## OverallQual:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GarageCars:GarageArea                                              
## YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GarageCars:GarageArea                                                
## OverallQual:YearBuilt:YearRemodAdd:GrLivArea:GarageCars:GarageArea                                                
## OverallQual:YearBuilt:TotalBsmtSF:GrLivArea:GarageCars:GarageArea                                              ** 
## OverallQual:YearRemodAdd:TotalBsmtSF:GrLivArea:GarageCars:GarageArea                                              
## YearBuilt:YearRemodAdd:TotalBsmtSF:GrLivArea:GarageCars:GarageArea                                                
## OverallQual:YearBuilt:X1stFlrSF:GrLivArea:GarageCars:GarageArea                                                *  
## OverallQual:YearRemodAdd:X1stFlrSF:GrLivArea:GarageCars:GarageArea                                                
## YearBuilt:YearRemodAdd:X1stFlrSF:GrLivArea:GarageCars:GarageArea                                                  
## OverallQual:TotalBsmtSF:X1stFlrSF:GrLivArea:GarageCars:GarageArea                                                 
## YearBuilt:TotalBsmtSF:X1stFlrSF:GrLivArea:GarageCars:GarageArea                                                   
## YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:GarageCars:GarageArea                                                
## OverallQual:YearBuilt:YearRemodAdd:FullBath:GarageCars:GarageArea                                                 
## OverallQual:YearBuilt:TotalBsmtSF:FullBath:GarageCars:GarageArea                                                  
## OverallQual:YearRemodAdd:TotalBsmtSF:FullBath:GarageCars:GarageArea                                            ** 
## YearBuilt:YearRemodAdd:TotalBsmtSF:FullBath:GarageCars:GarageArea                                                 
## OverallQual:YearBuilt:X1stFlrSF:FullBath:GarageCars:GarageArea                                                 *  
## OverallQual:YearRemodAdd:X1stFlrSF:FullBath:GarageCars:GarageArea                                              ***
## YearBuilt:YearRemodAdd:X1stFlrSF:FullBath:GarageCars:GarageArea                                                   
## OverallQual:TotalBsmtSF:X1stFlrSF:FullBath:GarageCars:GarageArea                                                  
## YearBuilt:TotalBsmtSF:X1stFlrSF:FullBath:GarageCars:GarageArea                                                    
## YearRemodAdd:TotalBsmtSF:X1stFlrSF:FullBath:GarageCars:GarageArea                                                 
## OverallQual:YearBuilt:GrLivArea:FullBath:GarageCars:GarageArea                                                    
## OverallQual:YearRemodAdd:GrLivArea:FullBath:GarageCars:GarageArea                                                 
## YearBuilt:YearRemodAdd:GrLivArea:FullBath:GarageCars:GarageArea                                                   
## OverallQual:TotalBsmtSF:GrLivArea:FullBath:GarageCars:GarageArea                                                  
## YearBuilt:TotalBsmtSF:GrLivArea:FullBath:GarageCars:GarageArea                                                 .  
## YearRemodAdd:TotalBsmtSF:GrLivArea:FullBath:GarageCars:GarageArea                                                 
## OverallQual:X1stFlrSF:GrLivArea:FullBath:GarageCars:GarageArea                                                 .  
## YearBuilt:X1stFlrSF:GrLivArea:FullBath:GarageCars:GarageArea                                                      
## YearRemodAdd:X1stFlrSF:GrLivArea:FullBath:GarageCars:GarageArea                                                   
## TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:GarageCars:GarageArea                                                    
## OverallQual:YearBuilt:YearRemodAdd:TotRmsAbvGrd:GarageCars:GarageArea                                             
## OverallQual:YearBuilt:TotalBsmtSF:TotRmsAbvGrd:GarageCars:GarageArea                                              
## OverallQual:YearRemodAdd:TotalBsmtSF:TotRmsAbvGrd:GarageCars:GarageArea                                           
## YearBuilt:YearRemodAdd:TotalBsmtSF:TotRmsAbvGrd:GarageCars:GarageArea                                             
## OverallQual:YearBuilt:X1stFlrSF:TotRmsAbvGrd:GarageCars:GarageArea                                                
## OverallQual:YearRemodAdd:X1stFlrSF:TotRmsAbvGrd:GarageCars:GarageArea                                             
## YearBuilt:YearRemodAdd:X1stFlrSF:TotRmsAbvGrd:GarageCars:GarageArea                                               
## OverallQual:TotalBsmtSF:X1stFlrSF:TotRmsAbvGrd:GarageCars:GarageArea                                              
## YearBuilt:TotalBsmtSF:X1stFlrSF:TotRmsAbvGrd:GarageCars:GarageArea                                                
## YearRemodAdd:TotalBsmtSF:X1stFlrSF:TotRmsAbvGrd:GarageCars:GarageArea                                             
## OverallQual:YearBuilt:GrLivArea:TotRmsAbvGrd:GarageCars:GarageArea                                                
## OverallQual:YearRemodAdd:GrLivArea:TotRmsAbvGrd:GarageCars:GarageArea                                             
## YearBuilt:YearRemodAdd:GrLivArea:TotRmsAbvGrd:GarageCars:GarageArea                                               
## OverallQual:TotalBsmtSF:GrLivArea:TotRmsAbvGrd:GarageCars:GarageArea                                              
## YearBuilt:TotalBsmtSF:GrLivArea:TotRmsAbvGrd:GarageCars:GarageArea                                                
## YearRemodAdd:TotalBsmtSF:GrLivArea:TotRmsAbvGrd:GarageCars:GarageArea                                             
## OverallQual:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageCars:GarageArea                                                
## YearBuilt:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageCars:GarageArea                                                  
## YearRemodAdd:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageCars:GarageArea                                               
## TotalBsmtSF:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageCars:GarageArea                                                
## OverallQual:YearBuilt:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                                 
## OverallQual:YearRemodAdd:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                              
## YearBuilt:YearRemodAdd:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                                
## OverallQual:TotalBsmtSF:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                               
## YearBuilt:TotalBsmtSF:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                                 
## YearRemodAdd:TotalBsmtSF:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                              
## OverallQual:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                              .  
## YearBuilt:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                                   
## YearRemodAdd:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                                
## TotalBsmtSF:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                                 
## OverallQual:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                                 
## YearBuilt:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                                   
## YearRemodAdd:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                                
## TotalBsmtSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                              .  
## X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                                   
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath                                       
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:TotRmsAbvGrd                                   
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:FullBath:TotRmsAbvGrd                                    
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:GrLivArea:FullBath:TotRmsAbvGrd                                    
## OverallQual:YearBuilt:YearRemodAdd:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd                                      
## OverallQual:YearBuilt:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd                                       
## OverallQual:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd                                    
## YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd                                      
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:GarageCars                                     
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:FullBath:GarageCars                                      
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:GrLivArea:FullBath:GarageCars                                      
## OverallQual:YearBuilt:YearRemodAdd:X1stFlrSF:GrLivArea:FullBath:GarageCars                                        
## OverallQual:YearBuilt:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:GarageCars                                         
## OverallQual:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:GarageCars                                      
## YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:GarageCars                                        
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:TotRmsAbvGrd:GarageCars                                  
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:GrLivArea:TotRmsAbvGrd:GarageCars                                  
## OverallQual:YearBuilt:YearRemodAdd:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageCars                                    
## OverallQual:YearBuilt:TotalBsmtSF:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageCars                                     
## OverallQual:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageCars                                  
## YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageCars                                    
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:FullBath:TotRmsAbvGrd:GarageCars                                   
## OverallQual:YearBuilt:YearRemodAdd:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageCars                                     
## OverallQual:YearBuilt:TotalBsmtSF:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageCars                                      
## OverallQual:YearRemodAdd:TotalBsmtSF:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageCars                                   
## YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageCars                                     
## OverallQual:YearBuilt:YearRemodAdd:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars                                     
## OverallQual:YearBuilt:TotalBsmtSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars                                      
## OverallQual:YearRemodAdd:TotalBsmtSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars                                   
## YearBuilt:YearRemodAdd:TotalBsmtSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars                                     
## OverallQual:YearBuilt:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars                                        
## OverallQual:YearRemodAdd:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars                                     
## YearBuilt:YearRemodAdd:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars                                       
## OverallQual:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars                                      
## YearBuilt:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars                                        
## YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars                                     
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:GarageArea                                     
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:FullBath:GarageArea                                      
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:GrLivArea:FullBath:GarageArea                                      
## OverallQual:YearBuilt:YearRemodAdd:X1stFlrSF:GrLivArea:FullBath:GarageArea                                        
## OverallQual:YearBuilt:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:GarageArea                                         
## OverallQual:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:GarageArea                                      
## YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:GarageArea                                        
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:TotRmsAbvGrd:GarageArea                                  
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:GrLivArea:TotRmsAbvGrd:GarageArea                                  
## OverallQual:YearBuilt:YearRemodAdd:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageArea                                    
## OverallQual:YearBuilt:TotalBsmtSF:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageArea                                     
## OverallQual:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageArea                                  
## YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageArea                                    
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:FullBath:TotRmsAbvGrd:GarageArea                                   
