Final Peer Assignment
Tahir Hussain
March 26, 2017
0.0.0.0.1 Load Packages
library(dplyr)
library(devtools)
install_github("StatsWithR/statsr")
library(GGally)
library(statsr)
library(psych)
library(broom)
library(xtable)
library(ggplot2)
library(GGally)
library(psych)
library(dtplyr)
library(gridExtra)
library(tidyr)0.0.0.0.2 Introduction
Before building a model it is necessary to explore the structure dataset. The relationship between dependent and independent and interactions among independent variables must be expedited.For visualizing these characteristics of variables we have to create comparative tables and plots. The original ames housing database has been partioned into train,test and validation datasets. We will study training dataset in detail. It contains 23 nominal,23 ordinal,14 discrete and 20 continuous variables.
Data Preparation
Missing Values In ames_train: Slightly more than 5% of values in dataset are missing. They are in the order of: Pool.QC(997),Misc.Feature(971), Alley(933),Fence(798),Lot.Frontage(167),Garage and Basement related variables are below 5%. We will have to treat variables that have more than 5% missing values. Most of the predictors are categorical variables.
Selection criteria:
- “Normal” Sale.Condition only.
- Home prices lesser than $500k.
- Gr Liv Area(area) limiting to above less than 4000 sqrFt.
- Same potential variables for all three sub datasets.
- Convert categoritcal variables.
- Treatment of Missing Values.
- Treatment of Outliers.
Exploratory analysis is necessary before modeling. Outliers in data can distort prediction and effect the accuracy of model. For example two quantitative variables like Lot.Frontage and Garage Live area when plotted show outliers in scatterplots.We can find data distribution with histogram to confirm that it is normally distributed. A transformation will be required if it skewed.When all tidying and normalization is completed, a model can be attempted.
0.0.0.1 Part 1 - Exploratory Data Analysis
0.0.0.1.1 Load Training dataset-list missing values and plot them.
setwd("C:/Users/Tahir Hussain/Desktop/CapstoneProject")
load("C:/Users/Tahir Hussain/Desktop/CapstoneProject/ames_train.RData")
load("C:/Users/Tahir Hussain/Desktop/CapstoneProject/ames_test.RData")
load("C:/Users/Tahir Hussain/Desktop/CapstoneProject/ames_validation.RData")
sum(is.na(ames_train)) / (nrow(ames_train) *ncol(ames_train))# Missing values % ## [1] 0.05816049colSums(sapply(ames_train, is.na))#Missing values by variable## PID area price MS.SubClass
## 0 0 0 0
## MS.Zoning Lot.Frontage Lot.Area Street
## 0 167 0 0
## Alley Lot.Shape Land.Contour Utilities
## 933 0 0 0
## Lot.Config Land.Slope Neighborhood Condition.1
## 0 0 0 0
## Condition.2 Bldg.Type House.Style Overall.Qual
## 0 0 0 0
## Overall.Cond Year.Built Year.Remod.Add Roof.Style
## 0 0 0 0
## Roof.Matl Exterior.1st Exterior.2nd Mas.Vnr.Type
## 0 0 0 0
## Mas.Vnr.Area Exter.Qual Exter.Cond Foundation
## 7 0 0 0
## Bsmt.Qual Bsmt.Cond Bsmt.Exposure BsmtFin.Type.1
## 21 21 21 21
## BsmtFin.SF.1 BsmtFin.Type.2 BsmtFin.SF.2 Bsmt.Unf.SF
## 1 21 1 1
## Total.Bsmt.SF Heating Heating.QC Central.Air
## 1 0 0 0
## Electrical X1st.Flr.SF X2nd.Flr.SF Low.Qual.Fin.SF
## 0 0 0 0
## Bsmt.Full.Bath Bsmt.Half.Bath Full.Bath Half.Bath
## 1 1 0 0
## Bedroom.AbvGr Kitchen.AbvGr Kitchen.Qual TotRms.AbvGrd
## 0 0 0 0
## Functional Fireplaces Fireplace.Qu Garage.Type
## 0 0 491 46
## Garage.Yr.Blt Garage.Finish Garage.Cars Garage.Area
## 48 46 1 1
## Garage.Qual Garage.Cond Paved.Drive Wood.Deck.SF
## 47 47 0 0
## Open.Porch.SF Enclosed.Porch X3Ssn.Porch Screen.Porch
## 0 0 0 0
## Pool.Area Pool.QC Fence Misc.Feature
## 0 997 798 971
## Misc.Val Mo.Sold Yr.Sold Sale.Type
## 0 0 0 0
## Sale.Condition
## 00.0.0.1.2 Creating 3 Subsets by filtering Essential Variables
ames_train <- ames_train %>% filter(Sale.Condition == "Normal" & price < 500001 &
area < 4001)
vars <- names(ames_train) %in% c("price", "area", "MS.SubClass", "Lot.Area",
"Overall.Qual", "Overall.Cond", "Year.Built", "Year.Remod.Add", "Total.Bsmt.SF",
"Bsmt.Half.Bath", "Central.Air", "Bsmt.Full.Bath", "Half.Bath", "Full.Bath",
"Bedroom.AbvGr", "Kitchen.AbvGr", "TotRms.AbvGrd", "Fireplaces", "Garage.Cars",
"Garage.Area", "X1st.Flr.SF", "X2nd.Flr.SF", "Wood.Deck.SF", "Open.Porch.SF",
"Enclosed.Porch", "Screen.Porch", "Pool.Area", "Bsmt.Full.Bath")
train <- ames_train[vars]
ames_test <- ames_test %>% filter(Sale.Condition == "Normal" & price < 500001 &
area < 4001)
vars <- names(ames_test) %in% c("price", "area", "MS.SubClass", "Lot.Area",
"Overall.Qual", "Overall.Cond", "Year.Built", "Year.Remod.Add", "Total.Bsmt.SF",
"Bsmt.Half.Bath", "Central.Air", "Bsmt.Full.Bath", "Half.Bath", "Full.Bath",
"Bedroom.AbvGr", "Kitchen.AbvGr", "TotRms.AbvGrd", "Fireplaces", "Garage.Cars",
"Garage.Area", "X1st.Flr.SF", "X2nd.Flr.SF", "Wood.Deck.SF", "Open.Porch.SF",
"Enclosed.Porch", "Screen.Porch", "Pool.Area", "Bsmt.Full.Bath")
test <- ames_test[vars]
ames_validation <- ames_validation %>% filter(Sale.Condition == "Normal" & price <
500001 & area < 4001)
vars <- names(ames_validation) %in% c("price", "area", "MS.SubClass", "Lot.Area",
"Overall.Qual", "Overall.Cond", "Year.Built", "Year.Remod.Add", "Total.Bsmt.SF",
"Bsmt.Half.Bath", "Central.Air", "Bsmt.Full.Bath", "Half.Bath", "Full.Bath",
"Bedroom.AbvGr", "Kitchen.AbvGr", "TotRms.AbvGrd", "Fireplaces", "Garage.Cars",
"Garage.Area", "X1st.Flr.SF", "X2nd.Flr.SF", "Wood.Deck.SF", "Open.Porch.SF",
"Enclosed.Porch", "Screen.Porch", "Pool.Area", "Bsmt.Full.Bath")
validation <- ames_validation[vars]0.0.0.1.3 Inferencial Statistics
head(describe(ames_train)) ## vars n mean sd median trimmed
## PID 1 832 714292099.48 188938380.01 535455575 711894738.22
## area 2 832 1446.62 486.67 1382 1402.46
## price 3 832 173656.22 69586.56 155000 165322.36
## MS.SubClass 4 832 57.90 43.36 50 50.14
## MS.Zoning* 5 832 6.00 0.80 6 6.07
## Lot.Frontage 6 676 68.49 24.13 69 67.51
## mad min max range skew kurtosis
## PID 12374565.38 526302030 1007100110 480798080 0.06 -1.99
## area 472.21 334 3672 3338 0.87 0.91
## price 48925.80 39300 500000 460700 1.34 2.31
## MS.SubClass 44.48 20 190 170 1.32 1.18
## MS.Zoning* 0.00 2 7 5 -2.65 9.30
## Lot.Frontage 16.31 21 313 292 2.03 16.54
## se
## PID 6550259.78
## area 16.87
## price 2412.48
## MS.SubClass 1.50
## MS.Zoning* 0.03
## Lot.Frontage 0.93tail(describe(ames_train))## vars n mean sd median trimmed mad min max
## Misc.Feature* 76 28 3.86 0.59 4 3.96 0.00 2 5
## Misc.Val 77 832 53.25 611.82 0 0.00 0.00 0 15500
## Mo.Sold 78 832 6.16 2.66 6 6.08 2.97 1 12
## Yr.Sold 79 832 2007.83 1.29 2008 2007.79 1.48 2006 2010
## Sale.Type* 80 832 9.68 1.54 10 10.00 0.00 1 10
## Sale.Condition* 81 832 5.00 0.00 5 5.00 0.00 5 5
## range skew kurtosis se
## Misc.Feature* 3 -2.06 4.63 0.11
## Misc.Val 15500 21.04 501.26 21.21
## Mo.Sold 11 0.25 -0.28 0.09
## Yr.Sold 4 0.07 -1.13 0.04
## Sale.Type* 9 -4.86 22.48 0.05
## Sale.Condition* 0 NaN NaN 0.00names(ames_train)## [1] "PID" "area" "price"
## [4] "MS.SubClass" "MS.Zoning" "Lot.Frontage"
## [7] "Lot.Area" "Street" "Alley"
## [10] "Lot.Shape" "Land.Contour" "Utilities"
## [13] "Lot.Config" "Land.Slope" "Neighborhood"
## [16] "Condition.1" "Condition.2" "Bldg.Type"
## [19] "House.Style" "Overall.Qual" "Overall.Cond"
## [22] "Year.Built" "Year.Remod.Add" "Roof.Style"
## [25] "Roof.Matl" "Exterior.1st" "Exterior.2nd"
## [28] "Mas.Vnr.Type" "Mas.Vnr.Area" "Exter.Qual"
## [31] "Exter.Cond" "Foundation" "Bsmt.Qual"
## [34] "Bsmt.Cond" "Bsmt.Exposure" "BsmtFin.Type.1"
## [37] "BsmtFin.SF.1" "BsmtFin.Type.2" "BsmtFin.SF.2"
## [40] "Bsmt.Unf.SF" "Total.Bsmt.SF" "Heating"
## [43] "Heating.QC" "Central.Air" "Electrical"
## [46] "X1st.Flr.SF" "X2nd.Flr.SF" "Low.Qual.Fin.SF"
## [49] "Bsmt.Full.Bath" "Bsmt.Half.Bath" "Full.Bath"
## [52] "Half.Bath" "Bedroom.AbvGr" "Kitchen.AbvGr"
## [55] "Kitchen.Qual" "TotRms.AbvGrd" "Functional"
## [58] "Fireplaces" "Fireplace.Qu" "Garage.Type"
## [61] "Garage.Yr.Blt" "Garage.Finish" "Garage.Cars"
## [64] "Garage.Area" "Garage.Qual" "Garage.Cond"
## [67] "Paved.Drive" "Wood.Deck.SF" "Open.Porch.SF"
## [70] "Enclosed.Porch" "X3Ssn.Porch" "Screen.Porch"
## [73] "Pool.Area" "Pool.QC" "Fence"
## [76] "Misc.Feature" "Misc.Val" "Mo.Sold"
## [79] "Yr.Sold" "Sale.Type" "Sale.Condition"dim(train) ## [1] 832 27dim(test) ## [1] 813 27dim(validation) ## [1] 762 270.0.0.1.4 Missing Values of Full subset
plot_Missing <- function(data_in, title = NULL){
temp_df <- as.data.frame(ifelse(is.na(data_in), 0, 1))
temp_df <- temp_df[,order(colSums(temp_df))]
data_temp <- expand.grid(list(x = 1:nrow(temp_df), y = colnames(temp_df)))
data_temp$m <- as.vector(as.matrix(temp_df))
data_temp <- data.frame(x = unlist(data_temp$x), y = unlist(data_temp$y), m = unlist(data_temp$m))
ggplot(data_temp) + geom_tile(aes(x=x, y=y, fill=factor(m))) + scale_fill_manual(values=c("white", "blue"), name="Missing\n(0=Yes, 1=No)") + theme_light() + ylab("Variables") + xlab("observ.No") + ggtitle("Missing Values")
}
plot_Missing(ames_train[,colSums(is.na(ames_train)) >0]) 
0.0.0.1.5 Visualizing Sales Price before and after transformation
sp1 <-ggplot(data = train, aes(x = (price), y = ..density..)) +
geom_histogram(fill = "green", colour="black", size = .2, bins = 30) +
ggtitle("Distribution of Price variabe w/out log transform ") + xlab("Price$") + geom_density()
sp2<- ggplot(data = train, aes(x =(log (price)), y = ..density..)) +
geom_histogram(fill = "blue", colour="black", size = .2, bins = 30) +
ggtitle("Distribution of Log Price") +
xlab("Log Price$ ") + geom_density()
grid.arrange(sp1,sp2) 
0.0.0.1.6 Visualizing Distribution of some important independent variables
p1 <- ggplot(data = train, aes(x = (area), y = ..density..)) +
geom_histogram(fill = "blue", colour="black", size = .2, bins = 30) +
ggtitle("Distribution variable Area") +
xlab("Area") +
geom_density()
p2 <-ggplot(data = train, aes(x = (Lot.Area), y = ..density..)) +
geom_histogram(fill = "blue", colour="black", size = .2, bins = 30) +
ggtitle("Distribution Lot Area variable ") + xlab("Lot.Area") +
geom_density()
p3 <- ggplot(data = train, aes(x = (Year.Built), y = ..density..)) +
geom_histogram(fill = "red", colour="black", size = .2, bins = 30) +
ggtitle("Distribution Age ") +
xlab("Year Built")+ geom_density()
p4 <- ggplot(data = train, aes(x = (Bedroom.AbvGr), y = ..density..)) +
geom_histogram(fill = "green", colour="black", size = .2, bins = 30) +
ggtitle("Bedrooms above ground ") +
xlab("Number of rooms") +
geom_density()
p5 <-ggplot(data = train, aes(x = (Full.Bath), y = ..density..)) +
geom_histogram(fill = "green", colour="black", size = .2, bins = 30) +
ggtitle("Distribution of variable Full Bath ") +
xlab("Number of Full Baths") + geom_density()
p6 <-ggplot(data =train, aes(x = (Half.Bath), y = ..density..)) +
geom_histogram(fill = "green", colour="black", size = .2, bins = 30) +
ggtitle("Distribution of variable Half Bath ") +
xlab("Number of Half Baths") + geom_density()
p7 <-ggplot(data = train, aes(x = (Overall.Qual), y = ..density..)) +
geom_histogram(fill = "green", colour="black", size = .2, bins = 30) +
ggtitle("Distribution of variable Overall Quality ") +
xlab("Overall Quality") + geom_density()
p8 <-ggplot(data = train, aes(x = (Overall.Cond), y = ..density..)) +
geom_histogram(fill = "green", colour="black", size = .2, bins = 30) +
ggtitle("Distribution of variable Overall Condition ") +
xlab("Overall condition") + geom_density()
grid.arrange(p1,p2,p3,p4,p6,p6,p7,p8) 
0.0.0.1.7 Various other Categorical Features
par(mfrow=c(3,2))
boxplot(price ~ as.factor(ames_train$Alley), ames_train, xlab = "Alley", ylab = "Sale Price")
boxplot(price ~ as.factor(ames_train$Garage.Finish),ames_train, xlab = "GarageFinish", ylab = "Sale Price")
boxplot(price ~ as.factor(ames_train$Foundation),ames_train, xlab = "Foundation", ylab = "Sale Price")
boxplot(price ~ as.factor(ames_train$Garage.Type), ames_train, xlab = "GarageType", ylab = "Sale Price")
boxplot(price ~ as.factor(ames_train$Heating.QC), ames_train, xlab = "HeatingQC", ylab = "Sale Price")
boxplot(price ~ as.factor(ames_train$BsmtFin.Type.1), ames_train, xlab = "BsmtFinType1", ylab = "Sale Price")
0.0.0.1.8 Ploting Correlation Matrix -Numeric Variables
library(reshape)
library(data.table)
library(corrplot)
require(ggplot2)
require(GGally)
data(train, package="reshape")## Warning in data(train, package = "reshape"): data set 'train' not foundggpairs(data=train, # data.frame with variables
columns=1:8, # columns to plot, default to all.
title="Density Data", # title of the plot
colour = "sex"
) # aesthetics, ggplot2 style## Warning in warn_if_args_exist(list(...)): Extra arguments: "colour" are
## being ignored. If these are meant to be aesthetics, submit them using the
## 'mapping' variable within ggpairs with ggplot2::aes or ggplot2::aes_string.
sapply(train, class)## area price MS.SubClass Lot.Area Overall.Qual
## "integer" "integer" "integer" "integer" "integer"
## Overall.Cond Year.Built Year.Remod.Add Total.Bsmt.SF Central.Air
## "integer" "integer" "integer" "integer" "factor"
## X1st.Flr.SF X2nd.Flr.SF Bsmt.Full.Bath Bsmt.Half.Bath Full.Bath
## "integer" "integer" "integer" "integer" "integer"
## Half.Bath Bedroom.AbvGr Kitchen.AbvGr TotRms.AbvGrd Fireplaces
## "integer" "integer" "integer" "integer" "integer"
## Garage.Cars Garage.Area Wood.Deck.SF Open.Porch.SF Enclosed.Porch
## "integer" "integer" "integer" "integer" "integer"
## Screen.Porch Pool.Area
## "integer" "integer"ggcorr(train[,-1],
label = TRUE,
label_alpha = TRUE)## Warning in ggcorr(train[, -1], label = TRUE, label_alpha = TRUE): data in
## column(s) 'Central.Air' are not numeric and were ignored
numeric<-sapply(train, is.numeric)
cormatrix<-cor(x=train[, numeric],use='complete')
topcor<-data.table(Features=rownames(cormatrix),cormatrix[,10])
setnames(topcor, names(topcor), c("Features","Correlation_with_price"))
topcor## Features Correlation_with_price
## 1: area 0.53873248
## 2: price 0.66246796
## 3: MS.SubClass -0.22913421
## 4: Lot.Area 0.27357052
## 5: Overall.Qual 0.46596631
## 6: Overall.Cond -0.16107736
## 7: Year.Built 0.29590951
## 8: Year.Remod.Add 0.25485123
## 9: Total.Bsmt.SF 0.79588401
## 10: X1st.Flr.SF 1.00000000
## 11: X2nd.Flr.SF -0.22372161
## 12: Bsmt.Full.Bath 0.27155104
## 13: Bsmt.Half.Bath -0.00173389
## 14: Full.Bath 0.38820268
## 15: Half.Bath -0.11660411
## 16: Bedroom.AbvGr 0.19214462
## 17: Kitchen.AbvGr 0.10699893
## 18: TotRms.AbvGrd 0.42125351
## 19: Fireplaces 0.41854555
## 20: Garage.Cars 0.46396043
## 21: Garage.Area 0.48340016
## 22: Wood.Deck.SF 0.28834383
## 23: Open.Porch.SF 0.21968645
## 24: Enclosed.Porch -0.09503726
## 25: Screen.Porch 0.05480161
## 26: Pool.Area 0.09789519
## Features Correlation_with_price0.0.0.2 Part 2 - Development and assessment of an initial model
0.0.0.2.1 Section 2.1 An Initial Model
1.Starting creating a simple,initial model based on the results of the exploratory data analysis. First variable selection can be done on the basis of corelation coefficients.
Highly correlated predictors are included(positive r),near zero predictors with negative r are not considered but moderately correlated predictors are included in models Predictors Ignored:BsmtFinSF2,LowOverallSF,KitchenAbvGr,EnclosedPorch X3SsnPorch,ScreenPorch,PoolArea,MiscVal.
2.A simple model depicts a simple regression model:The Formula for Multiple Regression: \[Y = a + b1 1 2 2 X + b X\] Y = A predicted value of Y (which is your dependent variable) a = The Y Intercept b1 = The change in Y for each 1 increment change in X1
b2 = The change in Y for each 1 increment change in X2 X =an X score (X is your Independent Variable) for which you are trying to predict
3.The variables selection depends on the resuots of explanatory data analysis. It ensures normal distribution,correlation criteria between candidate* predictors and response variables and variability. Extremes removed and essential transformation and missing values treated.
4.If I use OLS choosing only two response variables i.e ‘Neighborhood’ and ‘area’ and model them against ‘price’, we get R-Squared approx. 80% .The remaining variables of training dataset can give us around A total of 13% .*
5.We select model by using linear regression,stepwise regsubsets, k-folds paritition,Neural Network and leaps methods.The comparative study of criteria can be used for assessment of models.The regsubsets function (part of leaps library)performs best subset selection by identifying best model that contains a given number of predictors where ‘best’ is quantified using RSS. The summary ()command outputs the best set offset variables for each model size. R2 starts at 0.62 and ends a 0.91 for 14 variables.*
Our first choice for selecting variables is based on the coeficient r. The correlation coefficient r measures the strength and direction of a linear relationship between two variables -1 to less than zero negative and above zero to 1 positive relationship. zero(0) no relationship. I have given a coeficients list below for numeric variables. ** Candidate Training Models Model type and Tuning parameters 1.mod_lm - linear - None 2.mod_glm -generalized linear- None 3.mod_glmnet-regularized generalized linear- alpha, lambda 4.mod_tree random forest mtry 5.mod_elastic regularlized- lasso ridge fraction, lambda 6.mod_leap_back-linear regression with backward selection-nvmax 7.mod_reg_rf-regularized random forest mtry, coefReg 8.mod_svm-SVM with linear kernel-cost 9.mod_gbm -stochastic gradient boosting-n.trees, interaction.depth, shrinkage, n.minobsinnode 10.mod_bnet-bayesian neural networks- neurons 11.mod_k-10 - K-fold stepwise - Kn fold 12.mod_bas.lm-bayesian linear- prior
I will be using 1,6,10,11,12 for training initial and final models.
0.0.0.2.2 Initial Model Selection using corelations and Information criteria
0.0.0.2.3 Variable Importance:variable selection
0.0.0.2.4 find attributes that are highly corrected (ideally >0.75)
library(leaps)
library(mlbench)
library(caret)## Loading required package: latticelibrary(scales)##
## Attaching package: 'scales'## The following objects are masked from 'package:psych':
##
## alpha, rescalelibrary(corrplot)
train[train == ""] <- NA
set.seed(7)
correlationMatrix <- cor(train[,1:8])
print(correlationMatrix)## area price MS.SubClass Lot.Area
## area 1.00000000 0.74839629 0.08560739 0.21683410
## price 0.74839629 1.00000000 -0.06804648 0.25779063
## MS.SubClass 0.08560739 -0.06804648 1.00000000 -0.16917397
## Lot.Area 0.21683410 0.25779063 -0.16917397 1.00000000
## Overall.Qual 0.58928436 0.79977693 0.06579519 0.06532243
## Overall.Cond -0.11540037 -0.11941628 -0.13053616 -0.03696739
## Year.Built 0.24187375 0.56248112 0.08664430 -0.01141046
## Year.Remod.Add 0.36019575 0.54192677 0.06489436 0.02185116
## Overall.Qual Overall.Cond Year.Built Year.Remod.Add
## area 0.58928436 -0.11540037 0.24187375 0.36019575
## price 0.79977693 -0.11941628 0.56248112 0.54192677
## MS.SubClass 0.06579519 -0.13053616 0.08664430 0.06489436
## Lot.Area 0.06532243 -0.03696739 -0.01141046 0.02185116
## Overall.Qual 1.00000000 -0.12037181 0.56730637 0.53836547
## Overall.Cond -0.12037181 1.00000000 -0.37929442 0.04959354
## Year.Built 0.56730637 -0.37929442 1.00000000 0.57351727
## Year.Remod.Add 0.53836547 0.04959354 0.57351727 1.00000000highlyCorrelated <- findCorrelation(correlationMatrix, cutoff=0.5)
print(highlyCorrelated)## [1] 2 5 7cor(correlationMatrix)## area price MS.SubClass Lot.Area Overall.Qual
## area 1.0000000 0.8681130 -0.19286836 0.1444450 0.7635757
## price 0.8681130 1.0000000 -0.37655759 0.1215595 0.9317918
## MS.SubClass -0.1928684 -0.3765576 1.00000000 -0.5141325 -0.1890332
## Lot.Area 0.1444450 0.1215595 -0.51413246 1.0000000 -0.1257320
## Overall.Qual 0.7635757 0.9317918 -0.18903321 -0.1257320 1.0000000
## Overall.Cond -0.5090189 -0.5724203 -0.28897792 -0.1280124 -0.5846303
## Year.Built 0.4168642 0.7126395 -0.02409795 -0.2006869 0.7805055
## Year.Remod.Add 0.4071298 0.6557033 -0.19201971 -0.2917963 0.7119066
## Overall.Cond Year.Built Year.Remod.Add
## area -0.5090189 0.41686421 0.4071298
## price -0.5724203 0.71263953 0.6557033
## MS.SubClass -0.2889779 -0.02409795 -0.1920197
## Lot.Area -0.1280124 -0.20068687 -0.2917963
## Overall.Qual -0.5846303 0.78050554 0.7119066
## Overall.Cond 1.0000000 -0.76030465 -0.3616055
## Year.Built -0.7603046 1.00000000 0.7698006
## Year.Remod.Add -0.3616055 0.76980056 1.0000000corrplot(correlationMatrix)
control <- trainControl(method="repeatedcv", number=10, repeats=3)
model <- train(price~., data=train, method="lm", preProcess="scale", trControl=control)
importance <- varImp(model, scale=FALSE)
print(importance)## lm variable importance
##
## only 20 most important variables shown (out of 26)
##
## Overall
## Overall.Qual 13.211
## Year.Built 8.402
## Bedroom.AbvGr 7.106
## Total.Bsmt.SF 6.839
## Bsmt.Full.Bath 6.732
## Lot.Area 5.770
## Overall.Cond 5.357
## MS.SubClass 4.759
## Garage.Area 3.389
## Kitchen.AbvGr 3.377
## Pool.Area 2.950
## Fireplaces 2.913
## Year.Remod.Add 2.535
## X1st.Flr.SF 2.483
## X2nd.Flr.SF 2.222
## Central.AirY 2.171
## Wood.Deck.SF 1.948
## TotRms.AbvGrd 1.902
## area 1.844
## Full.Bath 1.388plot(importance)
numeric<-sapply(train, is.numeric)
cormatrix<-cor(x=train[, numeric],use='complete')
topcor<-data.table(Features=rownames(cormatrix),cormatrix[,10])
setnames(topcor, names(topcor), c("Features","Correlation_with_price"))
topcor## Features Correlation_with_price
## 1: area 0.53873248
## 2: price 0.66246796
## 3: MS.SubClass -0.22913421
## 4: Lot.Area 0.27357052
## 5: Overall.Qual 0.46596631
## 6: Overall.Cond -0.16107736
## 7: Year.Built 0.29590951
## 8: Year.Remod.Add 0.25485123
## 9: Total.Bsmt.SF 0.79588401
## 10: X1st.Flr.SF 1.00000000
## 11: X2nd.Flr.SF -0.22372161
## 12: Bsmt.Full.Bath 0.27155104
## 13: Bsmt.Half.Bath -0.00173389
## 14: Full.Bath 0.38820268
## 15: Half.Bath -0.11660411
## 16: Bedroom.AbvGr 0.19214462
## 17: Kitchen.AbvGr 0.10699893
## 18: TotRms.AbvGrd 0.42125351
## 19: Fireplaces 0.41854555
## 20: Garage.Cars 0.46396043
## 21: Garage.Area 0.48340016
## 22: Wood.Deck.SF 0.28834383
## 23: Open.Porch.SF 0.21968645
## 24: Enclosed.Porch -0.09503726
## 25: Screen.Porch 0.05480161
## 26: Pool.Area 0.09789519
## Features Correlation_with_pricepremodel<-regsubsets(log(price)~X1st.Flr.SF+Total.Bsmt.SF+Garage.Area+Fireplaces+TotRms.AbvGrd+Garage.Cars+Bsmt.Full.Bath+area+ Overall.Qual+ Lot.Area+Pool.Area+
Open.Porch.SF+Full.Bath+Year.Built +Bsmt.Half.Bath+ Kitchen.AbvGr+
Year.Remod.Add+Screen.Porch+Enclosed.Porch+Overall.Cond+ Bedroom.AbvGr+ MS.SubClass+Half.Bath+ X2nd.Flr.SF,data=ames_train,nvmax=20)
reg.full <-regsubsets(log(price)~.,data=train,nvmax=20)
reg.summary=summary(reg.full)
reg.summary## Subset selection object
## Call: regsubsets.formula(log(price) ~ ., data = train, nvmax = 20)
## 26 Variables (and intercept)
## Forced in Forced out
## area FALSE FALSE
## MS.SubClass FALSE FALSE
## Lot.Area FALSE FALSE
## Overall.Qual FALSE FALSE
## Overall.Cond FALSE FALSE
## Year.Built FALSE FALSE
## Year.Remod.Add FALSE FALSE
## Total.Bsmt.SF FALSE FALSE
## Central.AirY FALSE FALSE
## X1st.Flr.SF FALSE FALSE
## X2nd.Flr.SF FALSE FALSE
## Bsmt.Full.Bath FALSE FALSE
## Bsmt.Half.Bath FALSE FALSE
## Full.Bath FALSE FALSE
## Half.Bath FALSE FALSE
## Bedroom.AbvGr FALSE FALSE
## Kitchen.AbvGr FALSE FALSE
## TotRms.AbvGrd FALSE FALSE
## Fireplaces FALSE FALSE
## Garage.Cars FALSE FALSE
## Garage.Area FALSE FALSE
## Wood.Deck.SF FALSE FALSE
## Open.Porch.SF FALSE FALSE
## Enclosed.Porch FALSE FALSE
## Screen.Porch FALSE FALSE
## Pool.Area FALSE FALSE
## 1 subsets of each size up to 20
## Selection Algorithm: exhaustive
## area MS.SubClass Lot.Area Overall.Qual Overall.Cond Year.Built
## 1 ( 1 ) " " " " " " "*" " " " "
## 2 ( 1 ) "*" " " " " "*" " " " "
## 3 ( 1 ) "*" " " " " "*" " " " "
## 4 ( 1 ) "*" " " " " "*" " " "*"
## 5 ( 1 ) "*" " " " " "*" "*" "*"
## 6 ( 1 ) "*" " " " " "*" "*" "*"
## 7 ( 1 ) "*" " " "*" "*" "*" "*"
## 8 ( 1 ) "*" " " "*" "*" "*" "*"
## 9 ( 1 ) "*" " " "*" "*" "*" "*"
## 10 ( 1 ) "*" "*" "*" "*" "*" "*"
## 11 ( 1 ) "*" "*" "*" "*" "*" "*"
## 12 ( 1 ) "*" "*" "*" "*" "*" "*"
## 13 ( 1 ) "*" "*" "*" "*" "*" "*"
## 14 ( 1 ) "*" "*" "*" "*" "*" "*"
## 15 ( 1 ) "*" "*" "*" "*" "*" "*"
## 16 ( 1 ) "*" "*" "*" "*" "*" "*"
## 17 ( 1 ) "*" "*" "*" "*" "*" "*"
## 18 ( 1 ) "*" "*" "*" "*" "*" "*"
## 19 ( 1 ) "*" "*" "*" "*" "*" "*"
## 20 ( 1 ) "*" "*" "*" "*" "*" "*"
## Year.Remod.Add Total.Bsmt.SF Central.AirY X1st.Flr.SF
## 1 ( 1 ) " " " " " " " "
## 2 ( 1 ) " " " " " " " "
## 3 ( 1 ) " " "*" " " " "
## 4 ( 1 ) " " "*" " " " "
## 5 ( 1 ) " " "*" " " " "
## 6 ( 1 ) " " "*" " " " "
## 7 ( 1 ) " " "*" " " " "
## 8 ( 1 ) " " "*" " " " "
## 9 ( 1 ) " " "*" " " " "
## 10 ( 1 ) " " "*" " " " "
## 11 ( 1 ) "*" "*" " " " "
## 12 ( 1 ) "*" "*" "*" " "
## 13 ( 1 ) "*" "*" "*" " "
## 14 ( 1 ) "*" "*" "*" " "
## 15 ( 1 ) "*" "*" "*" " "
## 16 ( 1 ) "*" "*" "*" " "
## 17 ( 1 ) "*" "*" "*" " "
## 18 ( 1 ) "*" "*" "*" " "
## 19 ( 1 ) "*" "*" "*" " "
## 20 ( 1 ) "*" "*" "*" " "
## X2nd.Flr.SF Bsmt.Full.Bath Bsmt.Half.Bath Full.Bath Half.Bath
## 1 ( 1 ) " " " " " " " " " "
## 2 ( 1 ) " " " " " " " " " "
## 3 ( 1 ) " " " " " " " " " "
## 4 ( 1 ) " " " " " " " " " "
## 5 ( 1 ) " " " " " " " " " "
## 6 ( 1 ) " " "*" " " " " " "
## 7 ( 1 ) " " "*" " " " " " "
## 8 ( 1 ) " " "*" " " " " " "
## 9 ( 1 ) " " "*" " " " " " "
## 10 ( 1 ) " " "*" " " " " " "
## 11 ( 1 ) " " "*" " " " " " "
## 12 ( 1 ) " " "*" " " " " " "
## 13 ( 1 ) " " "*" " " " " " "
## 14 ( 1 ) " " "*" " " " " " "
## 15 ( 1 ) " " "*" " " " " " "
## 16 ( 1 ) " " "*" "*" " " " "
## 17 ( 1 ) " " "*" "*" " " " "
## 18 ( 1 ) " " "*" "*" " " " "
## 19 ( 1 ) " " "*" "*" " " " "
## 20 ( 1 ) " " "*" "*" " " " "
## Bedroom.AbvGr Kitchen.AbvGr TotRms.AbvGrd Fireplaces Garage.Cars
## 1 ( 1 ) " " " " " " " " " "
## 2 ( 1 ) " " " " " " " " " "
## 3 ( 1 ) " " " " " " " " " "
## 4 ( 1 ) " " " " " " " " " "
## 5 ( 1 ) " " " " " " " " " "
## 6 ( 1 ) " " " " " " " " " "
## 7 ( 1 ) " " " " " " " " " "
## 8 ( 1 ) " " " " " " " " " "
## 9 ( 1 ) " " " " " " "*" " "
## 10 ( 1 ) " " " " " " "*" " "
## 11 ( 1 ) " " " " " " "*" " "
## 12 ( 1 ) " " " " " " "*" " "
## 13 ( 1 ) "*" " " " " "*" " "
## 14 ( 1 ) "*" " " " " "*" " "
## 15 ( 1 ) "*" " " " " "*" " "
## 16 ( 1 ) "*" " " " " "*" " "
## 17 ( 1 ) "*" " " " " "*" " "
## 18 ( 1 ) "*" "*" "*" "*" " "
## 19 ( 1 ) "*" "*" "*" "*" " "
## 20 ( 1 ) "*" "*" "*" "*" "*"
## Garage.Area Wood.Deck.SF Open.Porch.SF Enclosed.Porch
## 1 ( 1 ) " " " " " " " "
## 2 ( 1 ) " " " " " " " "
## 3 ( 1 ) " " " " " " " "
## 4 ( 1 ) " " " " " " " "
## 5 ( 1 ) " " " " " " " "
## 6 ( 1 ) " " " " " " " "
## 7 ( 1 ) " " " " " " " "
## 8 ( 1 ) "*" " " " " " "
## 9 ( 1 ) "*" " " " " " "
## 10 ( 1 ) "*" " " " " " "
## 11 ( 1 ) "*" " " " " " "
## 12 ( 1 ) "*" " " " " " "
## 13 ( 1 ) "*" " " " " " "
## 14 ( 1 ) "*" " " " " " "
## 15 ( 1 ) "*" " " " " " "
## 16 ( 1 ) "*" " " " " " "
## 17 ( 1 ) "*" " " " " "*"
## 18 ( 1 ) "*" " " " " " "
## 19 ( 1 ) "*" " " " " "*"
## 20 ( 1 ) "*" " " " " "*"
## Screen.Porch Pool.Area
## 1 ( 1 ) " " " "
## 2 ( 1 ) " " " "
## 3 ( 1 ) " " " "
## 4 ( 1 ) " " " "
## 5 ( 1 ) " " " "
## 6 ( 1 ) " " " "
## 7 ( 1 ) " " " "
## 8 ( 1 ) " " " "
## 9 ( 1 ) " " " "
## 10 ( 1 ) " " " "
## 11 ( 1 ) " " " "
## 12 ( 1 ) " " " "
## 13 ( 1 ) " " " "
## 14 ( 1 ) "*" " "
## 15 ( 1 ) "*" "*"
## 16 ( 1 ) "*" "*"
## 17 ( 1 ) "*" "*"
## 18 ( 1 ) "*" "*"
## 19 ( 1 ) "*" "*"
## 20 ( 1 ) "*" "*"names(reg.summary)## [1] "which" "rsq" "rss" "adjr2" "cp" "bic" "outmat" "obj"reg.summary$rsq## [1] 0.6703822 0.7733771 0.8269802 0.8582385 0.8836282 0.8939002 0.9009340
## [8] 0.9068654 0.9100142 0.9129723 0.9152623 0.9174616 0.9183909 0.9189588
## [15] 0.9196222 0.9200497 0.9204128 0.9206910 0.9210765 0.9212310reg.summary$rss## [1] 38.981164 26.800811 20.461621 16.764957 13.762324 12.547547 11.715717
## [8] 11.014254 10.641878 10.292046 10.021224 9.761130 9.651235 9.584074
## [15] 9.505614 9.455062 9.412118 9.379221 9.333628 9.315356reg.summary$adjr2## [1] 0.6699851 0.7728303 0.8263533 0.8575528 0.8829238 0.8931285 0.9000924
## [8] 0.9059601 0.9090289 0.9119123 0.9141256 0.9162523 0.9170939 0.9175701
## [15] 0.9181447 0.9184801 0.9187507 0.9189351 0.9192298 0.9192885reg.summary$cp## [1] 2566.61197 1507.90556 957.86737 637.94936 378.46982 274.68294
## [7] 204.24438 145.15856 114.73085 86.26630 64.68220 44.03230
## [13] 36.46231 32.61366 27.78112 25.37886 23.63916 22.77435
## [19] 20.80400 21.21280reg.summary$bic## [1] -909.9238 -1214.9057 -1432.7230 -1591.7836 -1749.2601 -1819.4210
## [7] -1869.7673 -1914.4120 -1936.3034 -1957.3896 -1972.8520 -1988.0074
## [13] -1990.7036 -1989.7898 -1989.9051 -1987.6178 -1984.6815 -1980.8707
## [19] -1978.2011 -1973.1077library(ggvis)##
## Attaching package: 'ggvis'## The following objects are masked from 'package:scales':
##
## fullseq, zero_range## The following object is masked from 'package:ggplot2':
##
## resolutionlibrary(broom)
library(visreg)
rsq<-as.data.frame(reg.summary$rsq)
names(rsq) <- "R2"
rsq%>%
ggvis(x=~c(1:nrow(rsq)),y=~R2) %>%
layer_points(fill= ~R2) %>%
add_axis("y",title="R2") %>%
add_axis("x",title="Number of variables") rsq## R2
## 1 0.6703822
## 2 0.7733771
## 3 0.8269802
## 4 0.8582385
## 5 0.8836282
## 6 0.8939002
## 7 0.9009340
## 8 0.9068654
## 9 0.9100142
## 10 0.9129723
## 11 0.9152623
## 12 0.9174616
## 13 0.9183909
## 14 0.9189588
## 15 0.9196222
## 16 0.9200497
## 17 0.9204128
## 18 0.9206910
## 19 0.9210765
## 20 0.9212310plot(reg.summary$cp,xlab="Number of Variables",ylab="Cp") # Cp component
which.min(reg.summary$cp)## [1] 19plot(reg.full,scale="Cp")
coef(reg.full,10)## (Intercept) area MS.SubClass Lot.Area Overall.Qual
## 3.479384e+00 2.790665e-04 -5.166581e-04 2.510594e-06 8.498416e-02
## Overall.Cond Year.Built Total.Bsmt.SF Bsmt.Full.Bath Fireplaces
## 5.634072e-02 3.556950e-03 1.424930e-04 6.767876e-02 3.953227e-02
## Garage.Area
## 1.792540e-04reg.fwd=regsubsets(log(price)~.,data=train,nvmax=10,method="forward")
summary(reg.fwd)## Subset selection object
## Call: regsubsets.formula(log(price) ~ ., data = train, nvmax = 10,
## method = "forward")
## 26 Variables (and intercept)
## Forced in Forced out
## area FALSE FALSE
## MS.SubClass FALSE FALSE
## Lot.Area FALSE FALSE
## Overall.Qual FALSE FALSE
## Overall.Cond FALSE FALSE
## Year.Built FALSE FALSE
## Year.Remod.Add FALSE FALSE
## Total.Bsmt.SF FALSE FALSE
## Central.AirY FALSE FALSE
## X1st.Flr.SF FALSE FALSE
## X2nd.Flr.SF FALSE FALSE
## Bsmt.Full.Bath FALSE FALSE
## Bsmt.Half.Bath FALSE FALSE
## Full.Bath FALSE FALSE
## Half.Bath FALSE FALSE
## Bedroom.AbvGr FALSE FALSE
## Kitchen.AbvGr FALSE FALSE
## TotRms.AbvGrd FALSE FALSE
## Fireplaces FALSE FALSE
## Garage.Cars FALSE FALSE
## Garage.Area FALSE FALSE
## Wood.Deck.SF FALSE FALSE
## Open.Porch.SF FALSE FALSE
## Enclosed.Porch FALSE FALSE
## Screen.Porch FALSE FALSE
## Pool.Area FALSE FALSE
## 1 subsets of each size up to 10
## Selection Algorithm: forward
## area MS.SubClass Lot.Area Overall.Qual Overall.Cond Year.Built
## 1 ( 1 ) " " " " " " "*" " " " "
## 2 ( 1 ) "*" " " " " "*" " " " "
## 3 ( 1 ) "*" " " " " "*" " " " "
## 4 ( 1 ) "*" " " " " "*" " " "*"
## 5 ( 1 ) "*" " " " " "*" "*" "*"
## 6 ( 1 ) "*" " " " " "*" "*" "*"
## 7 ( 1 ) "*" " " "*" "*" "*" "*"
## 8 ( 1 ) "*" " " "*" "*" "*" "*"
## 9 ( 1 ) "*" " " "*" "*" "*" "*"
## 10 ( 1 ) "*" "*" "*" "*" "*" "*"
## Year.Remod.Add Total.Bsmt.SF Central.AirY X1st.Flr.SF
## 1 ( 1 ) " " " " " " " "
## 2 ( 1 ) " " " " " " " "
## 3 ( 1 ) " " "*" " " " "
## 4 ( 1 ) " " "*" " " " "
## 5 ( 1 ) " " "*" " " " "
## 6 ( 1 ) " " "*" " " " "
## 7 ( 1 ) " " "*" " " " "
## 8 ( 1 ) " " "*" " " " "
## 9 ( 1 ) " " "*" " " " "
## 10 ( 1 ) " " "*" " " " "
## X2nd.Flr.SF Bsmt.Full.Bath Bsmt.Half.Bath Full.Bath Half.Bath
## 1 ( 1 ) " " " " " " " " " "
## 2 ( 1 ) " " " " " " " " " "
## 3 ( 1 ) " " " " " " " " " "
## 4 ( 1 ) " " " " " " " " " "
## 5 ( 1 ) " " " " " " " " " "
## 6 ( 1 ) " " "*" " " " " " "
## 7 ( 1 ) " " "*" " " " " " "
## 8 ( 1 ) " " "*" " " " " " "
## 9 ( 1 ) " " "*" " " " " " "
## 10 ( 1 ) " " "*" " " " " " "
## Bedroom.AbvGr Kitchen.AbvGr TotRms.AbvGrd Fireplaces Garage.Cars
## 1 ( 1 ) " " " " " " " " " "
## 2 ( 1 ) " " " " " " " " " "
## 3 ( 1 ) " " " " " " " " " "
## 4 ( 1 ) " " " " " " " " " "
## 5 ( 1 ) " " " " " " " " " "
## 6 ( 1 ) " " " " " " " " " "
## 7 ( 1 ) " " " " " " " " " "
## 8 ( 1 ) " " " " " " " " " "
## 9 ( 1 ) " " " " " " "*" " "
## 10 ( 1 ) " " " " " " "*" " "
## Garage.Area Wood.Deck.SF Open.Porch.SF Enclosed.Porch
## 1 ( 1 ) " " " " " " " "
## 2 ( 1 ) " " " " " " " "
## 3 ( 1 ) " " " " " " " "
## 4 ( 1 ) " " " " " " " "
## 5 ( 1 ) " " " " " " " "
## 6 ( 1 ) " " " " " " " "
## 7 ( 1 ) " " " " " " " "
## 8 ( 1 ) "*" " " " " " "
## 9 ( 1 ) "*" " " " " " "
## 10 ( 1 ) "*" " " " " " "
## Screen.Porch Pool.Area
## 1 ( 1 ) " " " "
## 2 ( 1 ) " " " "
## 3 ( 1 ) " " " "
## 4 ( 1 ) " " " "
## 5 ( 1 ) " " " "
## 6 ( 1 ) " " " "
## 7 ( 1 ) " " " "
## 8 ( 1 ) " " " "
## 9 ( 1 ) " " " "
## 10 ( 1 ) " " " "plot(reg.fwd,scale="Cp")
coef(reg.fwd,10)## (Intercept) area MS.SubClass Lot.Area Overall.Qual
## 3.479384e+00 2.790665e-04 -5.166581e-04 2.510594e-06 8.498416e-02
## Overall.Cond Year.Built Total.Bsmt.SF Bsmt.Full.Bath Fireplaces
## 5.634072e-02 3.556950e-03 1.424930e-04 6.767876e-02 3.953227e-02
## Garage.Area
## 1.792540e-04Initial.model<-lm(log(price)~log(area)+Lot.Area+Overall.Qual+Overall.Cond +Year.Built+Total.Bsmt.SF+ Bsmt.Full.Bath + Fireplaces+Kitchen.AbvGr+
Garage.Area,data=(na.omit(train)))
names(premodel)## [1] "np" "nrbar" "d" "rbar" "thetab"
## [6] "first" "last" "vorder" "tol" "rss"
## [11] "bound" "nvmax" "ress" "ir" "nbest"
## [16] "lopt" "il" "ier" "xnames" "method"
## [21] "force.in" "force.out" "sserr" "intercept" "lindep"
## [26] "nullrss" "nn" "call"summary(premodel)## Subset selection object
## Call: regsubsets.formula(log(price) ~ X1st.Flr.SF + Total.Bsmt.SF +
## Garage.Area + Fireplaces + TotRms.AbvGrd + Garage.Cars +
## Bsmt.Full.Bath + area + Overall.Qual + Lot.Area + Pool.Area +
## Open.Porch.SF + Full.Bath + Year.Built + Bsmt.Half.Bath +
## Kitchen.AbvGr + Year.Remod.Add + Screen.Porch + Enclosed.Porch +
## Overall.Cond + Bedroom.AbvGr + MS.SubClass + Half.Bath +
## X2nd.Flr.SF, data = ames_train, nvmax = 20)
## 24 Variables (and intercept)
## Forced in Forced out
## X1st.Flr.SF FALSE FALSE
## Total.Bsmt.SF FALSE FALSE
## Garage.Area FALSE FALSE
## Fireplaces FALSE FALSE
## TotRms.AbvGrd FALSE FALSE
## Garage.Cars FALSE FALSE
## Bsmt.Full.Bath FALSE FALSE
## area FALSE FALSE
## Overall.Qual FALSE FALSE
## Lot.Area FALSE FALSE
## Pool.Area FALSE FALSE
## Open.Porch.SF FALSE FALSE
## Full.Bath FALSE FALSE
## Year.Built FALSE FALSE
## Bsmt.Half.Bath FALSE FALSE
## Kitchen.AbvGr FALSE FALSE
## Year.Remod.Add FALSE FALSE
## Screen.Porch FALSE FALSE
## Enclosed.Porch FALSE FALSE
## Overall.Cond FALSE FALSE
## Bedroom.AbvGr FALSE FALSE
## MS.SubClass FALSE FALSE
## Half.Bath FALSE FALSE
## X2nd.Flr.SF FALSE FALSE
## 1 subsets of each size up to 20
## Selection Algorithm: exhaustive
## X1st.Flr.SF Total.Bsmt.SF Garage.Area Fireplaces TotRms.AbvGrd
## 1 ( 1 ) " " " " " " " " " "
## 2 ( 1 ) " " " " " " " " " "
## 3 ( 1 ) " " "*" " " " " " "
## 4 ( 1 ) " " "*" " " " " " "
## 5 ( 1 ) " " "*" " " " " " "
## 6 ( 1 ) " " "*" " " " " " "
## 7 ( 1 ) " " "*" " " " " " "
## 8 ( 1 ) " " "*" "*" " " " "
## 9 ( 1 ) " " "*" "*" "*" " "
## 10 ( 1 ) " " "*" "*" "*" " "
## 11 ( 1 ) " " "*" "*" "*" " "
## 12 ( 1 ) " " "*" "*" "*" " "
## 13 ( 1 ) " " "*" "*" "*" " "
## 14 ( 1 ) " " "*" "*" "*" " "
## 15 ( 1 ) " " "*" "*" "*" " "
## 16 ( 1 ) " " "*" "*" "*" "*"
## 17 ( 1 ) " " "*" "*" "*" "*"
## 18 ( 1 ) " " "*" "*" "*" "*"
## 19 ( 1 ) "*" "*" "*" "*" "*"
## 20 ( 1 ) "*" "*" "*" "*" "*"
## Garage.Cars Bsmt.Full.Bath area Overall.Qual Lot.Area Pool.Area
## 1 ( 1 ) " " " " " " "*" " " " "
## 2 ( 1 ) " " " " "*" "*" " " " "
## 3 ( 1 ) " " " " "*" "*" " " " "
## 4 ( 1 ) " " " " "*" "*" " " " "
## 5 ( 1 ) " " " " "*" "*" " " " "
## 6 ( 1 ) " " "*" "*" "*" " " " "
## 7 ( 1 ) " " "*" "*" "*" "*" " "
## 8 ( 1 ) " " "*" "*" "*" "*" " "
## 9 ( 1 ) " " "*" "*" "*" "*" " "
## 10 ( 1 ) " " "*" "*" "*" "*" " "
## 11 ( 1 ) " " "*" "*" "*" "*" " "
## 12 ( 1 ) " " "*" "*" "*" "*" " "
## 13 ( 1 ) " " "*" "*" "*" "*" "*"
## 14 ( 1 ) " " "*" "*" "*" "*" "*"
## 15 ( 1 ) " " "*" "*" "*" "*" "*"
## 16 ( 1 ) " " "*" "*" "*" "*" "*"
## 17 ( 1 ) " " "*" "*" "*" "*" "*"
## 18 ( 1 ) " " "*" "*" "*" "*" "*"
## 19 ( 1 ) " " "*" "*" "*" "*" "*"
## 20 ( 1 ) " " "*" "*" "*" "*" "*"
## Open.Porch.SF Full.Bath Year.Built Bsmt.Half.Bath Kitchen.AbvGr
## 1 ( 1 ) " " " " " " " " " "
## 2 ( 1 ) " " " " " " " " " "
## 3 ( 1 ) " " " " " " " " " "
## 4 ( 1 ) " " " " "*" " " " "
## 5 ( 1 ) " " " " "*" " " " "
## 6 ( 1 ) " " " " "*" " " " "
## 7 ( 1 ) " " " " "*" " " " "
## 8 ( 1 ) " " " " "*" " " " "
## 9 ( 1 ) " " " " "*" " " " "
## 10 ( 1 ) " " " " "*" " " " "
## 11 ( 1 ) " " " " "*" " " " "
## 12 ( 1 ) " " " " "*" " " "*"
## 13 ( 1 ) " " " " "*" " " "*"
## 14 ( 1 ) " " " " "*" " " "*"
## 15 ( 1 ) " " " " "*" " " "*"
## 16 ( 1 ) " " " " "*" " " "*"
## 17 ( 1 ) " " " " "*" "*" "*"
## 18 ( 1 ) " " " " "*" "*" "*"
## 19 ( 1 ) " " " " "*" "*" "*"
## 20 ( 1 ) " " " " "*" "*" "*"
## Year.Remod.Add Screen.Porch Enclosed.Porch Overall.Cond
## 1 ( 1 ) " " " " " " " "
## 2 ( 1 ) " " " " " " " "
## 3 ( 1 ) " " " " " " " "
## 4 ( 1 ) " " " " " " " "
## 5 ( 1 ) " " " " " " "*"
## 6 ( 1 ) " " " " " " "*"
## 7 ( 1 ) " " " " " " "*"
## 8 ( 1 ) " " " " " " "*"
## 9 ( 1 ) " " " " " " "*"
## 10 ( 1 ) " " " " " " "*"
## 11 ( 1 ) "*" " " " " "*"
## 12 ( 1 ) "*" " " " " "*"
## 13 ( 1 ) "*" " " " " "*"
## 14 ( 1 ) "*" "*" " " "*"
## 15 ( 1 ) "*" "*" " " "*"
## 16 ( 1 ) "*" "*" " " "*"
## 17 ( 1 ) "*" "*" " " "*"
## 18 ( 1 ) "*" "*" "*" "*"
## 19 ( 1 ) "*" "*" "*" "*"
## 20 ( 1 ) "*" "*" "*" "*"
## Bedroom.AbvGr MS.SubClass Half.Bath X2nd.Flr.SF
## 1 ( 1 ) " " " " " " " "
## 2 ( 1 ) " " " " " " " "
## 3 ( 1 ) " " " " " " " "
## 4 ( 1 ) " " " " " " " "
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## 18 ( 1 ) "*" "*" " " " "
## 19 ( 1 ) "*" "*" " " " "
## 20 ( 1 ) "*" "*" " " "*"summary(Initial.model)##
## Call:
## lm(formula = log(price) ~ log(area) + Lot.Area + Overall.Qual +
## Overall.Cond + Year.Built + Total.Bsmt.SF + Bsmt.Full.Bath +
## Fireplaces + Kitchen.AbvGr + Garage.Area, data = (na.omit(train)))
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.81398 -0.06659 -0.00146 0.06441 0.53542
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.572e+00 4.038e-01 3.894 0.000107 ***
## log(area) 4.205e-01 1.761e-02 23.881 < 2e-16 ***
## Lot.Area 2.596e-06 4.077e-07 6.367 3.20e-10 ***
## Overall.Qual 7.592e-02 4.740e-03 16.018 < 2e-16 ***
## Overall.Cond 5.830e-02 3.946e-03 14.776 < 2e-16 ***
## Year.Built 3.237e-03 1.899e-04 17.046 < 2e-16 ***
## Total.Bsmt.SF 1.619e-04 1.288e-05 12.573 < 2e-16 ***
## Bsmt.Full.Bath 6.969e-02 8.329e-03 8.367 2.52e-16 ***
## Fireplaces 3.981e-02 7.159e-03 5.562 3.62e-08 ***
## Kitchen.AbvGr -1.142e-01 2.158e-02 -5.291 1.56e-07 ***
## Garage.Area 2.082e-04 2.459e-05 8.468 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.1129 on 821 degrees of freedom
## Multiple R-squared: 0.9115, Adjusted R-squared: 0.9104
## F-statistic: 845.2 on 10 and 821 DF, p-value: < 2.2e-16glance(Initial.model)## r.squared adj.r.squared sigma statistic p.value df logLik AIC
## 1 0.911466 0.9103877 0.112929 845.2278 0 11 639.5686 -1255.137
## BIC deviance df.residual
## 1 -1198.451 10.47018 821visreg(Initial.model) 
par(mfrow=c(1,3))
visreg(Initial.model)
rmse.Initial <-sqrt(mean(Initial.model$residuals^2))
rmse.Initial ## [1] 0.11218confint(Initial.model)## 2.5 % 97.5 %
## (Intercept) 7.796803e-01 2.364853e+00
## log(area) 3.859616e-01 4.550901e-01
## Lot.Area 1.795565e-06 3.396015e-06
## Overall.Qual 6.662063e-02 8.522853e-02
## Overall.Cond 5.055764e-02 6.604781e-02
## Year.Built 2.864585e-03 3.610140e-03
## Total.Bsmt.SF 1.366456e-04 1.872044e-04
## Bsmt.Full.Bath 5.334375e-02 8.604095e-02
## Fireplaces 2.576251e-02 5.386487e-02
## Kitchen.AbvGr -1.565523e-01 -7.182700e-02
## Garage.Area 1.599526e-04 2.564874e-04pred = predict(Initial.model)
mean(pred)## [1] 11.9928resid = residuals(Initial.model)
mean(resid)## [1] 2.084214e-18quantile(resid)## 0% 25% 50% 75% 100%
## -0.813980162 -0.066594019 -0.001464952 0.064407317 0.535418556plot(Initial.model)
0.0.0.2.5 Relative Selection of Variables with Relaimpo & Boruta
library(relaimpo)## Loading required package: MASS##
## Attaching package: 'MASS'## The following object is masked from 'package:dplyr':
##
## select## Loading required package: boot##
## Attaching package: 'boot'## The following object is masked from 'package:lattice':
##
## melanoma## The following object is masked from 'package:psych':
##
## logit## Loading required package: survey## Loading required package: grid## Loading required package: Matrix##
## Attaching package: 'Matrix'## The following object is masked from 'package:ggvis':
##
## band## The following object is masked from 'package:reshape':
##
## expand## The following object is masked from 'package:tidyr':
##
## expand## Loading required package: survival##
## Attaching package: 'survival'## The following object is masked from 'package:boot':
##
## aml## The following object is masked from 'package:caret':
##
## cluster##
## Attaching package: 'survey'## The following object is masked from 'package:graphics':
##
## dotchart## Loading required package: mitools## This is the global version of package relaimpo.## If you are a non-US user, a version with the interesting additional metric pmvd is available## from Ulrike Groempings web site at prof.beuth-hochschule.de/groemping.calc.relimp(Initial.model,type=c("lmg","last","first","pratt"),
rela=TRUE)## Response variable: log(price)
## Total response variance: 0.1423125
## Analysis based on 832 observations
##
## 10 Regressors:
## log(area) Lot.Area Overall.Qual Overall.Cond Year.Built Total.Bsmt.SF Bsmt.Full.Bath Fireplaces Kitchen.AbvGr Garage.Area
## Proportion of variance explained by model: 91.15%
## Metrics are normalized to sum to 100% (rela=TRUE).
##
## Relative importance metrics:
##
## lmg last first pratt
## log(area) 0.226522839 0.32869980 0.196329659 0.30683961
## Lot.Area 0.019161853 0.02336594 0.020104814 0.01871285
## Overall.Qual 0.242745019 0.14787622 0.230751537 0.24012106
## Overall.Cond 0.016840461 0.12583272 0.001790812 -0.01349749
## Year.Built 0.128017180 0.16747570 0.126379825 0.16569479
## Total.Bsmt.SF 0.134537260 0.09110945 0.151288172 0.12412623
## Bsmt.Full.Bath 0.031101569 0.04035314 0.034277100 0.03308613
## Fireplaces 0.077344693 0.01782820 0.096372752 0.04017127
## Kitchen.AbvGr 0.007405226 0.01613450 0.002820865 0.00578499
## Garage.Area 0.116323902 0.04132433 0.139884462 0.07896056
##
## Average coefficients for different model sizes:
##
## 1X 2Xs 3Xs 4Xs
## log(area) 8.576391e-01 7.411872e-01 6.549600e-01 5.902364e-01
## Lot.Area 8.889291e-06 6.473462e-06 5.066571e-06 4.223552e-06
## Overall.Qual 2.325595e-01 2.065824e-01 1.843048e-01 1.647255e-01
## Overall.Cond -2.465604e-02 5.073714e-03 2.292652e-02 3.402582e-02
## Year.Built 7.870414e-03 6.355961e-03 5.302985e-03 4.571323e-03
## Total.Bsmt.SF 6.290609e-04 5.124898e-04 4.216747e-04 3.511428e-04
## Bsmt.Full.Bath 2.301339e-01 1.668543e-01 1.293384e-01 1.070317e-01
## Fireplaces 3.044448e-01 2.309508e-01 1.784840e-01 1.403135e-01
## Kitchen.AbvGr -1.774777e-01 -1.600352e-01 -1.477185e-01 -1.387230e-01
## Garage.Area 1.175761e-03 9.348232e-04 7.496851e-04 6.068498e-04
## 5Xs 6Xs 7Xs 8Xs
## log(area) 5.410155e-01 5.031797e-01 4.738962e-01 4.512044e-01
## Lot.Area 3.695041e-06 3.343972e-06 3.094334e-06 2.902363e-06
## Overall.Qual 1.471372e-01 1.310376e-01 1.160721e-01 1.019960e-01
## Overall.Cond 4.128621e-02 4.635140e-02 5.015507e-02 5.323190e-02
## Year.Built 4.065017e-03 3.719088e-03 3.489489e-03 3.345907e-03
## Total.Bsmt.SF 2.964839e-04 2.541861e-04 2.214859e-04 1.962373e-04
## Bsmt.Full.Bath 9.354025e-02 8.508995e-02 7.949523e-02 7.550004e-02
## Fireplaces 1.118688e-01 9.011812e-02 7.309340e-02 5.953456e-02
## Kitchen.AbvGr -1.318404e-01 -1.263859e-01 -1.219982e-01 -1.185139e-01
## Garage.Area 4.961112e-04 4.097340e-04 3.418186e-04 2.878227e-04
## 9Xs 10Xs
## log(area) 4.337362e-01 4.205259e-01
## Lot.Area 2.741684e-06 2.595790e-06
## Overall.Qual 8.864663e-02 7.592458e-02
## Overall.Cond 5.588846e-02 5.830273e-02
## Year.Built 3.266995e-03 3.237363e-03
## Total.Bsmt.SF 1.767964e-04 1.619250e-04
## Bsmt.Full.Bath 7.237503e-02 6.969235e-02
## Fireplaces 4.862728e-02 3.981369e-02
## Kitchen.AbvGr -1.158975e-01 -1.141897e-01
## Garage.Area 2.442117e-04 2.082200e-04boot <- boot.relimp(Initial.model, b = 1000, type = c("lmg",
"last", "first", "pratt"), rank = TRUE,
diff = TRUE, rela = TRUE)
booteval.relimp(boot) # print result## Response variable: log(price)
## Total response variance: 0.1423125
## Analysis based on 832 observations
##
## 10 Regressors:
## log(area) Lot.Area Overall.Qual Overall.Cond Year.Built Total.Bsmt.SF Bsmt.Full.Bath Fireplaces Kitchen.AbvGr Garage.Area
## Proportion of variance explained by model: 91.15%
## Metrics are normalized to sum to 100% (rela=TRUE).
##
## Relative importance metrics:
##
## lmg last first pratt
## log(area) 0.226522839 0.32869980 0.196329659 0.30683961
## Lot.Area 0.019161853 0.02336594 0.020104814 0.01871285
## Overall.Qual 0.242745019 0.14787622 0.230751537 0.24012106
## Overall.Cond 0.016840461 0.12583272 0.001790812 -0.01349749
## Year.Built 0.128017180 0.16747570 0.126379825 0.16569479
## Total.Bsmt.SF 0.134537260 0.09110945 0.151288172 0.12412623
## Bsmt.Full.Bath 0.031101569 0.04035314 0.034277100 0.03308613
## Fireplaces 0.077344693 0.01782820 0.096372752 0.04017127
## Kitchen.AbvGr 0.007405226 0.01613450 0.002820865 0.00578499
## Garage.Area 0.116323902 0.04132433 0.139884462 0.07896056
##
## Average coefficients for different model sizes:
##
## 1X 2Xs 3Xs 4Xs
## log(area) 8.576391e-01 7.411872e-01 6.549600e-01 5.902364e-01
## Lot.Area 8.889291e-06 6.473462e-06 5.066571e-06 4.223552e-06
## Overall.Qual 2.325595e-01 2.065824e-01 1.843048e-01 1.647255e-01
## Overall.Cond -2.465604e-02 5.073714e-03 2.292652e-02 3.402582e-02
## Year.Built 7.870414e-03 6.355961e-03 5.302985e-03 4.571323e-03
## Total.Bsmt.SF 6.290609e-04 5.124898e-04 4.216747e-04 3.511428e-04
## Bsmt.Full.Bath 2.301339e-01 1.668543e-01 1.293384e-01 1.070317e-01
## Fireplaces 3.044448e-01 2.309508e-01 1.784840e-01 1.403135e-01
## Kitchen.AbvGr -1.774777e-01 -1.600352e-01 -1.477185e-01 -1.387230e-01
## Garage.Area 1.175761e-03 9.348232e-04 7.496851e-04 6.068498e-04
## 5Xs 6Xs 7Xs 8Xs
## log(area) 5.410155e-01 5.031797e-01 4.738962e-01 4.512044e-01
## Lot.Area 3.695041e-06 3.343972e-06 3.094334e-06 2.902363e-06
## Overall.Qual 1.471372e-01 1.310376e-01 1.160721e-01 1.019960e-01
## Overall.Cond 4.128621e-02 4.635140e-02 5.015507e-02 5.323190e-02
## Year.Built 4.065017e-03 3.719088e-03 3.489489e-03 3.345907e-03
## Total.Bsmt.SF 2.964839e-04 2.541861e-04 2.214859e-04 1.962373e-04
## Bsmt.Full.Bath 9.354025e-02 8.508995e-02 7.949523e-02 7.550004e-02
## Fireplaces 1.118688e-01 9.011812e-02 7.309340e-02 5.953456e-02
## Kitchen.AbvGr -1.318404e-01 -1.263859e-01 -1.219982e-01 -1.185139e-01
## Garage.Area 4.961112e-04 4.097340e-04 3.418186e-04 2.878227e-04
## 9Xs 10Xs
## log(area) 4.337362e-01 4.205259e-01
## Lot.Area 2.741684e-06 2.595790e-06
## Overall.Qual 8.864663e-02 7.592458e-02
## Overall.Cond 5.588846e-02 5.830273e-02
## Year.Built 3.266995e-03 3.237363e-03
## Total.Bsmt.SF 1.767964e-04 1.619250e-04
## Bsmt.Full.Bath 7.237503e-02 6.969235e-02
## Fireplaces 4.862728e-02 3.981369e-02
## Kitchen.AbvGr -1.158975e-01 -1.141897e-01
## Garage.Area 2.442117e-04 2.082200e-04
##
##
## Confidence interval information ( 1000 bootstrap replicates, bty= perc ):
## Relative Contributions with confidence intervals:
##
## Lower Upper
## percentage 0.95 0.95 0.95
## log(area).lmg 0.2265 AB________ 0.2045 0.2447
## Lot.Area.lmg 0.0192 ______GHI_ 0.0155 0.0387
## Overall.Qual.lmg 0.2427 AB________ 0.2227 0.2609
## Overall.Cond.lmg 0.0168 _______HI_ 0.0127 0.0233
## Year.Built.lmg 0.1280 __CDE_____ 0.1096 0.1482
## Total.Bsmt.SF.lmg 0.1345 __CDE_____ 0.1149 0.1516
## Bsmt.Full.Bath.lmg 0.0311 ______GH__ 0.0228 0.0418
## Fireplaces.lmg 0.0773 _____F____ 0.0655 0.0902
## Kitchen.AbvGr.lmg 0.0074 _________J 0.0041 0.0128
## Garage.Area.lmg 0.1163 __CDE_____ 0.0952 0.1379
##
## log(area).last 0.3287 A_________ 0.2651 0.3782
## Lot.Area.last 0.0234 _____FGHIJ 0.0160 0.0467
## Overall.Qual.last 0.1479 _BCD______ 0.1106 0.2009
## Overall.Cond.last 0.1258 __CDE_____ 0.0912 0.1652
## Year.Built.last 0.1675 _BCD______ 0.1266 0.2161
## Total.Bsmt.SF.last 0.0911 ___DE_____ 0.0595 0.1210
## Bsmt.Full.Bath.last 0.0404 _____FGH__ 0.0259 0.0598
## Fireplaces.last 0.0178 _______HIJ 0.0075 0.0298
## Kitchen.AbvGr.last 0.0161 ______GHIJ 0.0047 0.0334
## Garage.Area.last 0.0413 _____FGHI_ 0.0197 0.0643
##
## log(area).first 0.1963 _B________ 0.1807 0.2105
## Lot.Area.first 0.0201 ______GH__ 0.0154 0.0417
## Overall.Qual.first 0.2308 A_________ 0.2154 0.2440
## Overall.Cond.first 0.0018 ________IJ 0.0000 0.0084
## Year.Built.first 0.1264 ___DE_____ 0.1087 0.1421
## Total.Bsmt.SF.first 0.1513 __CD______ 0.1343 0.1653
## Bsmt.Full.Bath.first 0.0343 ______GH__ 0.0230 0.0472
## Fireplaces.first 0.0964 _____F____ 0.0828 0.1101
## Kitchen.AbvGr.first 0.0028 ________IJ 0.0004 0.0076
## Garage.Area.first 0.1399 __CDE_____ 0.1202 0.1593
##
## log(area).pratt 0.3068 A_________ 0.2693 0.3405
## Lot.Area.pratt 0.0187 _____FGH__ 0.0147 0.0392
## Overall.Qual.pratt 0.2401 _B________ 0.2057 0.2827
## Overall.Cond.pratt -0.0135 _________J -0.0292 0.0021
## Year.Built.pratt 0.1657 __C_______ 0.1373 0.2007
## Total.Bsmt.SF.pratt 0.1241 ___D______ 0.0962 0.1474
## Bsmt.Full.Bath.pratt 0.0331 _____FGH__ 0.0243 0.0441
## Fireplaces.pratt 0.0402 _____FGH__ 0.0251 0.0541
## Kitchen.AbvGr.pratt 0.0058 ________I_ 0.0018 0.0114
## Garage.Area.pratt 0.0790 ____E_____ 0.0513 0.1034
##
## Letters indicate the ranks covered by bootstrap CIs.
## (Rank bootstrap confidence intervals always obtained by percentile method)
## CAUTION: Bootstrap confidence intervals can be somewhat liberal.
##
##
## Differences between Relative Contributions:
##
## Lower Upper
## difference 0.95 0.95 0.95
## log(area)-Lot.Area.lmg 0.2074 * 0.1748 0.2248
## log(area)-Overall.Qual.lmg -0.0162 -0.0466 0.0131
## log(area)-Overall.Cond.lmg 0.2097 * 0.1855 0.2287
## log(area)-Year.Built.lmg 0.0985 * 0.0642 0.1279
## log(area)-Total.Bsmt.SF.lmg 0.0920 * 0.0616 0.1234
## log(area)-Bsmt.Full.Bath.lmg 0.1954 * 0.1689 0.2161
## log(area)-Fireplaces.lmg 0.1492 * 0.1242 0.1711
## log(area)-Kitchen.AbvGr.lmg 0.2191 * 0.1961 0.2388
## log(area)-Garage.Area.lmg 0.1102 * 0.0762 0.1428
## Lot.Area-Overall.Qual.lmg -0.2236 * -0.2402 -0.1964
## Lot.Area-Overall.Cond.lmg 0.0023 -0.0045 0.0215
## Lot.Area-Year.Built.lmg -0.1089 * -0.1289 -0.0834
## Lot.Area-Total.Bsmt.SF.lmg -0.1154 * -0.1319 -0.0871
## Lot.Area-Bsmt.Full.Bath.lmg -0.0119 -0.0237 0.0098
## Lot.Area-Fireplaces.lmg -0.0582 * -0.0702 -0.0339
## Lot.Area-Kitchen.AbvGr.lmg 0.0118 * 0.0059 0.0315
## Lot.Area-Garage.Area.lmg -0.0972 * -0.1179 -0.0687
## Overall.Qual-Overall.Cond.lmg 0.2259 * 0.2052 0.2441
## Overall.Qual-Year.Built.lmg 0.1147 * 0.0860 0.1405
## Overall.Qual-Total.Bsmt.SF.lmg 0.1082 * 0.0781 0.1408
## Overall.Qual-Bsmt.Full.Bath.lmg 0.2116 * 0.1878 0.2319
## Overall.Qual-Fireplaces.lmg 0.1654 * 0.1408 0.1890
## Overall.Qual-Kitchen.AbvGr.lmg 0.2353 * 0.2142 0.2537
## Overall.Qual-Garage.Area.lmg 0.1264 * 0.0917 0.1589
## Overall.Cond-Year.Built.lmg -0.1112 * -0.1307 -0.0920
## Overall.Cond-Total.Bsmt.SF.lmg -0.1177 * -0.1347 -0.0960
## Overall.Cond-Bsmt.Full.Bath.lmg -0.0143 * -0.0259 -0.0030
## Overall.Cond-Fireplaces.lmg -0.0605 * -0.0729 -0.0474
## Overall.Cond-Kitchen.AbvGr.lmg 0.0094 * 0.0023 0.0170
## Overall.Cond-Garage.Area.lmg -0.0995 * -0.1228 -0.0755
## Year.Built-Total.Bsmt.SF.lmg -0.0065 -0.0350 0.0258
## Year.Built-Bsmt.Full.Bath.lmg 0.0969 * 0.0770 0.1183
## Year.Built-Fireplaces.lmg 0.0507 * 0.0267 0.0774
## Year.Built-Kitchen.AbvGr.lmg 0.1206 * 0.1002 0.1407
## Year.Built-Garage.Area.lmg 0.0117 -0.0195 0.0451
## Total.Bsmt.SF-Bsmt.Full.Bath.lmg 0.1034 * 0.0825 0.1228
## Total.Bsmt.SF-Fireplaces.lmg 0.0572 * 0.0336 0.0789
## Total.Bsmt.SF-Kitchen.AbvGr.lmg 0.1271 * 0.1077 0.1444
## Total.Bsmt.SF-Garage.Area.lmg 0.0182 -0.0114 0.0457
## Bsmt.Full.Bath-Fireplaces.lmg -0.0462 * -0.0609 -0.0299
## Bsmt.Full.Bath-Kitchen.AbvGr.lmg 0.0237 * 0.0132 0.0340
## Bsmt.Full.Bath-Garage.Area.lmg -0.0852 * -0.1096 -0.0602
## Fireplaces-Kitchen.AbvGr.lmg 0.0699 * 0.0568 0.0827
## Fireplaces-Garage.Area.lmg -0.0390 * -0.0654 -0.0136
## Kitchen.AbvGr-Garage.Area.lmg -0.1089 * -0.1297 -0.0873
##
## log(area)-Lot.Area.last 0.3053 * 0.2268 0.3523
## log(area)-Overall.Qual.last 0.1808 * 0.0850 0.2465
## log(area)-Overall.Cond.last 0.2029 * 0.1154 0.2806
## log(area)-Year.Built.last 0.1612 * 0.0625 0.2354
## log(area)-Total.Bsmt.SF.last 0.2376 * 0.1641 0.3015
## log(area)-Bsmt.Full.Bath.last 0.2883 * 0.2257 0.3345
## log(area)-Fireplaces.last 0.3109 * 0.2451 0.3628
## log(area)-Kitchen.AbvGr.last 0.3126 * 0.2520 0.3593
## log(area)-Garage.Area.last 0.2874 * 0.2242 0.3420
## Lot.Area-Overall.Qual.last -0.1245 * -0.1693 -0.0850
## Lot.Area-Overall.Cond.last -0.1025 * -0.1413 -0.0616
## Lot.Area-Year.Built.last -0.1441 * -0.1872 -0.1028
## Lot.Area-Total.Bsmt.SF.last -0.0677 * -0.0994 -0.0243
## Lot.Area-Bsmt.Full.Bath.last -0.0170 -0.0364 0.0110
## Lot.Area-Fireplaces.last 0.0055 -0.0089 0.0320
## Lot.Area-Kitchen.AbvGr.last 0.0072 -0.0112 0.0358
## Lot.Area-Garage.Area.last -0.0180 -0.0401 0.0196
## Overall.Qual-Overall.Cond.last 0.0220 -0.0356 0.0901
## Overall.Qual-Year.Built.last -0.0196 -0.0886 0.0573
## Overall.Qual-Total.Bsmt.SF.last 0.0568 * 0.0023 0.1291
## Overall.Qual-Bsmt.Full.Bath.last 0.1075 * 0.0645 0.1568
## Overall.Qual-Fireplaces.last 0.1300 * 0.0900 0.1857
## Overall.Qual-Kitchen.AbvGr.last 0.1317 * 0.0871 0.1860
## Overall.Qual-Garage.Area.last 0.1066 * 0.0616 0.1664
## Overall.Cond-Year.Built.last -0.0416 -0.0954 0.0097
## Overall.Cond-Total.Bsmt.SF.last 0.0347 -0.0129 0.0844
## Overall.Cond-Bsmt.Full.Bath.last 0.0855 * 0.0389 0.1336
## Overall.Cond-Fireplaces.last 0.1080 * 0.0723 0.1491
## Overall.Cond-Kitchen.AbvGr.last 0.1097 * 0.0655 0.1551
## Overall.Cond-Garage.Area.last 0.0845 * 0.0396 0.1343
## Year.Built-Total.Bsmt.SF.last 0.0764 * 0.0221 0.1408
## Year.Built-Bsmt.Full.Bath.last 0.1271 * 0.0811 0.1798
## Year.Built-Fireplaces.last 0.1496 * 0.1092 0.2006
## Year.Built-Kitchen.AbvGr.last 0.1513 * 0.1061 0.2087
## Year.Built-Garage.Area.last 0.1262 * 0.0743 0.1909
## Total.Bsmt.SF-Bsmt.Full.Bath.last 0.0508 * 0.0094 0.0858
## Total.Bsmt.SF-Fireplaces.last 0.0733 * 0.0404 0.1040
## Total.Bsmt.SF-Kitchen.AbvGr.last 0.0750 * 0.0388 0.1078
## Total.Bsmt.SF-Garage.Area.last 0.0498 * 0.0130 0.0852
## Bsmt.Full.Bath-Fireplaces.last 0.0225 * 0.0024 0.0468
## Bsmt.Full.Bath-Kitchen.AbvGr.last 0.0242 * 0.0023 0.0458
## Bsmt.Full.Bath-Garage.Area.last -0.0010 -0.0278 0.0295
## Fireplaces-Kitchen.AbvGr.last 0.0017 -0.0196 0.0187
## Fireplaces-Garage.Area.last -0.0235 * -0.0493 -0.0002
## Kitchen.AbvGr-Garage.Area.last -0.0252 -0.0489 0.0022
##
## log(area)-Lot.Area.first 0.1762 * 0.1474 0.1902
## log(area)-Overall.Qual.first -0.0344 * -0.0528 -0.0148
## log(area)-Overall.Cond.first 0.1945 * 0.1768 0.2093
## log(area)-Year.Built.first 0.0699 * 0.0444 0.0942
## log(area)-Total.Bsmt.SF.first 0.0450 * 0.0213 0.0701
## log(area)-Bsmt.Full.Bath.first 0.1621 * 0.1382 0.1834
## log(area)-Fireplaces.first 0.1000 * 0.0799 0.1182
## log(area)-Kitchen.AbvGr.first 0.1935 * 0.1751 0.2089
## log(area)-Garage.Area.first 0.0564 * 0.0286 0.0848
## Lot.Area-Overall.Qual.first -0.2106 * -0.2245 -0.1819
## Lot.Area-Overall.Cond.first 0.0183 * 0.0112 0.0396
## Lot.Area-Year.Built.first -0.1063 * -0.1241 -0.0782
## Lot.Area-Total.Bsmt.SF.first -0.1312 * -0.1454 -0.1037
## Lot.Area-Bsmt.Full.Bath.first -0.0142 -0.0285 0.0106
## Lot.Area-Fireplaces.first -0.0763 * -0.0895 -0.0498
## Lot.Area-Kitchen.AbvGr.first 0.0173 * 0.0108 0.0389
## Lot.Area-Garage.Area.first -0.1198 * -0.1386 -0.0930
## Overall.Qual-Overall.Cond.first 0.2290 * 0.2122 0.2425
## Overall.Qual-Year.Built.first 0.1044 * 0.0821 0.1247
## Overall.Qual-Total.Bsmt.SF.first 0.0795 * 0.0557 0.1040
## Overall.Qual-Bsmt.Full.Bath.first 0.1965 * 0.1743 0.2144
## Overall.Qual-Fireplaces.first 0.1344 * 0.1131 0.1554
## Overall.Qual-Kitchen.AbvGr.first 0.2279 * 0.2122 0.2409
## Overall.Qual-Garage.Area.first 0.0909 * 0.0634 0.1173
## Overall.Cond-Year.Built.first -0.1246 * -0.1394 -0.1074
## Overall.Cond-Total.Bsmt.SF.first -0.1495 * -0.1639 -0.1308
## Overall.Cond-Bsmt.Full.Bath.first -0.0325 * -0.0448 -0.0198
## Overall.Cond-Fireplaces.first -0.0946 * -0.1081 -0.0786
## Overall.Cond-Kitchen.AbvGr.first -0.0010 -0.0064 0.0065
## Overall.Cond-Garage.Area.first -0.1381 * -0.1575 -0.1165
## Year.Built-Total.Bsmt.SF.first -0.0249 -0.0500 0.0022
## Year.Built-Bsmt.Full.Bath.first 0.0921 * 0.0705 0.1113
## Year.Built-Fireplaces.first 0.0300 * 0.0058 0.0541
## Year.Built-Kitchen.AbvGr.first 0.1236 * 0.1054 0.1398
## Year.Built-Garage.Area.first -0.0135 -0.0426 0.0152
## Total.Bsmt.SF-Bsmt.Full.Bath.first 0.1170 * 0.0970 0.1352
## Total.Bsmt.SF-Fireplaces.first 0.0549 * 0.0323 0.0762
## Total.Bsmt.SF-Kitchen.AbvGr.first 0.1485 * 0.1319 0.1625
## Total.Bsmt.SF-Garage.Area.first 0.0114 -0.0157 0.0364
## Bsmt.Full.Bath-Fireplaces.first -0.0621 * -0.0796 -0.0438
## Bsmt.Full.Bath-Kitchen.AbvGr.first 0.0315 * 0.0191 0.0445
## Bsmt.Full.Bath-Garage.Area.first -0.1056 * -0.1299 -0.0789
## Fireplaces-Kitchen.AbvGr.first 0.0936 * 0.0794 0.1076
## Fireplaces-Garage.Area.first -0.0435 * -0.0699 -0.0172
## Kitchen.AbvGr-Garage.Area.first -0.1371 * -0.1560 -0.1168
##
## log(area)-Lot.Area.pratt 0.2881 * 0.2395 0.3205
## log(area)-Overall.Qual.pratt 0.0667 * 0.0024 0.1225
## log(area)-Overall.Cond.pratt 0.3203 * 0.2797 0.3597
## log(area)-Year.Built.pratt 0.1411 * 0.0841 0.1885
## log(area)-Total.Bsmt.SF.pratt 0.1827 * 0.1360 0.2288
## log(area)-Bsmt.Full.Bath.pratt 0.2738 * 0.2349 0.3072
## log(area)-Fireplaces.pratt 0.2667 * 0.2248 0.3050
## log(area)-Kitchen.AbvGr.pratt 0.3011 * 0.2644 0.3350
## log(area)-Garage.Area.pratt 0.2279 * 0.1840 0.2734
## Lot.Area-Overall.Qual.pratt -0.2214 * -0.2592 -0.1837
## Lot.Area-Overall.Cond.pratt 0.0322 * 0.0175 0.0573
## Lot.Area-Year.Built.pratt -0.1470 * -0.1786 -0.1151
## Lot.Area-Total.Bsmt.SF.pratt -0.1054 * -0.1288 -0.0666
## Lot.Area-Bsmt.Full.Bath.pratt -0.0144 -0.0260 0.0087
## Lot.Area-Fireplaces.pratt -0.0215 -0.0352 0.0053
## Lot.Area-Kitchen.AbvGr.pratt 0.0129 * 0.0067 0.0342
## Lot.Area-Garage.Area.pratt -0.0602 * -0.0851 -0.0214
## Overall.Qual-Overall.Cond.pratt 0.2536 * 0.2157 0.2984
## Overall.Qual-Year.Built.pratt 0.0744 * 0.0201 0.1305
## Overall.Qual-Total.Bsmt.SF.pratt 0.1160 * 0.0679 0.1753
## Overall.Qual-Bsmt.Full.Bath.pratt 0.2070 * 0.1698 0.2489
## Overall.Qual-Fireplaces.pratt 0.1999 * 0.1608 0.2492
## Overall.Qual-Kitchen.AbvGr.pratt 0.2343 * 0.1985 0.2763
## Overall.Qual-Garage.Area.pratt 0.1612 * 0.1156 0.2163
## Overall.Cond-Year.Built.pratt -0.1792 * -0.2186 -0.1442
## Overall.Cond-Total.Bsmt.SF.pratt -0.1376 * -0.1651 -0.1026
## Overall.Cond-Bsmt.Full.Bath.pratt -0.0466 * -0.0658 -0.0277
## Overall.Cond-Fireplaces.pratt -0.0537 * -0.0718 -0.0342
## Overall.Cond-Kitchen.AbvGr.pratt -0.0193 * -0.0348 -0.0027
## Overall.Cond-Garage.Area.pratt -0.0925 * -0.1210 -0.0624
## Year.Built-Total.Bsmt.SF.pratt 0.0416 * 0.0006 0.0877
## Year.Built-Bsmt.Full.Bath.pratt 0.1326 * 0.1034 0.1681
## Year.Built-Fireplaces.pratt 0.1255 * 0.0946 0.1642
## Year.Built-Kitchen.AbvGr.pratt 0.1599 * 0.1295 0.1958
## Year.Built-Garage.Area.pratt 0.0867 * 0.0419 0.1363
## Total.Bsmt.SF-Bsmt.Full.Bath.pratt 0.0910 * 0.0608 0.1175
## Total.Bsmt.SF-Fireplaces.pratt 0.0840 * 0.0561 0.1095
## Total.Bsmt.SF-Kitchen.AbvGr.pratt 0.1183 * 0.0914 0.1424
## Total.Bsmt.SF-Garage.Area.pratt 0.0452 * 0.0088 0.0784
## Bsmt.Full.Bath-Fireplaces.pratt -0.0071 -0.0241 0.0131
## Bsmt.Full.Bath-Kitchen.AbvGr.pratt 0.0273 * 0.0160 0.0388
## Bsmt.Full.Bath-Garage.Area.pratt -0.0459 * -0.0725 -0.0169
## Fireplaces-Kitchen.AbvGr.pratt 0.0344 * 0.0185 0.0490
## Fireplaces-Garage.Area.pratt -0.0388 * -0.0690 -0.0119
## Kitchen.AbvGr-Garage.Area.pratt -0.0732 * -0.0973 -0.0468
##
## * indicates that CI for difference does not include 0.
## CAUTION: Bootstrap confidence intervals can be somewhat liberal.plot(booteval.relimp(boot,sort=TRUE)) # plot result
install.packages("Boruta")## Installing package into 'C:/Users/Tahir Hussain/Documents/R/win-library/3.2'
## (as 'lib' is unspecified)## Error in contrib.url(repos, "source"): trying to use CRAN without setting a mirrorlibrary(Boruta) ## Loading required package: rangertrain[train == ""] <- NA
str(train)## Classes 'tbl_df', 'tbl' and 'data.frame': 832 obs. of 27 variables:
## $ area : int 856 1049 1001 1039 1665 1922 936 889 1072 1342 ...
## $ price : int 126000 139500 124900 114000 227000 198500 93000 137500 140000 219500 ...
## $ MS.SubClass : int 30 120 30 70 60 85 20 20 180 120 ...
## $ Lot.Area : int 7890 4235 6060 8146 8400 7301 6000 12395 3675 6240 ...
## $ Overall.Qual : int 6 5 5 4 8 7 4 5 6 8 ...
## $ Overall.Cond : int 6 5 9 8 6 5 4 6 5 5 ...
## $ Year.Built : int 1939 1984 1930 1900 2001 2003 1953 1984 2005 2006 ...
## $ Year.Remod.Add: int 1950 1984 2007 2003 2001 2003 1953 1984 2005 2007 ...
## $ Total.Bsmt.SF : int 856 1049 837 405 810 0 936 864 547 1342 ...
## $ Central.Air : Factor w/ 2 levels "N","Y": 2 2 2 2 2 2 1 2 2 2 ...
## $ X1st.Flr.SF : int 856 1049 1001 717 810 495 936 889 1072 1342 ...
## $ X2nd.Flr.SF : int 0 0 0 322 855 1427 0 0 0 0 ...
## $ Bsmt.Full.Bath: int 1 1 0 0 1 0 0 0 1 0 ...
## $ Bsmt.Half.Bath: int 0 0 0 0 0 0 0 0 0 0 ...
## $ Full.Bath : int 1 2 1 1 2 3 1 1 1 2 ...
## $ Half.Bath : int 0 0 0 0 1 0 0 0 0 0 ...
## $ Bedroom.AbvGr : int 2 2 2 2 3 4 2 3 2 2 ...
## $ Kitchen.AbvGr : int 1 1 1 1 1 1 1 1 1 1 ...
## $ TotRms.AbvGrd : int 4 5 5 6 6 7 4 6 5 6 ...
## $ Fireplaces : int 1 0 0 0 0 1 0 0 0 1 ...
## $ Garage.Cars : int 2 1 1 1 2 2 2 2 2 2 ...
## $ Garage.Area : int 399 266 216 281 528 672 576 484 525 550 ...
## $ Wood.Deck.SF : int 0 0 154 0 0 0 0 0 0 0 ...
## $ Open.Porch.SF : int 0 105 0 0 45 0 32 0 44 35 ...
## $ Enclosed.Porch: int 0 0 42 168 0 177 112 0 0 0 ...
## $ Screen.Porch : int 166 0 0 111 0 0 0 0 0 0 ...
## $ Pool.Area : int 0 0 0 0 0 0 0 0 0 0 ...set.seed(123)
boruta.full <- Boruta(log(price)~.,data = train,doTrace = 2)## 1. run of importance source...## 2. run of importance source...## 3. run of importance source...## 4. run of importance source...## 5. run of importance source...## 6. run of importance source...## 7. run of importance source...## 8. run of importance source...## 9. run of importance source...## 10. run of importance source...## 11. run of importance source...## 12. run of importance source...## After 12 iterations, +34 secs:## confirmed 22 attributes: area, Bedroom.AbvGr, Bsmt.Full.Bath, Central.Air, Fireplaces and 17 more;## still have 4 attributes left.## 13. run of importance source...## 14. run of importance source...## 15. run of importance source...## 16. run of importance source...## After 16 iterations, +45 secs:## rejected 1 attribute: Pool.Area;## still have 3 attributes left.## 17. run of importance source...## 18. run of importance source...## 19. run of importance source...## 20. run of importance source...## 21. run of importance source...## 22. run of importance source...## 23. run of importance source...## 24. run of importance source...## 25. run of importance source...## 26. run of importance source...## 27. run of importance source...## 28. run of importance source...## 29. run of importance source...## 30. run of importance source...## 31. run of importance source...## 32. run of importance source...## 33. run of importance source...## 34. run of importance source...## 35. run of importance source...## 36. run of importance source...## 37. run of importance source...## 38. run of importance source...## 39. run of importance source...## 40. run of importance source...## 41. run of importance source...## 42. run of importance source...## 43. run of importance source...## 44. run of importance source...## 45. run of importance source...## 46. run of importance source...## 47. run of importance source...## 48. run of importance source...## 49. run of importance source...## 50. run of importance source...## 51. run of importance source...## 52. run of importance source...## 53. run of importance source...## 54. run of importance source...## 55. run of importance source...## 56. run of importance source...## After 56 iterations, +2.8 mins:## confirmed 1 attribute: Screen.Porch;## still have 2 attributes left.## 57. run of importance source...## 58. run of importance source...## 59. run of importance source...## 60. run of importance source...## 61. run of importance source...## 62. run of importance source...## 63. run of importance source...## 64. run of importance source...## 65. run of importance source...## 66. run of importance source...## 67. run of importance source...## 68. run of importance source...## 69. run of importance source...## 70. run of importance source...## 71. run of importance source...## 72. run of importance source...## 73. run of importance source...## 74. run of importance source...## 75. run of importance source...## 76. run of importance source...## 77. run of importance source...## 78. run of importance source...## 79. run of importance source...## 80. run of importance source...## 81. run of importance source...## 82. run of importance source...## 83. run of importance source...## 84. run of importance source...## 85. run of importance source...## 86. run of importance source...## 87. run of importance source...## 88. run of importance source...## 89. run of importance source...## 90. run of importance source...## 91. run of importance source...## 92. run of importance source...## 93. run of importance source...## 94. run of importance source...## 95. run of importance source...## 96. run of importance source...## 97. run of importance source...## 98. run of importance source...## 99. run of importance source...print(boruta.full)## Boruta performed 99 iterations in 4.914262 mins.
## 23 attributes confirmed important: area, Bedroom.AbvGr,
## Bsmt.Full.Bath, Central.Air, Fireplaces and 18 more;
## 1 attributes confirmed unimportant: Pool.Area;
## 2 tentative attributes left: Bsmt.Half.Bath, Enclosed.Porch;boruta.train <- Boruta(log(price)~log(area)+Total.Bsmt.SF+Fireplaces+Bsmt.Full.Bath+Overall.Qual+ Lot.Area+Year.Built+Year.Remod.Add+Overall.Cond+Overall.Cond,data = train,doTrace = 2)## 1. run of importance source...## 2. run of importance source...## 3. run of importance source...## 4. run of importance source...## 5. run of importance source...## 6. run of importance source...## 7. run of importance source...## 8. run of importance source...## 9. run of importance source...## 10. run of importance source...## After 10 iterations, +15 secs:## confirmed 9 attributes: Bsmt.Full.Bath, Fireplaces, log(area), Lot.Area, Overall.Cond and 4 more;## no more attributes left.print(boruta.train)## Boruta performed 10 iterations in 14.74638 secs.
## 9 attributes confirmed important: Bsmt.Full.Bath, Fireplaces,
## log(area), Lot.Area, Overall.Cond and 4 more;
## No attributes deemed unimportant.plot(boruta.train, xlab = "", xaxt = "n")
lz<-lapply(1:ncol(boruta.train$ImpHistory),function(i)
boruta.train$ImpHistory[is.finite(boruta.train$ImpHistory[,i]),i])
names(lz) <- colnames(boruta.train$ImpHistory)
Labels <- sort(sapply(lz,median))
axis(side = 1,las=2,labels = names(Labels),
at = 1:ncol(boruta.train$ImpHistory), cex.axis = 0.7)
full.boruta <- TentativeRoughFix(boruta.full)
summary(full.boruta)## Length Class Mode
## finalDecision 26 factor numeric
## ImpHistory 2871 -none- numeric
## pValue 1 -none- numeric
## maxRuns 1 -none- numeric
## light 1 -none- logical
## mcAdj 1 -none- logical
## timeTaken 1 difftime numeric
## roughfixed 1 -none- logical
## call 4 -none- call
## impSource 1 -none- character
## averageOver 1 -none- numeric
## originalDecision 26 factor numericfinal.boruta <- TentativeRoughFix(boruta.train)## Warning in TentativeRoughFix(boruta.train): There are no Tentative
## attributes! Returning original object.summary(final.boruta)## Length Class Mode
## finalDecision 9 factor numeric
## ImpHistory 120 -none- numeric
## pValue 1 -none- numeric
## maxRuns 1 -none- numeric
## light 1 -none- logical
## mcAdj 1 -none- logical
## timeTaken 1 difftime numeric
## roughfixed 1 -none- logical
## call 4 -none- call
## impSource 1 -none- character0.0.0.3 Section 2.2 Model Selection
Models *After variable selection using correlations,best criteria and Boruta** we come to model selection by using regression methods. We have linear regression stepwise,leaps regsubsets methods and bayesian ‘BAS’ method. We are concerned with the prediction of house prices therefore we can a predictive model method.
Model Selection Criteria Information and Non Information based Theoretic Procedures:
The R-squared statistic can be used to compare regression models.A larger R-squared value means that the independent variables can explain a larger percentage of the variation in the independent variable.
This may conflict with parsimony. The adjusted R-squared value takes this into account: \[ R2 = 1 - MSE/TSE = 1 - (1 - R2)[(n - 1) / (n - p - 1)]\]
R2 decreases if there are too many regressors in the model. AIC Akaike Information Criterion n ln(SSE / n) + 2p AIC Baysian Information Criterion n ln(SSE/n) + 2(p+2)s-2q2, where q = n^2/SSE C(p) or Cp Mallows \[C(p) SSE/n^2 + 2p - n\] SBC Schwartz Bayesian Information Criterion n\[ ln(SSE/n) + p ln(n)\] RMSE Root mean square error
Model Selection Strategies
Maximum R-squared Regression
Backward Selection Forward Selection Stepwise Selection LASSO Selection (1996)
Least Angle Regression
Neural Network Leaps Selection Ridge Selection K-fold partition
The selection criteria represent various approaches for balancing model accuracy with parsimony:
Recommendation: use the maximum adjusted R-squared value. Perform stepwise model selection by lowest AIC/BIC. USmallest RMSE in the model makes the optimal bias-variance trade-off. Use lowest Residual. Use minimum predictive error.
Summary Instead of viewing the coefficients, we might be interested in the fitted values and residuals for each of the original points in the regression.
Finally, several summary statistics are computed for the entire regression, such as R2,F-Statistics,Cp,RMSE,RSS and residuals.
I will apply some methods for model selection and compare the results.