## OverallQual:YearBuilt:YearRemodAdd:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageArea                                     
## OverallQual:YearBuilt:TotalBsmtSF:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageArea                                      
## OverallQual:YearRemodAdd:TotalBsmtSF:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageArea                                   
## YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageArea                                     
## OverallQual:YearBuilt:YearRemodAdd:GrLivArea:FullBath:TotRmsAbvGrd:GarageArea                                     
## OverallQual:YearBuilt:TotalBsmtSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageArea                                      
## OverallQual:YearRemodAdd:TotalBsmtSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageArea                                   
## YearBuilt:YearRemodAdd:TotalBsmtSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageArea                                     
## OverallQual:YearBuilt:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageArea                                        
## OverallQual:YearRemodAdd:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageArea                                     
## YearBuilt:YearRemodAdd:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageArea                                       
## OverallQual:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageArea                                      
## YearBuilt:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageArea                                        
## YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageArea                                     
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GarageCars:GarageArea                                    
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:GrLivArea:GarageCars:GarageArea                                    
## OverallQual:YearBuilt:YearRemodAdd:X1stFlrSF:GrLivArea:GarageCars:GarageArea                                      
## OverallQual:YearBuilt:TotalBsmtSF:X1stFlrSF:GrLivArea:GarageCars:GarageArea                                       
## OverallQual:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:GarageCars:GarageArea                                    
## YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:GarageCars:GarageArea                                      
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:FullBath:GarageCars:GarageArea                                     
## OverallQual:YearBuilt:YearRemodAdd:X1stFlrSF:FullBath:GarageCars:GarageArea                                       
## OverallQual:YearBuilt:TotalBsmtSF:X1stFlrSF:FullBath:GarageCars:GarageArea                                        
## OverallQual:YearRemodAdd:TotalBsmtSF:X1stFlrSF:FullBath:GarageCars:GarageArea                                     
## YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:FullBath:GarageCars:GarageArea                                       
## OverallQual:YearBuilt:YearRemodAdd:GrLivArea:FullBath:GarageCars:GarageArea                                       
## OverallQual:YearBuilt:TotalBsmtSF:GrLivArea:FullBath:GarageCars:GarageArea                                        
## OverallQual:YearRemodAdd:TotalBsmtSF:GrLivArea:FullBath:GarageCars:GarageArea                                     
## YearBuilt:YearRemodAdd:TotalBsmtSF:GrLivArea:FullBath:GarageCars:GarageArea                                       
## OverallQual:YearBuilt:X1stFlrSF:GrLivArea:FullBath:GarageCars:GarageArea                                          
## OverallQual:YearRemodAdd:X1stFlrSF:GrLivArea:FullBath:GarageCars:GarageArea                                       
## YearBuilt:YearRemodAdd:X1stFlrSF:GrLivArea:FullBath:GarageCars:GarageArea                                         
## OverallQual:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:GarageCars:GarageArea                                        
## YearBuilt:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:GarageCars:GarageArea                                          
## YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:GarageCars:GarageArea                                       
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:TotRmsAbvGrd:GarageCars:GarageArea                                 
## OverallQual:YearBuilt:YearRemodAdd:X1stFlrSF:TotRmsAbvGrd:GarageCars:GarageArea                                   
## OverallQual:YearBuilt:TotalBsmtSF:X1stFlrSF:TotRmsAbvGrd:GarageCars:GarageArea                                    
## OverallQual:YearRemodAdd:TotalBsmtSF:X1stFlrSF:TotRmsAbvGrd:GarageCars:GarageArea                                 
## YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:TotRmsAbvGrd:GarageCars:GarageArea                                   
## OverallQual:YearBuilt:YearRemodAdd:GrLivArea:TotRmsAbvGrd:GarageCars:GarageArea                                   
## OverallQual:YearBuilt:TotalBsmtSF:GrLivArea:TotRmsAbvGrd:GarageCars:GarageArea                                    
## OverallQual:YearRemodAdd:TotalBsmtSF:GrLivArea:TotRmsAbvGrd:GarageCars:GarageArea                                 
## YearBuilt:YearRemodAdd:TotalBsmtSF:GrLivArea:TotRmsAbvGrd:GarageCars:GarageArea                                   
## OverallQual:YearBuilt:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageCars:GarageArea                                      
## OverallQual:YearRemodAdd:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageCars:GarageArea                                   
## YearBuilt:YearRemodAdd:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageCars:GarageArea                                     
## OverallQual:TotalBsmtSF:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageCars:GarageArea                                    
## YearBuilt:TotalBsmtSF:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageCars:GarageArea                                      
## YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageCars:GarageArea                                   
## OverallQual:YearBuilt:YearRemodAdd:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                    
## OverallQual:YearBuilt:TotalBsmtSF:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                     
## OverallQual:YearRemodAdd:TotalBsmtSF:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                  
## YearBuilt:YearRemodAdd:TotalBsmtSF:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                    
## OverallQual:YearBuilt:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                       
## OverallQual:YearRemodAdd:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                    
## YearBuilt:YearRemodAdd:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                      
## OverallQual:TotalBsmtSF:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                     
## YearBuilt:TotalBsmtSF:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                       
## YearRemodAdd:TotalBsmtSF:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                    
## OverallQual:YearBuilt:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                       
## OverallQual:YearRemodAdd:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                    
## YearBuilt:YearRemodAdd:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                      
## OverallQual:TotalBsmtSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                  *  
## YearBuilt:TotalBsmtSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                       
## YearRemodAdd:TotalBsmtSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                    
## OverallQual:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                       
## YearBuilt:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                         
## YearRemodAdd:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                      
## TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                                       
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd                          
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:GarageCars                            
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageCars                        
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageCars                         
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars                         
## OverallQual:YearBuilt:YearRemodAdd:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars                           
## OverallQual:YearBuilt:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars                            
## OverallQual:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars                         
## YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars                           
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:GarageArea                            
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageArea                        
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageArea                         
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageArea                         
## OverallQual:YearBuilt:YearRemodAdd:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageArea                           
## OverallQual:YearBuilt:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageArea                            
## OverallQual:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageArea                         
## YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageArea                           
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:GarageCars:GarageArea                          
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:FullBath:GarageCars:GarageArea                           
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:GrLivArea:FullBath:GarageCars:GarageArea                           
## OverallQual:YearBuilt:YearRemodAdd:X1stFlrSF:GrLivArea:FullBath:GarageCars:GarageArea                             
## OverallQual:YearBuilt:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:GarageCars:GarageArea                              
## OverallQual:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:GarageCars:GarageArea                           
## YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:GarageCars:GarageArea                             
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:TotRmsAbvGrd:GarageCars:GarageArea                       
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:GrLivArea:TotRmsAbvGrd:GarageCars:GarageArea                       
## OverallQual:YearBuilt:YearRemodAdd:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageCars:GarageArea                         
## OverallQual:YearBuilt:TotalBsmtSF:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageCars:GarageArea                          
## OverallQual:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageCars:GarageArea                       
## YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageCars:GarageArea                         
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                        
## OverallQual:YearBuilt:YearRemodAdd:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                          
## OverallQual:YearBuilt:TotalBsmtSF:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                           
## OverallQual:YearRemodAdd:TotalBsmtSF:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                        
## YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                          
## OverallQual:YearBuilt:YearRemodAdd:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                          
## OverallQual:YearBuilt:TotalBsmtSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                           
## OverallQual:YearRemodAdd:TotalBsmtSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                        
## YearBuilt:YearRemodAdd:TotalBsmtSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                          
## OverallQual:YearBuilt:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                             
## OverallQual:YearRemodAdd:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                          
## YearBuilt:YearRemodAdd:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                            
## OverallQual:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                           
## YearBuilt:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                             
## YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                          
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars               
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageArea               
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:GarageCars:GarageArea                 
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:TotRmsAbvGrd:GarageCars:GarageArea             
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:FullBath:TotRmsAbvGrd:GarageCars:GarageArea              
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars:GarageArea              
## OverallQual:YearBuilt:YearRemodAdd:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                
## OverallQual:YearBuilt:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                 
## OverallQual:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars:GarageArea              
## YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars:GarageArea                
## OverallQual:YearBuilt:YearRemodAdd:TotalBsmtSF:X1stFlrSF:GrLivArea:FullBath:TotRmsAbvGrd:GarageCars:GarageArea    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 21490 on 675 degrees of freedom
## Multiple R-squared:  0.9662, Adjusted R-squared:  0.9268 
## F-statistic: 24.57 on 784 and 675 DF,  p-value: < 2.2e-16

Justisfication for the Fourth variation to multiply the variables versus adding

Variables when added produce the following stats

Multiple R-squared: 0.7737, Adjusted R-squared: 0.7721

F-statistic: 495.4 on 10 and 1449 DF, p-value: < 2.2e-16

Compared to variables when multipled product the following stats

Multiple R-squared: 0.9662, Adjusted R-squared: 0.9268

F-statistic: 24.57 on 784 and 675 DF, p-value: < 2.2e-16

Discussion on 4th submission:

The multiple R-squared of 96.62 > 70%. The Adjusted R-squared is 92.68 and higher the better. The F-statistic is 24.57 and higher the better. The p-value < 0.05.

#Graphical Analysis of Fourth model
layout(matrix(c(1,2,3,4),2,2)) # optional 4 graphs/page 
plot(Fourth_mod)

## Warning in sqrt(crit * p * (1 - hh)/hh): NaNs produced

## Warning in sqrt(crit * p * (1 - hh)/hh): NaNs produced

#For the variation model, we will narrow down the variables based on p-value and correlation test result value > 0.60

#https://www.statisticssolutions.com/pearsons-correlation-coefficient/

#Perfect: If the value is near ± 1, then it said to be a perfect correlation: as one variable increases, the other variable tends to also increase (if positive) or decrease (if negative).
#High degree: If the coefficient value lies between ± 0.50 and ± 1, then it is said to be a strong correlation.
#Moderate degree: If the value lies between ± 0.30 and ± 0.49, then it is said to be a medium correlation.
#Low degree: When the value lies below + .29, then it is said to be a small correlation.
#No correlation: When the value is zero.