0.0.0.3.1 Selecting a Model from training dataset
##
## Call:
## lm(formula = price ~ ., data = train)
##
## Residuals:
## Min 1Q Median 3Q Max
## -74931 -13803 -1484 11078 103188
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -1.212e+06 1.231e+05 -9.849 < 2e-16 ***
## area 3.032e+01 1.645e+01 1.844 0.065612 .
## MS.SubClass -1.084e+02 2.278e+01 -4.759 2.30e-06 ***
## Lot.Area 4.883e-01 8.462e-02 5.770 1.13e-08 ***
## Overall.Qual 1.335e+04 1.010e+03 13.211 < 2e-16 ***
## Overall.Cond 5.076e+03 9.475e+02 5.357 1.11e-07 ***
## Year.Built 4.517e+02 5.377e+01 8.402 < 2e-16 ***
## Year.Remod.Add 1.464e+02 5.778e+01 2.535 0.011445 *
## Total.Bsmt.SF 2.547e+01 3.724e+00 6.839 1.58e-11 ***
## Central.AirY -9.526e+03 4.388e+03 -2.171 0.030223 *
## X1st.Flr.SF 4.132e+01 1.664e+01 2.483 0.013229 *
## X2nd.Flr.SF 3.608e+01 1.624e+01 2.222 0.026554 *
## Bsmt.Full.Bath 1.211e+04 1.799e+03 6.732 3.18e-11 ***
## Bsmt.Half.Bath 1.236e+03 3.541e+03 0.349 0.727168
## Full.Bath -3.603e+03 2.596e+03 -1.388 0.165566
## Half.Bath -1.311e+03 2.390e+03 -0.548 0.583621
## Bedroom.AbvGr -1.110e+04 1.562e+03 -7.106 2.63e-12 ***
## Kitchen.AbvGr -1.870e+04 5.537e+03 -3.377 0.000767 ***
## TotRms.AbvGrd 2.064e+03 1.085e+03 1.902 0.057550 .
## Fireplaces 4.584e+03 1.574e+03 2.913 0.003677 **
## Garage.Cars -6.243e+02 2.678e+03 -0.233 0.815744
## Garage.Area 3.088e+01 9.113e+00 3.389 0.000736 ***
## Wood.Deck.SF 1.450e+01 7.442e+00 1.948 0.051747 .
## Open.Porch.SF 2.848e+00 1.431e+01 0.199 0.842264
## Enclosed.Porch 1.029e+01 1.496e+01 0.688 0.491824
## Screen.Porch 1.057e+01 1.564e+01 0.676 0.499087
## Pool.Area -7.637e+01 2.589e+01 -2.950 0.003270 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 23000 on 805 degrees of freedom
## Multiple R-squared: 0.8942, Adjusted R-squared: 0.8907
## F-statistic: 261.6 on 26 and 805 DF, p-value: < 2.2e-16## r.squared adj.r.squared sigma statistic p.value df logLik AIC
## 1 0.8941601 0.8907417 23001.31 261.5704 0 27 -9522.864 19101.73
## BIC deviance df.residual
## 1 19234 425893492525 805## term estimate std.error statistic p.value
## 1 (Intercept) -1.211947e+06 1.230556e+05 -9.8487733 1.099775e-21
## 2 area 3.031877e+01 1.644560e+01 1.8435800 6.561177e-02
## 3 MS.SubClass -1.084201e+02 2.278065e+01 -4.7593076 2.302683e-06
## 4 Lot.Area 4.882464e-01 8.461716e-02 5.7700638 1.130185e-08
## 5 Overall.Qual 1.334913e+04 1.010482e+03 13.2106636 3.316927e-36
## 6 Overall.Cond 5.075551e+03 9.475114e+02 5.3567181 1.106895e-07
## 7 Year.Built 4.517220e+02 5.376617e+01 8.4016027 1.982193e-16
## 8 Year.Remod.Add 1.464482e+02 5.777915e+01 2.5346195 1.144534e-02
## 9 Total.Bsmt.SF 2.546510e+01 3.723605e+00 6.8388294 1.579268e-11
## 10 Central.AirY -9.525989e+03 4.387851e+03 -2.1709922 3.022329e-02
## 11 X1st.Flr.SF 4.131964e+01 1.664073e+01 2.4830422 1.322922e-02
## 12 X2nd.Flr.SF 3.608194e+01 1.623774e+01 2.2221042 2.655351e-02
## 13 Bsmt.Full.Bath 1.211103e+04 1.798995e+03 6.7321080 3.177822e-11
## 14 Bsmt.Half.Bath 1.235989e+03 3.541340e+03 0.3490174 7.271675e-01
## 15 Full.Bath -3.603237e+03 2.596269e+03 -1.3878522 1.655661e-01
## 16 Half.Bath -1.310726e+03 2.390422e+03 -0.5483243 5.836213e-01
## 17 Bedroom.AbvGr -1.110326e+04 1.562459e+03 -7.1062749 2.628113e-12
## 18 Kitchen.AbvGr -1.869917e+04 5.536856e+03 -3.3772183 7.673724e-04
## 19 TotRms.AbvGrd 2.063940e+03 1.085238e+03 1.9018319 5.754987e-02
## 20 Fireplaces 4.584129e+03 1.573607e+03 2.9131336 3.677249e-03
## 21 Garage.Cars -6.243220e+02 2.678361e+03 -0.2330986 8.157441e-01
## 22 Garage.Area 3.088009e+01 9.112758e+00 3.3886653 7.364796e-04
## 23 Wood.Deck.SF 1.449856e+01 7.442318e+00 1.9481239 5.174734e-02
## 24 Open.Porch.SF 2.848424e+00 1.430915e+01 0.1990631 8.422637e-01
## 25 Enclosed.Porch 1.028916e+01 1.496116e+01 0.6877247 4.918243e-01
## 26 Screen.Porch 1.057325e+01 1.563553e+01 0.6762322 4.990875e-01
## 27 Pool.Area -7.636692e+01 2.588753e+01 -2.9499504 3.270367e-03
## price area MS.SubClass Lot.Area Overall.Qual Overall.Cond Year.Built
## 1 126000 856 30 7890 6 6 1939
## 2 139500 1049 120 4235 5 5 1984
## 3 124900 1001 30 6060 5 9 1930
## 4 114000 1039 70 8146 4 8 1900
## 5 227000 1665 60 8400 8 6 2001
## 6 198500 1922 85 7301 7 5 2003
## Year.Remod.Add Total.Bsmt.SF Central.Air X1st.Flr.SF X2nd.Flr.SF
## 1 1950 856 Y 856 0
## 2 1984 1049 Y 1049 0
## 3 2007 837 Y 1001 0
## 4 2003 405 Y 717 322
## 5 2001 810 Y 810 855
## 6 2003 0 Y 495 1427
## Bsmt.Full.Bath Bsmt.Half.Bath Full.Bath Half.Bath Bedroom.AbvGr
## 1 1 0 1 0 2
## 2 1 0 2 0 2
## 3 0 0 1 0 2
## 4 0 0 1 0 2
## 5 1 0 2 1 3
## 6 0 0 3 0 4
## Kitchen.AbvGr TotRms.AbvGrd Fireplaces Garage.Cars Garage.Area
## 1 1 4 1 2 399
## 2 1 5 0 1 266
## 3 1 5 0 1 216
## 4 1 6 0 1 281
## 5 1 6 0 2 528
## 6 1 7 1 2 672
## Wood.Deck.SF Open.Porch.SF Enclosed.Porch Screen.Porch Pool.Area
## 1 0 0 0 166 0
## 2 0 105 0 0 0
## 3 154 0 42 0 0
## 4 0 0 168 111 0
## 5 0 45 0 0 0
## 6 0 0 177 0 0
## .fitted .se.fit .resid .hat .sigma .cooksd
## 1 127528.09 3933.694 -1528.088 0.02924800 23015.54 5.073497e-06
## 2 130546.52 3213.091 8953.475 0.01951376 23013.40 1.139127e-04
## 3 123949.71 3362.531 950.291 0.02137113 23015.58 1.410704e-06
## 4 82412.48 4344.247 31587.522 0.03567170 22987.63 2.679392e-03
## 5 224887.30 3190.772 2112.695 0.01924361 23015.49 6.251283e-06
## 6 186481.25 5943.841 12018.748 0.06677735 23011.43 7.753687e-04
## .std.resid
## 1 -0.06742822
## 2 0.39311383
## 3 0.04176332
## 4 1.39846157
## 5 0.09274783
## 6 0.54089634##
## Marginal Posterior Summaries of Coefficients:
##
## Using BMA
##
## Based on the top 8524 models
## post mean post SD post p(B != 0)
## Intercept 1.199e+01 3.757e-03 1.000e+00
## area 2.930e-04 2.735e-05 9.964e-01
## MS.SubClass -5.387e-04 1.033e-04 9.998e-01
## Lot.Area 2.379e-06 3.967e-07 1.000e+00
## Overall.Qual 7.771e-02 4.780e-03 1.000e+00
## Overall.Cond 4.258e-02 4.395e-03 1.000e+00
## Year.Built 2.806e-03 2.311e-04 1.000e+00
## Year.Remod.Add 1.233e-03 2.725e-04 9.994e-01
## Total.Bsmt.SF 1.407e-04 1.381e-05 1.000e+00
## Central.AirY 9.574e-02 2.057e-02 9.992e-01
## X1st.Flr.SF 2.257e-06 2.099e-05 5.488e-02
## X2nd.Flr.SF 1.212e-06 1.966e-05 4.675e-02
## Bsmt.Full.Bath 6.728e-02 8.267e-03 1.000e+00
## Bsmt.Half.Bath 4.869e-03 1.306e-02 1.617e-01
## Full.Bath -5.500e-04 3.530e-03 5.609e-02
## Half.Bath -1.676e-05 1.963e-03 3.886e-02
## Bedroom.AbvGr -1.563e-02 1.018e-02 7.808e-01
## Kitchen.AbvGr -6.885e-03 1.862e-02 1.596e-01
## TotRms.AbvGrd 5.839e-04 2.472e-03 8.852e-02
## Fireplaces 3.837e-02 7.517e-03 9.999e-01
## Garage.Cars 4.948e-03 1.304e-02 1.672e-01
## Garage.Area 1.455e-04 5.005e-05 9.286e-01
## Wood.Deck.SF 2.280e-06 1.247e-05 6.369e-02
## Open.Porch.SF 3.859e-06 2.237e-05 5.936e-02
## Enclosed.Porch 2.187e-05 5.611e-05 1.718e-01
## Screen.Porch 9.153e-05 1.062e-04 4.924e-01
## Pool.Area -1.433e-04 1.729e-04 4.729e-01
## Start: AIC=-3689.88
## log(price) ~ area + MS.SubClass + Lot.Area + Overall.Qual + Overall.Cond +
## Year.Built + Year.Remod.Add + Total.Bsmt.SF + Central.Air +
## X1st.Flr.SF + X2nd.Flr.SF + Bsmt.Full.Bath + Bsmt.Half.Bath +
## Full.Bath + Half.Bath + Bedroom.AbvGr + Kitchen.AbvGr + TotRms.AbvGrd +
## Fireplaces + Garage.Cars + Garage.Area + Wood.Deck.SF + Open.Porch.SF +
## Enclosed.Porch + Screen.Porch + Pool.Area
##
## Df Sum of Sq RSS AIC
## - Half.Bath 1 0.00092 9.2449 -3691.8
## - Full.Bath 1 0.00288 9.2469 -3691.6
## - Wood.Deck.SF 1 0.01156 9.2556 -3690.8
## - Open.Porch.SF 1 0.01564 9.2596 -3690.5
## <none> 9.2440 -3689.9
## - Garage.Cars 1 0.02240 9.2664 -3689.9
## - X2nd.Flr.SF 1 0.02894 9.2729 -3689.3
## - X1st.Flr.SF 1 0.03721 9.2812 -3688.5
## - Bsmt.Half.Bath 1 0.04598 9.2900 -3687.8
## - Kitchen.AbvGr 1 0.05129 9.2953 -3687.3
## - TotRms.AbvGrd 1 0.05150 9.2955 -3687.3
## - area 1 0.05243 9.2964 -3687.2
## - Enclosed.Porch 1 0.05582 9.2998 -3686.9
## - Garage.Area 1 0.07314 9.3172 -3685.3
## - Screen.Porch 1 0.09833 9.3423 -3683.1
## - Bedroom.AbvGr 1 0.10499 9.3490 -3682.5
## - Pool.Area 1 0.12147 9.3655 -3681.0
## - MS.SubClass 1 0.19632 9.4403 -3674.4
## - Year.Remod.Add 1 0.22748 9.4715 -3671.7
## - Fireplaces 1 0.23419 9.4782 -3671.1
## - Central.Air 1 0.26825 9.5123 -3668.1
## - Lot.Area 1 0.38660 9.6306 -3657.8
## - Total.Bsmt.SF 1 0.63774 9.8818 -3636.4
## - Bsmt.Full.Bath 1 0.79905 10.0431 -3622.9
## - Overall.Cond 1 0.98715 10.2312 -3607.5
## - Year.Built 1 1.53646 10.7805 -3564.0
## - Overall.Qual 1 2.82227 12.0663 -3470.2
##
## Step: AIC=-3691.8
## log(price) ~ area + MS.SubClass + Lot.Area + Overall.Qual + Overall.Cond +
## Year.Built + Year.Remod.Add + Total.Bsmt.SF + Central.Air +
## X1st.Flr.SF + X2nd.Flr.SF + Bsmt.Full.Bath + Bsmt.Half.Bath +
## Full.Bath + Bedroom.AbvGr + Kitchen.AbvGr + TotRms.AbvGrd +
## Fireplaces + Garage.Cars + Garage.Area + Wood.Deck.SF + Open.Porch.SF +
## Enclosed.Porch + Screen.Porch + Pool.Area
##
## Df Sum of Sq RSS AIC
## - Full.Bath 1 0.00208 9.2470 -3693.6
## - Wood.Deck.SF 1 0.01135 9.2563 -3692.8
## - Open.Porch.SF 1 0.01508 9.2600 -3692.4
## - Garage.Cars 1 0.02175 9.2667 -3691.8
## <none> 9.2449 -3691.8
## - X2nd.Flr.SF 1 0.02850 9.2734 -3691.2
## - X1st.Flr.SF 1 0.03804 9.2830 -3690.4
## - Bsmt.Half.Bath 1 0.04650 9.2914 -3689.6
## - area 1 0.05158 9.2965 -3689.2
## - Kitchen.AbvGr 1 0.05212 9.2970 -3689.1
## - TotRms.AbvGrd 1 0.05288 9.2978 -3689.1
## - Enclosed.Porch 1 0.05609 9.3010 -3688.8
## - Garage.Area 1 0.07605 9.3210 -3687.0
## - Screen.Porch 1 0.09747 9.3424 -3685.1
## - Bedroom.AbvGr 1 0.10593 9.3509 -3684.3
## - Pool.Area 1 0.12082 9.3658 -3683.0
## - MS.SubClass 1 0.19548 9.4404 -3676.4
## - Year.Remod.Add 1 0.22674 9.4717 -3673.6
## - Fireplaces 1 0.23390 9.4788 -3673.0
## - Central.Air 1 0.26734 9.5123 -3670.1
## - Lot.Area 1 0.38707 9.6320 -3659.7
## - Total.Bsmt.SF 1 0.64177 9.8867 -3638.0
## - Bsmt.Full.Bath 1 0.80146 10.0464 -3624.6
## - Overall.Cond 1 0.99381 10.2387 -3608.8
## - Year.Built 1 1.65506 10.9000 -3556.8
## - Overall.Qual 1 2.82495 12.0699 -3472.0
##
## Step: AIC=-3693.61
## log(price) ~ area + MS.SubClass + Lot.Area + Overall.Qual + Overall.Cond +
## Year.Built + Year.Remod.Add + Total.Bsmt.SF + Central.Air +
## X1st.Flr.SF + X2nd.Flr.SF + Bsmt.Full.Bath + Bsmt.Half.Bath +
## Bedroom.AbvGr + Kitchen.AbvGr + TotRms.AbvGrd + Fireplaces +
## Garage.Cars + Garage.Area + Wood.Deck.SF + Open.Porch.SF +
## Enclosed.Porch + Screen.Porch + Pool.Area
##
## Df Sum of Sq RSS AIC
## - Wood.Deck.SF 1 0.01131 9.2583 -3694.6
## - Open.Porch.SF 1 0.01447 9.2615 -3694.3
## - Garage.Cars 1 0.02036 9.2674 -3693.8
## <none> 9.2470 -3693.6
## - X2nd.Flr.SF 1 0.02939 9.2764 -3693.0
## - X1st.Flr.SF 1 0.03905 9.2861 -3692.1
## - Bsmt.Half.Bath 1 0.04676 9.2938 -3691.4
## - area 1 0.04979 9.2968 -3691.1
## - TotRms.AbvGrd 1 0.05429 9.3013 -3690.7
## - Enclosed.Porch 1 0.05585 9.3029 -3690.6
## - Kitchen.AbvGr 1 0.06049 9.3075 -3690.2
## - Garage.Area 1 0.08130 9.3283 -3688.3
## - Screen.Porch 1 0.09752 9.3445 -3686.9
## - Bedroom.AbvGr 1 0.11007 9.3571 -3685.8
## - Pool.Area 1 0.12278 9.3698 -3684.6
## - MS.SubClass 1 0.19514 9.4421 -3678.2
## - Year.Remod.Add 1 0.22576 9.4728 -3675.5
## - Fireplaces 1 0.23637 9.4834 -3674.6
## - Central.Air 1 0.27019 9.5172 -3671.6
## - Lot.Area 1 0.38563 9.6326 -3661.6
## - Total.Bsmt.SF 1 0.64249 9.8895 -3639.7
## - Bsmt.Full.Bath 1 0.82164 10.0686 -3624.8
## - Overall.Cond 1 1.00792 10.2549 -3609.5
## - Year.Built 1 1.71755 10.9646 -3553.9
## - Overall.Qual 1 2.83177 12.0788 -3473.3
##
## Step: AIC=-3694.59
## log(price) ~ area + MS.SubClass + Lot.Area + Overall.Qual + Overall.Cond +
## Year.Built + Year.Remod.Add + Total.Bsmt.SF + Central.Air +
## X1st.Flr.SF + X2nd.Flr.SF + Bsmt.Full.Bath + Bsmt.Half.Bath +
## Bedroom.AbvGr + Kitchen.AbvGr + TotRms.AbvGrd + Fireplaces +
## Garage.Cars + Garage.Area + Open.Porch.SF + Enclosed.Porch +
## Screen.Porch + Pool.Area
##
## Df Sum of Sq RSS AIC
## - Open.Porch.SF 1 0.01243 9.2707 -3695.5
## - Garage.Cars 1 0.01992 9.2782 -3694.8
## <none> 9.2583 -3694.6
## - X2nd.Flr.SF 1 0.02969 9.2880 -3693.9
## - X1st.Flr.SF 1 0.03919 9.2975 -3693.1
## - area 1 0.05131 9.3096 -3692.0
## - Bsmt.Half.Bath 1 0.05342 9.3117 -3691.8
## - Enclosed.Porch 1 0.05460 9.3129 -3691.7
## - TotRms.AbvGrd 1 0.05539 9.3137 -3691.6
## - Kitchen.AbvGr 1 0.06507 9.3234 -3690.8
## - Garage.Area 1 0.08469 9.3430 -3689.0
## - Screen.Porch 1 0.09130 9.3496 -3688.4
## - Bedroom.AbvGr 1 0.11648 9.3748 -3686.2
## - Pool.Area 1 0.11913 9.3774 -3686.0
## - MS.SubClass 1 0.19863 9.4569 -3678.9
## - Year.Remod.Add 1 0.22734 9.4857 -3676.4
## - Fireplaces 1 0.24519 9.5035 -3674.8
## - Central.Air 1 0.26440 9.5227 -3673.2
## - Lot.Area 1 0.38244 9.6408 -3662.9
## - Total.Bsmt.SF 1 0.65358 9.9119 -3639.8
## - Bsmt.Full.Bath 1 0.87893 10.1372 -3621.1
## - Overall.Cond 1 1.07016 10.3285 -3605.6
## - Year.Built 1 1.78792 11.0462 -3549.7
## - Overall.Qual 1 2.82046 12.0788 -3475.3
##
## Step: AIC=-3695.48
## log(price) ~ area + MS.SubClass + Lot.Area + Overall.Qual + Overall.Cond +
## Year.Built + Year.Remod.Add + Total.Bsmt.SF + Central.Air +
## X1st.Flr.SF + X2nd.Flr.SF + Bsmt.Full.Bath + Bsmt.Half.Bath +
## Bedroom.AbvGr + Kitchen.AbvGr + TotRms.AbvGrd + Fireplaces +
## Garage.Cars + Garage.Area + Enclosed.Porch + Screen.Porch +
## Pool.Area
##
## Df Sum of Sq RSS AIC
## - Garage.Cars 1 0.01880 9.2895 -3695.8
## <none> 9.2707 -3695.5
## - X2nd.Flr.SF 1 0.03241 9.3032 -3694.6
## - X1st.Flr.SF 1 0.04106 9.3118 -3693.8
## - area 1 0.05016 9.3209 -3693.0
## - Enclosed.Porch 1 0.05205 9.3228 -3692.8
## - Bsmt.Half.Bath 1 0.05416 9.3249 -3692.6
## - TotRms.AbvGrd 1 0.05540 9.3261 -3692.5
## - Kitchen.AbvGr 1 0.06672 9.3375 -3691.5
## - Garage.Area 1 0.08578 9.3565 -3689.8
## - Screen.Porch 1 0.08754 9.3583 -3689.7
## - Pool.Area 1 0.11824 9.3890 -3686.9
## - Bedroom.AbvGr 1 0.12384 9.3946 -3686.4
## - MS.SubClass 1 0.20453 9.4753 -3679.3
## - Year.Remod.Add 1 0.22811 9.4989 -3677.3
## - Fireplaces 1 0.24310 9.5138 -3675.9
## - Central.Air 1 0.26733 9.5381 -3673.8
## - Lot.Area 1 0.37962 9.6504 -3664.1
## - Total.Bsmt.SF 1 0.68799 9.9587 -3637.9
## - Bsmt.Full.Bath 1 0.88087 10.1516 -3622.0
## - Overall.Cond 1 1.06273 10.3335 -3607.2
## - Year.Built 1 1.79560 11.0663 -3550.2
## - Overall.Qual 1 2.83448 12.1052 -3475.5
##
## Step: AIC=-3695.79
## log(price) ~ area + MS.SubClass + Lot.Area + Overall.Qual + Overall.Cond +
## Year.Built + Year.Remod.Add + Total.Bsmt.SF + Central.Air +
## X1st.Flr.SF + X2nd.Flr.SF + Bsmt.Full.Bath + Bsmt.Half.Bath +
## Bedroom.AbvGr + Kitchen.AbvGr + TotRms.AbvGrd + Fireplaces +
## Garage.Area + Enclosed.Porch + Screen.Porch + Pool.Area
##
## Df Sum of Sq RSS AIC
## <none> 9.2895 -3695.8
## - X2nd.Flr.SF 1 0.03348 9.3230 -3694.8
## - X1st.Flr.SF 1 0.04142 9.3310 -3694.1
## - area 1 0.04971 9.3393 -3693.4
## - Bsmt.Half.Bath 1 0.05457 9.3441 -3692.9
## - TotRms.AbvGrd 1 0.05792 9.3475 -3692.6
## - Enclosed.Porch 1 0.05917 9.3487 -3692.5
## - Kitchen.AbvGr 1 0.06168 9.3512 -3692.3
## - Screen.Porch 1 0.09077 9.3803 -3689.7
## - Pool.Area 1 0.12152 9.4111 -3687.0
## - Bedroom.AbvGr 1 0.12684 9.4164 -3686.5
## - MS.SubClass 1 0.19981 9.4894 -3680.1
## - Year.Remod.Add 1 0.23642 9.5260 -3676.9
## - Fireplaces 1 0.24625 9.5358 -3676.0
## - Central.Air 1 0.26447 9.5540 -3674.4
## - Lot.Area 1 0.38905 9.6786 -3663.7
## - Garage.Area 1 0.49250 9.7820 -3654.8
## - Total.Bsmt.SF 1 0.69127 9.9808 -3638.1
## - Bsmt.Full.Bath 1 0.88744 10.1770 -3621.9
## - Overall.Cond 1 1.05728 10.3468 -3608.1
## - Year.Built 1 1.89720 11.1867 -3543.2
## - Overall.Qual 1 2.93195 12.2215 -3469.6## Start: AIC=-3689.88
## log(price) ~ area + MS.SubClass + Lot.Area + Overall.Qual + Overall.Cond +
## Year.Built + Year.Remod.Add + Total.Bsmt.SF + Central.Air +
## X1st.Flr.SF + X2nd.Flr.SF + Bsmt.Full.Bath + Bsmt.Half.Bath +
## Full.Bath + Half.Bath + Bedroom.AbvGr + Kitchen.AbvGr + TotRms.AbvGrd +
## Fireplaces + Garage.Cars + Garage.Area + Wood.Deck.SF + Open.Porch.SF +
## Enclosed.Porch + Screen.Porch + Pool.Area
##
## Df Sum of Sq RSS AIC
## - Half.Bath 1 0.00092 9.2449 -3691.8
## - Full.Bath 1 0.00288 9.2469 -3691.6
## - Wood.Deck.SF 1 0.01156 9.2556 -3690.8
## - Open.Porch.SF 1 0.01564 9.2596 -3690.5
## <none> 9.2440 -3689.9
## - Garage.Cars 1 0.02240 9.2664 -3689.9
## - X2nd.Flr.SF 1 0.02894 9.2729 -3689.3
## - X1st.Flr.SF 1 0.03721 9.2812 -3688.5
## - Bsmt.Half.Bath 1 0.04598 9.2900 -3687.8
## - Kitchen.AbvGr 1 0.05129 9.2953 -3687.3
## - TotRms.AbvGrd 1 0.05150 9.2955 -3687.3
## - area 1 0.05243 9.2964 -3687.2
## - Enclosed.Porch 1 0.05582 9.2998 -3686.9
## - Garage.Area 1 0.07314 9.3172 -3685.3
## - Screen.Porch 1 0.09833 9.3423 -3683.1
## - Bedroom.AbvGr 1 0.10499 9.3490 -3682.5
## - Pool.Area 1 0.12147 9.3655 -3681.0
## - MS.SubClass 1 0.19632 9.4403 -3674.4
## - Year.Remod.Add 1 0.22748 9.4715 -3671.7
## - Fireplaces 1 0.23419 9.4782 -3671.1
## - Central.Air 1 0.26825 9.5123 -3668.1
## - Lot.Area 1 0.38660 9.6306 -3657.8
## - Total.Bsmt.SF 1 0.63774 9.8818 -3636.4
## - Bsmt.Full.Bath 1 0.79905 10.0431 -3622.9
## - Overall.Cond 1 0.98715 10.2312 -3607.5
## - Year.Built 1 1.53646 10.7805 -3564.0
## - Overall.Qual 1 2.82227 12.0663 -3470.2
##
## Step: AIC=-3691.8
## log(price) ~ area + MS.SubClass + Lot.Area + Overall.Qual + Overall.Cond +
## Year.Built + Year.Remod.Add + Total.Bsmt.SF + Central.Air +
## X1st.Flr.SF + X2nd.Flr.SF + Bsmt.Full.Bath + Bsmt.Half.Bath +
## Full.Bath + Bedroom.AbvGr + Kitchen.AbvGr + TotRms.AbvGrd +
## Fireplaces + Garage.Cars + Garage.Area + Wood.Deck.SF + Open.Porch.SF +
## Enclosed.Porch + Screen.Porch + Pool.Area
##
## Df Sum of Sq RSS AIC
## - Full.Bath 1 0.00208 9.2470 -3693.6
## - Wood.Deck.SF 1 0.01135 9.2563 -3692.8
## - Open.Porch.SF 1 0.01508 9.2600 -3692.4
## - Garage.Cars 1 0.02175 9.2667 -3691.8
## <none> 9.2449 -3691.8
## - X2nd.Flr.SF 1 0.02850 9.2734 -3691.2
## - X1st.Flr.SF 1 0.03804 9.2830 -3690.4
## - Bsmt.Half.Bath 1 0.04650 9.2914 -3689.6
## - area 1 0.05158 9.2965 -3689.2
## - Kitchen.AbvGr 1 0.05212 9.2970 -3689.1
## - TotRms.AbvGrd 1 0.05288 9.2978 -3689.1
## - Enclosed.Porch 1 0.05609 9.3010 -3688.8
## - Garage.Area 1 0.07605 9.3210 -3687.0
## - Screen.Porch 1 0.09747 9.3424 -3685.1
## - Bedroom.AbvGr 1 0.10593 9.3509 -3684.3
## - Pool.Area 1 0.12082 9.3658 -3683.0
## - MS.SubClass 1 0.19548 9.4404 -3676.4
## - Year.Remod.Add 1 0.22674 9.4717 -3673.6
## - Fireplaces 1 0.23390 9.4788 -3673.0
## - Central.Air 1 0.26734 9.5123 -3670.1
## - Lot.Area 1 0.38707 9.6320 -3659.7
## - Total.Bsmt.SF 1 0.64177 9.8867 -3638.0
## - Bsmt.Full.Bath 1 0.80146 10.0464 -3624.6
## - Overall.Cond 1 0.99381 10.2387 -3608.8
## - Year.Built 1 1.65506 10.9000 -3556.8
## - Overall.Qual 1 2.82495 12.0699 -3472.0
##
## Step: AIC=-3693.61
## log(price) ~ area + MS.SubClass + Lot.Area + Overall.Qual + Overall.Cond +
## Year.Built + Year.Remod.Add + Total.Bsmt.SF + Central.Air +
## X1st.Flr.SF + X2nd.Flr.SF + Bsmt.Full.Bath + Bsmt.Half.Bath +
## Bedroom.AbvGr + Kitchen.AbvGr + TotRms.AbvGrd + Fireplaces +
## Garage.Cars + Garage.Area + Wood.Deck.SF + Open.Porch.SF +
## Enclosed.Porch + Screen.Porch + Pool.Area
##
## Df Sum of Sq RSS AIC
## - Wood.Deck.SF 1 0.01131 9.2583 -3694.6
## - Open.Porch.SF 1 0.01447 9.2615 -3694.3
## - Garage.Cars 1 0.02036 9.2674 -3693.8
## <none> 9.2470 -3693.6
## - X2nd.Flr.SF 1 0.02939 9.2764 -3693.0
## - X1st.Flr.SF 1 0.03905 9.2861 -3692.1
## - Bsmt.Half.Bath 1 0.04676 9.2938 -3691.4
## - area 1 0.04979 9.2968 -3691.1
## - TotRms.AbvGrd 1 0.05429 9.3013 -3690.7
## - Enclosed.Porch 1 0.05585 9.3029 -3690.6
## - Kitchen.AbvGr 1 0.06049 9.3075 -3690.2
## - Garage.Area 1 0.08130 9.3283 -3688.3
## - Screen.Porch 1 0.09752 9.3445 -3686.9
## - Bedroom.AbvGr 1 0.11007 9.3571 -3685.8
## - Pool.Area 1 0.12278 9.3698 -3684.6
## - MS.SubClass 1 0.19514 9.4421 -3678.2
## - Year.Remod.Add 1 0.22576 9.4728 -3675.5
## - Fireplaces 1 0.23637 9.4834 -3674.6
## - Central.Air 1 0.27019 9.5172 -3671.6
## - Lot.Area 1 0.38563 9.6326 -3661.6
## - Total.Bsmt.SF 1 0.64249 9.8895 -3639.7
## - Bsmt.Full.Bath 1 0.82164 10.0686 -3624.8
## - Overall.Cond 1 1.00792 10.2549 -3609.5
## - Year.Built 1 1.71755 10.9646 -3553.9
## - Overall.Qual 1 2.83177 12.0788 -3473.3
##
## Step: AIC=-3694.59
## log(price) ~ area + MS.SubClass + Lot.Area + Overall.Qual + Overall.Cond +
## Year.Built + Year.Remod.Add + Total.Bsmt.SF + Central.Air +
## X1st.Flr.SF + X2nd.Flr.SF + Bsmt.Full.Bath + Bsmt.Half.Bath +
## Bedroom.AbvGr + Kitchen.AbvGr + TotRms.AbvGrd + Fireplaces +
## Garage.Cars + Garage.Area + Open.Porch.SF + Enclosed.Porch +
## Screen.Porch + Pool.Area
##
## Df Sum of Sq RSS AIC
## - Open.Porch.SF 1 0.01243 9.2707 -3695.5
## - Garage.Cars 1 0.01992 9.2782 -3694.8
## <none> 9.2583 -3694.6
## - X2nd.Flr.SF 1 0.02969 9.2880 -3693.9
## - X1st.Flr.SF 1 0.03919 9.2975 -3693.1
## - area 1 0.05131 9.3096 -3692.0
## - Bsmt.Half.Bath 1 0.05342 9.3117 -3691.8
## - Enclosed.Porch 1 0.05460 9.3129 -3691.7
## - TotRms.AbvGrd 1 0.05539 9.3137 -3691.6
## - Kitchen.AbvGr 1 0.06507 9.3234 -3690.8
## - Garage.Area 1 0.08469 9.3430 -3689.0
## - Screen.Porch 1 0.09130 9.3496 -3688.4
## - Bedroom.AbvGr 1 0.11648 9.3748 -3686.2
## - Pool.Area 1 0.11913 9.3774 -3686.0
## - MS.SubClass 1 0.19863 9.4569 -3678.9
## - Year.Remod.Add 1 0.22734 9.4857 -3676.4
## - Fireplaces 1 0.24519 9.5035 -3674.8
## - Central.Air 1 0.26440 9.5227 -3673.2
## - Lot.Area 1 0.38244 9.6408 -3662.9
## - Total.Bsmt.SF 1 0.65358 9.9119 -3639.8
## - Bsmt.Full.Bath 1 0.87893 10.1372 -3621.1
## - Overall.Cond 1 1.07016 10.3285 -3605.6
## - Year.Built 1 1.78792 11.0462 -3549.7
## - Overall.Qual 1 2.82046 12.0788 -3475.3
##
## Step: AIC=-3695.48
## log(price) ~ area + MS.SubClass + Lot.Area + Overall.Qual + Overall.Cond +
## Year.Built + Year.Remod.Add + Total.Bsmt.SF + Central.Air +
## X1st.Flr.SF + X2nd.Flr.SF + Bsmt.Full.Bath + Bsmt.Half.Bath +
## Bedroom.AbvGr + Kitchen.AbvGr + TotRms.AbvGrd + Fireplaces +
## Garage.Cars + Garage.Area + Enclosed.Porch + Screen.Porch +
## Pool.Area
##
## Df Sum of Sq RSS AIC
## - Garage.Cars 1 0.01880 9.2895 -3695.8
## <none> 9.2707 -3695.5
## - X2nd.Flr.SF 1 0.03241 9.3032 -3694.6
## - X1st.Flr.SF 1 0.04106 9.3118 -3693.8
## - area 1 0.05016 9.3209 -3693.0
## - Enclosed.Porch 1 0.05205 9.3228 -3692.8
## - Bsmt.Half.Bath 1 0.05416 9.3249 -3692.6
## - TotRms.AbvGrd 1 0.05540 9.3261 -3692.5
## - Kitchen.AbvGr 1 0.06672 9.3375 -3691.5
## - Garage.Area 1 0.08578 9.3565 -3689.8
## - Screen.Porch 1 0.08754 9.3583 -3689.7
## - Pool.Area 1 0.11824 9.3890 -3686.9
## - Bedroom.AbvGr 1 0.12384 9.3946 -3686.4
## - MS.SubClass 1 0.20453 9.4753 -3679.3
## - Year.Remod.Add 1 0.22811 9.4989 -3677.3
## - Fireplaces 1 0.24310 9.5138 -3675.9
## - Central.Air 1 0.26733 9.5381 -3673.8
## - Lot.Area 1 0.37962 9.6504 -3664.1
## - Total.Bsmt.SF 1 0.68799 9.9587 -3637.9
## - Bsmt.Full.Bath 1 0.88087 10.1516 -3622.0
## - Overall.Cond 1 1.06273 10.3335 -3607.2
## - Year.Built 1 1.79560 11.0663 -3550.2
## - Overall.Qual 1 2.83448 12.1052 -3475.5
##
## Step: AIC=-3695.79
## log(price) ~ area + MS.SubClass + Lot.Area + Overall.Qual + Overall.Cond +
## Year.Built + Year.Remod.Add + Total.Bsmt.SF + Central.Air +
## X1st.Flr.SF + X2nd.Flr.SF + Bsmt.Full.Bath + Bsmt.Half.Bath +
## Bedroom.AbvGr + Kitchen.AbvGr + TotRms.AbvGrd + Fireplaces +
## Garage.Area + Enclosed.Porch + Screen.Porch + Pool.Area
##
## Df Sum of Sq RSS AIC
## <none> 9.2895 -3695.8
## - X2nd.Flr.SF 1 0.03348 9.3230 -3694.8
## - X1st.Flr.SF 1 0.04142 9.3310 -3694.1
## - area 1 0.04971 9.3393 -3693.4
## - Bsmt.Half.Bath 1 0.05457 9.3441 -3692.9
## - TotRms.AbvGrd 1 0.05792 9.3475 -3692.6
## - Enclosed.Porch 1 0.05917 9.3487 -3692.5
## - Kitchen.AbvGr 1 0.06168 9.3512 -3692.3
## - Screen.Porch 1 0.09077 9.3803 -3689.7
## - Pool.Area 1 0.12152 9.4111 -3687.0
## - Bedroom.AbvGr 1 0.12684 9.4164 -3686.5
## - MS.SubClass 1 0.19981 9.4894 -3680.1
## - Year.Remod.Add 1 0.23642 9.5260 -3676.9
## - Fireplaces 1 0.24625 9.5358 -3676.0
## - Central.Air 1 0.26447 9.5540 -3674.4
## - Lot.Area 1 0.38905 9.6786 -3663.7
## - Garage.Area 1 0.49250 9.7820 -3654.8
## - Total.Bsmt.SF 1 0.69127 9.9808 -3638.1
## - Bsmt.Full.Bath 1 0.88744 10.1770 -3621.9
## - Overall.Cond 1 1.05728 10.3468 -3608.1
## - Year.Built 1 1.89720 11.1867 -3543.2
## - Overall.Qual 1 2.93195 12.2215 -3469.6## Start: AIC=-3562.34
## log(price) ~ area + MS.SubClass + Lot.Area + Overall.Qual + Overall.Cond +
## Year.Built + Year.Remod.Add + Total.Bsmt.SF + Central.Air +
## X1st.Flr.SF + X2nd.Flr.SF + Bsmt.Full.Bath + Bsmt.Half.Bath +
## Full.Bath + Half.Bath + Bedroom.AbvGr + Kitchen.AbvGr + TotRms.AbvGrd +
## Fireplaces + Garage.Cars + Garage.Area + Wood.Deck.SF + Open.Porch.SF +
## Enclosed.Porch + Screen.Porch + Pool.Area
##
## Df Sum of Sq RSS AIC
## - Half.Bath 1 0.00092 9.2449 -3569.0
## - Full.Bath 1 0.00288 9.2469 -3568.8
## - Wood.Deck.SF 1 0.01156 9.2556 -3568.0
## - Open.Porch.SF 1 0.01564 9.2596 -3567.7
## - Garage.Cars 1 0.02240 9.2664 -3567.0
## - X2nd.Flr.SF 1 0.02894 9.2729 -3566.5
## - X1st.Flr.SF 1 0.03721 9.2812 -3565.7
## - Bsmt.Half.Bath 1 0.04598 9.2900 -3564.9
## - Kitchen.AbvGr 1 0.05129 9.2953 -3564.5
## - TotRms.AbvGrd 1 0.05150 9.2955 -3564.4
## - area 1 0.05243 9.2964 -3564.4
## - Enclosed.Porch 1 0.05582 9.2998 -3564.1
## - Garage.Area 1 0.07314 9.3172 -3562.5
## <none> 9.2440 -3562.3
## - Screen.Porch 1 0.09833 9.3423 -3560.3
## - Bedroom.AbvGr 1 0.10499 9.3490 -3559.7
## - Pool.Area 1 0.12147 9.3655 -3558.2
## - MS.SubClass 1 0.19632 9.4403 -3551.6
## - Year.Remod.Add 1 0.22748 9.4715 -3548.8
## - Fireplaces 1 0.23419 9.4782 -3548.2
## - Central.Air 1 0.26825 9.5123 -3545.3
## - Lot.Area 1 0.38660 9.6306 -3535.0
## - Total.Bsmt.SF 1 0.63774 9.8818 -3513.6
## - Bsmt.Full.Bath 1 0.79905 10.0431 -3500.1
## - Overall.Cond 1 0.98715 10.2312 -3484.6
## - Year.Built 1 1.53646 10.7805 -3441.1
## - Overall.Qual 1 2.82227 12.0663 -3347.4
##
## Step: AIC=-3568.98
## log(price) ~ area + MS.SubClass + Lot.Area + Overall.Qual + Overall.Cond +
## Year.Built + Year.Remod.Add + Total.Bsmt.SF + Central.Air +
## X1st.Flr.SF + X2nd.Flr.SF + Bsmt.Full.Bath + Bsmt.Half.Bath +
## Full.Bath + Bedroom.AbvGr + Kitchen.AbvGr + TotRms.AbvGrd +
## Fireplaces + Garage.Cars + Garage.Area + Wood.Deck.SF + Open.Porch.SF +
## Enclosed.Porch + Screen.Porch + Pool.Area
##
## Df Sum of Sq RSS AIC
## - Full.Bath 1 0.00208 9.2470 -3575.5
## - Wood.Deck.SF 1 0.01135 9.2563 -3574.7
## - Open.Porch.SF 1 0.01508 9.2600 -3574.3
## - Garage.Cars 1 0.02175 9.2667 -3573.7
## - X2nd.Flr.SF 1 0.02850 9.2734 -3573.1
## - X1st.Flr.SF 1 0.03804 9.2830 -3572.3
## - Bsmt.Half.Bath 1 0.04650 9.2914 -3571.5
## - area 1 0.05158 9.2965 -3571.1
## - Kitchen.AbvGr 1 0.05212 9.2970 -3571.0
## - TotRms.AbvGrd 1 0.05288 9.2978 -3571.0
## - Enclosed.Porch 1 0.05609 9.3010 -3570.7
## <none> 9.2449 -3569.0
## - Garage.Area 1 0.07605 9.3210 -3568.9
## - Screen.Porch 1 0.09747 9.3424 -3567.0
## - Bedroom.AbvGr 1 0.10593 9.3509 -3566.2
## - Pool.Area 1 0.12082 9.3658 -3564.9
## - MS.SubClass 1 0.19548 9.4404 -3558.3
## - Year.Remod.Add 1 0.22674 9.4717 -3555.5
## - Fireplaces 1 0.23390 9.4788 -3554.9
## - Central.Air 1 0.26734 9.5123 -3552.0
## - Lot.Area 1 0.38707 9.6320 -3541.6
## - Total.Bsmt.SF 1 0.64177 9.8867 -3519.9
## - Bsmt.Full.Bath 1 0.80146 10.0464 -3506.5
## - Overall.Cond 1 0.99381 10.2387 -3490.8
## - Year.Built 1 1.65506 10.9000 -3438.7
## - Overall.Qual 1 2.82495 12.0699 -3353.9
##
## Step: AIC=-3575.52
## log(price) ~ area + MS.SubClass + Lot.Area + Overall.Qual + Overall.Cond +
## Year.Built + Year.Remod.Add + Total.Bsmt.SF + Central.Air +
## X1st.Flr.SF + X2nd.Flr.SF + Bsmt.Full.Bath + Bsmt.Half.Bath +
## Bedroom.AbvGr + Kitchen.AbvGr + TotRms.AbvGrd + Fireplaces +
## Garage.Cars + Garage.Area + Wood.Deck.SF + Open.Porch.SF +
## Enclosed.Porch + Screen.Porch + Pool.Area
##
## Df Sum of Sq RSS AIC
## - Wood.Deck.SF 1 0.01131 9.2583 -3581.2
## - Open.Porch.SF 1 0.01447 9.2615 -3580.9
## - Garage.Cars 1 0.02036 9.2674 -3580.4
## - X2nd.Flr.SF 1 0.02939 9.2764 -3579.6
## - X1st.Flr.SF 1 0.03905 9.2861 -3578.7
## - Bsmt.Half.Bath 1 0.04676 9.2938 -3578.0
## - area 1 0.04979 9.2968 -3577.8
## - TotRms.AbvGrd 1 0.05429 9.3013 -3577.4
## - Enclosed.Porch 1 0.05585 9.3029 -3577.2
## - Kitchen.AbvGr 1 0.06049 9.3075 -3576.8
## <none> 9.2470 -3575.5
## - Garage.Area 1 0.08130 9.3283 -3575.0
## - Screen.Porch 1 0.09752 9.3445 -3573.5
## - Bedroom.AbvGr 1 0.11007 9.3571 -3572.4
## - Pool.Area 1 0.12278 9.3698 -3571.3
## - MS.SubClass 1 0.19514 9.4421 -3564.9
## - Year.Remod.Add 1 0.22576 9.4728 -3562.2
## - Fireplaces 1 0.23637 9.4834 -3561.2
## - Central.Air 1 0.27019 9.5172 -3558.3
## - Lot.Area 1 0.38563 9.6326 -3548.2
## - Total.Bsmt.SF 1 0.64249 9.8895 -3526.4
## - Bsmt.Full.Bath 1 0.82164 10.0686 -3511.4
## - Overall.Cond 1 1.00792 10.2549 -3496.2
## - Year.Built 1 1.71755 10.9646 -3440.5
## - Overall.Qual 1 2.83177 12.0788 -3360.0
##
## Step: AIC=-3581.22
## log(price) ~ area + MS.SubClass + Lot.Area + Overall.Qual + Overall.Cond +
## Year.Built + Year.Remod.Add + Total.Bsmt.SF + Central.Air +
## X1st.Flr.SF + X2nd.Flr.SF + Bsmt.Full.Bath + Bsmt.Half.Bath +
## Bedroom.AbvGr + Kitchen.AbvGr + TotRms.AbvGrd + Fireplaces +
## Garage.Cars + Garage.Area + Open.Porch.SF + Enclosed.Porch +
## Screen.Porch + Pool.Area
##
## Df Sum of Sq RSS AIC
## - Open.Porch.SF 1 0.01243 9.2707 -3586.8
## - Garage.Cars 1 0.01992 9.2782 -3586.2
## - X2nd.Flr.SF 1 0.02969 9.2880 -3585.3
## - X1st.Flr.SF 1 0.03919 9.2975 -3584.4
## - area 1 0.05131 9.3096 -3583.3
## - Bsmt.Half.Bath 1 0.05342 9.3117 -3583.2
## - Enclosed.Porch 1 0.05460 9.3129 -3583.1
## - TotRms.AbvGrd 1 0.05539 9.3137 -3583.0
## - Kitchen.AbvGr 1 0.06507 9.3234 -3582.1
## <none> 9.2583 -3581.2
## - Garage.Area 1 0.08469 9.3430 -3580.4
## - Screen.Porch 1 0.09130 9.3496 -3579.8
## - Bedroom.AbvGr 1 0.11648 9.3748 -3577.5
## - Pool.Area 1 0.11913 9.3774 -3577.3
## - MS.SubClass 1 0.19863 9.4569 -3570.3
## - Year.Remod.Add 1 0.22734 9.4857 -3567.8
## - Fireplaces 1 0.24519 9.5035 -3566.2
## - Central.Air 1 0.26440 9.5227 -3564.5
## - Lot.Area 1 0.38244 9.6408 -3554.3
## - Total.Bsmt.SF 1 0.65358 9.9119 -3531.2
## - Bsmt.Full.Bath 1 0.87893 10.1372 -3512.5
## - Overall.Cond 1 1.07016 10.3285 -3496.9
## - Year.Built 1 1.78792 11.0462 -3441.0
## - Overall.Qual 1 2.82046 12.0788 -3366.7
##
## Step: AIC=-3586.83
## log(price) ~ area + MS.SubClass + Lot.Area + Overall.Qual + Overall.Cond +
## Year.Built + Year.Remod.Add + Total.Bsmt.SF + Central.Air +
## X1st.Flr.SF + X2nd.Flr.SF + Bsmt.Full.Bath + Bsmt.Half.Bath +
## Bedroom.AbvGr + Kitchen.AbvGr + TotRms.AbvGrd + Fireplaces +
## Garage.Cars + Garage.Area + Enclosed.Porch + Screen.Porch +
## Pool.Area
##
## Df Sum of Sq RSS AIC
## - Garage.Cars 1 0.01880 9.2895 -3591.9
## - X2nd.Flr.SF 1 0.03241 9.3032 -3590.6
## - X1st.Flr.SF 1 0.04106 9.3118 -3589.9
## - area 1 0.05016 9.3209 -3589.1
## - Enclosed.Porch 1 0.05205 9.3228 -3588.9
## - Bsmt.Half.Bath 1 0.05416 9.3249 -3588.7
## - TotRms.AbvGrd 1 0.05540 9.3261 -3588.6
## - Kitchen.AbvGr 1 0.06672 9.3375 -3587.6
## <none> 9.2707 -3586.8
## - Garage.Area 1 0.08578 9.3565 -3585.9
## - Screen.Porch 1 0.08754 9.3583 -3585.7
## - Pool.Area 1 0.11824 9.3890 -3583.0
## - Bedroom.AbvGr 1 0.12384 9.3946 -3582.5
## - MS.SubClass 1 0.20453 9.4753 -3575.4
## - Year.Remod.Add 1 0.22811 9.4989 -3573.3
## - Fireplaces 1 0.24310 9.5138 -3572.0
## - Central.Air 1 0.26733 9.5381 -3569.9
## - Lot.Area 1 0.37962 9.6504 -3560.2
## - Total.Bsmt.SF 1 0.68799 9.9587 -3534.0
## - Bsmt.Full.Bath 1 0.88087 10.1516 -3518.0
## - Overall.Cond 1 1.06273 10.3335 -3503.3
## - Year.Built 1 1.79560 11.0663 -3446.3
## - Overall.Qual 1 2.83448 12.1052 -3371.6
##
## Step: AIC=-3591.87
## log(price) ~ area + MS.SubClass + Lot.Area + Overall.Qual + Overall.Cond +
## Year.Built + Year.Remod.Add + Total.Bsmt.SF + Central.Air +
## X1st.Flr.SF + X2nd.Flr.SF + Bsmt.Full.Bath + Bsmt.Half.Bath +
## Bedroom.AbvGr + Kitchen.AbvGr + TotRms.AbvGrd + Fireplaces +
## Garage.Area + Enclosed.Porch + Screen.Porch + Pool.Area
##
## Df Sum of Sq RSS AIC
## - X2nd.Flr.SF 1 0.03348 9.3230 -3595.6
## - X1st.Flr.SF 1 0.04142 9.3310 -3594.9
## - area 1 0.04971 9.3393 -3594.2
## - Bsmt.Half.Bath 1 0.05457 9.3441 -3593.7
## - TotRms.AbvGrd 1 0.05792 9.3475 -3593.4
## - Enclosed.Porch 1 0.05917 9.3487 -3593.3
## - Kitchen.AbvGr 1 0.06168 9.3512 -3593.1
## <none> 9.2895 -3591.9
## - Screen.Porch 1 0.09077 9.3803 -3590.5
## - Pool.Area 1 0.12152 9.4111 -3587.8
## - Bedroom.AbvGr 1 0.12684 9.4164 -3587.3
## - MS.SubClass 1 0.19981 9.4894 -3580.9
## - Year.Remod.Add 1 0.23642 9.5260 -3577.7
## - Fireplaces 1 0.24625 9.5358 -3576.8
## - Central.Air 1 0.26447 9.5540 -3575.2
## - Lot.Area 1 0.38905 9.6786 -3564.5
## - Garage.Area 1 0.49250 9.7820 -3555.6
## - Total.Bsmt.SF 1 0.69127 9.9808 -3538.9
## - Bsmt.Full.Bath 1 0.88744 10.1770 -3522.7
## - Overall.Cond 1 1.05728 10.3468 -3508.9
## - Year.Built 1 1.89720 11.1867 -3444.0
## - Overall.Qual 1 2.93195 12.2215 -3370.4
##
## Step: AIC=-3595.6
## log(price) ~ area + MS.SubClass + Lot.Area + Overall.Qual + Overall.Cond +
## Year.Built + Year.Remod.Add + Total.Bsmt.SF + Central.Air +
## X1st.Flr.SF + Bsmt.Full.Bath + Bsmt.Half.Bath + Bedroom.AbvGr +
## Kitchen.AbvGr + TotRms.AbvGrd + Fireplaces + Garage.Area +
## Enclosed.Porch + Screen.Porch + Pool.Area
##
## Df Sum of Sq RSS AIC
## - X1st.Flr.SF 1 0.01061 9.3336 -3601.4
## - Enclosed.Porch 1 0.04936 9.3724 -3597.9
## - TotRms.AbvGrd 1 0.05385 9.3769 -3597.5
## - Bsmt.Half.Bath 1 0.05491 9.3779 -3597.4
## - Kitchen.AbvGr 1 0.05771 9.3807 -3597.2
## <none> 9.3230 -3595.6
## - Screen.Porch 1 0.09241 9.4154 -3594.1
## - Bedroom.AbvGr 1 0.11541 9.4384 -3592.1
## - Pool.Area 1 0.11916 9.4422 -3591.8
## - MS.SubClass 1 0.19950 9.5225 -3584.7
## - Year.Remod.Add 1 0.23855 9.5616 -3581.3
## - Central.Air 1 0.24981 9.5728 -3580.3
## - Fireplaces 1 0.25216 9.5752 -3580.1
## - Lot.Area 1 0.39594 9.7190 -3567.7
## - Garage.Area 1 0.50118 9.8242 -3558.8
## - Total.Bsmt.SF 1 0.67867 10.0017 -3543.9
## - Bsmt.Full.Bath 1 0.89318 10.2162 -3526.2
## - Overall.Cond 1 1.08487 10.4079 -3510.7
## - Year.Built 1 1.92572 11.2487 -3446.1
## - area 1 2.80690 12.1299 -3383.3
## - Overall.Qual 1 3.04195 12.3650 -3367.4
##
## Step: AIC=-3601.38
## log(price) ~ area + MS.SubClass + Lot.Area + Overall.Qual + Overall.Cond +
## Year.Built + Year.Remod.Add + Total.Bsmt.SF + Central.Air +
## Bsmt.Full.Bath + Bsmt.Half.Bath + Bedroom.AbvGr + Kitchen.AbvGr +
## TotRms.AbvGrd + Fireplaces + Garage.Area + Enclosed.Porch +
## Screen.Porch + Pool.Area
##
## Df Sum of Sq RSS AIC
## - Enclosed.Porch 1 0.04559 9.3792 -3604.0
## - Kitchen.AbvGr 1 0.04976 9.3834 -3603.7
## - TotRms.AbvGrd 1 0.05485 9.3885 -3603.2
## - Bsmt.Half.Bath 1 0.05638 9.3900 -3603.1
## <none> 9.3336 -3601.4
## - Screen.Porch 1 0.09188 9.4255 -3600.0
## - Pool.Area 1 0.11833 9.4520 -3597.6
## - Bedroom.AbvGr 1 0.13155 9.4652 -3596.5
## - MS.SubClass 1 0.23886 9.5725 -3587.1
## - Year.Remod.Add 1 0.24450 9.5781 -3586.6
## - Central.Air 1 0.25531 9.5889 -3585.6
## - Fireplaces 1 0.27045 9.6041 -3584.3
## - Lot.Area 1 0.40387 9.7375 -3572.9
## - Garage.Area 1 0.51973 9.8534 -3563.0
## - Bsmt.Full.Bath 1 0.89559 10.2292 -3531.9
## - Overall.Cond 1 1.07736 10.4110 -3517.2
## - Total.Bsmt.SF 1 1.36159 10.6952 -3494.8
## - Year.Built 1 1.91548 11.2491 -3452.8
## - Overall.Qual 1 3.03153 12.3652 -3374.1
## - area 1 3.05078 12.3844 -3372.8
##
## Step: AIC=-3604.05
## log(price) ~ area + MS.SubClass + Lot.Area + Overall.Qual + Overall.Cond +
## Year.Built + Year.Remod.Add + Total.Bsmt.SF + Central.Air +
## Bsmt.Full.Bath + Bsmt.Half.Bath + Bedroom.AbvGr + Kitchen.AbvGr +
## TotRms.AbvGrd + Fireplaces + Garage.Area + Screen.Porch +
## Pool.Area
##
## Df Sum of Sq RSS AIC
## - Kitchen.AbvGr 1 0.04979 9.4290 -3606.4
## - TotRms.AbvGrd 1 0.05137 9.4306 -3606.2
## - Bsmt.Half.Bath 1 0.05502 9.4342 -3605.9
## <none> 9.3792 -3604.0
## - Screen.Porch 1 0.07959 9.4588 -3603.7
## - Pool.Area 1 0.12110 9.5003 -3600.1
## - Bedroom.AbvGr 1 0.13704 9.5163 -3598.7
## - Central.Air 1 0.23623 9.6155 -3590.1
## - Year.Remod.Add 1 0.23689 9.6161 -3590.0
## - MS.SubClass 1 0.25361 9.6328 -3588.6
## - Fireplaces 1 0.28378 9.6630 -3586.0
## - Lot.Area 1 0.38863 9.7678 -3577.0
## - Garage.Area 1 0.52811 9.9073 -3565.2
## - Bsmt.Full.Bath 1 0.87969 10.2589 -3536.2
## - Overall.Cond 1 1.06676 10.4460 -3521.1
## - Total.Bsmt.SF 1 1.36646 10.7457 -3497.6
## - Year.Built 1 1.89578 11.2750 -3457.6
## - Overall.Qual 1 3.06024 12.4395 -3375.8
## - area 1 3.12198 12.5012 -3371.7
##
## Step: AIC=-3606.37
## log(price) ~ area + MS.SubClass + Lot.Area + Overall.Qual + Overall.Cond +
## Year.Built + Year.Remod.Add + Total.Bsmt.SF + Central.Air +
## Bsmt.Full.Bath + Bsmt.Half.Bath + Bedroom.AbvGr + TotRms.AbvGrd +
## Fireplaces + Garage.Area + Screen.Porch + Pool.Area
##
## Df Sum of Sq RSS AIC
## - TotRms.AbvGrd 1 0.0260 9.4551 -3610.8
## - Bsmt.Half.Bath 1 0.0549 9.4839 -3608.3
## <none> 9.4290 -3606.4
## - Screen.Porch 1 0.0859 9.5149 -3605.5
## - Pool.Area 1 0.1129 9.5419 -3603.2
## - Bedroom.AbvGr 1 0.1504 9.5794 -3599.9
## - Year.Remod.Add 1 0.2575 9.6866 -3590.7
## - Fireplaces 1 0.2871 9.7161 -3588.1
## - Central.Air 1 0.3210 9.7501 -3585.2
## - MS.SubClass 1 0.3950 9.8240 -3578.9
## - Lot.Area 1 0.3988 9.8278 -3578.6
## - Garage.Area 1 0.5005 9.9295 -3570.1
## - Bsmt.Full.Bath 1 0.8601 10.2891 -3540.5
## - Overall.Cond 1 1.0539 10.4829 -3524.9
## - Total.Bsmt.SF 1 1.3192 10.7482 -3504.1
## - Year.Built 1 1.9047 11.3337 -3460.0
## - Overall.Qual 1 3.2403 12.6693 -3367.3
## - area 1 3.3521 12.7811 -3360.0
##
## Step: AIC=-3610.79
## log(price) ~ area + MS.SubClass + Lot.Area + Overall.Qual + Overall.Cond +
## Year.Built + Year.Remod.Add + Total.Bsmt.SF + Central.Air +
## Bsmt.Full.Bath + Bsmt.Half.Bath + Bedroom.AbvGr + Fireplaces +
## Garage.Area + Screen.Porch + Pool.Area
##
## Df Sum of Sq RSS AIC
## - Bsmt.Half.Bath 1 0.0506 9.5056 -3613.1
## <none> 9.4551 -3610.8
## - Screen.Porch 1 0.0860 9.5410 -3610.0
## - Pool.Area 1 0.1056 9.5607 -3608.3
## - Bedroom.AbvGr 1 0.1244 9.5794 -3606.6
## - Year.Remod.Add 1 0.2560 9.7111 -3595.3
## - Fireplaces 1 0.2890 9.7441 -3592.5
## - Central.Air 1 0.3036 9.7586 -3591.2
## - Lot.Area 1 0.4044 9.8594 -3582.7
## - MS.SubClass 1 0.4054 9.8604 -3582.6
## - Garage.Area 1 0.5102 9.9653 -3573.8
## - Bsmt.Full.Bath 1 0.8425 10.2976 -3546.5
## - Overall.Cond 1 1.0694 10.5244 -3528.4
## - Total.Bsmt.SF 1 1.3207 10.7757 -3508.7
## - Year.Built 1 1.8946 11.3496 -3465.6
## - Overall.Qual 1 3.2744 12.7294 -3370.1
## - area 1 4.8938 14.3488 -3270.5
##
## Step: AIC=-3613.08
## log(price) ~ area + MS.SubClass + Lot.Area + Overall.Qual + Overall.Cond +
## Year.Built + Year.Remod.Add + Total.Bsmt.SF + Central.Air +
## Bsmt.Full.Bath + Bedroom.AbvGr + Fireplaces + Garage.Area +
## Screen.Porch + Pool.Area
##
## Df Sum of Sq RSS AIC
## <none> 9.5056 -3613.1
## - Pool.Area 1 0.0785 9.5841 -3613.0
## - Screen.Porch 1 0.0841 9.5897 -3612.5
## - Bedroom.AbvGr 1 0.1147 9.6203 -3609.8
## - Year.Remod.Add 1 0.2493 9.7549 -3598.3
## - Central.Air 1 0.2937 9.7993 -3594.5
## - Fireplaces 1 0.3310 9.8366 -3591.3
## - MS.SubClass 1 0.3976 9.9032 -3585.7
## - Lot.Area 1 0.4308 9.9364 -3582.9
## - Garage.Area 1 0.5148 10.0205 -3575.9
## - Bsmt.Full.Bath 1 0.7926 10.2982 -3553.2
## - Overall.Cond 1 1.1220 10.6276 -3527.0
## - Total.Bsmt.SF 1 1.3632 10.8688 -3508.3
## - Year.Built 1 1.9120 11.4176 -3467.3
## - Overall.Qual 1 3.2946 12.8002 -3372.2
## - area 1 4.8549 14.3606 -3276.5## r.squared adj.r.squared sigma statistic p.value df logLik
## 1 0.9214493 0.9194128 0.1070914 452.467 0 22 689.3394
## AIC BIC deviance df.residual
## 1 -1332.679 -1224.031 9.289544 810
##### Optimized Initial model.
model.opt <- bas.lm(log(price) ~ log(area+1) +log(Lot.Area)+ Bedroom.AbvGr+
+ Year.Built+Overall.Cond+Overall.Qual+Garage.Cars, data = na.omit(train), prior = "BIC", modelprior=uniform())
model.opt##
## Call:
## bas.lm(formula = log(price) ~ log(area + 1) + log(Lot.Area) + Bedroom.AbvGr + +Year.Built + Overall.Cond + Overall.Qual + Garage.Cars, data = na.omit(train), prior = "BIC", modelprior = uniform())
##
##
## Marginal Posterior Inclusion Probabilities:
## Intercept log(area + 1) log(Lot.Area) Bedroom.AbvGr Year.Built
## 1 1 1 1 1
## Overall.Cond Overall.Qual Garage.Cars
## 1 1 1summary(model.opt)## P(B != 0 | Y) model 1 model 2 model 3
## Intercept 1.0000000 1.0000 1.000000e+00 1.000000e+00
## log(area + 1) 1.0000000 1.0000 1.000000e+00 1.000000e+00
## log(Lot.Area) 1.0000000 1.0000 1.000000e+00 1.000000e+00
## Bedroom.AbvGr 0.9999999 1.0000 1.000000e+00 0.000000e+00
## Year.Built 1.0000000 1.0000 1.000000e+00 1.000000e+00
## Overall.Cond 1.0000000 1.0000 1.000000e+00 1.000000e+00
## Overall.Qual 1.0000000 1.0000 1.000000e+00 1.000000e+00
## Garage.Cars 0.9999995 1.0000 0.000000e+00 1.000000e+00
## BF NA 1.0000 4.782531e-07 1.158985e-07
## PostProbs NA 1.0000 0.000000e+00 0.000000e+00
## R2 NA 0.8887 8.838000e-01 8.834000e-01
## dim NA 8.0000 7.000000e+00 7.000000e+00
## logmarg NA -1098.9860 -1.113539e+03 -1.114957e+03
## model 4 model 5
## Intercept 1.000000e+00 1.000000e+00
## log(area + 1) 1.000000e+00 1.000000e+00
## log(Lot.Area) 1.000000e+00 1.000000e+00
## Bedroom.AbvGr 0.000000e+00 1.000000e+00
## Year.Built 1.000000e+00 1.000000e+00
## Overall.Cond 1.000000e+00 0.000000e+00
## Overall.Qual 1.000000e+00 1.000000e+00
## Garage.Cars 0.000000e+00 1.000000e+00
## BF 5.771756e-15 3.699457e-36
## PostProbs 0.000000e+00 0.000000e+00
## R2 8.776000e-01 8.635000e-01
## dim 6.000000e+00 7.000000e+00
## logmarg -1.131772e+03 -1.180571e+03image(model.opt)
plot(model.opt)
0.0.0.3.2 Using stepwise,from full model,backwards and then in forward direction
full.step.both <- step(full.model, direction='both')## Start: AIC=-3689.88
## log(price) ~ area + MS.SubClass + Lot.Area + Overall.Qual + Overall.Cond +
## Year.Built + Year.Remod.Add + Total.Bsmt.SF + Central.Air +
## X1st.Flr.SF + X2nd.Flr.SF + Bsmt.Full.Bath + Bsmt.Half.Bath +
## Full.Bath + Half.Bath + Bedroom.AbvGr + Kitchen.AbvGr + TotRms.AbvGrd +
## Fireplaces + Garage.Cars + Garage.Area + Wood.Deck.SF + Open.Porch.SF +
## Enclosed.Porch + Screen.Porch + Pool.Area
##
## Df Sum of Sq RSS AIC
## - Half.Bath 1 0.00092 9.2449 -3691.8
## - Full.Bath 1 0.00288 9.2469 -3691.6
## - Wood.Deck.SF 1 0.01156 9.2556 -3690.8
## - Open.Porch.SF 1 0.01564 9.2596 -3690.5
## <none> 9.2440 -3689.9
## - Garage.Cars 1 0.02240 9.2664 -3689.9
## - X2nd.Flr.SF 1 0.02894 9.2729 -3689.3
## - X1st.Flr.SF 1 0.03721 9.2812 -3688.5
## - Bsmt.Half.Bath 1 0.04598 9.2900 -3687.8
## - Kitchen.AbvGr 1 0.05129 9.2953 -3687.3
## - TotRms.AbvGrd 1 0.05150 9.2955 -3687.3
## - area 1 0.05243 9.2964 -3687.2
## - Enclosed.Porch 1 0.05582 9.2998 -3686.9
## - Garage.Area 1 0.07314 9.3172 -3685.3
## - Screen.Porch 1 0.09833 9.3423 -3683.1
## - Bedroom.AbvGr 1 0.10499 9.3490 -3682.5
## - Pool.Area 1 0.12147 9.3655 -3681.0
## - MS.SubClass 1 0.19632 9.4403 -3674.4
## - Year.Remod.Add 1 0.22748 9.4715 -3671.7
## - Fireplaces 1 0.23419 9.4782 -3671.1
## - Central.Air 1 0.26825 9.5123 -3668.1
## - Lot.Area 1 0.38660 9.6306 -3657.8
## - Total.Bsmt.SF 1 0.63774 9.8818 -3636.4
## - Bsmt.Full.Bath 1 0.79905 10.0431 -3622.9
## - Overall.Cond 1 0.98715 10.2312 -3607.5
## - Year.Built 1 1.53646 10.7805 -3564.0
## - Overall.Qual 1 2.82227 12.0663 -3470.2
##
## Step: AIC=-3691.8
## log(price) ~ area + MS.SubClass + Lot.Area + Overall.Qual + Overall.Cond +
## Year.Built + Year.Remod.Add + Total.Bsmt.SF + Central.Air +
## X1st.Flr.SF + X2nd.Flr.SF + Bsmt.Full.Bath + Bsmt.Half.Bath +
## Full.Bath + Bedroom.AbvGr + Kitchen.AbvGr + TotRms.AbvGrd +
## Fireplaces + Garage.Cars + Garage.Area + Wood.Deck.SF + Open.Porch.SF +
## Enclosed.Porch + Screen.Porch + Pool.Area
##
## Df Sum of Sq RSS AIC
## - Full.Bath 1 0.00208 9.2470 -3693.6
## - Wood.Deck.SF 1 0.01135 9.2563 -3692.8
## - Open.Porch.SF 1 0.01508 9.2600 -3692.4
## - Garage.Cars 1 0.02175 9.2667 -3691.8
## <none> 9.2449 -3691.8
## - X2nd.Flr.SF 1 0.02850 9.2734 -3691.2
## - X1st.Flr.SF 1 0.03804 9.2830 -3690.4
## + Half.Bath 1 0.00092 9.2440 -3689.9
## - Bsmt.Half.Bath 1 0.04650 9.2914 -3689.6
## - area 1 0.05158 9.2965 -3689.2
## - Kitchen.AbvGr 1 0.05212 9.2970 -3689.1
## - TotRms.AbvGrd 1 0.05288 9.2978 -3689.1
## - Enclosed.Porch 1 0.05609 9.3010 -3688.8
## - Garage.Area 1 0.07605 9.3210 -3687.0
## - Screen.Porch 1 0.09747 9.3424 -3685.1
## - Bedroom.AbvGr 1 0.10593 9.3509 -3684.3
## - Pool.Area 1 0.12082 9.3658 -3683.0
## - MS.SubClass 1 0.19548 9.4404 -3676.4
## - Year.Remod.Add 1 0.22674 9.4717 -3673.6
## - Fireplaces 1 0.23390 9.4788 -3673.0
## - Central.Air 1 0.26734 9.5123 -3670.1
## - Lot.Area 1 0.38707 9.6320 -3659.7
## - Total.Bsmt.SF 1 0.64177 9.8867 -3638.0
## - Bsmt.Full.Bath 1 0.80146 10.0464 -3624.6
## - Overall.Cond 1 0.99381 10.2387 -3608.8
## - Year.Built 1 1.65506 10.9000 -3556.8
## - Overall.Qual 1 2.82495 12.0699 -3472.0
##
## Step: AIC=-3693.61
## log(price) ~ area + MS.SubClass + Lot.Area + Overall.Qual + Overall.Cond +
## Year.Built + Year.Remod.Add + Total.Bsmt.SF + Central.Air +
## X1st.Flr.SF + X2nd.Flr.SF + Bsmt.Full.Bath + Bsmt.Half.Bath +
## Bedroom.AbvGr + Kitchen.AbvGr + TotRms.AbvGrd + Fireplaces +
## Garage.Cars + Garage.Area + Wood.Deck.SF + Open.Porch.SF +
## Enclosed.Porch + Screen.Porch + Pool.Area
##
## Df Sum of Sq RSS AIC
## - Wood.Deck.SF 1 0.01131 9.2583 -3694.6
## - Open.Porch.SF 1 0.01447 9.2615 -3694.3
## - Garage.Cars 1 0.02036 9.2674 -3693.8
## <none> 9.2470 -3693.6
## - X2nd.Flr.SF 1 0.02939 9.2764 -3693.0
## - X1st.Flr.SF 1 0.03905 9.2861 -3692.1
## + Full.Bath 1 0.00208 9.2449 -3691.8
## + Half.Bath 1 0.00012 9.2469 -3691.6
## - Bsmt.Half.Bath 1 0.04676 9.2938 -3691.4
## - area 1 0.04979 9.2968 -3691.1
## - TotRms.AbvGrd 1 0.05429 9.3013 -3690.7
## - Enclosed.Porch 1 0.05585 9.3029 -3690.6
## - Kitchen.AbvGr 1 0.06049 9.3075 -3690.2
## - Garage.Area 1 0.08130 9.3283 -3688.3
## - Screen.Porch 1 0.09752 9.3445 -3686.9
## - Bedroom.AbvGr 1 0.11007 9.3571 -3685.8
## - Pool.Area 1 0.12278 9.3698 -3684.6
## - MS.SubClass 1 0.19514 9.4421 -3678.2
## - Year.Remod.Add 1 0.22576 9.4728 -3675.5
## - Fireplaces 1 0.23637 9.4834 -3674.6
## - Central.Air 1 0.27019 9.5172 -3671.6
## - Lot.Area 1 0.38563 9.6326 -3661.6
## - Total.Bsmt.SF 1 0.64249 9.8895 -3639.7
## - Bsmt.Full.Bath 1 0.82164 10.0686 -3624.8
## - Overall.Cond 1 1.00792 10.2549 -3609.5
## - Year.Built 1 1.71755 10.9646 -3553.9
## - Overall.Qual 1 2.83177 12.0788 -3473.3
##
## Step: AIC=-3694.59
## log(price) ~ area + MS.SubClass + Lot.Area + Overall.Qual + Overall.Cond +
## Year.Built + Year.Remod.Add + Total.Bsmt.SF + Central.Air +
## X1st.Flr.SF + X2nd.Flr.SF + Bsmt.Full.Bath + Bsmt.Half.Bath +
## Bedroom.AbvGr + Kitchen.AbvGr + TotRms.AbvGrd + Fireplaces +
## Garage.Cars + Garage.Area + Open.Porch.SF + Enclosed.Porch +
## Screen.Porch + Pool.Area
##
## Df Sum of Sq RSS AIC
## - Open.Porch.SF 1 0.01243 9.2707 -3695.5
## - Garage.Cars 1 0.01992 9.2782 -3694.8
## <none> 9.2583 -3694.6
## - X2nd.Flr.SF 1 0.02969 9.2880 -3693.9
## + Wood.Deck.SF 1 0.01131 9.2470 -3693.6
## - X1st.Flr.SF 1 0.03919 9.2975 -3693.1
## + Full.Bath 1 0.00204 9.2563 -3692.8
## + Half.Bath 1 0.00005 9.2583 -3692.6
## - area 1 0.05131 9.3096 -3692.0
## - Bsmt.Half.Bath 1 0.05342 9.3117 -3691.8
## - Enclosed.Porch 1 0.05460 9.3129 -3691.7
## - TotRms.AbvGrd 1 0.05539 9.3137 -3691.6
## - Kitchen.AbvGr 1 0.06507 9.3234 -3690.8
## - Garage.Area 1 0.08469 9.3430 -3689.0
## - Screen.Porch 1 0.09130 9.3496 -3688.4
## - Bedroom.AbvGr 1 0.11648 9.3748 -3686.2
## - Pool.Area 1 0.11913 9.3774 -3686.0
## - MS.SubClass 1 0.19863 9.4569 -3678.9
## - Year.Remod.Add 1 0.22734 9.4857 -3676.4
## - Fireplaces 1 0.24519 9.5035 -3674.8
## - Central.Air 1 0.26440 9.5227 -3673.2
## - Lot.Area 1 0.38244 9.6408 -3662.9
## - Total.Bsmt.SF 1 0.65358 9.9119 -3639.8
## - Bsmt.Full.Bath 1 0.87893 10.1372 -3621.1
## - Overall.Cond 1 1.07016 10.3285 -3605.6
## - Year.Built 1 1.78792 11.0462 -3549.7
## - Overall.Qual 1 2.82046 12.0788 -3475.3
##
## Step: AIC=-3695.48
## log(price) ~ area + MS.SubClass + Lot.Area + Overall.Qual + Overall.Cond +
## Year.Built + Year.Remod.Add + Total.Bsmt.SF + Central.Air +
## X1st.Flr.SF + X2nd.Flr.SF + Bsmt.Full.Bath + Bsmt.Half.Bath +
## Bedroom.AbvGr + Kitchen.AbvGr + TotRms.AbvGrd + Fireplaces +
## Garage.Cars + Garage.Area + Enclosed.Porch + Screen.Porch +
## Pool.Area
##
## Df Sum of Sq RSS AIC
## - Garage.Cars 1 0.01880 9.2895 -3695.8
## <none> 9.2707 -3695.5
## + Open.Porch.SF 1 0.01243 9.2583 -3694.6
## - X2nd.Flr.SF 1 0.03241 9.3032 -3694.6
## + Wood.Deck.SF 1 0.00927 9.2615 -3694.3
## - X1st.Flr.SF 1 0.04106 9.3118 -3693.8
## + Full.Bath 1 0.00148 9.2693 -3693.6
## + Half.Bath 1 0.00000 9.2707 -3693.5
## - area 1 0.05016 9.3209 -3693.0
## - Enclosed.Porch 1 0.05205 9.3228 -3692.8
## - Bsmt.Half.Bath 1 0.05416 9.3249 -3692.6
## - TotRms.AbvGrd 1 0.05540 9.3261 -3692.5
## - Kitchen.AbvGr 1 0.06672 9.3375 -3691.5
## - Garage.Area 1 0.08578 9.3565 -3689.8
## - Screen.Porch 1 0.08754 9.3583 -3689.7
## - Pool.Area 1 0.11824 9.3890 -3686.9
## - Bedroom.AbvGr 1 0.12384 9.3946 -3686.4
## - MS.SubClass 1 0.20453 9.4753 -3679.3
## - Year.Remod.Add 1 0.22811 9.4989 -3677.3
## - Fireplaces 1 0.24310 9.5138 -3675.9
## - Central.Air 1 0.26733 9.5381 -3673.8
## - Lot.Area 1 0.37962 9.6504 -3664.1
## - Total.Bsmt.SF 1 0.68799 9.9587 -3637.9
## - Bsmt.Full.Bath 1 0.88087 10.1516 -3622.0
## - Overall.Cond 1 1.06273 10.3335 -3607.2
## - Year.Built 1 1.79560 11.0663 -3550.2
## - Overall.Qual 1 2.83448 12.1052 -3475.5
##
## Step: AIC=-3695.79
## log(price) ~ area + MS.SubClass + Lot.Area + Overall.Qual + Overall.Cond +
## Year.Built + Year.Remod.Add + Total.Bsmt.SF + Central.Air +
## X1st.Flr.SF + X2nd.Flr.SF + Bsmt.Full.Bath + Bsmt.Half.Bath +
## Bedroom.AbvGr + Kitchen.AbvGr + TotRms.AbvGrd + Fireplaces +
## Garage.Area + Enclosed.Porch + Screen.Porch + Pool.Area
##
## Df Sum of Sq RSS AIC
## <none> 9.2895 -3695.8
## + Garage.Cars 1 0.01880 9.2707 -3695.5
## + Open.Porch.SF 1 0.01131 9.2782 -3694.8
## - X2nd.Flr.SF 1 0.03348 9.3230 -3694.8
## + Wood.Deck.SF 1 0.00897 9.2806 -3694.6
## - X1st.Flr.SF 1 0.04142 9.3310 -3694.1
## + Full.Bath 1 0.00041 9.2891 -3693.8
## + Half.Bath 1 0.00002 9.2895 -3693.8
## - area 1 0.04971 9.3393 -3693.4
## - Bsmt.Half.Bath 1 0.05457 9.3441 -3692.9
## - TotRms.AbvGrd 1 0.05792 9.3475 -3692.6
## - Enclosed.Porch 1 0.05917 9.3487 -3692.5
## - Kitchen.AbvGr 1 0.06168 9.3512 -3692.3
## - Screen.Porch 1 0.09077 9.3803 -3689.7
## - Pool.Area 1 0.12152 9.4111 -3687.0
## - Bedroom.AbvGr 1 0.12684 9.4164 -3686.5
## - MS.SubClass 1 0.19981 9.4894 -3680.1
## - Year.Remod.Add 1 0.23642 9.5260 -3676.9
## - Fireplaces 1 0.24625 9.5358 -3676.0
## - Central.Air 1 0.26447 9.5540 -3674.4
## - Lot.Area 1 0.38905 9.6786 -3663.7
## - Garage.Area 1 0.49250 9.7820 -3654.8
## - Total.Bsmt.SF 1 0.69127 9.9808 -3638.1
## - Bsmt.Full.Bath 1 0.88744 10.1770 -3621.9
## - Overall.Cond 1 1.05728 10.3468 -3608.1
## - Year.Built 1 1.89720 11.1867 -3543.2
## - Overall.Qual 1 2.93195 12.2215 -3469.6print(summary(full.step.both))##
## Call:
## lm(formula = log(price) ~ area + MS.SubClass + Lot.Area + Overall.Qual +
## Overall.Cond + Year.Built + Year.Remod.Add + Total.Bsmt.SF +
## Central.Air + X1st.Flr.SF + X2nd.Flr.SF + Bsmt.Full.Bath +
## Bsmt.Half.Bath + Bedroom.AbvGr + Kitchen.AbvGr + TotRms.AbvGrd +
## Fireplaces + Garage.Area + Enclosed.Porch + Screen.Porch +
## Pool.Area, data = train)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.72737 -0.05898 0.00221 0.05893 0.53125
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.413e+00 5.016e-01 4.810 1.80e-06 ***
## area 1.572e-04 7.553e-05 2.082 0.037664 *
## MS.SubClass -4.409e-04 1.056e-04 -4.174 3.32e-05 ***
## Lot.Area 2.289e-06 3.930e-07 5.824 8.27e-09 ***
## Overall.Qual 7.423e-02 4.643e-03 15.989 < 2e-16 ***
## Overall.Cond 4.156e-02 4.328e-03 9.602 < 2e-16 ***
## Year.Built 2.936e-03 2.283e-04 12.862 < 2e-16 ***
## Year.Remod.Add 1.202e-03 2.647e-04 4.540 6.47e-06 ***
## Total.Bsmt.SF 1.331e-04 1.715e-05 7.764 2.49e-14 ***
## Central.AirY 9.757e-02 2.032e-02 4.802 1.87e-06 ***
## X1st.Flr.SF 1.467e-04 7.718e-05 1.900 0.057747 .
## X2nd.Flr.SF 1.285e-04 7.522e-05 1.708 0.087928 .
## Bsmt.Full.Bath 7.210e-02 8.197e-03 8.797 < 2e-16 ***
## Bsmt.Half.Bath 3.566e-02 1.635e-02 2.181 0.029444 *
## Bedroom.AbvGr -2.388e-02 7.180e-03 -3.326 0.000922 ***
## Kitchen.AbvGr -5.765e-02 2.486e-02 -2.319 0.020635 *
## TotRms.AbvGrd 1.129e-02 5.024e-03 2.247 0.024889 *
## Fireplaces 3.381e-02 7.296e-03 4.634 4.18e-06 ***
## Garage.Area 1.575e-04 2.403e-05 6.553 1.00e-10 ***
## Enclosed.Porch 1.571e-04 6.917e-05 2.271 0.023389 *
## Screen.Porch 2.024e-04 7.195e-05 2.813 0.005023 **
## Pool.Area -3.907e-04 1.200e-04 -3.255 0.001180 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.1071 on 810 degrees of freedom
## Multiple R-squared: 0.9214, Adjusted R-squared: 0.9194
## F-statistic: 452.5 on 21 and 810 DF, p-value: < 2.2e-16full.step.backward <- step(full.model, direction='backward')## Start: AIC=-3689.88
## log(price) ~ area + MS.SubClass + Lot.Area + Overall.Qual + Overall.Cond +
## Year.Built + Year.Remod.Add + Total.Bsmt.SF + Central.Air +
## X1st.Flr.SF + X2nd.Flr.SF + Bsmt.Full.Bath + Bsmt.Half.Bath +
## Full.Bath + Half.Bath + Bedroom.AbvGr + Kitchen.AbvGr + TotRms.AbvGrd +
## Fireplaces + Garage.Cars + Garage.Area + Wood.Deck.SF + Open.Porch.SF +
## Enclosed.Porch + Screen.Porch + Pool.Area
##
## Df Sum of Sq RSS AIC
## - Half.Bath 1 0.00092 9.2449 -3691.8
## - Full.Bath 1 0.00288 9.2469 -3691.6
## - Wood.Deck.SF 1 0.01156 9.2556 -3690.8
## - Open.Porch.SF 1 0.01564 9.2596 -3690.5
## <none> 9.2440 -3689.9
## - Garage.Cars 1 0.02240 9.2664 -3689.9
## - X2nd.Flr.SF 1 0.02894 9.2729 -3689.3
## - X1st.Flr.SF 1 0.03721 9.2812 -3688.5
## - Bsmt.Half.Bath 1 0.04598 9.2900 -3687.8
## - Kitchen.AbvGr 1 0.05129 9.2953 -3687.3
## - TotRms.AbvGrd 1 0.05150 9.2955 -3687.3
## - area 1 0.05243 9.2964 -3687.2
## - Enclosed.Porch 1 0.05582 9.2998 -3686.9
## - Garage.Area 1 0.07314 9.3172 -3685.3
## - Screen.Porch 1 0.09833 9.3423 -3683.1
## - Bedroom.AbvGr 1 0.10499 9.3490 -3682.5
## - Pool.Area 1 0.12147 9.3655 -3681.0
## - MS.SubClass 1 0.19632 9.4403 -3674.4
## - Year.Remod.Add 1 0.22748 9.4715 -3671.7
## - Fireplaces 1 0.23419 9.4782 -3671.1
## - Central.Air 1 0.26825 9.5123 -3668.1
## - Lot.Area 1 0.38660 9.6306 -3657.8
## - Total.Bsmt.SF 1 0.63774 9.8818 -3636.4
## - Bsmt.Full.Bath 1 0.79905 10.0431 -3622.9
## - Overall.Cond 1 0.98715 10.2312 -3607.5
## - Year.Built 1 1.53646 10.7805 -3564.0
## - Overall.Qual 1 2.82227 12.0663 -3470.2
##
## Step: AIC=-3691.8
## log(price) ~ area + MS.SubClass + Lot.Area + Overall.Qual + Overall.Cond +
## Year.Built + Year.Remod.Add + Total.Bsmt.SF + Central.Air +
## X1st.Flr.SF + X2nd.Flr.SF + Bsmt.Full.Bath + Bsmt.Half.Bath +
## Full.Bath + Bedroom.AbvGr + Kitchen.AbvGr + TotRms.AbvGrd +
## Fireplaces + Garage.Cars + Garage.Area + Wood.Deck.SF + Open.Porch.SF +
## Enclosed.Porch + Screen.Porch + Pool.Area
##
## Df Sum of Sq RSS AIC
## - Full.Bath 1 0.00208 9.2470 -3693.6
## - Wood.Deck.SF 1 0.01135 9.2563 -3692.8
## - Open.Porch.SF 1 0.01508 9.2600 -3692.4
## - Garage.Cars 1 0.02175 9.2667 -3691.8
## <none> 9.2449 -3691.8
## - X2nd.Flr.SF 1 0.02850 9.2734 -3691.2
## - X1st.Flr.SF 1 0.03804 9.2830 -3690.4
## - Bsmt.Half.Bath 1 0.04650 9.2914 -3689.6
## - area 1 0.05158 9.2965 -3689.2
## - Kitchen.AbvGr 1 0.05212 9.2970 -3689.1
## - TotRms.AbvGrd 1 0.05288 9.2978 -3689.1
## - Enclosed.Porch 1 0.05609 9.3010 -3688.8
## - Garage.Area 1 0.07605 9.3210 -3687.0
## - Screen.Porch 1 0.09747 9.3424 -3685.1
## - Bedroom.AbvGr 1 0.10593 9.3509 -3684.3
## - Pool.Area 1 0.12082 9.3658 -3683.0
## - MS.SubClass 1 0.19548 9.4404 -3676.4
## - Year.Remod.Add 1 0.22674 9.4717 -3673.6
## - Fireplaces 1 0.23390 9.4788 -3673.0
## - Central.Air 1 0.26734 9.5123 -3670.1
## - Lot.Area 1 0.38707 9.6320 -3659.7
## - Total.Bsmt.SF 1 0.64177 9.8867 -3638.0
## - Bsmt.Full.Bath 1 0.80146 10.0464 -3624.6
## - Overall.Cond 1 0.99381 10.2387 -3608.8
## - Year.Built 1 1.65506 10.9000 -3556.8
## - Overall.Qual 1 2.82495 12.0699 -3472.0
##
## Step: AIC=-3693.61
## log(price) ~ area + MS.SubClass + Lot.Area + Overall.Qual + Overall.Cond +
## Year.Built + Year.Remod.Add + Total.Bsmt.SF + Central.Air +
## X1st.Flr.SF + X2nd.Flr.SF + Bsmt.Full.Bath + Bsmt.Half.Bath +
## Bedroom.AbvGr + Kitchen.AbvGr + TotRms.AbvGrd + Fireplaces +
## Garage.Cars + Garage.Area + Wood.Deck.SF + Open.Porch.SF +
## Enclosed.Porch + Screen.Porch + Pool.Area
##
## Df Sum of Sq RSS AIC
## - Wood.Deck.SF 1 0.01131 9.2583 -3694.6
## - Open.Porch.SF 1 0.01447 9.2615 -3694.3
## - Garage.Cars 1 0.02036 9.2674 -3693.8
## <none> 9.2470 -3693.6
## - X2nd.Flr.SF 1 0.02939 9.2764 -3693.0
## - X1st.Flr.SF 1 0.03905 9.2861 -3692.1
## - Bsmt.Half.Bath 1 0.04676 9.2938 -3691.4
## - area 1 0.04979 9.2968 -3691.1
## - TotRms.AbvGrd 1 0.05429 9.3013 -3690.7
## - Enclosed.Porch 1 0.05585 9.3029 -3690.6
## - Kitchen.AbvGr 1 0.06049 9.3075 -3690.2
## - Garage.Area 1 0.08130 9.3283 -3688.3
## - Screen.Porch 1 0.09752 9.3445 -3686.9
## - Bedroom.AbvGr 1 0.11007 9.3571 -3685.8
## - Pool.Area 1 0.12278 9.3698 -3684.6
## - MS.SubClass 1 0.19514 9.4421 -3678.2
## - Year.Remod.Add 1 0.22576 9.4728 -3675.5
## - Fireplaces 1 0.23637 9.4834 -3674.6
## - Central.Air 1 0.27019 9.5172 -3671.6
## - Lot.Area 1 0.38563 9.6326 -3661.6
## - Total.Bsmt.SF 1 0.64249 9.8895 -3639.7
## - Bsmt.Full.Bath 1 0.82164 10.0686 -3624.8
## - Overall.Cond 1 1.00792 10.2549 -3609.5
## - Year.Built 1 1.71755 10.9646 -3553.9
## - Overall.Qual 1 2.83177 12.0788 -3473.3
##
## Step: AIC=-3694.59
## log(price) ~ area + MS.SubClass + Lot.Area + Overall.Qual + Overall.Cond +
## Year.Built + Year.Remod.Add + Total.Bsmt.SF + Central.Air +
## X1st.Flr.SF + X2nd.Flr.SF + Bsmt.Full.Bath + Bsmt.Half.Bath +
## Bedroom.AbvGr + Kitchen.AbvGr + TotRms.AbvGrd + Fireplaces +
## Garage.Cars + Garage.Area + Open.Porch.SF + Enclosed.Porch +
## Screen.Porch + Pool.Area
##
## Df Sum of Sq RSS AIC
## - Open.Porch.SF 1 0.01243 9.2707 -3695.5
## - Garage.Cars 1 0.01992 9.2782 -3694.8
## <none> 9.2583 -3694.6
## - X2nd.Flr.SF 1 0.02969 9.2880 -3693.9
## - X1st.Flr.SF 1 0.03919 9.2975 -3693.1
## - area 1 0.05131 9.3096 -3692.0
## - Bsmt.Half.Bath 1 0.05342 9.3117 -3691.8
## - Enclosed.Porch 1 0.05460 9.3129 -3691.7
## - TotRms.AbvGrd 1 0.05539 9.3137 -3691.6
## - Kitchen.AbvGr 1 0.06507 9.3234 -3690.8
## - Garage.Area 1 0.08469 9.3430 -3689.0
## - Screen.Porch 1 0.09130 9.3496 -3688.4
## - Bedroom.AbvGr 1 0.11648 9.3748 -3686.2
## - Pool.Area 1 0.11913 9.3774 -3686.0
## - MS.SubClass 1 0.19863 9.4569 -3678.9
## - Year.Remod.Add 1 0.22734 9.4857 -3676.4
## - Fireplaces 1 0.24519 9.5035 -3674.8
## - Central.Air 1 0.26440 9.5227 -3673.2
## - Lot.Area 1 0.38244 9.6408 -3662.9
## - Total.Bsmt.SF 1 0.65358 9.9119 -3639.8
## - Bsmt.Full.Bath 1 0.87893 10.1372 -3621.1
## - Overall.Cond 1 1.07016 10.3285 -3605.6
## - Year.Built 1 1.78792 11.0462 -3549.7
## - Overall.Qual 1 2.82046 12.0788 -3475.3
##
## Step: AIC=-3695.48
## log(price) ~ area + MS.SubClass + Lot.Area + Overall.Qual + Overall.Cond +
## Year.Built + Year.Remod.Add + Total.Bsmt.SF + Central.Air +
## X1st.Flr.SF + X2nd.Flr.SF + Bsmt.Full.Bath + Bsmt.Half.Bath +
## Bedroom.AbvGr + Kitchen.AbvGr + TotRms.AbvGrd + Fireplaces +
## Garage.Cars + Garage.Area + Enclosed.Porch + Screen.Porch +
## Pool.Area
##
## Df Sum of Sq RSS AIC
## - Garage.Cars 1 0.01880 9.2895 -3695.8
## <none> 9.2707 -3695.5
## - X2nd.Flr.SF 1 0.03241 9.3032 -3694.6
## - X1st.Flr.SF 1 0.04106 9.3118 -3693.8
## - area 1 0.05016 9.3209 -3693.0
## - Enclosed.Porch 1 0.05205 9.3228 -3692.8
## - Bsmt.Half.Bath 1 0.05416 9.3249 -3692.6
## - TotRms.AbvGrd 1 0.05540 9.3261 -3692.5
## - Kitchen.AbvGr 1 0.06672 9.3375 -3691.5
## - Garage.Area 1 0.08578 9.3565 -3689.8
## - Screen.Porch 1 0.08754 9.3583 -3689.7
## - Pool.Area 1 0.11824 9.3890 -3686.9
## - Bedroom.AbvGr 1 0.12384 9.3946 -3686.4
## - MS.SubClass 1 0.20453 9.4753 -3679.3
## - Year.Remod.Add 1 0.22811 9.4989 -3677.3
## - Fireplaces 1 0.24310 9.5138 -3675.9
## - Central.Air 1 0.26733 9.5381 -3673.8
## - Lot.Area 1 0.37962 9.6504 -3664.1
## - Total.Bsmt.SF 1 0.68799 9.9587 -3637.9
## - Bsmt.Full.Bath 1 0.88087 10.1516 -3622.0
## - Overall.Cond 1 1.06273 10.3335 -3607.2
## - Year.Built 1 1.79560 11.0663 -3550.2
## - Overall.Qual 1 2.83448 12.1052 -3475.5
##
## Step: AIC=-3695.79
## log(price) ~ area + MS.SubClass + Lot.Area + Overall.Qual + Overall.Cond +
## Year.Built + Year.Remod.Add + Total.Bsmt.SF + Central.Air +
## X1st.Flr.SF + X2nd.Flr.SF + Bsmt.Full.Bath + Bsmt.Half.Bath +
## Bedroom.AbvGr + Kitchen.AbvGr + TotRms.AbvGrd + Fireplaces +
## Garage.Area + Enclosed.Porch + Screen.Porch + Pool.Area
##
## Df Sum of Sq RSS AIC
## <none> 9.2895 -3695.8
## - X2nd.Flr.SF 1 0.03348 9.3230 -3694.8
## - X1st.Flr.SF 1 0.04142 9.3310 -3694.1
## - area 1 0.04971 9.3393 -3693.4
## - Bsmt.Half.Bath 1 0.05457 9.3441 -3692.9
## - TotRms.AbvGrd 1 0.05792 9.3475 -3692.6
## - Enclosed.Porch 1 0.05917 9.3487 -3692.5
## - Kitchen.AbvGr 1 0.06168 9.3512 -3692.3
## - Screen.Porch 1 0.09077 9.3803 -3689.7
## - Pool.Area 1 0.12152 9.4111 -3687.0
## - Bedroom.AbvGr 1 0.12684 9.4164 -3686.5
## - MS.SubClass 1 0.19981 9.4894 -3680.1
## - Year.Remod.Add 1 0.23642 9.5260 -3676.9
## - Fireplaces 1 0.24625 9.5358 -3676.0
## - Central.Air 1 0.26447 9.5540 -3674.4
## - Lot.Area 1 0.38905 9.6786 -3663.7
## - Garage.Area 1 0.49250 9.7820 -3654.8
## - Total.Bsmt.SF 1 0.69127 9.9808 -3638.1
## - Bsmt.Full.Bath 1 0.88744 10.1770 -3621.9
## - Overall.Cond 1 1.05728 10.3468 -3608.1
## - Year.Built 1 1.89720 11.1867 -3543.2
## - Overall.Qual 1 2.93195 12.2215 -3469.6print(summary(full.step.backward))##
## Call:
## lm(formula = log(price) ~ area + MS.SubClass + Lot.Area + Overall.Qual +
## Overall.Cond + Year.Built + Year.Remod.Add + Total.Bsmt.SF +
## Central.Air + X1st.Flr.SF + X2nd.Flr.SF + Bsmt.Full.Bath +
## Bsmt.Half.Bath + Bedroom.AbvGr + Kitchen.AbvGr + TotRms.AbvGrd +
## Fireplaces + Garage.Area + Enclosed.Porch + Screen.Porch +
## Pool.Area, data = train)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.72737 -0.05898 0.00221 0.05893 0.53125
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.413e+00 5.016e-01 4.810 1.80e-06 ***