#Using only variables where the variable's p-value < 0.001 and correlation test value > 0.60

for (i in 2:length(sc.data)) {
  if(is.numeric(sc.data[,i])){
  a <- cor.test(sc.data$SalePrice, sc.data[,i])
  #print(paste(colnames(sc.data)[i], " est:", a$estimate, " p=value:", a$p.value))
  if (a$p.value < 0.001 && a$estimate > 0.60) {
    print(paste(colnames(sc.data)[i], " cor:", a$estimate, " p=value:", a$p.value))
  }  
  }
}

## [1] "OverallQual  cor: 0.790981600583805  p=value: 2.18567526799377e-313"
## [1] "TotalBsmtSF  cor: 0.613580551559196  p=value: 9.48422939149901e-152"
## [1] "X1stFlrSF  cor: 0.605852184691915  p=value: 5.3947106189684e-147"
## [1] "GrLivArea  cor: 0.708624477612652  p=value: 4.51803364677756e-223"
## [1] "GarageCars  cor: 0.640409197258352  p=value: 2.49864416717662e-169"
## [1] "GarageArea  cor: 0.623431438918362  p=value: 5.26503816797456e-158"
## [1] "SalePrice  cor: 1  p=value: 0"

#Fifth variation using variables where p-value < 0.001 and correlation > 0.60; Rather than add the numeric variables, we will multiply them




Fifth_mod = lm(sc.data$SalePrice ~   OverallQual *   TotalBsmtSF * X1stFlrSF *  GrLivArea *  GarageCars * GarageArea , data = sc.data)

summary(Fifth_mod)