## area 1.572e-04 7.553e-05 2.082 0.037664 *
## MS.SubClass -4.409e-04 1.056e-04 -4.174 3.32e-05 ***
## Lot.Area 2.289e-06 3.930e-07 5.824 8.27e-09 ***
## Overall.Qual 7.423e-02 4.643e-03 15.989 < 2e-16 ***
## Overall.Cond 4.156e-02 4.328e-03 9.602 < 2e-16 ***
## Year.Built 2.936e-03 2.283e-04 12.862 < 2e-16 ***
## Year.Remod.Add 1.202e-03 2.647e-04 4.540 6.47e-06 ***
## Total.Bsmt.SF 1.331e-04 1.715e-05 7.764 2.49e-14 ***
## Central.AirY 9.757e-02 2.032e-02 4.802 1.87e-06 ***
## X1st.Flr.SF 1.467e-04 7.718e-05 1.900 0.057747 .
## X2nd.Flr.SF 1.285e-04 7.522e-05 1.708 0.087928 .
## Bsmt.Full.Bath 7.210e-02 8.197e-03 8.797 < 2e-16 ***
## Bsmt.Half.Bath 3.566e-02 1.635e-02 2.181 0.029444 *
## Bedroom.AbvGr -2.388e-02 7.180e-03 -3.326 0.000922 ***
## Kitchen.AbvGr -5.765e-02 2.486e-02 -2.319 0.020635 *
## TotRms.AbvGrd 1.129e-02 5.024e-03 2.247 0.024889 *
## Fireplaces 3.381e-02 7.296e-03 4.634 4.18e-06 ***
## Garage.Area 1.575e-04 2.403e-05 6.553 1.00e-10 ***
## Enclosed.Porch 1.571e-04 6.917e-05 2.271 0.023389 *
## Screen.Porch 2.024e-04 7.195e-05 2.813 0.005023 **
## Pool.Area -3.907e-04 1.200e-04 -3.255 0.001180 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.1071 on 810 degrees of freedom
## Multiple R-squared: 0.9214, Adjusted R-squared: 0.9194
## F-statistic: 452.5 on 21 and 810 DF, p-value: < 2.2e-16lowest.step.forward <- step(lm(price ~ 1, data=na.omit(train)), list(upper=full.model), direction='forward')## Start: AIC=18555.14
## price ~ 1
##
## Df Sum of Sq RSS AIC
## + Overall.Qual 1 2.5739e+12 1.4501e+12 17708
## + area 1 2.2538e+12 1.7701e+12 17874
## + Total.Bsmt.SF 1 1.7999e+12 2.2241e+12 18064
## + X1st.Flr.SF 1 1.7660e+12 2.2580e+12 18076
## + Garage.Cars 1 1.7497e+12 2.2742e+12 18082
## + Garage.Area 1 1.5801e+12 2.4438e+12 18142
## + Full.Bath 1 1.3282e+12 2.6957e+12 18224
## + Year.Built 1 1.2731e+12 2.7508e+12 18241
## + Year.Remod.Add 1 1.1818e+12 2.8422e+12 18268
## + TotRms.AbvGrd 1 1.1382e+12 2.8858e+12 18281
## + Fireplaces 1 1.0987e+12 2.9252e+12 18292
## + Wood.Deck.SF 1 7.3296e+11 3.2910e+12 18390
## + Open.Porch.SF 1 4.6071e+11 3.5632e+12 18456
## + Bsmt.Full.Bath 1 4.0364e+11 3.6203e+12 18469
## + X2nd.Flr.SF 1 3.9028e+11 3.6337e+12 18472
## + Half.Bath 1 3.5515e+11 3.6688e+12 18480
## + Central.Air 1 2.7011e+11 3.7538e+12 18499
## + Lot.Area 1 2.6742e+11 3.7565e+12 18500
## + Bedroom.AbvGr 1 2.2497e+11 3.7990e+12 18509
## + Enclosed.Porch 1 9.2731e+10 3.9312e+12 18538
## + Overall.Cond 1 5.7382e+10 3.9666e+12 18545
## + Kitchen.AbvGr 1 3.1067e+10 3.9929e+12 18551
## + MS.SubClass 1 1.8632e+10 4.0053e+12 18553
## + Bsmt.Half.Bath 1 1.3450e+10 4.0105e+12 18554
## + Pool.Area 1 1.3023e+10 4.0109e+12 18554
## + Screen.Porch 1 1.0229e+10 4.0137e+12 18555
## <none> 4.0239e+12 18555
##
## Step: AIC=17707.95
## price ~ Overall.Qual
##
## Df Sum of Sq RSS AIC
## + area 1 4.7335e+11 9.7670e+11 17381
## + X1st.Flr.SF 1 4.3167e+11 1.0184e+12 17416
## + Total.Bsmt.SF 1 3.6474e+11 1.0853e+12 17469
## + Garage.Area 1 2.6879e+11 1.1813e+12 17539
## + Garage.Cars 1 2.3846e+11 1.2116e+12 17561
## + TotRms.AbvGrd 1 2.0713e+11 1.2429e+12 17582
## + Lot.Area 1 1.7074e+11 1.2793e+12 17606
## + Fireplaces 1 1.6846e+11 1.2816e+12 17607
## + Wood.Deck.SF 1 1.5256e+11 1.2975e+12 17618
## + Bsmt.Full.Bath 1 1.2885e+11 1.3212e+12 17633
## + Full.Bath 1 1.1605e+11 1.3340e+12 17641
## + Year.Remod.Add 1 7.0260e+10 1.3798e+12 17669
## + Year.Built 1 7.0190e+10 1.3799e+12 17669
## + MS.SubClass 1 5.8846e+10 1.3912e+12 17676
## + Bedroom.AbvGr 1 5.8791e+10 1.3913e+12 17676
## + Open.Porch.SF 1 4.2403e+10 1.4077e+12 17685
## + X2nd.Flr.SF 1 2.3768e+10 1.4263e+12 17696
## + Half.Bath 1 2.1428e+10 1.4286e+12 17698
## + Central.Air 1 1.0588e+10 1.4395e+12 17704
## <none> 1.4501e+12 17708
## + Pool.Area 1 3.0726e+09 1.4470e+12 17708
## + Bsmt.Half.Bath 1 2.9574e+09 1.4471e+12 17708
## + Enclosed.Porch 1 2.4965e+09 1.4476e+12 17709
## + Overall.Cond 1 2.1874e+09 1.4479e+12 17709
## + Screen.Porch 1 1.5413e+09 1.4485e+12 17709
## + Kitchen.AbvGr 1 4.6268e+06 1.4501e+12 17710
##
## Step: AIC=17381.17
## price ~ Overall.Qual + area
##
## Df Sum of Sq RSS AIC
## + Total.Bsmt.SF 1 2.4375e+11 7.3295e+11 17144
## + X1st.Flr.SF 1 1.8790e+11 7.8881e+11 17205
## + X2nd.Flr.SF 1 1.7385e+11 8.0285e+11 17220
## + Bsmt.Full.Bath 1 1.5949e+11 8.1721e+11 17235
## + Year.Built 1 1.3253e+11 8.4418e+11 17262
## + Garage.Area 1 1.3004e+11 8.4666e+11 17264
## + Garage.Cars 1 1.0059e+11 8.7612e+11 17293
## + MS.SubClass 1 8.0106e+10 8.9660e+11 17312
## + Lot.Area 1 7.1632e+10 9.0507e+11 17320
## + Wood.Deck.SF 1 6.9219e+10 9.0749e+11 17322
## + Bedroom.AbvGr 1 6.1987e+10 9.1472e+11 17329
## + Year.Remod.Add 1 4.9334e+10 9.2737e+11 17340
## + Fireplaces 1 3.3938e+10 9.4277e+11 17354
## + Kitchen.AbvGr 1 3.1871e+10 9.4483e+11 17356
## + Central.Air 1 2.3807e+10 9.5290e+11 17363
## + Enclosed.Porch 1 1.6082e+10 9.6062e+11 17369
## + TotRms.AbvGrd 1 1.3855e+10 9.6285e+11 17371
## + Half.Bath 1 1.1566e+10 9.6514e+11 17373
## + Open.Porch.SF 1 8.5273e+09 9.6818e+11 17376
## <none> 9.7670e+11 17381
## + Pool.Area 1 1.0172e+09 9.7569e+11 17382
## + Bsmt.Half.Bath 1 5.1106e+08 9.7619e+11 17383
## + Screen.Porch 1 3.9012e+08 9.7631e+11 17383
## + Full.Bath 1 1.7415e+08 9.7653e+11 17383
## + Overall.Cond 1 7.4630e+07 9.7663e+11 17383
##
## Step: AIC=17144.3
## price ~ Overall.Qual + area + Total.Bsmt.SF
##
## Df Sum of Sq RSS AIC
## + Year.Built 1 7.4649e+10 6.5830e+11 17057
## + Bsmt.Full.Bath 1 6.6183e+10 6.6677e+11 17068
## + Garage.Area 1 5.8828e+10 6.7413e+11 17077
## + Year.Remod.Add 1 5.3735e+10 6.7922e+11 17083
## + Garage.Cars 1 4.7886e+10 6.8507e+11 17090
## + Bedroom.AbvGr 1 4.7578e+10 6.8538e+11 17091
## + Wood.Deck.SF 1 3.8326e+10 6.9463e+11 17102
## + Kitchen.AbvGr 1 3.3850e+10 6.9910e+11 17107
## + Lot.Area 1 3.0164e+10 7.0279e+11 17111
## + MS.SubClass 1 1.8785e+10 7.1417e+11 17125
## + Fireplaces 1 1.8475e+10 7.1448e+11 17125
## + X1st.Flr.SF 1 1.1210e+10 7.2174e+11 17134
## + Central.Air 1 1.0598e+10 7.2236e+11 17134
## + Enclosed.Porch 1 9.8493e+09 7.2310e+11 17135
## + TotRms.AbvGrd 1 9.4624e+09 7.2349e+11 17136
## + X2nd.Flr.SF 1 7.2485e+09 7.2571e+11 17138
## + Overall.Cond 1 4.8257e+09 7.2813e+11 17141
## + Half.Bath 1 3.9920e+09 7.2896e+11 17142
## + Pool.Area 1 2.6764e+09 7.3028e+11 17143
## <none> 7.3295e+11 17144
## + Bsmt.Half.Bath 1 1.0176e+09 7.3194e+11 17145
## + Open.Porch.SF 1 9.6923e+08 7.3198e+11 17145
## + Full.Bath 1 4.0779e+08 7.3255e+11 17146
## + Screen.Porch 1 2.6705e+07 7.3293e+11 17146
##
## Step: AIC=17056.93
## price ~ Overall.Qual + area + Total.Bsmt.SF + Year.Built
##
## Df Sum of Sq RSS AIC
## + Bsmt.Full.Bath 1 5.2149e+10 6.0616e+11 16990
## + Bedroom.AbvGr 1 4.6036e+10 6.1227e+11 16999
## + Lot.Area 1 3.7391e+10 6.2091e+11 17010
## + Overall.Cond 1 3.4221e+10 6.2408e+11 17015
## + MS.SubClass 1 3.1171e+10 6.2713e+11 17019
## + Garage.Area 1 3.0737e+10 6.2757e+11 17019
## + Kitchen.AbvGr 1 2.7474e+10 6.3083e+11 17024
## + Wood.Deck.SF 1 2.4813e+10 6.3349e+11 17027
## + Fireplaces 1 1.9016e+10 6.3929e+11 17035
## + Garage.Cars 1 1.8674e+10 6.3963e+11 17035
## + Year.Remod.Add 1 1.7157e+10 6.4115e+11 17037
## + Full.Bath 1 1.6440e+10 6.4187e+11 17038
## + X1st.Flr.SF 1 1.4942e+10 6.4336e+11 17040
## + X2nd.Flr.SF 1 1.1299e+10 6.4701e+11 17045
## + TotRms.AbvGrd 1 5.3965e+09 6.5291e+11 17052
## + Pool.Area 1 2.5615e+09 6.5574e+11 17056
## + Central.Air 1 1.7995e+09 6.5651e+11 17057
## <none> 6.5830e+11 17057
## + Screen.Porch 1 9.5292e+08 6.5735e+11 17058
## + Half.Bath 1 4.5465e+08 6.5785e+11 17058
## + Bsmt.Half.Bath 1 2.8845e+08 6.5802e+11 17059
## + Open.Porch.SF 1 8.6432e+07 6.5822e+11 17059
## + Enclosed.Porch 1 1.3064e+05 6.5830e+11 17059
##
## Step: AIC=16990.27
## price ~ Overall.Qual + area + Total.Bsmt.SF + Year.Built + Bsmt.Full.Bath
##
## Df Sum of Sq RSS AIC
## + MS.SubClass 1 3.6162e+10 5.6999e+11 16941
## + Bedroom.AbvGr 1 3.3516e+10 5.7264e+11 16945
## + Lot.Area 1 3.1268e+10 5.7489e+11 16948
## + Overall.Cond 1 3.0807e+10 5.7535e+11 16949
## + Kitchen.AbvGr 1 2.8741e+10 5.7742e+11 16952
## + Garage.Area 1 2.4985e+10 5.8117e+11 16957
## + Year.Remod.Add 1 1.7566e+10 5.8859e+11 16968
## + Wood.Deck.SF 1 1.4536e+10 5.9162e+11 16972
## + Garage.Cars 1 1.4145e+10 5.9201e+11 16973
## + X1st.Flr.SF 1 1.2319e+10 5.9384e+11 16975
## + Fireplaces 1 1.1455e+10 5.9470e+11 16976
## + Full.Bath 1 1.0086e+10 5.9607e+11 16978
## + X2nd.Flr.SF 1 9.3524e+09 5.9680e+11 16979
## + Pool.Area 1 3.7192e+09 6.0244e+11 16987
## + TotRms.AbvGrd 1 2.2529e+09 6.0390e+11 16989
## + Central.Air 1 1.7008e+09 6.0446e+11 16990
## <none> 6.0616e+11 16990
## + Bsmt.Half.Bath 1 6.2472e+08 6.0553e+11 16991
## + Half.Bath 1 5.8494e+08 6.0557e+11 16992
## + Screen.Porch 1 3.8761e+08 6.0577e+11 16992
## + Enclosed.Porch 1 8.3064e+07 6.0607e+11 16992
## + Open.Porch.SF 1 6.9895e+07 6.0609e+11 16992
##
## Step: AIC=16941.09
## price ~ Overall.Qual + area + Total.Bsmt.SF + Year.Built + Bsmt.Full.Bath +
## MS.SubClass
##
## Df Sum of Sq RSS AIC
## + Bedroom.AbvGr 1 4.7760e+10 5.2223e+11 16870
## + Lot.Area 1 2.3142e+10 5.4685e+11 16909
## + Overall.Cond 1 2.2469e+10 5.4752e+11 16910
## + Garage.Area 1 2.1249e+10 5.4875e+11 16912
## + Year.Remod.Add 1 1.5956e+10 5.5404e+11 16920
## + Garage.Cars 1 1.3722e+10 5.5627e+11 16923
## + Kitchen.AbvGr 1 1.3635e+10 5.5636e+11 16923
## + Wood.Deck.SF 1 1.1681e+10 5.5831e+11 16926
## + Fireplaces 1 1.1658e+10 5.5834e+11 16926
## + Full.Bath 1 7.1902e+09 5.6280e+11 16933
## + X1st.Flr.SF 1 6.2842e+09 5.6371e+11 16934
## + TotRms.AbvGrd 1 4.8852e+09 5.6511e+11 16936
## + X2nd.Flr.SF 1 4.2924e+09 5.6570e+11 16937
## + Pool.Area 1 3.3221e+09 5.6667e+11 16938
## <none> 5.6999e+11 16941
## + Bsmt.Half.Bath 1 6.3005e+08 5.6936e+11 16942
## + Central.Air 1 6.0138e+08 5.6939e+11 16942
## + Half.Bath 1 4.6502e+08 5.6953e+11 16942
## + Screen.Porch 1 2.8812e+08 5.6971e+11 16943
## + Open.Porch.SF 1 7.6997e+06 5.6999e+11 16943
## + Enclosed.Porch 1 5.6850e+06 5.6999e+11 16943
##
## Step: AIC=16870.28
## price ~ Overall.Qual + area + Total.Bsmt.SF + Year.Built + Bsmt.Full.Bath +
## MS.SubClass + Bedroom.AbvGr
##
## Df Sum of Sq RSS AIC
## + Overall.Cond 1 2.6797e+10 4.9544e+11 16829
## + Lot.Area 1 2.3008e+10 4.9923e+11 16835
## + Garage.Area 1 1.7698e+10 5.0454e+11 16844
## + Year.Remod.Add 1 1.1327e+10 5.1091e+11 16854
## + Garage.Cars 1 1.1171e+10 5.1106e+11 16854
## + Wood.Deck.SF 1 7.7954e+09 5.1444e+11 16860
## + Fireplaces 1 6.2191e+09 5.1601e+11 16862
## + Kitchen.AbvGr 1 5.7828e+09 5.1645e+11 16863
## + Pool.Area 1 3.9344e+09 5.1830e+11 16866
## + Full.Bath 1 3.8530e+09 5.1838e+11 16866
## + Central.Air 1 2.2589e+09 5.1997e+11 16869
## + X1st.Flr.SF 1 2.2368e+09 5.2000e+11 16869
## <none> 5.2223e+11 16870
## + Bsmt.Half.Bath 1 1.1915e+09 5.2104e+11 16870
## + X2nd.Flr.SF 1 8.4921e+08 5.2138e+11 16871
## + TotRms.AbvGrd 1 4.5057e+08 5.2178e+11 16872
## + Screen.Porch 1 3.4914e+08 5.2188e+11 16872
## + Half.Bath 1 2.2115e+08 5.2201e+11 16872
## + Enclosed.Porch 1 1.9867e+08 5.2204e+11 16872
## + Open.Porch.SF 1 1.8470e+08 5.2205e+11 16872
##
## Step: AIC=16828.45
## price ~ Overall.Qual + area + Total.Bsmt.SF + Year.Built + Bsmt.Full.Bath +
## MS.SubClass + Bedroom.AbvGr + Overall.Cond
##
## Df Sum of Sq RSS AIC
## + Lot.Area 1 2.4922e+10 4.7051e+11 16788
## + Garage.Area 1 1.8634e+10 4.7680e+11 16799
## + Garage.Cars 1 1.2268e+10 4.8317e+11 16810
## + Fireplaces 1 6.1366e+09 4.8930e+11 16820
## + Kitchen.AbvGr 1 3.7046e+09 4.9173e+11 16824
## + Wood.Deck.SF 1 3.6461e+09 4.9179e+11 16824
## + Pool.Area 1 3.1433e+09 4.9229e+11 16825
## + X1st.Flr.SF 1 2.7358e+09 4.9270e+11 16826
## + Year.Remod.Add 1 2.6799e+09 4.9276e+11 16826
## + Full.Bath 1 2.4201e+09 4.9302e+11 16826
## + X2nd.Flr.SF 1 1.2874e+09 4.9415e+11 16828
## <none> 4.9544e+11 16829
## + Bsmt.Half.Bath 1 6.0265e+08 4.9483e+11 16829
## + TotRms.AbvGrd 1 5.2959e+08 4.9491e+11 16830
## + Half.Bath 1 3.3434e+08 4.9510e+11 16830
## + Screen.Porch 1 1.6929e+08 4.9527e+11 16830
## + Open.Porch.SF 1 1.0869e+08 4.9533e+11 16830
## + Central.Air 1 8.0400e+07 4.9536e+11 16830
## + Enclosed.Porch 1 1.7396e+05 4.9544e+11 16831
##
## Step: AIC=16787.51
## price ~ Overall.Qual + area + Total.Bsmt.SF + Year.Built + Bsmt.Full.Bath +
## MS.SubClass + Bedroom.AbvGr + Overall.Cond + Lot.Area
##
## Df Sum of Sq RSS AIC
## + Garage.Area 1 1.6596e+10 4.5392e+11 16760
## + Garage.Cars 1 1.0167e+10 4.6035e+11 16771
## + Wood.Deck.SF 1 3.6525e+09 4.6686e+11 16783
## + Fireplaces 1 3.5350e+09 4.6698e+11 16783
## + Kitchen.AbvGr 1 3.0319e+09 4.6748e+11 16784
## + Pool.Area 1 2.8332e+09 4.6768e+11 16785
## + Full.Bath 1 2.5932e+09 4.6792e+11 16785
## + Year.Remod.Add 1 2.4963e+09 4.6802e+11 16785
## + X1st.Flr.SF 1 1.6563e+09 4.6886e+11 16787
## <none> 4.7051e+11 16788
## + X2nd.Flr.SF 1 6.7036e+08 4.6984e+11 16788
## + TotRms.AbvGrd 1 4.2311e+08 4.7009e+11 16789
## + Central.Air 1 3.1217e+08 4.7020e+11 16789
## + Screen.Porch 1 1.7979e+08 4.7034e+11 16789
## + Half.Bath 1 1.4241e+08 4.7037e+11 16789
## + Bsmt.Half.Bath 1 1.0849e+08 4.7041e+11 16789
## + Enclosed.Porch 1 8.7208e+07 4.7043e+11 16789
## + Open.Porch.SF 1 4.2736e+07 4.7047e+11 16789
##
## Step: AIC=16759.64
## price ~ Overall.Qual + area + Total.Bsmt.SF + Year.Built + Bsmt.Full.Bath +
## MS.SubClass + Bedroom.AbvGr + Overall.Cond + Lot.Area + Garage.Area
##
## Df Sum of Sq RSS AIC
## + Kitchen.AbvGr 1 4172047018 4.4975e+11 16754
## + Fireplaces 1 4129279985 4.4979e+11 16754
## + Wood.Deck.SF 1 2948125442 4.5097e+11 16756
## + Year.Remod.Add 1 2818725071 4.5110e+11 16757
## + Pool.Area 1 2271060820 4.5165e+11 16758
## + Full.Bath 1 1957164617 4.5196e+11 16758
## + Central.Air 1 1173024232 4.5275e+11 16760
## <none> 4.5392e+11 16760
## + X1st.Flr.SF 1 724246780 4.5320e+11 16760
## + TotRms.AbvGrd 1 322798135 4.5360e+11 16761
## + Screen.Porch 1 169274433 4.5375e+11 16761
## + X2nd.Flr.SF 1 169087699 4.5375e+11 16761
## + Bsmt.Half.Bath 1 126703964 4.5379e+11 16761
## + Garage.Cars 1 64566660 4.5385e+11 16762
## + Enclosed.Porch 1 62634475 4.5386e+11 16762
## + Half.Bath 1 10140514 4.5391e+11 16762
## + Open.Porch.SF 1 5351148 4.5391e+11 16762
##
## Step: AIC=16753.96
## price ~ Overall.Qual + area + Total.Bsmt.SF + Year.Built + Bsmt.Full.Bath +
## MS.SubClass + Bedroom.AbvGr + Overall.Cond + Lot.Area + Garage.Area +
## Kitchen.AbvGr
##
## Df Sum of Sq RSS AIC
## + Fireplaces 1 3814277571 4.4593e+11 16749
## + Central.Air 1 3080784548 4.4667e+11 16750
## + Pool.Area 1 2575115132 4.4717e+11 16751
## + Wood.Deck.SF 1 2522772288 4.4722e+11 16751
## + Year.Remod.Add 1 2439477375 4.4731e+11 16751
## + TotRms.AbvGrd 1 1860338891 4.4789e+11 16753
## + X1st.Flr.SF 1 1789162561 4.4796e+11 16753
## <none> 4.4975e+11 16754
## + Full.Bath 1 839059501 4.4891e+11 16754
## + X2nd.Flr.SF 1 706975669 4.4904e+11 16755
## + Half.Bath 1 191586696 4.4956e+11 16756
## + Bsmt.Half.Bath 1 99359602 4.4965e+11 16756
## + Screen.Porch 1 91893119 4.4966e+11 16756
## + Enclosed.Porch 1 90012170 4.4966e+11 16756
## + Open.Porch.SF 1 36617537 4.4971e+11 16756
## + Garage.Cars 1 3673957 4.4974e+11 16756
##
## Step: AIC=16748.87
## price ~ Overall.Qual + area + Total.Bsmt.SF + Year.Built + Bsmt.Full.Bath +
## MS.SubClass + Bedroom.AbvGr + Overall.Cond + Lot.Area + Garage.Area +
## Kitchen.AbvGr + Fireplaces
##
## Df Sum of Sq RSS AIC
## + Central.Air 1 3792964791 4.4214e+11 16744
## + Year.Remod.Add 1 3737749338 4.4220e+11 16744
## + Pool.Area 1 3717485580 4.4222e+11 16744
## + Wood.Deck.SF 1 2060768502 4.4387e+11 16747
## + TotRms.AbvGrd 1 1775926499 4.4416e+11 16748
## + X1st.Flr.SF 1 1176978451 4.4476e+11 16749
## <none> 4.4593e+11 16749
## + Full.Bath 1 590457984 4.4534e+11 16750
## + X2nd.Flr.SF 1 363581333 4.4557e+11 16750
## + Half.Bath 1 170717522 4.4576e+11 16751
## + Enclosed.Porch 1 56135685 4.4588e+11 16751
## + Open.Porch.SF 1 14048724 4.4592e+11 16751
## + Garage.Cars 1 6461168 4.4593e+11 16751
## + Bsmt.Half.Bath 1 956592 4.4593e+11 16751
## + Screen.Porch 1 45659 4.4593e+11 16751
##
## Step: AIC=16743.76
## price ~ Overall.Qual + area + Total.Bsmt.SF + Year.Built + Bsmt.Full.Bath +
## MS.SubClass + Bedroom.AbvGr + Overall.Cond + Lot.Area + Garage.Area +
## Kitchen.AbvGr + Fireplaces + Central.Air
##
## Df Sum of Sq RSS AIC
## + Pool.Area 1 3659204284 4.3848e+11 16739
## + Year.Remod.Add 1 3337149684 4.3880e+11 16740
## + Wood.Deck.SF 1 1705741917 4.4043e+11 16743
## + TotRms.AbvGrd 1 1675942135 4.4046e+11 16743
## + X1st.Flr.SF 1 1412730562 4.4073e+11 16743
## <none> 4.4214e+11 16744
## + Full.Bath 1 770783113 4.4137e+11 16744
## + X2nd.Flr.SF 1 552280907 4.4159e+11 16745
## + Half.Bath 1 99353510 4.4204e+11 16746
## + Garage.Cars 1 25118208 4.4211e+11 16746
## + Bsmt.Half.Bath 1 12402347 4.4213e+11 16746
## + Open.Porch.SF 1 6335391 4.4213e+11 16746
## + Enclosed.Porch 1 2006349 4.4214e+11 16746
## + Screen.Porch 1 235712 4.4214e+11 16746
##
## Step: AIC=16738.85
## price ~ Overall.Qual + area + Total.Bsmt.SF + Year.Built + Bsmt.Full.Bath +
## MS.SubClass + Bedroom.AbvGr + Overall.Cond + Lot.Area + Garage.Area +
## Kitchen.AbvGr + Fireplaces + Central.Air + Pool.Area
##
## Df Sum of Sq RSS AIC
## + Year.Remod.Add 1 3182754038 4.3530e+11 16735
## + TotRms.AbvGrd 1 2102306811 4.3638e+11 16737
## + Wood.Deck.SF 1 2101699305 4.3638e+11 16737
## + X1st.Flr.SF 1 1515714442 4.3697e+11 16738
## <none> 4.3848e+11 16739
## + Full.Bath 1 655618215 4.3783e+11 16740
## + X2nd.Flr.SF 1 597165100 4.3788e+11 16740
## + Half.Bath 1 186090342 4.3829e+11 16741
## + Bsmt.Half.Bath 1 119692086 4.3836e+11 16741
## + Screen.Porch 1 56913073 4.3842e+11 16741
## + Garage.Cars 1 47493124 4.3843e+11 16741
## + Open.Porch.SF 1 3463438 4.3848e+11 16741
## + Enclosed.Porch 1 636110 4.3848e+11 16741
##
## Step: AIC=16734.79
## price ~ Overall.Qual + area + Total.Bsmt.SF + Year.Built + Bsmt.Full.Bath +
## MS.SubClass + Bedroom.AbvGr + Overall.Cond + Lot.Area + Garage.Area +
## Kitchen.AbvGr + Fireplaces + Central.Air + Pool.Area + Year.Remod.Add
##
## Df Sum of Sq RSS AIC
## + Wood.Deck.SF 1 2022379545 4.3328e+11 16733
## + TotRms.AbvGrd 1 1997483702 4.3330e+11 16733
## + X1st.Flr.SF 1 1287320778 4.3401e+11 16734
## + Full.Bath 1 1267087231 4.3403e+11 16734
## <none> 4.3530e+11 16735
## + X2nd.Flr.SF 1 469337205 4.3483e+11 16736
## + Bsmt.Half.Bath 1 162494672 4.3514e+11 16737
## + Half.Bath 1 122406785 4.3518e+11 16737
## + Screen.Porch 1 103761118 4.3519e+11 16737
## + Garage.Cars 1 94154795 4.3520e+11 16737
## + Open.Porch.SF 1 4701214 4.3529e+11 16737
## + Enclosed.Porch 1 1158453 4.3530e+11 16737
##
## Step: AIC=16732.91
## price ~ Overall.Qual + area + Total.Bsmt.SF + Year.Built + Bsmt.Full.Bath +
## MS.SubClass + Bedroom.AbvGr + Overall.Cond + Lot.Area + Garage.Area +
## Kitchen.AbvGr + Fireplaces + Central.Air + Pool.Area + Year.Remod.Add +
## Wood.Deck.SF
##
## Df Sum of Sq RSS AIC
## + TotRms.AbvGrd 1 1948215943 4.3133e+11 16731
## + X1st.Flr.SF 1 1295692188 4.3198e+11 16732
## + Full.Bath 1 1251079281 4.3202e+11 16733
## <none> 4.3328e+11 16733
## + X2nd.Flr.SF 1 475243904 4.3280e+11 16734
## + Screen.Porch 1 228083452 4.3305e+11 16735
## + Half.Bath 1 138333087 4.3314e+11 16735
## + Garage.Cars 1 81242898 4.3319e+11 16735
## + Bsmt.Half.Bath 1 53679010 4.3322e+11 16735
## + Enclosed.Porch 1 2683972 4.3327e+11 16735
## + Open.Porch.SF 1 1417214 4.3327e+11 16735
##
## Step: AIC=16731.16
## price ~ Overall.Qual + area + Total.Bsmt.SF + Year.Built + Bsmt.Full.Bath +
## MS.SubClass + Bedroom.AbvGr + Overall.Cond + Lot.Area + Garage.Area +
## Kitchen.AbvGr + Fireplaces + Central.Air + Pool.Area + Year.Remod.Add +
## Wood.Deck.SF + TotRms.AbvGrd
##
## Df Sum of Sq RSS AIC
## + X1st.Flr.SF 1 1227105267 4.3010e+11 16731
## + Full.Bath 1 1098332201 4.3023e+11 16731
## <none> 4.3133e+11 16731
## + X2nd.Flr.SF 1 414604183 4.3091e+11 16732
## + Screen.Porch 1 203246082 4.3112e+11 16733
## + Garage.Cars 1 108726811 4.3122e+11 16733
## + Bsmt.Half.Bath 1 100256270 4.3123e+11 16733
## + Half.Bath 1 89854851 4.3124e+11 16733
## + Enclosed.Porch 1 10696285 4.3132e+11 16733
## + Open.Porch.SF 1 1992501 4.3133e+11 16733
##
## Step: AIC=16730.79
## price ~ Overall.Qual + area + Total.Bsmt.SF + Year.Built + Bsmt.Full.Bath +
## MS.SubClass + Bedroom.AbvGr + Overall.Cond + Lot.Area + Garage.Area +
## Kitchen.AbvGr + Fireplaces + Central.Air + Pool.Area + Year.Remod.Add +
## Wood.Deck.SF + TotRms.AbvGrd + X1st.Flr.SF
##
## Df Sum of Sq RSS AIC
## + X2nd.Flr.SF 1 2617560560 4.2748e+11 16728
## + Full.Bath 1 1060020608 4.2904e+11 16731
## <none> 4.3010e+11 16731
## + Screen.Porch 1 202620951 4.2990e+11 16732
## + Bsmt.Half.Bath 1 79744349 4.3002e+11 16733
## + Garage.Cars 1 67838749 4.3003e+11 16733
## + Enclosed.Porch 1 42984741 4.3006e+11 16733
## + Open.Porch.SF 1 17977259 4.3008e+11 16733
## + Half.Bath 1 10914178 4.3009e+11 16733
##
## Step: AIC=16727.71
## price ~ Overall.Qual + area + Total.Bsmt.SF + Year.Built + Bsmt.Full.Bath +
## MS.SubClass + Bedroom.AbvGr + Overall.Cond + Lot.Area + Garage.Area +
## Kitchen.AbvGr + Fireplaces + Central.Air + Pool.Area + Year.Remod.Add +
## Wood.Deck.SF + TotRms.AbvGrd + X1st.Flr.SF + X2nd.Flr.SF
##
## Df Sum of Sq RSS AIC
## <none> 4.2748e+11 16728
## + Full.Bath 1 907218456 4.2658e+11 16728
## + Enclosed.Porch 1 172903375 4.2731e+11 16729
## + Screen.Porch 1 163712936 4.2732e+11 16729
## + Garage.Cars 1 75952197 4.2741e+11 16730
## + Bsmt.Half.Bath 1 75623759 4.2741e+11 16730
## + Open.Porch.SF 1 361833 4.2748e+11 16730
## + Half.Bath 1 281479 4.2748e+11 16730print(summary(lowest.step.forward))##
## Call:
## lm(formula = price ~ Overall.Qual + area + Total.Bsmt.SF + Year.Built +
## Bsmt.Full.Bath + MS.SubClass + Bedroom.AbvGr + Overall.Cond +
## Lot.Area + Garage.Area + Kitchen.AbvGr + Fireplaces + Central.Air +
## Pool.Area + Year.Remod.Add + Wood.Deck.SF + TotRms.AbvGrd +
## X1st.Flr.SF + X2nd.Flr.SF, data = na.omit(train))
##
## Residuals:
## Min 1Q Median 3Q Max
## -72724 -13450 -1755 11413 104153
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -1.107e+06 1.041e+05 -10.636 < 2e-16 ***
## Overall.Qual 1.325e+04 9.953e+02 13.311 < 2e-16 ***
## area 2.781e+01 1.601e+01 1.737 0.082716 .
## Total.Bsmt.SF 2.586e+01 3.667e+00 7.050 3.83e-12 ***
## Year.Built 4.159e+02 4.763e+01 8.732 < 2e-16 ***
## Bsmt.Full.Bath 1.223e+04 1.727e+03 7.080 3.11e-12 ***
## MS.SubClass -1.089e+02 2.255e+01 -4.832 1.62e-06 ***
## Bedroom.AbvGr -1.130e+04 1.534e+03 -7.365 4.36e-13 ***
## Overall.Cond 5.257e+03 9.356e+02 5.619 2.64e-08 ***
## Lot.Area 4.819e-01 8.380e-02 5.751 1.26e-08 ***
## Garage.Area 2.993e+01 5.156e+00 5.804 9.29e-09 ***
## Kitchen.AbvGr -2.079e+04 5.332e+03 -3.900 0.000104 ***
## Fireplaces 4.906e+03 1.538e+03 3.191 0.001474 **
## Central.AirY -9.737e+03 4.333e+03 -2.247 0.024885 *
## Pool.Area -7.338e+01 2.489e+01 -2.949 0.003285 **
## Year.Remod.Add 1.284e+02 5.660e+01 2.269 0.023536 *
## Wood.Deck.SF 1.411e+01 7.291e+00 1.935 0.053382 .
## TotRms.AbvGrd 2.132e+03 1.074e+03 1.986 0.047409 *
## X1st.Flr.SF 4.175e+01 1.635e+01 2.553 0.010877 *
## X2nd.Flr.SF 3.564e+01 1.599e+01 2.230 0.026033 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 22940 on 812 degrees of freedom
## Multiple R-squared: 0.8938, Adjusted R-squared: 0.8913
## F-statistic: 359.5 on 19 and 812 DF, p-value: < 2.2e-16final.model <- regsubsets(price~.,data=train,nbest=10)
plot(final.model)
plot(final.model,scale="Cp")
0.0.0.3.3 RMSE comparison(full model,model.AIC,model.BIC)
predict.full <- exp(predict(full.model,train))
resid.full <- ames_train$price - predict.full
print(rmse.full <- sqrt(mean(resid.full^2)))## [1] 18441.86predict.AIC <- exp(predict(model.AIC,train))
resid.aic <- train$price - predict.AIC
print(rmse.aic <- sqrt(mean(resid.aic^2)))## [1] 18445.39predict.BIC <- exp(predict(model.BIC, train))
resid.BIC <- ames_train$price - predict.BIC
print(rmse.bic <- sqrt(mean(resid.BIC^2)))## [1] 18699.60.0.0.3.4 Calculate proportion of falling within prediction intervals(AIC & BIC)
predict.AIC <- exp(predict(model.AIC, train, interval = "prediction"))
coverage.prob.AIC <- mean(train$price > predict.AIC[,"lwr"] &
train$price < predict.AIC[,"upr"])
coverage.prob.AIC## [1] 0.9495192predict.BIC <- exp(predict(model.BIC, train, interval = "prediction"))
coverage.prob.BIC <- mean(train$price > predict.BIC[,"lwr"] &
train$price < predict.BIC[,"upr"])
coverage.prob.BIC## [1] 0.95432690.0.0.3.5 Other useful functions
coefficients(full.model)## (Intercept) area MS.SubClass Lot.Area Overall.Qual
## 2.498916e+00 1.637156e-04 -4.388242e-04 2.287374e-06 7.380319e-02
## Overall.Cond Year.Built Year.Remod.Add Total.Bsmt.SF Central.AirY
## 4.092825e-02 2.897454e-03 1.198090e-03 1.292802e-04 9.880291e-02
## X1st.Flr.SF X2nd.Flr.SF Bsmt.Full.Bath Bsmt.Half.Bath Full.Bath
## 1.395511e-04 1.200879e-04 6.991420e-02 3.301239e-02 -6.054216e-03
## Half.Bath Bedroom.AbvGr Kitchen.AbvGr TotRms.AbvGrd Fireplaces
## -3.143704e-03 -2.201090e-02 -5.451689e-02 1.070757e-02 3.310778e-02
## Garage.Cars Garage.Area Wood.Deck.SF Open.Porch.SF Enclosed.Porch
## 1.742961e-02 1.071464e-04 3.479209e-05 7.779078e-05 1.536721e-04
## Screen.Porch Pool.Area
## 2.131552e-04 -3.922601e-04confint(full.model, level=0.95) ## 2.5 % 97.5 %
## (Intercept) 1.373578e+00 3.624253e+00
## area 1.332149e-05 3.141098e-04
## MS.SubClass -6.471521e-04 -2.304963e-04
## Lot.Area 1.513554e-06 3.061193e-06
## Overall.Qual 6.456238e-02 8.304399e-02
## Overall.Cond 3.226331e-02 4.959319e-02
## Year.Built 2.405765e-03 3.389142e-03
## Year.Remod.Add 6.697029e-04 1.726478e-03
## Total.Bsmt.SF 9.522803e-05 1.633324e-04
## Central.AirY 5.867624e-02 1.389296e-01
## X1st.Flr.SF -1.262759e-05 2.917297e-04
## X2nd.Flr.SF -2.840536e-05 2.685812e-04
## Bsmt.Full.Bath 5.346248e-02 8.636592e-02
## Bsmt.Half.Bath 6.270138e-04 6.539776e-02
## Full.Bath -2.979696e-02 1.768853e-02
## Half.Bath -2.500399e-02 1.871658e-02
## Bedroom.AbvGr -3.629951e-02 -7.722291e-03
## Kitchen.AbvGr -1.051512e-01 -3.882614e-03
## TotRms.AbvGrd 7.831226e-04 2.063201e-02
## Fireplaces 1.871722e-02 4.749834e-02
## Garage.Cars -7.063858e-03 4.192309e-02
## Garage.Area 2.381069e-05 1.904821e-04
## Wood.Deck.SF -3.326754e-05 1.028517e-04
## Open.Porch.SF -5.306567e-05 2.086472e-04
## Enclosed.Porch 1.685302e-05 2.904912e-04
## Screen.Porch 7.016912e-05 3.561414e-04
## Pool.Area -6.290003e-04 -1.555200e-04mean(fitted(full.model)) # predicted values## [1] 11.9928mean(residuals(full.model)) # residuals## [1] -2.111486e-18anova(full.model) # anova table ## Analysis of Variance Table
##
## Response: log(price)
## Df Sum Sq Mean Sq F value Pr(>F)
## area 1 65.071 65.071 5666.5973 < 2.2e-16 ***
## MS.SubClass 1 1.663 1.663 144.8426 < 2.2e-16 ***
## Lot.Area 1 0.441 0.441 38.4027 9.181e-10 ***
## Overall.Qual 1 27.345 27.345 2381.3165 < 2.2e-16 ***
## Overall.Cond 1 0.132 0.132 11.4830 0.0007365 ***
## Year.Built 1 8.189 8.189 713.1439 < 2.2e-16 ***
## Year.Remod.Add 1 0.064 0.064 5.6151 0.0180413 *
## Total.Bsmt.SF 1 3.025 3.025 263.3902 < 2.2e-16 ***
## Central.Air 1 0.410 0.410 35.6770 3.493e-09 ***
## X1st.Flr.SF 1 0.107 0.107 9.3472 0.0023071 **
## X2nd.Flr.SF 1 0.022 0.022 1.9112 0.1672092
## Bsmt.Full.Bath 1 1.155 1.155 100.5968 < 2.2e-16 ***
## Bsmt.Half.Bath 1 0.049 0.049 4.2793 0.0388977 *
## Full.Bath 1 0.041 0.041 3.5876 0.0585693 .
## Half.Bath 1 0.001 0.001 0.1006 0.7512166
## Bedroom.AbvGr 1 0.206 0.206 17.9235 2.565e-05 ***
## Kitchen.AbvGr 1 0.013 0.013 1.1620 0.2813807
## TotRms.AbvGrd 1 0.045 0.045 3.8964 0.0487298 *
## Fireplaces 1 0.226 0.226 19.6567 1.055e-05 ***
## Garage.Cars 1 0.491 0.491 42.7783 1.089e-10 ***
## Garage.Area 1 0.069 0.069 6.0494 0.0141202 *
## Wood.Deck.SF 1 0.002 0.002 0.2072 0.6490632
## Open.Porch.SF 1 0.008 0.008 0.6975 0.4038695
## Enclosed.Porch 1 0.044 0.044 3.8606 0.0497754 *
## Screen.Porch 1 0.075 0.075 6.5293 0.0107937 *
## Pool.Area 1 0.121 0.121 10.5781 0.0011920 **
## Residuals 805 9.244 0.011
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1mean(vcov(full.model)) # covariance matrix for model parameters ## [1] 0.0004632929inflm.full <- influence.measures(full.model)
which(apply(inflm.full$is.inf, 1, any))## 20 21 61 74 89 94 113 137 138 142 164 181 184 186 209 223 247 257
## 20 21 61 74 89 94 113 137 138 142 164 181 184 186 209 223 247 257
## 271 282 290 291 297 299 308 324 326 353 377 379 380 390 396 401 404 405
## 271 282 290 291 297 299 308 324 326 353 377 379 380 390 396 401 404 405
## 411 422 427 433 458 465 466 471 493 505 514 530 553 554 559 579 586 610
## 411 422 427 433 458 465 466 471 493 505 514 530 553 554 559 579 586 610
## 655 657 697 704 726 749 790 795 800 815 817
## 655 657 697 704 726 749 790 795 800 815 8170.0.0.3.6 Which observations ‘are’ Influential
summary(inflm.full) # only these## Potentially influential observations of
## lm(formula = log(price) ~ ., data = train) :
##
## dfb.1_ dfb.area dfb.MS.S dfb.Lt.A dfb.Ov.Q dfb.Ov.C dfb.Yr.B dfb.Y.R.
## 20 0.02 0.05 -0.28 -0.03 -0.04 -0.31 -0.01 0.00
## 21 -0.04 -0.03 0.09 -0.03 0.01 0.04 -0.18 0.21
## 61 -0.15 0.03 0.00 -0.02 -0.09 -0.02 0.07 0.08
## 74 -0.06 0.00 0.01 0.03 -0.03 0.02 0.09 -0.02
## 89 -0.14 0.02 0.18 0.02 0.00 0.01 0.11 0.06
## 94 -0.06 0.01 -0.05 0.02 -0.09 -0.04 0.20 -0.11
## 113 -0.14 0.00 0.05 0.01 -0.05 0.17 0.06 0.11
## 137 0.11 -0.03 0.10 -0.04 -0.09 0.05 -0.02 -0.10
## 138 0.03 -0.01 0.02 0.00 -0.01 -0.02 -0.03 0.00
## 142 0.00 -0.01 0.00 0.00 0.00 0.00 0.00 0.00
## 164 -0.13 0.01 -0.02 0.31 -0.26 0.00 0.01 0.14
## 181 0.03 0.03 -0.14 0.03 -0.10 0.01 0.08 -0.10
## 184 0.00 -0.03 0.00 0.00 0.00 0.00 0.00 0.00
## 186 -0.16 0.05 0.05 0.04 -0.04 -0.06 0.07 0.12
## 209 0.16 -0.05 -0.09 -0.96 0.01 -0.11 -0.09 -0.08
## 223 -0.05 0.02 0.08 0.04 0.12 0.04 -0.09 0.13
## 247 -0.07 0.06 0.02 -0.01 0.01 0.10 0.00 0.07
## 257 0.01 0.00 0.01 0.00 0.01 -0.04 -0.01 0.01
## 271 -0.05 0.03 0.04 0.04 -0.02 0.20 0.11 -0.05
## 282 0.05 0.24 0.00 0.02 0.02 0.02 -0.01 -0.04
## 290 0.01 0.01 -0.01 0.03 0.02 -0.01 0.00 0.00
## 291 0.15 -0.01 -0.19 0.03 0.13 -0.01 -0.14 -0.04
## 297 -0.04 0.01 -0.22 -2.21_* -0.20 -0.13 -0.13 0.18
## 299 0.02 0.01 -0.01 0.01 0.02 0.01 0.00 -0.02
## 308 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
## 324 0.07 0.03 0.02 -0.01 -0.14 0.11 -0.04 -0.04
## 326 -0.05 0.07 -0.10 0.02 0.07 -0.01 0.00 0.06
## 353 0.01 0.00 -0.01 -0.01 0.01 0.00 0.00 -0.01
## 377 -0.06 0.02 -0.17 -0.02 -0.09 0.06 0.02 0.05
## 379 0.21 -0.09 0.01 -0.03 0.01 -0.07 -0.16 -0.08
## 380 0.00 0.00 -0.01 0.00 0.00 0.00 0.00 0.00
## 390 -0.03 -0.09 0.01 0.01 -0.09 0.04 0.08 -0.04
## 396 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
## 401 -0.03 0.01 0.00 -0.01 -0.02 -0.01 0.02 0.01
## 404 0.01 0.01 0.02 0.00 0.01 0.00 -0.01 0.00
## 405 0.00 0.01 0.00 -0.02 0.01 -0.03 -0.02 0.02
## 411 -0.02 0.01 0.09 0.02 0.20 0.02 -0.06 0.05
## 422 -0.24 0.04 -0.01 0.02 -0.14 0.19 0.19 0.05
## 427 0.00 -0.03 -0.05 0.01 -0.02 -0.05 -0.24 0.22
## 433 -0.01 0.00 0.00 0.00 0.00 -0.02 0.01 0.01
## 458 0.03 0.00 0.01 0.01 0.01 0.01 -0.03 0.00
## 465 -0.07 0.01 0.01 0.02 0.01 0.02 0.06 0.01
## 466 0.00 0.00 0.02 0.01 0.04 -0.02 -0.01 0.01
## 471 -0.01 0.00 0.00 -0.01 0.00 0.01 0.01 0.00
## 493 0.00 0.01 0.00 -0.02 0.01 -0.03 -0.02 0.02
## 505 0.00 0.00 0.00 0.00 0.00 0.00 0.01 -0.01
## 514 -0.06 -0.02 0.12 0.05 0.02 0.01 0.10 -0.02
## 530 -0.07 -0.08 0.28 0.02 0.04 -0.23 -0.44 0.49
## 553 -0.03 0.14 0.00 -0.01 -0.03 0.00 0.02 0.02
## 554 -0.07 0.05 0.03 0.01 -0.09 0.02 0.04 0.05
## 559 0.04 0.01 0.21 0.12 0.40 -0.06 0.14 -0.18
## 579 0.01 0.04 -0.21 0.02 0.11 0.02 -0.03 0.02
## 586 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
## 610 0.01 0.07 -0.14 -0.01 0.15 0.21 -0.11 0.03
## 655 0.05 0.00 0.06 0.05 0.13 0.02 0.15 -0.19
## 657 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
## 697 -0.10 -0.02 0.08 0.01 -0.05 -0.06 -0.03 0.13
## 704 0.03 -0.02 -0.02 0.00 -0.03 -0.06 -0.11 0.07
## 726 0.02 -0.01 0.03 0.00 -0.02 -0.01 -0.03 0.00
## 749 0.04 -0.17 0.00 0.00 0.00 0.01 0.00 -0.04
## 790 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
## 795 -0.07 -0.03 0.13 0.04 0.01 0.01 0.11 -0.02
## 800 0.18 -0.01 0.04 0.02 0.01 0.10 -0.06 -0.14
## 815 0.08 -0.01 0.17 -0.04 -0.06 -0.12 -0.20 0.09
## 817 0.00 0.00 0.00 0.01 0.01 0.01 0.00 0.00
## dfb.T.B. dfb.C.AY dfb.X1.F dfb.X2.F dfb.B.F. dfb.B.H. dfb.Fl.B
## 20 -0.07 0.07 -0.01 0.02 0.04 0.06 -0.27
## 21 0.09 -0.33 0.05 0.06 -0.08 -0.04 -0.21
## 61 -0.01 0.41 -0.02 0.00 0.08 0.06 -0.06
## 74 0.15 -0.22 -0.01 -0.01 -0.08 -0.04 0.03
## 89 0.15 0.02 0.07 0.02 0.07 0.04 -0.15
## 94 0.18 -0.07 -0.12 -0.06 0.00 -0.03 0.12
## 113 0.10 -0.45 -0.01 0.03 -0.06 -0.03 -0.19
## 137 -0.10 0.00 0.04 0.00 0.01 0.30 0.16
## 138 0.04 -0.01 0.01 0.00 0.01 0.01 0.02
## 142 0.00 0.00 0.01 0.01 0.00 0.00 0.00
## 164 -0.01 0.02 0.02 0.02 -0.03 -0.06 -0.14
## 181 -0.33 -0.24 0.02 -0.04 -0.05 -0.03 0.11
## 184 0.00 0.00 0.03 0.03 0.00 0.00 -0.01
## 186 -0.06 -0.09 -0.03 -0.04 0.05 0.04 -0.05
## 209 -0.04 0.04 0.05 0.02 0.10 -0.16 0.06
## 223 0.03 -0.09 -0.09 -0.07 0.11 0.03 0.10
## 247 -0.05 -0.16 -0.07 -0.09 0.04 0.01 0.05
## 257 0.00 -0.01 0.01 0.00 -0.03 -0.01 0.00
## 271 0.41 -0.07 -0.11 0.00 -0.03 0.00 -0.11
## 282 -0.01 -0.01 -0.25 -0.26 -0.02 -0.01 0.01
## 290 0.00 0.00 0.00 0.00 0.00 0.00 -0.03
## 291 -0.05 -0.02 -0.01 -0.03 0.06 0.00 0.08
## 297 -0.06 0.06 0.04 0.02 -0.11 0.13 -0.10
## 299 0.00 0.00 0.00 -0.01 -0.04 -0.01 -0.01
## 308 0.00 0.00 0.00 0.00 0.00 0.00 0.00
## 324 0.11 -0.03 0.03 0.05 -0.11 -0.05 0.08
## 326 0.06 0.05 -0.02 0.01 -0.09 -0.03 -0.17
## 353 0.00 0.02 0.00 0.00 0.00 0.00 -0.01
## 377 -0.01 -0.05 0.00 0.00 0.06 0.03 0.02
## 379 0.05 0.11 0.06 0.05 -0.06 -0.06 0.05
## 380 -0.01 -0.01 0.00 0.00 0.01 0.00 0.00
## 390 0.01 0.06 0.08 0.08 -0.02 0.00 0.00
## 396 0.00 0.00 0.00 0.00 0.00 -0.01 0.00
## 401 0.03 -0.04 0.00 0.00 0.06 0.01 -0.01
## 404 0.02 0.03 -0.01 0.00 0.00 -0.01 -0.02
## 405 -0.02 0.01 0.00 0.00 -0.02 0.12 -0.07
## 411 0.15 0.30 -0.04 -0.02 0.03 0.02 -0.07
## 422 0.05 0.39 0.02 0.02 -0.25 0.00 -0.25
## 427 0.03 0.07 0.01 0.01 0.12 0.01 0.01
## 433 0.02 0.01 -0.01 0.00 0.00 0.00 -0.02
## 458 0.12 -0.03 -0.02 0.00 0.01 0.01 0.01
## 465 0.00 -0.02 0.00 -0.01 -0.02 0.00 0.00
## 466 0.01 -0.03 0.00 0.00 -0.01 -0.01 -0.03
## 471 0.00 -0.01 0.00 0.00 0.00 0.00 0.00
## 493 -0.02 0.01 0.00 0.00 -0.02 0.12 -0.07
## 505 0.01 0.00 0.00 0.00 0.00 0.00 0.00
## 514 -0.01 -0.05 0.04 0.02 -0.17 -0.02 -0.19
## 530 0.21 -0.26 -0.05 -0.01 -0.06 -0.05 -0.01
## 553 -0.01 0.00 -0.13 -0.14 -0.01 -0.01 -0.03
## 554 -0.07 0.15 0.01 -0.03 -0.19 -0.05 0.02
## 559 -1.00 0.11 0.20 -0.02 0.00 -0.03 0.23
## 579 -0.06 -0.02 -0.02 -0.02 0.04 0.02 0.02
## 586 0.00 0.00 0.00 0.00 0.00 0.00 0.00
## 610 -0.14 0.84 -0.06 -0.14 0.07 0.08 0.27
## 655 -0.11 0.02 -0.01 0.01 -0.08 0.01 0.02
## 657 0.01 0.00 0.00 0.00 0.00 0.00 0.00
## 697 -0.06 -0.01 0.00 -0.01 0.11 0.04 0.05
## 704 0.02 0.04 0.01 0.01 -0.01 0.00 0.04
## 726 0.00 0.04 0.01 0.02 0.00 0.00 0.00
## 749 -0.01 0.01 0.17 0.17 -0.02 0.00 0.04
## 790 0.00 0.00 0.00 0.00 0.00 0.00 0.00
## 795 -0.01 -0.05 0.04 0.02 -0.18 -0.02 -0.20
## 800 -0.07 0.02 0.03 0.01 -0.06 -0.03 -0.09
## 815 -0.05 -0.17 0.06 0.03 -0.08 -0.01 -0.04
## 817 -0.04 0.00 0.01 0.00 0.02 0.00 0.00
## dfb.Hl.B dfb.B.AG dfb.K.AG dfb.TR.A dfb.Frpl dfb.Gr.C dfb.Gr.A
## 20 -0.23 -0.05 0.12 -0.10 0.02 0.19 -0.06
## 21 0.03 0.17 -0.11 -0.15 0.00 0.30 -0.10
## 61 -0.08 0.01 0.12 0.01 0.02 0.15 -0.20
## 74 0.05 0.06 0.24 -0.01 -0.01 -0.12 -0.01
## 89 0.26 -0.35 0.05 0.00 -0.02 -0.20 -0.01
## 94 -0.09 0.11 0.02 0.07 0.23 0.09 -0.14
## 113 -0.16 -0.24 -0.18 0.30 0.10 -0.01 -0.01
## 137 0.03 0.02 -0.13 0.03 0.04 0.11 -0.07
## 138 0.03 -0.01 -0.07 0.02 -0.03 0.01 -0.01
## 142 0.00 0.00 0.00 0.00 0.00 0.00 0.00
## 164 -0.09 -0.10 0.05 -0.04 0.17 0.08 -0.07
## 181 0.06 -0.13 0.35 -0.08 -0.01 0.17 -0.09
## 184 0.00 -0.01 0.00 0.00 0.00 0.00 0.00
## 186 -0.02 0.09 0.01 -0.03 0.04 -0.15 0.18
## 209 0.10 -0.06 -0.05 0.14 -0.02 -0.06 0.10
## 223 0.07 0.26 0.03 -0.13 -0.03 0.05 0.04
## 247 0.07 0.15 0.00 -0.07 0.10 -0.07 0.12
## 257 0.00 0.03 -0.06 -0.02 0.02 -0.03 0.01
## 271 -0.17 -0.11 0.06 0.04 -0.02 0.04 0.00
## 282 0.06 -0.04 0.00 0.03 -0.02 -0.01 0.03
## 290 0.00 -0.02 0.02 -0.01 -0.02 0.00 0.00
## 291 0.21 0.02 0.10 -0.05 0.09 -0.12 0.14
## 297 -0.07 0.10 0.02 -0.05 0.11 0.11 0.02
## 299 0.05 0.02 0.02 -0.03 -0.05 0.03 -0.03
## 308 0.00 0.00 0.00 0.00 0.00 0.00 0.00
## 324 -0.02 0.06 0.02 -0.30 0.03 -0.14 0.14
## 326 -0.05 -0.03 0.14 -0.20 -0.05 0.03 -0.11
## 353 0.00 -0.01 0.04 0.03 0.02 0.01 -0.01
## 377 -0.10 0.04 0.02 -0.05 0.06 0.05 -0.02
## 379 0.19 -0.04 -0.05 0.13 0.09 0.06 -0.10
## 380 0.00 -0.02 -0.02 0.00 0.00 0.00 0.00
## 390 0.03 -0.03 0.02 0.03 0.02 0.02 0.00
## 396 -0.01 0.00 0.00 0.00 0.00 0.00 0.00
## 401 0.00 0.01 0.05 -0.01 -0.02 -0.03 -0.01
## 404 -0.01 -0.01 0.10 -0.03 0.05 0.00 -0.02
## 405 -0.03 -0.01 0.04 -0.06 0.04 0.03 -0.03
## 411 -0.01 0.16 0.11 -0.04 -0.04 0.00 -0.06
## 422 -0.03 -0.29 0.25 0.01 -0.01 0.00 -0.02
## 427 0.02 -0.04 0.01 0.00 -0.02 0.15 -0.09
## 433 -0.01 0.01 0.01 0.00 0.00 0.01 -0.02
## 458 0.01 0.00 -0.07 -0.01 -0.03 0.02 -0.01
## 465 0.00 0.01 0.02 0.00 0.02 -0.10 0.02
## 466 0.01 0.02 0.04 0.00 0.01 -0.02 0.01
## 471 0.00 0.00 0.00 0.00 0.00 0.00 0.00
## 493 -0.03 -0.01 0.04 -0.06 0.04 0.03 -0.03
## 505 0.00 0.00 0.00 0.00 0.00 0.00 0.00
## 514 -0.15 -0.17 -0.25 0.24 -0.10 -0.11 0.06
## 530 -0.02 0.13 0.28 0.25 0.04 0.13 -0.02
## 553 -0.02 0.00 -0.01 0.03 0.03 0.02 -0.03
## 554 0.06 0.09 -0.18 -0.31 0.10 -0.13 0.12
## 559 -0.03 -0.04 -0.12 -0.13 -0.31 -0.24 0.09
## 579 -0.08 -0.02 0.10 -0.09 0.02 0.04 -0.03
## 586 0.00 0.00 0.00 0.00 0.00 0.00 0.00
## 610 0.33 -0.19 0.38 0.01 0.05 -0.06 0.01
## 655 -0.23 -0.11 -0.04 0.16 -0.10 -0.06 0.01
## 657 0.00 0.00 0.00 0.00 0.00 0.00 0.00
## 697 0.04 0.09 -0.04 0.06 0.08 0.00 -0.06
## 704 0.07 -0.04 0.01 0.01 0.01 0.00 0.01
## 726 -0.01 -0.03 0.04 0.03 -0.02 0.00 0.01
## 749 0.02 -0.01 -0.01 0.00 -0.02 0.01 -0.01
## 790 0.00 0.00 0.01 0.00 0.00 0.01 0.00
## 795 -0.16 -0.18 -0.27 0.25 -0.10 -0.12 0.07
## 800 0.09 -0.08 -0.07 0.11 0.02 0.22 -0.19
## 815 -0.02 -0.13 0.18 0.06 0.02 0.03 0.01
## 817 0.00 0.01 -0.01 0.01 0.00 0.00 0.00
## dfb.W.D. dfb.O.P. dfb.En.P dfb.Sc.P dfb.Pl.A dffit cov.r cook.d
## 20 -0.09 0.06 -0.02 0.02 -0.03 -0.63_* 0.84_* 0.01
## 21 0.02 -0.05 0.32 -0.02 0.04 0.83_* 1.01 0.03
## 61 -0.09 0.04 0.02 0.02 -0.02 -0.55_* 0.81_* 0.01
## 74 0.00 -0.04 -0.06 0.00 0.00 0.57_* 0.94 0.01
## 89 -0.25 -0.24 0.01 -0.09 0.00 0.84_* 0.55_* 0.03
## 94 0.11 0.03 -0.10 0.04 -0.03 -0.65_* 0.88_* 0.02
## 113 -0.11 -0.02 -0.10 -0.06 -0.03 0.74_* 0.83_* 0.02
## 137 0.01 0.02 -0.03 -0.04 -0.09 0.45 0.89_* 0.01
## 138 0.01 0.00 0.00 0.00 0.00 -0.10 1.13_* 0.00
## 142 0.00 0.00 0.00 0.00 0.00 -0.01 2.24_* 0.00
## 164 0.06 0.16 -0.05 -0.03 -0.03 0.58_* 0.88_* 0.01
## 181 0.03 0.03 -0.12 0.01 0.03 0.80_* 0.84_* 0.02
## 184 0.00 0.00 0.00 0.00 0.00 -0.04 1.20_* 0.00
## 186 0.00 0.03 -0.04 0.04 -0.03 -0.35 0.85_* 0.00
## 209 0.10 -0.06 0.01 0.02 0.02 -1.05_* 1.37_* 0.04
## 223 0.09 0.11 0.08 0.06 0.03 -0.49 0.76_* 0.01
## 247 0.00 0.04 -0.19 0.00 0.00 -0.37 0.89_* 0.01
## 257 -0.01 0.01 0.00 0.00 0.00 -0.12 1.12_* 0.00
## 271 0.00 -0.05 0.01 0.02 0.02 -0.55_* 1.04 0.01
## 282 0.04 0.00 -0.05 -0.01 0.01 0.29 1.21_* 0.00
## 290 0.04 0.00 0.00 0.00 0.00 0.07 1.20_* 0.00
## 291 0.07 0.01 -0.01 -0.01 0.00 -0.42 0.86_* 0.01
## 297 0.18 0.15 -0.04 0.07 -0.05 -2.30_* 1.89_* 0.19
## 299 0.01 -0.01 0.00 0.19 -0.01 0.22 1.10_* 0.00
## 308 0.00 0.00 0.00 0.00 0.00 0.00 1.15_* 0.00
## 324 0.18 -0.03 -0.04 -0.01 -0.03 0.55 1.13_* 0.01
## 326 -0.03 -0.06 -0.06 0.44 -0.04 0.60_* 0.95 0.01
## 353 -0.01 -0.01 0.00 -0.01 0.00 0.08 1.11_* 0.00
## 377 -0.05 0.05 0.01 0.01 -0.02 -0.35 0.83_* 0.00
## 379 0.15 -0.05 0.06 -0.05 -0.02 0.43 0.79_* 0.01
## 380 0.00 0.00 0.00 0.00 0.00 -0.05 1.10_* 0.00
## 390 0.00 0.00 0.06 0.01 0.00 -0.19 1.14_* 0.00
## 396 0.00 0.00 -0.01 0.00 0.00 -0.01 1.10_* 0.00
## 401 -0.02 0.00 -0.01 0.00 -0.01 0.15 1.13_* 0.00
## 404 0.00 0.00 -0.02 -0.01 0.00 0.14 1.10_* 0.00
## 405 0.08 -0.01 -0.02 -0.21 1.31_* 1.44_* 3.85_* 0.08
## 411 0.01 0.00 0.07 0.01 0.00 -0.54 0.89_* 0.01
## 422 0.01 0.05 0.16 0.05 0.02 -0.74_* 0.82_* 0.02
## 427 -0.06 -0.04 -0.03 -0.04 0.03 0.39 0.88_* 0.01
## 433 0.00 0.01 0.01 0.01 0.00 -0.06 1.13_* 0.00
## 458 0.01 0.00 0.00 0.00 0.01 -0.17 1.16_* 0.00
## 465 0.01 0.01 0.00 0.01 -0.01 -0.16 1.11_* 0.00
## 466 0.00 0.00 0.04 0.00 0.00 0.10 1.13_* 0.00
## 471 0.00 0.00 0.00 0.00 0.00 -0.02 1.15_* 0.00
## 493 0.08 -0.01 -0.02 -0.21 -0.56 -0.67_* 1.62_* 0.02
## 505 0.00 0.00 0.00 0.00 0.00 -0.01 1.12_* 0.00
## 514 -0.04 0.08 0.04 0.03 0.01 -0.55 1.12_* 0.01
## 530 0.26 0.01 -0.08 0.02 0.00 1.07_* 0.76_* 0.04
## 553 -0.01 0.00 -0.03 -0.01 0.00 0.16 1.11_* 0.00
## 554 0.03 0.00 -0.09 0.01 0.02 -0.67_* 0.94 0.02
## 559 -0.04 -0.06 0.07 0.02 0.03 1.26_* 0.44_* 0.06
## 579 0.02 0.04 0.00 0.02 0.00 -0.33 0.88_* 0.00
## 586 0.00 0.00 0.00 0.00 0.00 0.00 1.14_* 0.00
## 610 -0.02 -0.18 -0.36 -0.02 0.01 -1.38_* 0.20_* 0.07
## 655 0.12 0.10 0.06 -0.11 0.00 -0.50 0.77_* 0.01
## 657 0.00 0.00 -0.01 0.00 0.00 -0.02 1.13_* 0.00
## 697 0.06 0.08 0.08 0.04 -0.04 -0.32 0.84_* 0.00
## 704 0.00 -0.01 -0.03 -0.01 0.00 0.15 1.11_* 0.00
## 726 0.00 -0.01 0.01 0.00 0.00 0.11 1.11_* 0.00
## 749 -0.01 0.00 0.03 0.00 0.00 -0.19 1.20_* 0.00
## 790 0.00 0.00 0.00 0.00 0.00 0.01 1.13_* 0.00
## 795 -0.04 0.08 0.04 0.03 0.00 -0.58_* 1.11_* 0.01
## 800 -0.07 0.08 -0.12 -0.08 0.00 0.45 0.82_* 0.01
## 815 0.08 -0.05 -0.18 -0.02 -0.04 0.68_* 0.91 0.02
## 817 -0.01 0.00 0.00 0.00 0.00 0.05 1.10_* 0.00
## hat
## 20 0.05
## 21 0.13_*
## 61 0.04
## 74 0.06
## 89 0.03
## 94 0.06
## 113 0.06
## 137 0.04
## 138 0.09
## 142 0.54_*
## 164 0.05
## 181 0.07
## 184 0.14_*
## 186 0.02
## 209 0.31_*
## 223 0.02
## 247 0.03
## 257 0.08
## 271 0.10
## 282 0.16_*
## 290 0.14_*
## 291 0.03
## 297 0.53_*
## 299 0.08
## 308 0.10_*
## 324 0.14_*
## 326 0.07
## 353 0.07
## 377 0.02
## 379 0.02
## 380 0.06
## 390 0.10_*
## 396 0.06
## 401 0.09
## 404 0.07
## 405 0.74_*
## 411 0.05
## 422 0.06
## 427 0.03
## 433 0.08
## 458 0.11_*
## 465 0.08
## 466 0.09
## 471 0.10_*
## 493 0.38_*
## 505 0.07
## 514 0.14_*
## 530 0.09
## 553 0.08
## 554 0.08
## 559 0.05
## 579 0.02
## 586 0.09
## 610 0.04
## 655 0.03
## 657 0.09
## 697 0.01
## 704 0.08
## 726 0.07
## 749 0.14_*
## 790 0.08
## 795 0.14_*
## 800 0.03
## 815 0.07
## 817 0.06inflm.full # all## Influence measures of
## lm(formula = log(price) ~ ., data = train) :
##
## dfb.1_ dfb.area dfb.MS.S dfb.Lt.A dfb.Ov.Q dfb.Ov.C dfb.Yr.B
## 1 -1.73e-02 -1.32e-03 9.80e-03 2.54e-03 -1.09e-02 2.59e-03 1.07e-02
## 2 6.44e-03 -1.01e-02 3.86e-02 -8.02e-03 -2.73e-02 3.51e-05 -1.99e-04
## 3 2.90e-03 3.79e-04 1.19e-03 5.27e-04 1.39e-03 -5.86e-03 2.71e-03
## 4 -3.99e-02 -3.36e-02 2.42e-02 2.48e-03 -4.39e-02 -7.56e-04 -6.47e-02
## 5 -1.24e-03 3.49e-03 -7.60e-03 2.34e-03 1.41e-02 6.03e-03 4.58e-03
## 6 -3.87e-02 -4.51e-03 -1.26e-02 5.17e-03 1.13e-02 -6.11e-03 4.20e-02
## 7 1.31e-04 2.73e-04 -3.91e-03 -1.77e-03 -6.91e-03 1.79e-03 6.42e-03
## 8 -2.75e-02 6.42e-04 -1.15e-02 1.08e-02 -1.07e-02 1.16e-02 2.83e-02
## 9 3.14e-02 -3.96e-03 -4.47e-02 -1.07e-03 6.41e-04 3.09e-03 -2.22e-02
## 10 -1.13e-02 -5.36e-03 3.43e-02 -5.21e-04 2.08e-02 1.13e-03 1.22e-03
## 11 -5.07e-03 5.64e-04 -1.68e-03 1.56e-03 -2.98e-03 -1.64e-03 3.64e-03
## 12 -9.50e-02 3.71e-02 2.40e-02 1.87e-02 5.25e-02 1.48e-02 6.64e-02
## 13 -4.03e-02 5.72e-03 2.20e-02 3.07e-02 3.37e-03 2.74e-02 3.96e-02
## 14 6.28e-03 1.65e-03 5.25e-03 3.70e-03 -3.33e-03 5.89e-03 -2.47e-03
## 15 3.71e-03 -3.00e-04 1.50e-02 7.92e-03 2.20e-02 1.64e-02 -5.26e-03
## 16 -7.46e-03 6.10e-03 3.39e-03 4.04e-03 9.24e-03 2.01e-02 1.17e-02
## 17 1.30e-02 1.98e-03 1.17e-02 2.52e-02 4.50e-02 -4.77e-02 8.26e-03
## 18 2.64e-02 -5.38e-03 -1.98e-03 -2.80e-03 -1.34e-02 2.08e-02 -1.95e-02
## 19 4.10e-02 5.19e-03 1.76e-02 1.02e-02 -6.08e-03 3.33e-03 -2.69e-02
## 20 1.90e-02 5.44e-02 -2.84e-01 -2.87e-02 -4.06e-02 -3.09e-01 -1.01e-02
## 21 -3.60e-02 -3.30e-02 8.85e-02 -3.32e-02 7.80e-03 4.49e-02 -1.78e-01
## 22 8.39e-04 -1.89e-03 1.20e-02 -4.96e-04 -6.06e-04 -2.02e-03 6.29e-04
## 23 1.33e-02 7.60e-04 2.28e-02 3.04e-03 -4.27e-02 1.30e-02 -1.41e-03
## 24 -2.69e-02 8.78e-03 8.76e-02 -8.45e-03 -3.46e-02 9.65e-03 2.44e-02
## 25 -2.38e-02 3.06e-02 1.34e-02 1.10e-02 1.72e-02 -5.31e-02 -6.13e-02
## 26 1.50e-02 -4.01e-04 -1.58e-02 6.88e-04 4.63e-02 -6.04e-03 -2.37e-02
## 27 5.01e-02 -3.21e-03 4.65e-02 -7.65e-03 -3.13e-02 -5.18e-02 8.89e-03
## 28 -5.49e-02 -1.14e-04 -2.51e-02 3.74e-02 -2.35e-02 -4.05e-03 3.62e-02
## 29 -2.86e-02 2.77e-04 -3.53e-03 -4.01e-03 2.20e-03 -3.98e-02 -1.25e-01
## 30 3.87e-02 -1.49e-02 -1.23e-02 -2.08e-02 -2.75e-02 3.56e-02 3.24e-04
## 31 1.42e-03 -9.03e-05 1.54e-03 2.96e-04 -1.63e-04 6.48e-04 1.66e-04
## 32 -2.09e-03 6.38e-04 -4.98e-03 2.36e-03 3.15e-03 -2.90e-03 3.22e-03
## 33 -1.13e-01 3.56e-02 9.23e-02 1.53e-02 7.30e-02 1.02e-01 1.17e-01
## 34 3.16e-03 1.57e-04 1.65e-03 2.39e-04 -5.42e-03 8.05e-03 5.00e-03
## 35 -2.87e-04 7.39e-04 -4.00e-03 -1.53e-03 7.92e-04 2.14e-03 4.11e-03
## 36 -2.79e-03 -1.40e-03 -2.29e-03 1.35e-04 -1.27e-02 1.42e-03 2.60e-03
## 37 1.67e-02 1.01e-02 1.26e-02 -9.20e-03 -1.82e-02 1.60e-02 -9.21e-03
## 38 5.88e-03 2.31e-03 -1.53e-03 -2.52e-03 -7.77e-03 -7.07e-03 6.50e-03
## 39 6.27e-03 3.90e-04 -6.33e-03 -8.24e-04 -1.78e-03 1.15e-03 3.26e-04
## 40 2.16e-02 -2.80e-03 2.13e-02 1.68e-02 -1.91e-03 8.48e-02 -1.59e-01
## 41 -7.94e-03 9.51e-04 -4.03e-03 1.54e-03 3.11e-04 -2.81e-03 5.69e-03
## 42 4.60e-02 1.16e-02 1.33e-02 7.63e-03 3.04e-02 9.61e-02 4.42e-02
## 43 -1.13e-02 5.80e-03 4.09e-03 5.39e-03 -3.40e-03 -3.92e-03 5.08e-03
## 44 8.11e-03 -3.37e-03 -4.17e-03 9.37e-04 1.14e-03 -8.17e-03 -1.71e-02
## 45 2.49e-02 9.04e-03 1.10e-02 2.09e-03 -1.58e-02 1.40e-02 -1.14e-02
## 46 7.44e-04 -1.33e-05 1.66e-03 6.24e-04 2.83e-03 3.64e-03 -8.10e-04
## 47 2.72e-03 1.42e-03 -3.27e-03 -1.15e-03 -5.66e-03 2.06e-02 1.61e-02
## 48 -2.68e-02 -2.16e-02 5.02e-03 -1.01e-02 -4.37e-02 -1.71e-03 4.02e-02
## 49 1.60e-03 -5.35e-04 4.62e-04 -6.71e-04 5.85e-04 -7.51e-03 -2.08e-03
## 50 1.47e-02 -9.72e-03 -1.79e-02 9.70e-03 1.87e-02 -3.00e-02 -4.74e-03
## 51 2.39e-02 2.14e-03 -5.24e-03 5.27e-03 1.42e-02 1.30e-03 2.30e-03
## 52 8.89e-04 -1.85e-04 1.32e-03 -6.18e-04 -6.31e-04 4.47e-04 -1.38e-03
## 53 -2.06e-02 -3.57e-03 -2.46e-03 5.38e-03 -4.87e-03 3.87e-03 2.51e-02
## 54 -6.35e-03 -1.38e-02 7.52e-02 -7.49e-03 5.49e-02 -1.53e-02 -1.58e-02
## 55 -1.76e-02 2.75e-02 -2.68e-02 3.75e-02 2.03e-02 1.74e-02 4.91e-02
## 56 -9.77e-03 -1.25e-03 -3.20e-03 -2.30e-03 1.22e-02 -1.59e-03 2.42e-02
## 57 -3.52e-03 -2.16e-03 -1.32e-03 5.16e-03 8.35e-03 -5.57e-03 -3.00e-04
## 58 -6.20e-03 1.57e-03 -8.29e-03 -2.41e-04 4.33e-03 -3.51e-03 5.83e-03
## 59 -1.03e-02 1.05e-02 -2.30e-02 2.19e-02 5.92e-02 -1.60e-02 -8.89e-03
## 60 -4.73e-03 8.32e-03 -3.40e-03 -1.91e-03 -2.10e-02 7.49e-03 -3.81e-03
## 61 -1.47e-01 2.91e-02 -1.87e-03 -2.08e-02 -9.39e-02 -2.02e-02 6.53e-02
## 62 -2.74e-02 8.74e-03 -2.70e-02 -2.23e-03 -3.07e-03 -2.22e-02 6.28e-03
## 63 4.50e-02 -4.41e-03 -2.23e-03 -1.26e-02 -1.50e-02 2.91e-02 -3.09e-03
## 64 -8.28e-02 1.24e-02 1.08e-02 1.48e-02 -2.00e-04 1.44e-02 7.37e-02
## 65 -6.97e-03 -2.02e-03 1.10e-02 -6.44e-04 -9.63e-03 -1.12e-02 3.52e-03
## 66 2.24e-03 -7.29e-04 -7.20e-03 5.89e-03 3.40e-04 2.69e-02 1.86e-02
## 67 1.54e-02 3.83e-03 -4.96e-03 -6.48e-03 2.25e-02 -3.46e-03 -3.73e-04
## 68 1.25e-03 8.46e-05 -2.36e-03 3.25e-04 -8.00e-04 -3.50e-04 -1.19e-03
## 69 1.08e-01 -3.18e-02 1.26e-02 6.35e-03 7.18e-02 5.14e-02 -2.27e-02
## 70 -1.19e-01 5.19e-03 3.62e-02 3.53e-02 1.02e-02 5.58e-02 8.91e-02
## 71 -3.44e-02 -3.77e-03 -2.12e-02 1.49e-02 -9.02e-02 -9.41e-03 1.93e-02
## 72 -3.22e-03 1.36e-03 -6.08e-03 1.21e-03 -7.23e-03 3.40e-03 7.20e-03
## 73 3.09e-02 3.05e-04 -1.06e-02 -2.31e-03 2.15e-02 -1.45e-02 -1.52e-02
## 74 -6.21e-02 4.23e-03 1.14e-02 3.33e-02 -3.40e-02 1.85e-02 9.45e-02
## 75 -9.93e-03 8.70e-03 3.62e-02 -1.24e-04 -2.52e-02 8.38e-03 1.35e-02
## 76 2.70e-03 -2.43e-04 7.79e-03 -1.38e-03 -2.98e-03 1.83e-03 4.72e-03
## 77 -9.12e-04 2.08e-03 5.10e-03 -4.68e-04 -8.02e-03 -5.51e-04 -1.02e-02
## 78 1.17e-01 -4.95e-03 -2.15e-01 4.40e-03 1.52e-01 -1.91e-01 -6.78e-02
## 79 8.25e-03 6.54e-03 3.42e-02 -1.65e-02 1.58e-02 -2.98e-02 1.38e-02
## 80 1.15e-02 9.16e-03 1.80e-02 -1.30e-02 4.29e-02 -1.62e-02 -1.14e-02
## 81 5.52e-03 2.57e-03 6.01e-03 4.85e-03 -2.60e-03 5.63e-03 -2.81e-04
## 82 -3.98e-02 -7.76e-03 -2.28e-02 -6.19e-02 -2.45e-01 -2.05e-02 3.03e-02
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## 732 -1.55e-02 -8.49e-03 -8.40e-03 -3.14e-02 2.31e-02 -2.67e-02 -4.04e-02
## 733 9.29e-03 -2.74e-03 9.80e-04 -3.38e-03 -7.55e-03 1.23e-02 3.66e-03
## 734 2.64e-02 -3.06e-02 7.37e-02 9.66e-04 -6.23e-02 1.16e-01 1.67e-02
## 735 -1.37e-02 -7.94e-03 3.80e-02 1.11e-02 -1.17e-02 -1.33e-02 1.24e-02
## 736 -4.58e-03 -3.44e-03 -7.64e-03 -9.37e-04 -1.11e-02 1.01e-03 1.54e-03
## 737 -2.28e-03 4.12e-05 -4.67e-03 6.49e-04 3.73e-03 -2.84e-03 -2.06e-04
## 738 6.94e-03 3.43e-03 -2.17e-02 2.93e-03 -1.60e-02 6.96e-03 3.44e-04
## 739 5.66e-04 -4.36e-03 2.18e-02 -1.25e-03 -1.54e-02 1.50e-02 8.01e-03
## 740 1.45e-02 6.51e-04 1.35e-02 5.25e-03 -5.77e-03 8.06e-03 -3.97e-03
## 741 -6.72e-03 -4.12e-03 4.02e-02 -6.99e-03 -5.03e-02 -8.39e-03 -4.15e-02
## 742 -1.63e-03 2.41e-04 -1.72e-03 -2.18e-04 -2.05e-04 5.64e-04 -5.40e-04
## 743 1.95e-03 6.86e-04 -7.44e-03 -7.28e-04 3.93e-03 -4.63e-04 2.21e-03
## 744 2.85e-03 2.79e-03 -1.53e-02 6.83e-03 2.61e-03 8.94e-04 3.78e-04
## 745 -4.38e-02 1.58e-02 -1.19e-01 -9.65e-03 -6.62e-02 3.31e-02 1.60e-02
## 746 1.44e-04 -4.15e-05 2.49e-04 3.45e-04 3.17e-04 1.64e-05 -4.33e-04
## 747 6.13e-03 -4.22e-04 6.36e-03 -3.70e-03 -4.01e-03 4.41e-03 -5.29e-03
## 748 2.86e-04 1.66e-04 -8.08e-04 4.13e-04 4.04e-03 -1.26e-03 -7.92e-04
## 749 3.98e-02 -1.72e-01 2.77e-03 7.60e-04 4.49e-03 5.40e-03 -2.65e-03
## 750 5.58e-03 3.55e-02 -1.21e-02 2.50e-03 -1.98e-02 -1.74e-02 -4.78e-04
## 751 3.65e-02 -2.36e-03 2.88e-02 -4.05e-03 -9.99e-03 -2.36e-02 -1.38e-02
## 752 9.07e-03 -1.16e-04 -1.79e-03 -2.17e-02 4.99e-03 2.01e-02 -3.04e-02
## 753 -8.56e-03 1.13e-03 -6.22e-03 -1.82e-03 -5.13e-03 9.31e-03 -2.41e-04
## 754 -1.45e-02 2.01e-03 1.50e-03 -1.27e-04 -7.46e-03 -8.87e-03 -4.79e-03
## 755 -6.00e-03 2.74e-04 -1.33e-02 -7.00e-04 1.07e-02 -5.43e-03 4.73e-03
## 756 2.40e-04 -4.09e-04 -2.25e-03 7.24e-05 4.86e-04 -6.24e-03 -4.67e-04
## 757 -4.38e-02 -9.41e-04 -1.77e-02 1.23e-02 -1.52e-02 -1.56e-04 3.38e-02
## 758 2.54e-02 8.17e-03 -1.38e-03 5.68e-02 7.63e-03 -2.09e-02 -1.57e-02
## 759 4.84e-03 2.90e-04 3.73e-03 1.77e-03 3.01e-03 2.72e-04 -1.28e-03
## 760 -5.79e-03 -2.87e-05 4.53e-03 -1.79e-02 -1.58e-02 2.48e-02 -1.19e-02
## 761 1.79e-02 -6.30e-03 9.01e-02 8.28e-03 1.25e-01 6.48e-02 -3.50e-02
## 762 -3.64e-02 -2.60e-02 2.26e-02 5.65e-03 -3.16e-02 2.71e-02 6.40e-02
## 763 -9.58e-02 -4.22e-03 -4.83e-02 -1.64e-02 -5.28e-02 -1.17e-01 -5.78e-02
## 764 -3.57e-03 1.76e-03 -5.60e-03 -9.40e-04 -6.68e-03 2.95e-03 3.76e-03
## 765 -7.70e-04 1.19e-04 -1.32e-02 -4.83e-03 -9.30e-03 2.50e-04 3.29e-03
## 766 -1.19e-02 -1.32e-03 -6.79e-03 -3.30e-04 -3.90e-03 7.51e-03 -1.39e-02
## 767 -1.87e-02 5.15e-03 -1.92e-03 2.01e-02 6.07e-02 -5.94e-02 -2.49e-02
## 768 3.13e-02 2.49e-02 -1.25e-01 4.76e-02 6.23e-02 -9.88e-03 -1.45e-02
## 769 -2.01e-03 7.19e-04 6.61e-03 1.69e-04 -4.34e-03 5.31e-04 1.23e-03
## 770 7.68e-02 -9.83e-04 2.67e-02 -1.35e-02 9.94e-02 -5.63e-02 -6.24e-02
## 771 1.12e-02 5.56e-03 -3.36e-02 1.16e-02 7.27e-03 9.65e-04 -5.41e-03
## 772 5.46e-02 -4.55e-03 -1.56e-03 -2.88e-02 1.31e-02 7.32e-02 -4.40e-02
## 773 8.53e-02 1.46e-02 3.24e-02 -1.94e-02 7.47e-02 -3.24e-03 -6.76e-02
## 774 7.71e-02 -2.54e-02 2.33e-02 3.39e-03 2.19e-02 -1.77e-02 -1.62e-02
## 775 1.54e-02 -5.84e-03 -1.21e-02 -7.14e-03 2.56e-03 -3.56e-02 -1.62e-02
## 776 3.68e-04 -1.35e-02 -5.63e-03 -1.32e-03 2.72e-03 -9.61e-03 5.30e-03
## 777 -4.28e-03 1.63e-03 2.87e-03 6.91e-04 -2.07e-04 1.56e-03 3.39e-03
## 778 -1.02e-02 6.44e-03 -1.14e-02 8.31e-02 7.48e-03 3.40e-02 3.39e-02
## 779 2.85e-02 -3.92e-04 8.06e-03 3.36e-03 4.48e-03 -2.02e-02 1.47e-03
## 780 -1.28e-01 1.64e-02 6.05e-02 1.50e-03 -7.11e-02 1.05e-02 7.37e-02
## 781 5.03e-03 4.23e-03 -1.49e-02 -9.62e-04 1.47e-03 3.25e-03 -3.34e-05
## 782 2.16e-02 6.04e-03 1.30e-02 4.91e-03 -3.79e-02 1.14e-02 -3.62e-03
## 783 -7.01e-03 -6.83e-03 -2.41e-03 6.06e-03 -6.13e-02 -1.71e-03 3.08e-05
## 784 -2.83e-03 3.81e-03 6.77e-03 -3.84e-03 1.30e-02 4.44e-04 -3.33e-03
## 785 4.60e-03 -8.26e-03 8.68e-03 9.24e-03 1.09e-03 -1.07e-03 -9.17e-03
## 786 -1.84e-02 6.14e-03 6.35e-03 4.07e-03 9.65e-04 9.50e-03 1.04e-02
## 787 3.02e-02 -1.56e-03 8.27e-03 -3.26e-03 1.26e-02 1.03e-02 -1.66e-02
## 788 4.66e-02 -1.33e-02 -1.48e-02 -5.20e-03 2.54e-02 6.84e-03 -3.86e-02
## 789 6.58e-03 -1.19e-02 3.59e-03 -8.84e-04 -3.41e-04 -5.66e-02 -4.15e-02
## 790 -7.38e-04 4.93e-04 -2.56e-03 -6.09e-04 9.04e-04 -8.60e-04 -7.34e-04
## 791 -2.05e-03 6.30e-05 -4.32e-03 -7.09e-04 -5.11e-03 1.03e-03 1.65e-03
## 792 -6.68e-03 8.79e-04 9.64e-04 2.61e-03 4.21e-03 -1.74e-02 -9.02e-03
## 793 -9.58e-02 1.49e-02 9.75e-03 -3.12e-02 4.02e-02 -6.44e-03 2.33e-02
## 794 1.34e-01 -1.28e-02 4.06e-03 -1.78e-02 8.53e-02 -1.07e-02 -6.94e-02
## 795 -6.58e-02 -2.53e-02 1.28e-01 3.55e-02 1.39e-02 1.06e-02 1.08e-01
## 796 2.98e-03 9.01e-04 -2.69e-04 1.52e-03 4.95e-03 -8.58e-04 3.37e-03
## 797 -2.13e-02 2.96e-04 4.69e-03 5.31e-03 -1.27e-02 -4.92e-03 9.94e-03
## 798 1.06e-03 -5.91e-05 7.13e-04 -1.11e-04 1.88e-03 2.67e-04 -1.22e-03
## 799 8.81e-03 -3.05e-03 4.89e-03 -2.12e-03 1.07e-03 -3.05e-02 -2.30e-02
## 800 1.79e-01 -1.03e-02 4.28e-02 1.81e-02 1.26e-02 1.05e-01 -6.20e-02
## 801 2.45e-04 -4.03e-05 -2.03e-03 -1.44e-03 1.48e-03 -2.16e-03 5.62e-04
## 802 -1.36e-03 1.25e-03 1.67e-03 -3.61e-04 4.18e-04 2.33e-03 1.56e-03
## 803 2.99e-02 -1.75e-02 4.30e-02 -9.93e-03 -4.36e-02 -1.08e-02 -1.37e-02
## 804 2.20e-04 -9.05e-05 -4.94e-03 2.82e-03 -4.33e-03 -1.46e-03 2.44e-03
## 805 8.29e-03 -2.02e-03 -1.20e-02 -1.12e-03 3.57e-03 -2.30e-02 4.42e-03
## 806 7.57e-03 -1.40e-04 4.24e-03 7.98e-04 6.96e-03 2.20e-03 1.60e-04
## 807 -7.60e-03 2.44e-04 8.96e-03 1.52e-03 2.19e-04 5.63e-03 1.03e-04
## 808 1.72e-02 -1.28e-03 4.10e-03 -1.45e-03 6.41e-03 -1.38e-02 -4.34e-04
## 809 1.84e-03 6.87e-04 -7.73e-04 9.27e-04 -5.37e-04 3.53e-03 4.71e-03
## 810 -2.01e-02 1.37e-02 3.89e-03 6.04e-03 -3.32e-02 -5.40e-02 -1.73e-03
## 811 -2.93e-03 -1.54e-03 -3.32e-02 -2.95e-03 1.83e-02 -3.40e-02 1.23e-02
## 812 -1.14e-02 -5.25e-03 5.74e-04 1.88e-03 -1.56e-02 7.53e-03 -2.14e-03
## 813 2.24e-03 -1.06e-03 2.76e-03 -9.41e-04 8.87e-04 -2.03e-03 -3.64e-03
## 814 -1.36e-02 3.27e-03 -1.04e-02 2.46e-03 1.17e-03 3.04e-02 2.96e-02
## 815 8.22e-02 -1.15e-02 1.69e-01 -3.75e-02 -5.87e-02 -1.21e-01 -1.96e-01
## 816 1.66e-02 1.38e-03 -1.28e-02 -9.20e-04 2.55e-02 -1.40e-02 -6.07e-03
## 817 -3.42e-03 -1.03e-03 2.11e-03 7.64e-03 7.01e-03 6.05e-03 -5.92e-04
## 818 -1.78e-03 -1.25e-03 9.64e-03 -6.61e-04 -4.12e-03 -7.32e-03 1.27e-03
## 819 9.35e-03 6.14e-03 -2.53e-02 8.54e-03 7.57e-03 7.55e-04 -5.67e-03
## 820 -8.44e-02 2.94e-03 2.80e-02 1.59e-02 -4.73e-02 -1.24e-02 5.61e-02
## 821 1.06e-02 2.80e-03 7.25e-03 3.37e-03 1.72e-02 2.97e-03 -6.44e-03
## 822 -3.30e-02 8.04e-03 -5.32e-03 -1.29e-02 -3.06e-02 3.94e-02 1.22e-02
## 823 -4.18e-02 1.94e-02 -2.02e-04 2.64e-02 1.60e-03 1.59e-02 3.39e-02
## 824 5.18e-03 -1.46e-02 6.64e-02 6.62e-03 7.79e-03 1.30e-02 2.61e-02
## 825 8.82e-05 -4.02e-04 -4.41e-03 -1.15e-03 -2.89e-03 -5.81e-03 -2.51e-03
## 826 -6.80e-02 4.40e-03 4.53e-02 1.54e-02 -3.08e-02 1.22e-01 7.42e-02
## 827 4.15e-04 -1.17e-03 1.31e-02 -2.01e-02 -1.45e-02 1.68e-02 5.99e-03
## 828 3.07e-05 5.19e-08 1.69e-05 2.06e-05 1.36e-05 3.34e-05 2.65e-05
## 829 9.32e-04 4.11e-03 -1.26e-02 -1.03e-02 -2.73e-02 -2.66e-03 6.76e-03
## 830 -1.80e-03 6.01e-04 5.40e-04 1.34e-04 -4.34e-05 -6.58e-04 1.00e-03
## 831 1.11e-02 1.26e-03 1.54e-02 2.26e-02 4.63e-02 3.65e-02 3.48e-02
## 832 -3.87e-03 9.98e-04 3.72e-03 -3.38e-05 1.19e-03 2.21e-03 4.78e-03
## dfb.Y.R. dfb.T.B. dfb.C.AY dfb.X1.F dfb.X2.F dfb.B.F. dfb.B.H.
## 1 8.88e-03 1.20e-03 -4.69e-03 3.25e-03 1.42e-03 -7.84e-03 2.78e-03
## 2 -5.87e-03 6.72e-03 1.13e-02 8.66e-03 5.42e-03 3.32e-02 5.53e-03
## 3 -5.49e-03 -1.58e-03 -5.58e-04 -5.45e-04 -3.88e-04 3.48e-03 2.25e-03
## 4 1.03e-01 -6.36e-03 4.80e-02 2.69e-02 2.78e-02 -6.26e-03 -7.19e-03
## 5 -3.50e-03 -5.29e-03 -2.05e-03 -3.25e-03 -1.74e-03 1.40e-02 3.36e-03
## 6 3.50e-03 -5.79e-02 8.82e-03 4.05e-03 1.22e-02 1.10e-02 -1.99e-03
## 7 -4.40e-03 3.90e-03 -2.79e-02 6.15e-05 6.45e-04 -7.24e-03 -3.40e-03
## 8 4.20e-03 3.31e-03 -5.58e-03 -6.21e-03 -2.76e-03 -2.17e-02 -1.26e-02
## 9 -1.39e-02 3.55e-02 1.91e-03 -4.06e-03 3.35e-03 -1.81e-02 -2.50e-03
## 10 1.06e-02 1.22e-02 -5.70e-03 4.37e-04 -1.91e-03 -2.77e-02 -1.02e-02
## 11 2.42e-03 5.56e-04 2.09e-04 -9.23e-04 1.98e-04 -2.66e-03 -6.13e-04
## 12 3.92e-02 -4.15e-02 -7.14e-02 -2.94e-02 -3.40e-02 3.82e-02 2.12e-02
## 13 5.77e-03 -2.15e-02 5.77e-03 2.69e-03 1.07e-02 -2.38e-02 1.25e-02
## 14 -4.44e-03 -8.49e-04 -1.05e-03 -1.57e-03 -1.99e-04 -1.20e-02 -1.37e-03
## 15 -1.87e-04 -1.42e-03 -1.44e-02 -4.92e-05 -4.63e-03 -1.05e-02 -1.15e-01
## 16 -5.52e-03 -7.80e-03 2.34e-02 -4.56e-03 -5.08e-03 -1.64e-02 -2.37e-03
## 17 -2.18e-02 -3.33e-02 2.25e-02 4.86e-04 1.94e-03 -1.20e-02 1.80e-02
## 18 -1.12e-02 4.58e-02 -9.89e-03 -4.87e-03 1.28e-03 5.59e-04 -5.85e-02
## 19 -1.95e-02 -1.70e-02 5.37e-03 -5.67e-03 -2.11e-03 3.55e-02 6.73e-03
## 20 3.88e-03 -6.73e-02 7.36e-02 -5.08e-03 1.97e-02 3.67e-02 6.38e-02
## 21 2.11e-01 9.20e-02 -3.27e-01 5.19e-02 5.57e-02 -7.58e-02 -3.73e-02
## 22 -1.35e-03 2.03e-03 1.20e-03 5.32e-04 5.39e-04 -1.98e-03 -1.13e-03
## 23 -1.20e-02 -6.43e-03 3.65e-03 2.95e-03 6.45e-03 4.52e-02 1.44e-02
## 24 8.48e-03 1.23e-02 -1.61e-03 3.19e-03 2.86e-03 -3.32e-02 -6.12e-03
## 25 8.55e-02 1.95e-02 -2.82e-02 -2.70e-02 -3.80e-02 -6.97e-02 1.40e-02
## 26 3.83e-03 4.24e-03 -1.21e-02 6.06e-04 -7.67e-03 -2.00e-03 -2.98e-03
## 27 -6.08e-02 1.47e-01 -2.71e-02 -2.41e-02 7.75e-04 3.63e-02 3.85e-02
## 28 2.74e-02 1.84e-02 4.36e-04 1.72e-03 8.76e-04 -4.65e-02 -1.71e-02
## 29 1.47e-01 1.02e-02 1.89e-02 -1.52e-03 -1.20e-03 -4.33e-02 -2.45e-02
## 30 -4.23e-02 5.70e-02 -9.12e-03 1.38e-02 3.04e-03 -5.00e-02 -2.56e-02
## 31 -1.74e-03 2.93e-04 6.13e-04 5.73e-04 5.31e-04 -1.34e-03 3.85e-04
## 32 -6.15e-04 -1.38e-03 2.12e-03 -9.87e-04 5.93e-04 -4.68e-03 -5.65e-04
## 33 6.03e-03 -1.30e-02 -1.26e-01 -2.15e-02 -4.27e-02 -1.02e-01 -1.30e-02
## 34 -8.14e-03 -5.51e-03 -3.01e-03 6.94e-04 -2.43e-04 -3.48e-03 -2.24e-03
## 35 -3.48e-03 6.70e-04 2.82e-04 -5.26e-04 8.86e-05 7.65e-03 -1.83e-04
## 36 1.09e-03 -2.82e-04 4.00e-03 1.34e-03 2.72e-03 1.02e-02 4.13e-03
## 37 -9.16e-03 -1.63e-03 -7.94e-03 -8.72e-03 -1.79e-03 3.09e-02 1.45e-02
## 38 -1.16e-02 -8.60e-04 3.57e-03 2.73e-04 3.49e-03 1.12e-02 6.72e-03
## 39 -6.93e-03 -1.14e-03 2.83e-03 -1.14e-03 1.13e-04 5.52e-03 -1.19e-03
## 40 1.19e-01 8.43e-02 3.19e-02 4.79e-03 1.09e-02 -1.89e-02 -2.03e-02
## 41 3.58e-03 3.42e-04 -1.85e-04 -2.00e-03 2.19e-04 -3.84e-03 -1.79e-03
## 42 -9.53e-02 9.92e-03 -3.99e-02 -1.51e-02 -1.28e-02 1.34e-02 -2.68e-03
## 43 7.84e-03 -5.13e-03 -8.96e-03 -4.23e-03 -4.89e-03 -1.22e-02 1.61e-03
## 44 7.27e-03 -2.15e-03 8.94e-03 3.10e-03 2.97e-03 -2.15e-03 -7.75e-04
## 45 -1.63e-02 -1.13e-02 3.25e-03 -1.77e-03 4.38e-04 4.33e-02 1.57e-02
## 46 -3.85e-04 -1.12e-03 -1.81e-03 -4.66e-04 -1.41e-03 2.16e-03 1.47e-03
## 47 -1.84e-02 7.44e-03 -2.22e-03 1.89e-03 1.89e-03 1.43e-02 -7.45e-05
## 48 -8.04e-03 -2.00e-03 1.17e-02 2.16e-02 2.99e-02 3.90e-02 1.60e-02
## 49 5.02e-04 -1.05e-03 2.48e-03 1.38e-03 7.86e-04 2.24e-03 -1.34e-02
## 50 -4.42e-03 -1.54e-02 -9.81e-02 8.23e-03 4.51e-03 -9.09e-03 -1.60e-02
## 51 -2.84e-02 6.94e-03 7.29e-03 1.97e-03 3.35e-03 -1.91e-02 -9.34e-03
## 52 2.74e-04 5.23e-04 -4.21e-04 4.96e-04 2.11e-04 -1.48e-03 1.00e-03
## 53 -1.17e-03 -1.76e-02 5.04e-03 8.21e-03 5.51e-03 1.09e-02 -2.29e-03
## 54 2.03e-02 3.26e-03 -5.42e-03 -1.15e-03 -6.24e-03 3.07e-02 -8.17e-03
## 55 -2.57e-02 9.96e-02 -4.34e-02 -6.28e-02 -3.62e-02 1.11e-02 1.24e-02
## 56 -1.21e-02 1.27e-02 3.67e-03 3.26e-04 7.99e-03 -2.24e-02 2.39e-03
## 57 4.14e-03 -1.73e-02 8.97e-04 -8.32e-04 -2.14e-03 1.56e-02 1.10e-03
## 58 1.36e-03 7.52e-03 1.27e-03 2.47e-03 7.93e-04 -1.92e-02 -6.32e-03
## 59 1.77e-02 -2.37e-02 -1.20e-02 -1.47e-02 -1.82e-02 2.68e-02 -5.33e-03
## 60 9.42e-03 -2.32e-03 -1.85e-02 -7.98e-03 -1.26e-02 3.13e-03 4.20e-03
## 61 8.16e-02 -5.22e-03 4.08e-01 -2.11e-02 -4.94e-03 8.31e-02 6.37e-02
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## 711 -8.48e-03 -2.33e-04 4.13e-03 6.15e-03 4.39e-03 -7.44e-03 1.11e-02
## 712 1.83e-03 -1.79e-03 4.69e-03 1.56e-03 4.95e-04 4.82e-03 1.87e-03
## 713 -7.25e-04 -7.43e-03 -1.18e-02 -8.26e-03 -7.13e-03 4.13e-02 -2.92e-04
## 714 -2.10e-03 -5.82e-03 1.35e-02 8.74e-03 7.27e-03 3.12e-02 -5.53e-03
## 715 -6.64e-04 1.22e-03 2.30e-03 -2.01e-04 8.21e-04 -4.60e-03 -1.86e-03
## 716 1.81e-02 1.51e-02 -5.09e-03 -2.11e-02 -6.18e-03 1.60e-02 4.08e-03
## 717 3.54e-03 -1.16e-03 -8.50e-04 -2.29e-03 5.20e-05 1.13e-02 2.44e-03
## 718 -1.69e-03 2.80e-03 -5.14e-04 4.32e-03 7.98e-04 1.09e-02 4.53e-03
## 719 2.15e-03 -9.49e-04 1.50e-03 -3.03e-03 7.23e-04 -8.16e-03 2.96e-04
## 720 4.81e-02 2.57e-02 2.04e-03 5.15e-03 -1.12e-03 -2.27e-02 -6.80e-03
## 721 2.63e-03 7.78e-04 2.22e-03 -1.64e-03 4.76e-04 -5.89e-03 -3.28e-03
## 722 3.73e-02 9.60e-02 1.57e-02 -1.87e-02 1.76e-03 -6.61e-02 -1.64e-02
## 723 -4.49e-02 -1.98e-02 2.82e-02 1.30e-02 5.62e-03 -6.45e-02 -9.49e-04
## 724 -7.01e-05 -3.81e-04 9.14e-03 1.63e-03 5.68e-03 -1.48e-02 -7.95e-04
## 725 -5.16e-03 -5.15e-04 -1.20e-03 5.11e-04 -1.73e-03 -1.90e-02 -4.68e-03
## 726 -3.27e-03 4.81e-03 4.43e-02 1.44e-02 1.60e-02 5.08e-04 4.02e-03
## 727 2.52e-03 -2.88e-03 -2.03e-06 -2.22e-03 -2.52e-03 -6.54e-03 -2.41e-03
## 728 -9.00e-03 1.06e-03 -7.07e-03 7.41e-05 -5.31e-03 2.63e-02 2.05e-03
## 729 -8.13e-05 -1.13e-04 2.88e-04 2.02e-04 -1.72e-04 1.29e-03 1.56e-04
## 730 -6.20e-03 -7.08e-03 -1.29e-03 -2.80e-03 -3.15e-03 -5.50e-03 -4.77e-04
## 731 3.06e-03 9.47e-03 9.59e-03 2.31e-03 5.79e-03 -2.83e-02 -3.39e-03
## 732 5.37e-02 1.02e-01 1.25e-02 -3.85e-04 2.06e-02 5.42e-02 1.52e-03
## 733 -1.36e-02 5.04e-03 -4.45e-03 5.05e-05 1.61e-03 -4.89e-03 -3.41e-03
## 734 -4.56e-02 4.37e-02 -4.73e-02 8.67e-04 -3.08e-03 -4.72e-02 -4.05e-02
## 735 4.79e-03 8.72e-03 -5.40e-04 -5.40e-04 1.43e-04 -3.09e-02 -1.63e-02
## 736 3.93e-03 -1.22e-03 -1.74e-03 -1.79e-03 9.07e-04 -2.77e-03 -2.48e-03
## 737 2.83e-03 -8.12e-04 4.29e-04 -2.11e-03 -9.93e-04 -4.18e-03 -2.49e-03
## 738 -7.63e-03 -3.75e-03 -7.86e-04 5.09e-04 2.18e-03 2.21e-02 9.40e-03
## 739 -7.97e-03 8.37e-03 4.40e-04 3.92e-03 2.03e-03 -1.03e-02 -4.54e-03
## 740 -1.25e-02 -9.90e-03 3.08e-03 1.40e-03 1.70e-03 3.14e-02 1.54e-02
## 741 4.62e-02 1.28e-01 -1.55e-02 -2.03e-02 -7.77e-04 1.62e-02 1.80e-02
## 742 2.30e-03 9.78e-04 3.64e-04 -3.19e-04 2.19e-05 -1.37e-03 -7.03e-04
## 743 -4.07e-03 5.41e-04 1.63e-03 -2.20e-03 -4.37e-04 4.00e-03 -2.65e-03
## 744 -3.59e-03 -4.64e-03 5.33e-05 -1.94e-03 -7.33e-04 -6.60e-03 2.95e-04
## 745 3.25e-02 -9.47e-03 -3.28e-02 -7.51e-04 -1.17e-03 3.49e-02 1.44e-02
## 746 2.35e-04 -3.34e-04 -1.06e-04 2.42e-05 -4.35e-05 1.05e-04 -1.75e-03
## 747 -1.90e-03 8.40e-04 -1.87e-03 1.54e-03 -8.73e-04 7.61e-03 1.22e-03
## 748 3.14e-04 -5.42e-04 -4.05e-04 -4.31e-04 -6.05e-04 3.79e-03 2.96e-04
## 749 -4.13e-02 -8.51e-03 7.33e-03 1.70e-01 1.70e-01 -1.68e-02 -3.60e-04
## 750 -3.64e-03 -2.04e-02 1.63e-02 -3.02e-02 -3.17e-02 -3.25e-03 -3.01e-04
## 751 -3.35e-02 9.39e-02 1.37e-01 -4.09e-03 1.18e-02 5.52e-03 7.91e-03
## 752 1.60e-02 1.36e-02 -4.14e-02 4.38e-03 -1.85e-02 2.43e-02 6.47e-03
## 753 9.41e-03 4.97e-03 5.15e-04 -4.75e-04 5.73e-04 8.07e-03 6.22e-04
## 754 2.07e-02 -9.01e-03 5.02e-04 -7.35e-04 -8.23e-04 1.50e-02 6.83e-03
## 755 2.06e-03 -1.02e-02 8.37e-04 -4.49e-03 4.72e-04 3.93e-02 1.31e-02
## 756 4.22e-04 -4.28e-04 3.06e-03 7.98e-05 4.18e-04 4.51e-03 4.39e-04
## 757 1.75e-02 9.63e-03 -7.12e-03 -7.66e-03 5.13e-03 -2.68e-02 -1.60e-03
## 758 -9.47e-03 -1.15e-02 1.52e-02 -2.01e-02 -6.49e-03 1.78e-02 -2.37e-02
## 759 -4.20e-03 -2.41e-03 1.99e-03 2.13e-04 3.66e-04 -5.12e-03 -3.11e-04
## 760 1.63e-02 -5.90e-02 -8.97e-03 2.76e-02 2.69e-03 3.49e-02 1.90e-03
## 761 -7.12e-03 3.49e-02 1.37e-01 -3.95e-03 -1.06e-02 2.09e-02 1.72e-02
## 762 -2.05e-02 7.19e-03 3.34e-03 1.48e-02 1.92e-02 -2.21e-02 -2.15e-02
## 763 1.64e-01 2.63e-02 4.33e-02 1.41e-02 1.66e-02 7.75e-02 1.62e-03
## 764 5.89e-04 1.64e-03 -4.87e-04 -2.53e-04 8.28e-04 -6.47e-03 4.90e-04
## 765 -2.13e-03 2.71e-03 3.07e-05 2.13e-03 2.35e-03 5.90e-03 2.24e-03
## 766 2.55e-02 8.81e-03 -3.22e-03 6.99e-05 -2.87e-03 1.83e-02 1.06e-03
## 767 4.36e-02 -5.68e-02 1.68e-02 -1.76e-02 -1.03e-02 5.94e-02 2.00e-02
## 768 -2.27e-02 -1.70e-02 1.21e-02 -2.73e-02 -8.14e-03 1.06e-01 3.03e-02
## 769 1.21e-03 2.78e-03 1.82e-04 9.98e-04 4.92e-04 1.69e-03 -2.01e-04
## 770 -1.83e-02 -6.45e-03 -1.86e-01 5.45e-03 -6.42e-04 1.03e-01 8.13e-03
## 771 -7.69e-03 -1.51e-02 -1.15e-03 -5.77e-03 -2.23e-03 3.29e-02 1.21e-02
## 772 -2.21e-02 -5.16e-02 1.02e-03 3.02e-02 1.59e-02 -1.11e-02 -7.04e-04
## 773 -3.06e-02 1.16e-01 -4.80e-02 -6.03e-02 -3.28e-02 -5.33e-02 -1.29e-02
## 774 -6.88e-02 -2.23e-02 5.99e-02 3.50e-02 4.77e-02 -2.77e-02 -1.75e-02
## 775 -2.18e-04 -9.47e-06 1.27e-02 -3.08e-04 2.88e-03 2.72e-02 3.45e-03
## 776 -5.70e-03 -3.47e-05 1.34e-02 1.34e-02 8.06e-03 2.72e-02 3.23e-03
## 777 1.42e-03 -1.19e-03 -7.03e-04 -6.74e-05 -1.47e-04 -5.32e-03 3.58e-04
## 778 -2.12e-02 3.89e-03 -9.04e-03 -1.05e-02 -2.23e-03 -4.53e-02 -2.28e-02
## 779 -3.20e-02 -6.52e-03 1.11e-02 8.18e-03 4.77e-03 -1.53e-02 8.55e-03
## 780 7.12e-02 -1.14e-02 -6.10e-02 -6.75e-03 -1.73e-02 4.45e-02 2.01e-02
## 781 -1.53e-03 -2.25e-02 -1.36e-02 2.24e-04 2.51e-03 1.45e-02 7.60e-03
## 782 -1.94e-02 -1.03e-02 1.13e-02 3.63e-03 4.32e-03 4.00e-02 1.85e-02
## 783 1.04e-02 -3.00e-02 2.10e-02 -7.01e-03 1.44e-03 7.32e-02 1.95e-02
## 784 6.08e-03 -6.71e-03 -1.19e-03 -2.08e-03 -2.64e-03 1.01e-03 -3.86e-03
## 785 3.42e-03 -3.76e-03 3.18e-03 5.81e-04 -2.29e-03 -1.52e-02 -6.23e-03
## 786 1.02e-02 -4.86e-03 -5.90e-03 -4.63e-03 1.35e-04 -2.57e-02 -3.92e-03
## 787 -1.83e-02 -3.90e-03 1.75e-03 3.96e-03 3.05e-04 4.63e-04 -5.88e-02
## 788 -1.43e-02 1.56e-02 -8.49e-03 -8.75e-03 2.04e-03 -3.38e-02 -2.52e-02
## 789 3.33e-02 -1.09e-02 2.52e-02 6.82e-03 -7.05e-04 3.09e-02 1.05e-02
## 790 1.04e-03 -6.12e-04 3.15e-03 -9.45e-04 -5.65e-04 4.98e-03 1.64e-03
## 791 7.87e-04 1.24e-04 -7.64e-04 1.78e-04 2.00e-04 2.81e-03 8.39e-04
## 792 1.61e-02 -1.43e-03 6.30e-03 2.41e-03 1.01e-03 -1.09e-02 4.40e-03
## 793 8.05e-02 5.79e-02 -9.63e-03 -3.78e-02 -1.29e-02 4.34e-02 2.59e-02
## 794 -8.50e-02 -1.52e-02 3.57e-02 1.16e-02 1.25e-02 9.70e-02 1.29e-02
## 795 -1.59e-02 -6.09e-03 -5.13e-02 3.96e-02 2.31e-02 -1.76e-01 -2.05e-02
## 796 -6.59e-03 -3.12e-03 -3.14e-04 -8.22e-05 -9.17e-04 4.34e-03 2.93e-03
## 797 1.45e-02 -2.21e-03 -4.29e-03 8.64e-04 -9.85e-04 -4.78e-03 -2.73e-02
## 798 -1.22e-04 -1.78e-04 -2.01e-04 6.82e-05 -3.90e-04 1.54e-03 7.52e-05
## 799 1.25e-02 -4.77e-03 8.75e-03 3.22e-03 2.22e-03 1.07e-02 8.57e-03
## 800 -1.41e-01 -7.36e-02 1.74e-02 3.45e-02 9.44e-03 -5.75e-02 -3.47e-02
## 801 -7.68e-04 2.13e-03 2.52e-04 1.01e-04 1.37e-03 1.86e-03 4.20e-04
## 802 -1.32e-04 -7.91e-04 -2.18e-05 9.31e-04 -4.70e-04 4.84e-03 1.81e-03
## 803 -1.91e-02 3.30e-02 1.47e-02 1.36e-02 1.06e-02 -2.48e-02 7.21e-02
## 804 -2.27e-03 -1.05e-03 3.22e-03 3.25e-04 1.76e-03 1.30e-02 4.33e-03
## 805 -1.24e-02 9.48e-05 1.59e-02 7.72e-04 2.81e-03 2.86e-02 1.93e-03
## 806 -8.80e-03 -8.97e-04 -2.80e-03 -1.17e-03 -1.39e-03 3.45e-03 7.97e-04
## 807 7.74e-03 -2.70e-03 -7.25e-03 -1.54e-03 -2.98e-03 -1.03e-02 -1.87e-03
## 808 -1.80e-02 -5.10e-03 -7.85e-03 -2.75e-03 -7.04e-03 6.47e-03 4.69e-03
## 809 -6.47e-03 -3.60e-03 2.00e-04 -1.76e-03 -1.78e-03 8.84e-03 -9.12e-04
## 810 2.68e-02 -1.56e-02 3.51e-02 8.12e-03 1.57e-02 -2.44e-02 2.71e-02
## 811 -6.14e-03 1.24e-02 1.68e-02 -4.32e-03 2.47e-03 -3.44e-02 -2.22e-02
## 812 1.45e-02 6.31e-03 3.04e-03 2.39e-03 3.47e-03 -4.21e-03 -2.98e-03
## 813 8.42e-04 2.03e-04 6.02e-04 1.47e-03 1.00e-03 4.45e-03 2.83e-03
## 814 -1.32e-02 7.01e-03 -8.67e-03 -4.80e-03 -2.43e-03 -1.75e-02 -1.31e-02
## 815 9.26e-02 -4.60e-02 -1.70e-01 6.20e-02 2.66e-02 -7.78e-02 -1.06e-02
## 816 -1.22e-02 -3.60e-03 1.10e-02 -3.57e-03 1.07e-03 -8.72e-03 -6.70e-03
## 817 3.56e-03 -3.83e-02 -2.81e-03 8.97e-03 -1.52e-03 1.51e-02 8.79e-04
## 818 1.27e-03 2.75e-03 4.43e-03 1.59e-03 1.57e-03 -1.86e-03 -8.86e-04
## 819 -5.23e-03 -4.99e-03 -8.25e-04 -6.42e-03 -2.60e-03 1.99e-02 6.39e-03
## 820 4.34e-02 1.09e-02 2.08e-03 -4.11e-03 2.82e-03 -5.61e-02 -1.71e-02
## 821 -6.58e-03 -8.18e-03 -1.13e-03 2.45e-04 -2.51e-03 1.35e-02 4.24e-03
## 822 2.41e-02 2.61e-02 -2.24e-02 -1.12e-02 3.06e-03 -1.44e-02 -1.23e-02
## 823 1.37e-02 -1.81e-02 5.44e-03 -5.14e-03 -7.21e-05 -4.76e-02 8.21e-03
## 824 -3.05e-02 -8.86e-03 1.75e-03 1.95e-03 -8.42e-04 6.30e-02 -9.77e-03
## 825 2.67e-03 -2.24e-03 2.40e-03 -1.49e-03 -3.12e-04 5.44e-03 -1.60e-03
## 826 2.84e-04 4.02e-03 -7.05e-02 -5.40e-03 -9.83e-03 2.51e-02 1.06e-02
## 827 -6.25e-03 5.23e-03 -6.26e-03 7.19e-03 3.29e-03 1.40e-03 -5.99e-02
## 828 -5.97e-05 2.31e-05 1.57e-06 5.76e-06 9.67e-06 3.58e-05 -1.72e-04
## 829 -6.12e-03 1.09e-02 1.36e-04 2.53e-03 9.35e-03 2.00e-02 8.71e-03
## 830 1.11e-03 -3.23e-04 4.82e-04 -2.98e-04 -8.95e-05 5.37e-04 -4.29e-05
## 831 -4.71e-02 -4.18e-03 -1.18e-02 -1.19e-02 -8.73e-03 -3.70e-02 -3.36e-02
## 832 -1.70e-04 -1.18e-03 -7.72e-04 -2.53e-03 -1.50e-03 5.13e-03 -1.65e-03
## dfb.Fl.B dfb.Hl.B dfb.B.AG dfb.K.AG dfb.TR.A dfb.Frpl dfb.Gr.C
## 1 -1.56e-03 3.30e-03 -1.12e-03 -5.39e-03 9.88e-03 -6.77e-03 -1.72e-02
## 2 4.80e-02 3.10e-03 -1.62e-02 -2.66e-02 1.57e-02 -1.58e-02 -1.72e-02
## 3 4.45e-04 -1.33e-04 2.27e-03 -1.63e-03 9.74e-04 8.01e-04 -2.00e-03
## 4 1.34e-02 -4.47e-03 -4.98e-02 -1.23e-02 4.97e-02 -1.42e-02 -4.64e-03
## 5 4.74e-03 4.17e-03 1.14e-03 3.84e-03 -7.65e-03 -1.14e-02 -4.29e-03
## 6 3.47e-02 -5.77e-02 2.38e-02 -5.62e-03 -1.98e-02 1.72e-02 -4.61e-02
## 7 -2.69e-03 -1.06e-03 1.99e-03 -5.78e-03 -7.93e-03 9.21e-04 3.24e-03
## 8 -2.76e-02 -2.19e-02 1.38e-02 -2.80e-04 1.46e-02 -9.90e-04 2.65e-02
## 9 3.02e-02 2.27e-02 -8.86e-03 1.25e-02 -4.34e-03 1.58e-02 -5.15e-03
## 10 1.34e-02 -5.56e-03 -7.97e-03 -1.26e-02 1.34e-02 1.77e-02 -1.45e-02
## 11 -5.30e-03 5.43e-04 2.73e-04 1.50e-03 7.42e-06 -1.31e-03 2.33e-05
## 12 -2.00e-02 -6.77e-03 5.61e-02 1.87e-02 -1.92e-02 2.12e-02 -1.77e-01
## 13 6.30e-03 -8.03e-02 -3.77e-02 -5.58e-03 1.14e-02 -9.41e-02 -2.20e-02
## 14 -5.42e-03 5.94e-03 -1.77e-03 4.32e-03 -8.41e-03 1.76e-02 1.97e-03
## 15 -1.80e-02 -1.88e-02 3.06e-02 3.59e-03 -1.78e-02 4.35e-02 -9.34e-03
## 16 -7.86e-03 -6.04e-03 4.70e-03 1.38e-02 -7.12e-03 -4.34e-04 5.91e-03
## 17 -3.66e-02 3.17e-03 -2.41e-02 8.44e-03 2.80e-02 -8.61e-02 -1.91e-02
## 18 2.32e-02 1.72e-02 7.47e-03 -9.35e-03 1.85e-03 2.43e-02 2.81e-02
## 19 -1.10e-02 1.63e-02 3.10e-03 1.21e-02 -2.37e-02 3.46e-02 1.82e-02
## 20 -2.74e-01 -2.32e-01 -5.32e-02 1.18e-01 -9.77e-02 2.39e-02 1.91e-01
## 21 -2.11e-01 2.80e-02 1.66e-01 -1.06e-01 -1.47e-01 4.90e-03 2.97e-01
## 22 -1.56e-03 4.99e-03 2.54e-03 -4.74e-03 5.09e-03 -1.50e-03 -4.44e-03
## 23 8.82e-03 2.52e-02 -1.49e-02 6.38e-03 -1.39e-02 4.27e-02 -8.56e-02
## 24 2.21e-02 2.33e-02 3.71e-02 -2.14e-02 -8.14e-02 -4.19e-02 3.18e-02
## 25 -4.63e-02 -2.19e-02 1.07e-02 -7.17e-03 3.10e-02 -9.99e-02 6.67e-03
## 26 1.80e-02 4.90e-02 -2.27e-02 1.16e-02 -2.77e-03 1.46e-02 -2.27e-02
## 27 1.16e-02 1.56e-02 -7.35e-03 -4.96e-02 8.20e-02 2.20e-02 -5.34e-03
## 28 1.10e-02 -2.47e-02 1.34e-02 -2.97e-05 -1.37e-02 -3.02e-02 3.82e-02
## 29 -1.02e-01 2.85e-02 6.99e-02 2.48e-04 5.75e-03 2.67e-02 1.39e-01
## 30 1.60e-02 1.08e-01 2.39e-03 -9.02e-03 4.55e-03 5.27e-02 -2.64e-02
## 31 -5.13e-04 1.29e-03 -2.14e-03 9.26e-05 6.75e-04 -1.74e-03 -3.49e-03
## 32 1.35e-03 1.71e-03 -4.23e-03 2.12e-03 5.36e-04 -9.25e-03 -1.14e-03
## 33 -9.55e-02 -2.13e-02 1.24e-01 -2.68e-02 1.80e-02 2.13e-03 -5.76e-02
## 34 3.34e-03 2.78e-03 4.36e-03 -5.01e-03 7.00e-04 3.58e-03 -1.60e-04
## 35 -1.97e-03 -2.95e-03 4.68e-03 8.09e-04 -3.14e-03 -2.64e-03 -4.91e-03
## 36 5.81e-03 -3.34e-03 -1.22e-02 6.84e-04 4.54e-03 6.88e-04 -1.04e-02
## 37 1.87e-02 -4.78e-02 -3.45e-02 -1.67e-02 2.43e-02 1.97e-02 -1.62e-02
## 38 7.28e-03 -1.56e-02 -1.33e-02 -4.98e-03 3.17e-03 -9.23e-03 -5.59e-03
## 39 -2.49e-03 -4.56e-03 -4.40e-03 1.91e-03 1.07e-03 -5.16e-03 9.11e-03
## 40 7.34e-03 1.04e-01 -1.50e-02 2.51e-02 -4.57e-02 -3.08e-02 -4.18e-02
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## 689 -8.51e-02 -4.20e-02 1.12e-01 6.82e-02 -1.30e-01 -1.64e-02 1.38e-01
## 690 -3.57e-04 -1.94e-03 1.29e-03 2.62e-04 -2.94e-03 -1.57e-03 8.46e-05
## 691 -1.00e-02 -1.45e-02 2.16e-02 4.50e-04 -9.89e-03 5.06e-03 -2.80e-03
## 692 -6.65e-03 -1.13e-02 -4.74e-02 1.31e-02 1.58e-02 -2.66e-02 -1.53e-02
## 693 4.67e-03 -3.82e-02 2.89e-02 7.55e-03 -2.42e-02 3.56e-02 1.93e-02
## 694 2.79e-02 1.78e-02 -2.34e-02 4.86e-03 2.21e-02 1.10e-02 -5.93e-02
## 695 7.22e-03 6.17e-03 -3.80e-03 -7.63e-06 -2.33e-03 -1.61e-02 6.73e-03
## 696 -2.05e-02 -2.14e-02 5.33e-02 -7.54e-02 6.33e-02 -4.03e-02 -4.27e-02
## 697 5.48e-02 3.86e-02 9.43e-02 -3.96e-02 5.97e-02 7.91e-02 1.92e-03
## 698 -1.43e-02 -2.28e-02 4.86e-03 1.13e-03 -2.47e-03 -8.02e-03 -1.63e-02
## 699 3.75e-02 2.38e-02 8.58e-03 1.99e-02 -3.71e-02 -3.86e-02 -2.41e-03
## 700 -1.15e-02 -8.29e-03 -4.60e-03 -1.89e-03 1.62e-02 -1.93e-02 -5.95e-03
## 701 -6.96e-03 -1.02e-02 -1.66e-03 1.17e-02 -1.01e-02 -6.89e-03 -1.10e-03
## 702 -1.05e-02 -1.79e-02 -1.92e-02 3.33e-02 -5.72e-02 4.66e-02 -7.28e-03
## 703 -3.23e-03 -4.03e-03 9.25e-03 1.76e-03 -1.51e-02 1.21e-02 2.75e-03
## 704 4.44e-02 7.05e-02 -4.47e-02 8.09e-03 7.26e-03 1.03e-02 -3.43e-03
## 705 -3.51e-02 -3.41e-02 3.88e-02 -5.46e-02 2.55e-02 -6.84e-02 -9.82e-03
## 706 -1.02e-02 8.29e-03 1.62e-02 -1.63e-03 -1.14e-02 1.59e-02 -1.52e-02
## 707 -5.97e-04 -1.97e-02 -2.99e-03 8.78e-03 -8.43e-03 -4.50e-03 5.13e-03
## 708 4.65e-03 1.07e-02 3.59e-03 -1.64e-02 3.93e-02 1.52e-02 -3.21e-02
## 709 -4.11e-02 -4.13e-03 -1.41e-02 3.81e-02 1.52e-02 -6.52e-02 1.68e-02
## 710 -4.43e-05 -3.37e-05 -5.99e-06 -1.13e-05 2.28e-05 5.57e-05 1.88e-06
## 711 1.57e-02 1.41e-02 -3.37e-02 3.77e-04 1.17e-02 -4.85e-02 -6.77e-03
## 712 4.41e-03 1.90e-03 -1.64e-03 1.79e-03 -2.21e-03 -4.28e-04 -7.52e-03
## 713 -3.05e-02 -2.09e-02 4.69e-02 -3.31e-02 2.82e-02 -2.12e-02 1.95e-02
## 714 -7.23e-03 -1.15e-02 2.94e-02 -1.97e-02 2.98e-02 2.83e-02 -1.28e-02
## 715 -2.01e-03 -2.36e-03 -4.63e-03 4.90e-04 5.48e-03 -1.34e-03 5.63e-04
## 716 6.67e-03 -4.34e-02 2.13e-02 1.74e-02 -3.34e-02 -5.12e-03 2.02e-02
## 717 4.50e-03 3.31e-03 4.54e-04 3.57e-03 -8.52e-03 4.51e-03 -9.43e-03
## 718 -4.43e-03 -5.75e-03 2.59e-03 -6.55e-03 1.09e-03 -7.51e-03 1.15e-02
## 719 2.60e-03 3.79e-03 -3.09e-03 9.20e-03 -1.77e-02 -1.62e-02 -7.57e-03
## 720 -1.24e-02 5.04e-02 8.44e-03 6.76e-03 2.29e-03 -7.04e-03 -6.68e-03
## 721 6.75e-03 4.61e-03 -2.26e-03 -4.92e-04 6.45e-03 8.91e-03 6.02e-03
## 722 -1.80e-02 -2.62e-02 5.15e-02 3.73e-02 -5.91e-02 2.13e-02 1.03e-02
## 723 1.67e-02 9.35e-03 4.81e-02 1.34e-03 -6.63e-02 2.27e-02 -4.92e-02
## 724 5.34e-03 5.23e-03 -1.93e-02 1.98e-03 -9.14e-05 -2.80e-02 5.29e-03
## 725 -9.08e-03 -7.65e-03 6.39e-03 4.02e-03 -7.07e-03 -8.50e-03 -5.34e-03
## 726 3.95e-03 -1.03e-02 -2.70e-02 3.58e-02 2.95e-02 -2.29e-02 1.54e-03
## 727 1.23e-02 1.15e-02 1.70e-03 3.01e-04 -1.05e-02 -4.73e-03 -1.38e-04
## 728 1.19e-03 4.37e-02 1.05e-02 -7.88e-03 1.44e-02 -1.29e-02 1.90e-02
## 729 2.26e-03 1.19e-03 2.69e-04 9.44e-04 -2.61e-03 1.85e-04 -2.72e-03
## 730 -1.60e-02 2.70e-03 2.43e-02 6.21e-03 -6.61e-03 -7.74e-03 1.38e-02
## 731 2.91e-02 3.49e-02 -2.66e-02 -9.92e-03 2.60e-02 -4.19e-02 1.53e-02
## 732 -7.07e-02 1.71e-02 3.88e-02 7.79e-03 -2.85e-03 9.37e-02 -5.10e-02
## 733 1.25e-02 9.23e-03 4.83e-03 -1.09e-02 6.82e-03 1.00e-02 -1.08e-03
## 734 1.24e-01 2.95e-02 3.04e-02 -7.84e-02 4.66e-02 9.20e-02 -1.16e-02
## 735 -3.11e-02 -2.30e-02 2.81e-02 -2.33e-02 2.78e-02 -5.62e-03 1.06e-02
## 736 7.25e-03 -1.14e-02 1.10e-02 -5.18e-03 1.13e-02 1.82e-02 8.24e-04
## 737 3.37e-03 3.37e-03 2.68e-03 2.56e-03 -2.58e-03 6.26e-03 4.19e-03
## 738 -7.36e-03 8.13e-03 3.16e-03 5.27e-03 -9.62e-03 -5.90e-03 -5.62e-03
## 739 2.24e-02 1.56e-03 -9.36e-03 -1.20e-02 5.21e-03 -4.95e-03 -7.18e-03
## 740 -6.11e-03 1.14e-02 -1.63e-02 -5.75e-03 1.50e-02 -1.88e-02 7.06e-04
## 741 1.70e-02 2.05e-02 1.53e-02 -1.90e-02 2.43e-02 -2.01e-02 3.79e-02
## 742 -5.28e-04 -5.16e-04 -4.18e-04 1.54e-03 -1.64e-03 2.83e-04 -7.01e-04
## 743 -2.74e-04 -4.38e-03 -3.01e-03 5.02e-03 -1.27e-03 1.35e-02 -5.15e-03
## 744 -8.01e-03 3.11e-03 5.05e-03 8.77e-03 -7.43e-03 -4.83e-03 -9.55e-04
## 745 7.75e-03 -7.84e-02 3.07e-02 1.98e-02 -3.93e-02 3.29e-02 3.63e-02
## 746 2.31e-04 2.83e-04 8.39e-05 -5.02e-05 -1.55e-04 -1.12e-04 3.56e-04
## 747 -2.43e-03 -3.28e-03 5.52e-03 -3.24e-03 -1.56e-03 1.25e-02 7.85e-03
## 748 1.73e-03 3.65e-03 5.18e-04 3.76e-04 -2.38e-04 4.58e-05 -2.22e-03
## 749 3.79e-02 2.27e-02 -1.43e-02 -1.40e-02 4.83e-03 -1.77e-02 1.37e-02
## 750 1.13e-03 -6.07e-03 -2.36e-02 4.52e-03 -2.45e-03 -2.78e-03 7.55e-03
## 751 1.23e-02 2.10e-03 6.34e-02 3.90e-02 -6.82e-02 -5.47e-04 -2.94e-02
## 752 3.09e-02 9.89e-02 2.16e-02 -1.23e-02 -1.30e-02 2.13e-03 -2.17e-02
## 753 -2.68e-03 -2.13e-03 -6.02e-03 3.17e-03 -7.59e-04 -2.74e-03 1.81e-03
## 754 1.40e-02 7.44e-03 1.35e-03 7.50e-03 -1.65e-02 1.30e-02 -1.30e-02
## 755 1.83e-02 1.31e-02 -1.04e-02 -1.91e-03 1.27e-02 -2.43e-02 -3.50e-02
## 756 -2.81e-03 -2.65e-03 1.61e-03 4.42e-05 2.04e-03 -2.02e-03 1.29e-04
## 757 2.84e-03 4.80e-03 -4.05e-02 8.29e-04 3.87e-02 2.45e-02 -7.02e-02
## 758 -2.98e-02 -4.34e-02 -5.65e-02 3.45e-02 -2.69e-02 1.42e-01 2.12e-02
## 759 -6.13e-04 3.86e-03 -1.82e-03 3.36e-03 -2.82e-03 -3.61e-03 -1.23e-02
## 760 1.82e-02 5.18e-03 3.80e-02 -2.60e-02 -3.76e-02 -2.70e-03 -6.86e-04
## 761 -3.72e-02 6.57e-03 5.12e-02 9.58e-03 6.78e-02 -5.19e-02 9.09e-03
## 762 -4.28e-02 1.86e-02 6.29e-02 -1.81e-02 1.51e-02 4.30e-02 2.87e-02
## 763 -8.24e-02 -4.68e-02 4.01e-02 1.68e-02 -1.82e-02 7.88e-02 -4.27e-02
## 764 -7.12e-03 1.06e-04 -6.16e-03 4.73e-03 -2.01e-03 5.89e-03 -9.27e-04
## 765 -1.27e-02 -1.16e-02 -1.59e-03 4.90e-05 9.40e-03 4.10e-03 1.46e-03
## 766 4.99e-03 3.39e-02 1.29e-02 4.22e-03 -8.25e-03 -2.94e-03 -1.00e-02
## 767 -3.07e-02 4.70e-03 2.07e-02 3.00e-02 5.52e-03 -1.72e-02 -6.06e-03
## 768 -1.02e-02 3.77e-02 6.94e-02 8.64e-02 -9.60e-02 -3.21e-02 -1.20e-01
## 769 3.04e-03 -2.10e-03 1.25e-04 -9.00e-04 -7.83e-03 -5.80e-03 -6.90e-04
## 770 -3.42e-02 6.25e-02 1.41e-01 -6.70e-02 -7.29e-02 -4.67e-02 9.52e-03
## 771 -8.30e-03 1.09e-02 1.31e-02 1.50e-02 -1.02e-02 -1.41e-02 -1.98e-02
## 772 1.54e-02 2.72e-02 -9.69e-02 -4.13e-02 5.77e-02 4.32e-02 2.89e-02
## 773 -4.23e-02 1.87e-02 4.64e-02 -7.53e-03 5.49e-02 1.10e-01 -2.67e-02
## 774 -8.55e-02 -1.03e-01 -5.49e-02 -4.33e-02 6.66e-02 1.03e-02 5.17e-02
## 775 -6.33e-03 -7.93e-03 1.00e-02 -7.12e-03 1.55e-02 -7.67e-03 -5.81e-04
## 776 9.77e-03 4.20e-02 1.43e-02 1.84e-04 -4.48e-03 -1.55e-02 -1.75e-02
## 777 -7.71e-03 -9.72e-04 -2.10e-03 2.72e-03 -1.07e-03 -4.56e-03 -2.90e-03
## 778 8.13e-03 1.19e-02 -1.69e-02 1.35e-02 -1.12e-02 7.96e-03 8.06e-03
## 779 2.10e-03 4.85e-03 -2.48e-02 -7.36e-03 6.29e-03 -3.33e-02 2.44e-02
## 780 -2.79e-02 -9.38e-03 1.01e-01 -3.06e-02 1.27e-02 3.30e-02 -8.34e-02
## 781 5.41e-03 -2.92e-03 -4.27e-02 -4.42e-02 -4.66e-03 6.70e-03 3.40e-03
## 782 -1.26e-02 1.00e-02 -1.49e-02 -8.93e-04 -1.35e-02 -2.53e-02 4.82e-02
## 783 3.31e-02 2.17e-02 1.13e-03 -3.97e-03 2.03e-02 2.74e-02 3.77e-02
## 784 -1.22e-02 -8.77e-03 -3.13e-03 7.02e-03 -1.13e-02 1.79e-02 -1.53e-03
## 785 1.78e-02 9.87e-03 -5.79e-03 2.98e-05 1.83e-02 7.76e-03 -1.70e-02
## 786 -8.01e-03 -4.19e-02 -4.02e-03 4.94e-03 -1.19e-02 1.41e-02 1.56e-02
## 787 1.84e-02 1.21e-02 -2.00e-03 -2.03e-03 -1.11e-02 8.41e-03 2.08e-02
## 788 5.83e-02 2.55e-02 -7.41e-03 1.55e-02 -1.97e-02 7.82e-02 -2.09e-01
## 789 2.89e-02 1.94e-02 -8.35e-04 6.00e-03 2.69e-03 8.42e-03 -2.45e-02
## 790 -1.07e-03 -8.43e-04 -3.54e-03 8.10e-03 2.18e-03 -2.47e-03 6.13e-03
## 791 -2.71e-03 -2.99e-03 1.27e-03 -1.09e-04 2.20e-03 3.71e-03 7.28e-04
## 792 1.19e-03 5.88e-03 -7.32e-03 4.45e-03 -7.57e-03 1.28e-02 9.30e-03
## 793 -9.39e-02 -2.17e-02 3.26e-03 4.15e-02 4.30e-02 -2.45e-02 2.39e-02
## 794 6.48e-02 -2.58e-02 2.38e-02 -5.12e-02 2.91e-02 -7.00e-02 -6.56e-03
## 795 -1.99e-01 -1.55e-01 -1.76e-01 -2.72e-01 2.54e-01 -9.86e-02 -1.16e-01
## 796 3.00e-03 -3.06e-03 9.77e-04 -5.98e-04 -1.53e-03 -1.25e-02 2.80e-03
## 797 -1.55e-02 1.38e-03 3.23e-03 2.03e-03 2.94e-03 -2.27e-03 1.13e-04
## 798 -8.03e-04 -5.85e-04 1.56e-03 -2.46e-04 -1.28e-04 2.21e-03 3.07e-03
## 799 5.60e-03 6.63e-03 -9.01e-03 -2.67e-03 6.29e-03 5.64e-04 2.52e-03
## 800 -8.51e-02 8.63e-02 -8.36e-02 -7.37e-02 1.11e-01 2.06e-02 2.23e-01
## 801 -4.09e-03 -1.72e-03 -6.81e-03 -9.02e-04 6.42e-03 2.21e-03 2.22e-03
## 802 -1.91e-03 -1.74e-03 3.10e-03 8.89e-04 -5.07e-03 -2.36e-03 -1.08e-03
## 803 3.17e-02 2.76e-03 9.77e-03 -2.10e-02 -1.01e-03 -1.45e-03 8.51e-03
## 804 5.56e-03 3.98e-03 -6.57e-03 -2.49e-03 3.68e-03 -9.89e-03 5.53e-03
## 805 -8.50e-03 -1.47e-02 5.96e-03 -1.37e-03 1.26e-02 -2.58e-02 -5.18e-03
## 806 3.63e-03 2.56e-03 4.44e-03 -2.55e-03 1.36e-03 6.38e-04 9.37e-04
## 807 7.84e-04 2.82e-03 1.00e-02 -2.06e-03 8.98e-06 7.51e-03 5.53e-03
## 808 1.97e-02 2.24e-02 8.78e-04 -5.40e-03 1.10e-02 8.97e-03 -4.19e-03
## 809 -4.84e-03 -6.08e-03 5.66e-03 -2.89e-04 4.31e-03 -4.13e-03 -4.76e-03
## 810 -2.93e-02 -1.07e-01 -4.03e-02 -6.89e-03 -2.43e-02 -4.62e-02 1.22e-01
## 811 -2.29e-02 -2.47e-02 3.81e-02 1.68e-02 -2.22e-02 -1.95e-03 -4.36e-02
## 812 4.32e-03 2.00e-03 -5.48e-03 -2.58e-04 5.84e-03 3.47e-03 -5.38e-03
## 813 5.11e-03 4.40e-03 -5.00e-03 -1.54e-03 2.85e-03 1.92e-04 -7.52e-03
## 814 -9.82e-03 -1.14e-02 1.64e-02 5.91e-03 -9.91e-03 -5.30e-05 -1.44e-02
## 815 -4.30e-02 -1.69e-02 -1.29e-01 1.82e-01 6.36e-02 1.89e-02 2.67e-02
## 816 -8.19e-03 -1.44e-02 -5.58e-03 1.07e-02 -5.46e-03 9.15e-03 1.65e-04
## 817 4.25e-03 9.34e-04 8.10e-03 -1.22e-02 6.62e-03 -3.74e-03 2.22e-03
## 818 -2.38e-03 3.68e-03 3.08e-03 -2.15e-03 -7.77e-04 -1.31e-03 -4.88e-03
## 819 -5.27e-03 6.50e-03 1.60e-02 1.56e-02 -2.26e-02 -6.95e-03 -7.25e-03
## 820 -6.68e-02 -5.33e-02 -1.85e-02 2.77e-03 1.37e-02 -9.27e-03 6.22e-03
## 821 -9.40e-03 -1.06e-02 7.89e-03 2.15e-03 -6.69e-03 -1.46e-02 -5.83e-03
## 822 3.95e-03 -1.09e-02 7.39e-02 -1.19e-02 -3.97e-02 2.47e-02 -2.93e-03
## 823 -6.19e-02 -8.28e-03 -7.21e-02 4.59e-02 -1.52e-02 -3.94e-02 -7.84e-03
## 824 -1.01e-02 -2.08e-02 4.34e-02 -4.36e-02 6.15e-02 -2.70e-02 -3.41e-02
## 825 5.30e-03 3.42e-03 3.16e-03 2.10e-03 -3.03e-03 4.22e-03 6.28e-03
## 826 1.30e-02 1.83e-02 9.44e-03 -2.96e-02 3.79e-02 1.34e-02 -4.05e-02
## 827 -1.35e-02 -1.41e-02 -1.42e-03 -9.44e-03 5.67e-03 -4.21e-03 -1.13e-02
## 828 7.38e-05 3.96e-05 -2.18e-05 -5.41e-06 -3.80e-05 -1.19e-04 -1.89e-05
## 829 -7.46e-03 -2.14e-03 -3.12e-02 -4.13e-03 2.78e-04 -1.21e-02 2.20e-03
## 830 -1.94e-03 -1.72e-03 -7.12e-04 1.04e-03 -1.55e-03 -9.18e-04 1.49e-03
## 831 -3.76e-02 1.74e-02 6.13e-02 4.86e-03 9.98e-03 -3.26e-02 -2.12e-02
## 832 -5.47e-03 -7.12e-03 1.21e-04 2.64e-04 1.96e-03 5.04e-03 6.23e-03
## dfb.Gr.A dfb.W.D. dfb.O.P. dfb.En.P dfb.Sc.P dfb.Pl.A dffit
## 1 1.23e-02 1.42e-03 2.09e-03 8.63e-03 -2.04e-02 1.63e-03 -0.042564
## 2 2.09e-03 -1.56e-02 2.19e-02 4.28e-03 -1.69e-03 -4.47e-03 0.094645
## 3 2.71e-03 -2.45e-03 1.10e-03 3.84e-04 8.28e-04 -1.52e-03 -0.014318
## 4 1.25e-02 -2.06e-04 7.31e-04 8.15e-02 7.82e-02 -2.63e-03 0.206351
## 5 3.20e-03 -1.10e-02 -4.54e-03 -4.77e-04 -2.21e-03 2.95e-03 0.032474
## 6 5.12e-02 -1.83e-02 -1.41e-02 6.80e-02 7.03e-03 -2.12e-03 0.155710
## 7 5.34e-03 -2.30e-03 1.24e-03 3.93e-03 -5.10e-04 2.30e-03 0.037891
## 8 -1.42e-02 -1.03e-02 -6.07e-03 -3.96e-03 -4.17e-03 9.40e-03 0.075265
## 9 1.81e-03 1.14e-02 -9.01e-03 -1.01e-02 -1.85e-03 -1.81e-03 -0.080127
## 10 1.33e-02 -1.93e-02 -1.07e-02 1.63e-03 -7.13e-03 2.28e-03 0.079752
## 11 1.97e-03 -1.65e-03 -2.39e-03 -3.08e-04 -3.09e-04 1.23e-03 0.012376
## 12 1.42e-01 -3.23e-03 1.28e-02 -4.41e-02 1.86e-02 -1.38e-02 -0.252749
## 13 9.73e-03 3.19e-02 -2.24e-02 1.89e-02 -1.10e-01 2.42e-02 -0.220146
## 14 2.61e-03 -6.75e-03 -1.98e-03 -2.09e-03 -5.39e-04 8.32e-04 -0.038010
## 15 1.07e-02 7.41e-04 -1.13e-02 2.44e-03 -1.31e-03 2.51e-02 -0.136967
## 16 5.68e-04 6.93e-04 4.63e-03 -1.53e-03 1.93e-03 3.04e-03 -0.052984
## 17 1.87e-02 8.23e-03 -3.25e-03 1.84e-02 2.43e-02 7.26e-03 -0.140136
## 18 -1.86e-02 -2.53e-02 3.12e-03 -7.39e-03 -7.06e-03 1.35e-02 -0.097085
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## 690 -1.45e-04 1.08e-03 -7.08e-04 1.64e-03 -7.34e-04 9.65e-04 0.009504
## 691 3.11e-02 1.00e-02 -6.15e-03 -9.16e-03 -3.99e-03 8.42e-03 0.088433
## 692 5.48e-03 -2.92e-02 -2.17e-02 -1.33e-02 -8.13e-03 -2.26e-02 0.150463
## 693 -7.24e-03 5.82e-03 2.15e-02 4.14e-03 5.89e-03 2.41e-02 -0.172204
## 694 4.92e-02 -3.09e-02 4.26e-02 1.30e-02 9.17e-03 7.06e-03 -0.131140
## 695 -2.94e-03 4.76e-03 7.38e-03 7.41e-03 6.07e-03 5.56e-04 -0.035540
## 696 -2.35e-02 3.29e-02 4.68e-02 1.15e-02 -2.04e-03 -1.47e-02 0.252483
## 697 -5.90e-02 6.11e-02 7.67e-02 7.51e-02 3.93e-02 -3.83e-02 -0.319797
## 698 2.25e-02 -1.07e-02 1.08e-02 7.28e-03 6.91e-03 -3.15e-04 -0.053239
## 699 -8.00e-03 1.33e-03 4.03e-02 1.54e-02 2.09e-02 2.01e-02 -0.139973
## 700 -2.54e-03 -1.50e-02 -1.42e-02 -9.44e-03 -5.57e-03 -1.81e-02 0.101254
## 701 -5.62e-03 2.18e-02 -2.57e-03 -2.66e-04 1.27e-03 2.10e-03 0.042336
## 702 -9.60e-03 -1.72e-02 -2.13e-02 5.30e-02 -1.42e-02 9.10e-03 0.151196
## 703 -2.04e-03 -3.38e-03 -1.51e-02 -6.17e-04 -1.18e-03 -2.38e-04 -0.034535
## 704 1.46e-02 3.61e-03 -5.19e-03 -2.87e-02 -9.41e-03 2.96e-03 0.146877
## 705 -1.93e-02 -2.49e-02 -1.53e-02 -8.60e-03 -1.44e-02 -6.55e-03 0.237533
## 706 2.10e-02 1.47e-02 -1.30e-02 -6.08e-04 9.04e-04 -1.33e-03 -0.056607
## 707 -1.01e-02 -5.70e-03 5.93e-03 2.95e-03 5.37e-03 -6.45e-04 -0.035902
## 708 2.89e-03 6.68e-03 1.60e-02 3.28e-02 1.57e-02 -1.96e-02 -0.126828
## 709 -2.52e-02 4.36e-02 3.03e-02 1.06e-02 2.29e-02 1.17e-02 -0.130486
## 710 1.12e-06 -1.02e-05 2.55e-05 5.81e-06 4.92e-06 -5.91e-06 -0.000151
## 711 -1.33e-03 -3.59e-03 5.02e-03 7.16e-03 1.04e-02 1.96e-03 -0.068254
## 712 4.92e-03 2.47e-03 1.45e-03 1.88e-03 2.26e-03 -7.90e-04 -0.018823
## 713 4.57e-02 -2.87e-02 -1.64e-02 -9.15e-03 -1.39e-02 1.03e-02 0.161353
## 714 3.94e-03 -2.00e-03 3.19e-02 6.30e-02 -2.57e-03 -5.95e-03 0.105622
## 715 2.03e-03 5.98e-03 -1.51e-03 -1.59e-03 -1.55e-05 2.86e-04 0.014081
## 716 -5.58e-03 1.86e-02 1.12e-02 7.00e-03 1.33e-02 4.45e-03 -0.098263
## 717 9.61e-03 -1.21e-02 -5.60e-03 -1.10e-03 -3.33e-03 1.55e-04 0.027931
## 718 -1.02e-02 -8.82e-04 1.03e-02 3.26e-03 3.91e-03 -1.47e-03 -0.042925
## 719 7.26e-03 -1.40e-02 -7.15e-03 -1.60e-03 -9.01e-04 5.42e-03 0.048872
## 720 -6.26e-03 -1.47e-02 4.96e-03 -5.67e-03 -6.95e-03 8.82e-03 0.099193
## 721 -5.59e-03 7.42e-03 -1.26e-04 -1.85e-03 -1.44e-03 -7.54e-04 0.025760
## 722 -3.38e-03 6.48e-02 -1.13e-01 2.02e-03 1.60e-02 1.11e-02 -0.213583
## 723 1.92e-02 7.10e-02 2.89e-02 -1.11e-02 2.65e-02 -2.49e-02 -0.240532
## 724 -7.54e-03 9.04e-03 6.62e-03 -2.93e-03 2.12e-03 1.27e-03 0.063513
## 725 7.30e-03 1.79e-02 5.23e-03 1.53e-03 5.61e-03 2.22e-03 -0.039974
## 726 5.36e-03 -2.77e-04 -6.07e-03 8.74e-03 -8.40e-04 -4.66e-03 0.109490
## 727 2.92e-03 -3.63e-03 1.76e-03 1.52e-03 -2.43e-04 4.67e-03 0.038574
## 728 -8.35e-03 -1.94e-02 1.64e-02 -4.00e-03 -1.00e-02 6.04e-03 0.078664
## 729 2.21e-03 7.26e-04 -5.84e-04 4.99e-04 4.88e-04 2.27e-04 -0.006431
## 730 -1.49e-02 -6.05e-04 7.43e-04 -2.23e-03 1.59e-03 3.73e-03 -0.048418
## 731 -1.69e-02 4.15e-03 1.30e-02 -2.84e-04 3.87e-04 4.87e-03 0.117544
## 732 9.79e-03 -6.97e-02 -6.65e-02 1.79e-02 -4.41e-02 -1.34e-02 0.245165
## 733 5.54e-03 -1.30e-02 2.26e-04 -6.56e-03 -7.47e-03 -6.14e-04 0.038048
## 734 5.80e-02 -4.55e-02 -3.02e-02 -1.35e-02 -3.35e-02 6.77e-03 0.236565
## 735 1.43e-02 -8.49e-03 -9.80e-03 -4.97e-03 -5.75e-03 8.35e-03 0.104257
## 736 1.59e-03 6.43e-03 2.43e-03 -2.30e-04 -1.68e-02 -6.05e-04 -0.042369
## 737 -4.54e-03 9.46e-04 -1.71e-03 -1.18e-03 -1.44e-03 9.78e-04 0.017626
## 738 1.03e-02 -1.30e-02 4.56e-03 -4.19e-03 -3.71e-02 4.43e-03 -0.065938
## 739 1.26e-03 -5.49e-03 1.21e-02 1.41e-03 -6.36e-04 7.75e-04 0.047603
## 740 2.43e-03 -1.64e-02 5.77e-03 2.65e-03 2.94e-03 -1.40e-03 -0.062141
## 741 -2.75e-02 1.11e-02 -1.06e-02 -2.31e-02 8.61e-03 -4.36e-03 -0.167919
## 742 5.97e-04 -6.72e-04 -7.50e-04 -9.01e-04 -3.52e-04 7.26e-04 0.004867
## 743 2.00e-03 -2.35e-03 -2.13e-03 -1.91e-03 2.79e-02 -5.19e-03 0.038198
## 744 3.44e-03 8.81e-04 4.33e-03 -8.01e-04 2.85e-03 2.42e-03 -0.030540
## 745 -1.58e-02 5.44e-03 3.76e-02 1.14e-02 1.61e-02 -1.58e-02 -0.239861
## 746 -1.73e-04 3.14e-04 2.14e-04 8.17e-05 -1.76e-03 7.10e-04 -0.002866
## 747 -7.10e-03 -7.88e-03 2.15e-03 -6.69e-04 -1.46e-03 -1.55e-03 -0.031121
## 748 6.13e-04 1.04e-04 2.60e-03 -5.68e-05 -1.13e-03 -4.27e-04 0.010142
## 749 -6.35e-03 -8.95e-03 3.26e-03 3.14e-02 1.94e-03 2.88e-03 -0.186668
## 750 -6.49e-03 6.12e-03 1.44e-03 -1.23e-02 1.03e-03 -1.09e-03 0.063457
## 751 2.64e-02 1.19e-02 -2.72e-02 3.76e-02 5.70e-03 -6.58e-03 -0.228065
## 752 5.52e-02 -7.87e-02 1.29e-01 2.77e-03 -2.17e-02 3.78e-03 0.241779
## 753 -4.93e-03 -7.82e-03 -4.79e-03 -3.87e-03 -2.93e-03 1.94e-03 0.026002
## 754 6.05e-03 7.67e-03 3.07e-05 1.02e-02 6.65e-03 -4.03e-03 -0.050320
## 755 3.90e-02 -2.68e-02 5.83e-03 2.61e-03 -2.73e-03 9.29e-04 0.081852
## 756 -2.12e-03 -7.08e-04 3.10e-03 -8.38e-04 -3.44e-04 -3.73e-04 0.011465
## 757 7.46e-02 -4.92e-02 3.39e-02 1.54e-03 -8.08e-03 -3.26e-03 0.146893
## 758 5.46e-03 -4.20e-02 8.56e-02 -3.28e-02 -3.26e-02 -5.85e-03 0.249404
## 759 9.24e-03 9.54e-03 4.53e-03 1.39e-03 3.28e-03 -7.93e-05 -0.022960
## 760 2.09e-03 -3.92e-02 -1.12e-02 3.44e-03 -1.46e-02 -1.56e-03 0.134359
## 761 2.60e-03 -1.60e-02 -2.04e-03 5.75e-02 -2.76e-03 1.10e-03 -0.320745
## 762 -8.54e-03 -2.20e-02 9.41e-03 1.51e-01 -6.69e-03 7.47e-03 0.209910
## 763 -9.36e-04 -6.75e-02 -5.75e-02 -3.75e-02 -3.39e-02 -1.24e-02 0.280540
## 764 9.28e-04 -4.22e-03 1.65e-03 -3.01e-04 5.12e-04 -3.17e-04 -0.018544
## 765 -4.62e-03 3.45e-03 -1.92e-04 -1.30e-03 4.26e-04 -4.43e-03 -0.037012
## 766 6.16e-03 -1.43e-02 -1.18e-02 -3.92e-03 -7.17e-03 5.88e-03 0.059348
## 767 7.06e-03 5.19e-02 -2.83e-02 2.14e-02 2.22e-02 2.54e-03 -0.166143
## 768 7.76e-02 -7.75e-03 4.02e-02 4.00e-03 1.80e-02 6.68e-03 -0.292118
## 769 1.21e-04 2.59e-03 5.84e-04 9.38e-04 6.44e-04 2.37e-04 0.017451
## 770 -1.54e-02 -1.52e-02 2.36e-02 3.38e-02 -1.71e-02 5.79e-03 0.335280
## 771 2.75e-02 -8.02e-03 1.29e-02 7.29e-04 4.49e-03 1.67e-03 -0.079468
## 772 -3.80e-02 -7.76e-02 -1.39e-02 -5.92e-02 -4.80e-02 -1.43e-02 0.247373
## 773 4.56e-02 -2.42e-02 1.16e-02 -2.03e-01 -2.11e-01 1.96e-02 -0.351760
## 774 -2.20e-02 -3.47e-02 -3.46e-02 4.95e-02 -3.10e-02 -9.52e-03 0.263724
## 775 1.49e-02 -8.59e-03 -1.08e-02 -9.75e-03 -6.35e-03 -7.61e-05 0.069838
## 776 7.82e-03 -9.30e-03 -1.17e-02 6.38e-02 -1.27e-03 4.14e-03 0.090826
## 777 2.12e-03 4.07e-03 3.96e-03 2.29e-03 2.79e-03 3.28e-04 -0.014415
## 778 -1.71e-02 1.53e-02 2.06e-02 -6.46e-03 -7.11e-03 5.32e-03 0.127497
## 779 -2.59e-02 -5.90e-04 5.13e-03 4.54e-03 7.61e-03 -2.67e-03 -0.073459
## 780 4.61e-02 9.39e-04 2.55e-02 -4.29e-03 2.10e-02 -2.38e-02 -0.234584
## 781 -4.28e-03 5.75e-04 5.84e-03 2.12e-03 1.41e-03 -3.32e-03 -0.098123
## 782 -4.80e-02 -7.38e-03 1.41e-02 -1.32e-03 6.18e-03 -1.85e-03 -0.107373
## 783 -4.50e-02 -1.74e-02 2.94e-04 8.45e-03 7.68e-03 -2.10e-03 -0.173450
## 784 2.82e-03 -2.02e-04 6.76e-03 -3.76e-03 -4.41e-03 -2.82e-04 0.039666
## 785 1.47e-02 2.53e-02 8.43e-03 7.17e-03 7.15e-03 8.87e-04 -0.057058
## 786 -7.88e-03 1.17e-02 -1.00e-02 4.43e-03 7.84e-03 -9.03e-04 -0.068332
## 787 -3.27e-02 1.76e-02 9.57e-03 -2.52e-03 3.94e-04 9.66e-03 -0.084866
## 788 2.56e-01 -1.85e-02 -9.29e-03 -2.29e-02 -2.05e-02 5.52e-03 0.283058
## 789 9.63e-03 2.21e-03 -2.43e-03 1.27e-02 1.05e-02 -1.78e-03 -0.108215
## 790 -4.30e-03 -1.85e-03 2.52e-04 -4.69e-04 -1.60e-04 4.06e-04 0.014139
## 791 -5.45e-04 -3.48e-03 2.97e-03 9.78e-05 -5.55e-05 -9.15e-04 -0.012356
## 792 -2.14e-02 -1.86e-02 3.47e-03 1.77e-03 -2.57e-02 2.01e-03 -0.058882
## 793 -5.28e-02 3.44e-02 -9.20e-03 3.50e-02 2.64e-02 3.45e-03 -0.215328
## 794 -2.46e-02 -2.37e-02 2.71e-02 -4.60e-02 -2.34e-02 -1.06e-02 0.225557
## 795 6.77e-02 -4.46e-02 8.41e-02 3.95e-02 2.99e-02 4.28e-03 -0.581533
## 796 -1.73e-03 -1.72e-03 3.12e-03 3.82e-03 3.13e-03 9.92e-04 -0.018905
## 797 3.01e-03 7.01e-03 1.49e-03 9.98e-03 5.94e-03 6.94e-03 -0.043574
## 798 -3.61e-03 -8.04e-04 -3.19e-03 -1.99e-04 -4.51e-04 -1.83e-05 -0.007667
## 799 -5.11e-04 7.23e-03 3.72e-03 2.86e-03 3.92e-03 -6.05e-03 -0.042838
## 800 -1.91e-01 -7.35e-02 7.90e-02 -1.20e-01 -8.35e-02 2.65e-03 0.448990
## 801 -2.80e-03 4.67e-03 -6.86e-03 -1.97e-03 -2.02e-03 -2.41e-03 0.018314
## 802 -3.28e-03 -7.12e-03 2.21e-03 1.46e-03 7.15e-04 4.83e-04 -0.016164
## 803 -5.08e-03 7.16e-02 8.17e-02 5.02e-02 8.57e-03 -3.12e-02 0.171716
## 804 -7.04e-03 -8.68e-03 -4.27e-03 -1.35e-03 -1.80e-03 -3.08e-05 0.025698
## 805 -6.67e-03 -7.15e-04 7.62e-05 -1.88e-03 7.31e-02 -1.07e-02 0.098021
## 806 3.58e-04 2.29e-03 2.35e-03 1.79e-03 3.61e-04 -8.14e-04 -0.015232
## 807 -1.76e-03 5.50e-03 6.98e-03 5.08e-03 3.01e-03 1.45e-04 -0.026470
## 808 8.35e-03 8.88e-03 6.64e-03 -7.05e-03 2.84e-03 -4.69e-03 -0.055199
## 809 3.17e-03 -2.00e-03 3.66e-02 -3.24e-04 1.23e-04 -2.96e-04 0.042255
## 810 -1.11e-01 -9.20e-02 9.11e-03 -2.47e-04 1.94e-02 8.97e-04 -0.229425
## 811 3.80e-02 -4.53e-03 -2.00e-02 -1.67e-02 -8.00e-03 1.19e-02 0.126075
## 812 8.20e-03 -2.32e-03 7.32e-03 1.50e-02 3.64e-04 2.03e-03 0.033787
## 813 5.12e-03 8.00e-04 -4.89e-03 1.56e-03 5.80e-04 -1.98e-03 -0.014371
## 814 1.21e-02 -9.50e-03 -7.26e-03 -4.66e-03 -5.33e-03 8.83e-03 0.061372
## 815 8.61e-03 7.66e-02 -4.82e-02 -1.75e-01 -2.29e-02 -4.19e-02 0.683223
## 816 -5.01e-03 1.17e-02 -4.43e-03 -1.07e-02 -3.76e-03 8.41e-05 0.046233
## 817 -3.65e-03 -1.11e-02 -4.43e-03 -8.23e-04 -4.45e-03 -7.75e-04 0.052406
## 818 -1.30e-03 5.47e-04 -2.47e-03 5.46e-05 -2.51e-04 -2.35e-04 0.021929
## 819 1.25e-02 -5.20e-03 8.94e-03 -1.26e-03 2.72e-03 2.99e-03 -0.056200
## 820 1.95e-02 -2.41e-02 -1.95e-02 4.95e-03 1.05e-03 1.47e-02 0.158645
## 821 6.80e-03 2.72e-03 7.33e-03 2.85e-03 4.56e-03 9.37e-04 -0.043221
## 822 1.69e-02 -3.76e-02 -3.48e-02 -1.66e-02 9.48e-02 -1.01e-02 0.189968
## 823 -1.05e-03 1.25e-02 2.26e-02 1.76e-02 2.45e-02 8.13e-03 -0.145578
## 824 1.95e-02 3.56e-02 -1.23e-02 4.00e-04 -8.99e-03 -2.08e-03 0.162608
## 825 -7.66e-03 1.72e-02 2.94e-03 -7.21e-04 1.19e-04 -1.74e-03 0.026530
## 826 5.45e-02 -2.50e-02 -4.72e-02 3.73e-02 2.84e-03 -1.49e-03 -0.175711
## 827 1.40e-02 -1.95e-02 8.77e-03 3.14e-03 2.05e-03 1.36e-02 -0.087435
## 828 -4.83e-06 -3.34e-05 -7.27e-05 3.18e-05 2.47e-05 6.16e-05 -0.000285
## 829 1.10e-02 2.18e-03 -1.55e-02 -9.72e-03 -7.61e-03 -7.92e-03 0.083814
## 830 -1.52e-03 5.51e-04 -4.68e-04 1.21e-04 1.73e-04 3.25e-04 0.004780
## 831 2.61e-03 1.12e-01 1.23e-02 -5.31e-03 1.07e-03 7.64e-03 0.180706
## 832 -3.71e-03 -3.53e-03 -1.23e-03 1.44e-04 2.21e-02 -2.43e-03 0.030653
## cov.r cook.d hat inf
## 1 1.063 6.72e-05 0.02925
## 2 1.039 3.32e-04 0.01951
## 3 1.056 7.60e-06 0.02137
## 4 1.032 1.58e-03 0.03567
## 5 1.053 3.91e-05 0.01924
## 6 1.096 8.99e-04 0.06678
## 7 1.076 5.32e-05 0.03966
## 8 1.034 2.10e-04 0.01359
## 9 1.062 2.38e-04 0.03267
## 10 1.039 2.36e-04 0.01716
## 11 1.049 5.68e-06 0.01426
## 12 0.986 2.36e-03 0.02753
## 13 1.014 1.79e-03 0.03095
## 14 1.041 5.36e-05 0.01082
## 15 1.048 6.95e-04 0.03217
## 16 1.078 1.04e-04 0.04272
## 17 1.027 7.27e-04 0.02204
## 18 1.081 3.49e-04 0.04953
## 19 1.006 5.66e-04 0.01261
## 20 0.842 1.47e-02 0.04961 *
## 21 1.013 2.52e-02 0.12751 *
## 22 1.052 1.34e-05 0.01795
## 23 1.017 8.71e-04 0.02062
## 24 0.981 1.45e-03 0.01821
## 25 0.939 5.79e-03 0.03749
## 26 1.060 5.82e-04 0.03777
## 27 0.965 2.40e-03 0.02297
## 28 1.001 7.13e-04 0.01374
## 29 0.959 5.58e-03 0.04120
## 30 0.999 1.22e-03 0.01984
## 31 1.050 1.62e-06 0.01539
## 32 1.043 1.58e-05 0.00953
## 33 0.959 3.57e-03 0.02976
## 34 1.055 3.08e-05 0.02110
## 35 1.044 1.06e-05 0.01046
## 36 1.052 3.13e-05 0.01852
## 37 1.041 5.41e-04 0.02497
## 38 1.091 1.11e-04 0.05382
## 39 1.047 1.87e-05 0.01339
## 40 0.949 5.23e-03 0.03688
## 41 1.046 1.43e-05 0.01250
## 42 1.058 1.09e-03 0.04376
## 43 1.057 5.11e-05 0.02345
## 44 1.064 2.89e-05 0.02875
## 45 1.011 5.14e-04 0.01300
## 46 1.066 6.87e-06 0.02968
## 47 1.046 6.94e-05 0.01567
## 48 1.045 1.53e-03 0.04135
## 49 1.078 1.92e-05 0.04113
## 50 1.042 9.11e-04 0.03178
## 51 1.056 1.87e-04 0.02698
## 52 1.054 2.31e-06 0.01904
## 53 1.081 1.61e-04 0.04587
## 54 0.988 9.81e-04 0.01459
## 55 1.012 3.05e-03 0.04131
## 56 1.017 5.76e-04 0.01569
## 57 1.056 5.17e-05 0.02231
## 58 1.043 7.92e-05 0.01394
## 59 1.006 1.02e-03 0.01941
## 60 1.087 1.89e-04 0.05128
## 61 0.811 1.13e-02 0.03548 *
## 62 1.038 2.33e-04 0.01614
## 63 1.026 1.40e-03 0.03103
## 64 1.038 6.76e-04 0.02603
## 65 1.036 9.81e-05 0.01039
## 66 1.081 1.17e-04 0.04535
## 67 1.051 1.63e-04 0.02214
## 68 1.061 3.38e-06 0.02506
## 69 0.923 3.38e-03 0.02200
## 70 0.996 1.81e-03 0.02522
## 71 0.991 9.55e-04 0.01485
## 72 1.048 1.20e-05 0.01409
## 73 1.060 4.62e-04 0.03535
## 74 0.942 1.21e-02 0.06430 *
## 75 1.034 6.10e-04 0.02324
## 76 1.053 2.31e-05 0.01856
## 77 1.064 7.19e-05 0.02995
## 78 0.913 6.22e-03 0.03421
## 79 1.033 1.31e-03 0.03293
## 80 1.045 5.31e-04 0.02710
## 81 1.047 4.67e-05 0.01536
## 82 0.946 5.30e-03 0.03662
## 83 1.058 1.07e-04 0.02568
## 84 1.079 9.27e-06 0.04174
## 85 1.063 2.11e-03 0.05750
## 86 1.042 1.55e-04 0.01586
## 87 0.915 5.08e-03 0.02937
## 88 0.939 4.20e-03 0.02933
## 89 0.550 2.53e-02 0.03368 *
## 90 0.910 1.06e-02 0.05086
## 91 1.008 5.69e-04 0.01309
## 92 1.047 8.08e-04 0.03338
## 93 1.054 1.74e-05 0.01992
## 94 0.882 1.57e-02 0.06053 *
## 95 1.029 5.80e-04 0.02036
## 96 1.015 2.20e-03 0.03523
## 97 1.033 1.17e-04 0.00972
## 98 1.082 2.96e-05 0.04449
## 99 1.043 1.50e-04 0.01654
## 100 1.044 1.58e-06 0.00993
## 101 1.068 1.50e-04 0.03498
## 102 1.065 9.33e-07 0.02933
## 103 1.022 4.37e-04 0.01482
## 104 1.075 2.94e-04 0.04333
## 105 1.042 7.41e-05 0.01300
## 106 1.017 3.36e-04 0.01077
## 107 1.047 2.18e-05 0.01332
## 108 1.041 6.11e-04 0.02653
## 109 1.066 8.41e-03 0.09668
## 110 1.011 1.03e-03 0.02084
## 111 1.023 4.06e-04 0.01419
## 112 1.046 1.09e-06 0.01141
## 113 0.828 1.99e-02 0.05989 *
## 114 1.021 9.65e-04 0.02356
## 115 1.036 6.29e-04 0.02432
## 116 1.039 5.63e-04 0.02481
## 117 1.046 9.96e-05 0.01665
## 118 1.033 3.52e-04 0.01705
## 119 1.019 5.14e-04 0.01525
## 120 0.985 1.19e-03 0.01630
## 121 1.035 1.70e-03 0.03871
## 122 1.057 1.99e-07 0.02175
## 123 1.077 5.00e-04 0.04820
## 124 1.067 2.06e-04 0.03544
## 125 0.957 1.90e-03 0.01775
## 126 1.063 5.87e-05 0.02913
## 127 1.045 3.30e-04 0.02296
## 128 1.068 1.31e-05 0.03236
## 129 1.045 7.11e-05 0.01492
## 130 1.052 2.29e-07 0.01744
## 131 1.046 6.76e-05 0.01524
## 132 1.064 8.18e-04 0.04402
## 133 1.071 6.33e-04 0.04559
## 134 1.034 6.32e-04 0.02353
## 135 1.030 1.01e-03 0.02748
## 136 1.050 7.93e-06 0.01579
## 137 0.893 7.47e-03 0.03583 *
## 138 1.128 3.59e-04 0.08648 *
## 139 1.021 5.37e-03 0.06046
## 140 1.059 4.04e-04 0.03351
## 141 1.034 2.84e-04 0.01581
## 142 2.236 2.02e-06 0.53750 *
## 143 1.061 1.77e-04 0.03068
## 144 0.974 7.68e-04 0.00994
## 145 1.014 6.32e-04 0.01590
## 146 1.058 3.60e-05 0.02352
## 147 1.047 1.16e-04 0.01803
## 148 1.046 4.32e-05 0.01437
## 149 1.026 2.26e-04 0.01086
## 150 0.917 3.63e-03 0.02249
## 151 1.054 2.49e-04 0.02695
## 152 1.036 8.53e-05 0.00949
## 153 1.054 3.80e-06 0.01874
## 154 1.048 6.66e-04 0.03162
## 155 1.074 2.91e-05 0.03797
## 156 1.048 1.41e-05 0.01449
## 157 1.022 1.61e-03 0.03190
## 158 1.085 1.51e-05 0.04752
## 159 1.019 4.97e-04 0.01504
## 160 1.048 2.72e-06 0.01355
## 161 1.093 1.25e-05 0.05413
## 162 1.044 6.10e-03 0.07496
## 163 1.055 2.61e-04 0.02779
## 164 0.877 1.25e-02 0.04992 *
## 165 1.048 7.10e-08 0.01349
## 166 1.017 8.36e-04 0.02020
## 167 1.046 3.41e-05 0.01370
## 168 1.062 5.39e-04 0.03788
## 169 1.026 1.00e-03 0.02591
## 170 1.050 1.37e-05 0.01628
## 171 1.060 1.75e-04 0.02941
## 172 1.066 7.84e-06 0.03044
## 173 0.995 1.06e-03 0.01689
## 174 0.983 7.71e-03 0.05919
## 175 0.986 6.55e-03 0.05433
## 176 1.047 4.96e-05 0.01496
## 177 1.065 1.12e-05 0.02955
## 178 1.020 8.80e-04 0.02180
## 179 1.022 1.28e-03 0.02789
## 180 1.081 2.74e-04 0.04828
## 181 0.843 2.36e-02 0.07162 *
## 182 0.955 3.18e-03 0.02641
## 183 1.038 2.45e-04 0.01647
## 184 1.201 4.74e-05 0.13903 *
## 185 1.030 2.19e-03 0.04141
## 186 0.846 4.43e-03 0.01809 *
## 187 0.996 5.47e-04 0.01026
## 188 1.063 1.63e-05 0.02769
## 189 1.004 6.48e-04 0.01349
## 190 1.042 2.66e-04 0.01971
## 191 1.053 6.89e-04 0.03474
## 192 1.059 7.26e-04 0.03943
## 193 1.074 2.11e-04 0.04117
## 194 1.056 3.23e-07 0.02067
## 195 1.039 7.83e-05 0.01103
## 196 1.045 5.55e-05 0.01409
## 197 1.031 2.73e-04 0.01406
## 198 1.051 3.98e-04 0.02800
## 199 1.045 2.65e-06 0.01069
## 200 1.083 6.56e-05 0.04626
## 201 0.993 1.44e-03 0.02081
## 202 1.001 2.88e-03 0.03626
## 203 1.060 5.49e-04 0.03728
## 204 1.054 1.01e-04 0.02233
## 205 1.042 7.63e-04 0.02987
## 206 1.052 2.26e-07 0.01739
## 207 0.985 6.57e-04 0.01007
## 208 1.047 3.54e-04 0.02450
## 209 1.372 4.06e-02 0.30666 *
## 210 1.036 8.17e-05 0.00962
## 211 1.012 2.14e-03 0.03362
## 212 1.056 1.09e-04 0.02464
## 213 0.998 1.46e-03 0.02221
## 214 1.075 7.30e-03 0.09625
## 215 1.060 1.64e-05 0.02489
## 216 1.038 1.29e-03 0.03498
## 217 1.073 2.96e-06 0.03609
## 218 1.014 6.31e-04 0.01592
## 219 1.036 1.81e-03 0.03998
## 220 1.053 9.06e-07 0.01754
## 221 1.035 5.43e-04 0.02227
## 222 1.049 7.26e-05 0.01811
## 223 0.765 8.90e-03 0.02423 *
## 224 1.051 4.58e-03 0.06915
## 225 1.049 6.10e-05 0.01719
## 226 1.030 4.42e-04 0.01793
## 227 1.049 2.44e-07 0.01460
## 228 1.061 2.92e-04 0.03310
## 229 1.057 6.01e-06 0.02226
## 230 1.024 4.88e-04 0.01637
## 231 1.052 1.45e-04 0.02262
## 232 1.094 5.38e-06 0.05470
## 233 1.037 1.21e-04 0.01201
## 234 1.073 1.40e-04 0.03899
## 235 1.068 1.72e-04 0.03565
## 236 1.034 1.41e-04 0.01133
## 237 1.034 3.44e-04 0.01738
## 238 1.040 7.62e-05 0.01176
## 239 1.041 1.75e-04 0.01594
## 240 1.032 2.85e-04 0.01490
## 241 1.052 4.98e-04 0.03060
## 242 1.030 4.34e-04 0.01762
## 243 1.005 1.14e-03 0.02041
## 244 1.047 1.28e-05 0.01276
## 245 1.033 8.08e-04 0.02594
## 246 1.056 2.58e-03 0.05728
## 247 0.894 5.10e-03 0.02619 *
## 248 0.991 8.70e-04 0.01376
## 249 0.995 6.69e-03 0.05803
## 250 1.046 3.25e-03 0.05758
## 251 1.046 9.25e-05 0.01615
## 252 1.071 5.12e-05 0.03523
## 253 1.049 5.88e-05 0.01718
## 254 1.057 3.07e-04 0.03014
## 255 1.044 1.55e-04 0.01751
## 256 1.027 1.67e-04 0.00940
## 257 1.123 4.91e-04 0.08370 *
## 258 1.015 2.68e-03 0.03964
## 259 1.052 1.14e-06 0.01739
## 260 0.997 1.91e-03 0.02641
## 261 1.050 9.18e-04 0.03669
## 262 1.040 1.01e-04 0.01239
## 263 1.046 1.17e-06 0.01125
## 264 1.071 2.50e-07 0.03413
## 265 1.049 3.54e-08 0.01383
## 266 1.065 9.89e-07 0.02906
## 267 1.078 1.40e-04 0.04304
## 268 1.043 5.09e-05 0.01253
## 269 1.054 1.93e-05 0.02006
## 270 1.047 3.60e-05 0.01486
## 271 1.037 1.13e-02 0.09525 *
## 272 1.083 4.55e-03 0.08606
## 273 0.988 3.86e-03 0.03933
## 274 1.054 1.16e-05 0.01941
## 275 1.029 1.24e-03 0.03019
## 276 1.030 3.45e-04 0.01541
## 277 1.062 1.86e-04 0.03102
## 278 1.062 1.08e-07 0.02618
## 279 1.073 4.55e-03 0.08061
## 280 1.053 8.86e-05 0.02146
## 281 1.050 3.09e-04 0.02556
## 282 1.210 3.06e-03 0.15776 *
## 283 1.059 1.13e-03 0.04459
## 284 1.044 5.68e-05 0.01334
## 285 1.061 2.73e-04 0.03257
## 286 1.014 6.17e-04 0.01559
## 287 1.049 4.47e-06 0.01454
## 288 1.057 5.59e-07 0.02135
## 289 1.045 1.12e-04 0.01608
## 290 1.195 2.05e-04 0.13581 *
## 291 0.859 6.39e-03 0.02659 *
## 292 1.040 6.09e-04 0.02590
## 293 1.056 6.86e-05 0.02292
## 294 1.056 4.72e-05 0.02211
## 295 0.982 1.74e-03 0.02118
## 296 1.062 7.32e-04 0.04085
## 297 1.887 1.95e-01 0.53115 *
## 298 1.067 1.39e-04 0.03451
## 299 1.101 1.74e-03 0.07794 *
## 300 1.033 3.39e-04 0.01667
## 301 1.026 5.16e-04 0.01777
## 302 1.050 1.38e-05 0.01596
## 303 1.059 4.61e-05 0.02490
## 304 1.044 5.71e-05 0.01338
## 305 0.957 1.74e-03 0.01643
## 306 1.064 1.32e-04 0.03159
## 307 0.955 3.18e-03 0.02646
## 308 1.146 4.18e-07 0.09782 *
## 309 1.008 3.66e-04 0.00931
## 310 1.081 3.24e-04 0.04906
## 311 1.078 1.36e-03 0.05908
## 312 0.952 2.70e-03 0.02265
## 313 1.002 2.68e-03 0.03492
## 314 1.045 2.21e-04 0.02012
## 315 1.083 1.18e-04 0.04731
## 316 1.060 1.54e-03 0.04994
## 317 1.049 2.22e-05 0.01523
## 318 1.076 1.24e-06 0.03871
## 319 1.038 1.24e-04 0.01260
## 320 1.076 9.47e-05 0.04085
## 321 1.047 1.61e-05 0.01339
## 322 0.999 8.95e-04 0.01575
## 323 1.045 3.77e-04 0.02398
## 324 1.129 1.11e-02 0.13935 *
## 325 1.059 2.05e-05 0.02420
## 326 0.947 1.33e-02 0.07002 *
## 327 1.048 1.26e-04 0.01917
## 328 1.028 3.92e-04 0.01577
## 329 1.066 6.00e-07 0.03026
## 330 1.040 1.03e-04 0.01249
## 331 1.043 6.85e-04 0.02905
## 332 1.017 2.53e-04 0.00878
## 333 1.098 8.45e-07 0.05848
## 334 1.082 1.01e-03 0.05802
## 335 0.902 3.60e-03 0.02031
## 336 1.061 2.81e-05 0.02647
## 337 1.091 4.60e-05 0.05271
## 338 0.975 3.27e-03 0.03143
## 339 1.044 7.11e-05 0.01422
## 340 1.033 1.94e-03 0.04024
## 341 0.984 2.33e-03 0.02693
## 342 1.060 6.80e-05 0.02673
## 343 1.059 1.57e-03 0.04971
## 344 1.049 2.61e-05 0.01588
## 345 1.043 8.10e-05 0.01369
## 346 1.047 1.58e-04 0.01917
## 347 1.049 2.31e-05 0.01521
## 348 1.044 5.38e-04 0.02665
## 349 1.055 7.31e-07 0.02005
## 350 1.025 3.56e-04 0.01399
## 351 1.047 3.77e-05 0.01448
## 352 1.061 5.37e-06 0.02565
## 353 1.106 2.26e-04 0.06797 *
## 354 1.052 2.98e-05 0.01819
## 355 1.059 8.78e-04 0.04141
## 356 1.081 2.13e-04 0.04717
## 357 1.042 1.82e-04 0.01673
## 358 1.071 9.13e-05 0.03695
## 359 1.057 9.37e-06 0.02215
## 360 1.053 4.29e-06 0.01799
## 361 1.055 5.31e-06 0.02003
## 362 1.036 5.96e-04 0.02387
## 363 1.055 5.60e-05 0.02193
## 364 1.049 1.52e-05 0.01526
## 365 1.068 3.59e-07 0.03198
## 366 1.061 4.80e-04 0.03616
## 367 1.028 7.42e-04 0.02269
## 368 1.048 1.64e-04 0.02040
## 369 0.921 6.52e-03 0.03712
## 370 1.050 1.99e-06 0.01507
## 371 1.001 1.54e-03 0.02392
## 372 1.026 3.15e-04 0.01327
## 373 1.059 3.13e-06 0.02390
## 374 1.067 9.75e-06 0.03067
## 375 1.009 7.93e-04 0.01689
## 376 1.065 4.23e-05 0.03000
## 377 0.834 4.50e-03 0.01726 *
## 378 1.060 4.99e-04 0.03639
## 379 0.791 6.83e-03 0.02103 *
## 380 1.101 7.64e-05 0.06189 *
## 381 1.054 1.99e-04 0.02520
## 382 1.057 3.54e-05 0.02320
## 383 1.054 3.73e-05 0.02055
## 384 1.045 1.08e-05 0.01121
## 385 1.046 6.41e-05 0.01494
## 386 1.046 1.24e-04 0.01773
## 387 1.034 3.53e-04 0.01748
## 388 0.988 1.26e-03 0.01770
## 389 1.044 1.38e-04 0.01700
## 390 1.143 1.40e-03 0.10470 *
## 391 1.012 2.35e-03 0.03543
## 392 1.054 2.50e-06 0.01927
## 393 1.065 2.31e-04 0.03460
## 394 1.052 9.87e-04 0.03869
## 395 1.082 7.92e-04 0.05548
## 396 1.103 7.27e-06 0.06258 *
## 397 1.040 1.89e-04 0.01616
## 398 1.033 6.78e-03 0.07358
## 399 1.057 3.50e-05 0.02320
## 400 1.019 1.34e-03 0.02743
## 401 1.128 8.54e-04 0.09059 *
## 402 1.027 1.90e-03 0.03727
## 403 1.047 4.59e-05 0.01463
## 404 1.101 7.22e-04 0.06880 *
## 405 3.852 7.73e-02 0.73812 *
## 406 1.011 2.76e-03 0.03870
## 407 1.044 5.10e-05 0.01274
## 408 1.052 1.20e-06 0.01747
## 409 1.081 1.97e-05 0.04380
## 410 1.055 6.63e-05 0.02207
## 411 0.891 1.08e-02 0.04735 *
## 412 0.943 6.21e-03 0.04055
## 413 1.059 1.82e-04 0.02888
## 414 1.042 1.90e-04 0.01728
## 415 0.903 2.58e-03 0.01523
## 416 1.050 3.14e-05 0.01690
## 417 1.044 3.20e-04 0.02205
## 418 1.058 1.33e-03 0.04660
## 419 1.030 1.49e-04 0.00957
## 420 1.079 9.42e-06 0.04175
## 421 1.057 3.11e-04 0.03019
## 422 0.820 1.99e-02 0.05845 *
## 423 1.022 2.06e-04 0.00901
## 424 1.056 2.84e-05 0.02162
## 425 1.065 5.86e-05 0.03060
## 426 1.002 1.32e-03 0.02186
## 427 0.877 5.59e-03 0.02586 *
## 428 1.024 4.39e-04 0.01545
## 429 1.043 5.72e-04 0.02697
## 430 1.095 6.95e-05 0.05691
## 431 1.087 2.21e-03 0.07236
## 432 1.046 2.88e-05 0.01287
## 433 1.127 1.17e-04 0.08378 *
## 434 1.081 1.86e-05 0.04356
## 435 1.019 4.15e-04 0.01313
## 436 1.096 7.77e-04 0.06592
## 437 0.914 6.63e-03 0.03612
## 438 1.039 2.61e-03 0.04925
## 439 0.958 1.19e-03 0.01207
## 440 1.072 1.19e-04 0.03829
## 441 1.024 6.82e-04 0.02004
## 442 1.013 4.71e-04 0.01264
## 443 1.041 6.49e-05 0.01160
## 444 1.040 3.30e-04 0.02033
## 445 0.916 9.82e-03 0.04943
## 446 1.052 5.62e-05 0.01980
## 447 0.993 1.43e-03 0.02075
## 448 1.067 4.14e-04 0.03964
## 449 1.034 1.66e-04 0.01192
## 450 1.027 4.41e-04 0.01667
## 451 1.032 4.58e-04 0.01893
## 452 1.031 2.70e-04 0.01389
## 453 1.043 1.50e-05 0.00996
## 454 1.052 2.24e-04 0.02463
## 455 1.036 1.69e-04 0.01303
## 456 1.040 2.75e-04 0.01889
## 457 1.050 4.39e-05 0.01727
## 458 1.156 1.13e-03 0.11279 *
## 459 1.026 1.16e-03 0.02821
## 460 1.046 1.35e-05 0.01223
## 461 1.061 1.82e-04 0.03013
## 462 1.095 2.48e-03 0.07969
## 463 1.065 1.05e-03 0.04733
## 464 1.029 2.46e-04 0.01244
## 465 1.110 9.43e-04 0.07778 *
## 466 1.132 3.97e-04 0.08982 *
## 467 1.034 2.84e-04 0.01594
## 468 0.949 4.91e-03 0.03518
## 469 1.061 2.62e-04 0.03255
## 470 1.095 1.48e-03 0.07216
## 471 1.151 1.49e-05 0.10136 *
## 472 1.057 7.10e-05 0.02418
## 473 1.026 1.85e-04 0.00964
## 474 1.032 2.27e-03 0.04278
## 475 1.012 8.48e-04 0.01851
## 476 1.081 3.77e-04 0.04947
## 477 1.044 2.37e-04 0.01974
## 478 1.041 3.56e-04 0.02139
## 479 1.055 1.25e-05 0.02028
## 480 1.017 5.52e-03 0.06004
## 481 0.972 1.76e-03 0.01926
## 482 1.006 2.07e-03 0.03088
## 483 1.032 3.94e-03 0.05611
## 484 1.026 8.51e-04 0.02379
## 485 1.016 4.77e-04 0.01369
## 486 1.048 6.54e-04 0.03102
## 487 1.027 1.47e-03 0.03242
## 488 1.093 9.94e-05 0.05519
## 489 1.048 8.92e-06 0.01369
## 490 1.063 1.47e-04 0.03121
## 491 1.044 3.03e-05 0.01193
## 492 1.064 4.95e-05 0.02944
## 493 1.621 1.66e-02 0.37779 *
## 494 1.012 8.90e-04 0.01938
## 495 1.007 4.58e-04 0.01088
## 496 1.064 1.27e-05 0.02809
## 497 1.045 5.34e-08 0.01050
## 498 1.028 8.80e-04 0.02512
## 499 1.054 4.85e-04 0.03205
## 500 1.041 5.75e-05 0.01099
## 501 1.050 1.86e-08 0.01494
## 502 1.060 7.28e-07 0.02441
## 503 0.944 4.74e-03 0.03334
## 504 0.981 1.53e-03 0.01896
## 505 1.116 6.78e-06 0.07317 *
## 506 1.032 4.90e-04 0.01967
## 507 1.050 4.49e-06 0.01508
## 508 1.051 2.96e-03 0.05779
## 509 1.000 6.52e-03 0.05890
## 510 1.017 4.17e-04 0.01257
## 511 1.072 2.58e-05 0.03623
## 512 1.078 2.51e-05 0.04104
## 513 1.055 1.86e-07 0.01948
## 514 1.122 1.11e-02 0.13586 *
## 515 0.955 1.66e-03 0.01549
## 516 1.039 9.22e-05 0.01169
## 517 0.991 1.53e-03 0.02123
## 518 1.067 1.03e-06 0.03071
## 519 1.029 1.75e-04 0.01027
## 520 1.030 2.11e-04 0.01178
## 521 1.008 7.60e-03 0.06754
## 522 1.057 7.43e-05 0.02409
## 523 1.048 5.27e-05 0.01643
## 524 1.051 5.49e-06 0.01630
## 525 1.029 1.00e-03 0.02702
## 526 1.057 2.51e-05 0.02304
## 527 1.080 1.01e-03 0.05700
## 528 0.904 3.40e-03 0.01958
## 529 1.035 3.58e-04 0.01800
## 530 0.758 4.16e-02 0.08650 *
## 531 1.045 7.39e-04 0.03068
## 532 1.052 3.35e-03 0.06173
## 533 1.032 2.20e-04 0.01285
## 534 1.027 3.82e-04 0.01509
## 535 1.055 1.39e-05 0.02056
## 536 1.048 3.47e-05 0.01495
## 537 1.064 2.00e-04 0.03351
## 538 1.003 2.46e-03 0.03346
## 539 1.053 1.27e-04 0.02255
## 540 0.974 4.20e-03 0.03754
## 541 1.035 2.19e-04 0.01451
## 542 1.046 2.55e-04 0.02178
## 543 1.007 4.61e-03 0.05038
## 544 1.054 5.47e-04 0.03283
## 545 1.048 2.52e-03 0.05292
## 546 1.061 5.11e-04 0.03675
## 547 1.078 9.48e-05 0.04213
## 548 1.051 1.09e-04 0.02049
## 549 1.048 1.30e-04 0.01893
## 550 0.968 1.27e-03 0.01421
## 551 1.036 3.79e-04 0.01921
## 552 1.039 2.92e-04 0.01854
## 553 1.110 1.01e-03 0.07853 *
## 554 0.939 1.66e-02 0.07820 *
## 555 1.064 2.59e-04 0.03433
## 556 0.955 2.13e-03 0.01911
## 557 1.027 6.28e-04 0.02022
## 558 0.977 1.18e-03 0.01474
## 559 0.437 5.67e-02 0.05389 *
## 560 1.047 5.46e-04 0.02850
## 561 1.062 8.61e-05 0.02918
## 562 1.018 1.40e-03 0.02819
## 563 1.066 3.47e-05 0.03054
## 564 1.059 6.26e-04 0.03728
## 565 1.038 5.81e-04 0.02462
## 566 1.050 3.49e-05 0.01731
## 567 1.008 1.34e-03 0.02372
## 568 1.051 1.51e-04 0.02175
## 569 1.041 3.38e-04 0.02080
## 570 1.038 8.01e-05 0.01044
## 571 1.040 9.68e-05 0.01251
## 572 1.062 2.01e-04 0.03170
## 573 1.048 1.39e-04 0.01934
## 574 1.034 2.31e-04 0.01403
## 575 1.050 6.04e-05 0.01811
## 576 1.048 2.72e-06 0.01375
## 577 1.063 4.53e-04 0.03719
## 578 1.070 4.42e-04 0.04202
## 579 0.877 4.12e-03 0.01986 *
## 580 1.068 3.63e-05 0.03286
## 581 1.036 4.25e-04 0.02005
## 582 1.042 7.27e-05 0.01291
## 583 1.050 7.09e-08 0.01486
## 584 1.013 1.06e-03 0.02205
## 585 1.004 1.41e-03 0.02359
## 586 1.137 2.10e-07 0.09034 *
## 587 1.014 4.42e-04 0.01234
## 588 1.086 8.14e-05 0.04938
## 589 1.043 1.56e-05 0.00964
## 590 1.081 4.75e-03 0.08590
## 591 1.074 5.77e-05 0.03799
## 592 0.981 2.30e-03 0.02567
## 593 1.070 7.41e-05 0.03489
## 594 1.030 4.49e-04 0.01788
## 595 1.023 3.61e-04 0.01341
## 596 1.047 1.05e-06 0.01209
## 597 1.043 5.91e-05 0.01279
## 598 1.045 7.77e-05 0.01525
## 599 1.027 6.79e-04 0.02134
## 600 1.051 1.32e-05 0.01681
## 601 1.040 1.15e-04 0.01333
## 602 1.030 2.49e-04 0.01318
## 603 1.048 1.37e-04 0.01916
## 604 1.049 5.20e-05 0.01717
## 605 1.001 7.49e-04 0.01423
## 606 1.034 1.74e-04 0.01229
## 607 1.045 5.77e-05 0.01386
## 608 1.055 1.10e-03 0.04217
## 609 1.046 6.30e-07 0.01117
## 610 0.201 6.61e-02 0.03556 *
## 611 1.083 6.39e-04 0.05460
## 612 1.026 2.41e-04 0.01119
## 613 1.066 1.08e-05 0.02987
## 614 1.041 5.59e-05 0.01105
## 615 1.037 6.01e-05 0.00895
## 616 1.050 5.64e-04 0.03054
## 617 0.982 1.15e-03 0.01530
## 618 1.042 1.92e-04 0.01733
## 619 1.047 1.11e-04 0.01745
## 620 1.049 2.91e-07 0.01375
## 621 1.018 5.19e-04 0.01501
## 622 1.003 3.63e-03 0.04262
## 623 1.059 4.84e-05 0.02479
## 624 1.048 1.54e-04 0.01963
## 625 1.082 1.98e-04 0.04746
## 626 1.040 4.14e-05 0.00945
## 627 1.044 1.46e-04 0.01678
## 628 1.058 1.80e-06 0.02248
## 629 1.093 5.51e-04 0.06147
## 630 0.977 7.09e-03 0.05404
## 631 0.982 1.19e-03 0.01573
## 632 0.957 3.95e-03 0.03162
## 633 1.053 1.98e-05 0.01860
## 634 1.040 3.33e-05 0.00918
## 635 1.052 9.65e-04 0.03811
## 636 1.041 6.18e-05 0.01130
## 637 1.000 4.04e-03 0.04437
## 638 1.040 1.11e-04 0.01313
## 639 1.051 1.42e-06 0.01651
## 640 1.040 1.45e-03 0.03830
## 641 0.982 1.81e-03 0.02165
## 642 1.028 3.60e-03 0.05210
## 643 1.080 6.26e-06 0.04303
## 644 0.998 4.47e-03 0.04659
## 645 1.020 1.35e-03 0.02798
## 646 1.013 2.68e-03 0.03866
## 647 1.043 2.88e-04 0.02050
## 648 1.045 6.42e-05 0.01401
## 649 1.060 2.35e-06 0.02421
## 650 1.061 6.08e-05 0.02700
## 651 1.039 1.22e-03 0.03478
## 652 1.084 4.94e-06 0.04630
## 653 1.021 2.93e-04 0.01103
## 654 1.066 1.47e-03 0.05249
## 655 0.773 9.28e-03 0.02598 *
## 656 1.030 8.56e-04 0.02547
## 657 1.130 9.25e-06 0.08528 *
## 658 1.052 4.21e-04 0.02908
## 659 1.051 4.27e-05 0.01776
## 660 1.053 2.65e-06 0.01795
## 661 1.029 3.01e-04 0.01409
## 662 1.027 8.36e-04 0.02386
## 663 1.047 4.34e-05 0.01456
## 664 0.956 5.06e-03 0.03766
## 665 1.048 1.50e-07 0.01355
## 666 1.032 9.81e-04 0.02817
## 667 0.933 4.45e-03 0.02950
## 668 1.043 8.52e-05 0.01357
## 669 1.029 3.74e-04 0.01589
## 670 1.070 4.54e-05 0.03441
## 671 0.998 9.54e-04 0.01644
## 672 1.028 1.33e-04 0.00835
## 673 1.080 2.27e-08 0.04248
## 674 1.047 3.03e-04 0.02329
## 675 1.056 3.55e-07 0.02027
## 676 1.009 7.41e-04 0.01609
## 677 1.057 1.01e-03 0.04201
## 678 0.994 1.04e-02 0.07432
## 679 1.034 2.80e-04 0.01590
## 680 1.048 5.24e-05 0.01628
## 681 1.088 2.79e-05 0.05039
## 682 1.056 7.97e-05 0.02368
## 683 1.051 9.46e-07 0.01583
## 684 1.032 1.88e-04 0.01200
## 685 1.041 1.79e-04 0.01611
## 686 1.025 4.51e-04 0.01617
## 687 1.026 1.03e-03 0.02635
## 688 1.057 5.09e-04 0.03395
## 689 1.003 9.76e-03 0.07526
## 690 1.052 3.35e-06 0.01670
## 691 1.032 2.90e-04 0.01510
## 692 1.037 8.39e-04 0.02839
## 693 1.048 1.10e-03 0.03787
## 694 1.020 6.37e-04 0.01791
## 695 1.043 4.68e-05 0.01195
## 696 1.026 2.36e-03 0.04101
## 697 0.837 3.76e-03 0.01489 *
## 698 1.035 1.05e-04 0.00991
## 699 1.022 7.26e-04 0.02009
## 700 1.052 3.80e-04 0.02843
## 701 1.052 6.65e-05 0.02005
## 702 1.006 8.46e-04 0.01685
## 703 1.046 4.42e-05 0.01427
## 704 1.108 8.00e-04 0.07520 *
## 705 0.964 2.09e-03 0.02040
## 706 1.045 1.19e-04 0.01677
## 707 1.057 4.78e-05 0.02367
## 708 1.014 5.96e-04 0.01517
## 709 1.042 6.31e-04 0.02737
## 710 1.048 8.43e-10 0.01357
## 711 1.052 1.73e-04 0.02321
## 712 1.052 1.31e-05 0.01781
## 713 1.019 9.64e-04 0.02256
## 714 1.046 4.13e-04 0.02541
## 715 1.051 7.35e-06 0.01672
## 716 1.053 3.58e-04 0.02874
## 717 1.048 2.89e-05 0.01517
## 718 1.041 6.83e-05 0.01161
## 719 1.041 8.86e-05 0.01258
## 720 1.038 3.65e-04 0.01982
## 721 1.047 2.46e-05 0.01347
## 722 1.036 1.69e-03 0.03874
## 723 0.987 2.14e-03 0.02593
## 724 1.031 1.50e-04 0.01016
## 725 1.043 5.92e-05 0.01289
## 726 1.106 4.44e-04 0.07008 *
## 727 1.054 5.52e-05 0.02130
## 728 1.038 2.29e-04 0.01646
## 729 1.053 1.53e-06 0.01817
## 730 1.051 8.69e-05 0.02023
## 731 0.991 5.11e-04 0.00889
## 732 1.016 2.22e-03 0.03577
## 733 1.043 5.37e-05 0.01214
## 734 0.994 2.07e-03 0.02708
## 735 1.017 4.03e-04 0.01235
## 736 1.077 6.66e-05 0.04138
## 737 1.047 1.15e-05 0.01305
## 738 1.055 1.61e-04 0.02565
## 739 1.051 8.40e-05 0.01988
## 740 1.035 1.43e-04 0.01163
## 741 1.039 1.04e-03 0.03218
## 742 1.048 8.79e-07 0.01364
## 743 1.083 5.41e-05 0.04568
## 744 1.045 3.46e-05 0.01244
## 745 0.944 2.12e-03 0.01739
## 746 1.083 3.05e-07 0.04499
## 747 1.042 3.59e-05 0.01082
## 748 1.042 3.81e-06 0.00824
## 749 1.198 1.29e-03 0.14262 *
## 750 1.091 1.49e-04 0.05466
## 751 1.060 1.93e-03 0.05389
## 752 1.009 2.16e-03 0.03288
## 753 1.052 2.51e-05 0.01833
## 754 1.042 9.39e-05 0.01350
## 755 1.041 2.48e-04 0.01838
## 756 1.051 4.87e-06 0.01589
## 757 1.010 7.99e-04 0.01730
## 758 0.987 2.30e-03 0.02726
## 759 1.051 1.95e-05 0.01665
## 760 1.063 6.69e-04 0.04089
## 761 1.039 3.81e-03 0.05827
## 762 1.026 1.63e-03 0.03367
## 763 0.921 2.90e-03 0.01916
## 764 1.047 1.28e-05 0.01312
## 765 1.055 5.08e-05 0.02169
## 766 1.053 1.31e-04 0.02292
## 767 1.010 1.02e-03 0.02037
## 768 0.934 3.15e-03 0.02248
## 769 1.054 1.13e-05 0.01963
## 770 1.021 4.16e-03 0.05315
## 771 1.039 2.34e-04 0.01687
## 772 1.029 2.27e-03 0.04142
## 773 1.069 4.58e-03 0.07884
## 774 0.959 2.57e-03 0.02307
## 775 1.042 1.81e-04 0.01676
## 776 1.062 3.06e-04 0.03401
## 777 1.049 7.71e-06 0.01460
## 778 1.011 6.02e-04 0.01444
## 779 1.054 2.00e-04 0.02551
## 780 0.989 2.04e-03 0.02541
## 781 1.097 3.57e-04 0.06187
## 782 1.027 4.27e-04 0.01636
## 783 1.043 1.11e-03 0.03552
## 784 1.063 5.83e-05 0.02860
## 785 1.056 1.21e-04 0.02467
## 786 1.043 1.73e-04 0.01733
## 787 1.072 2.67e-04 0.04042
## 788 1.087 2.97e-03 0.07842
## 789 1.034 4.34e-04 0.01964
## 790 1.126 7.41e-06 0.08130 *
## 791 1.058 5.66e-06 0.02244
## 792 1.051 1.29e-04 0.02142
## 793 0.995 1.72e-03 0.02412
## 794 1.019 1.88e-03 0.03383
## 795 1.112 1.25e-02 0.13501 *
## 796 1.060 1.33e-05 0.02477
## 797 1.081 7.04e-05 0.04476
## 798 1.053 2.18e-06 0.01767
## 799 1.049 6.80e-05 0.01786
## 800 0.818 7.40e-03 0.02520 *
## 801 1.063 1.24e-05 0.02785
## 802 1.052 9.69e-06 0.01742
## 803 1.100 1.09e-03 0.07152
## 804 1.049 2.45e-05 0.01578
## 805 1.047 3.56e-04 0.02492
## 806 1.053 8.60e-06 0.01801
## 807 1.046 2.60e-05 0.01302
## 808 1.046 1.13e-04 0.01719
## 809 1.077 6.62e-05 0.04119
## 810 1.012 1.95e-03 0.03170
## 811 0.991 5.88e-04 0.01007
## 812 1.069 4.23e-05 0.03343
## 813 1.049 7.66e-06 0.01466
## 814 1.036 1.40e-04 0.01220
## 815 0.910 1.72e-02 0.07160 *
## 816 1.062 7.93e-05 0.02827
## 817 1.102 1.02e-04 0.06271 *
## 818 1.062 1.78e-05 0.02668
## 819 1.049 1.17e-04 0.01930
## 820 0.989 9.31e-04 0.01416
## 821 1.037 6.93e-05 0.00917
## 822 1.024 1.34e-03 0.02963
## 823 1.008 7.85e-04 0.01641
## 824 0.980 9.78e-04 0.01309
## 825 1.055 2.61e-05 0.02121
## 826 1.036 1.14e-03 0.03224
## 827 1.063 2.83e-04 0.03456
## 828 1.073 3.01e-09 0.03598
## 829 1.032 2.60e-04 0.01435
## 830 1.057 8.47e-07 0.02189
## 831 1.023 1.21e-03 0.02769
## 832 1.057 3.48e-05 0.02319plot(rstudent(full.model) ~ hatvalues(full.model)) # recommended by some
0.0.0.3.7 Diagnostic plots checks for heteroscedasticity and normality
layout(matrix(c(1,2,3,4),2,2)) # optional 4 graphs/page
plot(full.model)
0.0.0.4 Section 2.3 Initial Model Residuals
Because the aim is to reduce the prediction error so for a good prediction the residual should be minimized.