## 
## Call:
## lm(formula = sc.data$SalePrice ~ OverallQual * TotalBsmtSF * 
##     X1stFlrSF * GrLivArea * GarageCars * GarageArea, data = sc.data)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -150828  -13623     129   13992  159904 
## 
## Coefficients:
##                                                                     Estimate
## (Intercept)                                                       -5.919e+04
## OverallQual                                                        1.230e+04
## TotalBsmtSF                                                       -2.912e+02
## X1stFlrSF                                                          4.627e+01
## GrLivArea                                                          2.485e+02
## GarageCars                                                         2.666e+05
## GarageArea                                                         4.536e+02
## OverallQual:TotalBsmtSF                                            6.825e+01
## OverallQual:X1stFlrSF                                              5.816e+00
## TotalBsmtSF:X1stFlrSF                                              3.480e-01
## OverallQual:GrLivArea                                             -3.995e+01
## TotalBsmtSF:GrLivArea                                              5.422e-02
## X1stFlrSF:GrLivArea                                               -1.847e-01
## OverallQual:GarageCars                                            -1.128e+04
## TotalBsmtSF:GarageCars                                            -2.054e+02
## X1stFlrSF:GarageCars                                               8.372e+00
## GrLivArea:GarageCars                                              -4.306e+02
## OverallQual:GarageArea                                            -2.409e+02
## TotalBsmtSF:GarageArea                                             6.128e-01
## X1stFlrSF:GarageArea                                               6.614e-02
## GrLivArea:GarageArea                                              -3.117e-01
## GarageCars:GarageArea                                             -9.487e+02
## OverallQual:TotalBsmtSF:X1stFlrSF                                 -7.585e-02
## OverallQual:TotalBsmtSF:GrLivArea                                 -1.339e-02
## OverallQual:X1stFlrSF:GrLivArea                                    2.965e-02
## TotalBsmtSF:X1stFlrSF:GrLivArea                                   -9.755e-05
## OverallQual:TotalBsmtSF:GarageCars                                -1.308e+01
## OverallQual:X1stFlrSF:GarageCars                                  -3.731e+01
## TotalBsmtSF:X1stFlrSF:GarageCars                                  -1.684e-02
## OverallQual:GrLivArea:GarageCars                                   5.493e+01
## TotalBsmtSF:GrLivArea:GarageCars                                   4.430e-01
## X1stFlrSF:GrLivArea:GarageCars                                     1.791e-01
## OverallQual:TotalBsmtSF:GarageArea                                 4.600e-02
## OverallQual:X1stFlrSF:GarageArea                                   1.442e-01
## TotalBsmtSF:X1stFlrSF:GarageArea                                  -1.155e-03
## OverallQual:GrLivArea:GarageArea                                   1.565e-01
## TotalBsmtSF:GrLivArea:GarageArea                                  -6.792e-04
## X1stFlrSF:GrLivArea:GarageArea                                     1.087e-04
## OverallQual:GarageCars:GarageArea                                  1.767e+02
## TotalBsmtSF:GarageCars:GarageArea                                  6.508e-01
## X1stFlrSF:GarageCars:GarageArea                                    2.342e-01
## GrLivArea:GarageCars:GarageArea                                    8.660e-01
## OverallQual:TotalBsmtSF:X1stFlrSF:GrLivArea                        2.311e-05
## OverallQual:TotalBsmtSF:X1stFlrSF:GarageCars                       4.565e-02
## OverallQual:TotalBsmtSF:GrLivArea:GarageCars                      -4.624e-02
## OverallQual:X1stFlrSF:GrLivArea:GarageCars                        -1.039e-02
## TotalBsmtSF:X1stFlrSF:GrLivArea:GarageCars                        -1.976e-04
## OverallQual:TotalBsmtSF:X1stFlrSF:GarageArea                       6.744e-05
## OverallQual:TotalBsmtSF:GrLivArea:GarageArea                       3.673e-05
## OverallQual:X1stFlrSF:GrLivArea:GarageArea                        -1.200e-04
## TotalBsmtSF:X1stFlrSF:GrLivArea:GarageArea                         7.679e-07
## OverallQual:TotalBsmtSF:GarageCars:GarageArea                     -9.927e-02
## OverallQual:X1stFlrSF:GarageCars:GarageArea                       -5.119e-02
## TotalBsmtSF:X1stFlrSF:GarageCars:GarageArea                       -2.498e-06
## OverallQual:GrLivArea:GarageCars:GarageArea                       -1.539e-01
## TotalBsmtSF:GrLivArea:GarageCars:GarageArea                       -6.498e-04
## X1stFlrSF:GrLivArea:GarageCars:GarageArea                         -3.584e-04
## OverallQual:TotalBsmtSF:X1stFlrSF:GrLivArea:GarageCars             8.491e-06
## OverallQual:TotalBsmtSF:X1stFlrSF:GrLivArea:GarageArea            -5.641e-08
## OverallQual:TotalBsmtSF:X1stFlrSF:GarageCars:GarageArea           -8.426e-06
## OverallQual:TotalBsmtSF:GrLivArea:GarageCars:GarageArea            9.590e-05
## OverallQual:X1stFlrSF:GrLivArea:GarageCars:GarageArea              6.963e-05
## TotalBsmtSF:X1stFlrSF:GrLivArea:GarageCars:GarageArea              1.872e-07
## OverallQual:TotalBsmtSF:X1stFlrSF:GrLivArea:GarageCars:GarageArea -2.429e-08
##                                                                   Std. Error
## (Intercept)                                                        9.820e+04
## OverallQual                                                        2.547e+04
## TotalBsmtSF                                                        2.164e+02
## X1stFlrSF                                                          2.249e+02
## GrLivArea                                                          1.467e+02
## GarageCars                                                         2.656e+05
## GarageArea                                                         1.021e+03
## OverallQual:TotalBsmtSF                                            4.971e+01
## OverallQual:X1stFlrSF                                              4.532e+01
## TotalBsmtSF:X1stFlrSF                                              1.878e-01
## OverallQual:GrLivArea                                              2.708e+01
## TotalBsmtSF:GrLivArea                                              1.983e-01
## X1stFlrSF:GrLivArea                                                2.017e-01
## OverallQual:GarageCars                                             3.857e+04
## TotalBsmtSF:GarageCars                                             2.906e+02
## X1stFlrSF:GarageCars                                               2.889e+02
## GrLivArea:GarageCars                                               1.799e+02
## OverallQual:GarageArea                                             1.437e+02
## TotalBsmtSF:GarageArea                                             1.146e+00
## X1stFlrSF:GarageArea                                               1.193e+00
## GrLivArea:GarageArea                                               6.979e-01
## GarageCars:GarageArea                                              2.622e+02
## OverallQual:TotalBsmtSF:X1stFlrSF                                  4.229e-02
## OverallQual:TotalBsmtSF:GrLivArea                                  3.693e-02
## OverallQual:X1stFlrSF:GrLivArea                                    3.681e-02
## TotalBsmtSF:X1stFlrSF:GrLivArea                                    1.191e-04
## OverallQual:TotalBsmtSF:GarageCars                                 4.343e+01
## OverallQual:X1stFlrSF:GarageCars                                   4.351e+01
## TotalBsmtSF:X1stFlrSF:GarageCars                                   2.322e-01
## OverallQual:GrLivArea:GarageCars                                   2.569e+01
## TotalBsmtSF:GrLivArea:GarageCars                                   1.998e-01
## X1stFlrSF:GrLivArea:GarageCars                                     1.705e-01
## OverallQual:TotalBsmtSF:GarageArea                                 1.659e-01
## OverallQual:X1stFlrSF:GarageArea                                   1.791e-01
## TotalBsmtSF:X1stFlrSF:GarageArea                                   8.974e-04
## OverallQual:GrLivArea:GarageArea                                   8.763e-02
## TotalBsmtSF:GrLivArea:GarageArea                                   8.154e-04
## X1stFlrSF:GrLivArea:GarageArea                                     