Comparison has to carried out on lm model(model.full,model.AIC and model.BIC) Model residuals analysis is the most important measure to find the goodness of fit.The residuals should not be correlated with another variable.Adjacent residuals should not be autocorrelated.They should have consistency.These values cause outliers. There have to be very little outliers.The residuals should have a normal distribution. Negative values indicate leakage information. Missing values and inadequate subset could be possibly casusing curvature.
If the distribution becomes better with bayesian method or not. The RMSE for full model and AIC is same.The RMSE for BIC model is higher. Normality and Homoscedicity is also plotted.
Durbin Watson test is to be performed to test the residual correlations.
0.0.0.4.1 Residual Plots for Initial.model and bas.lm AIC and BIC models.
library(car)##
## Attaching package: 'car'## The following object is masked from 'package:boot':
##
## logit## The following object is masked from 'package:psych':
##
## logit## The following object is masked from 'package:dplyr':
##
## recodecrPlots(Initial.model)
plot(Initial.model)
plot(model.AIC)
plot(model.BIC) 
##### Normality test of residues
plot(resid(model.AIC),main="AIC Histogram of Normality",xlab='standard residuals',ylab='Frequency')
plot(resid(model.BIC),main="BIC Histogram of Normality",xlab='standard residuals',ylab='Frequency')
##### Colinearity(multiple relationship between variables)
vif(model.BIC,which=1)## area MS.SubClass Lot.Area Overall.Qual Overall.Cond
## 3.738386 1.224176 1.158667 2.646775 1.624380
## Year.Built Year.Remod.Add Total.Bsmt.SF Central.Air Bsmt.Full.Bath
## 2.924490 2.034977 1.904032 1.369218 1.227042
## Bedroom.AbvGr Fireplaces Garage.Area Screen.Porch Pool.Area
## 1.912153 1.590301 1.710804 1.057359 1.066940vif(model.AIC,which=1)## area MS.SubClass Lot.Area Overall.Qual Overall.Cond
## 97.900645 1.520487 1.177307 2.755175 1.653301
## Year.Built Year.Remod.Add Total.Bsmt.SF Central.Air X1st.Flr.SF
## 3.184413 2.060783 3.367174 1.532142 54.972270
## X2nd.Flr.SF Bsmt.Full.Bath Bsmt.Half.Bath Bedroom.AbvGr Kitchen.AbvGr
## 72.311277 1.302641 1.162242 2.430316 1.657956
## TotRms.AbvGrd Fireplaces Garage.Area Enclosed.Porch Screen.Porch
## 4.239248 1.658238 1.750801 1.289097 1.072265
## Pool.Area
## 1.1396360.0.0.4.2 Homoscedicity test of residues
plot(model.AIC,which=1)
plot(model.BIC,which=1) ##### Autocorrelation of residuals
durbinWatsonTest(model.BIC)## lag Autocorrelation D-W Statistic p-value
## 1 -0.01010267 2.019984 0.748
## Alternative hypothesis: rho != 0durbinWatsonTest(model.AIC)## lag Autocorrelation D-W Statistic p-value
## 1 -0.0004720813 2.00085 0.952
## Alternative hypothesis: rho != 0durbinWatsonTest(resid.BIC)## [1] 2.052704durbinWatsonTest(resid.AIC)## Error in durbinWatsonTest(resid.AIC): object 'resid.AIC' not found0.0.0.5 Section 2.4 Initial Model RMSE
Initial.model<-lm(log(price)~log(area)+Lot.Area+Overall.Qual+Overall.Cond +Year.Built+Total.Bsmt.SF+ Bsmt.Full.Bath + Fireplaces+Kitchen.AbvGr+
Garage.Area,data=(na.omit(train)))
predict.Initial <- exp(predict(Initial.model, train))
resid.Initial <- train$price - predict.Initial
rmse.Initial<- sqrt(mean(resid.Initial^2))
rmse.Initial## [1] 19788.970.0.0.6 Cross Validation
1.You can do K-Fold cross-validation using the cv.lm() function in the DAAG package.K-fold cross-validation
2.Sum the MSE for each fold, divide by the number of observations, and take the square root to get the cross-validated standard error of estimate. You can assess R2 shrinkage via K-fold cross-validation. Using the crossval() function from the bootstrap package, do the following: Assessing R2 shrinkage using 10-Fold Cross-Validation
##
## Attaching package: 'bootstrap'## The following object is masked from 'package:broom':
##
## bootstrap##
## Attaching package: 'DAAG'## The following object is masked from 'package:car':
##
## vif## The following object is masked from 'package:survival':
##
## lung## The following object is masked from 'package:MASS':
##
## hills## The following object is masked from 'package:psych':
##
## cities##
## Attaching package: 'crossval'## The following object is masked from 'package:bootstrap':
##
## crossval## The following object is masked from 'package:caret':
##
## confusionMatrix## Error in min(K, max(groupsize)): invalid 'type' (closure) of argument## [,1]
## price 1.891201## Error in is.data.frame(y): object 'results' not foundAutomatic Selection is controversial because of this reason it is better to use a semi automatic approach. #### Stepwise Regression
library(MASS)
fit <- lm(price~area+Lot.Area+Bedroom.AbvGr,data=train)
step <- stepAIC(fit, direction="both")## Start: AIC=17719.3
## price ~ area + Lot.Area + Bedroom.AbvGr
##
## Df Sum of Sq RSS AIC
## <none> 1.4629e+12 17719
## - Lot.Area 1 4.3329e+10 1.5062e+12 17742
## - Bedroom.AbvGr 1 2.6870e+11 1.7316e+12 17858
## - area 1 2.1313e+12 3.5942e+12 18465step$anova # display results## Stepwise Model Path
## Analysis of Deviance Table
##
## Initial Model:
## price ~ area + Lot.Area + Bedroom.AbvGr
##
## Final Model:
## price ~ area + Lot.Area + Bedroom.AbvGr
##
##
## Step Df Deviance Resid. Df Resid. Dev AIC
## 1 828 1.462921e+12 17719.3Subsets of each size to report. Here, the ten best models will be reported for each subset size (1 predictor, 2 predictors, etc.).
0.0.0.6.1 All Subsets Regression
library(leaps)
attach(train)
leaps<-regsubsets(price~area+Lot.Area+Bedroom.AbvGr+Lot.Area,data=train,
nbest=10)
summary(leaps)# view results## Subset selection object
## Call: regsubsets.formula(price ~ area + Lot.Area + Bedroom.AbvGr +
## Lot.Area, data = train, nbest = 10)
## 3 Variables (and intercept)
## Forced in Forced out
## area FALSE FALSE
## Lot.Area FALSE FALSE
## Bedroom.AbvGr FALSE FALSE
## 10 subsets of each size up to 3
## Selection Algorithm: exhaustive
## area Lot.Area Bedroom.AbvGr
## 1 ( 1 ) "*" " " " "
## 1 ( 2 ) " " "*" " "
## 1 ( 3 ) " " " " "*"
## 2 ( 1 ) "*" " " "*"
## 2 ( 2 ) "*" "*" " "
## 2 ( 3 ) " " "*" "*"
## 3 ( 1 ) "*" "*" "*"par(mfrow=c(1,1))
plot(leaps,scale="r2")# View Plots
plot(leaps,scale="bic") 
**Discussion on All subsets All subsets regression*
1.Other options for plot( ) are bic, Cp, and adjr2. Other options for plotting with subset( ) are bic, cp, adjr2, and rss. 2.Relative Importance The relaimpo package provides measures of relative importance for each of the predictors in the model. See help(calc.relimp) for details on the four measures of relative importance provided. 3.Calculate Relative Importance for Each Predictor 4.Relative Importance of Variables in Train.(relaimpo)
0.0.0.6.2 Variable Assessment
## Response variable: price
## Total response variance: 4842289529
## Analysis based on 832 observations
##
## 3 Regressors:
## area Lot.Area Bedroom.AbvGr
## Proportion of variance explained by model: 63.64%
## Metrics are normalized to sum to 100% (rela=TRUE).
##
## Relative importance metrics:
##
## lmg last first pratt
## area 0.85172635 0.87229019 0.82070172 1.07606061
## Lot.Area 0.05627967 0.01773382 0.09737699 0.04306666
## Bedroom.AbvGr 0.09199398 0.10997599 0.08192129 -0.11912727
##
## Average coefficients for different model sizes:
##
## 1X 2Xs 3Xs
## area 107.010407 118.897345 1.308462e+02
## Lot.Area 1.749038 1.113643 7.213858e-01
## Bedroom.AbvGr 20399.500348 -4945.051969 -2.766416e+040.0.0.6.3 Bootstrap Measures of Relative Importance (1000 samples)
boot <- boot.relimp(Initial.model, b = 1000, type = c("lmg",
"last", "first", "pratt"), rank = TRUE,
diff = TRUE, rela = TRUE)
booteval.relimp(boot) # print result## Response variable: log(price)
## Total response variance: 0.1423125
## Analysis based on 832 observations
##
## 10 Regressors:
## log(area) Lot.Area Overall.Qual Overall.Cond Year.Built Total.Bsmt.SF Bsmt.Full.Bath Fireplaces Kitchen.AbvGr Garage.Area
## Proportion of variance explained by model: 91.15%
## Metrics are normalized to sum to 100% (rela=TRUE).
##
## Relative importance metrics:
##
## lmg last first pratt
## log(area) 0.226522839 0.32869980 0.196329659 0.30683961
## Lot.Area 0.019161853 0.02336594 0.020104814 0.01871285
## Overall.Qual 0.242745019 0.14787622 0.230751537 0.24012106
## Overall.Cond 0.016840461 0.12583272 0.001790812 -0.01349749
## Year.Built 0.128017180 0.16747570 0.126379825 0.16569479
## Total.Bsmt.SF 0.134537260 0.09110945 0.151288172 0.12412623
## Bsmt.Full.Bath 0.031101569 0.04035314 0.034277100 0.03308613
## Fireplaces 0.077344693 0.01782820 0.096372752 0.04017127
## Kitchen.AbvGr 0.007405226 0.01613450 0.002820865 0.00578499
## Garage.Area 0.116323902 0.04132433 0.139884462 0.07896056
##
## Average coefficients for different model sizes:
##
## 1X 2Xs 3Xs 4Xs
## log(area) 8.576391e-01 7.411872e-01 6.549600e-01 5.902364e-01
## Lot.Area 8.889291e-06 6.473462e-06 5.066571e-06 4.223552e-06
## Overall.Qual 2.325595e-01 2.065824e-01 1.843048e-01 1.647255e-01
## Overall.Cond -2.465604e-02 5.073714e-03 2.292652e-02 3.402582e-02
## Year.Built 7.870414e-03 6.355961e-03 5.302985e-03 4.571323e-03
## Total.Bsmt.SF 6.290609e-04 5.124898e-04 4.216747e-04 3.511428e-04
## Bsmt.Full.Bath 2.301339e-01 1.668543e-01 1.293384e-01 1.070317e-01
## Fireplaces 3.044448e-01 2.309508e-01 1.784840e-01 1.403135e-01
## Kitchen.AbvGr -1.774777e-01 -1.600352e-01 -1.477185e-01 -1.387230e-01
## Garage.Area 1.175761e-03 9.348232e-04 7.496851e-04 6.068498e-04
## 5Xs 6Xs 7Xs 8Xs
## log(area) 5.410155e-01 5.031797e-01 4.738962e-01 4.512044e-01
## Lot.Area 3.695041e-06 3.343972e-06 3.094334e-06 2.902363e-06
## Overall.Qual 1.471372e-01 1.310376e-01 1.160721e-01 1.019960e-01
## Overall.Cond 4.128621e-02 4.635140e-02 5.015507e-02 5.323190e-02
## Year.Built 4.065017e-03 3.719088e-03 3.489489e-03 3.345907e-03
## Total.Bsmt.SF 2.964839e-04 2.541861e-04 2.214859e-04 1.962373e-04
## Bsmt.Full.Bath 9.354025e-02 8.508995e-02 7.949523e-02 7.550004e-02
## Fireplaces 1.118688e-01 9.011812e-02 7.309340e-02 5.953456e-02
## Kitchen.AbvGr -1.318404e-01 -1.263859e-01 -1.219982e-01 -1.185139e-01
## Garage.Area 4.961112e-04 4.097340e-04 3.418186e-04 2.878227e-04
## 9Xs 10Xs
## log(area) 4.337362e-01 4.205259e-01
## Lot.Area 2.741684e-06 2.595790e-06
## Overall.Qual 8.864663e-02 7.592458e-02
## Overall.Cond 5.588846e-02 5.830273e-02
## Year.Built 3.266995e-03 3.237363e-03
## Total.Bsmt.SF 1.767964e-04 1.619250e-04
## Bsmt.Full.Bath 7.237503e-02 6.969235e-02
## Fireplaces 4.862728e-02 3.981369e-02
## Kitchen.AbvGr -1.158975e-01 -1.141897e-01
## Garage.Area 2.442117e-04 2.082200e-04
##
##
## Confidence interval information ( 1000 bootstrap replicates, bty= perc ):
## Relative Contributions with confidence intervals:
##
## Lower Upper
## percentage 0.95 0.95 0.95
## log(area).lmg 0.2265 AB________ 0.2035 0.2443
## Lot.Area.lmg 0.0192 ______GHI_ 0.0153 0.0390
## Overall.Qual.lmg 0.2427 AB________ 0.2221 0.2609
## Overall.Cond.lmg 0.0168 _______HI_ 0.0127 0.0241
## Year.Built.lmg 0.1280 __CDE_____ 0.1097 0.1475
## Total.Bsmt.SF.lmg 0.1345 __CDE_____ 0.1153 0.1516
## Bsmt.Full.Bath.lmg 0.0311 ______GH__ 0.0220 0.0424
## Fireplaces.lmg 0.0773 _____F____ 0.0655 0.0897
## Kitchen.AbvGr.lmg 0.0074 _________J 0.0038 0.0128
## Garage.Area.lmg 0.1163 __CDE_____ 0.0927 0.1383
##
## log(area).last 0.3287 A_________ 0.2665 0.3804
## Lot.Area.last 0.0234 _____FGHIJ 0.0163 0.0458
## Overall.Qual.last 0.1479 _BCD______ 0.1077 0.1959
## Overall.Cond.last 0.1258 __CDE_____ 0.0902 0.1684
## Year.Built.last 0.1675 _BCD______ 0.1267 0.2134
## Total.Bsmt.SF.last 0.0911 ___DE_____ 0.0601 0.1236
## Bsmt.Full.Bath.last 0.0404 _____FGH__ 0.0240 0.0601
## Fireplaces.last 0.0178 _______HIJ 0.0080 0.0311
## Kitchen.AbvGr.last 0.0161 ______GHIJ 0.0042 0.0329
## Garage.Area.last 0.0413 _____FGHI_ 0.0195 0.0634
##
## log(area).first 0.1963 _B________ 0.1800 0.2105
## Lot.Area.first 0.0201 ______GH__ 0.0156 0.0431
## Overall.Qual.first 0.2308 A_________ 0.2151 0.2447
## Overall.Cond.first 0.0018 ________IJ 0.0000 0.0088
## Year.Built.first 0.1264 ___DE_____ 0.1094 0.1422
## Total.Bsmt.SF.first 0.1513 __CD______ 0.1352 0.1659
## Bsmt.Full.Bath.first 0.0343 ______GH__ 0.0222 0.0484
## Fireplaces.first 0.0964 _____F____ 0.0830 0.1098
## Kitchen.AbvGr.first 0.0028 ________IJ 0.0004 0.0080
## Garage.Area.first 0.1399 __CDE_____ 0.1173 0.1591
##
## log(area).pratt 0.3068 A_________ 0.2680 0.3407
## Lot.Area.pratt 0.0187 _____FGH__ 0.0147 0.0399
## Overall.Qual.pratt 0.2401 _B________ 0.2040 0.2775
## Overall.Cond.pratt -0.0135 _________J -0.0290 0.0025
## Year.Built.pratt 0.1657 __C_______ 0.1371 0.1992
## Total.Bsmt.SF.pratt 0.1241 ___D______ 0.0962 0.1483
## Bsmt.Full.Bath.pratt 0.0331 _____FGH__ 0.0225 0.0445
## Fireplaces.pratt 0.0402 _____FGH__ 0.0262 0.0535
## Kitchen.AbvGr.pratt 0.0058 ________I_ 0.0014 0.0112
## Garage.Area.pratt 0.0790 ____E_____ 0.0528 0.1045
##
## Letters indicate the ranks covered by bootstrap CIs.
## (Rank bootstrap confidence intervals always obtained by percentile method)
## CAUTION: Bootstrap confidence intervals can be somewhat liberal.
##
##
## Differences between Relative Contributions:
##
## Lower Upper
## difference 0.95 0.95 0.95
## log(area)-Lot.Area.lmg 0.2074 * 0.1770 0.2249
## log(area)-Overall.Qual.lmg -0.0162 -0.0464 0.0149
## log(area)-Overall.Cond.lmg 0.2097 * 0.1837 0.2278
## log(area)-Year.Built.lmg 0.0985 * 0.0609 0.1287
## log(area)-Total.Bsmt.SF.lmg 0.0920 * 0.0614 0.1204
## log(area)-Bsmt.Full.Bath.lmg 0.1954 * 0.1679 0.2185
## log(area)-Fireplaces.lmg 0.1492 * 0.1236 0.1708
## log(area)-Kitchen.AbvGr.lmg 0.2191 * 0.1948 0.2367
## log(area)-Garage.Area.lmg 0.1102 * 0.0765 0.1442
## Lot.Area-Overall.Qual.lmg -0.2236 * -0.2422 -0.1943
## Lot.Area-Overall.Cond.lmg 0.0023 -0.0055 0.0222
## Lot.Area-Year.Built.lmg -0.1089 * -0.1292 -0.0821
## Lot.Area-Total.Bsmt.SF.lmg -0.1154 * -0.1323 -0.0868
## Lot.Area-Bsmt.Full.Bath.lmg -0.0119 -0.0229 0.0108
## Lot.Area-Fireplaces.lmg -0.0582 * -0.0710 -0.0327
## Lot.Area-Kitchen.AbvGr.lmg 0.0118 * 0.0056 0.0316
## Lot.Area-Garage.Area.lmg -0.0972 * -0.1168 -0.0666
## Overall.Qual-Overall.Cond.lmg 0.2259 * 0.2046 0.2435
## Overall.Qual-Year.Built.lmg 0.1147 * 0.0871 0.1404
## Overall.Qual-Total.Bsmt.SF.lmg 0.1082 * 0.0793 0.1398
## Overall.Qual-Bsmt.Full.Bath.lmg 0.2116 * 0.1878 0.2333
## Overall.Qual-Fireplaces.lmg 0.1654 * 0.1412 0.1899
## Overall.Qual-Kitchen.AbvGr.lmg 0.2353 * 0.2145 0.2546
## Overall.Qual-Garage.Area.lmg 0.1264 * 0.0930 0.1609
## Overall.Cond-Year.Built.lmg -0.1112 * -0.1303 -0.0919
## Overall.Cond-Total.Bsmt.SF.lmg -0.1177 * -0.1347 -0.0963
## Overall.Cond-Bsmt.Full.Bath.lmg -0.0143 * -0.0266 -0.0024
## Overall.Cond-Fireplaces.lmg -0.0605 * -0.0722 -0.0470
## Overall.Cond-Kitchen.AbvGr.lmg 0.0094 * 0.0028 0.0175
## Overall.Cond-Garage.Area.lmg -0.0995 * -0.1222 -0.0732
## Year.Built-Total.Bsmt.SF.lmg -0.0065 -0.0325 0.0243
## Year.Built-Bsmt.Full.Bath.lmg 0.0969 * 0.0765 0.1195
## Year.Built-Fireplaces.lmg 0.0507 * 0.0266 0.0759
## Year.Built-Kitchen.AbvGr.lmg 0.1206 * 0.1015 0.1411
## Year.Built-Garage.Area.lmg 0.0117 -0.0214 0.0450
## Total.Bsmt.SF-Bsmt.Full.Bath.lmg 0.1034 * 0.0827 0.1222
## Total.Bsmt.SF-Fireplaces.lmg 0.0572 * 0.0354 0.0793
## Total.Bsmt.SF-Kitchen.AbvGr.lmg 0.1271 * 0.1070 0.1451
## Total.Bsmt.SF-Garage.Area.lmg 0.0182 -0.0090 0.0474
## Bsmt.Full.Bath-Fireplaces.lmg -0.0462 * -0.0613 -0.0297
## Bsmt.Full.Bath-Kitchen.AbvGr.lmg 0.0237 * 0.0130 0.0347
## Bsmt.Full.Bath-Garage.Area.lmg -0.0852 * -0.1108 -0.0570
## Fireplaces-Kitchen.AbvGr.lmg 0.0699 * 0.0565 0.0825
## Fireplaces-Garage.Area.lmg -0.0390 * -0.0641 -0.0124
## Kitchen.AbvGr-Garage.Area.lmg -0.1089 * -0.1301 -0.0847
##
## log(area)-Lot.Area.last 0.3053 * 0.2290 0.3567
## log(area)-Overall.Qual.last 0.1808 * 0.0869 0.2531
## log(area)-Overall.Cond.last 0.2029 * 0.1137 0.2749
## log(area)-Year.Built.last 0.1612 * 0.0642 0.2418
## log(area)-Total.Bsmt.SF.last 0.2376 * 0.1631 0.2979
## log(area)-Bsmt.Full.Bath.last 0.2883 * 0.2268 0.3426
## log(area)-Fireplaces.last 0.3109 * 0.2447 0.3642
## log(area)-Kitchen.AbvGr.last 0.3126 * 0.2534 0.3650
## log(area)-Garage.Area.last 0.2874 * 0.2233 0.3446
## Lot.Area-Overall.Qual.last -0.1245 * -0.1673 -0.0834
## Lot.Area-Overall.Cond.last -0.1025 * -0.1433 -0.0602
## Lot.Area-Year.Built.last -0.1441 * -0.1850 -0.1001
## Lot.Area-Total.Bsmt.SF.last -0.0677 * -0.1000 -0.0252
## Lot.Area-Bsmt.Full.Bath.last -0.0170 -0.0356 0.0102
## Lot.Area-Fireplaces.last 0.0055 -0.0074 0.0320
## Lot.Area-Kitchen.AbvGr.last 0.0072 -0.0102 0.0346
## Lot.Area-Garage.Area.last -0.0180 -0.0387 0.0199
## Overall.Qual-Overall.Cond.last 0.0220 -0.0451 0.0831
## Overall.Qual-Year.Built.last -0.0196 -0.0876 0.0484
## Overall.Qual-Total.Bsmt.SF.last 0.0568 0.0000 0.1189
## Overall.Qual-Bsmt.Full.Bath.last 0.1075 * 0.0668 0.1579
## Overall.Qual-Fireplaces.last 0.1300 * 0.0847 0.1799
## Overall.Qual-Kitchen.AbvGr.last 0.1317 * 0.0862 0.1832
## Overall.Qual-Garage.Area.last 0.1066 * 0.0607 0.1596
## Overall.Cond-Year.Built.last -0.0416 -0.0924 0.0083
## Overall.Cond-Total.Bsmt.SF.last 0.0347 -0.0126 0.0900
## Overall.Cond-Bsmt.Full.Bath.last 0.0855 * 0.0401 0.1363
## Overall.Cond-Fireplaces.last 0.1080 * 0.0725 0.1516
## Overall.Cond-Kitchen.AbvGr.last 0.1097 * 0.0677 0.1579
## Overall.Cond-Garage.Area.last 0.0845 * 0.0436 0.1359
## Year.Built-Total.Bsmt.SF.last 0.0764 * 0.0213 0.1371
## Year.Built-Bsmt.Full.Bath.last 0.1271 * 0.0775 0.1790
## Year.Built-Fireplaces.last 0.1496 * 0.1085 0.1946
## Year.Built-Kitchen.AbvGr.last 0.1513 * 0.1036 0.2021
## Year.Built-Garage.Area.last 0.1262 * 0.0747 0.1823
## Total.Bsmt.SF-Bsmt.Full.Bath.last 0.0508 * 0.0138 0.0921
## Total.Bsmt.SF-Fireplaces.last 0.0733 * 0.0431 0.1068
## Total.Bsmt.SF-Kitchen.AbvGr.last 0.0750 * 0.0431 0.1110
## Total.Bsmt.SF-Garage.Area.last 0.0498 * 0.0154 0.0878
## Bsmt.Full.Bath-Fireplaces.last 0.0225 * 0.0008 0.0436
## Bsmt.Full.Bath-Kitchen.AbvGr.last 0.0242 * 0.0017 0.0462
## Bsmt.Full.Bath-Garage.Area.last -0.0010 -0.0302 0.0277
## Fireplaces-Kitchen.AbvGr.last 0.0017 -0.0180 0.0190
## Fireplaces-Garage.Area.last -0.0235 -0.0474 0.0003
## Kitchen.AbvGr-Garage.Area.last -0.0252 -0.0512 0.0027
##
## log(area)-Lot.Area.first 0.1762 * 0.1469 0.1906
## log(area)-Overall.Qual.first -0.0344 * -0.0543 -0.0149
## log(area)-Overall.Cond.first 0.1945 * 0.1754 0.2096
## log(area)-Year.Built.first 0.0699 * 0.0436 0.0941
## log(area)-Total.Bsmt.SF.first 0.0450 * 0.0213 0.0687
## log(area)-Bsmt.Full.Bath.first 0.1621 * 0.1367 0.1828
## log(area)-Fireplaces.first 0.1000 * 0.0798 0.1181
## log(area)-Kitchen.AbvGr.first 0.1935 * 0.1748 0.2076
## log(area)-Garage.Area.first 0.0564 * 0.0292 0.0860
## Lot.Area-Overall.Qual.first -0.2106 * -0.2262 -0.1794
## Lot.Area-Overall.Cond.first 0.0183 * 0.0109 0.0407
## Lot.Area-Year.Built.first -0.1063 * -0.1241 -0.0772
## Lot.Area-Total.Bsmt.SF.first -0.1312 * -0.1458 -0.1022
## Lot.Area-Bsmt.Full.Bath.first -0.0142 -0.0277 0.0113
## Lot.Area-Fireplaces.first -0.0763 * -0.0905 -0.0481
## Lot.Area-Kitchen.AbvGr.first 0.0173 * 0.0104 0.0405
## Lot.Area-Garage.Area.first -0.1198 * -0.1374 -0.0916
## Overall.Qual-Overall.Cond.first 0.2290 * 0.2110 0.2430
## Overall.Qual-Year.Built.first 0.1044 * 0.0828 0.1252
## Overall.Qual-Total.Bsmt.SF.first 0.0795 * 0.0576 0.1028
## Overall.Qual-Bsmt.Full.Bath.first 0.1965 * 0.1741 0.2157
## Overall.Qual-Fireplaces.first 0.1344 * 0.1134 0.1536
## Overall.Qual-Kitchen.AbvGr.first 0.2279 * 0.2115 0.2420
## Overall.Qual-Garage.Area.first 0.0909 * 0.0636 0.1206
## Overall.Cond-Year.Built.first -0.1246 * -0.1405 -0.1081
## Overall.Cond-Total.Bsmt.SF.first -0.1495 * -0.1639 -0.1317
## Overall.Cond-Bsmt.Full.Bath.first -0.0325 * -0.0461 -0.0199
## Overall.Cond-Fireplaces.first -0.0946 * -0.1088 -0.0786
## Overall.Cond-Kitchen.AbvGr.first -0.0010 -0.0062 0.0056
## Overall.Cond-Garage.Area.first -0.1381 * -0.1568 -0.1144
## Year.Built-Total.Bsmt.SF.first -0.0249 -0.0484 0.0009
## Year.Built-Bsmt.Full.Bath.first 0.0921 * 0.0704 0.1121
## Year.Built-Fireplaces.first 0.0300 * 0.0069 0.0543
## Year.Built-Kitchen.AbvGr.first 0.1236 * 0.1062 0.1399
## Year.Built-Garage.Area.first -0.0135 -0.0416 0.0177
## Total.Bsmt.SF-Bsmt.Full.Bath.first 0.1170 * 0.0969 0.1346
## Total.Bsmt.SF-Fireplaces.first 0.0549 * 0.0320 0.0748
## Total.Bsmt.SF-Kitchen.AbvGr.first 0.1485 * 0.1316 0.1628
## Total.Bsmt.SF-Garage.Area.first 0.0114 -0.0154 0.0390
## Bsmt.Full.Bath-Fireplaces.first -0.0621 * -0.0798 -0.0430
## Bsmt.Full.Bath-Kitchen.AbvGr.first 0.0315 * 0.0187 0.0451
## Bsmt.Full.Bath-Garage.Area.first -0.1056 * -0.1308 -0.0765
## Fireplaces-Kitchen.AbvGr.first 0.0936 * 0.0794 0.1073
## Fireplaces-Garage.Area.first -0.0435 * -0.0684 -0.0159
## Kitchen.AbvGr-Garage.Area.first -0.1371 * -0.1550 -0.1134
##
## log(area)-Lot.Area.pratt 0.2881 * 0.2407 0.3218
## log(area)-Overall.Qual.pratt 0.0667 * 0.0035 0.1270
## log(area)-Overall.Cond.pratt 0.3203 * 0.2773 0.3551
## log(area)-Year.Built.pratt 0.1411 * 0.0822 0.1885
## log(area)-Total.Bsmt.SF.pratt 0.1827 * 0.1346 0.2254
## log(area)-Bsmt.Full.Bath.pratt 0.2738 * 0.2334 0.3078
## log(area)-Fireplaces.pratt 0.2667 * 0.2248 0.3040
## log(area)-Kitchen.AbvGr.pratt 0.3011 * 0.2622 0.3352
## log(area)-Garage.Area.pratt 0.2279 * 0.1788 0.2741
## Lot.Area-Overall.Qual.pratt -0.2214 * -0.2562 -0.1828
## Lot.Area-Overall.Cond.pratt 0.0322 * 0.0170 0.0585
## Lot.Area-Year.Built.pratt -0.1470 * -0.1790 -0.1143
## Lot.Area-Total.Bsmt.SF.pratt -0.1054 * -0.1301 -0.0673
## Lot.Area-Bsmt.Full.Bath.pratt -0.0144 -0.0255 0.0113
## Lot.Area-Fireplaces.pratt -0.0215 -0.0346 0.0043
## Lot.Area-Kitchen.AbvGr.pratt 0.0129 * 0.0065 0.0353
## Lot.Area-Garage.Area.pratt -0.0602 * -0.0831 -0.0240
## Overall.Qual-Overall.Cond.pratt 0.2536 * 0.2123 0.2945
## Overall.Qual-Year.Built.pratt 0.0744 * 0.0192 0.1274
## Overall.Qual-Total.Bsmt.SF.pratt 0.1160 * 0.0661 0.1708
## Overall.Qual-Bsmt.Full.Bath.pratt 0.2070 * 0.1683 0.2483
## Overall.Qual-Fireplaces.pratt 0.1999 * 0.1583 0.2458
## Overall.Qual-Kitchen.AbvGr.pratt 0.2343 * 0.1971 0.2735
## Overall.Qual-Garage.Area.pratt 0.1612 * 0.1148 0.2139
## Overall.Cond-Year.Built.pratt -0.1792 * -0.2205 -0.1447
## Overall.Cond-Total.Bsmt.SF.pratt -0.1376 * -0.1706 -0.1061
## Overall.Cond-Bsmt.Full.Bath.pratt -0.0466 * -0.0672 -0.0265
## Overall.Cond-Fireplaces.pratt -0.0537 * -0.0750 -0.0334
## Overall.Cond-Kitchen.AbvGr.pratt -0.0193 * -0.0363 -0.0027
## Overall.Cond-Garage.Area.pratt -0.0925 * -0.1213 -0.0602
## Year.Built-Total.Bsmt.SF.pratt 0.0416 * 0.0044 0.0894
## Year.Built-Bsmt.Full.Bath.pratt 0.1326 * 0.1033 0.1677
## Year.Built-Fireplaces.pratt 0.1255 * 0.0954 0.1619
## Year.Built-Kitchen.AbvGr.pratt 0.1599 * 0.1300 0.1943
## Year.Built-Garage.Area.pratt 0.0867 * 0.0441 0.1340
## Total.Bsmt.SF-Bsmt.Full.Bath.pratt 0.0910 * 0.0632 0.1199
## Total.Bsmt.SF-Fireplaces.pratt 0.0840 * 0.0545 0.1126
## Total.Bsmt.SF-Kitchen.AbvGr.pratt 0.1183 * 0.0909 0.1443
## Total.Bsmt.SF-Garage.Area.pratt 0.0452 * 0.0119 0.0822
## Bsmt.Full.Bath-Fireplaces.pratt -0.0071 -0.0254 0.0112
## Bsmt.Full.Bath-Kitchen.AbvGr.pratt 0.0273 * 0.0156 0.0391
## Bsmt.Full.Bath-Garage.Area.pratt -0.0459 * -0.0757 -0.0167
## Fireplaces-Kitchen.AbvGr.pratt 0.0344 * 0.0195 0.0490
## Fireplaces-Garage.Area.pratt -0.0388 * -0.0679 -0.0112
## Kitchen.AbvGr-Garage.Area.pratt -0.0732 * -0.0969 -0.0468
##
## * indicates that CI for difference does not include 0.
## CAUTION: Bootstrap confidence intervals can be somewhat liberal.plot(booteval.relimp(boot,sort=TRUE)) # plot result 
##### Broomified Model. Handling data in better way.
## term estimate std.error statistic p.value
## 1 (Intercept) -2.814172095 0.5267174499 -5.342850 1.185549e-07
## 2 log(area + 1) 0.541480676 0.0275913326 19.625028 1.261812e-70
## 3 log(Lot.Area) 0.139920234 0.0093701391 14.932567 8.640525e-45
## 4 Bedroom.AbvGr -0.041190547 0.0073096797 -5.635069 2.404277e-08
## 5 Full.Bath -0.038618083 0.0126445595 -3.054126 2.329979e-03
## 6 Half.Bath -0.043808010 0.0106725406 -4.104741 4.451606e-05
## 7 Year.Built 0.004485599 0.0002276678 19.702390 4.472342e-71
## 8 Overall.Cond 0.059730326 0.0043591344 13.702336 1.222129e-38
## 9 Overall.Qual 0.093104653 0.0052996283 17.568148 6.621479e-59
## 10 Garage.Cars 0.049854403 0.0081816516 6.093440 1.696987e-09##
## Call:
## lm(formula = log(price) ~ log(area + 1) + log(Lot.Area) + Bedroom.AbvGr +
## Full.Bath + Half.Bath + Year.Built + Overall.Cond + Overall.Qual +
## Garage.Cars, data = train)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.85645 -0.07301 0.00168 0.07470 0.47083
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -2.8141721 0.5267174 -5.343 1.19e-07 ***
## log(area + 1) 0.5414807 0.0275913 19.625 < 2e-16 ***
## log(Lot.Area) 0.1399202 0.0093701 14.933 < 2e-16 ***
## Bedroom.AbvGr -0.0411905 0.0073097 -5.635 2.40e-08 ***
## Full.Bath -0.0386181 0.0126446 -3.054 0.00233 **
## Half.Bath -0.0438080 0.0106725 -4.105 4.45e-05 ***
## Year.Built 0.0044856 0.0002277 19.702 < 2e-16 ***
## Overall.Cond 0.0597303 0.0043591 13.702 < 2e-16 ***
## Overall.Qual 0.0931047 0.0052996 17.568 < 2e-16 ***
## Garage.Cars 0.0498544 0.0081817 6.093 1.70e-09 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.125 on 822 degrees of freedom
## Multiple R-squared: 0.8914, Adjusted R-squared: 0.8902
## F-statistic: 749.8 on 9 and 822 DF, p-value: < 2.2e-16## log.price. log.area...1. log.Lot.Area. Bedroom.AbvGr Full.Bath Half.Bath
## 1 11.74404 6.753438 8.973351 2 1 0
## 2 11.84582 6.956545 8.351139 2 2 0
## 3 11.73527 6.909753 8.709465 2 1 0
## 4 11.64395 6.946976 9.005282 2 1 0
## 5 12.33271 7.418181 9.035987 3 2 1
## 6 12.19854 7.561642 8.895767 4 3 0
## Year.Built Overall.Cond Overall.Qual Garage.Cars .fitted .se.fit
## 1 1939 6 6 2 11.69153 0.01335293
## 2 1984 5 5 1 11.67500 0.01306882
## 3 1930 9 5 1 11.73511 0.01490820
## 4 1900 8 4 1 11.50926 0.01453308
## 5 2001 6 8 2 12.40094 0.01052895
## 6 2003 5 7 2 12.27914 0.01566601
## .resid .hat .sigma .cooksd .std.resid
## 1 0.0525041107 0.011414005 0.1250474 2.061014e-04 0.422501864
## 2 0.1708236845 0.010933463 0.1249172 2.087796e-03 1.374288397
## 3 0.0001553784 0.014227736 0.1250610 2.262816e-09 0.001252117
## 4 0.1346971617 0.013520733 0.1249714 1.613713e-03 1.085068142
## 5 -0.0682369920 0.007096677 0.1250381 2.145685e-04 -0.547909639
## 6 -0.0805951567 0.015710930 0.1250288 6.743099e-04 -0.649965286## log.price. log.area...1. log.Lot.Area. Bedroom.AbvGr Full.Bath Half.Bath
## 1 11.74404 6.753438 8.973351 2 1 0
## 2 11.84582 6.956545 8.351139 2 2 0
## 3 11.73527 6.909753 8.709465 2 1 0
## 4 11.64395 6.946976 9.005282 2 1 0
## 5 12.33271 7.418181 9.035987 3 2 1
## 6 12.19854 7.561642 8.895767 4 3 0
## Year.Built Overall.Cond Overall.Qual Garage.Cars .fitted .se.fit
## 1 1939 6 6 2 11.69153 0.01335293
## 2 1984 5 5 1 11.67500 0.01306882
## 3 1930 9 5 1 11.73511 0.01490820
## 4 1900 8 4 1 11.50926 0.01453308
## 5 2001 6 8 2 12.40094 0.01052895
## 6 2003 5 7 2 12.27914 0.01566601
## .resid .hat .sigma .cooksd .std.resid
## 1 0.0525041107 0.011414005 0.1250474 2.061014e-04 0.422501864
## 2 0.1708236845 0.010933463 0.1249172 2.087796e-03 1.374288397
## 3 0.0001553784 0.014227736 0.1250610 2.262816e-09 0.001252117
## 4 0.1346971617 0.013520733 0.1249714 1.613713e-03 1.085068142
## 5 -0.0682369920 0.007096677 0.1250381 2.145685e-04 -0.547909639
## 6 -0.0805951567 0.015710930 0.1250288 6.743099e-04 -0.649965286## r.squared adj.r.squared sigma statistic p.value df logLik
## 1 0.8914218 0.890233 0.1249849 749.8423 0 10 554.6695
## AIC BIC deviance df.residual
## 1 -1087.339 -1035.377 12.84064 822Instead of viewing the coefficients, we might be interested in the fitted values and residuals for each of the original points in the regression.
0.0.0.6.4 Stepwise regression-Discussion
In stepwise regression, we pass the full model to step function. It iteratively searches the full scope of variables in backwards directions by default if scope is not given. It performs multiple iteractions by droping one X variable at a time. In each iteration, multiple models are built by dropping each of the X variables at a time. The AIC of the models is also computed and the model that yields the lowest AIC is retained for the next iteration.
In simpler terms, the variable that gives the minimum AIC when dropped, is dropped for the next iteration, until there is no significant drop in AIC is noticed.
The code below shows how stepwise regression can be done. We are providing the full model here, so a backwards stepwise will be performed, which means, variables will only be removed. In forward stepwise, variables will be progressively added.
model.AIC <- stepAIC(Initial.model, k = 2)## Start: AIC=-3450.45
## log(price) ~ log(area + 1) + log(Lot.Area) + Bedroom.AbvGr +
## Full.Bath + Half.Bath + Year.Built + Overall.Cond + Overall.Qual +
## Garage.Cars
##
## Df Sum of Sq RSS AIC
## <none> 12.841 -3450.5
## - Full.Bath 1 0.1457 12.986 -3443.1
## - Half.Bath 1 0.2632 13.104 -3435.6
## - Bedroom.AbvGr 1 0.4960 13.337 -3420.9
## - Garage.Cars 1 0.5800 13.421 -3415.7
## - Overall.Cond 1 2.9329 15.774 -3281.3
## - log(Lot.Area) 1 3.4832 16.324 -3252.8
## - Overall.Qual 1 4.8213 17.662 -3187.2
## - log(area + 1) 1 6.0164 18.857 -3132.7
## - Year.Built 1 6.0639 18.905 -3130.6model.BIC <- stepAIC(Initial.model, k =log(nrow(train)))## Start: AIC=-3403.21
## log(price) ~ log(area + 1) + log(Lot.Area) + Bedroom.AbvGr +
## Full.Bath + Half.Bath + Year.Built + Overall.Cond + Overall.Qual +
## Garage.Cars
##
## Df Sum of Sq RSS AIC
## <none> 12.841 -3403.2
## - Full.Bath 1 0.1457 12.986 -3400.6
## - Half.Bath 1 0.2632 13.104 -3393.1
## - Bedroom.AbvGr 1 0.4960 13.337 -3378.4
## - Garage.Cars 1 0.5800 13.421 -3373.2
## - Overall.Cond 1 2.9329 15.774 -3238.8
## - log(Lot.Area) 1 3.4832 16.324 -3210.2
## - Overall.Qual 1 4.8213 17.662 -3144.7
## - log(area + 1) 1 6.0164 18.857 -3090.2
## - Year.Built 1 6.0639 18.905 -3088.1BIC(model.AIC)## [1] -1035.3770.0.0.6.5 RMSE comparison
predict.AIC <- exp(predict(model.AIC, train))
resid.AIC <- train$price - predict.AIC
rmse.AIC <- sqrt(mean(resid.AIC^2))
rmse.AIC## [1] 23191.25predict.BIC <- exp(predict(model.BIC, train))
resid.BIC <- ames_train$price - predict.BIC
rmse.BIC <- sqrt(mean(resid.BIC^2))
rmse.BIC## [1] 23191.25difference= rmse.BIC -rmse.AIC
difference## [1] 0Calculate proportion of observations that fall within prediction intervals for model.AIC and model.BIC and compare.
0.0.0.6.6 Proportion and Intervals-Coverage Probabilities
predict.AIC <- exp(predict(model.AIC, train, interval = "prediction"))
coverage.prob.AIC <- mean(train$price > predict.AIC[,"lwr"] &
train$price < predict.AIC[,"upr"])
coverage.prob.AIC## [1] 0.9471154predict.BIC <- exp(predict(model.BIC, train, interval = "prediction"))
coverage.prob.BIC <- mean(train$price > predict.BIC[,"lwr"] &
train$price < predict.BIC[,"upr"])
coverage.prob.BIC## [1] 0.9471154model.bas <- bas.lm(log(price) ~ log(area+1) +log(Lot.Area)+ Bedroom.AbvGr+
Full.Bath + Half.Bath + Year.Built+Overall.Cond+ Overall.Qual+Garage.Cars,
data = train, prior = "AIC", modelprior=uniform())
model.bas##
## Call:
## bas.lm(formula = log(price) ~ log(area + 1) + log(Lot.Area) + Bedroom.AbvGr + Full.Bath + Half.Bath + Year.Built + Overall.Cond + Overall.Qual + Garage.Cars, data = train, prior = "AIC", modelprior = uniform())
##
##
## Marginal Posterior Inclusion Probabilities:
## Intercept log(area + 1) log(Lot.Area) Bedroom.AbvGr Full.Bath
## 1.0000 1.0000 1.0000 1.0000 0.9755
## Half.Bath Year.Built Overall.Cond Overall.Qual Garage.Cars
## 0.9992 1.0000 1.0000 1.0000 1.0000summary(model.bas)## P(B != 0 | Y) model 1 model 2 model 3
## Intercept 1.0000000 1.0000 1.000000e+00 1.000000e+00
## log(area + 1) 1.0000000 1.0000 1.000000e+00 1.000000e+00
## log(Lot.Area) 1.0000000 1.0000 1.000000e+00 1.000000e+00
## Bedroom.AbvGr 0.9999996 1.0000 1.000000e+00 1.000000e+00
## Full.Bath 0.9754846 1.0000 0.000000e+00 1.000000e+00
## Half.Bath 0.9991608 1.0000 1.000000e+00 0.000000e+00
## Year.Built 1.0000000 1.0000 1.000000e+00 1.000000e+00
## Overall.Cond 1.0000000 1.0000 1.000000e+00 1.000000e+00
## Overall.Qual 1.0000000 1.0000 1.000000e+00 1.000000e+00
## Garage.Cars 1.0000000 1.0000 1.000000e+00 1.000000e+00
## BF NA 1.0000 2.487233e-02 5.868622e-04
## PostProbs NA 0.9749 2.420000e-02 6.000000e-04
## R2 NA 0.8914 8.902000e-01 8.892000e-01
## dim NA 10.0000 9.000000e+00 9.000000e+00
## logmarg NA -1071.8879 -1.075582e+03 -1.079329e+03
## model 4 model 5
## Intercept 1.000000e+00 1.000000e+00
## log(area + 1) 1.000000e+00 1.000000e+00
## log(Lot.Area) 1.000000e+00 1.000000e+00
## Bedroom.AbvGr 1.000000e+00 0.000000e+00
## Full.Bath 0.000000e+00 1.000000e+00
## Half.Bath 0.000000e+00 1.000000e+00
## Year.Built 1.000000e+00 1.000000e+00
## Overall.Cond 1.000000e+00 1.000000e+00
## Overall.Qual 1.000000e+00 1.000000e+00
## Garage.Cars 1.000000e+00 1.000000e+00
## BF 2.738992e-04 3.859634e-07
## PostProbs 3.000000e-04 0.000000e+00
## R2 8.887000e-01 8.872000e-01
## dim 8.000000e+00 9.000000e+00
## logmarg -1.080091e+03 -1.086655e+03image(model.bas,rotate=TRUE)
final_model <- bas.lm(data=na.omit(train),log(price) ~ log(area+1) +log(Lot.Area)+ Bedroom.AbvGr+
Full.Bath + Half.Bath + Year.Built+Overall.Cond+ Overall.Qual+Garage.Cars,
modelprior = uniform(),
prior="ZS-null",
method = "MCMC")
final_model##
## Call:
## bas.lm(formula = log(price) ~ log(area + 1) + log(Lot.Area) + Bedroom.AbvGr + Full.Bath + Half.Bath + Year.Built + Overall.Cond + Overall.Qual + Garage.Cars, data = na.omit(train), prior = "ZS-null", modelprior = uniform(), method = "MCMC")
##
##
## Marginal Posterior Inclusion Probabilities:
## Intercept log(area + 1) log(Lot.Area) Bedroom.AbvGr Full.Bath
## 1.0000 0.9992 0.9963 0.9993 0.7814
## Half.Bath Year.Built Overall.Cond Overall.Qual Garage.Cars
## 0.9622 0.9984 0.9986 0.9998 0.9974par(mfrow=c(1,2))
plot(final_model)
coef.final <- coef(final_model)
coef.final##
## Marginal Posterior Summaries of Coefficients:
##
## Using BMA
##
## Based on the top 15 models
## post mean post SD post p(B != 0)
## Intercept 11.9927955 0.0043470 1.0000000
## log(area + 1) 0.5311945 0.0357287 0.9992188
## log(Lot.Area) 0.1403280 0.0128688 0.9962891
## Bedroom.AbvGr -0.0418327 0.0076243 0.9993164
## Full.Bath -0.0301075 0.0194711 0.7814453
## Half.Bath -0.0402160 0.0139676 0.9622070
## Year.Built 0.0044184 0.0003076 0.9984375
## Overall.Cond 0.0597379 0.0049655 0.9986328
## Overall.Qual 0.0931287 0.0066196 0.9998047
## Garage.Cars 0.0494525 0.0086311 0.99736330.0.0.7 Section 2.3 Initial Model Residuals
Because the aim is to reduce the prediction error so for a good prediction the residual should be minimized.
Comparison has to carried out on lm model(model.full,model.AIC and model.BIC). Model residuals analysis is the most important measure to find the goodness of fit.The residuals should not be correlated with another variable.Adjacent residuals should not be autocorrelated.They should have consistency.These values cause outliers. There have to be very little outliers.The residuals should have a normal distribution. Negative values indicate leakage information. Missing values and inadequate subset could be possibly casusing curvature.
If the distribution becomes better with bayesian method or not. The RMSE for full model and AIC is same.The RMSE for BIC model is higher. Normality and Homoscedicity is also plotted.
Durbin Watson test is to be performed to test the residual correlations.
0.0.0.7.1 Residual Plots
library(car)
crPlots(Initial.model)
plot(Initial.model)
plot(model.AIC)
plot(model.BIC)
0.0.0.7.2 Normality test of residues
plot(resid(model.AIC),main="AIC Histogram of Normality",xlab='standard residuals',ylab='Frequency')
plot(resid(model.BIC),main="BIC Histogram of Normality",xlab='standard residuals',ylab='Frequency')
0.0.0.7.3 Colinearity(multiple relationship between variables)
vif(model.BIC)## log(area + 1) log(Lot.Area) Bedroom.AbvGr Full.Bath Half.Bath
## 4.4622 1.3012 1.8491 2.4563 1.4966
## Year.Built Overall.Cond Overall.Qual Garage.Cars
## 2.3259 1.2312 2.6356 1.9425vif(model.AIC)## log(area + 1) log(Lot.Area) Bedroom.AbvGr Full.Bath Half.Bath
## 4.4622 1.3012 1.8491 2.4563 1.4966
## Year.Built Overall.Cond Overall.Qual Garage.Cars
## 2.3259 1.2312 2.6356 1.94250.0.0.7.4 Homoscedicity test of residues
plot(model.AIC,which=1)
plot(model.BIC,which=1) ##### Autocorrelation of residuals
library(car)
library(lmtest)## Loading required package: zoo##
## Attaching package: 'zoo'## The following objects are masked from 'package:base':
##
## as.Date, as.Date.numericdurbinWatsonTest(model.BIC)## lag Autocorrelation D-W Statistic p-value
## 1 0.01718345 1.965107 0.582
## Alternative hypothesis: rho != 0durbinWatsonTest(model.AIC)## lag Autocorrelation D-W Statistic p-value
## 1 0.01718345 1.965107 0.628
## Alternative hypothesis: rho != 0durbinWatsonTest(resid.BIC)## [1] 2.00807durbinWatsonTest(resid.AIC)## [1] 2.00807You can calculate it directly based on the model output. Be specific about the units of your RMSE (depending on whether you transformed your response variable). The value you report will be more meaningful if it is in the original units (dollars).
0.0.0.7.5 Section 2.4 Initial Model RMSE
Initial.model<-lm(log(price)~log(area)+Lot.Area+Overall.Qual+Overall.Cond +Year.Built+Total.Bsmt.SF+ Bsmt.Full.Bath + Fireplaces+Kitchen.AbvGr+
Garage.Area,data=(na.omit(train)))
predict.Initial <- exp(predict(Initial.model, train))
resid.Initial <- train$price - predict.Initial
rmse.Initial<- sqrt(mean(resid.Initial^2))
rmse.Initial## [1] 19788.970.0.0.8 Section 2.5 Overfitting
No model is without short comings. We have to identify those and adapt the model in order to minimize them.This way we can improve the model. This process is repeated a number and critical values are measured and compared till satisfication. Find out if the model is:
- Doing well on training set.
- Poor performance with out-of-sample.
- Compare performance on both in-sample and out-of-sample data sets.
- To do this overfitting dataset
ames_testhas to be compared with ames_train. Here we are going to compare test and train models for overfitting. Use your model from above to generate predictions for the housing prices in the test data set. Accuracy of predicted prices against actual prices. The difference in coverage prbabilities are also compared. The RMSE error is also giving indication for the over/under estimation
0.0.0.9 Section 2.5 Overfitting
0.0.0.9.1 Price Prediction-Coverage Probabilities-Linear-Bayesian
Initial.model<-lm(log(price)~log(area)+Lot.Area+Overall.Qual+Overall.Cond +Year.Built+Total.Bsmt.SF+ Bsmt.Full.Bath + Fireplaces+Kitchen.AbvGr+
Garage.Area,data=(na.omit(test)))0.0.0.9.2 Prediction and Coverage Probabilities(Test dataset)-LM
predict.Initial <- exp(predict(Initial.model,
newdata=test,interval = "prediction"))
coverage.prob.Initial <- mean(test$price > predict.Initial[,"lwr"] &
test$price < predict.Initial[,"upr"])
coverage.prob.Initial## [1] 0.9507995cp_test=coverage.prob.Initial0.0.0.9.3 Prediction and Coverage probability(Train dataset)-LM
## [1] 0.9507212## [1] -7.835415e-05For predicting home prices I used stepwise method for both training and test datasets
0.0.0.9.4 Predicting prices(Train dataset)-Bayesian Model-BIC
model.bic <- stepAIC(Initial.model2,k =log(nrow(train)))## Start: AIC=-3480.94
## log(price) ~ log(Garage.Area + 1) + log(Total.Bsmt.SF + 1) +
## Garage.Cars + log(area) + Full.Bath + Half.Bath + Bedroom.AbvGr +
## Year.Built + log(X1st.Flr.SF) + log(X2nd.Flr.SF + 1) + log(Lot.Area) +
## Central.Air + Overall.Cond + Overall.Qual
##
## Df Sum of Sq RSS AIC
## - Half.Bath 1 0.0013 11.233 -3487.6
## - Full.Bath 1 0.0026 11.235 -3487.5
## - log(X2nd.Flr.SF + 1) 1 0.0078 11.240 -3487.1
## - log(Garage.Area + 1) 1 0.0274 11.260 -3485.6
## - log(X1st.Flr.SF) 1 0.0519 11.284 -3483.8
## <none> 11.232 -3480.9
## - Central.Air 1 0.1748 11.407 -3474.8
## - Garage.Cars 1 0.3460 11.578 -3462.4
## - Bedroom.AbvGr 1 0.4434 11.676 -3455.5
## - log(Total.Bsmt.SF + 1) 1 0.5331 11.765 -3449.1
## - log(area) 1 0.8788 12.111 -3425.0
## - Overall.Cond 1 2.0340 13.266 -3349.2
## - log(Lot.Area) 1 2.1088 13.341 -3344.5
## - Year.Built 1 3.1719 14.404 -3280.7
## - Overall.Qual 1 4.0600 15.292 -3230.9
##
## Step: AIC=-3487.57
## log(price) ~ log(Garage.Area + 1) + log(Total.Bsmt.SF + 1) +
## Garage.Cars + log(area) + Full.Bath + Bedroom.AbvGr + Year.Built +
## log(X1st.Flr.SF) + log(X2nd.Flr.SF + 1) + log(Lot.Area) +
## Central.Air + Overall.Cond + Overall.Qual
##
## Df Sum of Sq RSS AIC
## - Full.Bath 1 0.0049 11.238 -3493.9
## - log(X2nd.Flr.SF + 1) 1 0.0076 11.241 -3493.7
## - log(Garage.Area + 1) 1 0.0288 11.262 -3492.2
## - log(X1st.Flr.SF) 1 0.0507 11.284 -3490.5
## <none> 11.233 -3487.6
## - Central.Air 1 0.1762 11.410 -3481.3
## - Garage.Cars 1 0.3513 11.585 -3468.7
## - Bedroom.AbvGr 1 0.4430 11.677 -3462.1
## - log(Total.Bsmt.SF + 1) 1 0.5340 11.768 -3455.7
## - log(area) 1 0.9626 12.196 -3425.9
## - Overall.Cond 1 2.0348 13.268 -3355.8
## - log(Lot.Area) 1 2.1199 13.353 -3350.5
## - Year.Built 1 3.6904 14.924 -3258.0
## - Overall.Qual 1 4.0643 15.298 -3237.4
##
## Step: AIC=-3493.93
## log(price) ~ log(Garage.Area + 1) + log(Total.Bsmt.SF + 1) +
## Garage.Cars + log(area) + Bedroom.AbvGr + Year.Built + log(X1st.Flr.SF) +
## log(X2nd.Flr.SF + 1) + log(Lot.Area) + Central.Air + Overall.Cond +
## Overall.Qual
##
## Df Sum of Sq RSS AIC
## - log(X2nd.Flr.SF + 1) 1 0.0076 11.246 -3500.1
## - log(Garage.Area + 1) 1 0.0260 11.264 -3498.7
## - log(X1st.Flr.SF) 1 0.0510 11.289 -3496.9
## <none> 11.238 -3493.9
## - Central.Air 1 0.1849 11.423 -3487.1
## - Garage.Cars 1 0.3467 11.585 -3475.4
## - Bedroom.AbvGr 1 0.4635 11.702 -3467.0
## - log(Total.Bsmt.SF + 1) 1 0.5469 11.785 -3461.1
## - log(area) 1 0.9659 12.204 -3432.1
## - Overall.Cond 1 2.0402 13.279 -3361.9
## - log(Lot.Area) 1 2.1379 13.376 -3355.8
## - Year.Built 1 3.9371 15.175 -3250.8
## - Overall.Qual 1 4.0606 15.299 -3244.0
##
## Step: AIC=-3500.09
## log(price) ~ log(Garage.Area + 1) + log(Total.Bsmt.SF + 1) +
## Garage.Cars + log(area) + Bedroom.AbvGr + Year.Built + log(X1st.Flr.SF) +
## log(Lot.Area) + Central.Air + Overall.Cond + Overall.Qual
##
## Df Sum of Sq RSS AIC
## - log(Garage.Area + 1) 1 0.0268 11.273 -3504.8
## <none> 11.246 -3500.1
## - Central.Air 1 0.1843 11.430 -3493.3
## - Garage.Cars 1 0.3518 11.598 -3481.2
## - Bedroom.AbvGr 1 0.4637 11.710 -3473.2
## - log(Total.Bsmt.SF + 1) 1 0.5447 11.791 -3467.5
## - log(X1st.Flr.SF) 1 0.7145 11.960 -3455.6
## - Overall.Cond 1 2.0345 13.280 -3368.5
## - log(Lot.Area) 1 2.1353 13.381 -3362.2
## - Overall.Qual 1 4.0531 15.299 -3250.7
## - Year.Built 1 4.1777 15.424 -3244.0
## - log(area) 1 4.8584 16.104 -3208.1
##
## Step: AIC=-3504.84
## log(price) ~ log(Total.Bsmt.SF + 1) + Garage.Cars + log(area) +
## Bedroom.AbvGr + Year.Built + log(X1st.Flr.SF) + log(Lot.Area) +
## Central.Air + Overall.Cond + Overall.Qual
##
## Df Sum of Sq RSS AIC
## <none> 11.273 -3504.8
## - Central.Air 1 0.1614 11.434 -3499.7
## - Garage.Cars 1 0.3798 11.653 -3484.0
## - Bedroom.AbvGr 1 0.4607 11.733 -3478.2
## - log(Total.Bsmt.SF + 1) 1 0.5402 11.813 -3472.6
## - log(X1st.Flr.SF) 1 0.7240 11.997 -3459.8
## - Overall.Cond 1 2.0323 13.305 -3373.7
## - log(Lot.Area) 1 2.1086 13.381 -3368.9
## - Overall.Qual 1 4.0696 15.342 -3255.1
## - Year.Built 1 4.2427 15.515 -3245.8
## - log(area) 1 4.9053 16.178 -3211.0pred_price <-predict(model.bic)
P = predict(model.bic)
pred.test= data.frame(predicted = P )
mean_price=mean(P)
print(mean_price)## [1] 11.9928actual_price=mean(log(ames_train$price))
print(actual_price)## [1] 11.99280.0.0.9.5 Predicting prices (Test dataset)-Bayesian Model-BIC
model.init <- stepAIC(Initial.model, k =log(nrow(test)))## Start: AIC=-3549.18
## log(price) ~ log(area) + Lot.Area + Overall.Qual + Overall.Cond +
## Year.Built + Total.Bsmt.SF + Bsmt.Full.Bath + Fireplaces +
## Kitchen.AbvGr + Garage.Area
##
## Df Sum of Sq RSS AIC
## <none> 9.4360 -3549.2
## - Lot.Area 1 0.4102 9.8462 -3521.3
## - Bsmt.Full.Bath 1 0.4659 9.9020 -3516.7
## - Kitchen.AbvGr 1 0.4749 9.9110 -3516.0
## - Fireplaces 1 0.5700 10.0060 -3508.2
## - Garage.Area 1 0.9310 10.3670 -3479.4
## - Overall.Cond 1 1.7579 11.1940 -3417.0
## - Total.Bsmt.SF 1 2.0233 11.4593 -3397.9
## - Overall.Qual 1 2.2940 11.7301 -3379.0
## - Year.Built 1 3.0065 12.4426 -3331.0
## - log(area) 1 8.0485 17.4845 -3054.4pred_price <-predict(model.init)
P = predict(model.init)
pred.test= data.frame(predicted = P )
mean_price=mean(P)
print(mean_price) ## [1] 12.02297actual_price=mean(log(test$price))
actual_price## [1] 12.022970.0.0.9.6 Regression Model with Leaps for Train and Test datasets
0.0.0.9.7 Best model with leaps
library(leaps)
regsubsets.out <-
regsubsets(price ~ area +Lot.Area + Overall.Qual + Overall.Cond + Year.Built + Total.Bsmt.SF + X2nd.Flr.SF + Bedroom.AbvGr,
data = na.omit(test),
nbest = 1, # 1 best model for each number of predictors
nvmax = NULL, # NULL for no limit on number of variables
force.in = NULL, force.out = NULL,
method = "exhaustive")
regsubsets.out ## Subset selection object
## Call: regsubsets.formula(price ~ area + Lot.Area + Overall.Qual + Overall.Cond +
## Year.Built + Total.Bsmt.SF + X2nd.Flr.SF + Bedroom.AbvGr,
## data = na.omit(test), nbest = 1, nvmax = NULL, force.in = NULL,
## force.out = NULL, method = "exhaustive")
## 8 Variables (and intercept)
## Forced in Forced out
## area FALSE FALSE
## Lot.Area FALSE FALSE
## Overall.Qual FALSE FALSE
## Overall.Cond FALSE FALSE
## Year.Built FALSE FALSE
## Total.Bsmt.SF FALSE FALSE
## X2nd.Flr.SF FALSE FALSE
## Bedroom.AbvGr FALSE FALSE
## 1 subsets of each size up to 8
## Selection Algorithm: exhaustivesummary.out <- summary(regsubsets.out)
as.data.frame(summary.out$outmat)## area Lot.Area Overall.Qual Overall.Cond Year.Built Total.Bsmt.SF
## 1 ( 1 ) *
## 2 ( 1 ) * *
## 3 ( 1 ) * * *
## 4 ( 1 ) * * * *
## 5 ( 1 ) * * * * *
## 6 ( 1 ) * * * * * *
## 7 ( 1 ) * * * * * *
## 8 ( 1 ) * * * * * *
## X2nd.Flr.SF Bedroom.AbvGr
## 1 ( 1 )
## 2 ( 1 )
## 3 ( 1 )
## 4 ( 1 )
## 5 ( 1 )
## 6 ( 1 )
## 7 ( 1 ) *
## 8 ( 1 ) * *summary(regsubsets.out)## Subset selection object
## Call: regsubsets.formula(price ~ area + Lot.Area + Overall.Qual + Overall.Cond +
## Year.Built + Total.Bsmt.SF + X2nd.Flr.SF + Bedroom.AbvGr,
## data = na.omit(test), nbest = 1, nvmax = NULL, force.in = NULL,
## force.out = NULL, method = "exhaustive")
## 8 Variables (and intercept)
## Forced in Forced out
## area FALSE FALSE
## Lot.Area FALSE FALSE
## Overall.Qual FALSE FALSE
## Overall.Cond FALSE FALSE
## Year.Built FALSE FALSE
## Total.Bsmt.SF FALSE FALSE
## X2nd.Flr.SF FALSE FALSE
## Bedroom.AbvGr FALSE FALSE
## 1 subsets of each size up to 8
## Selection Algorithm: exhaustive
## area Lot.Area Overall.Qual Overall.Cond Year.Built Total.Bsmt.SF
## 1 ( 1 ) " " " " "*" " " " " " "
## 2 ( 1 ) "*" " " "*" " " " " " "
## 3 ( 1 ) "*" " " "*" " " " " "*"
## 4 ( 1 ) "*" " " "*" " " "*" "*"
## 5 ( 1 ) "*" "*" "*" " " "*" "*"
## 6 ( 1 ) "*" "*" "*" "*" "*" "*"
## 7 ( 1 ) "*" "*" "*" "*" "*" "*"
## 8 ( 1 ) "*" "*" "*" "*" "*" "*"
## X2nd.Flr.SF Bedroom.AbvGr
## 1 ( 1 ) " " " "
## 2 ( 1 ) " " " "
## 3 ( 1 ) " " " "
## 4 ( 1 ) " " " "
## 5 ( 1 ) " " " "
## 6 ( 1 ) " " " "
## 7 ( 1 ) " " "*"
## 8 ( 1 ) "*" "*"regsubsets.out <-
regsubsets(price ~ area +Lot.Area + Overall.Qual + Overall.Cond + Year.Built + Total.Bsmt.SF + X2nd.Flr.SF + Bedroom.AbvGr,
data = na.omit(train),
nbest = 1, # 1 best model for each number of predictors
nvmax = NULL, # NULL for no limit on number of variables
force.in = NULL, force.out = NULL,
method = "exhaustive")
regsubsets.out ## Subset selection object
## Call: regsubsets.formula(price ~ area + Lot.Area + Overall.Qual + Overall.Cond +
## Year.Built + Total.Bsmt.SF + X2nd.Flr.SF + Bedroom.AbvGr,
## data = na.omit(train), nbest = 1, nvmax = NULL, force.in = NULL,
## force.out = NULL, method = "exhaustive")
## 8 Variables (and intercept)
## Forced in Forced out
## area FALSE FALSE
## Lot.Area FALSE FALSE
## Overall.Qual FALSE FALSE
## Overall.Cond FALSE FALSE
## Year.Built FALSE FALSE
## Total.Bsmt.SF FALSE FALSE
## X2nd.Flr.SF FALSE FALSE
## Bedroom.AbvGr FALSE FALSE
## 1 subsets of each size up to 8
## Selection Algorithm: exhaustivesummary.out <- summary(regsubsets.out)
as.data.frame(summary.out$outmat)## area Lot.Area Overall.Qual Overall.Cond Year.Built Total.Bsmt.SF
## 1 ( 1 ) *
## 2 ( 1 ) * *
## 3 ( 1 ) * * *
## 4 ( 1 ) * * * *
## 5 ( 1 ) * * * *
## 6 ( 1 ) * * * * *
## 7 ( 1 ) * * * * * *
## 8 ( 1 ) * * * * * *
## X2nd.Flr.SF Bedroom.AbvGr
## 1 ( 1 )
## 2 ( 1 )
## 3 ( 1 )
## 4 ( 1 )
## 5 ( 1 ) *
## 6 ( 1 ) *
## 7 ( 1 ) *
## 8 ( 1 ) * *summary(regsubsets.out)## Subset selection object
## Call: regsubsets.formula(price ~ area + Lot.Area + Overall.Qual + Overall.Cond +
## Year.Built + Total.Bsmt.SF + X2nd.Flr.SF + Bedroom.AbvGr,
## data = na.omit(train), nbest = 1, nvmax = NULL, force.in = NULL,
## force.out = NULL, method = "exhaustive")
## 8 Variables (and intercept)
## Forced in Forced out
## area FALSE FALSE
## Lot.Area FALSE FALSE
## Overall.Qual FALSE FALSE
## Overall.Cond FALSE FALSE
## Year.Built FALSE FALSE
## Total.Bsmt.SF FALSE FALSE
## X2nd.Flr.SF FALSE FALSE
## Bedroom.AbvGr FALSE FALSE
## 1 subsets of each size up to 8
## Selection Algorithm: exhaustive
## area Lot.Area Overall.Qual Overall.Cond Year.Built Total.Bsmt.SF
## 1 ( 1 ) " " " " "*" " " " " " "
## 2 ( 1 ) "*" " " "*" " " " " " "
## 3 ( 1 ) "*" " " "*" " " " " "*"
## 4 ( 1 ) "*" " " "*" " " "*" "*"
## 5 ( 1 ) "*" " " "*" " " "*" "*"
## 6 ( 1 ) "*" " " "*" "*" "*" "*"
## 7 ( 1 ) "*" "*" "*" "*" "*" "*"
## 8 ( 1 ) "*" "*" "*" "*" "*" "*"
## X2nd.Flr.SF Bedroom.AbvGr
## 1 ( 1 ) " " " "
## 2 ( 1 ) " " " "
## 3 ( 1 ) " " " "
## 4 ( 1 ) " " " "
## 5 ( 1 ) " " "*"
## 6 ( 1 ) " " "*"
## 7 ( 1 ) " " "*"
## 8 ( 1 ) "*" "*"0.0.0.10 Part 3 Development of a Final Model
Having experimented with various regression methods I can conclude that the best regression model can be achieved with stepwise regsubsetting and K-fold methods. Bayesian “BAS” is also a very suitable method with rich and easy diagnostics. The selection of variable can be achieved by comparing the information criteria,Cp,adjusted R-squared,RMSE,AIC/BIC.Confirmation of maximum variables till no further performance and prediction improvement are made sure. Boruta and regsubsetting provides these verifications. Boruta gives
Selected more than 20 variables and then selected final model with these Diagnosed by various cross validation methods.
0.0.0.11 Section 3.1 Final Model,leaps regsubset,bayesian method and stepwise.
0.0.0.11.1 Bayesian Method for Regression
0.0.0.11.2 Classification Tree
library(rpart)
library(rpart.plot)
rpartFull <- rpart(price ~ ., data = train)
rpartFull## n= 832
##
## node), split, n, deviance, yval
## * denotes terminal node
##
## 1) root 832 4.023943e+12 173656.2
## 2) Overall.Qual< 6.5 550 8.319631e+11 140155.2
## 4) area< 1323 337 2.552093e+11 124099.4
## 8) Total.Bsmt.SF< 832.5 121 8.970261e+10 103450.0 *
## 9) Total.Bsmt.SF>=832.5 216 8.501077e+10 135666.8 *
## 5) area>=1323 213 3.524287e+11 165558.1
## 10) Garage.Cars< 1.5 66 4.763567e+10 139158.7 *
## 11) Garage.Cars>=1.5 147 2.381442e+11 177410.8
## 22) X2nd.Flr.SF< 1047.5 136 1.488035e+11 172286.7 *
## 23) X2nd.Flr.SF>=1047.5 11 4.162045e+10 240763.6 *
## 3) Overall.Qual>=6.5 282 1.370798e+12 238995.1
## 6) Garage.Cars< 2.5 203 4.071408e+11 211297.9
## 12) Total.Bsmt.SF< 1493 172 2.469360e+11 201728.7
## 24) area< 1751 112 9.955158e+10 188438.2 *
## 25) area>=1751 60 9.067250e+10 226537.5 *
## 13) Total.Bsmt.SF>=1493 31 5.706633e+10 264392.0 *
## 7) Garage.Cars>=2.5 79 4.077677e+11 310166.3
## 14) Overall.Qual< 8.5 55 1.664454e+11 278825.2
## 28) area< 1887 22 2.240332e+10 232393.5 *
## 29) area>=1887 33 6.499243e+10 309779.7 *
## 15) Overall.Qual>=8.5 24 6.349181e+10 381989.6 * rpart.plot <- rpart(price ~ ., data = train)
library(rpart)
rpart1 <- rpart(price ~ ., data = train,control = rpart.control(maxdepth = 2))
rpart1a <- as.party(rpart1)## Error in eval(expr, envir, enclos): could not find function "as.party"plot(rpart1a)## Error in plot(rpart1a): object 'rpart1a' not foundrpart1b <-as.party(rpartFull)## Error in eval(expr, envir, enclos): could not find function "as.party"plot(rpart1b)## Error in plot(rpart1b): object 'rpart1b' not foundFinal.model <- bas.lm(log(price) ~log(Total.Bsmt.SF + 1) + log(area)+ Bedroom.AbvGr + Year.Built + log(X1st.Flr.SF) +
log(Lot.Area) + Overall.Cond+Overall.Qual+TotRms.AbvGrd+
Bsmt.Full.Bath+Garage.Cars+Garage.Area+Year.Remod.Add+
Kitchen.AbvGr+Fireplaces+MS.SubClass+Half.Bath+Full.Bath,
data =train, prior = "BIC",modelprior=uniform())
Final.model##
## Call:
## bas.lm(formula = log(price) ~ log(Total.Bsmt.SF + 1) + log(area) + Bedroom.AbvGr + Year.Built + log(X1st.Flr.SF) + log(Lot.Area) + Overall.Cond + Overall.Qual + TotRms.AbvGrd + Bsmt.Full.Bath + Garage.Cars + Garage.Area + Year.Remod.Add + Kitchen.AbvGr + Fireplaces + MS.SubClass + Half.Bath + Full.Bath, data = train, prior = "BIC", modelprior = uniform())
##
##
## Marginal Posterior Inclusion Probabilities:
## Intercept log(Total.Bsmt.SF + 1) log(area)
## 1.00000 0.99999 1.00000
## Bedroom.AbvGr Year.Built log(X1st.Flr.SF)
## 0.62405 1.00000 1.00000
## log(Lot.Area) Overall.Cond Overall.Qual
## 1.00000 1.00000 1.00000
## TotRms.AbvGrd Bsmt.Full.Bath Garage.Cars
## 0.08543 1.00000 0.13888
## Garage.Area Year.Remod.Add Kitchen.AbvGr
## 0.93368 0.98571 0.98284
## Fireplaces MS.SubClass Half.Bath
## 0.99999 0.03807 0.03411
## Full.Bath
## 0.05115summary(Final.model)## P(B != 0 | Y) model 1 model 2 model 3
## Intercept 1.00000000 1.0000 1.0000000 1.0000000
## log(Total.Bsmt.SF + 1) 0.99999458 1.0000 1.0000000 1.0000000
## log(area) 1.00000000 1.0000 1.0000000 1.0000000
## Bedroom.AbvGr 0.62405134 1.0000 0.0000000 1.0000000
## Year.Built 1.00000000 1.0000 1.0000000 1.0000000
## log(X1st.Flr.SF) 0.99999912 1.0000 1.0000000 1.0000000
## log(Lot.Area) 1.00000000 1.0000 1.0000000 1.0000000
## Overall.Cond 1.00000000 1.0000 1.0000000 1.0000000
## Overall.Qual 1.00000000 1.0000 1.0000000 1.0000000
## TotRms.AbvGrd 0.08542856 0.0000 0.0000000 1.0000000
## Bsmt.Full.Bath 1.00000000 1.0000 1.0000000 1.0000000
## Garage.Cars 0.13888327 0.0000 0.0000000 0.0000000
## Garage.Area 0.93368434 1.0000 1.0000000 1.0000000
## Year.Remod.Add 0.98571228 1.0000 1.0000000 1.0000000
## Kitchen.AbvGr 0.98283900 1.0000 1.0000000 1.0000000
## Fireplaces 0.99998878 1.0000 1.0000000 1.0000000
## MS.SubClass 0.03806871 0.0000 0.0000000 0.0000000
## Half.Bath 0.03411016 0.0000 0.0000000 0.0000000
## Full.Bath 0.05114819 0.0000 0.0000000 0.0000000
## BF NA 1.0000 0.6802189 0.1328129
## PostProbs NA 0.4001 0.2721000 0.0531000
## R2 NA 0.9177 0.9169000 0.9179000
## dim NA 14.0000 13.0000000 15.0000000
## logmarg NA -993.8561 -994.2414310 -995.8749041
## model 4 model 5
## Intercept 1.00000000 1.00000000
## log(Total.Bsmt.SF + 1) 1.00000000 1.00000000
## log(area) 1.00000000 1.00000000
## Bedroom.AbvGr 1.00000000 1.00000000
## Year.Built 1.00000000 1.00000000
## log(X1st.Flr.SF) 1.00000000 1.00000000
## log(Lot.Area) 1.00000000 1.00000000
## Overall.Cond 1.00000000 1.00000000
## Overall.Qual 1.00000000 1.00000000
## TotRms.AbvGrd 0.00000000 0.00000000
## Bsmt.Full.Bath 1.00000000 1.00000000
## Garage.Cars 1.00000000 1.00000000
## Garage.Area 1.00000000 0.00000000
## Year.Remod.Add 1.00000000 1.00000000
## Kitchen.AbvGr 1.00000000 1.00000000
## Fireplaces 1.00000000 1.00000000
## MS.SubClass 0.00000000 0.00000000
## Half.Bath 0.00000000 0.00000000
## Full.Bath 0.00000000 0.00000000
## BF 0.08125174 0.07646485
## PostProbs 0.03250000 0.03060000
## R2 0.91780000 0.91720000
## dim 15.00000000 14.00000000
## logmarg -996.36629343 -996.42701444image(Final.model, rotate = F)
coef(Final.model)##
## Marginal Posterior Summaries of Coefficients:
##
## Using BMA
##
## Based on the top 262144 models
## post mean post SD post p(B != 0)
## Intercept 1.199e+01 3.790e-03 1.000e+00
## log(Total.Bsmt.SF + 1) 2.140e-02 3.852e-03 1.000e+00
## log(area) 3.777e-01 2.880e-02 1.000e+00
## Bedroom.AbvGr -1.173e-02 1.061e-02 6.241e-01
## Year.Built 3.223e-03 2.224e-04 1.000e+00
## log(X1st.Flr.SF) 1.112e-01 1.808e-02 1.000e+00
## log(Lot.Area) 9.660e-02 9.301e-03 1.000e+00
## Overall.Cond 4.848e-02 4.266e-03 1.000e+00
## Overall.Qual 8.192e-02 4.895e-03 1.000e+00
## TotRms.AbvGrd 6.042e-04 2.530e-03 8.543e-02
## Bsmt.Full.Bath 7.077e-02 8.203e-03 1.000e+00
## Garage.Cars 4.044e-03 1.186e-02 1.389e-01
## Garage.Area 1.421e-04 4.717e-05 9.337e-01
## Year.Remod.Add 1.049e-03 3.004e-04 9.857e-01
## Kitchen.AbvGr -8.481e-02 2.506e-02 9.828e-01
## Fireplaces 3.981e-02 7.289e-03 1.000e+00
## MS.SubClass -1.866e-06 2.724e-05 3.807e-02
## Half.Bath 5.780e-05 1.982e-03 3.411e-02
## Full.Bath 5.263e-04 3.433e-03 5.115e-020.0.0.11.3 Verification of Variable for Final Model
## 1. run of importance source...## 2. run of importance source...## 3. run of importance source...## 4. run of importance source...## 5. run of importance source...## 6. run of importance source...## 7. run of importance source...## 8. run of importance source...## 9. run of importance source...## 10. run of importance source...## 11. run of importance source...## 12. run of importance source...## After 12 iterations, +32 secs:## confirmed 22 attributes: area, Bedroom.AbvGr, Bsmt.Full.Bath, Central.Air, Fireplaces and 17 more;## still have 4 attributes left.## 13. run of importance source...## 14. run of importance source...## 15. run of importance source...## 16. run of importance source...## After 16 iterations, +42 secs:## rejected 1 attribute: Pool.Area;## still have 3 attributes left.## 17. run of importance source...## 18. run of importance source...## 19. run of importance source...## 20. run of importance source...## 21. run of importance source...## 22. run of importance source...## 23. run of importance source...## 24. run of importance source...## 25. run of importance source...## 26. run of importance source...## 27. run of importance source...## 28. run of importance source...## 29. run of importance source...## 30. run of importance source...## 31. run of importance source...## 32. run of importance source...## 33. run of importance source...## 34. run of importance source...## 35. run of importance source...## 36. run of importance source...## 37. run of importance source...## 38. run of importance source...## 39. run of importance source...## 40. run of importance source...## 41. run of importance source...## 42. run of importance source...## 43. run of importance source...## 44. run of importance source...## 45. run of importance source...## 46. run of importance source...## 47. run of importance source...## 48. run of importance source...## 49. run of importance source...## 50. run of importance source...## 51. run of importance source...## 52. run of importance source...## 53. run of importance source...## 54. run of importance source...## 55. run of importance source...## 56. run of importance source...## After 56 iterations, +2.5 mins:## confirmed 1 attribute: Screen.Porch;## still have 2 attributes left.## 57. run of importance source...## 58. run of importance source...## 59. run of importance source...## 60. run of importance source...## 61. run of importance source...## 62. run of importance source...## 63. run of importance source...## 64. run of importance source...## 65. run of importance source...## 66. run of importance source...## 67. run of importance source...## 68. run of importance source...## 69. run of importance source...## 70. run of importance source...## 71. run of importance source...## 72. run of importance source...## 73. run of importance source...## 74. run of importance source...## 75. run of importance source...## 76. run of importance source...## 77. run of importance source...## 78. run of importance source...## 79. run of importance source...## 80. run of importance source...## 81. run of importance source...## 82. run of importance source...## 83. run of importance source...## 84. run of importance source...## 85. run of importance source...## 86. run of importance source...## 87. run of importance source...## 88. run of importance source...## 89. run of importance source...## 90. run of importance source...## 91. run of importance source...## 92. run of importance source...## 93. run of importance source...## 94. run of importance source...## 95. run of importance source...## 96. run of importance source...## 97. run of importance source...## 98. run of importance source...## 99. run of importance source...## Boruta performed 99 iterations in 4.476898 mins.
## 23 attributes confirmed important: area, Bedroom.AbvGr,
## Bsmt.Full.Bath, Central.Air, Fireplaces and 18 more;
## 1 attributes confirmed unimportant: Pool.Area;
## 2 tentative attributes left: Bsmt.Half.Bath, Enclosed.Porch;## 1. run of importance source...## 2. run of importance source...## 3. run of importance source...## 4. run of importance source...## 5. run of importance source...## 6. run of importance source...## 7. run of importance source...## 8. run of importance source...## 9. run of importance source...## 10. run of importance source...## 11. run of importance source...## After 11 iterations, +22 secs:## confirmed 18 attributes: Bedroom.AbvGr, Bsmt.Full.Bath, Fireplaces, Full.Bath, Garage.Area and 13 more;## no more attributes left.## Boruta performed 11 iterations in 21.97065 secs.