6.488e-04
## OverallQual:GarageCars:GarageArea                                  3.415e+01
## TotalBsmtSF:GarageCars:GarageArea                                  3.060e-01
## X1stFlrSF:GarageCars:GarageArea                                    3.596e-01
## GrLivArea:GarageCars:GarageArea                                    2.125e-01
## OverallQual:TotalBsmtSF:X1stFlrSF:GrLivArea                        2.282e-05
## OverallQual:TotalBsmtSF:X1stFlrSF:GarageCars                       3.170e-02
## OverallQual:TotalBsmtSF:GrLivArea:GarageCars                       2.826e-02
## OverallQual:X1stFlrSF:GrLivArea:GarageCars                         2.535e-02
## TotalBsmtSF:X1stFlrSF:GrLivArea:GarageCars                         1.274e-04
## OverallQual:TotalBsmtSF:X1stFlrSF:GarageArea                       1.070e-04
## OverallQual:TotalBsmtSF:GrLivArea:GarageArea                       1.005e-04
## OverallQual:X1stFlrSF:GrLivArea:GarageArea                         8.411e-05
## TotalBsmtSF:X1stFlrSF:GrLivArea:GarageArea                         5.127e-07
## OverallQual:TotalBsmtSF:GarageCars:GarageArea                      4.129e-02
## OverallQual:X1stFlrSF:GarageCars:GarageArea                        5.025e-02
## TotalBsmtSF:X1stFlrSF:GarageCars:GarageArea                        2.276e-04
## OverallQual:GrLivArea:GarageCars:GarageArea                        2.651e-02
## TotalBsmtSF:GrLivArea:GarageCars:GarageArea                        2.382e-04
## X1stFlrSF:GrLivArea:GarageCars:GarageArea                          2.335e-04
## OverallQual:TotalBsmtSF:X1stFlrSF:GrLivArea:GarageCars             1.694e-05
## OverallQual:TotalBsmtSF:X1stFlrSF:GrLivArea:GarageArea             4.994e-08
## OverallQual:TotalBsmtSF:X1stFlrSF:GarageCars:GarageArea            2.865e-05
## OverallQual:TotalBsmtSF:GrLivArea:GarageCars:GarageArea            2.969e-05
## OverallQual:X1stFlrSF:GrLivArea:GarageCars:GarageArea              3.184e-05
## TotalBsmtSF:X1stFlrSF:GrLivArea:GarageCars:GarageArea              1.385e-07
## OverallQual:TotalBsmtSF:X1stFlrSF:GrLivArea:GarageCars:GarageArea  1.587e-08
##                                                                   t value
## (Intercept)                                                        -0.603
## OverallQual                                                         0.483
## TotalBsmtSF                                                        -1.346
## X1stFlrSF                                                           0.206
## GrLivArea                                                           1.694
## GarageCars                                                          1.004
## GarageArea                                                          0.444
## OverallQual:TotalBsmtSF                                             1.373
## OverallQual:X1stFlrSF                                               0.128
## TotalBsmtSF:X1stFlrSF                                               1.853
## OverallQual:GrLivArea                                              -1.475
## TotalBsmtSF:GrLivArea                                               0.273
## X1stFlrSF:GrLivArea                                                -0.916
## OverallQual:GarageCars                                             -0.292
## TotalBsmtSF:GarageCars                                             -0.707
## X1stFlrSF:GarageCars                                                0.029
## GrLivArea:GarageCars                                               -2.393
## OverallQual:GarageArea                                             -1.676
## TotalBsmtSF:GarageArea                                              0.535
## X1stFlrSF:GarageArea                                                0.055
## GrLivArea:GarageArea                                               -0.447
## GarageCars:GarageArea                                              -3.618
## OverallQual:TotalBsmtSF:X1stFlrSF                                  -1.794
## OverallQual:TotalBsmtSF:GrLivArea                                  -0.362
## OverallQual:X1stFlrSF:GrLivArea                                     0.806
## TotalBsmtSF:X1stFlrSF:GrLivArea                                    -0.819
## OverallQual:TotalBsmtSF:GarageCars                                 -0.301
## OverallQual:X1stFlrSF:GarageCars                                   -0.858
## TotalBsmtSF:X1stFlrSF:GarageCars                                   -0.073
## OverallQual:GrLivArea:GarageCars                                    2.138
## TotalBsmtSF:GrLivArea:GarageCars                                    2.217
## X1stFlrSF:GrLivArea:GarageCars                                      1.051
## OverallQual:TotalBsmtSF:GarageArea                                  0.277
## OverallQual:X1stFlrSF:GarageArea                                    0.805
## TotalBsmtSF:X1stFlrSF:GarageArea                                   -1.287
## OverallQual:GrLivArea:GarageArea                                    1.786
## TotalBsmtSF:GrLivArea:GarageArea                                   -0.833
## X1stFlrSF:GrLivArea:GarageArea                                      0.168
## OverallQual:GarageCars:GarageArea                                   5.173
## TotalBsmtSF:GarageCars:GarageArea                                   2.127
## X1stFlrSF:GarageCars:GarageArea                                     0.651
## GrLivArea:GarageCars:GarageArea                                     4.076
## OverallQual:TotalBsmtSF:X1stFlrSF:GrLivArea                         1.013
## OverallQual:TotalBsmtSF:X1stFlrSF:GarageCars                        1.440
## OverallQual:TotalBsmtSF:GrLivArea:GarageCars                       -1.636
## OverallQual:X1stFlrSF:GrLivArea:GarageCars                         -0.410
## TotalBsmtSF:X1stFlrSF:GrLivArea:GarageCars                         -1.551
## OverallQual:TotalBsmtSF:X1stFlrSF:GarageArea                        0.630
## OverallQual:TotalBsmtSF:GrLivArea:GarageArea                        0.365
## OverallQual:X1stFlrSF:GrLivArea:GarageArea                         -1.427
## TotalBsmtSF:X1stFlrSF:GrLivArea:GarageArea                          1.498
## OverallQual:TotalBsmtSF:GarageCars:GarageArea                      -2.404
## OverallQual:X1stFlrSF:GarageCars:GarageArea                        -1.019
## TotalBsmtSF:X1stFlrSF:GarageCars:GarageArea                        -0.011
## OverallQual:GrLivArea:GarageCars:GarageArea                        -5.807
## TotalBsmtSF:GrLivArea:GarageCars:GarageArea                        -2.727
## X1stFlrSF:GrLivArea:GarageCars:GarageArea                          -1.535
## OverallQual:TotalBsmtSF:X1stFlrSF:GrLivArea:GarageCars              0.501
## OverallQual:TotalBsmtSF:X1stFlrSF:GrLivArea:GarageArea             -1.129
## OverallQual:TotalBsmtSF:X1stFlrSF:GarageCars:GarageArea            -0.294
## OverallQual:TotalBsmtSF:GrLivArea:GarageCars:GarageArea             3.230
## OverallQual:X1stFlrSF:GrLivArea:GarageCars:GarageArea               2.187
## TotalBsmtSF:X1stFlrSF:GrLivArea:GarageCars:GarageArea               1.352
## OverallQual:TotalBsmtSF:X1stFlrSF:GrLivArea:GarageCars:GarageArea  -1.530
##                                                                   Pr(>|t|)
## (Intercept)                                                       0.546754
## OverallQual                                                       0.629180
## TotalBsmtSF                                                       0.178682
## X1stFlrSF                                                         0.836987
## GrLivArea                                                         0.090518
## GarageCars                                                        0.315714
## GarageArea                                                        0.657014
## OverallQual:TotalBsmtSF                                           0.170017
## OverallQual:X1stFlrSF                                             0.897906
## TotalBsmtSF:X1stFlrSF                                             0.064088
## OverallQual:GrLivArea                                             0.140359
## TotalBsmtSF:GrLivArea                                             0.784553
## X1stFlrSF:GrLivArea                                               0.360082
## OverallQual:GarageCars                                            0.769994
## TotalBsmtSF:GarageCars                                            0.479761
## X1stFlrSF:GarageCars                                              0.976888
## GrLivArea:GarageCars                                              0.016852
## OverallQual:GarageArea                                            