## 18 attributes confirmed important: Bedroom.AbvGr, Bsmt.Full.Bath,
## Fireplaces, Full.Bath, Garage.Area and 13 more;
## No attributes deemed unimportant.
## Boruta performed 99 iterations in 4.476898 mins.
## Tentatives roughfixed over the last 99 iterations.
## 23 attributes confirmed important: area, Bedroom.AbvGr,
## Bsmt.Full.Bath, Central.Air, Fireplaces and 18 more;
## 3 attributes confirmed unimportant: Bsmt.Half.Bath,
## Enclosed.Porch, Pool.Area;## Warning in TentativeRoughFix(boruta.train): There are no Tentative
## attributes! Returning original object.## Boruta performed 11 iterations in 21.97065 secs.
## 18 attributes confirmed important: Bedroom.AbvGr, Bsmt.Full.Bath,
## Fireplaces, Full.Bath, Garage.Area and 13 more;
## No attributes deemed unimportant.0.0.0.11.4 Cross validation of Final model
## Start: AIC=-3668.13
## log(price) ~ log(Total.Bsmt.SF + 1) + log(area) + Bedroom.AbvGr +
## Year.Built + log(X1st.Flr.SF) + log(Lot.Area) + Overall.Cond +
## Overall.Qual + TotRms.AbvGrd + Bsmt.Full.Bath + Garage.Cars +
## Garage.Area + Year.Remod.Add + Kitchen.AbvGr + Fireplaces +
## MS.SubClass + Half.Bath + Full.Bath
##
## Df Sum of Sq RSS AIC
## - MS.SubClass 1 0.0014 9.6745 -3670.0
## - Half.Bath 1 0.0030 9.6761 -3669.9
## - Full.Bath 1 0.0118 9.6849 -3669.1
## - Garage.Cars 1 0.0140 9.6871 -3668.9
## <none> 9.6731 -3668.1
## - TotRms.AbvGrd 1 0.0299 9.7030 -3667.6
## - Garage.Area 1 0.0907 9.7638 -3662.4
## - Bedroom.AbvGr 1 0.1193 9.7924 -3659.9
## - Year.Remod.Add 1 0.1486 9.8217 -3657.4
## - Kitchen.AbvGr 1 0.1754 9.8485 -3655.2
## - log(X1st.Flr.SF) 1 0.3296 10.0027 -3642.3
## - Fireplaces 1 0.3465 10.0196 -3640.8
## - log(Total.Bsmt.SF + 1) 1 0.3886 10.0617 -3637.4
## - Bsmt.Full.Bath 1 0.9053 10.5785 -3595.7
## - log(Lot.Area) 1 0.9936 10.6667 -3588.8
## - log(area) 1 1.3370 11.0101 -3562.4
## - Overall.Cond 1 1.6453 11.3184 -3539.4
## - Year.Built 1 2.1722 11.8453 -3501.6
## - Overall.Qual 1 3.2732 12.9463 -3427.6
##
## Step: AIC=-3670.01
## log(price) ~ log(Total.Bsmt.SF + 1) + log(area) + Bedroom.AbvGr +
## Year.Built + log(X1st.Flr.SF) + log(Lot.Area) + Overall.Cond +
## Overall.Qual + TotRms.AbvGrd + Bsmt.Full.Bath + Garage.Cars +
## Garage.Area + Year.Remod.Add + Kitchen.AbvGr + Fireplaces +
## Half.Bath + Full.Bath
##
## Df Sum of Sq RSS AIC
## - Half.Bath 1 0.0033 9.6777 -3671.7
## - Full.Bath 1 0.0123 9.6868 -3671.0
## - Garage.Cars 1 0.0136 9.6881 -3670.8
## <none> 9.6745 -3670.0
## - TotRms.AbvGrd 1 0.0316 9.7061 -3669.3
## + MS.SubClass 1 0.0014 9.6731 -3668.1
## - Garage.Area 1 0.0909 9.7653 -3664.2
## - Bedroom.AbvGr 1 0.1181 9.7925 -3661.9
## - Year.Remod.Add 1 0.1478 9.8222 -3659.4
## - Kitchen.AbvGr 1 0.2150 9.8895 -3653.7
## - Fireplaces 1 0.3456 10.0201 -3642.8
## - log(X1st.Flr.SF) 1 0.3772 10.0517 -3640.2
## - log(Total.Bsmt.SF + 1) 1 0.3873 10.0618 -3639.4
## - Bsmt.Full.Bath 1 0.9045 10.5790 -3597.6
## - log(Lot.Area) 1 1.3202 10.9947 -3565.6
## - log(area) 1 1.4370 11.1115 -3556.8
## - Overall.Cond 1 1.6730 11.3475 -3539.3
## - Year.Built 1 2.1710 11.8455 -3503.6
## - Overall.Qual 1 3.2898 12.9643 -3428.5
##
## Step: AIC=-3671.73
## log(price) ~ log(Total.Bsmt.SF + 1) + log(area) + Bedroom.AbvGr +
## Year.Built + log(X1st.Flr.SF) + log(Lot.Area) + Overall.Cond +
## Overall.Qual + TotRms.AbvGrd + Bsmt.Full.Bath + Garage.Cars +
## Garage.Area + Year.Remod.Add + Kitchen.AbvGr + Fireplaces +
## Full.Bath
##
## Df Sum of Sq RSS AIC
## - Full.Bath 1 0.0093 9.6871 -3672.9
## - Garage.Cars 1 0.0150 9.6927 -3672.4
## <none> 9.6777 -3671.7
## - TotRms.AbvGrd 1 0.0306 9.7083 -3671.1
## + Half.Bath 1 0.0033 9.6745 -3670.0
## + MS.SubClass 1 0.0017 9.6761 -3669.9
## - Garage.Area 1 0.0885 9.7662 -3666.2
## - Bedroom.AbvGr 1 0.1167 9.7945 -3663.8
## - Year.Remod.Add 1 0.1486 9.8263 -3661.1
## - Kitchen.AbvGr 1 0.2144 9.8922 -3655.5
## - Fireplaces 1 0.3471 10.0249 -3644.4
## - log(Total.Bsmt.SF + 1) 1 0.3884 10.0661 -3641.0
## - log(X1st.Flr.SF) 1 0.4768 10.1546 -3633.7
## - Bsmt.Full.Bath 1 0.9053 10.5830 -3599.3
## - log(Lot.Area) 1 1.3317 11.0095 -3566.5
## - Overall.Cond 1 1.6744 11.3521 -3541.0
## - log(area) 1 2.0682 11.7459 -3512.6
## - Year.Built 1 2.5111 12.1889 -3481.8
## - Overall.Qual 1 3.2881 12.9659 -3430.4
##
## Step: AIC=-3672.93
## log(price) ~ log(Total.Bsmt.SF + 1) + log(area) + Bedroom.AbvGr +
## Year.Built + log(X1st.Flr.SF) + log(Lot.Area) + Overall.Cond +
## Overall.Qual + TotRms.AbvGrd + Bsmt.Full.Bath + Garage.Cars +
## Garage.Area + Year.Remod.Add + Kitchen.AbvGr + Fireplaces
##
## Df Sum of Sq RSS AIC
## - Garage.Cars 1 0.0186 9.7056 -3673.3
## <none> 9.6871 -3672.9
## - TotRms.AbvGrd 1 0.0300 9.7171 -3672.4
## + Full.Bath 1 0.0093 9.6777 -3671.7
## + MS.SubClass 1 0.0019 9.6852 -3671.1
## + Half.Bath 1 0.0003 9.6868 -3671.0
## - Garage.Area 1 0.0826 9.7696 -3667.9
## - Bedroom.AbvGr 1 0.1119 9.7990 -3665.4
## - Year.Remod.Add 1 0.1654 9.8525 -3660.8
## - Kitchen.AbvGr 1 0.2053 9.8923 -3657.5
## - Fireplaces 1 0.3442 10.0313 -3645.9
## - log(Total.Bsmt.SF + 1) 1 0.3836 10.0707 -3642.6
## - log(X1st.Flr.SF) 1 0.4743 10.1614 -3635.2
## - Bsmt.Full.Bath 1 0.8961 10.5832 -3601.3
## - log(Lot.Area) 1 1.3302 11.0173 -3567.9
## - Overall.Cond 1 1.6666 11.3537 -3542.9
## - log(area) 1 2.3589 12.0460 -3493.6
## - Year.Built 1 2.6979 12.3850 -3470.5
## - Overall.Qual 1 3.3298 13.0169 -3429.1
##
## Step: AIC=-3673.34
## log(price) ~ log(Total.Bsmt.SF + 1) + log(area) + Bedroom.AbvGr +
## Year.Built + log(X1st.Flr.SF) + log(Lot.Area) + Overall.Cond +
## Overall.Qual + TotRms.AbvGrd + Bsmt.Full.Bath + Garage.Area +
## Year.Remod.Add + Kitchen.AbvGr + Fireplaces
##
## Df Sum of Sq RSS AIC
## <none> 9.7056 -3673.3
## + Garage.Cars 1 0.0186 9.6871 -3672.9
## - TotRms.AbvGrd 1 0.0314 9.7370 -3672.7
## + Full.Bath 1 0.0129 9.6927 -3672.4
## + MS.SubClass 1 0.0015 9.7041 -3671.5
## + Half.Bath 1 0.0005 9.7052 -3671.4
## - Bedroom.AbvGr 1 0.1163 9.8219 -3665.4
## - Year.Remod.Add 1 0.1723 9.8780 -3660.7
## - Kitchen.AbvGr 1 0.1938 9.8995 -3658.9
## - Fireplaces 1 0.3500 10.0556 -3645.9
## - log(Total.Bsmt.SF + 1) 1 0.3932 10.0988 -3642.3
## - log(X1st.Flr.SF) 1 0.4617 10.1674 -3636.7
## - Garage.Area 1 0.4694 10.1750 -3636.0
## - Bsmt.Full.Bath 1 0.9012 10.6069 -3601.5
## - log(Lot.Area) 1 1.3381 11.0438 -3567.9
## - Overall.Cond 1 1.6559 11.3615 -3544.3
## - log(area) 1 2.4051 12.1107 -3491.1
## - Year.Built 1 2.8042 12.5098 -3464.2
## - Overall.Qual 1 3.4359 13.1416 -3423.2## Stepwise Model Path
## Analysis of Deviance Table
##
## Initial Model:
## log(price) ~ log(Total.Bsmt.SF + 1) + log(area) + Bedroom.AbvGr +
## Year.Built + log(X1st.Flr.SF) + log(Lot.Area) + Overall.Cond +
## Overall.Qual + TotRms.AbvGrd + Bsmt.Full.Bath + Garage.Cars +
## Garage.Area + Year.Remod.Add + Kitchen.AbvGr + Fireplaces +
## MS.SubClass + Half.Bath + Full.Bath
##
## Final Model:
## log(price) ~ log(Total.Bsmt.SF + 1) + log(area) + Bedroom.AbvGr +
## Year.Built + log(X1st.Flr.SF) + log(Lot.Area) + Overall.Cond +
## Overall.Qual + TotRms.AbvGrd + Bsmt.Full.Bath + Garage.Area +
## Year.Remod.Add + Kitchen.AbvGr + Fireplaces
##
##
## Step Df Deviance Resid. Df Resid. Dev AIC
## 1 813 9.673101 -3668.130
## 2 - MS.SubClass 1 0.001370346 814 9.674471 -3670.012
## 3 - Half.Bath 1 0.003276487 815 9.677748 -3671.731
## 4 - Full.Bath 1 0.009318860 816 9.687067 -3672.930
## 5 - Garage.Cars 1 0.018572802 817 9.705640 -3673.336
0.0.0.11.5 Leaps regsubset method for regression
## Start: AIC=-3668.13
## log(price) ~ log(Total.Bsmt.SF + 1) + log(area) + Bedroom.AbvGr +
## Year.Built + log(X1st.Flr.SF) + log(Lot.Area) + Overall.Cond +
## Overall.Qual + TotRms.AbvGrd + Bsmt.Full.Bath + Garage.Cars +
## Garage.Area + Year.Remod.Add + Kitchen.AbvGr + Fireplaces +
## MS.SubClass + Half.Bath + Full.Bath
##
## Df Sum of Sq RSS AIC
## - MS.SubClass 1 0.0014 9.6745 -3670.0
## - Half.Bath 1 0.0030 9.6761 -3669.9
## - Full.Bath 1 0.0118 9.6849 -3669.1
## - Garage.Cars 1 0.0140 9.6871 -3668.9
## <none> 9.6731 -3668.1
## - TotRms.AbvGrd 1 0.0299 9.7030 -3667.6
## - Garage.Area 1 0.0907 9.7638 -3662.4
## - Bedroom.AbvGr 1 0.1193 9.7924 -3659.9
## - Year.Remod.Add 1 0.1486 9.8217 -3657.4
## - Kitchen.AbvGr 1 0.1754 9.8485 -3655.2
## - log(X1st.Flr.SF) 1 0.3296 10.0027 -3642.3
## - Fireplaces 1 0.3465 10.0196 -3640.8
## - log(Total.Bsmt.SF + 1) 1 0.3886 10.0617 -3637.4
## - Bsmt.Full.Bath 1 0.9053 10.5785 -3595.7
## - log(Lot.Area) 1 0.9936 10.6667 -3588.8
## - log(area) 1 1.3370 11.0101 -3562.4
## - Overall.Cond 1 1.6453 11.3184 -3539.4
## - Year.Built 1 2.1722 11.8453 -3501.6
## - Overall.Qual 1 3.2732 12.9463 -3427.6
##
## Step: AIC=-3670.01
## log(price) ~ log(Total.Bsmt.SF + 1) + log(area) + Bedroom.AbvGr +
## Year.Built + log(X1st.Flr.SF) + log(Lot.Area) + Overall.Cond +
## Overall.Qual + TotRms.AbvGrd + Bsmt.Full.Bath + Garage.Cars +
## Garage.Area + Year.Remod.Add + Kitchen.AbvGr + Fireplaces +
## Half.Bath + Full.Bath
##
## Df Sum of Sq RSS AIC
## - Half.Bath 1 0.0033 9.6777 -3671.7
## - Full.Bath 1 0.0123 9.6868 -3671.0
## - Garage.Cars 1 0.0136 9.6881 -3670.8
## <none> 9.6745 -3670.0
## - TotRms.AbvGrd 1 0.0316 9.7061 -3669.3
## - Garage.Area 1 0.0909 9.7653 -3664.2
## - Bedroom.AbvGr 1 0.1181 9.7925 -3661.9
## - Year.Remod.Add 1 0.1478 9.8222 -3659.4
## - Kitchen.AbvGr 1 0.2150 9.8895 -3653.7
## - Fireplaces 1 0.3456 10.0201 -3642.8
## - log(X1st.Flr.SF) 1 0.3772 10.0517 -3640.2
## - log(Total.Bsmt.SF + 1) 1 0.3873 10.0618 -3639.4
## - Bsmt.Full.Bath 1 0.9045 10.5790 -3597.6
## - log(Lot.Area) 1 1.3202 10.9947 -3565.6
## - log(area) 1 1.4370 11.1115 -3556.8
## - Overall.Cond 1 1.6730 11.3475 -3539.3
## - Year.Built 1 2.1710 11.8455 -3503.6
## - Overall.Qual 1 3.2898 12.9643 -3428.5
##
## Step: AIC=-3671.73
## log(price) ~ log(Total.Bsmt.SF + 1) + log(area) + Bedroom.AbvGr +
## Year.Built + log(X1st.Flr.SF) + log(Lot.Area) + Overall.Cond +
## Overall.Qual + TotRms.AbvGrd + Bsmt.Full.Bath + Garage.Cars +
## Garage.Area + Year.Remod.Add + Kitchen.AbvGr + Fireplaces +
## Full.Bath
##
## Df Sum of Sq RSS AIC
## - Full.Bath 1 0.0093 9.6871 -3672.9
## - Garage.Cars 1 0.0150 9.6927 -3672.4
## <none> 9.6777 -3671.7
## - TotRms.AbvGrd 1 0.0306 9.7083 -3671.1
## - Garage.Area 1 0.0885 9.7662 -3666.2
## - Bedroom.AbvGr 1 0.1167 9.7945 -3663.8
## - Year.Remod.Add 1 0.1486 9.8263 -3661.1
## - Kitchen.AbvGr 1 0.2144 9.8922 -3655.5
## - Fireplaces 1 0.3471 10.0249 -3644.4
## - log(Total.Bsmt.SF + 1) 1 0.3884 10.0661 -3641.0
## - log(X1st.Flr.SF) 1 0.4768 10.1546 -3633.7
## - Bsmt.Full.Bath 1 0.9053 10.5830 -3599.3
## - log(Lot.Area) 1 1.3317 11.0095 -3566.5
## - Overall.Cond 1 1.6744 11.3521 -3541.0
## - log(area) 1 2.0682 11.7459 -3512.6
## - Year.Built 1 2.5111 12.1889 -3481.8
## - Overall.Qual 1 3.2881 12.9659 -3430.4
##
## Step: AIC=-3672.93
## log(price) ~ log(Total.Bsmt.SF + 1) + log(area) + Bedroom.AbvGr +
## Year.Built + log(X1st.Flr.SF) + log(Lot.Area) + Overall.Cond +
## Overall.Qual + TotRms.AbvGrd + Bsmt.Full.Bath + Garage.Cars +
## Garage.Area + Year.Remod.Add + Kitchen.AbvGr + Fireplaces
##
## Df Sum of Sq RSS AIC
## - Garage.Cars 1 0.0186 9.7056 -3673.3
## <none> 9.6871 -3672.9
## - TotRms.AbvGrd 1 0.0300 9.7171 -3672.4
## - Garage.Area 1 0.0826 9.7696 -3667.9
## - Bedroom.AbvGr 1 0.1119 9.7990 -3665.4
## - Year.Remod.Add 1 0.1654 9.8525 -3660.8
## - Kitchen.AbvGr 1 0.2053 9.8923 -3657.5
## - Fireplaces 1 0.3442 10.0313 -3645.9
## - log(Total.Bsmt.SF + 1) 1 0.3836 10.0707 -3642.6
## - log(X1st.Flr.SF) 1 0.4743 10.1614 -3635.2
## - Bsmt.Full.Bath 1 0.8961 10.5832 -3601.3
## - log(Lot.Area) 1 1.3302 11.0173 -3567.9
## - Overall.Cond 1 1.6666 11.3537 -3542.9
## - log(area) 1 2.3589 12.0460 -3493.6
## - Year.Built 1 2.6979 12.3850 -3470.5
## - Overall.Qual 1 3.3298 13.0169 -3429.1
##
## Step: AIC=-3673.34
## log(price) ~ log(Total.Bsmt.SF + 1) + log(area) + Bedroom.AbvGr +
## Year.Built + log(X1st.Flr.SF) + log(Lot.Area) + Overall.Cond +
## Overall.Qual + TotRms.AbvGrd + Bsmt.Full.Bath + Garage.Area +
## Year.Remod.Add + Kitchen.AbvGr + Fireplaces
##
## Df Sum of Sq RSS AIC
## <none> 9.7056 -3673.3
## - TotRms.AbvGrd 1 0.0314 9.7370 -3672.7
## - Bedroom.AbvGr 1 0.1163 9.8219 -3665.4
## - Year.Remod.Add 1 0.1723 9.8780 -3660.7
## - Kitchen.AbvGr 1 0.1938 9.8995 -3658.9
## - Fireplaces 1 0.3500 10.0556 -3645.9
## - log(Total.Bsmt.SF + 1) 1 0.3932 10.0988 -3642.3
## - log(X1st.Flr.SF) 1 0.4617 10.1674 -3636.7
## - Garage.Area 1 0.4694 10.1750 -3636.0
## - Bsmt.Full.Bath 1 0.9012 10.6069 -3601.5
## - log(Lot.Area) 1 1.3381 11.0438 -3567.9
## - Overall.Cond 1 1.6559 11.3615 -3544.3
## - log(area) 1 2.4051 12.1107 -3491.1
## - Year.Built 1 2.8042 12.5098 -3464.2
## - Overall.Qual 1 3.4359 13.1416 -3423.2## Start: AIC=-3578.38
## log(price) ~ log(Total.Bsmt.SF + 1) + log(area) + Bedroom.AbvGr +
## Year.Built + log(X1st.Flr.SF) + log(Lot.Area) + Overall.Cond +
## Overall.Qual + TotRms.AbvGrd + Bsmt.Full.Bath + Garage.Cars +
## Garage.Area + Year.Remod.Add + Kitchen.AbvGr + Fireplaces +
## MS.SubClass + Half.Bath + Full.Bath
##
## Df Sum of Sq RSS AIC
## - MS.SubClass 1 0.0014 9.6745 -3585.0
## - Half.Bath 1 0.0030 9.6761 -3584.8
## - Full.Bath 1 0.0118 9.6849 -3584.1
## - Garage.Cars 1 0.0140 9.6871 -3583.9
## - TotRms.AbvGrd 1 0.0299 9.7030 -3582.5
## <none> 9.6731 -3578.4
## - Garage.Area 1 0.0907 9.7638 -3577.3
## - Bedroom.AbvGr 1 0.1193 9.7924 -3574.9
## - Year.Remod.Add 1 0.1486 9.8217 -3572.4
## - Kitchen.AbvGr 1 0.1754 9.8485 -3570.1
## - log(X1st.Flr.SF) 1 0.3296 10.0027 -3557.2
## - Fireplaces 1 0.3465 10.0196 -3555.8
## - log(Total.Bsmt.SF + 1) 1 0.3886 10.0617 -3552.3
## - Bsmt.Full.Bath 1 0.9053 10.5785 -3510.7
## - log(Lot.Area) 1 0.9936 10.6667 -3503.8
## - log(area) 1 1.3370 11.0101 -3477.4
## - Overall.Cond 1 1.6453 11.3184 -3454.4
## - Year.Built 1 2.1722 11.8453 -3416.6
## - Overall.Qual 1 3.2732 12.9463 -3342.6
##
## Step: AIC=-3584.98
## log(price) ~ log(Total.Bsmt.SF + 1) + log(area) + Bedroom.AbvGr +
## Year.Built + log(X1st.Flr.SF) + log(Lot.Area) + Overall.Cond +
## Overall.Qual + TotRms.AbvGrd + Bsmt.Full.Bath + Garage.Cars +
## Garage.Area + Year.Remod.Add + Kitchen.AbvGr + Fireplaces +
## Half.Bath + Full.Bath
##
## Df Sum of Sq RSS AIC
## - Half.Bath 1 0.0033 9.6777 -3591.4
## - Full.Bath 1 0.0123 9.6868 -3590.6
## - Garage.Cars 1 0.0136 9.6881 -3590.5
## - TotRms.AbvGrd 1 0.0316 9.7061 -3589.0
## <none> 9.6745 -3585.0
## - Garage.Area 1 0.0909 9.7653 -3583.9
## - Bedroom.AbvGr 1 0.1181 9.7925 -3581.6
## - Year.Remod.Add 1 0.1478 9.8222 -3579.1
## - Kitchen.AbvGr 1 0.2150 9.8895 -3573.4
## - Fireplaces 1 0.3456 10.0201 -3562.5
## - log(X1st.Flr.SF) 1 0.3772 10.0517 -3559.9
## - log(Total.Bsmt.SF + 1) 1 0.3873 10.0618 -3559.0
## - Bsmt.Full.Bath 1 0.9045 10.5790 -3517.3
## - log(Lot.Area) 1 1.3202 10.9947 -3485.3
## - log(area) 1 1.4370 11.1115 -3476.5
## - Overall.Cond 1 1.6730 11.3475 -3459.0
## - Year.Built 1 2.1710 11.8455 -3423.3
## - Overall.Qual 1 3.2898 12.9643 -3348.2
##
## Step: AIC=-3591.43
## log(price) ~ log(Total.Bsmt.SF + 1) + log(area) + Bedroom.AbvGr +
## Year.Built + log(X1st.Flr.SF) + log(Lot.Area) + Overall.Cond +
## Overall.Qual + TotRms.AbvGrd + Bsmt.Full.Bath + Garage.Cars +
## Garage.Area + Year.Remod.Add + Kitchen.AbvGr + Fireplaces +
## Full.Bath
##
## Df Sum of Sq RSS AIC
## - Full.Bath 1 0.0093 9.6871 -3597.3
## - Garage.Cars 1 0.0150 9.6927 -3596.9
## - TotRms.AbvGrd 1 0.0306 9.7083 -3595.5
## <none> 9.6777 -3591.4
## - Garage.Area 1 0.0885 9.7662 -3590.6
## - Bedroom.AbvGr 1 0.1167 9.7945 -3588.2
## - Year.Remod.Add 1 0.1486 9.8263 -3585.5
## - Kitchen.AbvGr 1 0.2144 9.8922 -3579.9
## - Fireplaces 1 0.3471 10.0249 -3568.8
## - log(Total.Bsmt.SF + 1) 1 0.3884 10.0661 -3565.4
## - log(X1st.Flr.SF) 1 0.4768 10.1546 -3558.1
## - Bsmt.Full.Bath 1 0.9053 10.5830 -3523.8
## - log(Lot.Area) 1 1.3317 11.0095 -3490.9
## - Overall.Cond 1 1.6744 11.3521 -3465.4
## - log(area) 1 2.0682 11.7459 -3437.0
## - Year.Built 1 2.5111 12.1889 -3406.2
## - Overall.Qual 1 3.2881 12.9659 -3354.8
##
## Step: AIC=-3597.35
## log(price) ~ log(Total.Bsmt.SF + 1) + log(area) + Bedroom.AbvGr +
## Year.Built + log(X1st.Flr.SF) + log(Lot.Area) + Overall.Cond +
## Overall.Qual + TotRms.AbvGrd + Bsmt.Full.Bath + Garage.Cars +
## Garage.Area + Year.Remod.Add + Kitchen.AbvGr + Fireplaces
##
## Df Sum of Sq RSS AIC
## - Garage.Cars 1 0.0186 9.7056 -3602.5
## - TotRms.AbvGrd 1 0.0300 9.7171 -3601.5
## <none> 9.6871 -3597.3
## - Garage.Area 1 0.0826 9.7696 -3597.0
## - Bedroom.AbvGr 1 0.1119 9.7990 -3594.5
## - Year.Remod.Add 1 0.1654 9.8525 -3590.0
## - Kitchen.AbvGr 1 0.2053 9.8923 -3586.6
## - Fireplaces 1 0.3442 10.0313 -3575.0
## - log(Total.Bsmt.SF + 1) 1 0.3836 10.0707 -3571.8
## - log(X1st.Flr.SF) 1 0.4743 10.1614 -3564.3
## - Bsmt.Full.Bath 1 0.8961 10.5832 -3530.5
## - log(Lot.Area) 1 1.3302 11.0173 -3497.0
## - Overall.Cond 1 1.6666 11.3537 -3472.0
## - log(area) 1 2.3589 12.0460 -3422.7
## - Year.Built 1 2.6979 12.3850 -3399.7
## - Overall.Qual 1 3.3298 13.0169 -3358.3
##
## Step: AIC=-3602.48
## log(price) ~ log(Total.Bsmt.SF + 1) + log(area) + Bedroom.AbvGr +
## Year.Built + log(X1st.Flr.SF) + log(Lot.Area) + Overall.Cond +
## Overall.Qual + TotRms.AbvGrd + Bsmt.Full.Bath + Garage.Area +
## Year.Remod.Add + Kitchen.AbvGr + Fireplaces
##
## Df Sum of Sq RSS AIC
## - TotRms.AbvGrd 1 0.0314 9.7370 -3606.5
## <none> 9.7056 -3602.5
## - Bedroom.AbvGr 1 0.1163 9.8219 -3599.3
## - Year.Remod.Add 1 0.1723 9.8780 -3594.6
## - Kitchen.AbvGr 1 0.1938 9.8995 -3592.8
## - Fireplaces 1 0.3500 10.0556 -3579.7
## - log(Total.Bsmt.SF + 1) 1 0.3932 10.0988 -3576.2
## - log(X1st.Flr.SF) 1 0.4617 10.1674 -3570.5
## - Garage.Area 1 0.4694 10.1750 -3569.9
## - Bsmt.Full.Bath 1 0.9012 10.6069 -3535.3
## - log(Lot.Area) 1 1.3381 11.0438 -3501.7
## - Overall.Cond 1 1.6559 11.3615 -3478.1
## - log(area) 1 2.4051 12.1107 -3425.0
## - Year.Built 1 2.8042 12.5098 -3398.0
## - Overall.Qual 1 3.4359 13.1416 -3357.0
##
## Step: AIC=-3606.52
## log(price) ~ log(Total.Bsmt.SF + 1) + log(area) + Bedroom.AbvGr +
## Year.Built + log(X1st.Flr.SF) + log(Lot.Area) + Overall.Cond +
## Overall.Qual + Bsmt.Full.Bath + Garage.Area + Year.Remod.Add +
## Kitchen.AbvGr + Fireplaces
##
## Df Sum of Sq RSS AIC
## <none> 9.7370 -3606.5
## - Bedroom.AbvGr 1 0.0881 9.8251 -3605.7
## - Kitchen.AbvGr 1 0.1645 9.9015 -3599.3
## - Year.Remod.Add 1 0.1745 9.9115 -3598.5
## - Fireplaces 1 0.3540 10.0910 -3583.5
## - log(Total.Bsmt.SF + 1) 1 0.3863 10.1233 -3580.9
## - log(X1st.Flr.SF) 1 0.4575 10.1945 -3575.0
## - Garage.Area 1 0.4690 10.2060 -3574.1
## - Bsmt.Full.Bath 1 0.8815 10.6185 -3541.1
## - log(Lot.Area) 1 1.4350 11.1720 -3498.9
## - Overall.Cond 1 1.6814 11.4184 -3480.7
## - Year.Built 1 2.7831 12.5201 -3404.1
## - Overall.Qual 1 3.5019 13.2390 -3357.6
## - log(area) 1 3.5209 13.2579 -3356.4##
## Call:
## lm(formula = log(price) ~ log(Total.Bsmt.SF + 1) + log(area) +
## Bedroom.AbvGr + Year.Built + log(X1st.Flr.SF) + log(Lot.Area) +
## Overall.Cond + Overall.Qual + TotRms.AbvGrd + Bsmt.Full.Bath +
## Garage.Area + Year.Remod.Add + Kitchen.AbvGr + Fireplaces,
## data = na.omit(train))
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.79372 -0.06114 -0.00193 0.06426 0.46489
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -1.7208258 0.5069813 -3.394 0.000721 ***
## log(Total.Bsmt.SF + 1) 0.0218761 0.0038026 5.753 1.24e-08 ***
## log(area) 0.3732704 0.0262337 14.229 < 2e-16 ***
## Bedroom.AbvGr -0.0223625 0.0071480 -3.128 0.001820 **
## Year.Built 0.0032668 0.0002126 15.364 < 2e-16 ***
## log(X1st.Flr.SF) 0.1086250 0.0174232 6.235 7.26e-10 ***
## log(Lot.Area) 0.0961725 0.0090615 10.613 < 2e-16 ***
## Overall.Cond 0.0486805 0.0041232 11.806 < 2e-16 ***
## Overall.Qual 0.0805164 0.0047344 17.007 < 2e-16 ***
## TotRms.AbvGrd 0.0081077 0.0049880 1.625 0.104456
## Bsmt.Full.Bath 0.0706328 0.0081094 8.710 < 2e-16 ***
## Garage.Area 0.0001540 0.0000245 6.286 5.30e-10 ***
## Year.Remod.Add 0.0010245 0.0002690 3.809 0.000150 ***
## Kitchen.AbvGr -0.0922838 0.0228473 -4.039 5.87e-05 ***
## Fireplaces 0.0386499 0.0071206 5.428 7.52e-08 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.109 on 817 degrees of freedom
## Multiple R-squared: 0.9179, Adjusted R-squared: 0.9165
## F-statistic: 652.7 on 14 and 817 DF, p-value: < 2.2e-16##
## Call:
## lm(formula = log(price) ~ log(Total.Bsmt.SF + 1) + log(area) +
## Bedroom.AbvGr + Year.Built + log(X1st.Flr.SF) + log(Lot.Area) +
## Overall.Cond + Overall.Qual + Bsmt.Full.Bath + Garage.Area +
## Year.Remod.Add + Kitchen.AbvGr + Fireplaces, data = na.omit(train))
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.79493 -0.06288 -0.00231 0.06402 0.45808
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -1.846e+00 5.016e-01 -3.680 0.000248 ***
## log(Total.Bsmt.SF + 1) 2.167e-02 3.804e-03 5.696 1.71e-08 ***
## log(area) 3.941e-01 2.291e-02 17.198 < 2e-16 ***
## Bedroom.AbvGr -1.813e-02 6.663e-03 -2.721 0.006655 **
## Year.Built 3.251e-03 2.126e-04 15.291 < 2e-16 ***
## log(X1st.Flr.SF) 1.081e-01 1.744e-02 6.199 8.99e-10 ***
## log(Lot.Area) 9.842e-02 8.964e-03 10.980 < 2e-16 ***
## Overall.Cond 4.900e-02 4.123e-03 11.885 < 2e-16 ***
## Overall.Qual 8.107e-02 4.727e-03 17.152 < 2e-16 ***
## Bsmt.Full.Bath 6.967e-02 8.096e-03 8.605 < 2e-16 ***
## Garage.Area 1.539e-04 2.452e-05 6.277 5.61e-10 ***
## Year.Remod.Add 1.031e-03 2.692e-04 3.829 0.000139 ***
## Kitchen.AbvGr -8.096e-02 2.178e-02 -3.717 0.000215 ***
## Fireplaces 3.886e-02 7.127e-03 5.453 6.55e-08 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.1091 on 818 degrees of freedom
## Multiple R-squared: 0.9177, Adjusted R-squared: 0.9164
## F-statistic: 701.3 on 13 and 818 DF, p-value: < 2.2e-160.0.0.11.6 Linear model with interaction and its analysis
##
## Call:
## lm(formula = log(price) ~ log(Total.Bsmt.SF + 1) + log(area) *
## Bedroom.AbvGr * Year.Built + log(X1st.Flr.SF) + log(Lot.Area) +
## Overall.Cond * Overall.Qual + TotRms.AbvGrd + Bsmt.Full.Bath +
## Garage.Cars + Garage.Area + Year.Remod.Add + Kitchen.AbvGr +
## Fireplaces + MS.SubClass + Half.Bath + Full.Bath, data = na.omit(train))
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.78163 -0.06115 -0.00061 0.06028 0.47302
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 4.343e+01 1.730e+01 2.510 0.01226
## log(Total.Bsmt.SF + 1) 2.170e-02 3.865e-03 5.615 2.70e-08
## log(area) -6.505e+00 2.419e+00 -2.690 0.00730
## Bedroom.AbvGr -7.963e+00 6.011e+00 -1.325 0.18561
## Year.Built -1.922e-02 8.810e-03 -2.181 0.02946
## log(X1st.Flr.SF) 1.082e-01 2.174e-02 4.977 7.90e-07
## log(Lot.Area) 9.585e-02 1.021e-02 9.392 < 2e-16
## Overall.Cond 8.188e-02 1.632e-02 5.016 6.50e-07
## Overall.Qual 1.049e-01 1.643e-02 6.385 2.89e-10
## TotRms.AbvGrd 6.522e-03 5.045e-03 1.293 0.19648
## Bsmt.Full.Bath 6.788e-02 8.229e-03 8.249 6.46e-16
## Garage.Cars 1.438e-02 1.249e-02 1.151 0.25004
## Garage.Area 1.063e-04 4.225e-05 2.515 0.01210
## Year.Remod.Add 7.772e-04 2.740e-04 2.836 0.00468
## Kitchen.AbvGr -9.498e-02 2.524e-02 -3.763 0.00018
## Fireplaces 3.857e-02 7.158e-03 5.388 9.35e-08
## MS.SubClass -1.030e-04 1.296e-04 -0.795 0.42680
## Half.Bath 2.826e-03 1.145e-02 0.247 0.80515
## Full.Bath 8.890e-04 1.272e-02 0.070 0.94428
## log(area):Bedroom.AbvGr 1.316e+00 8.094e-01 1.626 0.10430
## log(area):Year.Built 3.456e-03 1.236e-03 2.797 0.00527
## Bedroom.AbvGr:Year.Built 3.914e-03 3.062e-03 1.278 0.20152
## Overall.Cond:Overall.Qual -5.522e-03 2.950e-03 -1.872 0.06161
## log(area):Bedroom.AbvGr:Year.Built -6.520e-04 4.122e-04 -1.582 0.11406
##
## (Intercept) *
## log(Total.Bsmt.SF + 1) ***
## log(area) **
## Bedroom.AbvGr
## Year.Built *
## log(X1st.Flr.SF) ***
## log(Lot.Area) ***
## Overall.Cond ***
## Overall.Qual ***
## TotRms.AbvGrd
## Bsmt.Full.Bath ***
## Garage.Cars
## Garage.Area *
## Year.Remod.Add **
## Kitchen.AbvGr ***
## Fireplaces ***
## MS.SubClass
## Half.Bath
## Full.Bath
## log(area):Bedroom.AbvGr
## log(area):Year.Built **
## Bedroom.AbvGr:Year.Built
## Overall.Cond:Overall.Qual .
## log(area):Bedroom.AbvGr:Year.Built
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.1075 on 808 degrees of freedom
## Multiple R-squared: 0.921, Adjusted R-squared: 0.9187
## F-statistic: 409.4 on 23 and 808 DF, p-value: < 2.2e-16## r.squared adj.r.squared sigma statistic p.value df logLik AIC
## 1 0.9209797 0.9187304 0.1075439 409.4444 0 24 686.8601 -1323.72
## BIC deviance df.residual
## 1 -1205.624 9.345074 808## 2.5 % 97.5 %
## (Intercept) 9.469098e+00 77.3873183434
## log(Total.Bsmt.SF + 1) 1.411465e-02 0.0292875950
## log(area) -1.125247e+01 -1.7578151055
## Bedroom.AbvGr -1.976243e+01 3.8355545352
## Year.Built -3.650952e-02 -0.0019228676
## log(X1st.Flr.SF) 6.553052e-02 0.1508898315
## log(Lot.Area) 7.581477e-02 0.1158807782
## Overall.Cond 4.983728e-02 0.1139243224
## Overall.Qual 7.265499e-02 0.1371590314
## TotRms.AbvGrd -3.381194e-03 0.0164252403
## Bsmt.Full.Bath 5.172938e-02 0.0840353526
## Garage.Cars -1.014066e-02 0.0388966727
## Garage.Area 2.331953e-05 0.0001891964
## Year.Remod.Add 2.393571e-04 0.0013151415
## Kitchen.AbvGr -1.445222e-01 -0.0454304679
## Fireplaces 2.451594e-02 0.0526156154
## MS.SubClass -3.573803e-04 0.0001513266
## Half.Bath -1.965544e-02 0.0253081694
## Full.Bath -2.407194e-02 0.0258499964
## log(area):Bedroom.AbvGr -2.725365e-01 2.9049144352
## log(area):Year.Built 1.031108e-03 0.0058815472
## Bedroom.AbvGr:Year.Built -2.096319e-03 0.0099246021
## Overall.Cond:Overall.Qual -1.131399e-02 0.0002691105
## log(area):Bedroom.AbvGr:Year.Built -1.461002e-03 0.0001570324## [1] 11.9928## [1] 0.1059814## [1] 1.220155e-18## 0% 25% 50% 75% 100%
## -0.7816257781 -0.0611500663 -0.0006125184 0.0602807665 0.4730200464
0.0.0.12 Section 3.2 Transformation
Transformations of variable is used to make the skewed distribution to nearly normally distributed. Following methods are used for this purpose. log, exp, sqrt, sqr, cube root, cube, etc. box-cox: y(!) = (y ! “1) !, ! # 0 log y, ! = 0
I have used transformation to normalize distribution and to get rid of skewness making the mean near zero.
0.0.0.12.1 Models without log transform of dependent variable.
## Start: AIC=18555.14
## price ~ 1
##
## Df Sum of Sq RSS AIC
## + Overall.Qual 1 2.5739e+12 1.4501e+12 17708
## + area 1 2.2538e+12 1.7701e+12 17874
## + Total.Bsmt.SF 1 1.7999e+12 2.2241e+12 18064
## + X1st.Flr.SF 1 1.7660e+12 2.2580e+12 18076
## + Garage.Cars 1 1.7497e+12 2.2742e+12 18082
## + Garage.Area 1 1.5801e+12 2.4438e+12 18142
## + Full.Bath 1 1.3282e+12 2.6957e+12 18224
## + Year.Built 1 1.2731e+12 2.7508e+12 18241
## + Year.Remod.Add 1 1.1818e+12 2.8422e+12 18268
## + TotRms.AbvGrd 1 1.1382e+12 2.8858e+12 18281
## + Fireplaces 1 1.0987e+12 2.9252e+12 18292
## + Wood.Deck.SF 1 7.3296e+11 3.2910e+12 18390
## + Open.Porch.SF 1 4.6071e+11 3.5632e+12 18456
## + Bsmt.Full.Bath 1 4.0364e+11 3.6203e+12 18469
## + X2nd.Flr.SF 1 3.9028e+11 3.6337e+12 18472
## + Half.Bath 1 3.5515e+11 3.6688e+12 18480
## + Central.Air 1 2.7011e+11 3.7538e+12 18499
## + Lot.Area 1 2.6742e+11 3.7565e+12 18500
## + Bedroom.AbvGr 1 2.2497e+11 3.7990e+12 18509
## + Enclosed.Porch 1 9.2731e+10 3.9312e+12 18538
## + Overall.Cond 1 5.7382e+10 3.9666e+12 18545
## + Kitchen.AbvGr 1 3.1067e+10 3.9929e+12 18551
## + MS.SubClass 1 1.8632e+10 4.0053e+12 18553
## + Bsmt.Half.Bath 1 1.3450e+10 4.0105e+12 18554
## + Pool.Area 1 1.3023e+10 4.0109e+12 18554
## + Screen.Porch 1 1.0229e+10 4.0137e+12 18555
## <none> 4.0239e+12 18555
##
## Step: AIC=17707.95
## price ~ Overall.Qual
##
## Df Sum of Sq RSS AIC
## + area 1 4.7335e+11 9.7670e+11 17381
## + X1st.Flr.SF 1 4.3167e+11 1.0184e+12 17416
## + Total.Bsmt.SF 1 3.6474e+11 1.0853e+12 17469
## + Garage.Area 1 2.6879e+11 1.1813e+12 17539
## + Garage.Cars 1 2.3846e+11 1.2116e+12 17561
## + TotRms.AbvGrd 1 2.0713e+11 1.2429e+12 17582
## + Lot.Area 1 1.7074e+11 1.2793e+12 17606
## + Fireplaces 1 1.6846e+11 1.2816e+12 17607
## + Wood.Deck.SF 1 1.5256e+11 1.2975e+12 17618
## + Bsmt.Full.Bath 1 1.2885e+11 1.3212e+12 17633
## + Full.Bath 1 1.1605e+11 1.3340e+12 17641
## + Year.Remod.Add 1 7.0260e+10 1.3798e+12 17669
## + Year.Built 1 7.0190e+10 1.3799e+12 17669
## + MS.SubClass 1 5.8846e+10 1.3912e+12 17676
## + Bedroom.AbvGr 1 5.8791e+10 1.3913e+12 17676
## + Open.Porch.SF 1 4.2403e+10 1.4077e+12 17685
## + X2nd.Flr.SF 1 2.3768e+10 1.4263e+12 17696
## + Half.Bath 1 2.1428e+10 1.4286e+12 17698
## + Central.Air 1 1.0588e+10 1.4395e+12 17704
## <none> 1.4501e+12 17708
## + Pool.Area 1 3.0726e+09 1.4470e+12 17708
## + Bsmt.Half.Bath 1 2.9574e+09 1.4471e+12 17708
## + Enclosed.Porch 1 2.4965e+09 1.4476e+12 17709
## + Overall.Cond 1 2.1874e+09 1.4479e+12 17709
## + Screen.Porch 1 1.5413e+09 1.4485e+12 17709
## + Kitchen.AbvGr 1 4.6268e+06 1.4501e+12 17710
## - Overall.Qual 1 2.5739e+12 4.0239e+12 18555
##
## Step: AIC=17381.17
## price ~ Overall.Qual + area
##
## Df Sum of Sq RSS AIC
## + Total.Bsmt.SF 1 2.4375e+11 7.3295e+11 17144
## + X1st.Flr.SF 1 1.8790e+11 7.8881e+11 17205
## + X2nd.Flr.SF 1 1.7385e+11 8.0285e+11 17220
## + Bsmt.Full.Bath 1 1.5949e+11 8.1721e+11 17235
## + Year.Built 1 1.3253e+11 8.4418e+11 17262
## + Garage.Area 1 1.3004e+11 8.4666e+11 17264
## + Garage.Cars 1 1.0059e+11 8.7612e+11 17293
## + MS.SubClass 1 8.0106e+10 8.9660e+11 17312
## + Lot.Area 1 7.1632e+10 9.0507e+11 17320
## + Wood.Deck.SF 1 6.9219e+10 9.0749e+11 17322
## + Bedroom.AbvGr 1 6.1987e+10 9.1472e+11 17329
## + Year.Remod.Add 1 4.9334e+10 9.2737e+11 17340
## + Fireplaces 1 3.3938e+10 9.4277e+11 17354
## + Kitchen.AbvGr 1 3.1871e+10 9.4483e+11 17356
## + Central.Air 1 2.3807e+10 9.5290e+11 17363
## + Enclosed.Porch 1 1.6082e+10 9.6062e+11 17369
## + TotRms.AbvGrd 1 1.3855e+10 9.6285e+11 17371
## + Half.Bath 1 1.1566e+10 9.6514e+11 17373
## + Open.Porch.SF 1 8.5273e+09 9.6818e+11 17376
## <none> 9.7670e+11 17381
## + Pool.Area 1 1.0172e+09 9.7569e+11 17382
## + Bsmt.Half.Bath 1 5.1106e+08 9.7619e+11 17383
## + Screen.Porch 1 3.9012e+08 9.7631e+11 17383
## + Full.Bath 1 1.7415e+08 9.7653e+11 17383
## + Overall.Cond 1 7.4630e+07 9.7663e+11 17383
## - area 1 4.7335e+11 1.4501e+12 17708
## - Overall.Qual 1 7.9344e+11 1.7701e+12 17874
##
## Step: AIC=17144.3
## price ~ Overall.Qual + area + Total.Bsmt.SF
##
## Df Sum of Sq RSS AIC
## + Year.Built 1 7.4649e+10 6.5830e+11 17057
## + Bsmt.Full.Bath 1 6.6183e+10 6.6677e+11 17068
## + Garage.Area 1 5.8828e+10 6.7413e+11 17077
## + Year.Remod.Add 1 5.3735e+10 6.7922e+11 17083
## + Garage.Cars 1 4.7886e+10 6.8507e+11 17090
## + Bedroom.AbvGr 1 4.7578e+10 6.8538e+11 17091
## + Wood.Deck.SF 1 3.8326e+10 6.9463e+11 17102
## + Kitchen.AbvGr 1 3.3850e+10 6.9910e+11 17107
## + Lot.Area 1 3.0164e+10 7.0279e+11 17111
## + MS.SubClass 1 1.8785e+10 7.1417e+11 17125
## + Fireplaces 1 1.8475e+10 7.1448e+11 17125
## + X1st.Flr.SF 1 1.1210e+10 7.2174e+11 17134
## + Central.Air 1 1.0598e+10 7.2236e+11 17134
## + Enclosed.Porch 1 9.8493e+09 7.2310e+11 17135
## + TotRms.AbvGrd 1 9.4624e+09 7.2349e+11 17136
## + X2nd.Flr.SF 1 7.2485e+09 7.2571e+11 17138
## + Overall.Cond 1 4.8257e+09 7.2813e+11 17141
## + Half.Bath 1 3.9920e+09 7.2896e+11 17142
## + Pool.Area 1 2.6764e+09 7.3028e+11 17143
## <none> 7.3295e+11 17144
## + Bsmt.Half.Bath 1 1.0176e+09 7.3194e+11 17145
## + Open.Porch.SF 1 9.6923e+08 7.3198e+11 17145
## + Full.Bath 1 4.0779e+08 7.3255e+11 17146
## + Screen.Porch 1 2.6705e+07 7.3293e+11 17146
## - Total.Bsmt.SF 1 2.4375e+11 9.7670e+11 17381
## - area 1 3.5236e+11 1.0853e+12 17469
## - Overall.Qual 1 4.2483e+11 1.1578e+12 17523
##
## Step: AIC=17056.93
## price ~ Overall.Qual + area + Total.Bsmt.SF + Year.Built
##
## Df Sum of Sq RSS AIC
## + Bsmt.Full.Bath 1 5.2149e+10 6.0616e+11 16990
## + Bedroom.AbvGr 1 4.6036e+10 6.1227e+11 16999
## + Lot.Area 1 3.7391e+10 6.2091e+11 17010
## + Overall.Cond 1 3.4221e+10 6.2408e+11 17015
## + MS.SubClass 1 3.1171e+10 6.2713e+11 17019
## + Garage.Area 1 3.0737e+10 6.2757e+11 17019
## + Kitchen.AbvGr 1 2.7474e+10 6.3083e+11 17024
## + Wood.Deck.SF 1 2.4813e+10 6.3349e+11 17027
## + Fireplaces 1 1.9016e+10 6.3929e+11 17035
## + Garage.Cars 1 1.8674e+10 6.3963e+11 17035
## + Year.Remod.Add 1 1.7157e+10 6.4115e+11 17037
## + Full.Bath 1 1.6440e+10 6.4187e+11 17038
## + X1st.Flr.SF 1 1.4942e+10 6.4336e+11 17040
## + X2nd.Flr.SF 1 1.1299e+10 6.4701e+11 17045
## + TotRms.AbvGrd 1 5.3965e+09 6.5291e+11 17052
## + Pool.Area 1 2.5615e+09 6.5574e+11 17056
## + Central.Air 1 1.7995e+09 6.5651e+11 17057
## <none> 6.5830e+11 17057
## + Screen.Porch 1 9.5292e+08 6.5735e+11 17058
## + Half.Bath 1 4.5465e+08 6.5785e+11 17058
## + Bsmt.Half.Bath 1 2.8845e+08 6.5802e+11 17059
## + Open.Porch.SF 1 8.6432e+07 6.5822e+11 17059
## + Enclosed.Porch 1 1.3064e+05 6.5830e+11 17059
## - Year.Built 1 7.4649e+10 7.3295e+11 17144
## - Total.Bsmt.SF 1 1.8587e+11 8.4418e+11 17262
## - Overall.Qual 1 1.9650e+11 8.5480e+11 17272
## - area 1 3.9914e+11 1.0574e+12 17449
##
## Step: AIC=16990.27
## price ~ Overall.Qual + area + Total.Bsmt.SF + Year.Built + Bsmt.Full.Bath
##
## Df Sum of Sq RSS AIC
## + MS.SubClass 1 3.6162e+10 5.6999e+11 16941
## + Bedroom.AbvGr 1 3.3516e+10 5.7264e+11 16945
## + Lot.Area 1 3.1268e+10 5.7489e+11 16948
## + Overall.Cond 1 3.0807e+10 5.7535e+11 16949
## + Kitchen.AbvGr 1 2.8741e+10 5.7742e+11 16952
## + Garage.Area 1 2.4985e+10 5.8117e+11 16957
## + Year.Remod.Add 1 1.7566e+10 5.8859e+11 16968
## + Wood.Deck.SF 1 1.4536e+10 5.9162e+11 16972
## + Garage.Cars 1 1.4145e+10 5.9201e+11 16973
## + X1st.Flr.SF 1 1.2319e+10 5.9384e+11 16975
## + Fireplaces 1 1.1455e+10 5.9470e+11 16976
## + Full.Bath 1 1.0086e+10 5.9607e+11 16978
## + X2nd.Flr.SF 1 9.3524e+09 5.9680e+11 16979
## + Pool.Area 1 3.7192e+09 6.0244e+11 16987
## + TotRms.AbvGrd 1 2.2529e+09 6.0390e+11 16989
## + Central.Air 1 1.7008e+09 6.0446e+11 16990
## <none> 6.0616e+11 16990
## + Bsmt.Half.Bath 1 6.2472e+08 6.0553e+11 16991
## + Half.Bath 1 5.8494e+08 6.0557e+11 16992
## + Screen.Porch 1 3.8761e+08 6.0577e+11 16992
## + Enclosed.Porch 1 8.3064e+07 6.0607e+11 16992
## + Open.Porch.SF 1 6.9895e+07 6.0609e+11 16992
## - Bsmt.Full.Bath 1 5.2149e+10 6.5830e+11 17057
## - Year.Built 1 6.0615e+10 6.6677e+11 17068
## - Total.Bsmt.SF 1 1.1955e+11 7.2571e+11 17138
## - Overall.Qual 1 1.9728e+11 8.0344e+11 17223
## - area 1 4.2349e+11 1.0296e+12 17429
##
## Step: AIC=16941.09
## price ~ Overall.Qual + area + Total.Bsmt.SF + Year.Built + Bsmt.Full.Bath +
## MS.SubClass
##
## Df Sum of Sq RSS AIC
## + Bedroom.AbvGr 1 4.7760e+10 5.2223e+11 16870
## + Lot.Area 1 2.3142e+10 5.4685e+11 16909
## + Overall.Cond 1 2.2469e+10 5.4752e+11 16910
## + Garage.Area 1 2.1249e+10 5.4875e+11 16912
## + Year.Remod.Add 1 1.5956e+10 5.5404e+11 16920
## + Garage.Cars 1 1.3722e+10 5.5627e+11 16923
## + Kitchen.AbvGr 1 1.3635e+10 5.5636e+11 16923
## + Wood.Deck.SF 1 1.1681e+10 5.5831e+11 16926
## + Fireplaces 1 1.1658e+10 5.5834e+11 16926
## + Full.Bath 1 7.1902e+09 5.6280e+11 16933
## + X1st.Flr.SF 1 6.2842e+09 5.6371e+11 16934
## + TotRms.AbvGrd 1 4.8852e+09 5.6511e+11 16936
## + X2nd.Flr.SF 1 4.2924e+09 5.6570e+11 16937
## + Pool.Area 1 3.3221e+09 5.6667e+11 16938
## <none> 5.6999e+11 16941
## + Bsmt.Half.Bath 1 6.3005e+08 5.6936e+11 16942
## + Central.Air 1 6.0138e+08 5.6939e+11 16942
## + Half.Bath 1 4.6502e+08 5.6953e+11 16942
## + Screen.Porch 1 2.8812e+08 5.6971e+11 16943
## + Open.Porch.SF 1 7.6997e+06 5.6999e+11 16943
## + Enclosed.Porch 1 5.6850e+06 5.6999e+11 16943
## - MS.SubClass 1 3.6162e+10 6.0616e+11 16990
## - Bsmt.Full.Bath 1 5.7140e+10 6.2713e+11 17019
## - Total.Bsmt.SF 1 6.9222e+10 6.3922e+11 17035
## - Year.Built 1 7.2393e+10 6.4239e+11 17039
## - Overall.Qual 1 2.0605e+11 7.7605e+11 17196
## - area 1 4.5059e+11 1.0206e+12 17424
##
## Step: AIC=16870.28
## price ~ Overall.Qual + area + Total.Bsmt.SF + Year.Built + Bsmt.Full.Bath +
## MS.SubClass + Bedroom.AbvGr
##
## Df Sum of Sq RSS AIC
## + Overall.Cond 1 2.6797e+10 4.9544e+11 16829
## + Lot.Area 1 2.3008e+10 4.9923e+11 16835
## + Garage.Area 1 1.7698e+10 5.0454e+11 16844
## + Year.Remod.Add 1 1.1327e+10 5.1091e+11 16854
## + Garage.Cars 1 1.1171e+10 5.1106e+11 16854
## + Wood.Deck.SF 1 7.7954e+09 5.1444e+11 16860
## + Fireplaces 1 6.2191e+09 5.1601e+11 16862
## + Kitchen.AbvGr 1 5.7828e+09 5.1645e+11 16863
## + Pool.Area 1 3.9344e+09 5.1830e+11 16866
## + Full.Bath 1 3.8530e+09 5.1838e+11 16866
## + Central.Air 1 2.2589e+09 5.1997e+11 16869
## + X1st.Flr.SF 1 2.2368e+09 5.2000e+11 16869
## <none> 5.2223e+11 16870
## + Bsmt.Half.Bath 1 1.1915e+09 5.2104e+11 16870
## + X2nd.Flr.SF 1 8.4921e+08 5.2138e+11 16871
## + TotRms.AbvGrd 1 4.5057e+08 5.2178e+11 16872
## + Screen.Porch 1 3.4914e+08 5.2188e+11 16872
## + Half.Bath 1 2.2115e+08 5.2201e+11 16872
## + Enclosed.Porch 1 1.9867e+08 5.2204e+11 16872
## + Open.Porch.SF 1 1.8470e+08 5.2205e+11 16872
## - Bsmt.Full.Bath 1 4.2609e+10 5.6484e+11 16934
## - Bedroom.AbvGr 1 4.7760e+10 5.6999e+11 16941
## - MS.SubClass 1 5.0407e+10 5.7264e+11 16945
## - Total.Bsmt.SF 1 6.0978e+10 5.8321e+11 16960
## - Year.Built 1 7.5424e+10 5.9766e+11 16981
## - Overall.Qual 1 1.5252e+11 6.7476e+11 17082
## - area 1 4.3210e+11 9.5434e+11 17370
##
## Step: AIC=16828.45
## price ~ Overall.Qual + area + Total.Bsmt.SF + Year.Built + Bsmt.Full.Bath +
## MS.SubClass + Bedroom.AbvGr + Overall.Cond
##
## Df Sum of Sq RSS AIC
## + Lot.Area 1 2.4922e+10 4.7051e+11 16788
## + Garage.Area 1 1.8634e+10 4.7680e+11 16799
## + Garage.Cars 1 1.2268e+10 4.8317e+11 16810
## + Fireplaces 1 6.1366e+09 4.8930e+11 16820
## + Kitchen.AbvGr 1 3.7046e+09 4.9173e+11 16824
## + Wood.Deck.SF 1 3.6461e+09 4.9179e+11 16824
## + Pool.Area 1 3.1433e+09 4.9229e+11 16825
## + X1st.Flr.SF 1 2.7358e+09 4.9270e+11 16826
## + Year.Remod.Add 1 2.6799e+09 4.9276e+11 16826
## + Full.Bath 1 2.4201e+09 4.9302e+11 16826
## + X2nd.Flr.SF 1 1.2874e+09 4.9415e+11 16828
## <none> 4.9544e+11 16829
## + Bsmt.Half.Bath 1 6.0265e+08 4.9483e+11 16829
## + TotRms.AbvGrd 1 5.2959e+08 4.9491e+11 16830
## + Half.Bath 1 3.3434e+08 4.9510e+11 16830
## + Screen.Porch 1 1.6929e+08 4.9527e+11 16830
## + Open.Porch.SF 1 1.0869e+08 4.9533e+11 16830
## + Central.Air 1 8.0400e+07 4.9536e+11 16830
## + Enclosed.Porch 1 1.7396e+05 4.9544e+11 16831
## - Overall.Cond 1 2.6797e+10 5.2223e+11 16870
## - Bsmt.Full.Bath 1 3.8572e+10 5.3401e+11 16889
## - MS.SubClass 1 4.0469e+10 5.3591e+11 16892
## - Bedroom.AbvGr 1 5.2088e+10 5.4752e+11 16910
## - Total.Bsmt.SF 1 7.1185e+10 5.6662e+11 16938
## - Year.Built 1 9.9424e+10 5.9486e+11 16979
## - Overall.Qual 1 1.2201e+11 6.1745e+11 17010
## - area 1 4.4899e+11 9.4443e+11 17363
##
## Step: AIC=16787.51
## price ~ Overall.Qual + area + Total.Bsmt.SF + Year.Built + Bsmt.Full.Bath +
## MS.SubClass + Bedroom.AbvGr + Overall.Cond + Lot.Area
##
## Df Sum of Sq RSS AIC
## + Garage.Area 1 1.6596e+10 4.5392e+11 16760
## + Garage.Cars 1 1.0167e+10 4.6035e+11 16771
## + Wood.Deck.SF 1 3.6525e+09 4.6686e+11 16783
## + Fireplaces 1 3.5350e+09 4.6698e+11 16783
## + Kitchen.AbvGr 1 3.0319e+09 4.6748e+11 16784
## + Pool.Area 1 2.8332e+09 4.6768e+11 16785
## + Full.Bath 1 2.5932e+09 4.6792e+11 16785
## + Year.Remod.Add 1 2.4963e+09 4.6802e+11 16785
## + X1st.Flr.SF 1 1.6563e+09 4.6886e+11 16787
## <none> 4.7051e+11 16788
## + X2nd.Flr.SF 1 6.7036e+08 4.6984e+11 16788
## + TotRms.AbvGrd 1 4.2311e+08 4.7009e+11 16789
## + Central.Air 1 3.1217e+08 4.7020e+11 16789
## + Screen.Porch 1 1.7979e+08 4.7034e+11 16789
## + Half.Bath 1 1.4241e+08 4.7037e+11 16789
## + Bsmt.Half.Bath 1 1.0849e+08 4.7041e+11 16789
## + Enclosed.Porch 1 8.7208e+07 4.7043e+11 16789
## + Open.Porch.SF 1 4.2736e+07 4.7047e+11 16789
## - Lot.Area 1 2.4922e+10 4.9544e+11 16829
## - Overall.Cond 1 2.8711e+10 4.9923e+11 16835
## - MS.SubClass 1 3.1390e+10 5.0190e+11 16839
## - Bsmt.Full.Bath 1 3.3274e+10 5.0379e+11 16842
## - Bedroom.AbvGr 1 5.2108e+10 5.2262e+11 16873
## - Total.Bsmt.SF 1 6.0575e+10 5.3109e+11 16886
## - Year.Built 1 1.0597e+11 5.7648e+11 16955
## - Overall.Qual 1 1.3007e+11 6.0059e+11 16989
## - area 1 4.0672e+11 8.7724e+11 17304
##
## Step: AIC=16759.64
## price ~ Overall.Qual + area + Total.Bsmt.SF + Year.Built + Bsmt.Full.Bath +
## MS.SubClass + Bedroom.AbvGr + Overall.Cond + Lot.Area + Garage.Area
##
## Df Sum of Sq RSS AIC
## + Kitchen.AbvGr 1 4.1720e+09 4.4975e+11 16754
## + Fireplaces 1 4.1293e+09 4.4979e+11 16754
## + Wood.Deck.SF 1 2.9481e+09 4.5097e+11 16756
## + Year.Remod.Add 1 2.8187e+09 4.5110e+11 16757
## + Pool.Area 1 2.2711e+09 4.5165e+11 16758
## + Full.Bath 1 1.9572e+09 4.5196e+11 16758
## + Central.Air 1 1.1730e+09 4.5275e+11 16760
## <none> 4.5392e+11 16760
## + X1st.Flr.SF 1 7.2425e+08 4.5320e+11 16760
## + TotRms.AbvGrd 1 3.2280e+08 4.5360e+11 16761
## + Screen.Porch 1 1.6927e+08 4.5375e+11 16761
## + X2nd.Flr.SF 1 1.6909e+08 4.5375e+11 16761
## + Bsmt.Half.Bath 1 1.2670e+08 4.5379e+11 16761
## + Garage.Cars 1 6.4567e+07 4.5385e+11 16762
## + Enclosed.Porch 1 6.2634e+07 4.5386e+11 16762
## + Half.Bath 1 1.0141e+07 4.5391e+11 16762
## + Open.Porch.SF 1 5.3511e+06 4.5391e+11 16762
## - Garage.Area 1 1.6596e+10 4.7051e+11 16788
## - Lot.Area 1 2.2883e+10 4.7680e+11 16799
## - MS.SubClass 1 2.8127e+10 4.8205e+11 16808
## - Overall.Cond 1 2.9544e+10 4.8346e+11 16810
## - Bsmt.Full.Bath 1 2.9934e+10 4.8385e+11 16811
## - Bedroom.AbvGr 1 4.8580e+10 5.0250e+11 16842
## - Total.Bsmt.SF 1 5.1316e+10 5.0524e+11 16847
## - Year.Built 1 8.0304e+10 5.3422e+11 16893
## - Overall.Qual 1 1.2285e+11 5.7677e+11 16957
## - area 1 3.4780e+11 8.0172e+11 17231
##
## Step: AIC=16753.96
## price ~ Overall.Qual + area + Total.Bsmt.SF + Year.Built + Bsmt.Full.Bath +
## MS.SubClass + Bedroom.AbvGr + Overall.Cond + Lot.Area + Garage.Area +
## Kitchen.AbvGr
##
## Df Sum of Sq RSS AIC
## + Fireplaces 1 3.8143e+09 4.4593e+11 16749
## + Central.Air 1 3.0808e+09 4.4667e+11 16750
## + Pool.Area 1 2.5751e+09 4.4717e+11 16751
## + Wood.Deck.SF 1 2.5228e+09 4.4722e+11 16751
## + Year.Remod.Add 1 2.4395e+09 4.4731e+11 16751
## + TotRms.AbvGrd 1 1.8603e+09 4.4789e+11 16753
## + X1st.Flr.SF 1 1.7892e+09 4.4796e+11 16753
## <none> 4.4975e+11 16754
## + Full.Bath 1 8.3906e+08 4.4891e+11 16754
## + X2nd.Flr.SF 1 7.0698e+08 4.4904e+11 16755
## + Half.Bath 1 1.9159e+08 4.4956e+11 16756
## + Bsmt.Half.Bath 1 9.9360e+07 4.4965e+11 16756
## + Screen.Porch 1 9.1893e+07 4.4966e+11 16756
## + Enclosed.Porch 1 9.0012e+07 4.4966e+11 16756
## + Open.Porch.SF 1 3.6618e+07 4.4971e+11 16756
## + Garage.Cars 1 3.6740e+06 4.4974e+11 16756
## - Kitchen.AbvGr 1 4.1720e+09 4.5392e+11 16760
## - Garage.Area 1 1.7736e+10 4.6748e+11 16784
## - MS.SubClass 1 1.9027e+10 4.6877e+11 16786
## - Lot.Area 1 2.2058e+10 4.7181e+11 16792
## - Overall.Cond 1 2.7226e+10 4.7697e+11 16801
## - Bsmt.Full.Bath 1 3.0568e+10 4.8031e+11 16807
## - Bedroom.AbvGr 1 4.1083e+10 4.9083e+11 16825
## - Total.Bsmt.SF 1 5.4119e+10 5.0387e+11 16847
## - Year.Built 1 7.2411e+10 5.2216e+11 16876
## - Overall.Qual 1 1.1436e+11 5.6410e+11 16940
## - area 1 3.4892e+11 7.9866e+11 17230
##
## Step: AIC=16748.87
## price ~ Overall.Qual + area + Total.Bsmt.SF + Year.Built + Bsmt.Full.Bath +
## MS.SubClass + Bedroom.AbvGr + Overall.Cond + Lot.Area + Garage.Area +
## Kitchen.AbvGr + Fireplaces
##
## Df Sum of Sq RSS AIC
## + Central.Air 1 3.7930e+09 4.4214e+11 16744
## + Year.Remod.Add 1 3.7377e+09 4.4220e+11 16744
## + Pool.Area 1 3.7175e+09 4.4222e+11 16744
## + Wood.Deck.SF 1 2.0608e+09 4.4387e+11 16747
## + TotRms.AbvGrd 1 1.7759e+09 4.4416e+11 16748
## + X1st.Flr.SF 1 1.1770e+09 4.4476e+11 16749
## <none> 4.4593e+11 16749
## + Full.Bath 1 5.9046e+08 4.4534e+11 16750
## + X2nd.Flr.SF 1 3.6358e+08 4.4557e+11 16750
## + Half.Bath 1 1.7072e+08 4.4576e+11 16751
## + Enclosed.Porch 1 5.6136e+07 4.4588e+11 16751
## + Open.Porch.SF 1 1.4049e+07 4.4592e+11 16751
## + Garage.Cars 1 6.4612e+06 4.4593e+11 16751
## + Bsmt.Half.Bath 1 9.5659e+05 4.4593e+11 16751
## + Screen.Porch 1 4.5659e+04 4.4593e+11 16751
## - Fireplaces 1 3.8143e+09 4.4975e+11 16754
## - Kitchen.AbvGr 1 3.8570e+09 4.4979e+11 16754
## - Garage.Area 1 1.8279e+10 4.6421e+11 16780
## - MS.SubClass 1 1.9190e+10 4.6512e+11 16782
## - Lot.Area 1 1.9552e+10 4.6549e+11 16783
## - Overall.Cond 1 2.7158e+10 4.7309e+11 16796
## - Bsmt.Full.Bath 1 2.7774e+10 4.7371e+11 16797
## - Bedroom.AbvGr 1 3.7261e+10 4.8319e+11 16814
## - Total.Bsmt.SF 1 5.2944e+10 4.9888e+11 16840
## - Year.Built 1 7.2607e+10 5.1854e+11 16872
## - Overall.Qual 1 1.0954e+11 5.5547e+11 16930
## - area 1 2.9088e+11 7.3681e+11 17165
##
## Step: AIC=16743.76
## price ~ Overall.Qual + area + Total.Bsmt.SF + Year.Built + Bsmt.Full.Bath +
## MS.SubClass + Bedroom.AbvGr + Overall.Cond + Lot.Area + Garage.Area +
## Kitchen.AbvGr + Fireplaces + Central.Air
##
## Df Sum of Sq RSS AIC
## + Pool.Area 1 3.6592e+09 4.3848e+11 16739
## + Year.Remod.Add 1 3.3371e+09 4.3880e+11 16740
## + Wood.Deck.SF 1 1.7057e+09 4.4043e+11 16743
## + TotRms.AbvGrd 1 1.6759e+09 4.4046e+11 16743
## + X1st.Flr.SF 1 1.4127e+09 4.4073e+11 16743
## <none> 4.4214e+11 16744
## + Full.Bath 1 7.7078e+08 4.4137e+11 16744
## + X2nd.Flr.SF 1 5.5228e+08 4.4159e+11 16745
## + Half.Bath 1 9.9354e+07 4.4204e+11 16746
## + Garage.Cars 1 2.5118e+07 4.4211e+11 16746
## + Bsmt.Half.Bath 1 1.2402e+07 4.4213e+11 16746
## + Open.Porch.SF 1 6.3354e+06 4.4213e+11 16746
## + Enclosed.Porch 1 2.0063e+06 4.4214e+11 16746
## + Screen.Porch 1 2.3571e+05 4.4214e+11 16746
## - Central.Air 1 3.7930e+09 4.4593e+11 16749
## - Fireplaces 1 4.5265e+09 4.4667e+11 16750
## - Kitchen.AbvGr 1 5.9709e+09 4.4811e+11 16753
## - MS.SubClass 1 1.7578e+10 4.5972e+11 16774
## - Lot.Area 1 2.0008e+10 4.6215e+11 16779
## - Garage.Area 1 2.0504e+10 4.6264e+11 16780
## - Bsmt.Full.Bath 1 2.7549e+10 4.6969e+11 16792
## - Overall.Cond 1 3.0946e+10 4.7309e+11 16798
## - Bedroom.AbvGr 1 3.2308e+10 4.7445e+11 16800
## - Total.Bsmt.SF 1 5.5162e+10 4.9730e+11 16840
## - Year.Built 1 7.6110e+10 5.1825e+11 16874
## - Overall.Qual 1 1.0879e+11 5.5093e+11 16925
## - area 1 2.7776e+11 7.1990e+11 17147
##
## Step: AIC=16738.85
## price ~ Overall.Qual + area + Total.Bsmt.SF + Year.Built + Bsmt.Full.Bath +
## MS.SubClass + Bedroom.AbvGr + Overall.Cond + Lot.Area + Garage.Area +
## Kitchen.AbvGr + Fireplaces + Central.Air + Pool.Area
##
## Df Sum of Sq RSS AIC
## + Year.Remod.Add 1 3.1828e+09 4.3530e+11 16735
## + TotRms.AbvGrd 1 2.1023e+09 4.3638e+11 16737
## + Wood.Deck.SF 1 2.1017e+09 4.3638e+11 16737
## + X1st.Flr.SF 1 1.5157e+09 4.3697e+11 16738
## <none> 4.3848e+11 16739
## + Full.Bath 1 6.5562e+08 4.3783e+11 16740
## + X2nd.Flr.SF 1 5.9717e+08 4.3788e+11 16740
## + Half.Bath 1 1.8609e+08 4.3829e+11 16741
## + Bsmt.Half.Bath 1 1.1969e+08 4.3836e+11 16741
## + Screen.Porch 1 5.6913e+07 4.3842e+11 16741
## + Garage.Cars 1 4.7493e+07 4.3843e+11 16741
## + Open.Porch.SF 1 3.4634e+06 4.3848e+11 16741
## + Enclosed.Porch 1 6.3611e+05 4.3848e+11 16741
## - Pool.Area 1 3.6592e+09 4.4214e+11 16744
## - Central.Air 1 3.7347e+09 4.4222e+11 16744
## - Fireplaces 1 5.7327e+09 4.4421e+11 16748
## - Kitchen.AbvGr 1 6.3166e+09 4.4480e+11 16749
## - MS.SubClass 1 1.7329e+10 4.5581e+11 16769
## - Lot.Area 1 1.9351e+10 4.5783e+11 16773
## - Garage.Area 1 1.9858e+10 4.5834e+11 16774
## - Bsmt.Full.Bath 1 2.8152e+10 4.6663e+11 16789
## - Overall.Cond 1 2.9870e+10 4.6835e+11 16792
## - Bedroom.AbvGr 1 3.2189e+10 4.7067e+11 16796
## - Total.Bsmt.SF 1 5.5940e+10 4.9442e+11 16837
## - Year.Built 1 7.5318e+10 5.1380e+11 16869
## - Overall.Qual 1 1.0590e+11 5.4438e+11 16917
## - area 1 2.8047e+11 7.1895e+11 17148
##
## Step: AIC=16734.79
## price ~ Overall.Qual + area + Total.Bsmt.SF + Year.Built + Bsmt.Full.Bath +
## MS.SubClass + Bedroom.AbvGr + Overall.Cond + Lot.Area + Garage.Area +
## Kitchen.AbvGr + Fireplaces + Central.Air + Pool.Area + Year.Remod.Add
##
## Df Sum of Sq RSS AIC
## + Wood.Deck.SF 1 2.0224e+09 4.3328e+11 16733
## + TotRms.AbvGrd 1 1.9975e+09 4.3330e+11 16733
## + X1st.Flr.SF 1 1.2873e+09 4.3401e+11 16734
## + Full.Bath 1 1.2671e+09 4.3403e+11 16734
## <none> 4.3530e+11 16735
## + X2nd.Flr.SF 1 4.6934e+08 4.3483e+11 16736
## + Bsmt.Half.Bath 1 1.6249e+08 4.3514e+11 16737
## + Half.Bath 1 1.2241e+08 4.3518e+11 16737
## + Screen.Porch 1 1.0376e+08 4.3519e+11 16737
## + Garage.Cars 1 9.4155e+07 4.3520e+11 16737
## + Open.Porch.SF 1 4.7012e+06 4.3529e+11 16737
## + Enclosed.Porch 1 1.1585e+06 4.3530e+11 16737
## - Year.Remod.Add 1 3.1828e+09 4.3848e+11 16739
## - Central.Air 1 3.3473e+09 4.3865e+11 16739
## - Pool.Area 1 3.5048e+09 4.3880e+11 16740
## - Kitchen.AbvGr 1 5.5752e+09 4.4087e+11 16743
## - Fireplaces 1 7.0476e+09 4.4235e+11 16746
## - MS.SubClass 1 1.7680e+10 4.5298e+11 16766
## - Lot.Area 1 1.8819e+10 4.5412e+11 16768
## - Garage.Area 1 2.0137e+10 4.5544e+11 16770
## - Overall.Cond 1 2.0182e+10 4.5548e+11 16771
## - Bsmt.Full.Bath 1 2.8499e+10 4.6380e+11 16786
## - Bedroom.AbvGr 1 2.9318e+10 4.6462e+11 16787
## - Year.Built 1 4.4777e+10 4.8007e+11 16814
## - Total.Bsmt.SF 1 5.7083e+10 4.9238e+11 16835
## - Overall.Qual 1 9.8930e+10 5.3423e+11 16903
## - area 1 2.4813e+11 6.8343e+11 17108
##
## Step: AIC=16732.91
## price ~ Overall.Qual + area + Total.Bsmt.SF + Year.Built + Bsmt.Full.Bath +
## MS.SubClass + Bedroom.AbvGr + Overall.Cond + Lot.Area + Garage.Area +
## Kitchen.AbvGr + Fireplaces + Central.Air + Pool.Area + Year.Remod.Add +
## Wood.Deck.SF
##
## Df Sum of Sq RSS AIC
## + TotRms.AbvGrd 1 1.9482e+09 4.3133e+11 16731
## + X1st.Flr.SF 1 1.2957e+09 4.3198e+11 16732
## + Full.Bath 1 1.2511e+09 4.3202e+11 16733
## <none> 4.3328e+11 16733
## + X2nd.Flr.SF 1 4.7524e+08 4.3280e+11 16734
## + Screen.Porch 1 2.2808e+08 4.3305e+11 16735
## + Half.Bath 1 1.3833e+08 4.3314e+11 16735
## + Garage.Cars 1 8.1243e+07 4.3319e+11 16735
## - Wood.Deck.SF 1 2.0224e+09 4.3530e+11 16735
## + Bsmt.Half.Bath 1 5.3679e+07 4.3322e+11 16735
## + Enclosed.Porch 1 2.6840e+06 4.3327e+11 16735
## + Open.Porch.SF 1 1.4172e+06 4.3327e+11 16735
## - Central.Air 1 2.9890e+09 4.3626e+11 16737
## - Year.Remod.Add 1 3.1034e+09 4.3638e+11 16737
## - Pool.Area 1 3.8867e+09 4.3716e+11 16738
## - Kitchen.AbvGr 1 5.0552e+09 4.3833e+11 16741
## - Fireplaces 1 6.4423e+09 4.3972e+11 16743
## - MS.SubClass 1 1.7333e+10 4.5061e+11 16764
## - Overall.Cond 1 1.7505e+10 4.5078e+11 16764
## - Lot.Area 1 1.8955e+10 4.5223e+11 16767
## - Garage.Area 1 1.9175e+10 4.5245e+11 16767
## - Bsmt.Full.Bath 1 2.5902e+10 4.5918e+11 16779
## - Bedroom.AbvGr 1 2.8265e+10 4.6154e+11 16784
## - Year.Built 1 4.0980e+10 4.7426e+11 16806
## - Total.Bsmt.SF 1 5.5790e+10 4.8907e+11 16832
## - Overall.Qual 1 1.0037e+11 5.3364e+11 16904
## - area 1 2.3378e+11 6.6706e+11 17090
##
## Step: AIC=16731.16
## price ~ Overall.Qual + area + Total.Bsmt.SF + Year.Built + Bsmt.Full.Bath +
## MS.SubClass + Bedroom.AbvGr + Overall.Cond + Lot.Area + Garage.Area +
## Kitchen.AbvGr + Fireplaces + Central.Air + Pool.Area + Year.Remod.Add +
## Wood.Deck.SF + TotRms.AbvGrd
##
## Df Sum of Sq RSS AIC
## + X1st.Flr.SF 1 1.2271e+09 4.3010e+11 16731
## + Full.Bath 1 1.0983e+09 4.3023e+11 16731
## <none> 4.3133e+11 16731
## + X2nd.Flr.SF 1 4.1460e+08 4.3091e+11 16732
## + Screen.Porch 1 2.0325e+08 4.3112e+11 16733
## - TotRms.AbvGrd 1 1.9482e+09 4.3328e+11 16733
## + Garage.Cars 1 1.0873e+08 4.3122e+11 16733
## - Wood.Deck.SF 1 1.9731e+09 4.3330e+11 16733
## + Bsmt.Half.Bath 1 1.0026e+08 4.3123e+11 16733
## + Half.Bath 1 8.9855e+07 4.3124e+11 16733
## + Enclosed.Porch 1 1.0696e+07 4.3132e+11 16733
## + Open.Porch.SF 1 1.9925e+06 4.3133e+11 16733
## - Central.Air 1 2.9005e+09 4.3423e+11 16735
## - Year.Remod.Add 1 3.0022e+09 4.3433e+11 16735
## - Pool.Area 1 4.3039e+09 4.3563e+11 16737
## - Fireplaces 1 6.3851e+09 4.3771e+11 16741
## - Kitchen.AbvGr 1 6.6844e+09 4.3801e+11 16742
## - MS.SubClass 1 1.5043e+10 4.4637e+11 16758
## - Overall.Cond 1 1.7244e+10 4.4857e+11 16762
## - Lot.Area 1 1.8559e+10 4.4989e+11 16764
## - Garage.Area 1 1.9167e+10 4.5049e+11 16765
## - Bsmt.Full.Bath 1 2.6862e+10 4.5819e+11 16779
## - Bedroom.AbvGr 1 2.9817e+10 4.6114e+11 16785
## - Year.Built 1 4.1374e+10 4.7270e+11 16805
## - Total.Bsmt.SF 1 5.6701e+10 4.8803e+11 16832
## - Overall.Qual 1 9.7011e+10 5.2834e+11 16898
## - area 1 1.5060e+11 5.8193e+11 16978
##
## Step: AIC=16730.79
## price ~ Overall.Qual + area + Total.Bsmt.SF + Year.Built + Bsmt.Full.Bath +
## MS.SubClass + Bedroom.AbvGr + Overall.Cond + Lot.Area + Garage.Area +
## Kitchen.AbvGr + Fireplaces + Central.Air + Pool.Area + Year.Remod.Add +
## Wood.Deck.SF + TotRms.AbvGrd + X1st.Flr.SF
##
## Df Sum of Sq RSS AIC
## + X2nd.Flr.SF 1 2.6176e+09 4.2748e+11 16728
## + Full.Bath 1 1.0600e+09 4.2904e+11 16731
## <none> 4.3010e+11 16731
## - X1st.Flr.SF 1 1.2271e+09 4.3133e+11 16731
## + Screen.Porch 1 2.0262e+08 4.2990e+11 16732
## - TotRms.AbvGrd 1 1.8796e+09 4.3198e+11 16732
## - Wood.Deck.SF 1 1.9820e+09 4.3208e+11 16733
## + Bsmt.Half.Bath 1 7.9744e+07 4.3002e+11 16733
## + Garage.Cars 1 6.7839e+07 4.3003e+11 16733
## + Enclosed.Porch 1 4.2985e+07 4.3006e+11 16733
## + Open.Porch.SF 1 1.7977e+07 4.3008e+11 16733
## + Half.Bath 1 1.0914e+07 4.3009e+11 16733
## - Year.Remod.Add 1 2.7873e+09 4.3289e+11 16734
## - Central.Air 1 3.1041e+09 4.3320e+11 16735
## - Pool.Area 1 4.4022e+09 4.3450e+11 16737
## - Fireplaces 1 5.5661e+09 4.3567e+11 16740
## - Kitchen.AbvGr 1 7.6422e+09 4.3774e+11 16743
## - MS.SubClass 1 1.2146e+10 4.4225e+11 16752
## - Overall.Cond 1 1.7579e+10 4.4768e+11 16762
## - Lot.Area 1 1.7917e+10 4.4802e+11 16763
## - Garage.Area 1 1.8122e+10 4.4822e+11 16763
## - Total.Bsmt.SF 1 2.5353e+10 4.5545e+11 16776
## - Bsmt.Full.Bath 1 2.6750e+10 4.5685e+11 16779
## - Bedroom.AbvGr 1 2.7061e+10 4.5716e+11 16780
## - Year.Built 1 4.2116e+10 4.7222e+11 16807
## - Overall.Qual 1 9.7902e+10 5.2800e+11 16899
## - area 1 1.3740e+11 5.6750e+11 16959
##
## Step: AIC=16727.71
## price ~ Overall.Qual + area + Total.Bsmt.SF + Year.Built + Bsmt.Full.Bath +
## MS.SubClass + Bedroom.AbvGr + Overall.Cond + Lot.Area + Garage.Area +
## Kitchen.AbvGr + Fireplaces + Central.Air + Pool.Area + Year.Remod.Add +
## Wood.Deck.SF + TotRms.AbvGrd + X1st.Flr.SF + X2nd.Flr.SF
##
## Df Sum of Sq RSS AIC
## <none> 4.2748e+11 16728
## + Full.Bath 1 9.0722e+08 4.2658e+11 16728
## - area 1 1.5889e+09 4.2907e+11 16729
## + Enclosed.Porch 1 1.7290e+08 4.2731e+11 16729
## + Screen.Porch 1 1.6371e+08 4.2732e+11 16729
## - Wood.Deck.SF 1 1.9704e+09 4.2945e+11 16730
## + Garage.Cars 1 7.5952e+07 4.2741e+11 16730
## + Bsmt.Half.Bath 1 7.5624e+07 4.2741e+11 16730
## + Open.Porch.SF 1 3.6183e+05 4.2748e+11 16730
## + Half.Bath 1 2.8148e+05 4.2748e+11 16730
## - TotRms.AbvGrd 1 2.0757e+09 4.2956e+11 16730
## - X2nd.Flr.SF 1 2.6176e+09 4.3010e+11 16731
## - Central.Air 1 2.6589e+09 4.3014e+11 16731
## - Year.Remod.Add 1 2.7102e+09 4.3019e+11 16731
## - X1st.Flr.SF 1 3.4301e+09 4.3091e+11 16732
## - Pool.Area 1 4.5768e+09 4.3206e+11 16735
## - Fireplaces 1 5.3595e+09 4.3284e+11 16736
## - Kitchen.AbvGr 1 8.0072e+09 4.3549e+11 16741
## - MS.SubClass 1 1.2292e+10 4.3977e+11 16749
## - Overall.Cond 1 1.6623e+10 4.4411e+11 16758
## - Lot.Area 1 1.7410e+10 4.4489e+11 16759
## - Garage.Area 1 1.7733e+10 4.4522e+11 16760
## - Total.Bsmt.SF 1 2.6165e+10 4.5365e+11 16775
## - Bsmt.Full.Bath 1 2.6392e+10 4.5388e+11 16776
## - Bedroom.AbvGr 1 2.8557e+10 4.5604e+11 16780
## - Year.Built 1 4.0138e+10 4.6762e+11 16800
## - Overall.Qual 1 9.3274e+10 5.2076e+11 16890## [1] "(Intercept)" "Overall.Qual" "area" "Total.Bsmt.SF"
## [5] "Year.Built" "Bsmt.Full.Bath" "MS.SubClass" "Bedroom.AbvGr"
## [9] "Overall.Cond" "Lot.Area" "Garage.Area" "Kitchen.AbvGr"
## [13] "Fireplaces" "Central.AirY" "Pool.Area" "Year.Remod.Add"
## [17] "Wood.Deck.SF" "TotRms.AbvGrd" "X1st.Flr.SF" "X2nd.Flr.SF"Comparison of models without transform and another with transforming dependent variable and many response variables. R-squared,F-Value,p-value residuals and RMSE.
0.0.0.12.2 Comparison of Without and with transform
##
## Call:
## lm(formula = price ~ area + Lot.Area + Garage.Area + Total.Bsmt.SF +
## Garage.Cars + Full.Bath + Half.Bath + Bedroom.AbvGr + Year.Built +
## X1st.Flr.SF + X2nd.Flr.SF + Central.Air + Overall.Cond +
## Overall.Qual, data = na.omit(train))
##
## Coefficients:
## (Intercept) area Lot.Area Garage.Area Total.Bsmt.SF
## -1.172e+06 4.059e+01 6.508e-01 3.275e+01 3.186e+01
## Garage.Cars Full.Bath Half.Bath Bedroom.AbvGr Year.Built
## -5.068e+02 -7.993e+03 -6.989e+02 -1.167e+04 5.590e+02
## X1st.Flr.SF X2nd.Flr.SF Central.AirY Overall.Cond Overall.Qual
## 4.124e+01 3.143e+01 -7.162e+03 7.325e+03 1.438e+04##
## Call:
## lm(formula = log(price) ~ log(area) + log(Lot.Area) + log(Garage.Area +
## 1) + log(Total.Bsmt.SF + 1) + Garage.Cars + Full.Bath + Half.Bath +
## Bedroom.AbvGr + Year.Built + log(X1st.Flr.SF) + log(X2nd.Flr.SF +
## 1) + Central.Air + Overall.Cond + Overall.Qual, data = na.omit(train))
##
## Coefficients:
## (Intercept) log(area) log(Lot.Area)
## -1.314383 0.468054 0.117261
## log(Garage.Area + 1) log(Total.Bsmt.SF + 1) Garage.Cars
## -0.006562 0.025036 0.048721
## Full.Bath Half.Bath Bedroom.AbvGr
## -0.005490 0.003722 -0.039392
## Year.Built log(X1st.Flr.SF) log(X2nd.Flr.SF + 1)
## 0.003653 0.098768 -0.003630
## Central.AirY Overall.Cond Overall.Qual
## 0.077536 0.052957 0.086568## [1] -4.537925e-13## [1] -3.115534e-19## 2.5 % 97.5 %
## (Intercept) -1.361086e+06 -9.820055e+05
## area 7.110726e+00 7.406796e+01
## Lot.Area 4.773544e-01 8.242506e-01
## Garage.Area 1.379114e+01 5.171140e+01
## Total.Bsmt.SF 2.434553e+01 3.937309e+01
## Garage.Cars -6.059945e+03 5.046258e+03
## Full.Bath -1.316951e+04 -2.816803e+03
## Half.Bath -5.660108e+03 4.262289e+03
## Bedroom.AbvGr -1.447659e+04 -8.869932e+03
## Year.Built 4.608435e+02 6.571586e+02
## X1st.Flr.SF 6.994519e+00 7.548937e+01
## X2nd.Flr.SF -2.233027e+00 6.509950e+01
## Central.AirY -1.591563e+04 1.591552e+03
## Overall.Cond 5.523820e+03 9.126681e+03
## Overall.Qual 1.233222e+04 1.643758e+04## 2.5 % 97.5 %
## (Intercept) -2.358227428 -0.270538774
## log(area) 0.353142220 0.582966590
## log(Lot.Area) 0.098676706 0.135845577
## log(Garage.Area + 1) -0.015688136 0.002564775
## log(Total.Bsmt.SF + 1) 0.017143874 0.032927825
## Garage.Cars 0.029656523 0.067784701
## Full.Bath -0.030157612 0.019177306
## Half.Bath -0.020081841 0.027525833
## Bedroom.AbvGr -0.053006962 -0.025777761
## Year.Built 0.003181167 0.004125363
## log(X1st.Flr.SF) -0.001015218 0.198552142
## log(X2nd.Flr.SF + 1) -0.013075492 0.005815758
## Central.AirY 0.034857233 0.120214377
## Overall.Cond 0.044410793 0.061502477
## Overall.Qual 0.076679684 0.096455645
## [1] Inf## [1] 21739.91## [1] 0.8747555## [1] 0.9033951step-wise regression with lm models
## Start: AIC=18555.14
## price ~ 1
##
## Df Sum of Sq RSS AIC
## + Overall.Qual 1 2.5739e+12 1.4501e+12 17708
## + area 1 2.2538e+12 1.7701e+12 17874
## + Total.Bsmt.SF 1 1.7999e+12 2.2241e+12 18064
## + X1st.Flr.SF 1 1.7660e+12 2.2580e+12 18076
## + Garage.Cars 1 1.7497e+12 2.2742e+12 18082
## + Garage.Area 1 1.5801e+12 2.4438e+12 18142
## + Full.Bath 1 1.3282e+12 2.6957e+12 18224
## + Year.Built 1 1.2731e+12 2.7508e+12 18241
## + Year.Remod.Add 1 1.1818e+12 2.8422e+12 18268
## + TotRms.AbvGrd 1 1.1382e+12 2.8858e+12 18281
## + Fireplaces 1 1.0987e+12 2.9252e+12 18292
## + Wood.Deck.SF 1 7.3296e+11 3.2910e+12 18390
## + Open.Porch.SF 1 4.6071e+11 3.5632e+12 18456
## + Bsmt.Full.Bath 1 4.0364e+11 3.6203e+12 18469
## + X2nd.Flr.SF 1 3.9028e+11 3.6337e+12 18472
## + Half.Bath 1 3.5515e+11 3.6688e+12 18480
## + Central.Air 1 2.7011e+11 3.7538e+12 18499
## + Lot.Area 1 2.6742e+11 3.7565e+12 18500
## + Bedroom.AbvGr 1 2.2497e+11 3.7990e+12 18509
## + Enclosed.Porch 1 9.2731e+10 3.9312e+12 18538
## + Overall.Cond 1 5.7382e+10 3.9666e+12 18545
## + Kitchen.AbvGr 1 3.1067e+10 3.9929e+12 18551
## + MS.SubClass 1 1.8632e+10 4.0053e+12 18553
## + Bsmt.Half.Bath 1 1.3450e+10 4.0105e+12 18554
## + Pool.Area 1 1.3023e+10 4.0109e+12 18554
## + Screen.Porch 1 1.0229e+10 4.0137e+12 18555
## <none> 4.0239e+12 18555
##
## Step: AIC=17707.95
## price ~ Overall.Qual
##
## Df Sum of Sq RSS AIC
## + area 1 4.7335e+11 9.7670e+11 17381
## + X1st.Flr.SF 1 4.3167e+11 1.0184e+12 17416
## + Total.Bsmt.SF 1 3.6474e+11 1.0853e+12 17469
## + Garage.Area 1 2.6879e+11 1.1813e+12 17539
## + Garage.Cars 1 2.3846e+11 1.2116e+12 17561
## + TotRms.AbvGrd 1 2.0713e+11 1.2429e+12 17582
## + Lot.Area 1 1.7074e+11 1.2793e+12 17606
## + Fireplaces 1 1.6846e+11 1.2816e+12 17607
## + Wood.Deck.SF 1 1.5256e+11 1.2975e+12 17618
## + Bsmt.Full.Bath 1 1.2885e+11 1.3212e+12 17633
## + Full.Bath 1 1.1605e+11 1.3340e+12 17641
## + Year.Remod.Add 1 7.0260e+10 1.3798e+12 17669
## + Year.Built 1 7.0190e+10 1.3799e+12 17669
## + MS.SubClass 1 5.8846e+10 1.3912e+12 17676
## + Bedroom.AbvGr 1 5.8791e+10 1.3913e+12 17676
## + Open.Porch.SF 1 4.2403e+10 1.4077e+12 17685
## + X2nd.Flr.SF 1 2.3768e+10 1.4263e+12 17696
## + Half.Bath 1 2.1428e+10 1.4286e+12 17698
## + Central.Air 1 1.0588e+10 1.4395e+12 17704
## <none> 1.4501e+12 17708
## + Pool.Area 1 3.0726e+09 1.4470e+12 17708
## + Bsmt.Half.Bath 1 2.9574e+09 1.4471e+12 17708
## + Enclosed.Porch 1 2.4965e+09 1.4476e+12 17709
## + Overall.Cond 1 2.1874e+09 1.4479e+12 17709
## + Screen.Porch 1 1.5413e+09 1.4485e+12 17709
## + Kitchen.AbvGr 1 4.6268e+06 1.4501e+12 17710
## - Overall.Qual 1 2.5739e+12 4.0239e+12 18555
##
## Step: AIC=17381.17
## price ~ Overall.Qual + area
##
## Df Sum of Sq RSS AIC
## + Total.Bsmt.SF 1 2.4375e+11 7.3295e+11 17144
## + X1st.Flr.SF 1 1.8790e+11 7.8881e+11 17205
## + X2nd.Flr.SF 1 1.7385e+11 8.0285e+11 17220
## + Bsmt.Full.Bath 1 1.5949e+11 8.1721e+11 17235
## + Year.Built 1 1.3253e+11 8.4418e+11 17262
## + Garage.Area 1 1.3004e+11 8.4666e+11 17264
## + Garage.Cars 1 1.0059e+11 8.7612e+11 17293
## + MS.SubClass 1 8.0106e+10 8.9660e+11 17312
## + Lot.Area 1 7.1632e+10 9.0507e+11 17320
## + Wood.Deck.SF 1 6.9219e+10 9.0749e+11 17322
## + Bedroom.AbvGr 1 6.1987e+10 9.1472e+11 17329
## + Year.Remod.Add 1 4.9334e+10 9.2737e+11 17340
## + Fireplaces 1 3.3938e+10 9.4277e+11 17354
## + Kitchen.AbvGr 1 3.1871e+10 9.4483e+11 17356
## + Central.Air 1 2.3807e+10 9.5290e+11 17363
## + Enclosed.Porch 1 1.6082e+10 9.6062e+11 17369
## + TotRms.AbvGrd 1 1.3855e+10 9.6285e+11 17371
## + Half.Bath 1 1.1566e+10 9.6514e+11 17373
## + Open.Porch.SF 1 8.5273e+09 9.6818e+11 17376
## <none> 9.7670e+11 17381
## + Pool.Area 1 1.0172e+09 9.7569e+11 17382
## + Bsmt.Half.Bath 1 5.1106e+08 9.7619e+11 17383
## + Screen.Porch 1 3.9012e+08 9.7631e+11 17383
## + Full.Bath 1 1.7415e+08 9.7653e+11 17383
## + Overall.Cond 1 7.4630e+07 9.7663e+11 17383
## - area 1 4.7335e+11 1.4501e+12 17708
## - Overall.Qual 1 7.9344e+11 1.7701e+12 17874
##
## Step: AIC=17144.3
## price ~ Overall.Qual + area + Total.Bsmt.SF
##
## Df Sum of Sq RSS AIC
## + Year.Built 1 7.4649e+10 6.5830e+11 17057
## + Bsmt.Full.Bath 1 6.6183e+10 6.6677e+11 17068
## + Garage.Area 1 5.8828e+10 6.7413e+11 17077
## + Year.Remod.Add 1 5.3735e+10 6.7922e+11 17083
## + Garage.Cars 1 4.7886e+10 6.8507e+11 17090
## + Bedroom.AbvGr 1 4.7578e+10 6.8538e+11 17091
## + Wood.Deck.SF 1 3.8326e+10 6.9463e+11 17102
## + Kitchen.AbvGr 1 3.3850e+10 6.9910e+11 17107
## + Lot.Area 1 3.0164e+10 7.0279e+11 17111
## + MS.SubClass 1 1.8785e+10 7.1417e+11 17125
## + Fireplaces 1 1.8475e+10 7.1448e+11 17125
## + X1st.Flr.SF 1 1.1210e+10 7.2174e+11 17134
## + Central.Air 1 1.0598e+10 7.2236e+11 17134
## + Enclosed.Porch 1 9.8493e+09 7.2310e+11 17135
## + TotRms.AbvGrd 1 9.4624e+09 7.2349e+11 17136
## + X2nd.Flr.SF 1 7.2485e+09 7.2571e+11 17138
## + Overall.Cond 1 4.8257e+09 7.2813e+11 17141
## + Half.Bath 1 3.9920e+09 7.2896e+11 17142
## + Pool.Area 1 2.6764e+09 7.3028e+11 17143
## <none> 7.3295e+11 17144
## + Bsmt.Half.Bath 1 1.0176e+09 7.3194e+11 17145
## + Open.Porch.SF 1 9.6923e+08 7.3198e+11 17145
## + Full.Bath 1 4.0779e+08 7.3255e+11 17146
## + Screen.Porch 1 2.6705e+07 7.3293e+11 17146
## - Total.Bsmt.SF 1 2.4375e+11 9.7670e+11 17381
## - area 1 3.5236e+11 1.0853e+12 17469
## - Overall.Qual 1 4.2483e+11 1.1578e+12 17523
##
## Step: AIC=17056.93
## price ~ Overall.Qual + area + Total.Bsmt.SF + Year.Built
##
## Df Sum of Sq RSS AIC
## + Bsmt.Full.Bath 1 5.2149e+10 6.0616e+11 16990
## + Bedroom.AbvGr 1 4.6036e+10 6.1227e+11 16999
## + Lot.Area 1 3.7391e+10 6.2091e+11 17010
## + Overall.Cond 1 3.4221e+10 6.2408e+11 17015
## + MS.SubClass 1 3.1171e+10 6.2713e+11 17019
## + Garage.Area 1 3.0737e+10 6.2757e+11 17019
## + Kitchen.AbvGr 1 2.7474e+10 6.3083e+11 17024
## + Wood.Deck.SF 1 2.4813e+10 6.3349e+11 17027
## + Fireplaces 1 1.9016e+10 6.3929e+11 17035
## + Garage.Cars 1 1.8674e+10 6.3963e+11 17035
## + Year.Remod.Add 1 1.7157e+10 6.4115e+11 17037
## + Full.Bath 1 1.6440e+10 6.4187e+11 17038
## + X1st.Flr.SF 1 1.4942e+10 6.4336e+11 17040
## + X2nd.Flr.SF 1 1.1299e+10 6.4701e+11 17045
## + TotRms.AbvGrd 1 5.3965e+09 6.5291e+11 17052
## + Pool.Area 1 2.5615e+09 6.5574e+11 17056
## + Central.Air 1 1.7995e+09 6.5651e+11 17057
## <none> 6.5830e+11 17057
## + Screen.Porch 1 9.5292e+08 6.5735e+11 17058
## + Half.Bath 1 4.5465e+08 6.5785e+11 17058
## + Bsmt.Half.Bath 1 2.8845e+08 6.5802e+11 17059
## + Open.Porch.SF 1 8.6432e+07 6.5822e+11 17059
## + Enclosed.Porch 1 1.3064e+05 6.5830e+11 17059
## - Year.Built 1 7.4649e+10 7.3295e+11 17144
## - Total.Bsmt.SF 1 1.8587e+11 8.4418e+11 17262
## - Overall.Qual 1 1.9650e+11 8.5480e+11 17272
## - area 1 3.9914e+11 1.0574e+12 17449
##
## Step: AIC=16990.27
## price ~ Overall.Qual + area + Total.Bsmt.SF + Year.Built + Bsmt.Full.Bath
##
## Df Sum of Sq RSS AIC
## + MS.SubClass 1 3.6162e+10 5.6999e+11 16941
## + Bedroom.AbvGr 1 3.3516e+10 5.7264e+11 16945
## + Lot.Area 1 3.1268e+10 5.7489e+11 16948
## + Overall.Cond 1 3.0807e+10 5.7535e+11 16949
## + Kitchen.AbvGr 1 2.8741e+10 5.7742e+11 16952
## + Garage.Area 1 2.4985e+10 5.8117e+11 16957
## + Year.Remod.Add 1 1.7566e+10 5.8859e+11 16968
## + Wood.Deck.SF 1 1.4536e+10 5.9162e+11 16972
## + Garage.Cars 1 1.4145e+10 5.9201e+11 16973
## + X1st.Flr.SF 1 1.2319e+10 5.9384e+11 16975
## + Fireplaces 1 1.1455e+10 5.9470e+11 16976
## + Full.Bath 1 1.0086e+10 5.9607e+11 16978
## + X2nd.Flr.SF 1 9.3524e+09 5.9680e+11 16979
## + Pool.Area 1 3.7192e+09 6.0244e+11 16987
## + TotRms.AbvGrd 1 2.2529e+09 6.0390e+11 16989
## + Central.Air 1 1.7008e+09 6.0446e+11 16990
## <none> 6.0616e+11 16990
## + Bsmt.Half.Bath 1 6.2472e+08 6.0553e+11 16991
## + Half.Bath 1 5.8494e+08 6.0557e+11 16992
## + Screen.Porch 1 3.8761e+08 6.0577e+11 16992
## + Enclosed.Porch 1 8.3064e+07 6.0607e+11 16992
## + Open.Porch.SF 1 6.9895e+07 6.0609e+11 16992
## - Bsmt.Full.Bath 1 5.2149e+10 6.5830e+11 17057
## - Year.Built 1 6.0615e+10 6.6677e+11 17068
## - Total.Bsmt.SF 1 1.1955e+11 7.2571e+11 17138
## - Overall.Qual 1 1.9728e+11 8.0344e+11 17223
## - area 1 4.2349e+11 1.0296e+12 17429
##
## Step: AIC=16941.09
## price ~ Overall.Qual + area + Total.Bsmt.SF + Year.Built + Bsmt.Full.Bath +
## MS.SubClass
##
## Df Sum of Sq RSS AIC
## + Bedroom.AbvGr 1 4.7760e+10 5.2223e+11 16870
## + Lot.Area 1 2.3142e+10 5.4685e+11 16909
## + Overall.Cond 1 2.2469e+10 5.4752e+11 16910
## + Garage.Area 1 2.1249e+10 5.4875e+11 16912
## + Year.Remod.Add 1 1.5956e+10 5.5404e+11 16920
## + Garage.Cars 1 1.3722e+10 5.5627e+11 16923
## + Kitchen.AbvGr 1 1.3635e+10 5.5636e+11 16923
## + Wood.Deck.SF 1 1.1681e+10 5.5831e+11 16926
## + Fireplaces 1 1.1658e+10 5.5834e+11 16926
## + Full.Bath 1 7.1902e+09 5.6280e+11 16933
## + X1st.Flr.SF 1 6.2842e+09 5.6371e+11 16934
## + TotRms.AbvGrd 1 4.8852e+09 5.6511e+11 16936
## + X2nd.Flr.SF 1 4.2924e+09 5.6570e+11 16937
## + Pool.Area 1 3.3221e+09 5.6667e+11 16938
## <none> 5.6999e+11 16941
## + Bsmt.Half.Bath 1 6.3005e+08 5.6936e+11 16942
## + Central.Air 1 6.0138e+08 5.6939e+11 16942
## + Half.Bath 1 4.6502e+08 5.6953e+11 16942
## + Screen.Porch 1 2.8812e+08 5.6971e+11 16943
## + Open.Porch.SF 1 7.6997e+06 5.6999e+11 16943
## + Enclosed.Porch 1 5.6850e+06 5.6999e+11 16943
## - MS.SubClass 1 3.6162e+10 6.0616e+11 16990
## - Bsmt.Full.Bath 1 5.7140e+10 6.2713e+11 17019
## - Total.Bsmt.SF 1 6.9222e+10 6.3922e+11 17035
## - Year.Built 1 7.2393e+10 6.4239e+11 17039
## - Overall.Qual 1 2.0605e+11 7.7605e+11 17196
## - area 1 4.5059e+11 1.0206e+12 17424
##
## Step: AIC=16870.28
## price ~ Overall.Qual + area + Total.Bsmt.SF + Year.Built + Bsmt.Full.Bath +
## MS.SubClass + Bedroom.AbvGr
##
## Df Sum of Sq RSS AIC
## + Overall.Cond 1 2.6797e+10 4.9544e+11 16829
## + Lot.Area 1 2.3008e+10 4.9923e+11 16835
## + Garage.Area 1 1.7698e+10 5.0454e+11 16844
## + Year.Remod.Add 1 1.1327e+10 5.1091e+11 16854
## + Garage.Cars 1 1.1171e+10 5.1106e+11 16854
## + Wood.Deck.SF 1 7.7954e+09 5.1444e+11 16860
## + Fireplaces 1 6.2191e+09 5.1601e+11 16862
## + Kitchen.AbvGr 1 5.7828e+09 5.1645e+11 16863
## + Pool.Area 1 3.9344e+09 5.1830e+11 16866
## + Full.Bath 1 3.8530e+09 5.1838e+11 16866
## + Central.Air 1 2.2589e+09 5.1997e+11 16869
## + X1st.Flr.SF 1 2.2368e+09 5.2000e+11 16869
## <none> 5.2223e+11 16870
## + Bsmt.Half.Bath 1 1.1915e+09 5.2104e+11 16870
## + X2nd.Flr.SF 1 8.4921e+08 5.2138e+11 16871
## + TotRms.AbvGrd 1 4.5057e+08 5.2178e+11 16872
## + Screen.Porch 1 3.4914e+08 5.2188e+11 16872
## + Half.Bath 1 2.2115e+08 5.2201e+11 16872
## + Enclosed.Porch 1 1.9867e+08 5.2204e+11 16872
## + Open.Porch.SF 1 1.8470e+08 5.2205e+11 16872
## - Bsmt.Full.Bath 1 4.2609e+10 5.6484e+11 16934
## - Bedroom.AbvGr 1 4.7760e+10 5.6999e+11 16941
## - MS.SubClass 1 5.0407e+10 5.7264e+11 16945
## - Total.Bsmt.SF 1 6.0978e+10 5.8321e+11 16960
## - Year.Built 1 7.5424e+10 5.9766e+11 16981
## - Overall.Qual 1 1.5252e+11 6.7476e+11 17082
## - area 1 4.3210e+11 9.5434e+11 17370
##
## Step: AIC=16828.45
## price ~ Overall.Qual + area + Total.Bsmt.SF + Year.Built + Bsmt.Full.Bath +
## MS.SubClass + Bedroom.AbvGr + Overall.Cond
##
## Df Sum of Sq RSS AIC
## + Lot.Area 1 2.4922e+10 4.7051e+11 16788
## + Garage.Area 1 1.8634e+10 4.7680e+11 16799
## + Garage.Cars 1 1.2268e+10 4.8317e+11 16810
## + Fireplaces 1 6.1366e+09 4.8930e+11 16820
## + Kitchen.AbvGr 1 3.7046e+09 4.9173e+11 16824
## + Wood.Deck.SF 1 3.6461e+09 4.9179e+11 16824
## + Pool.Area 1 3.1433e+09 4.9229e+11 16825
## + X1st.Flr.SF 1 2.7358e+09 4.9270e+11 16826
## + Year.Remod.Add 1 2.6799e+09 4.9276e+11 16826
## + Full.Bath 1 2.4201e+09 4.9302e+11 16826
## + X2nd.Flr.SF 1 1.2874e+09 4.9415e+11 16828
## <none> 4.9544e+11 16829
## + Bsmt.Half.Bath 1 6.0265e+08 4.9483e+11 16829
## + TotRms.AbvGrd 1 5.2959e+08 4.9491e+11 16830
## + Half.Bath 1 3.3434e+08 4.9510e+11 16830
## + Screen.Porch 1 1.6929e+08 4.9527e+11 16830
## + Open.Porch.SF 1 1.0869e+08 4.9533e+11 16830
## + Central.Air 1 8.0400e+07 4.9536e+11 16830
## + Enclosed.Porch 1 1.7396e+05 4.9544e+11 16831
## - Overall.Cond 1 2.6797e+10 5.2223e+11 16870
## - Bsmt.Full.Bath 1 3.8572e+10 5.3401e+11 16889
## - MS.SubClass 1 4.0469e+10 5.3591e+11 16892
## - Bedroom.AbvGr 1 5.2088e+10 5.4752e+11 16910
## - Total.Bsmt.SF 1 7.1185e+10 5.6662e+11 16938
## - Year.Built 1 9.9424e+10 5.9486e+11 16979
## - Overall.Qual 1 1.2201e+11 6.1745e+11 17010
## - area 1 4.4899e+11 9.4443e+11 17363
##
## Step: AIC=16787.51
## price ~ Overall.Qual + area + Total.Bsmt.SF + Year.Built + Bsmt.Full.Bath +
## MS.SubClass + Bedroom.AbvGr + Overall.Cond + Lot.Area
##
## Df Sum of Sq RSS AIC
## + Garage.Area 1 1.6596e+10 4.5392e+11 16760
## + Garage.Cars 1 1.0167e+10 4.6035e+11 16771
## + Wood.Deck.SF 1 3.6525e+09 4.6686e+11 16783
## + Fireplaces 1 3.5350e+09 4.6698e+11 16783
## + Kitchen.AbvGr 1 3.0319e+09 4.6748e+11 16784
## + Pool.Area 1 2.8332e+09 4.6768e+11 16785
## + Full.Bath 1 2.5932e+09 4.6792e+11 16785
## + Year.Remod.Add 1 2.4963e+09 4.6802e+11 16785
## + X1st.Flr.SF 1 1.6563e+09 4.6886e+11 16787
## <none> 4.7051e+11 16788
## + X2nd.Flr.SF 1 6.7036e+08 4.6984e+11 16788
## + TotRms.AbvGrd 1 4.2311e+08 4.7009e+11 16789
## + Central.Air 1 3.1217e+08 4.7020e+11 16789
## + Screen.Porch 1 1.7979e+08 4.7034e+11 16789
## + Half.Bath 1 1.4241e+08 4.7037e+11 16789
## + Bsmt.Half.Bath 1 1.0849e+08 4.7041e+11 16789
## + Enclosed.Porch 1 8.7208e+07 4.7043e+11 16789
## + Open.Porch.SF 1 4.2736e+07 4.7047e+11 16789
## - Lot.Area 1 2.4922e+10 4.9544e+11 16829
## - Overall.Cond 1 2.8711e+10 4.9923e+11 16835
## - MS.SubClass 1 3.1390e+10 5.0190e+11 16839
## - Bsmt.Full.Bath 1 3.3274e+10 5.0379e+11 16842
## - Bedroom.AbvGr 1 5.2108e+10 5.2262e+11 16873
## - Total.Bsmt.SF 1 6.0575e+10 5.3109e+11 16886
## - Year.Built 1 1.0597e+11 5.7648e+11 16955
## - Overall.Qual 1 1.3007e+11 6.0059e+11 16989
## - area 1 4.0672e+11 8.7724e+11 17304
##
## Step: AIC=16759.64
## price ~ Overall.Qual + area + Total.Bsmt.SF + Year.Built + Bsmt.Full.Bath +
## MS.SubClass + Bedroom.AbvGr + Overall.Cond + Lot.Area + Garage.Area
##
## Df Sum of Sq RSS AIC
## + Kitchen.AbvGr 1 4.1720e+09 4.4975e+11 16754
## + Fireplaces 1 4.1293e+09 4.4979e+11 16754
## + Wood.Deck.SF 1 2.9481e+09 4.5097e+11 16756
## + Year.Remod.Add 1 2.8187e+09 4.5110e+11 16757
## + Pool.Area 1 2.2711e+09 4.5165e+11 16758
## + Full.Bath 1 1.9572e+09 4.5196e+11 16758
## + Central.Air 1 1.1730e+09 4.5275e+11 16760
## <none> 4.5392e+11 16760
## + X1st.Flr.SF 1 7.2425e+08 4.5320e+11 16760
## + TotRms.AbvGrd 1 3.2280e+08 4.5360e+11 16761
## + Screen.Porch 1 1.6927e+08 4.5375e+11 16761
## + X2nd.Flr.SF 1 1.6909e+08 4.5375e+11 16761
## + Bsmt.Half.Bath 1 1.2670e+08 4.5379e+11 16761
## + Garage.Cars 1 6.4567e+07 4.5385e+11 16762
## + Enclosed.Porch 1 6.2634e+07 4.5386e+11 16762
## + Half.Bath 1 1.0141e+07 4.5391e+11 16762
## + Open.Porch.SF 1 5.3511e+06 4.5391e+11 16762
## - Garage.Area 1 1.6596e+10 4.7051e+11 16788
## - Lot.Area 1 2.2883e+10 4.7680e+11 16799
## - MS.SubClass 1 2.8127e+10 4.8205e+11 16808
## - Overall.Cond 1 2.9544e+10 4.8346e+11 16810
## - Bsmt.Full.Bath 1 2.9934e+10 4.8385e+11 16811
## - Bedroom.AbvGr 1 4.8580e+10 5.0250e+11 16842
## - Total.Bsmt.SF 1 5.1316e+10 5.0524e+11 16847
## - Year.Built 1 8.0304e+10 5.3422e+11 16893
## - Overall.Qual 1 1.2285e+11 5.7677e+11 16957
## - area 1 3.4780e+11 8.0172e+11 17231
##
## Step: AIC=16753.96
## price ~ Overall.Qual + area + Total.Bsmt.SF + Year.Built + Bsmt.Full.Bath +
## MS.SubClass + Bedroom.AbvGr + Overall.Cond + Lot.Area + Garage.Area +
## Kitchen.AbvGr
##
## Df Sum of Sq RSS AIC
## + Fireplaces 1 3.8143e+09 4.4593e+11 16749
## + Central.Air 1 3.0808e+09 4.4667e+11 16750
## + Pool.Area 1 2.5751e+09 4.4717e+11 16751
## + Wood.Deck.SF 1 2.5228e+09 4.4722e+11 16751
## + Year.Remod.Add 1 2.4395e+09 4.4731e+11 16751
## + TotRms.AbvGrd 1 1.8603e+09 4.4789e+11 16753
## + X1st.Flr.SF 1 1.7892e+09 4.4796e+11 16753
## <none> 4.4975e+11 16754
## + Full.Bath 1 8.3906e+08 4.4891e+11 16754
## + X2nd.Flr.SF 1 7.0698e+08 4.4904e+11 16755
## + Half.Bath 1 1.9159e+08 4.4956e+11 16756
## + Bsmt.Half.Bath 1 9.9360e+07 4.4965e+11 16756
## + Screen.Porch 1 9.1893e+07 4.4966e+11 16756
## + Enclosed.Porch 1 9.0012e+07 4.4966e+11 16756
## + Open.Porch.SF 1 3.6618e+07 4.4971e+11 16756
## + Garage.Cars 1 3.6740e+06 4.4974e+11 16756
## - Kitchen.AbvGr 1 4.1720e+09 4.5392e+11 16760
## - Garage.Area 1 1.7736e+10 4.6748e+11 16784
## - MS.SubClass 1 1.9027e+10 4.6877e+11 16786
## - Lot.Area 1 2.2058e+10 4.7181e+11 16792
## - Overall.Cond 1 2.7226e+10 4.7697e+11 16801
## - Bsmt.Full.Bath 1 3.0568e+10 4.8031e+11 16807
## - Bedroom.AbvGr 1 4.1083e+10 4.9083e+11 16825
## - Total.Bsmt.SF 1 5.4119e+10 5.0387e+11 16847
## - Year.Built 1 7.2411e+10 5.2216e+11 16876
## - Overall.Qual 1 1.1436e+11 5.6410e+11 16940
## - area 1 3.4892e+11 7.9866e+11 17230
##
## Step: AIC=16748.87
## price ~ Overall.Qual + area + Total.Bsmt.SF + Year.Built + Bsmt.Full.Bath +
## MS.SubClass + Bedroom.AbvGr + Overall.Cond + Lot.Area + Garage.Area +
## Kitchen.AbvGr + Fireplaces
##
## Df Sum of Sq RSS AIC
## + Central.Air 1 3.7930e+09 4.4214e+11 16744
## + Year.Remod.Add 1 3.7377e+09 4.4220e+11 16744
## + Pool.Area 1 3.7175e+09 4.4222e+11 16744
## + Wood.Deck.SF 1 2.0608e+09 4.4387e+11 16747
## + TotRms.AbvGrd 1 1.7759e+09 4.4416e+11 16748
## + X1st.Flr.SF 1 1.1770e+09 4.4476e+11 16749
## <none> 4.4593e+11 16749
## + Full.Bath 1 5.9046e+08 4.4534e+11 16750
## + X2nd.Flr.SF 1 3.6358e+08 4.4557e+11 16750
## + Half.Bath 1 1.7072e+08 4.4576e+11 16751
## + Enclosed.Porch 1 5.6136e+07 4.4588e+11 16751
## + Open.Porch.SF 1 1.4049e+07 4.4592e+11 16751
## + Garage.Cars 1 6.4612e+06 4.4593e+11 16751
## + Bsmt.Half.Bath 1 9.5659e+05 4.4593e+11 16751
## + Screen.Porch 1 4.5659e+04 4.4593e+11 16751
## - Fireplaces 1 3.8143e+09 4.4975e+11 16754
## - Kitchen.AbvGr 1 3.8570e+09 4.4979e+11 16754
## - Garage.Area 1 1.8279e+10 4.6421e+11 16780
## - MS.SubClass 1 1.9190e+10 4.6512e+11 16782
## - Lot.Area 1 1.9552e+10 4.6549e+11 16783
## - Overall.Cond 1 2.7158e+10 4.7309e+11 16796
## - Bsmt.Full.Bath 1 2.7774e+10 4.7371e+11 16797
## - Bedroom.AbvGr 1 3.7261e+10 4.8319e+11 16814
## - Total.Bsmt.SF 1 5.2944e+10 4.9888e+11 16840
## - Year.Built 1 7.2607e+10 5.1854e+11 16872
## - Overall.Qual 1 1.0954e+11 5.5547e+11 16930
## - area 1 2.9088e+11 7.3681e+11 17165
##
## Step: AIC=16743.76
## price ~ Overall.Qual + area + Total.Bsmt.SF + Year.Built + Bsmt.Full.Bath +
## MS.SubClass + Bedroom.AbvGr + Overall.Cond + Lot.Area + Garage.Area +
## Kitchen.AbvGr + Fireplaces + Central.Air
##
## Df Sum of Sq RSS AIC
## + Pool.Area 1 3.6592e+09 4.3848e+11 16739
## + Year.Remod.Add 1 3.3371e+09 4.3880e+11 16740
## + Wood.Deck.SF 1 1.7057e+09 4.4043e+11 16743
## + TotRms.AbvGrd 1 1.6759e+09 4.4046e+11 16743
## + X1st.Flr.SF 1 1.4127e+09 4.4073e+11 16743
## <none> 4.4214e+11 16744
## + Full.Bath 1 7.7078e+08 4.4137e+11 16744
## + X2nd.Flr.SF 1 5.5228e+08 4.4159e+11 16745
## + Half.Bath 1 9.9354e+07 4.4204e+11 16746
## + Garage.Cars 1 2.5118e+07 4.4211e+11 16746
## + Bsmt.Half.Bath 1 1.2402e+07 4.4213e+11 16746
## + Open.Porch.SF 1 6.3354e+06 4.4213e+11 16746
## + Enclosed.Porch 1 2.0063e+06 4.4214e+11 16746
## + Screen.Porch 1 2.3571e+05 4.4214e+11 16746
## - Central.Air 1 3.7930e+09 4.4593e+11 16749
## - Fireplaces 1 4.5265e+09 4.4667e+11 16750
## - Kitchen.AbvGr 1 5.9709e+09 4.4811e+11 16753
## - MS.SubClass 1 1.7578e+10 4.5972e+11 16774
## - Lot.Area 1 2.0008e+10 4.6215e+11 16779
## - Garage.Area 1 2.0504e+10 4.6264e+11 16780
## - Bsmt.Full.Bath 1 2.7549e+10 4.6969e+11 16792
## - Overall.Cond 1 3.0946e+10 4.7309e+11 16798
## - Bedroom.AbvGr 1 3.2308e+10 4.7445e+11 16800
## - Total.Bsmt.SF 1 5.5162e+10 4.9730e+11 16840
## - Year.Built 1 7.6110e+10 5.1825e+11 16874
## - Overall.Qual 1 1.0879e+11 5.5093e+11 16925
## - area 1 2.7776e+11 7.1990e+11 17147
##
## Step: AIC=16738.85
## price ~ Overall.Qual + area + Total.Bsmt.SF + Year.Built + Bsmt.Full.Bath +
## MS.SubClass + Bedroom.AbvGr + Overall.Cond + Lot.Area + Garage.Area +
## Kitchen.AbvGr + Fireplaces + Central.Air + Pool.Area
##
## Df Sum of Sq RSS AIC
## + Year.Remod.Add 1 3.1828e+09 4.3530e+11 16735
## + TotRms.AbvGrd 1 2.1023e+09 4.3638e+11 16737
## + Wood.Deck.SF 1 2.1017e+09 4.3638e+11 16737
## + X1st.Flr.SF 1 1.5157e+09 4.3697e+11 16738
## <none> 4.3848e+11 16739
## + Full.Bath 1 6.5562e+08 4.3783e+11 16740
## + X2nd.Flr.SF 1 5.9717e+08 4.3788e+11 16740
## + Half.Bath 1 1.8609e+08 4.3829e+11 16741
## + Bsmt.Half.Bath 1 1.1969e+08 4.3836e+11 16741
## + Screen.Porch 1 5.6913e+07 4.3842e+11 16741
## + Garage.Cars 1 4.7493e+07 4.3843e+11 16741
## + Open.Porch.SF 1 3.4634e+06 4.3848e+11 16741
## + Enclosed.Porch 1 6.3611e+05 4.3848e+11 16741
## - Pool.Area 1 3.6592e+09 4.4214e+11 16744
## - Central.Air 1 3.7347e+09 4.4222e+11 16744
## - Fireplaces 1 5.7327e+09 4.4421e+11 16748
## - Kitchen.AbvGr 1 6.3166e+09 4.4480e+11 16749
## - MS.SubClass 1 1.7329e+10 4.5581e+11 16769
## - Lot.Area 1 1.9351e+10 4.5783e+11 16773
## - Garage.Area 1 1.9858e+10 4.5834e+11 16774
## - Bsmt.Full.Bath 1 2.8152e+10 4.6663e+11 16789
## - Overall.Cond 1 2.9870e+10 4.6835e+11 16792
## - Bedroom.AbvGr 1 3.2189e+10 4.7067e+11 16796
## - Total.Bsmt.SF 1 5.5940e+10 4.9442e+11 16837
## - Year.Built 1 7.5318e+10 5.1380e+11 16869
## - Overall.Qual 1 1.0590e+11 5.4438e+11 16917
## - area 1 2.8047e+11 7.1895e+11 17148
##
## Step: AIC=16734.79
## price ~ Overall.Qual + area + Total.Bsmt.SF + Year.Built + Bsmt.Full.Bath +
## MS.SubClass + Bedroom.AbvGr + Overall.Cond + Lot.Area + Garage.Area +
## Kitchen.AbvGr + Fireplaces + Central.Air + Pool.Area + Year.Remod.Add
##
## Df Sum of Sq RSS AIC
## + Wood.Deck.SF 1 2.0224e+09 4.3328e+11 16733
## + TotRms.AbvGrd 1 1.9975e+09 4.3330e+11 16733
## + X1st.Flr.SF 1 1.2873e+09 4.3401e+11 16734
## + Full.Bath 1 1.2671e+09 4.3403e+11 16734
## <none> 4.3530e+11 16735
## + X2nd.Flr.SF 1 4.6934e+08 4.3483e+11 16736
## + Bsmt.Half.Bath 1 1.6249e+08 4.3514e+11 16737
## + Half.Bath 1 1.2241e+08 4.3518e+11 16737
## + Screen.Porch 1 1.0376e+08 4.3519e+11 16737
## + Garage.Cars 1 9.4155e+07 4.3520e+11 16737
## + Open.Porch.SF 1 4.7012e+06 4.3529e+11 16737
## + Enclosed.Porch 1 1.1585e+06 4.3530e+11 16737
## - Year.Remod.Add 1 3.1828e+09 4.3848e+11 16739
## - Central.Air 1 3.3473e+09 4.3865e+11 16739
## - Pool.Area 1 3.5048e+09 4.3880e+11 16740
## - Kitchen.AbvGr 1 5.5752e+09 4.4087e+11 16743
## - Fireplaces 1 7.0476e+09 4.4235e+11 16746
## - MS.SubClass 1 1.7680e+10 4.5298e+11 16766
## - Lot.Area 1 1.8819e+10 4.5412e+11 16768
## - Garage.Area 1 2.0137e+10 4.5544e+11 16770
## - Overall.Cond 1 2.0182e+10 4.5548e+11 16771
## - Bsmt.Full.Bath 1 2.8499e+10 4.6380e+11 16786
## - Bedroom.AbvGr 1 2.9318e+10 4.6462e+11 16787
## - Year.Built 1 4.4777e+10 4.8007e+11 16814
## - Total.Bsmt.SF 1 5.7083e+10 4.9238e+11 16835
## - Overall.Qual 1 9.8930e+10 5.3423e+11 16903
## - area 1 2.4813e+11 6.8343e+11 17108
##
## Step: AIC=16732.91
## price ~ Overall.Qual + area + Total.Bsmt.SF + Year.Built + Bsmt.Full.Bath +
## MS.SubClass + Bedroom.AbvGr + Overall.Cond + Lot.Area + Garage.Area +
## Kitchen.AbvGr + Fireplaces + Central.Air + Pool.Area + Year.Remod.Add +
## Wood.Deck.SF
##
## Df Sum of Sq RSS AIC
## + TotRms.AbvGrd 1 1.9482e+09 4.3133e+11 16731
## + X1st.Flr.SF 1 1.2957e+09 4.3198e+11 16732
## + Full.Bath 1 1.2511e+09 4.3202e+11 16733
## <none> 4.3328e+11 16733
## + X2nd.Flr.SF 1 4.7524e+08 4.3280e+11 16734
## + Screen.Porch 1 2.2808e+08 4.3305e+11 16735
## + Half.Bath 1 1.3833e+08 4.3314e+11 16735
## + Garage.Cars 1 8.1243e+07 4.3319e+11 16735
## - Wood.Deck.SF 1 2.0224e+09 4.3530e+11 16735
## + Bsmt.Half.Bath 1 5.3679e+07 4.3322e+11 16735
## + Enclosed.Porch 1 2.6840e+06 4.3327e+11 16735
## + Open.Porch.SF 1 1.4172e+06 4.3327e+11 16735
## - Central.Air 1 2.9890e+09 4.3626e+11 16737
## - Year.Remod.Add 1 3.1034e+09 4.3638e+11 16737
## - Pool.Area 1 3.8867e+09 4.3716e+11 16738
## - Kitchen.AbvGr 1 5.0552e+09 4.3833e+11 16741
## - Fireplaces 1 6.4423e+09 4.3972e+11 16743
## - MS.SubClass 1 1.7333e+10 4.5061e+11 16764
## - Overall.Cond 1 1.7505e+10 4.5078e+11 16764
## - Lot.Area 1 1.8955e+10 4.5223e+11 16767
## - Garage.Area 1 1.9175e+10 4.5245e+11 16767
## - Bsmt.Full.Bath 1 2.5902e+10 4.5918e+11 16779
## - Bedroom.AbvGr 1 2.8265e+10 4.6154e+11 16784
## - Year.Built 1 4.0980e+10 4.7426e+11 16806
## - Total.Bsmt.SF 1 5.5790e+10 4.8907e+11 16832
## - Overall.Qual 1 1.0037e+11 5.3364e+11 16904
## - area 1 2.3378e+11 6.6706e+11 17090
##
## Step: AIC=16731.16
## price ~ Overall.Qual + area + Total.Bsmt.SF + Year.Built + Bsmt.Full.Bath +
## MS.SubClass + Bedroom.AbvGr + Overall.Cond + Lot.Area + Garage.Area +
## Kitchen.AbvGr + Fireplaces + Central.Air + Pool.Area + Year.Remod.Add +
## Wood.Deck.SF + TotRms.AbvGrd
##
## Df Sum of Sq RSS AIC
## + X1st.Flr.SF 1 1.2271e+09 4.3010e+11 16731
## + Full.Bath 1 1.0983e+09 4.3023e+11 16731
## <none> 4.3133e+11 16731
## + X2nd.Flr.SF 1 4.1460e+08 4.3091e+11 16732
## + Screen.Porch 1 2.0325e+08 4.3112e+11 16733
## - TotRms.AbvGrd 1 1.9482e+09 4.3328e+11 16733
## + Garage.Cars 1 1.0873e+08 4.3122e+11 16733
## - Wood.Deck.SF 1 1.9731e+09 4.3330e+11 16733
## + Bsmt.Half.Bath 1 1.0026e+08 4.3123e+11 16733
## + Half.Bath 1 8.9855e+07 4.3124e+11 16733
## + Enclosed.Porch 1 1.0696e+07 4.3132e+11 16733
## + Open.Porch.SF 1 1.9925e+06 4.3133e+11 16733
## - Central.Air 1 2.9005e+09 4.3423e+11 16735
## - Year.Remod.Add 1 3.0022e+09 4.3433e+11 16735
## - Pool.Area 1 4.3039e+09 4.3563e+11 16737
## - Fireplaces 1 6.3851e+09 4.3771e+11 16741
## - Kitchen.AbvGr 1 6.6844e+09 4.3801e+11 16742
## - MS.SubClass 1 1.5043e+10 4.4637e+11 16758
## - Overall.Cond 1 1.7244e+10 4.4857e+11 16762
## - Lot.Area 1 1.8559e+10 4.4989e+11 16764
## - Garage.Area 1 1.9167e+10 4.5049e+11 16765
## - Bsmt.Full.Bath 1 2.6862e+10 4.5819e+11 16779
## - Bedroom.AbvGr 1 2.9817e+10 4.6114e+11 16785
## - Year.Built 1 4.1374e+10 4.7270e+11 16805
## - Total.Bsmt.SF 1 5.6701e+10 4.8803e+11 16832
## - Overall.Qual 1 9.7011e+10 5.2834e+11 16898
## - area 1 1.5060e+11 5.8193e+11 16978
##
## Step: AIC=16730.79
## price ~ Overall.Qual + area + Total.Bsmt.SF + Year.Built + Bsmt.Full.Bath +
## MS.SubClass + Bedroom.AbvGr + Overall.Cond + Lot.Area + Garage.Area +
## Kitchen.AbvGr + Fireplaces + Central.Air + Pool.Area + Year.Remod.Add +
## Wood.Deck.SF + TotRms.AbvGrd + X1st.Flr.SF
##
## Df Sum of Sq RSS AIC
## + X2nd.Flr.SF 1 2.6176e+09 4.2748e+11 16728
## + Full.Bath 1 1.0600e+09 4.2904e+11 16731
## <none> 4.3010e+11 16731
## - X1st.Flr.SF 1 1.2271e+09 4.3133e+11 16731
## + Screen.Porch 1 2.0262e+08 4.2990e+11 16732
## - TotRms.AbvGrd 1 1.8796e+09 4.3198e+11 16732
## - Wood.Deck.SF 1 1.9820e+09 4.3208e+11 16733
## + Bsmt.Half.Bath 1 7.9744e+07 4.3002e+11 16733
## + Garage.Cars 1 6.7839e+07 4.3003e+11 16733
## + Enclosed.Porch 1 4.2985e+07 4.3006e+11 16733
## + Open.Porch.SF 1 1.7977e+07 4.3008e+11 16733
## + Half.Bath 1 1.0914e+07 4.3009e+11 16733
## - Year.Remod.Add 1 2.7873e+09 4.3289e+11 16734
## - Central.Air 1 3.1041e+09 4.3320e+11 16735
## - Pool.Area 1 4.4022e+09 4.3450e+11 16737
## - Fireplaces 1 5.5661e+09 4.3567e+11 16740
## - Kitchen.AbvGr 1 7.6422e+09 4.3774e+11 16743
## - MS.SubClass 1 1.2146e+10 4.4225e+11 16752
## - Overall.Cond 1 1.7579e+10 4.4768e+11 16762
## - Lot.Area 1 1.7917e+10 4.4802e+11 16763
## - Garage.Area 1 1.8122e+10 4.4822e+11 16763
## - Total.Bsmt.SF 1 2.5353e+10 4.5545e+11 16776
## - Bsmt.Full.Bath 1 2.6750e+10 4.5685e+11 16779
## - Bedroom.AbvGr 1 2.7061e+10 4.5716e+11 16780
## - Year.Built 1 4.2116e+10 4.7222e+11 16807
## - Overall.Qual 1 9.7902e+10 5.2800e+11 16899
## - area 1 1.3740e+11 5.6750e+11 16959
##
## Step: AIC=16727.71
## price ~ Overall.Qual + area + Total.Bsmt.SF + Year.Built + Bsmt.Full.Bath +
## MS.SubClass + Bedroom.AbvGr + Overall.Cond + Lot.Area + Garage.Area +
## Kitchen.AbvGr + Fireplaces + Central.Air + Pool.Area + Year.Remod.Add +
## Wood.Deck.SF + TotRms.AbvGrd + X1st.Flr.SF + X2nd.Flr.SF
##
## Df Sum of Sq RSS AIC
## <none> 4.2748e+11 16728
## + Full.Bath 1 9.0722e+08 4.2658e+11 16728
## - area 1 1.5889e+09 4.2907e+11 16729
## + Enclosed.Porch 1 1.7290e+08 4.2731e+11 16729
## + Screen.Porch 1 1.6371e+08 4.2732e+11 16729
## - Wood.Deck.SF 1 1.9704e+09 4.2945e+11 16730
## + Garage.Cars 1 7.5952e+07 4.2741e+11 16730
## + Bsmt.Half.Bath 1 7.5624e+07 4.2741e+11 16730
## + Open.Porch.SF 1 3.6183e+05 4.2748e+11 16730
## + Half.Bath 1 2.8148e+05 4.2748e+11 16730
## - TotRms.AbvGrd 1 2.0757e+09 4.2956e+11 16730
## - X2nd.Flr.SF 1 2.6176e+09 4.3010e+11 16731
## - Central.Air 1 2.6589e+09 4.3014e+11 16731
## - Year.Remod.Add 1 2.7102e+09 4.3019e+11 16731
## - X1st.Flr.SF 1 3.4301e+09 4.3091e+11 16732
## - Pool.Area 1 4.5768e+09 4.3206e+11 16735
## - Fireplaces 1 5.3595e+09 4.3284e+11 16736
## - Kitchen.AbvGr 1 8.0072e+09 4.3549e+11 16741
## - MS.SubClass 1 1.2292e+10 4.3977e+11 16749
## - Overall.Cond 1 1.6623e+10 4.4411e+11 16758
## - Lot.Area 1 1.7410e+10 4.4489e+11 16759
## - Garage.Area 1 1.7733e+10 4.4522e+11 16760
## - Total.Bsmt.SF 1 2.6165e+10 4.5365e+11 16775
## - Bsmt.Full.Bath 1 2.6392e+10 4.5388e+11 16776
## - Bedroom.AbvGr 1 2.8557e+10 4.5604e+11 16780
## - Year.Built 1 4.0138e+10 4.6762e+11 16800
## - Overall.Qual 1 9.3274e+10 5.2076e+11 16890## [1] "(Intercept)" "Overall.Qual" "area" "Total.Bsmt.SF"
## [5] "Year.Built" "Bsmt.Full.Bath" "MS.SubClass" "Bedroom.AbvGr"
## [9] "Overall.Cond" "Lot.Area" "Garage.Area" "Kitchen.AbvGr"
## [13] "Fireplaces" "Central.AirY" "Pool.Area" "Year.Remod.Add"
## [17] "Wood.Deck.SF" "TotRms.AbvGrd" "X1st.Flr.SF" "X2nd.Flr.SF"##
## Call:
## lm(formula = price ~ 1, data = train)
##
## Residuals:
## Min 1Q Median 3Q Max
## -134356 -44681 -18656 30594 326344
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 173656 2412 71.98 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 69590 on 831 degrees of freedom##
## Call:
## lm(formula = price ~ ., data = train)
##
## Residuals:
## Min 1Q Median 3Q Max
## -74931 -13803 -1484 11078 103188
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -1.212e+06 1.231e+05 -9.849 < 2e-16 ***
## area 3.032e+01 1.645e+01 1.844 0.065612 .
## MS.SubClass -1.084e+02 2.278e+01 -4.759 2.30e-06 ***
## Lot.Area 4.883e-01 8.462e-02 5.770 1.13e-08 ***
## Overall.Qual 1.335e+04 1.010e+03 13.211 < 2e-16 ***
## Overall.Cond 5.076e+03 9.475e+02 5.357 1.11e-07 ***
## Year.Built 4.517e+02 5.377e+01 8.402 < 2e-16 ***
## Year.Remod.Add 1.464e+02 5.778e+01 2.535 0.011445 *
## Total.Bsmt.SF 2.547e+01 3.724e+00 6.839 1.58e-11 ***
## Central.AirY -9.526e+03 4.388e+03 -2.171 0.030223 *
## X1st.Flr.SF 4.132e+01 1.664e+01 2.483 0.013229 *
## X2nd.Flr.SF 3.608e+01 1.624e+01 2.222 0.026554 *
## Bsmt.Full.Bath 1.211e+04 1.799e+03 6.732 3.18e-11 ***
## Bsmt.Half.Bath 1.236e+03 3.541e+03 0.349 0.727168
## Full.Bath -3.603e+03 2.596e+03 -1.388 0.165566
## Half.Bath -1.311e+03 2.390e+03 -0.548 0.583621
## Bedroom.AbvGr -1.110e+04 1.562e+03 -7.106 2.63e-12 ***
## Kitchen.AbvGr -1.870e+04 5.537e+03 -3.377 0.000767 ***
## TotRms.AbvGrd 2.064e+03 1.085e+03 1.902 0.057550 .
## Fireplaces 4.584e+03 1.574e+03 2.913 0.003677 **
## Garage.Cars -6.243e+02 2.678e+03 -0.233 0.815744
## Garage.Area 3.088e+01 9.113e+00 3.389 0.000736 ***
## Wood.Deck.SF 1.450e+01 7.442e+00 1.948 0.051747 .
## Open.Porch.SF 2.848e+00 1.431e+01 0.199 0.842264
## Enclosed.Porch 1.029e+01 1.496e+01 0.688 0.491824
## Screen.Porch 1.057e+01 1.564e+01 0.676 0.499087
## Pool.Area -7.637e+01 2.589e+01 -2.950 0.003270 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 23000 on 805 degrees of freedom
## Multiple R-squared: 0.8942, Adjusted R-squared: 0.8907
## F-statistic: 261.6 on 26 and 805 DF, p-value: < 2.2e-16## [1] 0## [1] 0.8907417## Stepwise Model Path
## Analysis of Deviance Table
##
## Initial Model:
## log(price) ~ log(Total.Bsmt.SF + 1) + log(area) + Bedroom.AbvGr +
## Year.Built + log(X1st.Flr.SF) + log(Lot.Area) + Overall.Cond +
## Overall.Qual + TotRms.AbvGrd + Bsmt.Full.Bath + Garage.Cars +
## Garage.Area + Year.Remod.Add + Kitchen.AbvGr + Fireplaces +
## MS.SubClass + Half.Bath + Full.Bath
##
## Final Model:
## log(price) ~ log(Total.Bsmt.SF + 1) + log(area) + Bedroom.AbvGr +
## Year.Built + log(X1st.Flr.SF) + log(Lot.Area) + Overall.Cond +
## Overall.Qual + TotRms.AbvGrd + Bsmt.Full.Bath + Garage.Area +
## Year.Remod.Add + Kitchen.AbvGr + Fireplaces
##
##
## Step Df Deviance Resid. Df Resid. Dev AIC
## 1 813 9.673101 -3668.130
## 2 - MS.SubClass 1 0.001370346 814 9.674471 -3670.012
## 3 - Half.Bath 1 0.003276487 815 9.677748 -3671.731
## 4 - Full.Bath 1 0.009318860 816 9.687067 -3672.930
## 5 - Garage.Cars 1 0.018572802 817 9.705640 -3673.336
0.0.0.12.3 calculating RMSE for a model.
summary(without.model)$sigma ## [1] 24626.610.0.0.12.4 Second method
score <- predict(without.model, train) 0.0.0.12.5 Get the actual values
train$price[is.na(train$price)] <- 0
actual = train$price
mean(actual)## [1] 173656.20.0.0.12.6 Calculate the RMSE long hand
(mean((actual - score)^2))^0.5 ## [1] 24403.610.0.0.12.7 Final Model by using Bayesian Method
AIC.bas <- bas.lm(log(price) ~log(Garage.Area + 1) +
log(Total.Bsmt.SF + 1) + Garage.Cars + log(area) +
Full.Bath + Half.Bath +
Bedroom.AbvGr + Year.Built + log(X1st.Flr.SF) +
log(X2nd.Flr.SF + 1) +log(Lot.Area) + Central.Air + Overall.Cond+Overall.Qual, data =na.omit(train),
prior = "AIC",modelprior=uniform())
AIC.bas##
## Call:
## bas.lm(formula = log(price) ~ log(Garage.Area + 1) + log(Total.Bsmt.SF + 1) + Garage.Cars + log(area) + Full.Bath + Half.Bath + Bedroom.AbvGr + Year.Built + log(X1st.Flr.SF) + log(X2nd.Flr.SF + 1) + log(Lot.Area) + Central.Air + Overall.Cond + Overall.Qual, data = na.omit(train), prior = "AIC", modelprior = uniform())
##
##
## Marginal Posterior Inclusion Probabilities:
## Intercept log(Garage.Area + 1) log(Total.Bsmt.SF + 1)
## 1.0000 0.4978 1.0000
## Garage.Cars log(area) Full.Bath
## 1.0000 1.0000 0.2923
## Half.Bath Bedroom.AbvGr Year.Built
## 0.2899 1.0000 1.0000
## log(X1st.Flr.SF) log(X2nd.Flr.SF + 1) log(Lot.Area)
## 0.8803 0.4115 1.0000
## Central.AirY Overall.Cond Overall.Qual
## 0.9942 1.0000 1.0000summary(AIC.bas)## P(B != 0 | Y) model 1 model 2
## Intercept 1.0000000 1.0000 1.0000000
## log(Garage.Area + 1) 0.4978436 0.0000 1.0000000
## log(Total.Bsmt.SF + 1) 1.0000000 1.0000 1.0000000
## Garage.Cars 0.9999945 1.0000 1.0000000
## log(area) 1.0000000 1.0000 1.0000000
## Full.Bath 0.2923140 0.0000 0.0000000
## Half.Bath 0.2899258 0.0000 0.0000000
## Bedroom.AbvGr 0.9999998 1.0000 1.0000000
## Year.Built 1.0000000 1.0000 1.0000000
## log(X1st.Flr.SF) 0.8803172 1.0000 1.0000000
## log(X2nd.Flr.SF + 1) 0.4115000 0.0000 0.0000000
## log(Lot.Area) 1.0000000 1.0000 1.0000000
## Central.AirY 0.9942209 1.0000 1.0000000
## Overall.Cond 1.0000000 1.0000 1.0000000
## Overall.Qual 1.0000000 1.0000 1.0000000
## BF NA 1.0000 0.9909467
## PostProbs NA 0.1467 0.1454000
## R2 NA 0.9047 0.9049000
## dim NA 11.0000 12.0000000
## logmarg NA -1018.7154 -1018.7244550
## model 3 model 4 model 5
## Intercept 1.0000000 1.000000 1.0000000
## log(Garage.Area + 1) 0.0000000 1.000000 1.0000000
## log(Total.Bsmt.SF + 1) 1.0000000 1.000000 1.0000000
## Garage.Cars 1.0000000 1.000000 1.0000000
## log(area) 1.0000000 1.000000 1.0000000
## Full.Bath 0.0000000 0.000000 1.0000000
## Half.Bath 0.0000000 0.000000 0.0000000
## Bedroom.AbvGr 1.0000000 1.000000 1.0000000
## Year.Built 1.0000000 1.000000 1.0000000
## log(X1st.Flr.SF) 1.0000000 1.000000 1.0000000
## log(X2nd.Flr.SF + 1) 1.0000000 1.000000 0.0000000
## log(Lot.Area) 1.0000000 1.000000 1.0000000
## Central.AirY 1.0000000 1.000000 1.0000000
## Overall.Cond 1.0000000 1.000000 1.0000000
## Overall.Qual 1.0000000 1.000000 1.0000000
## BF 0.5008923 0.482127 0.4373706
## PostProbs 0.0735000 0.070700 0.0642000
## R2 0.9047000 0.905000 0.9049000
## dim 12.0000000 13.000000 13.0000000
## logmarg -1019.4067246 -1019.444908 -1019.5423349image(AIC.bas, rotate = F)
coef(AIC.bas)##
## Marginal Posterior Summaries of Coefficients:
##
## Using BMA
##
## Based on the top 16384 models
## post mean post SD post p(B != 0)
## Intercept 11.9927955 0.0040637 1.0000000
## log(Garage.Area + 1) -0.0031993 0.0045690 0.4978436
## log(Total.Bsmt.SF + 1) 0.0251912 0.0040171 1.0000000
## Garage.Cars 0.0444416 0.0095886 0.9999945
## log(area) 0.4574010 0.0570836 1.0000000
## Full.Bath -0.0015900 0.0069031 0.2923140
## Half.Bath 0.0014271 0.0066043 0.2899258
## Bedroom.AbvGr -0.0397790 0.0068988 0.9999998
## Year.Built 0.0036647 0.0002217 1.0000000
## log(X1st.Flr.SF) 0.1059955 0.0521764 0.8803172
## log(X2nd.Flr.SF + 1) -0.0025436 0.0047593 0.4115000
## log(Lot.Area) 0.1171650 0.0094822 1.0000000
## Central.AirY 0.0746779 0.0223200 0.9942209
## Overall.Cond 0.0529705 0.0043663 1.0000000
## Overall.Qual 0.0864533 0.0050286 1.0000000BIC.bas <- bas.lm(log(price) ~log(Garage.Area + 1) +
log(Total.Bsmt.SF + 1) + Garage.Cars + log(area) +
Full.Bath + Half.Bath +
Bedroom.AbvGr + Year.Built + log(X1st.Flr.SF) +
log(X2nd.Flr.SF + 1) +
log(Lot.Area) + Overall.Cond+Overall.Qual,
data =na.omit(train), prior = "BIC",
modelprior=uniform())
BIC.bas##
## Call:
## bas.lm(formula = log(price) ~ log(Garage.Area + 1) + log(Total.Bsmt.SF + 1) + Garage.Cars + log(area) + Full.Bath + Half.Bath + Bedroom.AbvGr + Year.Built + log(X1st.Flr.SF) + log(X2nd.Flr.SF + 1) + log(Lot.Area) + Overall.Cond + Overall.Qual, data = na.omit(train), prior = "BIC", modelprior = uniform())
##
##
## Marginal Posterior Inclusion Probabilities:
## Intercept log(Garage.Area + 1) log(Total.Bsmt.SF + 1)
## 1.00000 0.03856 1.00000
## Garage.Cars log(area) Full.Bath
## 0.99996 1.00000 0.04898
## Half.Bath Bedroom.AbvGr Year.Built
## 0.04306 0.99999 1.00000
## log(X1st.Flr.SF) log(X2nd.Flr.SF + 1) log(Lot.Area)
## 0.85638 0.18067 1.00000
## Overall.Cond Overall.Qual
## 1.00000 1.00000summary(BIC.bas)## P(B != 0 | Y) model 1 model 2
## Intercept 1.00000000 1.0000 1.0000000
## log(Garage.Area + 1) 0.03855625 0.0000 0.0000000
## log(Total.Bsmt.SF + 1) 1.00000000 1.0000 1.0000000
## Garage.Cars 0.99996052 1.0000 1.0000000
## log(area) 1.00000000 1.0000 1.0000000
## Full.Bath 0.04897608 0.0000 0.0000000
## Half.Bath 0.04306068 0.0000 0.0000000
## Bedroom.AbvGr 0.99999409 1.0000 1.0000000
## Year.Built 1.00000000 1.0000 1.0000000
## log(X1st.Flr.SF) 0.85638295 1.0000 0.0000000
## log(X2nd.Flr.SF + 1) 0.18067164 0.0000 1.0000000
## log(Lot.Area) 1.00000000 1.0000 1.0000000
## Overall.Cond 1.00000000 1.0000 1.0000000
## Overall.Qual 1.00000000 1.0000 1.0000000
## BF NA 1.0000 0.1766875
## PostProbs NA 0.7160 0.1265000
## R2 NA 0.9033 0.9029000
## dim NA 10.0000 10.0000000
## logmarg NA -1047.2501 -1048.9834280
## model 3 model 4 model 5
## Intercept 1.000000e+00 1.000000e+00 1.000000e+00
## log(Garage.Area + 1) 0.000000e+00 0.000000e+00 0.000000e+00
## log(Total.Bsmt.SF + 1) 1.000000e+00 1.000000e+00 1.000000e+00
## Garage.Cars 1.000000e+00 1.000000e+00 1.000000e+00
## log(area) 1.000000e+00 1.000000e+00 1.000000e+00
## Full.Bath 1.000000e+00 0.000000e+00 0.000000e+00
## Half.Bath 0.000000e+00 1.000000e+00 0.000000e+00
## Bedroom.AbvGr 1.000000e+00 1.000000e+00 1.000000e+00
## Year.Built 1.000000e+00 1.000000e+00 1.000000e+00
## log(X1st.Flr.SF) 1.000000e+00 1.000000e+00 1.000000e+00
## log(X2nd.Flr.SF + 1) 0.000000e+00 0.000000e+00 1.000000e+00
## log(Lot.Area) 1.000000e+00 1.000000e+00 1.000000e+00
## Overall.Cond 1.000000e+00 1.000000e+00 1.000000e+00
## Overall.Qual 1.000000e+00 1.000000e+00 1.000000e+00
## BF 5.142395e-02 4.658921e-02 4.518892e-02
## PostProbs 3.680000e-02 3.340000e-02 3.240000e-02
## R2 9.034000e-01 9.034000e-01 9.034000e-01
## dim 1.100000e+01 1.100000e+01 1.100000e+01
## logmarg -1.050218e+03 -1.050316e+03 -1.050347e+03image(BIC.bas, rotate = F)
coef(BIC.bas)##
## Marginal Posterior Summaries of Coefficients:
##
## Using BMA
##
## Based on the top 8192 models
## post mean post SD post p(B != 0)
## Intercept 1.199e+01 4.090e-03 1.000e+00
## log(Garage.Area + 1) -9.198e-05 9.950e-04 3.856e-02
## log(Total.Bsmt.SF + 1) 2.750e-02 3.981e-03 1.000e+00
## Garage.Cars 4.166e-02 7.849e-03 1.000e+00
## log(area) 4.489e-01 5.434e-02 1.000e+00
## Full.Bath -4.966e-04 3.356e-03 4.898e-02
## Half.Bath 3.437e-04 2.858e-03 4.306e-02
## Bedroom.AbvGr -3.850e-02 6.915e-03 1.000e+00
## Year.Built 3.919e-03 2.041e-04 1.000e+00
## log(X1st.Flr.SF) 1.132e-01 5.060e-02 8.564e-01
## log(X2nd.Flr.SF + 1) -1.921e-03 4.518e-03 1.807e-01
## log(Lot.Area) 1.174e-01 9.494e-03 1.000e+00
## Overall.Cond 5.799e-02 4.121e-03 1.000e+00
## Overall.Qual 8.630e-02 5.056e-03 1.000e+00Verfication was carried out by measuring and comparing criteria.
0.0.0.12.8 Cross validation of Final model.(Stepwise methods)
library(MASS)
step <- stepAIC(Final.lm, direction="both")## Start: AIC=-3668.13
## log(price) ~ log(Total.Bsmt.SF + 1) + log(area) + Bedroom.AbvGr +
## Year.Built + log(X1st.Flr.SF) + log(Lot.Area) + Overall.Cond +
## Overall.Qual + TotRms.AbvGrd + Bsmt.Full.Bath + Garage.Cars +
## Garage.Area + Year.Remod.Add + Kitchen.AbvGr + Fireplaces +
## MS.SubClass + Half.Bath + Full.Bath
##
## Df Sum of Sq RSS AIC
## - MS.SubClass 1 0.0014 9.6745 -3670.0
## - Half.Bath 1 0.0030 9.6761 -3669.9
## - Full.Bath 1 0.0118 9.6849 -3669.1
## - Garage.Cars 1 0.0140 9.6871 -3668.9
## <none> 9.6731 -3668.1
## - TotRms.AbvGrd 1 0.0299 9.7030 -3667.6
## - Garage.Area 1 0.0907 9.7638 -3662.4
## - Bedroom.AbvGr 1 0.1193 9.7924 -3659.9
## - Year.Remod.Add 1 0.1486 9.8217 -3657.4
## - Kitchen.AbvGr 1 0.1754 9.8485 -3655.2
## - log(X1st.Flr.SF) 1 0.3296 10.0027 -3642.3
## - Fireplaces 1 0.3465 10.0196 -3640.8
## - log(Total.Bsmt.SF + 1) 1 0.3886 10.0617 -3637.4
## - Bsmt.Full.Bath 1 0.9053 10.5785 -3595.7
## - log(Lot.Area) 1 0.9936 10.6667 -3588.8
## - log(area) 1 1.3370 11.0101 -3562.4
## - Overall.Cond 1 1.6453 11.3184 -3539.4
## - Year.Built 1 2.1722 11.8453 -3501.6
## - Overall.Qual 1 3.2732 12.9463 -3427.6
##
## Step: AIC=-3670.01
## log(price) ~ log(Total.Bsmt.SF + 1) + log(area) + Bedroom.AbvGr +
## Year.Built + log(X1st.Flr.SF) + log(Lot.Area) + Overall.Cond +
## Overall.Qual + TotRms.AbvGrd + Bsmt.Full.Bath + Garage.Cars +
## Garage.Area + Year.Remod.Add + Kitchen.AbvGr + Fireplaces +
## Half.Bath + Full.Bath
##
## Df Sum of Sq RSS AIC
## - Half.Bath 1 0.0033 9.6777 -3671.7
## - Full.Bath 1 0.0123 9.6868 -3671.0
## - Garage.Cars 1 0.0136 9.6881 -3670.8
## <none> 9.6745 -3670.0
## - TotRms.AbvGrd 1 0.0316 9.7061 -3669.3
## + MS.SubClass 1 0.0014 9.6731 -3668.1
## - Garage.Area 1 0.0909 9.7653 -3664.2
## - Bedroom.AbvGr 1 0.1181 9.7925 -3661.9
## - Year.Remod.Add 1 0.1478 9.8222 -3659.4
## - Kitchen.AbvGr 1 0.2150 9.8895 -3653.7
## - Fireplaces 1 0.3456 10.0201 -3642.8
## - log(X1st.Flr.SF) 1 0.3772 10.0517 -3640.2
## - log(Total.Bsmt.SF + 1) 1 0.3873 10.0618 -3639.4
## - Bsmt.Full.Bath 1 0.9045 10.5790 -3597.6
## - log(Lot.Area) 1 1.3202 10.9947 -3565.6
## - log(area) 1 1.4370 11.1115 -3556.8
## - Overall.Cond 1 1.6730 11.3475 -3539.3
## - Year.Built 1 2.1710 11.8455 -3503.6
## - Overall.Qual 1 3.2898 12.9643 -3428.5
##
## Step: AIC=-3671.73
## log(price) ~ log(Total.Bsmt.SF + 1) + log(area) + Bedroom.AbvGr +
## Year.Built + log(X1st.Flr.SF) + log(Lot.Area) + Overall.Cond +
## Overall.Qual + TotRms.AbvGrd + Bsmt.Full.Bath + Garage.Cars +
## Garage.Area + Year.Remod.Add + Kitchen.AbvGr + Fireplaces +
## Full.Bath
##
## Df Sum of Sq RSS AIC
## - Full.Bath 1 0.0093 9.6871 -3672.9
## - Garage.Cars 1 0.0150 9.6927 -3672.4
## <none> 9.6777 -3671.7
## - TotRms.AbvGrd 1 0.0306 9.7083 -3671.1
## + Half.Bath 1 0.0033 9.6745 -3670.0
## + MS.SubClass 1 0.0017 9.6761 -3669.9
## - Garage.Area 1 0.0885 9.7662 -3666.2
## - Bedroom.AbvGr 1 0.1167 9.7945 -3663.8
## - Year.Remod.Add 1 0.1486 9.8263 -3661.1
## - Kitchen.AbvGr 1 0.2144 9.8922 -3655.5
## - Fireplaces 1 0.3471 10.0249 -3644.4
## - log(Total.Bsmt.SF + 1) 1 0.3884 10.0661 -3641.0
## - log(X1st.Flr.SF) 1 0.4768 10.1546 -3633.7
## - Bsmt.Full.Bath 1 0.9053 10.5830 -3599.3
## - log(Lot.Area) 1 1.3317 11.0095 -3566.5
## - Overall.Cond 1 1.6744 11.3521 -3541.0
## - log(area) 1 2.0682 11.7459 -3512.6
## - Year.Built 1 2.5111 12.1889 -3481.8
## - Overall.Qual 1 3.2881 12.9659 -3430.4
##
## Step: AIC=-3672.93
## log(price) ~ log(Total.Bsmt.SF + 1) + log(area) + Bedroom.AbvGr +
## Year.Built + log(X1st.Flr.SF) + log(Lot.Area) + Overall.Cond +
## Overall.Qual + TotRms.AbvGrd + Bsmt.Full.Bath + Garage.Cars +
## Garage.Area + Year.Remod.Add + Kitchen.AbvGr + Fireplaces
##
## Df Sum of Sq RSS AIC
## - Garage.Cars 1 0.0186 9.7056 -3673.3
## <none> 9.6871 -3672.9
## - TotRms.AbvGrd 1 0.0300 9.7171 -3672.4
## + Full.Bath 1 0.0093 9.6777 -3671.7
## + MS.SubClass 1 0.0019 9.6852 -3671.1
## + Half.Bath 1 0.0003 9.6868 -3671.0
## - Garage.Area 1 0.0826 9.7696 -3667.9
## - Bedroom.AbvGr 1 0.1119 9.7990 -3665.4
## - Year.Remod.Add 1 0.1654 9.8525 -3660.8
## - Kitchen.AbvGr 1 0.2053 9.8923 -3657.5
## - Fireplaces 1 0.3442 10.0313 -3645.9
## - log(Total.Bsmt.SF + 1) 1 0.3836 10.0707 -3642.6
## - log(X1st.Flr.SF) 1 0.4743 10.1614 -3635.2
## - Bsmt.Full.Bath 1 0.8961 10.5832 -3601.3
## - log(Lot.Area) 1 1.3302 11.0173 -3567.9
## - Overall.Cond 1 1.6666 11.3537 -3542.9
## - log(area) 1 2.3589 12.0460 -3493.6
## - Year.Built 1 2.6979 12.3850 -3470.5
## - Overall.Qual 1 3.3298 13.0169 -3429.1
##
## Step: AIC=-3673.34
## log(price) ~ log(Total.Bsmt.SF + 1) + log(area) + Bedroom.AbvGr +
## Year.Built + log(X1st.Flr.SF) + log(Lot.Area) + Overall.Cond +
## Overall.Qual + TotRms.AbvGrd + Bsmt.Full.Bath + Garage.Area +
## Year.Remod.Add + Kitchen.AbvGr + Fireplaces
##
## Df Sum of Sq RSS AIC
## <none> 9.7056 -3673.3
## + Garage.Cars 1 0.0186 9.6871 -3672.9
## - TotRms.AbvGrd 1 0.0314 9.7370 -3672.7
## + Full.Bath 1 0.0129 9.6927 -3672.4
## + MS.SubClass 1 0.0015 9.7041 -3671.5
## + Half.Bath 1 0.0005 9.7052 -3671.4
## - Bedroom.AbvGr 1 0.1163 9.8219 -3665.4
## - Year.Remod.Add 1 0.1723 9.8780 -3660.7
## - Kitchen.AbvGr 1 0.1938 9.8995 -3658.9
## - Fireplaces 1 0.3500 10.0556 -3645.9
## - log(Total.Bsmt.SF + 1) 1 0.3932 10.0988 -3642.3
## - log(X1st.Flr.SF) 1 0.4617 10.1674 -3636.7
## - Garage.Area 1 0.4694 10.1750 -3636.0
## - Bsmt.Full.Bath 1 0.9012 10.6069 -3601.5
## - log(Lot.Area) 1 1.3381 11.0438 -3567.9
## - Overall.Cond 1 1.6559 11.3615 -3544.3
## - log(area) 1 2.4051 12.1107 -3491.1
## - Year.Built 1 2.8042 12.5098 -3464.2
## - Overall.Qual 1 3.4359 13.1416 -3423.2step$anova # display results ## Stepwise Model Path
## Analysis of Deviance Table
##
## Initial Model:
## log(price) ~ log(Total.Bsmt.SF + 1) + log(area) + Bedroom.AbvGr +
## Year.Built + log(X1st.Flr.SF) + log(Lot.Area) + Overall.Cond +
## Overall.Qual + TotRms.AbvGrd + Bsmt.Full.Bath + Garage.Cars +
## Garage.Area + Year.Remod.Add + Kitchen.AbvGr + Fireplaces +
## MS.SubClass + Half.Bath + Full.Bath
##
## Final Model:
## log(price) ~ log(Total.Bsmt.SF + 1) + log(area) + Bedroom.AbvGr +
## Year.Built + log(X1st.Flr.SF) + log(Lot.Area) + Overall.Cond +
## Overall.Qual + TotRms.AbvGrd + Bsmt.Full.Bath + Garage.Area +
## Year.Remod.Add + Kitchen.AbvGr + Fireplaces
##
##
## Step Df Deviance Resid. Df Resid. Dev AIC
## 1 813 9.673101 -3668.130
## 2 - MS.SubClass 1 0.001370346 814 9.674471 -3670.012
## 3 - Half.Bath 1 0.003276487 815 9.677748 -3671.731
## 4 - Full.Bath 1 0.009318860 816 9.687067 -3672.930
## 5 - Garage.Cars 1 0.018572802 817 9.705640 -3673.336plot(Initial.model2,Final.lm,which=1:4) 
0.0.0.12.9 Final model using multiple linear regression(lm)method.
library(visreg)
Final.lm <- lm(log(price) ~log(Total.Bsmt.SF + 1) + log(area)+ Bedroom.AbvGr + Year.Built + log(X1st.Flr.SF) +
log(Lot.Area) + Overall.Cond+Overall.Qual,
data =train)
predict.Final <- exp(predict(Final.lm, train))
resid.Final <- train$price - predict.Final
rmse.Final <- sqrt(mean(resid.Final^2))
rmse.Final## [1] 22160.99summary(Final.lm)##
## Call:
## lm(formula = log(price) ~ log(Total.Bsmt.SF + 1) + log(area) +
## Bedroom.AbvGr + Year.Built + log(X1st.Flr.SF) + log(Lot.Area) +
## Overall.Cond + Overall.Qual, data = train)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.80336 -0.06908 0.00160 0.07343 0.39921
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -2.7512763 0.4139264 -6.647 5.45e-11 ***
## log(Total.Bsmt.SF + 1) 0.0285325 0.0040306 7.079 3.11e-12 ***
## log(area) 0.4518322 0.0228800 19.748 < 2e-16 ***
## Bedroom.AbvGr -0.0410143 0.0070021 -5.857 6.79e-09 ***
## Year.Built 0.0042744 0.0001921 22.246 < 2e-16 ***
## log(X1st.Flr.SF) 0.1399698 0.0184166 7.600 8.05e-14 ***
## log(Lot.Area) 0.1260728 0.0094410 13.354 < 2e-16 ***
## Overall.Cond 0.0572853 0.0041833 13.694 < 2e-16 ***
## Overall.Qual 0.0902493 0.0050714 17.796 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.1199 on 823 degrees of freedom
## Multiple R-squared: 0.8999, Adjusted R-squared: 0.8989
## F-statistic: 925.1 on 8 and 823 DF, p-value: < 2.2e-16plot(resid(Final.lm))
plot(Final.lm)
visreg(Final.lm)
anova(Final.lm)## Analysis of Variance Table
##
## Response: log(price)
## Df Sum Sq Mean Sq F value Pr(>F)
## log(Total.Bsmt.SF + 1) 1 18.390 18.390 1278.79 < 2.2e-16 ***
## log(area) 1 55.259 55.259 3842.49 < 2.2e-16 ***
## Bedroom.AbvGr 1 4.494 4.494 312.49 < 2.2e-16 ***
## Year.Built 1 14.586 14.586 1014.23 < 2.2e-16 ***
## log(X1st.Flr.SF) 1 3.024 3.024 210.26 < 2.2e-16 ***
## log(Lot.Area) 1 1.870 1.870 130.02 < 2.2e-16 ***
## Overall.Cond 1 4.250 4.250 295.52 < 2.2e-16 ***
## Overall.Qual 1 4.554 4.554 316.69 < 2.2e-16 ***
## Residuals 823 11.836 0.014
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1model.resid<-Final.lm$residuals
plot(model.resid, main="Residuals",pch=20)
abline(0,0, lwd=2, col="blueviolet")
qqnorm(residuals(Final.lm))
qqline(residuals(Final.lm))
#### Section 3.5 Model Testing
Model Testing:
1.Good balance in model can be achieved with the number of predictors we include in the model.
Too few: An underspecified model tends to produce biased estimates. Too many: An overspecified model tends to have less precise estimates. Just right: A model with the correct terms has no bias and the most precise estimates. 2.For a good regression model, you want to include the variables that you are specifically testing along with other variables that affect the response in order to avoid biased results.
Adjusted R-squared and Predicted R-squared: Generally, you choose the models that have higher adjusted and predicted R-squared values.
The adjusted R squared increases only if the new term improves the model more than would be expected by chance and it can also decrease with poor quality predictors. The predicted R-squared is a form of cross-validation and it can also decrease. Cross-validation determines how well your model generalizes to other data sets by partitioning your data.
P-values for the predictors: In regression, low p-values indicate terms that are statistically significant. Reducing the model refers to the practice of including all candidate predictors in the model.
3.Stepwise regression and Best subsets regression: These are two automated procedures that can identify useful predictors during the exploratory stages of model building. With best subsets regression, it provides Mallows Cp, which is a statistic specifically designed to help you manage the tradeoff between precision and bias.
Once one has completed the above steps and satisfied themselves that their chosen model is the best, testing of the model with independent data becomes necessary. Ground-truthing the predictive capability of the model should therefore be addressed and results reported . Various methods of model testing exist: bootstrapping, randomization,and prospective sampling.
More robust estimates of prediction error will be provided by using independent data.The strengths and weakness of summary statistics of predictive power resulting from these validation procedures.
In real world environments we have to watch certain shortcomings in models:
1.The best model can be only as good as the variables measured by the study. The results for the variables you include in the analysis can be biased by the significant variables that you do not include.
2.Your sample might be unusual, either by chance or by data collection methodology. False positives and false negatives are part of the game when working with samples. 3.P-values can change based on the specific terms in the model. In particular, multicollinearity can sap significance and make it difficult to determine the role of each predictor. 4.If you assess enough models, you will find variables that appear to be significant but are only correlated by chance. This form of data mining can make random data appear significant. A low predicted R-squared is a good way to check for this problem. P-values, predicted and adjusted R-squared, and Mallows Cp can suggest different models. RMSE is also an important indicator. Stepwise regression and best subsets regression are great tools and can get you close to the correct model. However, studies have found that they generally do not pick the correct model.
5.Select variables based on their relationships and coefficient signs and effects magnitudes.Align your model with the theory of parsimony and adjust as required. Keep the model as simple as possible because they produce more accurate predictions. We can use anova to compare models provided we apply consistent conditions to construct models out-of-sample.We can know their statistical merits. 6. Residual Plots As we evaluate models, we check the residual plots because they can help us to avoid inadequate models and help us to adjust our model for better results. As an example, the bias in underspecified models can show up as patterns in the residuals, such as the need to model curvature. The simplest model that produces random residuals is a good candidate for being a relatively precise and unbiased model.
0.0.0.12.10 Testing Bayesian(“BAS”)Linear (“lm”)-Redudced train datset
library(BAS)
BIC.trbas <- bas.lm(log(price) ~log(Garage.Area+1) +
log(Total.Bsmt.SF + 1) + Garage.Cars + log(area) +
Full.Bath + Half.Bath +
Bedroom.AbvGr + Year.Built + log(X1st.Flr.SF) +
log(X2nd.Flr.SF + 1) +
log(Lot.Area) + Overall.Cond+Overall.Qual,
data =na.omit(train), prior = "BIC",
modelprior=uniform())
BIC.trbas##
## Call:
## bas.lm(formula = log(price) ~ log(Garage.Area + 1) + log(Total.Bsmt.SF + 1) + Garage.Cars + log(area) + Full.Bath + Half.Bath + Bedroom.AbvGr + Year.Built + log(X1st.Flr.SF) + log(X2nd.Flr.SF + 1) + log(Lot.Area) + Overall.Cond + Overall.Qual, data = na.omit(train), prior = "BIC", modelprior = uniform())
##
##
## Marginal Posterior Inclusion Probabilities:
## Intercept log(Garage.Area + 1) log(Total.Bsmt.SF + 1)
## 1.00000 0.03856 1.00000
## Garage.Cars log(area) Full.Bath
## 0.99996 1.00000 0.04898
## Half.Bath Bedroom.AbvGr Year.Built
## 0.04306 0.99999 1.00000
## log(X1st.Flr.SF) log(X2nd.Flr.SF + 1) log(Lot.Area)
## 0.85638 0.18067 1.00000
## Overall.Cond Overall.Qual
## 1.00000 1.00000image(BIC.trbas, rotate = F)
coef(BIC.trbas)##
## Marginal Posterior Summaries of Coefficients:
##
## Using BMA
##
## Based on the top 8192 models
## post mean post SD post p(B != 0)
## Intercept 1.199e+01 4.090e-03 1.000e+00
## log(Garage.Area + 1) -9.198e-05 9.950e-04 3.856e-02
## log(Total.Bsmt.SF + 1) 2.750e-02 3.981e-03 1.000e+00
## Garage.Cars 4.166e-02 7.849e-03 1.000e+00
## log(area) 4.489e-01 5.434e-02 1.000e+00
## Full.Bath -4.966e-04 3.356e-03 4.898e-02
## Half.Bath 3.437e-04 2.858e-03 4.306e-02
## Bedroom.AbvGr -3.850e-02 6.915e-03 1.000e+00
## Year.Built 3.919e-03 2.041e-04 1.000e+00
## log(X1st.Flr.SF) 1.132e-01 5.060e-02 8.564e-01
## log(X2nd.Flr.SF + 1) -1.921e-03 4.518e-03 1.807e-01
## log(Lot.Area) 1.174e-01 9.494e-03 1.000e+00
## Overall.Cond 5.799e-02 4.121e-03 1.000e+00
## Overall.Qual 8.630e-02 5.056e-03 1.000e+00train.lm <- lm(log(price) ~log(Total.Bsmt.SF + 1) + log(area)+ Bedroom.AbvGr + Year.Built + log(X2nd.Flr.SF + 1 ) +
log(Lot.Area) + Overall.Cond+Overall.Qual,
data =na.omit(train))
train.lm##
## Call:
## lm(formula = log(price) ~ log(Total.Bsmt.SF + 1) + log(area) +
## Bedroom.AbvGr + Year.Built + log(X2nd.Flr.SF + 1) + log(Lot.Area) +
## Overall.Cond + Overall.Qual, data = na.omit(train))
##
## Coefficients:
## (Intercept) log(Total.Bsmt.SF + 1) log(area)
## -2.597157 0.029274 0.595433
## Bedroom.AbvGr Year.Built log(X2nd.Flr.SF + 1)
## -0.041745 0.004165 -0.013163
## log(Lot.Area) Overall.Cond Overall.Qual
## 0.129074 0.057612 0.091045coef(train.lm)## (Intercept) log(Total.Bsmt.SF + 1) log(area)
## -2.597156663 0.029274253 0.595432729
## Bedroom.AbvGr Year.Built log(X2nd.Flr.SF + 1)
## -0.041745016 0.004164575 -0.013162715
## log(Lot.Area) Overall.Cond Overall.Qual
## 0.129074412 0.057612145 0.091045476plot(train.lm)
visreg(train.lm)
##### Cross validation by Stepwise methods
library(MASS)
step <- stepAIC(train.lm, direction="back")## Start: AIC=-3517.33
## log(price) ~ log(Total.Bsmt.SF + 1) + log(area) + Bedroom.AbvGr +
## Year.Built + log(X2nd.Flr.SF + 1) + log(Lot.Area) + Overall.Cond +
## Overall.Qual
##
## Df Sum of Sq RSS AIC
## <none> 11.877 -3517.3
## - Bedroom.AbvGr 1 0.5127 12.390 -3484.2
## - log(Total.Bsmt.SF + 1) 1 0.7640 12.641 -3467.5
## - log(X2nd.Flr.SF + 1) 1 0.7888 12.666 -3465.8
## - Overall.Cond 1 2.7248 14.602 -3347.5
## - log(Lot.Area) 1 2.7596 14.637 -3345.5
## - Overall.Qual 1 4.6451 16.523 -3244.7
## - Year.Built 1 6.6104 18.488 -3151.2
## - log(area) 1 8.2212 20.099 -3081.7step$anova # display results ## Stepwise Model Path
## Analysis of Deviance Table
##
## Initial Model:
## log(price) ~ log(Total.Bsmt.SF + 1) + log(area) + Bedroom.AbvGr +
## Year.Built + log(X2nd.Flr.SF + 1) + log(Lot.Area) + Overall.Cond +
## Overall.Qual
##
## Final Model:
## log(price) ~ log(Total.Bsmt.SF + 1) + log(area) + Bedroom.AbvGr +
## Year.Built + log(X2nd.Flr.SF + 1) + log(Lot.Area) + Overall.Cond +
## Overall.Qual
##
##
## Step Df Deviance Resid. Df Resid. Dev AIC
## 1 823 11.87747 -3517.326plot(Initial.model,train.lm,which=1:4) 
A<-AIC(train.lm)
B<-BIC(train.lm)
imptrain=A-B
imptrain## [1] -47.238320.0.0.12.11 RMSE
predict.BIC <- exp(predict(model.BIC, train))
resid.BIC <- ames_train$price - predict.BIC
rmse.train <- sqrt(mean(resid.BIC^2))
rmse.train## [1] 23191.250.0.0.12.12 Calculate proportion falling within prediction intervals-train(lm)
predict.lm <- exp(predict(train.lm, newdata=train, interval = "prediction"))0.0.0.12.13 Calculate coverage probability within prediction intervals-train(lm)
coverage.prob.train <- mean(train$price > predict.lm[,"lwr"] &
train$price < predict.lm[,"upr"])
coverage.prob.train## [1] 0.9495192Calculate coverage probability within prediction intervals-BIC.bas
coverage.prob.BIC <- mean(train$price > predict.BIC[,"lwr"] &
train$price < predict.BIC[,"upr"])## Error in predict.BIC[, "lwr"]: incorrect number of dimensionscoverage.prob.BIC## [1] 0.94711540.0.0.12.14 Testing Bayesian(“BAs”) & Linear (“lm”)-Redudced test datset
test.reg <- bas.lm(log(price) ~ log(Total.Bsmt.SF + 1) +log(area) +
Bedroom.AbvGr + Year.Built +log(X2nd.Flr.SF +1)+ log(Lot.Area) + Overall.Cond+Overall.Qual,
data =na.omit(test), prior ="BIC",
modelprior=uniform())
image(test.reg, rotate = F)
coef(test.reg)##
## Marginal Posterior Summaries of Coefficients:
##
## Using BMA
##
## Based on the top 256 models
## post mean post SD post p(B != 0)
## Intercept 12.022974 0.004076 1.000000
## log(Total.Bsmt.SF + 1) 0.032896 0.003701 1.000000
## log(area) 0.638674 0.023990 1.000000
## Bedroom.AbvGr -0.036039 0.006752 0.999980
## Year.Built 0.003665 0.000192 1.000000
## log(X2nd.Flr.SF + 1) -0.013523 0.001686 1.000000
## log(Lot.Area) 0.116978 0.009020 1.000000
## Overall.Cond 0.049430 0.004120 1.000000
## Overall.Qual 0.083671 0.004942 1.000000plot(test.reg) 
test.lm <- lm(log(price) ~log(Total.Bsmt.SF + 1) + log(area)+ Bedroom.AbvGr + Year.Built + log(X2nd.Flr.SF + 1 ) +
log(Lot.Area) + Overall.Cond+Overall.Qual,
data =na.omit(test))
test.lm##
## Call:
## lm(formula = log(price) ~ log(Total.Bsmt.SF + 1) + log(area) +
## Bedroom.AbvGr + Year.Built + log(X2nd.Flr.SF + 1) + log(Lot.Area) +
## Overall.Cond + Overall.Qual, data = na.omit(test))
##
## Coefficients:
## (Intercept) log(Total.Bsmt.SF + 1) log(area)
## -1.761644 0.032896 0.638675
## Bedroom.AbvGr Year.Built log(X2nd.Flr.SF + 1)
## -0.036040 0.003665 -0.013523
## log(Lot.Area) Overall.Cond Overall.Qual
## 0.116978 0.049430 0.083671augment(test.lm)## log.price. log.Total.Bsmt.SF...1. log.area. Bedroom.AbvGr Year.Built
## 1 12.63101 7.601402 7.600902 3 2004
## 2 12.45877 7.298445 7.516977 3 1957
## 3 11.66135 6.580639 6.782192 2 1952
## 4 11.87374 6.816736 7.049255 3 1968
## 5 12.53358 7.353722 7.353082 2 2005
## 6 12.20607 6.867974 7.382124 3 1999
## 7 11.56172 6.606650 7.201916 2 1939
## 8 12.22588 6.569481 7.712891 3 1980
## 9 12.44902 7.161622 7.792349 4 1954
## 10 11.96081 6.329721 7.432484 4 1910
## 11 11.36210 6.270988 6.405228 2 1920
## 12 12.39214 6.831954 7.541152 3 2003
## 13 12.49874 7.704361 7.703910 4 1970
## 14 12.40492 7.314553 7.313887 2 1987
## 15 11.95118 6.546785 7.255591 3 1999
## 16 11.88103 7.104144 7.330405 4 1957
## 17 11.71587 6.641182 7.218910 2 1971
## 18 11.85652 6.744059 6.742881 1 2004
## 19 11.78295 6.762730 6.804615 2 1983
## 20 12.34583 6.675823 7.324490 3 1929
## 21 12.67608 7.421776 7.718685 3 2002
## 22 12.13296 6.647688 7.366445 3 2004
## 23 11.77529 6.437752 7.160069 3 1992
## 24 12.14420 7.126891 7.212294 3 1977
## 25 11.75587 6.785588 7.220374 3 1931
## 26 12.14685 6.728629 7.020191 2 2004
## 27 12.20657 6.677083 7.496652 4 1920
## 28 11.90834 6.752270 7.273093 3 1978
## 29 11.82774 6.834109 7.560080 4 1948
## 30 11.96400 7.575585 7.575072 6 1977
## 31 11.32055 6.759255 6.758095 1 1940
## 32 12.03172 7.080868 7.270313 3 1956
## 33 11.58989 6.628041 7.319865 4 1940
## 34 12.08743 6.955593 7.454720 3 1956
## 35 12.36734 6.880384 7.501634 3 2002
## 36 11.95118 6.639876 7.393878 2 2003
## 37 11.58989 6.725034 7.198184 3 1956
## 38 11.95118 6.398595 7.090077 2 2004
## 39 12.07254 6.555357 7.463363 3 1968
## 40 12.80078 7.116394 7.761745 4 1993
## 41 12.12757 7.070724 7.090077 2 2003
## 42 11.81303 6.740519 6.794587 2 1949
## 43 11.91839 6.538140 7.351158 3 1939
## 44 12.18075 7.044033 7.135687 1 2008
## 45 12.25486 6.645091 7.371489 3 2008
## 46 11.79810 6.645091 6.643790 2 1972
## 47 12.56549 7.446001 7.445418 3 2002
## 48 11.69441 6.645091 6.766192 2 1971
## 49 12.15478 7.393263 7.366445 4 1964
## 50 11.82774 6.928538 7.564238 4 1910
## 51 11.65269 6.708084 7.109879 3 1926
## 52 11.63956 6.265301 6.995766 3 1973
## 53 12.02874 7.145984 7.142037 3 1960
## 54 12.72189 7.007601 7.688913 3 2008
## 55 11.84940 6.591674 7.211557 3 1941
## 56 12.07824 6.593045 7.284821 2 1999
## 57 11.73607 6.855409 6.854355 2 1952
## 58 11.56172 6.329721 7.137278 2 1939
## 59 11.77721 6.844815 6.843750 3 1975
## 60 12.25914 6.971669 7.625107 4 1996
## 61 11.71178 6.877296 6.876265 3 1975
## 62 12.83468 7.700295 7.832808 1 2004
## 63 12.52453 7.436617 7.436028 3 2008
## 64 11.07442 6.487684 6.875232 4 1927
## 65 11.87757 6.820016 7.062192 3 1920
## 66 12.05234 6.705639 7.455877 3 1992
## 67 11.59451 6.867974 6.866933 2 1920
## 68 12.40656 6.940222 7.784473 4 1940
## 69 12.18587 7.057037 7.424165 3 1977
## 70 11.41861 6.915723 6.981935 3 1922
## 71 12.45683 7.201916 7.528869 3 2007
## 72 12.01370 7.070724 7.284821 3 1967
## 73 11.54248 6.660575 7.096721 2 1925
## 74 11.87060 7.102499 7.101676 3 1967
## 75 12.56375 7.374002 7.373374 0 2001
## 76 11.74404 7.353082 7.352441 4 1968
## 77 11.98262 6.932448 6.990257 3 1966
## 78 11.85474 6.605298 7.293018 2 1922
## 79 12.50618 6.803505 7.492760 3 2006
## 80 11.68267 6.705639 6.704414 3 1990
## 81 11.60824 6.580639 7.157735 2 1947
## 82 11.71994 6.182085 7.263330 3 1915
## 83 11.68688 6.856462 6.855409 2 1924
## 84 11.74543 7.058758 7.058758 3 1955
## 85 11.79056 6.705639 7.109879 3 1948
## 86 11.90497 7.085901 7.085064 3 1959
## 87 11.80932 6.850126 6.849066 2 1967
## 88 11.80881 0.000000 7.370231 4 1959
## 89 12.28690 7.528869 7.515345 3 2004
## 90 12.23999 6.859615 7.655391 4 1969
## 91 11.60733 7.087574 7.086738 2 1916
## 92 11.76757 6.945051 6.944087 2 1974
## 93 11.79810 6.584791 6.642487 1 1998
## 94 12.50618 7.259116 7.301822 1 1977
## 95 11.73607 7.060476 7.059618 3 1950
## 96 12.36947 6.896694 7.535297 3 1999
## 97 11.65269 6.248043 6.939254 2 1980
## 98 11.73607 6.993933 6.993015 3 1954
## 99 12.61087 7.041412 7.906547 4 1976
## 100 11.81303 7.034388 7.113956 3 1956
## 101 11.84940 7.022868 7.021976 2 2003
## 102 11.23849 6.665684 6.664409 2 1928
## 103 12.72189 7.551187 7.550661 3 1959
## 104 12.01974 6.814543 7.233455 4 1952
## 105 11.84582 6.916715 6.915723 2 1952
## 106 12.42078 7.417580 7.427739 1 1997
## 107 11.98293 7.132498 7.131699 3 1964
## 108 12.03172 6.693324 7.360104 3 1995
## 109 12.49500 6.936343 7.804659 4 1998
## 110 11.75587 6.947937 6.946976 2 1925
## 111 12.22955 6.715383 7.487734 3 1997
## 112 11.98293 7.044033 7.043160 2 2006
## 113 12.19096 6.771936 7.554335 4 2002
## 114 11.92768 6.849066 7.832411 5 1973
## 115 10.98529 6.033086 6.395262 2 1940
## 116 11.89136 6.690842 7.344719 3 1976
## 117 12.14153 6.539586 7.311886 3 1995
## 118 12.20607 7.003974 7.724888 4 1918
## 119 11.66565 6.755769 6.754604 2 1958
## 120 12.27839 6.890609 7.543803 3 2000
## 121 12.27839 7.305860 7.305188 3 1968
## 122 12.63460 7.430707 7.434848 3 2004
## 123 12.50618 6.916715 7.733246 4 2003
## 124 12.28765 7.299797 7.309212 3 1997
## 125 11.59451 6.493754 6.762730 2 1920
## 126 11.69525 0.000000 7.200425 3 1957
## 127 11.85652 6.597146 7.288928 4 1968
## 128 12.44114 7.015712 7.586296 3 2005
## 129 12.06681 6.555357 7.300473 3 1994
## 130 11.60824 6.785588 7.225481 3 1938
## 131 12.10349 7.262629 7.261927 3 1964
## 132 11.84940 6.744059 6.742881 1 2003
## 133 12.47717 7.297091 7.753194 4 1990
## 134 11.75979 6.447306 7.143618 2 1980
## 135 12.21850 7.223296 7.222566 2 2006
## 136 11.64833 6.816736 6.815640 2 1958
## 137 12.20607 6.345636 7.434848 3 1997
## 138 11.72804 6.796824 6.979145 2 1956
## 139 12.07767 6.638568 7.411556 3 1993
## 140 12.35234 6.871091 7.491088 3 2001
## 141 12.28765 6.858565 7.483807 3 1999
## 142 11.97980 6.538140 7.262629 3 1977
## 143 13.04332 7.482682 7.927324 4 2007
## 144 11.94471 6.590301 7.349874 4 1968
## 145 12.90669 7.288244 7.935230 4 1995
## 146 12.15478 7.126087 7.158514 3 1977
## 147 11.35627 6.089045 6.767343 2 1923
## 148 11.84940 6.807935 7.312553 3 1946
## 149 11.98293 6.532334 7.564238 5 1916
## 150 12.49313 7.050123 7.757906 4 1941
## 151 12.66033 7.497762 7.768533 3 1971
## 152 12.30592 7.358194 7.357556 3 2001
## 153 12.61154 7.316548 7.333676 2 2006
## 154 11.54248 6.746412 6.866933 2 1926
## 155 12.01974 7.239215 7.238497 3 1957
## 156 11.88449 6.378426 7.037028 3 1958
## 157 11.82701 6.902743 7.525640 4 1954
## 158 12.48200 7.068172 7.710653 3 1993
## 159 11.84940 6.947937 7.216709 3 1957
## 160 12.23077 6.859615 7.502186 3 2002
## 161 12.59473 7.293698 8.158516 3 1880
## 162 11.94406 6.776507 7.255591 4 1915
## 163 11.97351 6.997596 6.996681 3 1966
## 164 11.77529 6.695799 6.977281 2 1940
## 165 11.47210 6.182085 6.894670 2 1971
## 166 11.71178 0.000000 7.232010 2 1954
## 167 12.66508 7.403670 7.403061 3 2008
## 168 12.19349 7.057898 7.230563 3 1972
## 169 12.25486 7.341484 7.636752 3 1978
## 170 12.29911 6.685861 7.461640 3 1940
## 171 11.79810 6.818924 6.817831 3 1970
## 172 11.27720 6.350886 6.999422 2 1924
## 173 11.74404 6.759255 7.250636 3 1938
## 174 11.95118 7.016610 7.015712 3 2003
## 175 11.99535 6.961296 6.966967 1 1990
## 176 12.14420 6.728629 7.436028 3 2003
## 177 12.90421 7.396335 7.803027 4 1994
## 178 12.33929 7.008505 7.507690 4 1984
## 179 12.04355 6.411818 7.241366 3 2007
## 180 12.10071 7.136483 7.135687 3 1986
## 181 11.99381 6.536692 7.238497 3 1977
## 182 11.49170 6.437752 6.841615 3 1948
## 183 12.26434 6.765039 7.477604 3 2007
## 184 11.71913 6.511745 6.828712 3 1949
## 185 12.75996 7.242082 7.779885 3 1997
## 186 12.05525 7.128496 7.127694 3 1964
## 187 11.75979 6.973543 6.972606 2 1950
## 188 12.33271 7.361375 7.360740 3 2002
## 189 11.98293 5.973810 7.434848 3 1994
## 190 12.04355 7.208600 7.191429 2 1959
## 191 11.97035 7.172425 7.171657 3 1964
## 192 12.03053 6.614726 7.306531 3 2005
## 193 11.81229 6.818924 6.817831 2 1979
## 194 12.15478 6.753438 7.061334 2 2005
## 195 12.16598 6.597146 7.516433 4 2005
## 196 11.91371 6.744059 6.742881 1 2004
## 197 11.79056 6.816736 6.839476 2 1964
## 198 12.10625 7.205635 7.315884 1 2005
## 199 12.42320 7.387709 7.387090 3 2007
## 200 12.30818 7.375256 7.374629 2 2005
## 201 12.08391 6.734592 7.426549 4 1915
## 202 12.19096 6.715383 8.033334 5 1920
## 203 11.82774 6.447306 7.185387 3 1993
## 204 11.90158 6.705639 7.116394 3 1916
## 205 11.86005 6.833032 7.338888 3 1936
## 206 12.54254 7.515889 7.515345 3 2004
## 207 11.91839 6.934397 6.933423 3 1977
## 208 12.33138 6.765039 7.477604 3 2005
## 209 11.93819 6.932448 7.460490 3 1935
## 210 12.31940 7.167809 7.402452 3 1954
## 211 12.79386 7.459915 7.459339 3 2008
## 212 12.76569 7.288244 7.707063 4 2004
## 213 11.58525 6.902743 7.771489 4 1892
## 214 12.26905 7.391415 7.390799 3 1975
## 215 12.15214 6.852243 7.382746 3 1997
## 216 11.95118 7.149917 7.149132 2 1960
## 217 11.99226 5.953243 7.232733 3 1997
## 218 11.97035 7.070724 7.084226 3 1975
## 219 12.56024 7.178545 7.177782 1 2001
## 220 12.41044 7.435438 7.434848 3 2008
## 221 12.16525 6.660575 7.565275 4 1979
## 222 12.27839 6.985642 7.412160 3 1960
## 223 11.84223 7.087574 7.086738 2 1956
## 224 11.66993 6.186209 7.399398 2 1910
## 225 11.94471 7.051856 7.050989 3 1966
## 226 11.61729 6.762730 6.854355 3 1954
## 227 11.60824 6.565265 7.092574 3 1950
## 228 12.44863 6.956545 7.557995 3 1998
## 229 11.73607 6.641182 7.218910 3 1970
## 230 12.20607 6.758095 7.455298 3 2002
## 231 12.00089 6.725034 7.416980 4 1976
## 232 11.01863 6.527958 6.806829 1 1922
## 233 12.40901 7.329750 7.329094 3 1979
## 234 12.10071 7.155396 7.154615 2 1992
## 235 11.60824 0.000000 7.231287 1 1949
## 236 11.84940 5.888878 7.502186 4 1900
## 237 11.95118 7.021976 7.028201 3 1963
## 238 12.06047 6.613384 7.345365 3 1999
## 239 12.12269 6.670766 7.306531 3 2004
## 240 12.03573 6.605298 7.307202 3 2006
## 241 12.45254 7.029088 7.736307 4 2002
## 242 12.61487 7.315218 7.912057 4 1986
## 243 12.28765 7.344073 7.343426 3 2005
## 244 11.83863 6.796824 6.795706 3 1965
## 245 11.89819 6.511745 7.203406 3 1920
## 246 12.77705 7.036148 7.811163 4 2004
## 247 11.81303 7.100852 7.419381 3 1948
## 248 11.98293 6.437752 7.299121 3 1926
## 249 11.75194 6.952729 6.951772 3 1963
## 250 12.30134 7.239933 7.362645 2 2004
## 251 12.36734 7.379632 7.132498 1 1960
## 252 12.84113 7.561642 7.561122 3 2005
## 253 11.98418 7.044033 7.043160 2 2005
## 254 12.63134 7.441320 7.440734 3 2007
## 255 12.15478 6.678342 7.322510 3 2000
## 256 12.27373 6.734592 7.470224 3 1999
## 257 11.80560 6.859615 7.099202 3 1968
## 258 12.04355 6.347389 7.560080 4 1968
## 259 12.15478 7.130099 7.841493 6 1969
## 260 12.10016 7.106606 7.142827 3 1965
## 261 11.62625 0.000000 7.550661 4 1978
## 262 11.84940 6.511745 7.203406 3 1929
## 263 12.35879 6.863803 7.642044 4 2004
## 264 12.08108 6.613384 7.313887 3 1999
## 265 12.20857 6.690842 7.427739 3 1998
## 266 12.36734 6.511745 7.605392 4 1928
## 267 11.84940 7.102499 7.101676 2 1965
## 268 12.16264 7.155396 7.154615 2 1992
## 269 12.15478 6.716595 7.597396 4 1971
## 270 12.61818 7.404888 7.508787 2 1971
## 271 11.97035 7.040536 7.039660 3 1967
## 272 12.13886 6.725034 7.444249 3 1993
## 273 11.91772 6.398595 7.109062 2 2005
## 274 11.68826 6.687109 7.412160 2 1940
## 275 11.87060 6.947937 7.520776 3 1949
## 276 11.83501 6.916715 7.041412 2 1928
## 277 12.04355 6.867974 7.368970 3 1999
## 278 11.51293 0.000000 7.416980 4 1965
## 279 11.94471 6.966967 6.966024 3 1968
## 280 12.38422 6.883463 7.575585 3 1997
## 281 11.41311 6.304449 6.995766 3 1970
## 282 11.81303 6.816736 6.829794 3 1965
## 283 11.95118 6.629363 7.516977 4 1966
## 284 12.30592 7.309881 7.309212 3 2002
## 285 12.34583 6.812345 7.735433 4 1977
## 286 11.87757 7.087574 7.086738 3 1968
## 287 12.24047 7.237778 7.237059 3 2003
## 288 11.76757 6.224558 7.288928 3 1910
## 289 12.19400 7.039660 7.808323 3 1952
## 290 12.54254 6.991177 7.562162 3 1998
## 291 12.22163 6.049733 7.409742 3 1994
## 292 11.99843 7.083388 7.082549 2 1989
## 293 11.49272 0.000000 6.921658 2 1956
## 294 12.36734 6.900731 7.531016 3 2000
## 295 11.96400 6.391917 7.474205 4 1920
## 296 11.87060 6.752270 7.283448 4 1975
## 297 11.91839 6.897705 7.605392 4 1939
## 298 12.32386 6.945051 7.750184 4 1999
## 299 11.69316 6.825460 6.860664 2 1938
## 300 12.34148 6.511745 7.619233 3 1996
## 301 12.00151 7.140453 7.139660 3 1958
## 302 11.98293 7.063904 7.079184 3 1992
## 303 12.06393 6.605298 7.297091 3 2005
## 304 11.84223 5.921578 7.011214 3 1971
## 305 11.96400 7.134094 7.133296 2 1960
## 306 12.85970 7.484369 7.844241 4 1997
## 307 11.85652 0.000000 7.711101 5 1979
## 308 11.84940 6.511745 7.301148 4 1925
## 309 12.50618 7.631917 7.896181 4 1994
## 310 12.30138 7.207119 7.213768 1 2002
## 311 12.79386 7.548029 7.572503 3 2003
## 312 11.95761 6.539586 7.280697 3 1999
## 313 12.25961 6.678342 7.493317 3 1998
## 314 11.81673 6.888572 6.887553 3 1967
## 315 12.97154 8.071219 8.079618 4 1992
## 316 12.92391 7.250636 8.032035 4 1998
## 317 11.73607 6.716595 6.715383 2 1955
## 318 12.05234 6.599870 7.249926 3 2005
## 319 12.14420 6.651572 7.413367 3 1995
## 320 12.62807 7.301822 7.724005 4 2003
## 321 11.68688 7.350516 7.349874 4 1960
## 322 12.19552 7.427144 7.452402 3 1967
## 323 12.08954 6.985642 7.028201 2 1966
## 324 11.91839 6.859615 7.366445 3 1938
## 325 12.42922 7.374629 7.406103 2 2004
## 326 12.07824 6.645091 7.336937 3 2005
## 327 12.00151 6.781058 7.477604 2 1914
## 328 12.36734 7.028201 7.653495 4 1935
## 329 12.31043 6.717805 7.474205 3 2002
## 330 12.65396 7.273093 7.674617 3 2000
## 331 11.95118 6.814543 7.509883 4 1915
## 332 11.57119 6.182085 6.894670 2 1970
## 333 12.17045 7.209340 7.215975 3 2007
## 334 11.08214 6.385194 6.761573 3 1920
## 335 11.89819 7.035269 7.095893 3 1962
## 336 12.12269 7.248504 7.198184 2 1999
## 337 11.76174 6.814543 7.268920 3 1950
## 338 11.41861 6.137727 6.895683 2 1973
## 339 11.85083 6.880384 7.363280 3 1939
## 340 11.89819 6.690842 7.344719 3 1978
## 341 11.65269 6.799056 7.203406 3 1936
## 342 12.29911 6.751101 7.598399 4 2002
## 343 12.10071 7.169350 7.168580 3 1985
## 344 11.87060 6.478510 7.301148 3 1920
## 345 12.30592 7.086738 7.516977 4 1998
## 346 11.94146 6.923629 6.932448 3 1976
## 347 11.87060 6.828712 6.827629 2 1980
## 348 12.71289 7.450661 7.450080 3 2008
## 349 11.87060 6.680855 7.216709 1 1993
## 350 12.39255 6.996681 7.346010 2 2006
## 351 11.81857 6.859615 6.858565 2 1956
## 352 11.63071 6.783325 6.782192 3 1972
## 353 12.23539 6.701960 7.417580 3 2007
## 354 11.89136 6.898715 6.897705 3 1994
## 355 12.07254 7.239215 7.252762 3 1988
## 356 12.45293 7.415175 7.414573 3 2007
## 357 11.76757 7.043160 7.042286 3 1956
## 358 11.88449 6.898715 6.897705 3 1994
## 359 11.91036 6.762730 7.021084 3 1966
## 360 11.40199 6.182085 6.894670 2 1971
## 361 12.02575 5.953243 7.225481 3 2004
## 362 11.96972 7.274480 7.273786 4 1958
## 363 12.08673 6.648985 7.309212 3 1942
## 364 12.05234 7.087574 7.153834 3 1977
## 365 11.60733 0.000000 6.946976 2 1950
## 366 12.12269 7.382124 7.409136 3 1986
## 367 12.12540 6.516193 7.536364 3 1975
## 368 12.71890 7.444833 7.444249 2 2007
## 369 12.59134 7.325808 7.337588 3 2006
## 370 12.57764 6.836259 7.894691 4 1990
## 371 11.81303 6.848005 7.293018 4 1954
## 372 12.43718 6.972606 7.776954 4 1998
## 373 12.50618 7.422971 