0.093994
## TotalBsmtSF:GarageArea                                            0.592945
## X1stFlrSF:GarageArea                                              0.955781
## GrLivArea:GarageArea                                              0.655185
## GarageCars:GarageArea                                             0.000307
## OverallQual:TotalBsmtSF:X1stFlrSF                                 0.073098
## OverallQual:TotalBsmtSF:GrLivArea                                 0.717046
## OverallQual:X1stFlrSF:GrLivArea                                   0.420642
## TotalBsmtSF:X1stFlrSF:GrLivArea                                   0.413045
## OverallQual:TotalBsmtSF:GarageCars                                0.763358
## OverallQual:X1stFlrSF:GarageCars                                  0.391309
## TotalBsmtSF:X1stFlrSF:GarageCars                                  0.942204
## OverallQual:GrLivArea:GarageCars                                  0.032687
## TotalBsmtSF:GrLivArea:GarageCars                                  0.026776
## X1stFlrSF:GrLivArea:GarageCars                                    0.293592
## OverallQual:TotalBsmtSF:GarageArea                                0.781589
## OverallQual:X1stFlrSF:GarageArea                                  0.420858
## TotalBsmtSF:X1stFlrSF:GarageArea                                  0.198223
## OverallQual:GrLivArea:GarageArea                                  0.074275
## TotalBsmtSF:GrLivArea:GarageArea                                  0.405027
## X1stFlrSF:GrLivArea:GarageArea                                    0.866970
## OverallQual:GarageCars:GarageArea                                 2.64e-07
## TotalBsmtSF:GarageCars:GarageArea                                 0.033594
## X1stFlrSF:GarageCars:GarageArea                                   0.515021
## GrLivArea:GarageCars:GarageArea                                   4.84e-05
## OverallQual:TotalBsmtSF:X1stFlrSF:GrLivArea                       0.311379
## OverallQual:TotalBsmtSF:X1stFlrSF:GarageCars                      0.150054
## OverallQual:TotalBsmtSF:GrLivArea:GarageCars                      0.102026
## OverallQual:X1stFlrSF:GrLivArea:GarageCars                        0.681981
## TotalBsmtSF:X1stFlrSF:GrLivArea:GarageCars                        0.121094
## OverallQual:TotalBsmtSF:X1stFlrSF:GarageArea                      0.528578
## OverallQual:TotalBsmtSF:GrLivArea:GarageArea                      0.714879
## OverallQual:X1stFlrSF:GrLivArea:GarageArea                        0.153832
## TotalBsmtSF:X1stFlrSF:GrLivArea:GarageArea                        0.134398
## OverallQual:TotalBsmtSF:GarageCars:GarageArea                     0.016348
## OverallQual:X1stFlrSF:GarageCars:GarageArea                       0.308527
## TotalBsmtSF:X1stFlrSF:GarageCars:GarageArea                       0.991244
## OverallQual:GrLivArea:GarageCars:GarageArea                       7.87e-09
## TotalBsmtSF:GrLivArea:GarageCars:GarageArea                       0.006463
## X1stFlrSF:GrLivArea:GarageCars:GarageArea                         0.125021
## OverallQual:TotalBsmtSF:X1stFlrSF:GrLivArea:GarageCars            0.616314
## OverallQual:TotalBsmtSF:X1stFlrSF:GrLivArea:GarageArea            0.258899
## OverallQual:TotalBsmtSF:X1stFlrSF:GarageCars:GarageArea           0.768703
## OverallQual:TotalBsmtSF:GrLivArea:GarageCars:GarageArea           0.001268
## OverallQual:X1stFlrSF:GrLivArea:GarageCars:GarageArea             0.028937
## TotalBsmtSF:X1stFlrSF:GrLivArea:GarageCars:GarageArea             0.176739
## OverallQual:TotalBsmtSF:X1stFlrSF:GrLivArea:GarageCars:GarageArea 0.126125
##                                                                      
## (Intercept)                                                          
## OverallQual                                                          
## TotalBsmtSF                                                          
## X1stFlrSF                                                            
## GrLivArea                                                         .  
## GarageCars                                                           
## GarageArea                                                           
## OverallQual:TotalBsmtSF                                              
## OverallQual:X1stFlrSF                                                
## TotalBsmtSF:X1stFlrSF                                             .  
## OverallQual:GrLivArea                                                
## TotalBsmtSF:GrLivArea                                                
## X1stFlrSF:GrLivArea                                                  
## OverallQual:GarageCars                                               
## TotalBsmtSF:GarageCars                                               
## X1stFlrSF:GarageCars                                                 
## GrLivArea:GarageCars                                              *  
## OverallQual:GarageArea                                            .  
## TotalBsmtSF:GarageArea                                               
## X1stFlrSF:GarageArea                                                 
## GrLivArea:GarageArea                                                 
## GarageCars:GarageArea                                             ***
## OverallQual:TotalBsmtSF:X1stFlrSF                                 .  
## OverallQual:TotalBsmtSF:GrLivArea                                    
## OverallQual:X1stFlrSF:GrLivArea                                      
## TotalBsmtSF:X1stFlrSF:GrLivArea                                      
## OverallQual:TotalBsmtSF:GarageCars                                   
## OverallQual:X1stFlrSF:GarageCars                                     
## TotalBsmtSF:X1stFlrSF:GarageCars                                     
## OverallQual:GrLivArea:GarageCars                                  *  
## TotalBsmtSF:GrLivArea:GarageCars                                  *  
## X1stFlrSF:GrLivArea:GarageCars                                       
## OverallQual:TotalBsmtSF:GarageArea                                   
## OverallQual:X1stFlrSF:GarageArea                                     
## TotalBsmtSF:X1stFlrSF:GarageArea                                     
## OverallQual:GrLivArea:GarageArea                                  .  
## TotalBsmtSF:GrLivArea:GarageArea                                     
## X1stFlrSF:GrLivArea:GarageArea                                       
## OverallQual:GarageCars:GarageArea                                 ***
## TotalBsmtSF:GarageCars:GarageArea                                 *  
## X1stFlrSF:GarageCars:GarageArea                                      
## GrLivArea:GarageCars:GarageArea                                   ***
## OverallQual:TotalBsmtSF:X1stFlrSF:GrLivArea                          
## OverallQual:TotalBsmtSF:X1stFlrSF:GarageCars                         
## OverallQual:TotalBsmtSF:GrLivArea:GarageCars                         
## OverallQual:X1stFlrSF:GrLivArea:GarageCars                           
## TotalBsmtSF:X1stFlrSF:GrLivArea:GarageCars                           
## OverallQual:TotalBsmtSF:X1stFlrSF:GarageArea                         
## OverallQual:TotalBsmtSF:GrLivArea:GarageArea                         
## OverallQual:X1stFlrSF:GrLivArea:GarageArea                           
## TotalBsmtSF:X1stFlrSF:GrLivArea:GarageArea                           
## OverallQual:TotalBsmtSF:GarageCars:GarageArea                     *  
## OverallQual:X1stFlrSF:GarageCars:GarageArea                          
## TotalBsmtSF:X1stFlrSF:GarageCars:GarageArea                          
## OverallQual:GrLivArea:GarageCars:GarageArea                       ***
## TotalBsmtSF:GrLivArea:GarageCars:GarageArea                       ** 
## X1stFlrSF:GrLivArea:GarageCars:GarageArea                            
## OverallQual:TotalBsmtSF:X1stFlrSF:GrLivArea:GarageCars               
## OverallQual:TotalBsmtSF:X1stFlrSF:GrLivArea:GarageArea               
## OverallQual:TotalBsmtSF:X1stFlrSF:GarageCars:GarageArea              
## OverallQual:TotalBsmtSF:GrLivArea:GarageCars:GarageArea           ** 
## OverallQual:X1stFlrSF:GrLivArea:GarageCars:GarageArea             *  
## TotalBsmtSF:X1stFlrSF:GrLivArea:GarageCars:GarageArea                
## OverallQual:TotalBsmtSF:X1stFlrSF:GrLivArea:GarageCars:GarageArea    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 27840 on 1396 degrees of freedom
## Multiple R-squared:  0.8825, Adjusted R-squared:  0.8772 
## F-statistic: 166.5 on 63 and 1396 DF,  p-value: < 2.2e-16

#Graphical Analysis of Fourth model
layout(matrix(c(1,2,3,4),2,2)) # optional 4 graphs/page 
plot(Fifth_mod)

## Warning in sqrt(crit * p * (1 - hh)/hh): NaNs produced

## Warning in sqrt(crit * p * (1 - hh)/hh): NaNs produced

Residual standard error: 27840 on 1396 degrees of freedom

Multiple R-squared: 0.8825, Adjusted R-squared: 0.8772

F-statistic: 166.5 on 63 and 1396 DF, p-value: < 2.2e-16

Discussion on 5th submission:

The multiple R-squared of 88.25 > 70%. The Adjusted R-squared is 87.72 and higher the better. The F-statistic is 166.5 and higher the better. The p-value < 0.05.

Compiled submission results:

First iteration: (All variables)

Second iteration: (#Second variation using variables where p-value < 0.05)

Third iteration: (Using only variables where the variable’s p-value < 0.001 and correlation test value > 0.50)

Fourth iteration: (Fourth variation using variables where p-value < 0.001 and correlation > 0.50; Rather than add the numeric variables, we will multiply them)

Fifth iteration: (Fifth variation using variables where p-value < 0.001 and correlation > 0.60; Rather than add the numeric variables, we will multiply them)

Final iteration

#For the Sixth variation, we will narrow down the variables based on p-value and correlation test result value > 0.70

#https://www.statisticssolutions.com/pearsons-correlation-coefficient/

#Perfect: If the value is near ± 1, then it said to be a perfect correlation: as one variable increases, the other variable tends to also increase (if positive) or decrease (if negative).
#High degree: If the coefficient value lies between ± 0.50 and ± 1, then it is said to be a strong correlation.
#Moderate degree: If the value lies between ± 0.30 and ± 0.49, then it is said to be a medium correlation.
#Low degree: When the value lies below + .29, then it is said to be a small correlation.
#No correlation: When the value is zero.

#Using only variables where the variable's p-value < 0.001 and correlation test value > 0.70

for (i in 2:length(sc.data)) {
  if(is.numeric(sc.data[,i])){
  a <- cor.test(sc.data$SalePrice, sc.data[,i])
  #print(paste(colnames(sc.data)[i], " est:", a$estimate, " p=value:", a$p.value))
  if (a$p.value < 0.001 && a$estimate > 0.70) {
    print(paste(colnames(sc.data)[i], " cor:", a$estimate, " p=value:", a$p.value))
  }  
  }
}

## [1] "OverallQual  cor: 0.790981600583805  p=value: 2.18567526799377e-313"
## [1] "GrLivArea  cor: 0.708624477612652  p=value: 4.51803364677756e-223"
## [1] "SalePrice  cor: 1  p=value: 0"

#Sixth variation using variables where p-value < 0.001 and correlation > 0.70; Rather than add the numeric variables, we will multiply them and make one of them quadratic
set.seed(100)  # setting seed to reproduce results of random sampling
trainingRowIndex <- sample(1:nrow(sc.data), 0.8*nrow(sc.data))  # row indices for training data
trainingData <- sc.data[trainingRowIndex, ]  # model training data
testData  <- sc.data[-trainingRowIndex, ]    # test data

Sixth_mod <- lm((sc.data$SalePrice) ~ OverallQual * GrLivArea   , data = sc.data)

summary(Sixth_mod)

## 
## Call:
## lm(formula = (sc.data$SalePrice) ~ OverallQual * GrLivArea, data = sc.data)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -527522  -20527      30   17832  271107 
## 
## Coefficients:
##                        Estimate Std. Error t value Pr(>|t|)    
## (Intercept)           10031.529  12099.368   0.829  0.40719    
## OverallQual           15409.364   1948.165   7.910 5.06e-15 ***
## GrLivArea               -23.428      8.103  -2.891  0.00389 ** 
## OverallQual:GrLivArea    11.620      1.128  10.305  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 41050 on 1456 degrees of freedom
## Multiple R-squared:  0.7336, Adjusted R-squared:  0.7331 
## F-statistic:  1337 on 3 and 1456 DF,  p-value: < 2.2e-16

#Graphical Analysis of Fourth model
layout(matrix(c(1,2,3,4),2,2)) # optional 4 graphs/page 
plot(Sixth_mod)

Residual standard error: 41050 on 1456 degrees of freedom

Multiple R-squared: 0.7336, Adjusted R-squared: 0.7331

F-statistic: 1337 on 3 and 1456 DF, p-value: < 2.2e-16

Discussion on 6th submission:

The multiple R-squared of 73.36 > 70%. The Adjusted R-squared is 73.31 and higher the better. The F-statistic is 1337 and higher the better. The p-value < 0.05.

kaggle_test <- read.csv("c:\\Users\\ajaya\\Documents\\AJAY\\Computational Math\\Final\\test.csv")

SalePrice <- predict(Sixth_mod, newdata = kaggle_test, type="response")

kagglefile <- cbind.data.frame(kaggle_test$Id, SalePrice)


write.csv(kagglefile,'C:\\Users\\ajaya\\Documents\\AJAY\\Computational Math\\Final\\ajaj6.csv',row.names = F)

Result from Final variation ()

Kaggle score: 0.21936 User name: ajayarora35

AArora_Final

Ajay Arora

May 9, 2018

Data fields

Here’s a brief version of what you’ll find in the data description file.

Choosing Variables:

X = OverallQual

Y = Sales price

Probability:

1st quartile of “X”: x = 5.0

1st quartile of “Y”: y = 129975

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

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

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

Count Table (Professor, I have 2 count tables – the initial question and the amended question)

P(AB)=P(A)P(B) ?

Chi-Square

Descriptive and Inferential Statistics

Univariate Statistics

Scatterplot of X and Y

Correlation Matrix for any 3 quantitative variables in dataset.

Linear Algebra and Correlation

Precision Matrix Detailed Steps (Rounded to 4 decimal places)

Precision matrix or inverse (verify with R)

Calculus-Based Probability & Statistics.

Modeling

How to know if the model is best fit for your data?

Justisfication for the Fourth variation to multiply the variables versus adding

Compiled submission results:

Result from Final variation ()

Kaggle score: 0.21936 User name: ajayarora35