7.422374 3 2000
## 374 12.52453 7.463363 7.462789 2 1985
## 375 12.20607 7.373374 7.409742 3 1959
## 376 12.45254 7.377134 7.381502 3 2006
## 377 12.20607 6.912743 6.927558 1 1988
## 378 12.17819 6.569481 7.546974 3 1994
## 379 12.01673 6.900731 7.415175 3 1955
## 380 12.14153 6.831954 7.380256 3 1997
## 381 12.32386 7.387090 7.386471 3 2005
## 382 11.51293 6.916715 7.126891 3 1920
## 383 12.08391 6.799056 7.556428 3 1928
## 384 12.30138 6.751101 7.596392 3 1932
## 385 12.32341 7.408531 7.415175 3 1998
## 386 11.96081 7.228388 7.227662 3 1960
## 387 11.84223 6.705639 7.356280 5 1924
## 388 11.93819 7.168580 7.167809 3 1954
## 389 11.38509 6.304449 6.995766 3 1970
## 390 11.65269 0.000000 7.479300 3 1960
## 391 11.51293 7.100852 7.238497 3 1915
## 392 12.18075 6.706862 7.346010 3 1920
## 393 12.05525 7.243513 7.242798 2 1990
## 394 12.46458 7.508239 7.507690 3 2005
## 395 11.40756 0.000000 7.167038 2 1967
## 396 12.22047 6.875232 7.553811 4 2002
## 397 12.23563 6.624065 7.633854 3 1974
## 398 12.31043 6.781058 7.426549 3 1988
## 399 12.05525 6.954639 6.987490 2 1976
## 400 11.84142 6.617403 7.486613 4 1914
## 401 11.84223 6.495266 7.130899 3 1910
## 402 12.53538 7.531552 7.512071 2 1967
## 403 12.42521 6.950815 7.890957 4 1980
## 404 11.82408 6.985642 7.299797 4 1951
## 405 11.07442 6.928538 6.927558 2 1918
## 406 11.91839 7.310550 7.309881 3 1989
## 407 12.32386 6.799056 7.604894 3 1948
## 408 11.44999 6.304449 6.995766 3 1970
## 409 11.77529 7.083388 7.093405 2 1987
## 410 12.34583 7.181592 7.180831 2 2007
## 411 11.72804 6.331502 7.113956 2 1980
## 412 11.89068 7.149132 7.696213 4 1900
## 413 11.65269 6.338594 7.103322 3 1920
## 414 12.38631 7.029088 7.610853 3 1995
## 415 12.10625 6.947937 7.177019 3 1974
## 416 12.07254 6.255750 7.288928 3 1963
## 417 11.91505 6.790097 7.581720 4 1915
## 418 12.50618 7.388328 7.395722 3 2002
## 419 11.88449 6.475433 6.866933 0 1965
## 420 12.39462 7.234177 7.217443 2 1954
## 421 11.63071 6.834109 6.833032 3 1957
## 422 11.93164 6.814543 7.351158 4 1950
## 423 12.13619 6.842683 7.491088 3 2000
## 424 12.12811 7.274480 7.273786 2 1970
## 425 12.40492 7.654917 7.654443 3 1968
## 426 11.31904 6.285998 7.203406 3 1915
## 427 12.04942 6.755769 7.447751 4 1962
## 428 12.30138 7.486053 7.485492 3 1979
## 429 11.72804 6.816736 6.815640 3 1964
## 430 11.64395 6.424869 7.116394 3 1910
## 431 11.76679 6.804615 7.228388 3 1935
## 432 11.80186 6.725034 7.286876 4 1949
## 433 12.14950 6.418365 7.863651 4 1921
## 434 11.57119 6.745236 7.667626 2 1898
## 435 12.82799 7.522400 7.932362 4 1993
## 436 12.06105 6.665684 7.397562 4 1969
## 437 11.99843 7.117206 7.116394 3 1984
## 438 12.15478 7.313887 7.313220 3 2004
## 439 11.76757 6.762730 6.761573 3 1950
## 440 11.83138 7.050123 7.049255 3 1953
## 441 11.89136 6.875232 7.207860 3 1954
## 442 12.01067 7.196687 7.195937 3 1967
## 443 12.08954 6.695799 7.373374 3 1992
## 444 12.50061 6.994850 7.702556 3 1999
## 445 12.85448 7.696667 7.696213 3 2003
## 446 11.72804 6.947937 6.946976 3 1978
## 447 12.07824 7.121252 7.133296 3 1995
## 448 11.66135 6.204558 6.937314 3 1972
## 449 12.43718 7.389564 7.388946 2 2004
## 450 12.34583 6.883463 7.736744 4 1999
## 451 11.75587 6.751101 7.153052 4 1954
## 452 11.91839 7.126891 7.126087 3 1957
## 453 12.12269 7.180831 7.822044 5 1890
## 454 11.56172 6.762730 6.761573 3 1962
## 455 11.87409 7.145984 7.145196 3 1977
## 456 11.19821 6.523562 6.638568 2 1925
## 457 11.77529 5.484797 7.174724 3 1910
## 458 12.07824 6.725034 7.589842 4 1968
## 459 11.88449 6.947937 6.946976 3 1968
## 460 12.07539 7.125283 7.124478 3 1973
## 461 12.03469 6.629363 7.321189 2 2000
## 462 11.84940 6.846943 7.374629 2 1940
## 463 12.83201 7.491645 7.491088 2 2003
## 464 12.12269 6.587550 7.299121 4 1972
## 465 12.25248 7.349231 7.348588 2 2006
## 466 11.82041 7.042286 7.041412 3 1959
## 467 11.83501 6.830874 7.342132 3 1890
## 468 12.14950 6.591674 7.283448 3 2005
## 469 12.58861 7.364547 7.379008 3 2007
## 470 12.10349 7.050123 7.049255 3 1964
## 471 12.27373 7.229114 7.228388 2 2004
## 472 12.37582 6.848005 7.511525 3 2003
## 473 11.73527 6.993015 7.533159 2 1890
## 474 12.06105 6.685861 7.397562 4 1966
## 475 12.46844 7.305860 7.305188 2 2004
## 476 12.12811 7.198931 7.198184 3 2003
## 477 11.98916 6.762730 7.299121 5 1969
## 478 11.46058 6.137727 6.895683 1 1973
## 479 12.51319 7.677400 7.694393 3 1990
## 480 12.27607 6.739337 7.665753 5 1916
## 481 12.61154 7.374629 7.406103 2 2004
## 482 12.17045 6.733402 7.373374 3 2004
## 483 12.59134 7.084226 7.681099 3 1974
## 484 12.32386 7.219642 7.344719 2 2004
## 485 11.89751 6.580639 7.176255 3 1969
## 486 11.77529 6.776507 6.810142 3 1977
## 487 12.47801 7.358194 7.676010 3 1968
## 488 12.45293 7.354362 7.356918 2 1966
## 489 11.99535 6.969791 7.160069 3 1959
## 490 12.02575 6.916715 7.305188 3 1964
## 491 11.77529 6.884487 7.443078 3 2004
## 492 11.95118 7.198931 7.198184 2 2001
## 493 12.42118 6.877296 7.734121 4 2000
## 494 12.27839 7.301822 7.309212 3 1998
## 495 12.50432 7.063904 7.932721 6 2000
## 496 12.36094 7.279319 7.472501 3 1992
## 497 12.12811 6.725034 7.448916 3 1998
## 498 11.85652 6.762730 6.761573 2 1951
## 499 12.06681 6.903747 7.156177 3 1978
## 500 11.88449 6.900731 6.899723 3 1967
## 501 12.25486 7.282761 7.298445 3 1991
## 502 11.79810 6.744059 6.742881 1 2003
## 503 11.88449 7.003974 7.003065 3 1996
## 504 11.80560 6.878326 7.443664 3 2004
## 505 12.53897 7.259116 7.556951 3 2004
## 506 11.76757 6.842683 6.841615 2 1956
## 507 11.77529 6.892642 6.856462 2 1953
## 508 12.45410 7.356918 7.377759 3 2007
## 509 11.86358 7.016610 7.015712 3 2004
## 510 12.37792 7.095064 7.657755 4 1970
## 511 12.14791 6.573680 7.414573 3 1934
## 512 12.07767 7.234898 7.358194 1 2007
## 513 11.92172 6.947937 6.946976 3 1977
## 514 12.54219 7.023759 7.818430 5 2003
## 515 12.10071 7.287561 7.450661 3 1968
## 516 11.80932 6.916715 6.915723 2 1953
## 517 12.04942 6.478510 7.355002 3 1980
## 518 11.83501 6.705639 6.704414 2 1982
## 519 12.33271 7.370860 7.370231 3 2006
## 520 11.90834 6.962243 6.961296 2 1977
## 521 11.34451 6.447306 6.445720 1 1970
## 522 11.91170 6.580639 7.565275 4 1927
## 523 12.16707 7.138867 7.210080 2 1979
## 524 12.05525 7.192934 7.192182 3 1958
## 525 12.01612 6.616065 7.412160 3 2003
## 526 12.12811 7.059618 7.422971 4 1918
## 527 11.78980 6.680855 6.679599 2 1972
## 528 12.27135 7.217443 7.317212 2 2005
## 529 12.53177 7.054450 7.631432 3 1988
## 530 12.45877 7.387090 7.413367 3 2008
## 531 11.04105 6.762730 6.761573 3 1965
## 532 12.52198 7.011214 7.648263 3 1998
## 533 11.97035 6.958448 7.055313 3 1968
## 534 11.57590 0.000000 6.782192 3 1959
## 535 12.42922 7.333676 7.333023 3 2007
## 536 12.21850 6.609349 7.738052 5 1963
## 537 11.68182 6.920672 6.919684 2 1920
## 538 11.89136 6.762730 7.090077 1 1965
## 539 11.75194 6.959399 6.958448 3 1963
## 540 12.29911 6.742881 7.564238 4 2003
## 541 11.26446 5.379897 6.841615 2 1916
## 542 11.31447 0.000000 6.850126 2 1952
## 543 12.38422 6.859615 7.760041 4 1932
## 544 11.96049 6.805723 6.830874 2 1977
## 545 11.80560 7.041412 7.040536 3 1976
## 546 12.27793 6.706862 7.546446 4 2002
## 547 10.85900 5.602119 6.591674 2 1935
## 548 11.00210 5.673323 6.082219 1 1920
## 549 11.89819 6.842683 6.903747 2 1992
## 550 11.72400 7.003974 7.550661 4 1923
## 551 12.37582 7.029088 7.616284 3 2002
## 552 11.33857 0.000000 6.739337 3 1957
## 553 12.38212 7.224753 7.277939 2 2006
## 554 11.86005 6.373320 7.269617 3 1921
## 555 11.83863 6.517671 7.275865 3 1900
## 556 11.84868 6.660575 7.255591 3 1948
## 557 12.02575 7.324490 7.323831 3 1964
## 558 12.11997 6.909753 7.169350 2 1979
## 559 12.42922 7.044033 7.695303 4 2000
## 560 12.08391 6.927558 7.213032 2 1959
## 561 11.75194 6.762730 6.761573 3 1972
## 562 12.01370 6.888572 6.927558 3 1964
## 563 12.56724 6.962243 7.724447 3 2001
## 564 12.72784 7.133296 7.768533 3 1999
## 565 12.44114 7.430114 7.429521 2 2006
## 566 11.82041 6.947937 6.946976 3 1953
## 567 12.20607 7.172425 7.171657 1 2005
## 568 12.20607 7.130099 7.876259 6 1969
## 569 11.81229 6.549651 7.069874 2 1937
## 570 11.22524 6.350886 6.349139 2 1925
## 571 12.24047 6.835185 7.535297 3 1988
## 572 11.91772 7.290975 7.290293 3 1959
## 573 11.37939 0.000000 6.946976 2 1949
## 574 12.14420 6.836259 7.470224 4 1930
## 575 12.26905 6.742881 7.593878 4 2003
## 576 11.58989 6.458338 7.197435 3 1920
## 577 11.93819 7.016610 7.015712 3 2003
## 578 11.91772 6.893656 6.892642 3 1977
## 579 12.77987 7.063904 7.824046 5 2005
## 580 11.35041 6.930495 6.929517 2 1910
## 581 12.17922 7.217443 7.216709 2 2005
## 582 11.83790 6.834109 7.336937 4 1930
## 583 12.24289 6.762730 7.454720 3 2003
## 584 12.58622 7.259116 7.951559 4 1978
## 585 11.90497 7.012115 7.051856 3 1961
## 586 12.12269 7.039660 7.442493 3 1978
## 587 11.83138 6.845880 7.321850 4 1920
## 588 11.60368 6.645091 6.674561 2 1924
## 589 12.25961 6.742881 7.574558 4 2003
## 590 11.93492 6.551080 7.331060 3 1948
## 591 12.12323 6.013715 7.257708 3 2002
## 592 11.96400 6.716595 7.311218 3 1937
## 593 12.29225 7.271009 7.270313 3 1976
## 594 11.65269 6.913737 6.912743 2 1955
## 595 12.35449 7.413367 7.419381 3 2003
## 596 11.69525 6.983790 7.221105 3 1950
## 597 11.95118 7.034388 7.497207 3 1957
## 598 11.66135 6.827629 6.826545 2 1957
## 599 11.96718 6.916715 6.999422 3 1978
## 600 12.38839 7.029973 7.752335 4 2003
## 601 12.15452 6.816736 7.262629 3 1918
## 602 11.82408 7.074963 7.434848 4 1925
## 603 11.97666 7.104144 7.796469 4 1985
## 604 11.79810 6.799056 7.491088 4 1974
## 605 11.75194 6.856462 7.009409 3 1967
## 606 11.58989 6.904751 6.903747 3 1940
## 607 11.75194 6.862758 6.861711 3 1966
## 608 11.54829 6.511745 7.221836 3 1925
## 609 11.06664 6.683361 6.733402 2 1920
## 610 12.03765 6.575076 7.607878 5 1900
## 611 11.61729 6.523562 7.215240 2 1910
## 612 12.45683 7.063904 7.747165 4 1950
## 613 12.09458 7.320527 7.319865 3 1967
## 614 12.09458 6.989335 7.537430 4 1974
## 615 11.51293 6.705639 6.704414 2 1938
## 616 12.51356 7.366445 7.378384 3 2001
## 617 11.40756 0.000000 6.946976 2 1949
## 618 12.02874 6.591674 7.610358 3 1910
## 619 11.84940 6.842683 6.841615 2 1980
## 620 11.31447 6.582025 6.734592 2 1950
## 621 11.77529 6.796824 6.795706 3 1967
## 622 12.03172 7.113956 7.261225 2 1921
## 623 12.33050 7.249215 7.370860 2 2003
## 624 12.53897 6.874198 7.463363 0 1976
## 625 11.24505 6.591674 7.174724 3 1940
## 626 11.51192 6.675823 6.674561 2 1958
## 627 12.12811 6.890609 6.941190 1 1989
## 628 12.48749 7.142827 7.759614 3 1996
## 629 11.98916 7.132498 7.267525 3 1961
## 630 11.82408 6.629363 6.966024 1 1925
## 631 11.84223 6.875232 7.401231 4 1957
## 632 12.34126 7.313220 7.487734 3 1965
## 633 12.42922 6.961296 7.883823 4 1968
## 634 12.71640 7.239933 7.862882 4 1999
## 635 11.75587 6.680855 7.383368 3 1910
## 636 12.14950 6.725034 7.412764 3 1994
## 637 11.75979 6.892642 6.891626 3 1963
## 638 12.03765 6.896694 7.004882 2 1980
## 639 11.81303 6.523562 7.068172 2 1900
## 640 12.10016 6.563856 7.255591 3 1968
## 641 12.30138 6.817831 7.660114 4 1996
## 642 11.90429 7.001246 7.000334 3 1996
## 643 11.96400 6.994850 6.993933 2 2005
## 644 11.76757 6.796824 6.795706 3 1968
## 645 11.89819 6.752270 7.186901 3 1974
## 646 11.91170 6.720220 6.783325 2 1992
## 647 12.12215 6.539586 7.280697 3 1999
## 648 12.01370 6.705639 7.589336 4 1964
## 649 11.91505 6.398595 7.090077 2 2004
## 650 11.93819 7.025538 7.024649 3 1956
## 651 11.38509 6.755769 6.754604 3 1971
## 652 12.70685 7.189922 7.839132 4 1996
## 653 12.67576 7.385851 7.385231 2 2006
## 654 12.08391 6.629363 7.329750 3 2000
## 655 12.10071 6.664409 7.319202 3 2003
## 656 11.73607 6.961296 6.982863 3 1925
## 657 11.98916 6.378426 7.418181 3 1925
## 658 12.07824 7.137278 7.143618 3 2005
## 659 11.50791 6.255750 6.815640 2 1930
## 660 11.98449 7.185387 7.224753 3 1978
## 661 11.93164 7.047517 7.387709 3 1926
## 662 12.16525 6.850126 7.401231 3 1998
## 663 11.72804 6.838405 6.837333 2 1950
## 664 11.65269 5.579730 7.173192 3 1976
## 665 12.66033 5.634790 7.910591 2 1986
## 666 11.80186 6.867974 6.950815 3 1976
## 667 11.88103 6.498282 6.979145 3 1950
## 668 11.70355 6.424869 7.149132 3 1910
## 669 12.03172 6.821107 7.462789 4 1882
## 670 11.75194 6.922644 7.046647 3 1960
## 671 12.10625 6.735780 7.423568 3 1999
## 672 11.77452 6.762730 6.761573 3 1958
## 673 11.82704 7.427144 7.426549 4 1976
## 674 11.90834 6.276643 7.001246 2 1930
## 675 11.40199 0.000000 6.905753 3 1945
## 676 11.82041 6.985642 6.984716 3 1958
## 677 11.77144 6.740519 6.739337 2 1982
## 678 12.46844 7.458763 7.458186 3 2005
## 679 12.34583 6.851185 7.517521 3 2001
## 680 12.01370 6.988413 7.044033 3 1963
## 681 11.64837 6.529419 7.221105 3 1910
## 682 11.61277 7.006695 7.005789 2 1925
## 683 12.56024 7.428927 7.962764 4 1992
## 684 11.67844 6.762730 6.761573 3 1959
## 685 12.11997 7.057037 7.063904 3 1993
## 686 11.49272 6.762730 6.761573 2 1925
## 687 12.06105 6.821107 7.400010 3 1996
## 688 11.71994 6.816736 6.815640 3 1962
## 689 11.56172 6.645091 7.226936 3 1941
## 690 11.94146 7.121252 7.198184 2 1998
## 691 11.66135 6.475433 7.019297 2 1920
## 692 12.55673 7.380256 7.362011 2 2003
## 693 12.41187 7.387090 7.386471 3 2005
## 694 12.72487 7.111512 7.867871 4 1998
## 695 11.91839 6.875232 7.169350 3 1954
## 696 11.72481 6.898715 6.897705 3 1994
## 697 12.16003 6.778785 7.433667 3 1997
## 698 11.95118 6.329721 7.034388 3 1936
## 699 11.69525 6.816736 6.815640 2 1958
## 700 12.00762 6.327937 7.468513 4 1988
## 701 11.92437 7.455298 7.454720 4 1976
## 702 12.15214 6.767343 7.396335 3 2004
## 703 12.02754 7.370231 7.369601 3 1971
## 704 11.93819 7.053586 7.326466 3 1955
## 705 12.34583 7.019297 7.591357 4 1978
## 706 12.11176 6.626718 7.383368 3 1995
## 707 12.38839 5.849325 7.726654 3 1890
## 708 11.71994 6.411818 7.184629 3 1953
## 709 12.52453 7.374629 7.406103 2 2004
## 710 12.02455 7.241366 7.358831 3 1958
## 711 11.89136 7.048386 7.047517 3 1961
## 712 11.81303 7.023759 7.591357 4 1928
## 713 11.32055 6.042633 6.562444 2 1940
## 714 11.95761 5.953243 7.265430 3 1999
## 715 11.67844 6.720220 7.374002 3 1910
## 716 11.95118 6.690842 7.344719 3 1976
## 717 10.86857 6.542472 6.541030 2 1941
## 718 11.77529 6.831954 7.182352 3 1929
## 719 12.27373 6.900731 7.630461 3 1999
## 720 12.01370 6.513230 7.231287 3 2000
## 721 12.12811 7.130099 7.272398 2 1959
## 722 12.06681 6.529419 7.352441 3 2005
## 723 11.91839 7.156177 7.390181 3 1976
## 724 13.05301 7.876259 7.875879 2 2001
## 725 12.50540 7.019297 7.607381 3 1996
## 726 11.94730 6.617403 7.401842 3 1946
## 727 11.61954 6.762730 6.761573 3 1972
## 728 11.63071 6.842683 6.891626 2 1954
## 729 12.01370 6.716595 7.635787 4 1956
## 730 12.77987 7.396335 7.813996 4 1998
## 731 12.10625 6.831954 7.380256 3 1997
## 732 12.10071 7.574558 7.699389 3 1970
## 733 12.14950 6.962243 7.520235 3 1992
## 734 11.99535 6.493754 7.185387 3 2003
## 735 12.38003 7.007601 7.662468 4 1991
## 736 11.56172 6.220590 6.911747 2 1930
## 737 11.92504 6.398595 7.090077 2 2004
## 738 11.61729 6.182085 6.894670 2 1973
## 739 11.79056 6.964136 6.963190 3 1962
## 740 11.47210 0.000000 7.036148 4 1947
## 741 11.76368 6.879356 6.878326 3 1969
## 742 12.32386 6.700731 7.696213 4 1993
## 743 11.63514 6.901737 6.954639 2 1922
## 744 11.76718 6.857514 7.110696 3 1959
## 745 11.88103 6.744059 6.742881 1 2004
## 746 12.47801 7.356918 7.356280 3 2008
## 747 11.69107 6.852243 6.851185 2 1973
## 748 11.60368 6.665684 6.664409 2 1924
## 749 11.70355 6.331502 7.113956 2 1980
## 750 12.60149 7.441907 7.448916 3 2007
## 751 10.97678 6.437752 6.704414 2 1910
## 752 11.94146 0.000000 7.111512 2 1951
## 753 12.01733 6.548219 7.313887 3 1993
## 754 11.57119 6.580639 6.740519 2 1920
## 755 12.54687 6.998510 7.816820 4 2005
## 756 11.51293 6.876265 6.875232 2 1923
## 757 11.99226 7.224753 7.201916 3 1967
## 758 12.01370 6.401917 7.314553 3 1923
## 759 12.17045 7.262629 7.261927 3 1998
## 760 11.86005 6.350886 7.198184 3 1950
## 761 11.58989 6.265301 6.995766 3 1972
## 762 12.38422 7.223296 7.872455 4 1918
## 763 12.03112 6.660575 7.384610 4 1964
## 764 12.08391 7.248504 7.198184 2 1997
## 765 11.71178 6.496775 7.188413 3 1920
## 766 12.33929 7.158514 7.682022 3 2002
## 767 12.07254 6.595781 7.477604 3 1937
## 768 11.72804 6.880384 7.383989 4 1938
## 769 12.16003 7.292337 7.299121 3 1999
## 770 11.75587 6.975414 6.974479 2 1977
## 771 11.49272 0.000000 7.332369 4 1945
## 772 11.96081 6.255750 7.198931 2 1983
## 773 12.24047 7.288928 7.288244 3 1998
## 774 11.77913 6.587550 7.299121 3 1976
## 775 11.81303 6.629363 7.292337 3 1906
## 776 11.94665 7.008505 7.729296 5 1960
## 777 12.35449 7.388328 7.387709 3 2005
## 778 11.71994 6.755769 6.770789 3 1971
## 779 12.22096 7.316548 7.315884 3 1996
## 780 12.16003 6.779922 7.492760 3 2005
## 781 11.81303 7.380879 7.380256 4 1958
## 782 12.10625 6.723832 7.413970 3 2004
## 783 12.13216 7.306531 7.305860 3 1968
## 784 11.57119 6.447306 7.171657 3 1970
## 785 11.52288 6.274762 7.013016 3 1920
## 786 12.61154 7.057037 7.711549 3 2000
## 787 11.84223 7.123673 7.397562 3 1958
## 788 12.46844 6.982863 7.942362 4 1995
## 789 11.73126 6.958448 6.957497 3 1966
## 790 11.88449 6.963190 6.962243 3 1955
## 791 11.83138 6.878326 7.443664 3 2004
## 792 11.96718 0.000000 7.294377 2 1959
## 793 12.31043 6.872128 7.712444 4 1997
## 794 12.07254 6.860664 7.406711 3 1999
## 795 12.10293 6.672033 7.289611 3 1998
## 796 11.58989 0.000000 7.026427 2 1949
## 797 11.83138 6.693324 7.259820 3 1951
## 798 11.47210 6.858565 7.216709 4 1920
## 799 12.38839 7.444833 7.444249 3 2004
## 800 11.75194 6.934397 7.433075 3 1924
## 801 11.95118 6.493754 7.206377 3 1966
## 802 11.86710 6.967909 6.961296 2 1978
## 803 11.94471 6.639876 7.393878 2 2003
## 804 12.36521 7.348588 7.347944 3 2003
## 805 12.07539 7.260523 7.259820 3 1981
## 806 11.74006 6.434547 7.217443 3 1910
## 807 12.54076 6.970730 7.661527 4 1996
## 808 12.20607 7.217443 7.641084 3 2003
## 809 11.87583 6.744059 6.742881 1 2003
## 810 11.37366 6.511745 6.733402 3 1930
## 811 12.76359 7.047517 7.840313 4 2005
## 812 12.06681 7.173958 7.427739 3 1970
## 813 12.17561 6.804615 7.448334 2 1940
## log.X2nd.Flr.SF...1. log.Lot.Area. Overall.Cond Overall.Qual .fitted
## 1 0.000000 9.248214 5 8 12.57861
## 2 0.000000 9.577896 7 6 12.31285
## 3 0.000000 9.354960 6 5 11.67848
## 4 0.000000 9.367344 6 6 11.96454
## 5 0.000000 8.897409 5 9 12.49452
## 6 6.470800 7.880426 5 8 12.14892
## 7 6.150603 8.699515 5 6 11.77415
## 8 6.760415 9.194109 8 6 12.41142
## 9 0.000000 9.447071 7 6 12.42189
## 10 6.634633 8.881836 9 7 12.03010
## 11 0.000000 9.115810 7 4 11.24803
## 12 6.767343 8.853665 5 7 12.29013
## 13 0.000000 9.671871 6 8 12.58611
## 14 0.000000 8.307459 6 7 12.21530
## 15 6.580639 7.852439 5 7 11.96911
## 16 0.000000 9.055089 6 5 11.95701
## 17 6.398595 7.560080 5 5 11.68312
## 18 0.000000 8.395252 5 6 11.80737
## 19 0.000000 9.092120 5 5 11.73225
## 20 6.587550 9.344434 7 8 12.11775
## 21 6.335054 9.521495 5 8 12.58689
## 22 6.700731 9.026418 5 7 12.19726
## 23 6.498282 9.252346 5 5 11.87639
## 24 0.000000 9.677653 6 6 12.14816
## 25 6.013715 8.738735 6 6 11.78233
## 26 0.000000 9.693939 5 7 12.18352
## 27 6.804615 8.934323 6 7 11.97471
## 28 6.375025 7.735870 6 6 11.86498
## 29 6.900731 9.336532 5 5 11.95199
## 30 0.000000 9.016149 4 5 12.02659
## 31 0.000000 9.420763 5 4 11.53562
## 32 0.000000 9.559235 6 5 12.00921
## 33 6.628041 9.114270 5 4 11.65649
## 34 0.000000 9.510075 6 5 12.11711
## 35 6.733402 9.044286 5 8 12.36925
## 36 6.760415 7.803027 5 7 12.10299
## 37 6.226537 9.033842 5 4 11.67267
## 38 6.398595 8.075583 5 7 11.94146
## 39 6.555357 9.367344 6 6 12.13178
## 40 7.002156 9.483645 5 8 12.52187
## 41 0.000000 9.218606 5 7 12.18014
## 42 0.000000 9.169518 7 5 11.70840
## 43 6.538140 8.764990 6 5 11.79935
## 44 0.000000 8.346879 5 6 12.07712
## 45 6.690842 9.104980 5 8 12.30806
## 46 0.000000 9.041330 7 5 11.67826
## 47 0.000000 9.727347 5 8 12.52291
## 48 0.000000 9.038959 6 5 11.70306
## 49 0.000000 10.505068 5 5 12.13538
## 50 6.928538 9.120634 8 6 12.02480
## 51 6.008813 8.281471 8 6 11.73632
## 52 6.342121 7.698483 6 6 11.64958
## 53 0.000000 9.137770 5 5 11.84535
## 54 6.961296 9.333266 5 9 12.62943
## 55 6.390241 8.735686 5 5 11.66843
## 56 6.593045 8.080237 5 6 11.96815
## 57 0.000000 9.301095 6 6 11.81098
## 58 6.329721 9.111624 5 6 11.76954
## 59 0.000000 9.126959 6 5 11.74808
## 60 6.892642 9.977342 5 7 12.41640
## 61 0.000000 9.245321 6 5 11.78376
## 62 0.000000 8.895082 5 8 12.76075
## 63 0.000000 9.323133 5 8 12.49131
## 64 0.000000 9.287301 6 4 11.47955
## 65 0.000000 9.074635 5 5 11.62963
## 66 6.800170 8.949365 6 6 12.16770
## 67 0.000000 8.699515 4 4 11.36556
## 68 7.087574 10.089552 7 7 12.42124
## 69 0.000000 10.433616 6 5 12.28594
## 70 0.000000 9.188708 4 3 11.38543
## 71 6.255750 9.190240 5 8 12.43908
## 72 0.000000 9.162725 5 5 11.96265
## 73 0.000000 8.738735 5 4 11.57784
## 74 0.000000 9.245225 5 5 11.85637
## 75 0.000000 8.501673 5 8 12.43561
## 76 0.000000 9.067393 5 5 11.97160
## 77 0.000000 9.503010 5 5 11.80611
## 78 6.401917 9.264829 7 6 11.93157
## 79 6.787845 9.268892 5 8 12.40125
## 80 0.000000 9.379323 5 6 11.77326
## 81 6.336826 8.160518 7 5 11.72402
## 82 6.532334 8.661294 7 6 11.76463
## 83 0.000000 8.699515 7 5 11.60445
## 84 0.000000 8.669056 8 3 11.69709
## 85 6.013715 8.995165 8 6 11.90030
## 86 0.000000 9.077951 6 6 11.92943
## 87 0.000000 9.035749 5 5 11.69827
## 88 6.150603 9.748003 4 4 11.57142
## 89 0.000000 9.116030 5 7 12.42245
## 90 6.928538 9.312446 5 6 12.17116
## 91 0.000000 8.476371 7 4 11.62070
## 92 0.000000 9.282754 5 5 11.81663
## 93 0.000000 8.308446 5 7 11.78954
## 94 0.000000 9.906583 7 7 12.44165
## 95 0.000000 9.294682 5 5 11.77160
## 96 6.786717 9.289152 5 7 12.32454
## 97 6.248043 7.457609 6 6 11.64772
## 98 0.000000 8.914626 6 5 11.74651
## 99 7.340187 9.100860 9 8 12.69795
## 100 0.000000 9.749170 6 4 11.84637
## 101 0.000000 9.053219 5 4 11.86471
## 102 0.000000 9.104980 3 6 11.42423
## 103 0.000000 9.769956 8 7 12.50558
## 104 6.165418 9.050172 4 5 11.68442
## 105 0.000000 9.455480 6 5 11.78658
## 106 0.000000 8.742574 5 8 12.44924
## 107 0.000000 9.082507 6 6 11.97960
## 108 6.642487 9.246094 5 6 12.10454
## 109 7.125283 9.694370 5 8 12.58467
## 110 0.000000 8.881836 7 6 11.77460
## 111 6.782192 9.141740 5 6 12.18001
## 112 0.000000 8.071843 5 7 12.02615
## 113 6.945051 9.074062 5 7 12.28025
## 114 7.115582 8.285009 4 6 12.09034
## 115 0.000000 8.594154 5 2 10.97992
## 116 6.613384 7.744137 5 6 11.84969
## 117 6.694562 9.475086 5 6 12.09477
## 118 7.060476 8.956093 8 6 12.13818
## 119 0.000000 8.882808 7 5 11.68282
## 120 6.782192 9.066239 5 6 12.22375
## 121 0.000000 9.979476 6 6 12.21570
## 122 0.000000 9.218705 5 8 12.46349
## 123 7.151485 9.375177 5 8 12.51905
## 124 0.000000 9.130864 5 6 12.17567
## 125 4.836282 9.214532 8 6 11.64661
## 126 0.000000 9.111624 6 5 11.68294
## 127 6.597146 9.084097 6 5 11.86834
## 128 6.755769 9.177301 5 7 12.37035
## 129 6.659294 9.002701 5 6 12.02955
## 130 6.093570 9.133459 4 5 11.67381
## 131 0.000000 9.227689 5 6 12.03461
## 132 0.000000 8.397283 5 6 11.80394
## 133 6.682109 9.379154 5 7 12.41979
## 134 6.456770 8.988696 5 6 11.91164
## 135 0.000000 8.770594 5 8 12.31204
## 136 0.000000 9.225229 5 5 11.66500
## 137 6.734592 9.025696 5 7 12.20481
## 138 0.000000 8.915969 5 5 11.72526
## 139 6.794587 9.210340 5 6 12.12203
## 140 6.721426 9.428270 5 7 12.31995
## 141 6.720220 9.504948 5 7 12.31654
## 142 6.591674 8.980927 6 6 11.99030
## 143 6.886532 9.565003 5 9 12.78574
## 144 6.590301 9.367344 6 6 12.02393
## 145 7.173958 9.624963 5 8 12.65986
## 146 0.000000 9.171600 7 6 12.10402
## 147 0.000000 8.682708 7 4 11.43365
## 148 6.390241 9.104980 6 5 11.85100
## 149 6.888572 8.865312 8 5 11.88472
## 150 7.050123 9.109636 9 7 12.39629
## 151 0.000000 9.775484 9 7 12.73703
## 152 0.000000 8.879055 5 8 12.36101
## 153 0.000000 9.293946 5 9 12.53096
## 154 0.000000 8.850518 7 5 11.63318
## 155 0.000000 9.384294 5 6 12.01154
## 156 0.000000 9.257415 8 6 11.99166
## 157 6.461468 9.161675 4 6 11.97397
## 158 6.925595 9.366660 5 8 12.51104
## 159 0.000000 9.153770 5 4 11.79373
## 160 6.758095 8.922658 5 7 12.27069
## 161 7.506042 9.819345 9 7 12.54947
## 162 6.293419 9.446598 8 5 11.80405
## 163 0.000000 9.281544 7 6 11.96898
## 164 0.000000 8.881836 8 5 11.80640
## 165 6.224558 7.426549 5 6 11.53134
## 166 0.000000 9.657267 5 4 11.65889
## 167 0.000000 9.579349 5 9 12.58282
## 168 0.000000 9.144201 7 6 12.12626
## 169 0.000000 9.486076 6 6 12.40757
## 170 6.660575 9.482274 6 7 12.12803
## 171 0.000000 8.977146 5 5 11.64540
## 172 6.263398 9.169518 5 6 11.63488
## 173 6.308098 8.738735 5 6 11.77304
## 174 0.000000 9.524786 5 6 12.04697
## 175 0.000000 9.285262 6 7 12.14353
## 176 6.759255 9.221280 5 6 12.17903
## 177 6.637258 10.749120 7 8 12.81294
## 178 6.576470 10.082470 5 6 12.23154
## 179 6.670766 9.311904 5 6 12.07075
## 180 0.000000 9.812742 5 6 12.09891
## 181 6.556778 9.296518 7 6 12.06166
## 182 5.746203 8.847360 7 4 11.48971
## 183 6.805723 9.284427 5 8 12.39555
## 184 5.533389 8.995165 7 5 11.59141
## 185 6.893656 9.153982 5 8 12.55120
## 186 0.000000 9.449357 5 6 11.97040
## 187 0.000000 9.169518 7 4 11.74976
## 188 0.000000 9.190954 5 7 12.31963
## 189 6.647688 9.224933 5 6 12.12240
## 190 0.000000 9.735365 6 5 12.03067
## 191 0.000000 9.143132 7 6 12.06296
## 192 6.614726 9.095827 5 6 12.08719
## 193 0.000000 8.846497 7 5 11.79800
## 194 0.000000 9.168163 5 7 12.15278
## 195 7.007601 9.995611 5 5 12.20090
## 196 0.000000 8.395252 5 6 11.80737
## 197 0.000000 9.246286 7 6 11.88721
## 198 0.000000 8.065265 5 7 12.23725
## 199 0.000000 9.142597 5 8 12.43366
## 200 0.000000 9.103534 5 8 12.44944
## 201 6.734592 9.653487 7 6 11.96433
## 202 6.906755 9.671745 3 7 12.21928
## 203 6.538140 8.192017 5 6 11.85564
## 204 0.000000 9.056490 8 6 11.87567
## 205 6.159095 8.719317 6 5 11.79000
## 206 0.000000 9.338030 5 8 12.53166
## 207 0.000000 9.631679 8 5 11.97354
## 208 6.805723 9.190444 5 7 12.29355
## 209 6.388561 8.855093 5 5 11.83062
## 210 0.000000 9.600895 7 6 12.22711
## 211 0.000000 9.356862 5 9 12.59458
## 212 6.637258 9.086363 5 9 12.57505
## 213 6.902743 8.794825 4 5 11.77119
## 214 0.000000 9.145588 7 5 12.16706
## 215 6.498282 9.228082 5 6 12.13140
## 216 0.000000 9.594241 4 5 11.89002
## 217 6.447306 9.090656 5 6 11.99063
## 218 0.000000 9.310186 5 7 12.04845
## 219 0.000000 8.420242 5 9 12.34236
## 220 0.000000 9.256747 5 8 12.48276
## 221 6.740519 9.336003 5 7 12.23268
## 222 0.000000 10.366278 5 6 12.23998
## 223 0.000000 9.104980 5 6 11.90933
## 224 6.453625 8.577347 8 6 11.91005
## 225 0.000000 9.305651 6 5 11.87517
## 226 0.000000 9.231613 5 4 11.55432
## 227 5.416100 8.855806 4 5 11.60235
## 228 6.781058 9.310186 5 8 12.42355
## 229 6.398595 7.769801 6 5 11.71738
## 230 6.768493 9.006754 5 7 12.24710
## 231 6.725034 9.224243 5 7 12.11622
## 232 0.000000 9.212338 1 1 11.02005
## 233 0.000000 9.916897 6 7 12.34842
## 234 0.000000 8.531096 5 8 12.18707
## 235 0.000000 9.375855 7 4 11.74208
## 236 6.660575 8.939843 9 5 11.86255
## 237 0.000000 9.071078 6 5 11.82119
## 238 6.675823 7.731931 5 6 11.92958
## 239 6.555357 9.641083 5 7 12.23363
## 240 6.625392 9.027979 5 7 12.16656
## 241 7.040536 9.328123 5 8 12.51703
## 242 7.071573 9.247636 5 7 12.48654
## 243 0.000000 9.371609 5 7 12.34013
## 244 0.000000 9.041922 8 5 11.76808
## 245 6.511745 9.277064 7 5 11.74416
## 246 7.195187 9.400878 5 8 12.57882
## 247 6.093570 9.169518 6 5 11.94776
## 248 6.602588 8.853665 8 7 11.99087
## 249 0.000000 8.979165 6 6 11.84302
## 250 0.000000 8.278936 5 7 12.25353
## 251 0.000000 9.510445 7 6 12.14515
## 252 0.000000 9.557964 5 9 12.67546
## 253 0.000000 8.065265 5 7 12.02171
## 254 0.000000 9.348187 5 8 12.49374
## 255 6.545350 9.039908 5 6 12.07556
## 256 6.820016 9.155673 5 6 12.17791
## 257 0.000000 9.017968 5 5 11.82388
## 258 6.549651 9.229358 6 7 12.21827
## 259 7.167809 9.176887 5 6 12.20774
## 260 0.000000 9.143132 8 5 12.01181
## 261 6.371612 9.097172 5 6 11.89395
## 262 6.511745 8.648221 6 7 11.82150
## 263 7.029088 9.224440 5 7 12.36308
## 264 6.613384 7.731931 5 6 11.91032
## 265 6.778785 9.076809 5 6 12.13701
## 266 6.511745 9.900984 7 6 12.15084
## 267 0.000000 9.123693 7 5 11.96973
## 268 0.000000 8.518193 5 8 12.18556
## 269 6.799056 9.602585 5 6 12.17243
## 270 0.000000 11.653982 5 7 12.62615
## 271 0.000000 9.169518 7 5 11.90473
## 272 6.778785 9.136801 5 6 12.13737
## 273 6.436150 7.841493 5 7 11.92936
## 274 6.331502 8.939581 6 4 11.82247
## 275 6.520621 9.258750 6 6 12.09948
## 276 0.000000 8.869398 7 5 11.75976
## 277 6.437752 7.880426 5 8 12.14097
## 278 0.000000 9.192685 5 5 11.77459
## 279 0.000000 9.017484 8 5 11.89059
## 280 6.883463 8.909100 5 7 12.29674
## 281 6.304449 7.568379 7 4 11.50725
## 282 0.000000 9.002701 7 5 11.73649
## 283 6.670766 8.948976 5 6 12.02515
## 284 0.000000 9.457435 5 7 12.31620
## 285 6.880384 9.530538 7 7 12.45874
## 286 0.000000 9.214731 6 5 11.89587
## 287 0.000000 9.083643 5 7 12.22768
## 288 6.552508 9.200290 8 5 11.79258
## 289 6.278521 9.182352 7 5 12.25724
## 290 6.732211 9.393578 5 8 12.43776
## 291 6.629363 9.885578 6 7 12.31949
## 292 0.000000 8.270525 5 8 12.09720
## 293 0.000000 8.959954 5 5 11.47010
## 294 6.773080 9.241451 5 7 12.32021
## 295 6.639876 8.881836 7 7 11.99651
## 296 6.400257 7.744137 6 6 11.82518
## 297 6.639876 8.738735 5 7 12.05098
## 298 7.159292 9.430279 5 7 12.43881
## 299 0.000000 8.749098 7 5 11.66390
## 300 6.601230 9.263028 5 7 12.35394
## 301 0.000000 9.118225 6 6 11.96714
## 302 0.000000 9.164925 5 7 12.09032
## 303 6.605298 9.063347 5 6 12.07718
## 304 6.280396 9.259131 7 5 11.78997
## 305 0.000000 9.298351 5 6 11.97787
## 306 6.650279 9.408453 5 8 12.59729
## 307 7.033506 9.164820 6 5 11.92877
## 308 6.511745 9.405496 8 6 11.93700
## 309 6.411818 9.480978 5 8 12.63603
## 310 0.000000 9.313619 5 8 12.39079
## 311 0.000000 9.423676 5 9 12.65925
## 312 6.606650 8.234300 5 7 12.02923
## 313 6.818924 9.162305 5 6 12.18794
## 314 0.000000 9.185023 5 5 11.70554
## 315 0.000000 9.448727 5 8 12.84324
## 316 7.249926 9.264544 5 9 12.77193
## 317 0.000000 9.016149 7 5 11.66108
## 318 6.514713 8.856946 5 5 11.94029
## 319 6.786717 8.987197 5 6 12.10495
## 320 6.660575 9.412791 5 8 12.53685
## 321 0.000000 9.049232 5 5 11.93842
## 322 0.000000 9.790935 5 6 12.23856
## 323 0.000000 9.339613 8 6 12.08098
## 324 6.378426 8.719317 6 5 11.81284
## 325 0.000000 8.245647 5 7 12.28183
## 326 6.645091 9.233764 5 6 12.12333
## 327 6.790097 9.287301 7 7 12.10697
## 328 6.771936 9.527193 7 6 12.17697
## 329 6.785588 9.203316 5 7 12.28061
## 330 6.519147 9.310186 5 9 12.60299
## 331 6.814543 7.824046 8 7 11.93820
## 332 6.224558 7.533159 6 6 11.58957
## 333 0.000000 9.172327 5 7 12.23832
## 334 6.070738 9.104980 6 4 11.31055
## 335 0.000000 9.160099 5 6 11.90585
## 336 0.000000 8.675564 5 7 12.17685
## 337 6.265301 9.068085 6 5 11.83539
## 338 6.137727 7.375256 5 4 11.36569
## 339 6.406880 8.769507 5 6 11.85490
## 340 6.613384 7.768110 5 6 11.85982
## 341 6.107023 8.738735 4 5 11.60647
## 342 7.031741 9.075665 5 7 12.30672
## 343 0.000000 9.323669 5 6 12.06013
## 344 6.478510 9.104980 9 7 12.05202
## 345 6.469250 9.727347 5 7 12.33494
## 346 0.000000 9.066470 5 5 11.75448
## 347 0.000000 8.988696 5 6 11.80969
## 348 0.000000 9.288782 5 9 12.58040
## 349 6.340359 9.554993 5 5 12.03385
## 350 6.084499 9.002701 5 7 12.24462
## 351 0.000000 9.044876 7 4 11.68059
## 352 0.000000 8.948976 5 5 11.62550
## 353 6.738152 9.002701 6 7 12.28885
## 354 0.000000 9.039315 7 5 11.89314
## 355 0.000000 9.346356 5 6 12.12984
## 356 0.000000 9.270965 5 8 12.46714
## 357 0.000000 9.166493 6 5 11.81639
## 358 0.000000 9.131838 5 5 11.80510
## 359 0.000000 9.278933 7 5 11.89286
## 360 6.224558 7.426549 3 6 11.43248
## 361 6.447306 9.183380 5 7 12.10618
## 362 0.000000 9.185023 6 6 12.02898
## 363 6.609349 8.922658 7 6 11.93779
## 364 0.000000 9.222763 6 6 12.05632
## 365 0.000000 8.881836 5 4 11.37147
## 366 0.000000 9.426741 5 6 12.23649
## 367 6.642487 9.261984 6 6 12.18927
## 368 0.000000 9.001839 5 9 12.57529
## 369 0.000000 9.355566 5 8 12.42126
## 370 7.185387 9.127502 5 6 12.37509
## 371 6.161207 9.008469 6 4 11.74126
## 372 7.153052 9.286375 5 7 12.43639
## 373 0.000000 9.337325 5 7 12.37081
## 374 0.000000 8.789203 5 8 12.39856
## 375 0.000000 9.998889 7 6 12.30341
## 376 0.000000 9.175542 5 8 12.42994
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## 806 6.434547 8.954157 7 4 11.59354
## 807 6.967909 9.304741 5 7 12.35993
## 808 6.580639 9.343647 5 7 12.42648
## 809 0.000000 8.397283 5 6 11.80394
## 810 0.000000 8.386629 7 5 11.46454
## 811 7.228388 9.419628 5 8 12.60322
## 812 0.000000 9.249561 6 7 12.29525
## 813 6.385194 9.425452 6 5 11.98921
## .se.fit .resid .hat .sigma .cooksd
## 1 0.010334407 0.0524036340 0.007905651 0.1162871 1.814172e-04
## 2 0.011060025 0.1459211226 0.009054798 0.1161869 1.614878e-03
## 3 0.009275501 -0.0171393937 0.006368560 0.1163004 1.558495e-05
## 4 0.007545586 -0.0908021019 0.004214562 0.1162576 2.882284e-04
## 5 0.012580869 0.0390513183 0.011716227 0.1162937 1.504596e-04
## 6 0.012814479 0.0571509295 0.012155376 0.1162842 3.346276e-04
## 7 0.011503120 -0.2124347454 0.009794849 0.1160577 3.707853e-03
## 8 0.015504606 -0.1855419280 0.017794590 0.1161142 5.222656e-03
## 9 0.015944314 0.0271324087 0.018818204 0.1162979 1.183532e-04
## 10 0.016516605 -0.0692852774 0.020193336 0.1162757 8.304877e-04
## 11 0.014411072 0.1140696174 0.015373016 0.1162312 1.696991e-03
## 12 0.008050771 0.1020051578 0.004797792 0.1162460 4.145597e-04
## 13 0.013386703 -0.0873686791 0.013265199 0.1162605 8.553589e-04
## 14 0.011527121 0.1896193813 0.009835766 0.1161074 2.966765e-03
## 15 0.012014181 -0.0179318446 0.010684515 0.1163002 2.887082e-05
## 16 0.011719622 -0.0759706772 0.010167021 0.1162707 4.925903e-04
## 17 0.014989138 0.0327469746 0.016631056 0.1162961 1.516887e-04
## 18 0.012013204 0.0491454907 0.010682778 0.1162889 2.168225e-04
## 19 0.009068551 0.0507065982 0.006087547 0.1162881 1.303164e-04
## 20 0.015418103 0.2280828833 0.017596583 0.1160181 7.801139e-03
## 21 0.009610839 0.0891829105 0.006837370 0.1162591 4.534565e-04
## 22 0.008603682 -0.0642993987 0.005479428 0.1162797 1.883846e-04
## 23 0.011212755 -0.1011005387 0.009306602 0.1162467 7.971564e-04
## 24 0.007597907 -0.0039667501 0.004273212 0.1163019 5.577862e-07
## 25 0.008999968 -0.0264600307 0.005995817 0.1162982 3.494432e-05
## 26 0.011463715 -0.0366684354 0.009727859 0.1162947 1.097026e-04
## 27 0.013405113 0.2318622688 0.013301710 0.1160099 6.041195e-03
## 28 0.012185424 0.0433597888 0.010991267 0.1162918 1.737584e-04
## 29 0.009699660 -0.1242583379 0.006964333 0.1162187 8.968606e-04
## 30 0.023322478 -0.0625877860 0.040263903 0.1162801 1.408365e-03
## 31 0.014629389 -0.2150679000 0.015842324 0.1160501 6.222497e-03
## 32 0.008386418 0.0225106973 0.005206183 0.1162992 2.192579e-05
## 33 0.010966746 -0.0666033969 0.008902707 0.1162780 3.306787e-04
## 34 0.010878042 -0.0296831052 0.008759272 0.1162972 6.460295e-05
## 35 0.009040819 -0.0019079980 0.006050371 0.1163019 1.833720e-07
## 36 0.013418921 -0.1518046907 0.013329126 0.1161768 2.595084e-03
## 37 0.010479577 -0.0827866177 0.008129316 0.1162650 4.657879e-04
## 38 0.012138222 0.0097216126 0.010906281 0.1163014 8.665675e-06
## 39 0.007428261 -0.0592361137 0.004084518 0.1162831 1.188483e-04
## 40 0.009465520 0.2789085068 0.006632168 0.1158819 4.300142e-03
## 41 0.008545400 -0.0525707064 0.005405443 0.1162871 1.242083e-04
## 42 0.009248314 0.1046280115 0.006331282 0.1162430 5.773356e-04
## 43 0.008181820 0.1190384942 0.004955259 0.1162257 5.832838e-04
## 44 0.013848188 0.1036382176 0.014195555 0.1162436 1.290431e-03
## 45 0.010724724 -0.0531930426 0.008514101 0.1162867 2.015577e-04
## 46 0.011619984 0.1198428737 0.009994880 0.1162243 1.204623e-03
## 47 0.010079480 0.0425832217 0.007520431 0.1162922 1.138677e-04
## 48 0.008603335 -0.0086501132 0.005478986 0.1163015 3.409101e-06
## 49 0.014111582 0.0194024828 0.014740693 0.1162999 4.701705e-05
## 50 0.012604188 -0.1970659616 0.011759701 0.1160914 3.846080e-03
## 51 0.012473608 -0.0836350089 0.011517300 0.1162641 6.781297e-04
## 52 0.013105858 -0.0100258858 0.012714445 0.1163014 1.078404e-05
## 53 0.007827585 0.1833857955 0.004535468 0.1161209 1.265977e-03
## 54 0.011465270 0.0924561570 0.009730497 0.1162557 6.976280e-04
## 55 0.008747498 0.1809720769 0.005664143 0.1161255 1.543175e-03
## 56 0.012242406 0.1100884862 0.011094304 0.1162363 1.130832e-03
## 57 0.009701249 -0.0749128197 0.006966615 0.1162717 3.260847e-04
## 58 0.012624172 -0.2078276806 0.011797020 0.1160677 4.291516e-03
## 59 0.009475295 0.0291269418 0.006645872 0.1162974 4.699564e-05
## 60 0.010970156 -0.1572617945 0.008908244 0.1161683 1.844738e-03
## 61 0.009252329 -0.0719882820 0.006336780 0.1162740 2.735507e-04
## 62 0.020840711 0.0739353933 0.032150782 0.1162717 1.543138e-03
## 63 0.009448611 0.0332131348 0.006608494 0.1162960 6.075826e-05
## 64 0.013402162 -0.4051290611 0.013295854 0.1154079 1.843542e-02
## 65 0.011753487 0.2479350196 0.010225863 0.1159690 5.277491e-03
## 66 0.008963202 -0.1153657957 0.005946931 0.1162302 6.587973e-04
## 67 0.014358860 0.2289431076 0.015261822 0.1160166 6.784908e-03
## 68 0.012213631 -0.0146769749 0.011042212 0.1163008 2.000312e-05
## 69 0.014014738 -0.1000728181 0.014539064 0.1162475 1.233144e-03
## 70 0.014745586 0.0331881458 0.016094985 0.1162960 1.506171e-04
## 71 0.008855860 0.0177515124 0.005805345 0.1163003 1.522229e-05
## 72 0.008757960 0.0510539659 0.005677700 0.1162879 1.231122e-04
## 73 0.012883154 -0.0353606997 0.012286011 0.1162952 1.295132e-04
## 74 0.007580374 0.0142272412 0.004253513 0.1163009 7.141929e-06
## 75 0.019595683 0.1281399726 0.028424139 0.1162114 4.066559e-03
## 76 0.012042366 -0.2275594342 0.010734706 0.1160214 4.671736e-03
## 77 0.008658263 0.1765090035 0.005549170 0.1161341 1.437868e-03
## 78 0.012767665 -0.0768292190 0.012066725 0.1162700 6.002208e-04
## 79 0.009823957 0.1049258484 0.007143966 0.1162426 6.562295e-04
## 80 0.014408270 -0.0905896260 0.015367038 0.1162573 1.069849e-03
## 81 0.012142726 -0.1157861248 0.010914375 0.1162294 1.230178e-03
## 82 0.010960499 -0.0446856230 0.008892566 0.1162912 1.486775e-04
## 83 0.009957211 0.0824319340 0.007339085 0.1162653 4.162508e-04
## 84 0.018079012 0.0483360296 0.024194458 0.1162891 4.882646e-04
## 85 0.011087713 -0.1097435998 0.009100190 0.1162369 9.180649e-04
## 86 0.007324433 -0.0244603744 0.003971134 0.1162987 1.969794e-05
## 87 0.008123995 0.1110487112 0.004885464 0.1162356 5.003924e-04
## 88 0.025761925 0.2373926277 0.049127324 0.1159842 2.518470e-02
## 89 0.009529803 -0.1355455214 0.006722555 0.1162029 1.029645e-03
## 90 0.008199767 0.0688345753 0.004977021 0.1162765 1.959027e-04
## 91 0.014034907 -0.0133707312 0.014580942 0.1163010 2.207893e-05
## 92 0.008452138 -0.0490651493 0.005288100 0.1162890 1.058218e-04
## 93 0.014108643 0.0085690339 0.014734553 0.1163016 9.166808e-06
## 94 0.016134815 0.0645238854 0.019270565 0.1162792 6.860583e-04
## 95 0.008359022 -0.0355332433 0.005172225 0.1162952 5.427194e-05
## 96 0.008236753 0.0449257229 0.005022022 0.1162911 8.421041e-05
## 97 0.014154877 0.0049711690 0.014831283 0.1163018 3.105979e-06
## 98 0.007643686 -0.0104408067 0.004324862 0.1163014 3.911371e-06
## 99 0.016918312 -0.0870767308 0.021187542 0.1162605 1.379145e-03
## 100 0.010711529 -0.0333357166 0.008493162 0.1162960 7.896262e-05
## 101 0.014082671 -0.0153160645 0.014680356 0.1163007 2.917431e-05
## 102 0.021283048 -0.1857367049 0.033530045 0.1161107 1.018537e-02
## 103 0.013120114 0.2163057656 0.012742121 0.1160479 5.030842e-03
## 104 0.011891782 0.3353224075 0.010467919 0.1156920 9.886663e-03
## 105 0.008716322 0.0592376019 0.005623841 0.1162831 1.641537e-04
## 106 0.014708522 -0.0284599514 0.016014174 0.1162975 1.101842e-04
## 107 0.006848914 0.0033243109 0.003472241 0.1163019 3.178032e-07
## 108 0.008791883 -0.0728210957 0.005721769 0.1162734 2.524369e-04
## 109 0.010065784 -0.0896647460 0.007500008 0.1162586 5.034637e-04
## 110 0.010887914 -0.0187298239 0.008775176 0.1163001 2.576932e-05
## 111 0.008961815 0.0495304782 0.005945090 0.1162887 1.213967e-04
## 112 0.011232465 -0.0432196826 0.009339350 0.1162919 1.462022e-04
## 113 0.008899821 -0.0892911454 0.005863123 0.1162590 3.890249e-04
## 114 0.017250995 -0.1626617907 0.022029002 0.1161570 5.012310e-03
## 115 0.015197325 0.0053680428 0.017096247 0.1163018 4.194061e-06
## 116 0.012209370 0.0416737592 0.011034508 0.1162926 1.611536e-04
## 117 0.010139570 0.0467637993 0.007610366 0.1162902 1.389904e-04
## 118 0.013550969 0.0678945269 0.013592746 0.1162769 5.296491e-04
## 119 0.009307286 -0.0171711533 0.006412283 0.1163004 1.575154e-05
## 120 0.009666437 0.0546403675 0.006916706 0.1162859 1.722183e-04
## 121 0.008984738 0.0626949610 0.005975542 0.1162808 1.955115e-04
## 122 0.009487214 0.1711151414 0.006662602 0.1161440 1.626115e-03
## 123 0.009560307 -0.0128697303 0.006765660 0.1163011 9.342640e-06
## 124 0.008114149 0.1119862635 0.004873629 0.1162345 5.076326e-04
## 125 0.016352174 -0.0521013466 0.019793268 0.1162871 4.599430e-04
## 126 0.025613870 0.0123029051 0.048564274 0.1163011 6.678783e-05
## 127 0.009397389 -0.0118200503 0.006537036 0.1163012 7.610973e-06
## 128 0.008554958 0.0707900791 0.005417541 0.1162750 2.257301e-04
## 129 0.008300193 0.0372579477 0.005099680 0.1162945 5.882279e-05
## 130 0.011863032 -0.0655783663 0.010417366 0.1162787 3.762695e-04
## 131 0.007570434 0.0688740476 0.004242366 0.1162764 1.669306e-04
## 132 0.011949353 0.0454557937 0.010569519 0.1162908 1.834793e-04
## 133 0.008372556 0.0573755325 0.005188988 0.1162842 1.419642e-04
## 134 0.010596774 -0.1518577618 0.008312159 0.1161774 1.603104e-03
## 135 0.009953487 -0.0935420560 0.007333596 0.1162547 5.356094e-04
## 136 0.009193715 -0.0166701159 0.006256747 0.1163005 1.448110e-05
## 137 0.007812268 0.0012583841 0.004517736 0.1163019 5.937507e-08
## 138 0.007924239 0.0027722306 0.004648166 0.1163019 2.965590e-07
## 139 0.008527016 -0.0443594914 0.005382210 0.1162914 8.805322e-05
## 140 0.008946492 0.0323846326 0.005924778 0.1162963 5.171726e-05
## 141 0.009217262 -0.0288908289 0.006288838 0.1162975 4.372140e-05
## 142 0.007299294 -0.0105029527 0.003943921 0.1163014 3.606678e-06
## 143 0.011514003 0.2575809314 0.009813393 0.1159427 5.461809e-03
## 144 0.008678168 -0.0792238953 0.005574714 0.1162682 2.910145e-04
## 145 0.010181058 0.2468284569 0.007672772 0.1159728 3.904424e-03
## 146 0.008720106 0.0507566426 0.005628725 0.1162881 1.206209e-04
## 147 0.010170649 -0.0773824862 0.007657092 0.1162696 3.829567e-04
## 148 0.007716543 -0.0016027971 0.004407700 0.1163019 9.395720e-08
## 149 0.015619205 0.0982053358 0.018058611 0.1162494 1.485619e-03
## 150 0.015035116 0.0968392578 0.016733241 0.1162509 1.334948e-03
## 151 0.018854161 -0.0767058593 0.026313640 0.1162696 1.343148e-03
## 152 0.010251229 -0.0550924494 0.007778904 0.1162856 1.972466e-04
## 153 0.012676992 0.0805781317 0.011895945 0.1162668 6.506568e-04
## 154 0.009500776 -0.0906975310 0.006681664 0.1162576 4.581658e-04
## 155 0.008165930 0.0082040972 0.004936030 0.1163016 2.759697e-06
## 156 0.011332069 -0.1071745198 0.009505718 0.1162398 9.153519e-04
## 157 0.010836950 -0.1469685838 0.008693219 0.1161852 1.571583e-03
## 158 0.009372429 -0.0290460794 0.006502357 0.1162974 4.571262e-05
## 159 0.010878718 0.0556634422 0.008760359 0.1162852 2.272106e-04
## 160 0.007814720 -0.0399204429 0.004520572 0.1162934 5.979205e-05
## 161 0.024221739 0.0452626918 0.043428731 0.1162905 7.997371e-04
## 162 0.012231909 0.1400072371 0.011075287 0.1161958 1.825801e-03
## 163 0.009203375 0.0045307065 0.006269901 0.1163018 1.071963e-06
## 164 0.011022746 -0.0311131903 0.008993860 0.1162967 7.291326e-05
## 165 0.014562571 -0.0592336199 0.015697937 0.1162829 4.675697e-04
## 166 0.026329360 0.0528888976 0.051315327 0.1162862 1.311766e-03
## 167 0.012934918 0.0822617834 0.012384939 0.1162653 7.067058e-04
## 168 0.008580562 0.0672303808 0.005450019 0.1162776 2.048330e-04
## 169 0.012144733 -0.1527061760 0.010917983 0.1161757 2.140499e-03
## 170 0.010451930 0.1710762045 0.008086479 0.1161439 1.978404e-03
## 171 0.009740747 0.1527082851 0.007023458 0.1161761 1.366225e-03
## 172 0.015623353 -0.3576795042 0.018068204 0.1156023 1.971807e-02
## 173 0.009781687 -0.0290020193 0.007082621 0.1162974 4.969907e-05
## 174 0.010100980 -0.0957915903 0.007552549 0.1162524 5.787050e-04
## 175 0.012367094 -0.1481799594 0.011321444 0.1161830 2.091677e-03
## 176 0.009647083 -0.0348366772 0.006889038 0.1162954 6.972049e-05
## 177 0.016673204 0.0912682619 0.020578069 0.1162564 1.469699e-03
## 178 0.011721261 0.1077521419 0.010169864 0.1162391 9.912190e-04
## 179 0.011182305 -0.0271920408 0.009256124 0.1162980 5.734743e-05
## 180 0.009188737 0.0017990610 0.006249973 0.1163019 1.684766e-07
## 181 0.010171690 -0.0678543830 0.007658658 0.1162771 2.945170e-04
## 182 0.012069222 0.0019913401 0.010782638 0.1163019 3.593821e-07
## 183 0.010080401 -0.1312054923 0.007521806 0.1162091 1.081205e-03
## 184 0.012068652 0.1277187705 0.010781620 0.1162136 1.478200e-03
## 185 0.009470004 0.2087608582 0.006638452 0.1160668 2.411428e-03
## 186 0.008071939 0.0848514492 0.004823055 0.1162632 2.883793e-04
## 187 0.011189976 0.0100265790 0.009268828 0.1163014 7.808052e-06
## 188 0.007888666 0.0130769806 0.004606527 0.1163010 6.539176e-06
## 189 0.008730882 -0.1394680438 0.005642645 0.1161972 9.130008e-04
## 190 0.010808672 0.0128850021 0.008647910 0.1163011 1.201568e-05
## 191 0.008168006 -0.0926104426 0.004938540 0.1162558 3.518380e-04
## 192 0.009669935 -0.0566627658 0.006921713 0.1162846 1.853387e-04
## 193 0.010453412 0.0142868725 0.008088772 0.1163009 1.380179e-05
## 194 0.008753703 0.0020027312 0.005672182 0.1163019 1.892606e-07
## 195 0.015038577 -0.0349234007 0.016740946 0.1162953 1.737005e-04
## 196 0.012013204 0.1063433049 0.010682778 0.1162407 1.015213e-03
## 197 0.009888482 -0.0966540152 0.007238119 0.1162516 5.642861e-04
## 198 0.015721465 -0.1309992036 0.018295848 0.1162083 2.679493e-03
## 199 0.009593726 -0.0104668577 0.006813042 0.1163014 6.223514e-06
## 200 0.009851893 -0.1412583062 0.007184654 0.1161943 1.196247e-03
## 201 0.011883921 0.1195705207 0.010454085 0.1162246 1.255412e-03
## 202 0.021920754 -0.0283259907 0.035569477 0.1162975 2.523654e-04
## 203 0.009946603 -0.0279004557 0.007323455 0.1162978 4.758248e-05
## 204 0.012701702 0.0259168684 0.011942365 0.1162983 6.757948e-05
## 205 0.008388004 0.0700517535 0.005208153 0.1162755 2.124131e-04
## 206 0.009609248 0.0108852890 0.006835106 0.1163013 6.753151e-06
## 207 0.014187599 -0.0551449669 0.014899933 0.1162854 3.840249e-04
## 208 0.008521903 0.0378313215 0.005375758 0.1162942 6.396591e-05
## 209 0.010515641 0.1075714375 0.008185364 0.1162395 7.919448e-04
## 210 0.009534004 0.0922954091 0.006728483 0.1162560 4.778211e-04
## 211 0.012305801 0.1992751495 0.011209500 0.1160867 3.744622e-03
## 212 0.011955785 0.1906366129 0.010580902 0.1161051 3.230716e-03
## 213 0.020269832 -0.1859398345 0.030413526 0.1161109 9.199464e-03
## 214 0.013029116 0.1019864267 0.012565980 0.1162455 1.102526e-03
## 215 0.008777470 0.0207409951 0.005703024 0.1162996 2.041062e-05
## 216 0.012047605 0.0611603862 0.010744048 0.1162817 3.377653e-04
## 217 0.009313879 0.0016270232 0.006421370 0.1163019 1.416233e-07
## 218 0.010155231 -0.0780962218 0.007633894 0.1162690 3.888538e-04
## 219 0.015573947 0.2178814440 0.017954111 0.1160429 7.268835e-03
## 220 0.009468233 -0.0723140660 0.006635970 0.1162738 2.892392e-04
## 221 0.008278537 -0.0674266418 0.005073103 0.1162775 1.916366e-04
## 222 0.012122206 0.0384148461 0.010877517 0.1162940 1.349435e-04
## 223 0.008525376 -0.0670975488 0.005380140 0.1162777 2.013801e-04
## 224 0.015115884 -0.2401229414 0.016913503 0.1159875 8.299299e-03
## 225 0.007425116 0.0695399275 0.004081060 0.1162760 1.636505e-04
## 226 0.009911809 0.0629612763 0.007272309 0.1162806 2.405931e-04
## 227 0.010682030 0.0058873154 0.008446448 0.1163018 2.449065e-06
## 228 0.009287221 0.0250779815 0.006384664 0.1162986 3.345112e-05
## 229 0.012741445 0.0186917732 0.012017215 0.1163001 3.537774e-05
## 230 0.007923436 -0.0410239710 0.004647223 0.1162929 6.492902e-05
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## 313 0.009155187 0.0716770988 0.006204416 0.1162743 2.654554e-04
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## 317 0.009799137 0.0749875804 0.007107914 0.1162716 3.334577e-04
## 318 0.011788864 0.1120512463 0.010287513 0.1162340 1.084550e-03
## 319 0.008287023 0.0392479950 0.005083509 0.1162937 6.506528e-05
## 320 0.009400106 0.0912147981 0.006540816 0.1162571 4.535096e-04
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## 325 0.013004335 0.1473887409 0.012518226 0.1161841 2.293703e-03
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## 329 0.008295472 0.0298242718 0.005093880 0.1162972 3.764854e-05
## 330 0.011277496 0.0509693347 0.009414383 0.1162879 2.049981e-04
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## 338 0.016145068 0.0529268775 0.019295066 0.1162867 4.622172e-04
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## 342 0.008785047 -0.0076153882 0.005712874 0.1163016 2.756380e-06
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## 346 0.008475438 0.1869708711 0.005317295 0.1161136 1.545231e-03
## 347 0.008887873 0.0609081237 0.005847392 0.1162820 1.805222e-04
## 348 0.012337652 0.1324880839 0.011267603 0.1162069 1.663993e-03
## 349 0.019665090 -0.1632458367 0.028625847 0.1161550 6.649569e-03
## 350 0.010638426 0.1479297748 0.008377631 0.1161837 1.533429e-03
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## 352 0.010286232 0.0052094510 0.007832116 0.1163018 1.775892e-06
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## 357 0.007158849 -0.0488233353 0.003793612 0.1162891 7.494336e-05
## 358 0.010095732 0.0793893202 0.007544702 0.1162679 3.970712e-04
## 359 0.009111018 0.0174964123 0.006144694 0.1163003 1.566304e-05
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## 418 0.009857317 0.0336269783 0.007192567 0.1162959 6.786620e-05
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## 428 0.008844752 -0.0630470188 0.005790790 0.1162805 1.915294e-04
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## 430 0.011079575 0.0930804730 0.009086836 0.1162551 6.594512e-04
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## 446 0.008426536 -0.0407085106 0.005256112 0.1162930 7.239966e-05
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## 448 0.015419788 0.0225998128 0.017600431 0.1162992 7.660915e-05
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## 450 0.008869452 -0.0408412221 0.005823178 0.1162930 8.082659e-05
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## 452 0.007325372 -0.0679524481 0.003972152 0.1162771 1.520607e-04
## 453 0.018785257 -0.0174620522 0.026121659 0.1163003 6.907261e-05
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## 455 0.010473770 -0.1342767868 0.008120310 0.1162046 1.223997e-03
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## 459 0.009737837 0.0675857142 0.007019263 0.1162773 2.674507e-04
## 460 0.008777287 -0.0261995015 0.005702787 0.1162983 3.256602e-05
## 461 0.014657780 0.0883651718 0.015903873 0.1162595 1.054664e-03
## 462 0.012006666 -0.0880073546 0.010671153 0.1162600 6.945315e-04
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## 464 0.016545768 -0.0624112823 0.020264708 0.1162807 6.763524e-04
## 465 0.011509520 -0.1045370973 0.009805752 0.1162429 8.988868e-04
## 466 0.007922299 0.0632854738 0.004645890 0.1162804 1.544706e-04
## 467 0.014105778 0.1493943346 0.014728571 0.1161806 2.785102e-03
## 468 0.009442624 0.0036629930 0.006600120 0.1163019 7.380739e-07
## 469 0.009544118 0.1506280837 0.006742766 0.1161796 1.275412e-03
## 470 0.009533249 0.1582406360 0.006727418 0.1161669 1.404338e-03
## 471 0.011229815 0.0102704478 0.009334943 0.1163014 8.252029e-06
## 472 0.008971887 0.0186427480 0.005958460 0.1163001 1.723728e-05
## 473 0.018257674 -0.0919239581 0.024675013 0.1162556 1.802769e-03
## 474 0.012056848 -0.0571803073 0.010760540 0.1162843 2.956978e-04
## 475 0.010333780 0.2254841964 0.007904691 0.1160273 3.358414e-03
## 476 0.008334906 -0.0685847128 0.005142425 0.1162766 2.010133e-04
## 477 0.013980321 0.1673557112 0.014467743 0.1161497 3.431343e-03
## 478 0.019028925 0.0094209093 0.026803717 0.1163015 2.065874e-05
## 479 0.013361899 -0.1320141293 0.013216087 0.1162074 1.945466e-03
## 480 0.014151351 0.2695367429 0.014823894 0.1159065 9.126295e-03
## 481 0.012960226 0.2450918175 0.012433450 0.1159758 6.298549e-03
## 482 0.009099833 0.0616221465 0.006129617 0.1162815 1.938079e-04
## 483 0.011064931 0.0996082375 0.009062832 0.1162483 7.531581e-04
## 484 0.013510841 0.1115474117 0.013512362 0.1162344 1.420990e-03
## 485 0.008896825 0.0472916842 0.005859177 0.1162899 1.090522e-04
## 486 0.013634889 0.0755402773 0.013761624 0.1162710 6.640290e-04
## 487 0.012655935 -0.1049414435 0.011856459 0.1162423 1.099849e-03
## 488 0.013943400 0.1199748100 0.014391427 0.1162237 1.753877e-03
## 489 0.008960492 0.0425990252 0.005943336 0.1162922 8.977001e-05
## 490 0.007005919 -0.0767419495 0.003633262 0.1162703 1.772752e-04
## 491 0.010480946 -0.3741462496 0.008131439 0.1155439 9.516252e-03
## 492 0.010984123 -0.1063279544 0.008930942 0.1162409 8.454897e-04
## 493 0.009427586 -0.0778591958 0.006579115 0.1162693 3.323875e-04
## 494 0.008544716 -0.0503770882 0.005404577 0.1162883 1.140404e-04
## 495 0.017960720 0.0687456912 0.023878881 0.1162760 9.741403e-04
## 496 0.010399310 0.0377051778 0.008005261 0.1162943 9.512239e-05
## 497 0.008122986 -0.1251844846 0.004884250 0.1162176 6.357344e-04
## 498 0.013513580 0.2629639187 0.013517842 0.1159261 7.900329e-03
## 499 0.006669012 0.0084089064 0.003292225 0.1163016 1.927334e-06
## 500 0.009955598 0.0658963595 0.007336707 0.1162785 2.659158e-04
## 501 0.007582068 0.0165035713 0.004255414 0.1163005 9.614480e-06
## 502 0.011949353 -0.0058375007 0.010569519 0.1163018 3.025956e-06
## 503 0.010904541 -0.0881343719 0.008801998 0.1162600 5.723676e-04
## 504 0.012348248 -0.3102195288 0.011286965 0.1157797 9.139005e-03
## 505 0.009567330 0.0552487693 0.006775604 0.1162855 1.724338e-04
## 506 0.008900015 0.0576931184 0.005863378 0.1162840 1.624156e-04
## 507 0.010066982 0.0731498307 0.007501793 0.1162731 3.351631e-04
## 508 0.009889279 -0.0217789338 0.007239286 0.1162994 2.865522e-05
## 509 0.011021243 -0.0979379707 0.008991407 0.1162501 7.222690e-04
## 510 0.013999372 -0.0167804741 0.014507201 0.1163004 3.459467e-05
## 511 0.009191070 0.1209924091 0.006253147 0.1162231 7.624078e-04
## 512 0.015791445 -0.2104661771 0.018459087 0.1160601 6.980428e-03
## 513 0.010412692 0.0527528060 0.008025878 0.1162869 1.866840e-04
## 514 0.012317344 0.0855171891 0.011230539 0.1162623 6.909416e-04
## 515 0.011576762 -0.0375059032 0.009920663 0.1162943 1.170911e-04
## 516 0.008602410 0.0116472766 0.005477807 0.1163012 6.179461e-06
## 517 0.007134263 -0.0163559520 0.003767599 0.1163005 8.352549e-06
## 518 0.014234445 0.0587874247 0.014998491 0.1162832 4.394067e-04
## 519 0.009575485 -0.0938967217 0.006787160 0.1162544 4.989170e-04
## 520 0.012873551 0.0216701553 0.012267702 0.1162994 4.856604e-05
## 521 0.015499120 0.0759487520 0.017781998 0.1162705 8.744401e-04
## 522 0.011925827 0.0134268752 0.010527943 0.1163010 1.594448e-05
## 523 0.007920115 0.0760656154 0.004643329 0.1162708 2.230349e-04
## 524 0.007404682 0.0004964971 0.004058628 0.1163020 8.296009e-09
## 525 0.008132698 -0.1829363728 0.004895937 0.1161218 1.360890e-03
## 526 0.012840943 0.0984442192 0.012205633 0.1162494 9.970838e-04
## 527 0.013509364 0.0490309264 0.013509407 0.1162889 2.744825e-04
## 528 0.013329086 0.0752802391 0.013151257 0.1162712 6.294367e-04
## 529 0.009095987 0.1477740732 0.006124437 0.1161843 1.113583e-03
## 530 0.009488906 -0.0056273079 0.006664979 0.1163018 1.759271e-06
## 531 0.010675857 -0.5534560138 0.008436688 0.1146361 2.161829e-02
## 532 0.009219954 0.0894378409 0.006292511 0.1162588 4.192504e-04
## 533 0.007728048 0.1318557262 0.004420853 0.1162084 6.377882e-04
## 534 0.026641348 0.1130103012 0.052538646 0.1162298 6.147746e-03
## 535 0.013360725 -0.0868258569 0.013213765 0.1162610 8.414001e-04
## 536 0.011460020 -0.0124857427 0.009721588 0.1163011 1.271087e-05
## 537 0.014099365 0.0266294535 0.014715181 0.1162981 8.840779e-05
## 538 0.016495180 -0.1460118358 0.020140980 0.1161854 3.678354e-03
## 539 0.009762081 -0.0821781881 0.007054257 0.1162655 3.974087e-04
## 540 0.008994249 0.0176568127 0.005988201 0.1163003 1.554039e-05
## 541 0.015105505 0.0515424703 0.016890286 0.1162875 3.818453e-04
## 542 0.026207750 0.1392446692 0.050842390 0.1161925 8.999750e-03
## 543 0.012739229 0.0884047603 0.012013035 0.1162596 7.910895e-04
## 544 0.008952991 0.0880836200 0.005933389 0.1162602 3.831653e-04
## 545 0.010507983 0.0621842041 0.008173447 0.1162811 2.642518e-04
## 546 0.009233863 -0.0251237295 0.006311511 0.1162986 3.318371e-05
## 547 0.011987864 -0.3156019705 0.010637758 0.1157617 8.903132e-03
## 548 0.020048598 0.2195260872 0.029753257 0.1160357 1.252756e-02
## 549 0.008654989 -0.0684894472 0.005544974 0.1162767 2.163219e-04
## 550 0.012675002 -0.0689149825 0.011892210 0.1162762 4.757789e-04
## 551 0.008783634 -0.0836472928 0.005711037 0.1162643 3.324432e-04
## 552 0.027180513 0.1541789285 0.054686710 0.1161672 1.196477e-02
## 553 0.009704905 0.0168862340 0.006971866 0.1163004 1.658118e-05
## 554 0.009840512 0.0432526799 0.007168065 0.1162919 1.118924e-04
## 555 0.014056146 -0.0465249303 0.014625105 0.1162902 2.681584e-04
## 556 0.008012261 -0.0531913034 0.004752003 0.1162867 1.116399e-04
## 557 0.007415291 -0.0978819124 0.004070267 0.1162504 3.233660e-04
## 558 0.007922136 -0.0051095857 0.004645699 0.1163018 1.006911e-06
## 559 0.009981124 -0.0836048183 0.007374378 0.1162642 4.302700e-04
## 560 0.009282095 -0.0394713921 0.006377618 0.1162936 8.277604e-05
## 561 0.010598158 0.1481436692 0.008314330 0.1161834 1.526052e-03
## 562 0.012798302 0.1017577980 0.012124706 0.1162458 1.058099e-03
## 563 0.009202672 0.0514026489 0.006268944 0.1162877 1.379595e-04
## 564 0.009421631 0.1818668245 0.006570806 0.1161236 1.811239e-03
## 565 0.010327837 -0.0809126062 0.007895602 0.1162666 4.319434e-04
## 566 0.009742686 -0.0322563127 0.007026255 0.1162963 6.098202e-05
## 567 0.014406900 0.1218073775 0.015364117 0.1162212 1.933871e-03
## 568 0.017979671 0.0380908139 0.023929299 0.1162940 2.997312e-04
## 569 0.014769423 -0.0685048551 0.016147064 0.1162764 6.438725e-04
## 570 0.015838704 0.0281340516 0.018569738 0.1162976 1.255092e-04
## 571 0.007302636 -0.0180225939 0.003947534 0.1163002 1.062967e-05
## 572 0.011617109 -0.0496346072 0.009989933 0.1162886 2.065269e-04
## 573 0.025423982 0.1246668245 0.047846880 0.1162145 6.746303e-03
## 574 0.011663033 0.3848217496 0.010069074 0.1154983 1.251477e-02
## 575 0.008907470 -0.0333902049 0.005873206 0.1162959 5.449465e-05
## 576 0.010449111 -0.0251218315 0.008082118 0.1162985 4.263834e-05
## 577 0.010760745 -0.0139588177 0.008571388 0.1163009 1.397493e-05
## 578 0.013583521 0.0414662245 0.013658130 0.1162926 1.985406e-04
## 579 0.012917614 0.2110967650 0.012351825 0.1160601 4.641023e-03
## 580 0.016265466 -0.1255274062 0.019583915 0.1162159 2.640461e-03
## 581 0.009342718 0.0231349254 0.006461197 0.1162991 2.881400e-05
## 582 0.011056925 0.1577195039 0.009049722 0.1161675 1.885499e-03
## 583 0.009426748 0.0671927906 0.006577946 0.1162776 2.475096e-04
## 584 0.012098486 -0.0125453940 0.010834990 0.1163011 1.433454e-05
## 585 0.008899910 -0.0085834934 0.005863240 0.1163016 3.594989e-06
## 586 0.008529575 -0.0812763491 0.005385442 0.1162664 2.957768e-04
## 587 0.012256470 0.0503013091 0.011119809 0.1162883 2.366424e-04
## 588 0.012542365 0.0245425857 0.011644622 0.1162987 5.905596e-05
## 589 0.009011012 -0.0234500394 0.006010542 0.1162990 2.751448e-05
## 590 0.010151245 -0.1687139031 0.007627902 0.1161483 1.813350e-03
## 591 0.012240654 -0.0549786053 0.011091129 0.1162856 2.819516e-04
## 592 0.008451428 0.0658189436 0.005287212 0.1162786 1.903957e-04
## 593 0.014253310 0.1367754544 0.015038272 0.1162002 2.385061e-03
## 594 0.010147711 0.0139179163 0.007622592 0.1163009 1.233165e-05
## 595 0.009461054 -0.1011041241 0.006625911 0.1162468 5.645230e-04
## 596 0.008533968 -0.1861384394 0.005390989 0.1161153 1.552958e-03
## 597 0.013156765 -0.0972127421 0.012813409 0.1162507 1.021966e-03
## 598 0.008995673 -0.0028490511 0.005990097 0.1163019 4.047407e-07
## 599 0.009090330 0.0315002691 0.006116822 0.1162966 5.053679e-05
## 600 0.009102360 -0.0545937774 0.006133021 0.1162859 1.522048e-04
## 601 0.013381333 0.1886987589 0.013254558 0.1161086 3.986732e-03
## 602 0.012013837 -0.0360273639 0.010683903 0.1162949 1.165330e-04
## 603 0.018269346 -0.0744359182 0.024706572 0.1162715 1.183671e-03
## 604 0.009605415 -0.1782617596 0.006829655 0.1161305 1.809638e-03
## 605 0.007504549 -0.0573836542 0.004168844 0.1162842 1.138530e-04
## 606 0.009773129 -0.1185329898 0.007070233 0.1162262 8.287034e-04
## 607 0.010129878 -0.0044614710 0.007595825 0.1163018 1.262635e-06
## 608 0.010006788 -0.2043112308 0.007412349 0.1160766 2.583013e-03
## 609 0.014915878 -0.1188573637 0.016468883 0.1162250 1.978172e-03
## 610 0.015639647 0.1440022051 0.018105911 0.1161888 3.202974e-03
## 611 0.014719813 0.0584725956 0.016038772 0.1162833 4.658476e-04
## 612 0.012857888 0.2349422549 0.012237868 0.1160024 5.694391e-03
## 613 0.009555400 0.0501402624 0.006758717 0.1162884 1.416615e-04
## 614 0.007981972 -0.0386137720 0.004716142 0.1162939 5.838502e-05
## 615 0.009766276 0.0458414583 0.007060322 0.1162906 1.237712e-04
## 616 0.009588006 0.0846572131 0.006804921 0.1162633 4.066361e-04
## 617 0.024573118 0.0397570491 0.044697891 0.1162931 6.367337e-04
## 618 0.014235604 -0.1620606736 0.015000933 0.1161591 3.339842e-03
## 619 0.008249631 0.1264846224 0.005037738 0.1162158 6.696098e-04
## 620 0.011979588 -0.1064795654 0.010623075 0.1162406 1.012006e-03
## 621 0.011062604 0.0324018091 0.009059021 0.1162963 7.966145e-05
## 622 0.014736328 -0.0689394376 0.016074780 0.1162761 6.490532e-04
## 623 0.012996868 0.0012843853 0.012503854 0.1163019 1.739753e-07
## 624 0.022412622 -0.0598223843 0.037183633 0.1162821 1.180637e-03
## 625 0.020781179 -0.1493290747 0.031967365 0.1161786 6.256617e-03
## 626 0.012389866 0.1813203128 0.011363176 0.1161238 3.143714e-03
## 627 0.013888655 0.0420643920 0.014278641 0.1162923 2.138611e-04
## 628 0.009748302 0.0319154756 0.007034358 0.1162965 5.976991e-05
## 629 0.008506419 0.0072941772 0.005356241 0.1163017 2.369199e-06
## 630 0.014851388 0.1684855919 0.016326781 0.1161473 3.939566e-03
## 631 0.008628044 -0.1052956208 0.005510502 0.1162422 5.080839e-04
## 632 0.027349198 -0.0650278667 0.055367600 0.1162780 2.158008e-03
## 633 0.012778726 0.0156386615 0.012087643 0.1163006 2.491311e-05
## 634 0.011852861 0.0074647974 0.010399511 0.1163017 4.866908e-06
## 635 0.013396779 -0.0978991655 0.013285176 0.1162499 1.075638e-03
## 636 0.009919977 -0.1085226571 0.007284300 0.1162384 7.159833e-04
## 637 0.008882468 0.0742446807 0.005840281 0.1162723 2.679021e-04
## 638 0.007450932 0.0318554061 0.004109488 0.1162965 3.458238e-05
## 639 0.014327210 0.1586613510 0.015194616 0.1161650 3.243808e-03
## 640 0.008290096 0.1009130542 0.005087279 0.1162471 4.304615e-04
## 641 0.008427835 -0.0560791691 0.005257734 0.1162850 1.374373e-04
## 642 0.011137742 -0.0452529262 0.009182497 0.1162909 1.575400e-04
## 643 0.010539387 0.0500609893 0.008222374 0.1162884 1.723025e-04
## 644 0.010153948 0.1330497342 0.007631965 0.1162064 1.128347e-03
## 645 0.011851043 0.1483171013 0.010396320 0.1161829 1.920718e-03
## 646 0.010177491 0.1292485433 0.007667396 0.1162118 1.069815e-03
## 647 0.009970616 0.0939490148 0.007358859 0.1162543 5.421686e-04
## 648 0.007495020 -0.1258248602 0.004158264 0.1162168 5.459946e-04
## 649 0.012883996 0.0009761926 0.012287617 0.1163019 9.871921e-08
## 650 0.008092152 0.0430816182 0.004847241 0.1162920 7.471763e-05
## 651 0.012399731 -0.0913988015 0.011381277 0.1162567 8.000891e-04
## 652 0.009523042 0.1670956146 0.006713019 0.1161514 1.562509e-03
## 653 0.012427878 0.1449698955 0.011433006 0.1161881 2.022218e-03
## 654 0.013648436 0.1681511293 0.013788984 0.1161484 3.296979e-03
## 655 0.008725241 -0.0587991131 0.005635357 0.1162833 1.620674e-04
## 656 0.009579351 0.0167309540 0.006792642 0.1163004 1.585347e-05
## 657 0.015280956 -0.0676574484 0.017284927 0.1162770 6.738567e-04
## 658 0.008999877 -0.0749580921 0.005995696 0.1162717 2.804298e-04
## 659 0.009354229 -0.0977719317 0.006477129 0.1162504 5.159162e-04
## 660 0.009095056 0.0453897159 0.006123183 0.1162909 1.050391e-04
## 661 0.009947593 0.0214463424 0.007324913 0.1162995 2.812022e-05
## 662 0.008614213 0.0329378765 0.005492850 0.1162961 4.955610e-05
## 663 0.010697000 0.0179417830 0.008470138 0.1163002 2.281046e-05
## 664 0.012457914 -0.0345395727 0.011488337 0.1162955 1.153590e-04
## 665 0.018555640 -0.0860538435 0.025486981 0.1162613 1.634585e-03
## 666 0.008924150 -0.0581319652 0.005895222 0.1162838 1.658020e-04
## 667 0.009758358 -0.0094785496 0.007048878 0.1163015 5.282895e-06
## 668 0.010694109 0.0946469248 0.008465560 0.1162536 6.344203e-04
## 669 0.022337274 -0.1188400971 0.036934042 0.1162234 4.625565e-03
## 670 0.009586180 -0.0071070427 0.006802329 0.1163017 2.864759e-06
## 671 0.013863218 -0.1560888614 0.014226386 0.1161696 2.933648e-03
## 672 0.010968647 0.1946416252 0.008905793 0.1160971 2.825128e-03
## 673 0.012514748 -0.3061456235 0.011593397 0.1157932 9.147861e-03
## 674 0.015351081 0.1233706222 0.017443934 0.1162190 2.261920e-03
## 675 0.025471136 -0.0137484020 0.048024532 0.1163009 8.238346e-05
## 676 0.009167514 -0.0964371639 0.006221135 0.1162518 4.818401e-04
## 677 0.011513758 0.1378071480 0.009812974 0.1161992 1.563269e-03
## 678 0.008545545 0.0522896641 0.005405626 0.1162872 1.228881e-04
## 679 0.008939921 0.0108476429 0.005916078 0.1163013 5.794054e-06
## 680 0.008488763 0.1308349454 0.005334028 0.1162098 7.590533e-04
## 681 0.013106826 -0.0271466488 0.012716323 0.1162980 7.907407e-05
## 682 0.011419877 -0.1305680109 0.009653601 0.1162098 1.380107e-03
## 683 0.010383011 -0.0776071550 0.007980187 0.1162694 4.016982e-04
## 684 0.010958092 0.0092920499 0.008888662 0.1163015 6.425968e-06
## 685 0.008402128 0.0898928508 0.005225708 0.1162585 3.509702e-04
## 686 0.010518931 0.0050422164 0.008190486 0.1163018 1.741085e-06
## 687 0.010459084 -0.1212295908 0.008097553 0.1162226 9.948489e-04
## 688 0.009278750 0.0678716824 0.006373023 0.1162771 2.445682e-04
## 689 0.008763389 -0.1728066909 0.005684741 0.1161410 1.412237e-03
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## .std.resid
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## 721 0.537914005
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## 724 0.752855643
## 725 1.310543990
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## 727 0.282836889
## 728 -1.703473462
## 729 -1.235351605
## 730 1.384183836
## 731 -0.258369351
## 732 -3.527216966
## 733 -0.552374390
## 734 -0.622387163
## 735 0.152428248
## 736 -1.423488598
## 737 -0.131642752
## 738 0.681750935
## 739 0.728844540
## 740 -0.407600603
## 741 0.047964652
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## 743 0.133087768
## 744 0.331721840
## 745 0.634461288
## 746 0.567826985
## 747 0.577762276
## 748 1.508046176
## 749 -0.403624396
## 750 0.961678640
## 751 -1.002349978
## 752 2.711164998
## 753 -0.085811232
## 754 -0.042351536
## 755 -0.372706324
## 756 -0.801041280
## 757 -0.079846465
## 758 0.924641172
## 759 -0.465134630
## 760 -0.954326180
## 761 0.218688276
## 762 1.042378310
## 763 0.173111872
## 764 -0.647430689
## 765 -0.083199361
## 766 -1.427784372
## 767 1.179491778
## 768 0.650347918
## 769 -0.877649523
## 770 -0.530112088
## 771 1.136768824
## 772 -1.561294272
## 773 -0.548282790
## 774 -3.402942399
## 775 -0.166402561
## 776 -1.103744151
## 777 0.172016439
## 778 1.566526268
## 779 -0.594945090
## 780 -1.186289498
## 781 -1.168760610
## 782 -1.430049428
## 783 -0.285965973
## 784 -0.345062193
## 785 -0.422112614
## 786 0.850220288
## 787 -2.545557445
## 788 0.314940287
## 789 -0.152608101
## 790 0.212104566
## 791 -2.461114286
## 792 0.297199793
## 793 -0.862855657
## 794 -0.446537938
## 795 0.482991902
## 796 1.304879052
## 797 0.035974809
## 798 -0.350832422
## 799 -0.167219771
## 800 -0.253194474
## 801 0.799178839
## 802 -0.537176352
## 803 -1.370930586
## 804 0.552401538
## 805 -0.773344481
## 806 1.266260801
## 807 1.559731080
## 808 -1.902005200
## 809 0.621803774
## 810 -0.786626814
## 811 1.384507835
## 812 -1.970505483
## 813 1.615216386glance(test.lm)## r.squared adj.r.squared sigma statistic p.value df logLik
## 1 0.8939669 0.8929119 0.1162296 847.3173 0 9 600.6567
## AIC BIC deviance df.residual
## 1 -1181.313 -1134.306 10.86149 804coef(test.lm)## (Intercept) log(Total.Bsmt.SF + 1) log(area)
## -1.761643596 0.032896193 0.638675047
## Bedroom.AbvGr Year.Built log(X2nd.Flr.SF + 1)
## -0.036039756 0.003665396 -0.013523102
## log(Lot.Area) Overall.Cond Overall.Qual
## 0.116977819 0.049430411 0.083670791plot(test.lm)
visreg(test.lm)
##### Cross validation by Stepwise methods
0.0.0.12.15 Calculate proportion falling within prediction intervals-(test.lm)
predict.test <- exp(predict(test.lm, test, interval = "prediction"))
coverage.prob.test <- mean(test$price > predict.test[,"lwr"] &
test$price < predict.test[,"upr"])
coverage.prob.test## [1] 0.95202950.0.0.12.16 RMSE comparison
resid.test <- test$price - predict.test
rmse.test <- sqrt(mean(resid.test^2))
rmse.test## [1] 41314.980.0.0.12.17 Summarising the results
## log.price. log.Total.Bsmt.SF...1. log.area. Bedroom.AbvGr Year.Built
## 1 11.74404 6.753438 6.752270 2 1939
## 2 11.84582 6.956545 6.955593 2 1984
## 3 11.73527 6.731018 6.908755 2 1930
## 4 11.64395 6.006353 6.946014 2 1900
## 5 12.33271 6.698268 7.417580 3 2001
## 6 12.19854 0.000000 7.561122 4 2003
## 7 11.44035 6.842683 6.841615 2 1953
## 8 11.83138 6.762730 6.790097 3 1984
## 9 11.84940 6.306275 6.977281 2 2005
## 10 12.29911 7.202661 7.201916 2 2006
## 11 11.82041 6.437752 7.149917 3 1991
## 12 11.28978 6.759255 6.758095 2 1920
## 13 11.97666 7.240650 7.239933 3 1963
## 14 12.27373 7.337588 7.336937 3 2002
## 15 12.00151 6.787845 7.426549 3 1993
## 16 11.11245 6.762730 6.761573 2 1914
## 17 12.23077 7.384610 7.383989 3 1977
## 18 11.78486 5.953243 6.994850 2 1993
## 19 12.10625 7.287561 7.303843 3 2006
## 20 11.49272 6.304449 6.995766 3 1970
## 21 12.49117 7.123673 7.878534 4 1880
## 22 11.56647 6.265301 6.995766 3 1971
## 23 12.21106 7.290975 7.290293 3 2007
## 24 12.08673 6.629363 7.360740 3 2000
## 25 12.20607 7.010312 7.644919 3 1973
## 26 13.01700 7.598399 7.623642 2 2005
## 27 11.42191 5.252273 6.786717 2 1938
## 28 12.20357 7.189168 7.188413 3 2005
## 29 12.24047 6.726233 7.521859 4 1923
## 30 11.95118 7.146772 7.145984 3 1960
## 31 12.30138 7.198184 7.204893 3 2008
## 32 12.18587 6.736967 7.466799 3 1999
## 33 11.02679 6.200509 6.198479 1 1921
## 34 12.18075 6.744059 7.615791 4 1976
## 35 11.76950 6.896694 6.895683 3 1966
## 36 12.58108 7.326466 7.683404 4 2000
## 37 11.80560 6.989335 6.984716 3 1983
## 38 12.13350 7.180070 7.179308 3 1958
## 39 11.80186 6.830874 6.829794 2 1963
## 40 11.90497 6.602588 7.335634 3 1895
## 41 12.27839 6.742881 7.580189 4 2004
## 42 11.78295 6.645091 7.447751 3 1949
## 43 11.60368 6.842683 6.841615 2 1920
## 44 11.60824 6.089045 7.114769 2 1910
## 45 12.09849 7.260523 7.259820 3 2004
## 46 11.84940 6.909753 7.403061 4 1972
## 47 11.92834 7.130099 7.129298 3 1960
## 48 12.73964 7.179308 7.790696 3 1993
## 49 12.36734 6.883463 7.470224 3 1991
## 50 11.18442 6.070738 6.510258 2 1925
## 51 11.94471 6.896694 7.393878 3 1954
## 52 11.76135 6.796824 6.795706 3 1976
## 53 11.97035 6.762730 7.068172 3 1978
## 54 12.44509 7.189168 7.188413 2 2006
## 55 12.03765 6.690842 7.802618 4 1919
## 56 12.55849 7.068172 7.695758 3 1997
## 57 12.12540 5.953243 7.225481 3 2004
## 58 12.27373 7.370860 7.370231 3 1999
## 59 12.55293 7.303843 7.288928 3 2007
## 60 11.87757 6.704414 7.432484 3 1916
## 61 11.11988 6.705639 6.919684 2 1920
## 62 11.90497 7.029088 7.098376 3 1975
## 63 11.97666 7.136483 7.135687 3 1959
## 64 11.69525 7.021976 7.029973 2 1920
## 65 11.81229 6.755769 6.754604 2 1982
## 66 12.12811 6.896694 7.080026 1 1956
## 67 11.79434 6.660575 7.252762 4 1939
## 68 11.98605 6.867974 6.946976 3 1978
## 69 12.01370 6.645091 7.226936 3 1920
## 70 11.51293 7.044033 7.170888 2 1924
## 71 12.15425 6.834109 7.395722 3 1997
## 72 11.62536 6.842683 6.841615 2 1969
## 73 11.88449 6.469250 7.182352 2 1926
## 74 11.67844 7.273093 7.272398 4 1955
## 75 12.01974 6.629363 7.329094 2 2000
## 76 11.90497 6.965080 7.222566 3 1956
## 77 11.50288 0.000000 6.829794 3 1961
## 78 11.36210 6.447306 6.445720 1 1970
## 79 12.01370 7.003065 7.266129 3 1962
## 80 12.26198 7.112327 7.111512 1 1981
## 81 12.25486 7.257003 7.256297 3 1997
## 82 12.33929 7.427144 7.431892 3 1991
## 83 11.79056 6.834109 6.833032 2 1956
## 84 13.05622 7.807510 7.820038 2 2005
## 85 12.38839 7.365813 7.577122 3 1992
## 86 11.92834 6.865891 6.864848 2 1960
## 87 11.19821 6.447306 6.445720 1 1970
## 88 11.23189 6.447306 6.445720 1 1972
## 89 12.70685 7.315218 7.314553 1 1998
## 90 11.58525 6.536692 7.109879 3 1917
## 91 12.12811 6.605298 7.622664 3 1980
## 92 12.01461 6.597146 7.489971 4 1972
## 93 11.73607 6.963190 6.962243 3 1955
## 94 11.97980 6.577861 7.845416 3 1890
## 95 12.10349 7.145196 7.179308 2 2001
## 96 11.98293 6.591674 7.176255 2 1940
## 97 11.59918 6.811244 6.810142 3 1957
## 98 11.93819 6.111467 6.941190 3 1978
## 99 11.79245 6.970730 6.946976 3 1963
## 100 12.12757 6.665684 7.368340 3 2005
## 101 11.75194 6.529419 7.211557 3 1914
## 102 11.86358 6.762730 7.050989 3 1953
## 103 11.62625 6.695799 6.694562 2 1958
## 104 11.30097 5.877736 6.955593 2 1910
## 105 11.81303 7.008505 7.007601 3 1957
## 106 12.17303 7.250636 7.425954 3 1994
## 107 12.35665 7.267525 7.272398 3 2003
## 108 11.64395 7.131699 7.168580 3 1964
## 109 12.45683 6.373320 7.731492 4 1958
## 110 11.66993 6.892642 7.380256 3 1941
## 111 12.26905 6.887553 7.566311 3 2003
## 112 12.26434 6.684612 7.415175 3 1996
## 113 12.21850 6.744059 7.510431 2 1924
## 114 12.02575 7.153052 7.152269 2 1970
## 115 11.83863 6.959399 6.958448 3 1968
## 116 11.53273 6.729824 7.106606 2 1951
## 117 12.20056 7.112327 7.111512 3 2009
## 118 11.74404 6.783325 6.782192 2 1970
## 119 12.20607 6.821107 7.528869 3 2002
## 120 12.53538 7.314553 7.413970 2 2000
## 121 11.88449 6.850126 7.234898 3 1967
## 122 12.66981 7.590347 7.589842 3 2003
## 123 11.89478 6.480045 7.168580 2 1921
## 124 11.37251 6.107023 6.579251 1 1900
## 125 12.26905 7.214504 7.213768 2 2005
## 126 12.47610 7.393263 7.392648 2 1994
## 127 12.28995 7.115582 7.122060 1 1995
## 128 11.90497 6.306275 6.977281 2 2005
## 129 11.63514 6.785588 6.784457 2 1939
## 130 11.98605 6.529419 7.242798 3 1976
## 131 11.88449 6.848005 6.846943 2 1978
## 132 12.41105 7.139660 7.160846 1 1996
## 133 11.80186 6.913737 6.912743 2 1956
## 134 12.19602 7.436617 7.436028 3 1971
## 135 12.23077 7.340836 7.340187 3 2001
## 136 12.56024 7.237778 7.707512 4 1992
## 137 12.07254 6.677083 7.154615 3 1966
## 138 11.98293 0.000000 7.540090 4 1981
## 139 12.51356 7.193686 7.962764 4 1977
## 140 11.26446 6.177944 6.801283 2 1910
## 141 11.62178 6.739337 6.738152 2 1925
## 142 11.86990 7.180831 7.773594 3 1915
## 143 11.74006 6.680855 7.050989 3 1922
## 144 11.74006 6.762730 6.761573 2 1962
## 145 12.41714 7.286876 7.286192 3 2006
## 146 12.33050 7.379632 7.393878 3 1994
## 147 12.46997 7.450661 7.450080 3 1996
## 148 11.81303 6.816736 7.119636 3 1961
## 149 12.07767 6.635947 7.379632 3 1992
## 150 11.28351 6.610696 6.840547 2 1930
## 151 12.24289 7.082549 7.644919 3 1984
## 152 11.65269 6.776507 6.799056 3 1968
## 153 12.42802 7.412764 7.412160 3 2006
## 154 12.00762 6.908755 6.907755 1 1963
## 155 12.30138 7.375256 7.818430 5 1962
## 156 11.81303 7.002156 7.001246 3 1955
## 157 11.80335 6.947937 6.946976 3 1959
## 158 11.63071 6.829794 6.828712 2 1952
## 159 11.91839 6.645091 7.370231 3 1955
## 160 11.50288 6.815640 6.835185 2 1953
## 161 11.89341 6.975414 6.974479 2 1975
## 162 11.95118 7.112327 7.651596 5 1910
## 163 12.60737 7.541683 7.454720 3 2007
## 164 12.45293 7.218910 7.416378 2 1954
## 165 12.07824 7.014814 7.036148 2 1987
## 166 11.69525 6.440947 7.104144 3 1980
## 167 12.67920 7.163172 7.821643 4 1994
## 168 12.15478 6.734592 7.426549 2 2004
## 169 12.07197 7.028201 7.060476 3 1966
## 170 11.35041 6.464588 6.463029 2 1925
## 171 11.87826 6.831954 7.408531 3 1910
## 172 12.46844 6.740519 7.763446 4 1980
## 173 12.10071 7.198931 7.198184 2 1993
## 174 12.37370 7.549083 7.548556 3 1956
## 175 11.06507 0.000000 6.492240 2 1947
## 176 12.31493 6.755769 7.489412 3 2001
## 177 11.92504 6.398595 7.090077 2 2005
## 178 11.91505 7.317212 7.316548 2 1953
## 179 11.91772 6.908755 7.383368 5 1953
## 180 13.12236 7.954021 7.899524 3 2003
## 181 11.43928 0.000000 6.946976 2 1950
## 182 12.57764 7.258412 7.257708 2 2001
## 183 11.75194 6.830874 6.829794 3 1956
## 184 11.53273 6.916715 7.327781 4 1926
## 185 12.15478 6.695799 7.585281 3 1977
## 186 11.22791 6.705639 6.704414 2 1922
## 187 11.59486 7.095893 7.095064 3 1959
## 188 11.86534 7.117206 7.116394 3 1966
## 189 12.10071 7.177782 7.199678 2 1990
## 190 11.79056 6.880384 6.879356 2 1948
## 191 11.93426 6.357842 7.207860 2 1941
## 192 11.06664 5.916202 6.507278 2 1945
## 193 12.61818 7.282074 7.940940 4 1990
## 194 12.11176 7.082549 7.327781 3 1984
## 195 11.82774 6.734592 6.756932 2 1982
## 196 12.03172 6.806829 7.403670 3 1993
## 197 12.56375 6.951772 7.588830 3 1998
## 198 12.14153 6.725034 7.643483 5 1966
## 199 12.30138 6.659294 7.579679 3 1994
## 200 11.41861 6.645091 6.672033 2 1930
## 201 11.28225 6.304449 6.995766 3 1972
## 202 12.46651 6.936343 7.749322 3 1945
## 203 12.94204 7.791110 7.809541 4 2007
## 204 11.79056 7.145984 7.145196 2 1954
## 205 12.74257 7.442493 7.991592 5 2004
## 206 12.17561 7.123673 7.122867 2 2006
## 207 11.82679 7.019297 7.018402 3 1963
## 208 11.89819 7.015712 7.014814 3 1950
## 209 12.53177 7.275865 7.670429 4 1958
## 210 12.21350 6.744059 7.376508 3 2004
## 211 11.35041 6.285998 7.013915 3 1976
## 212 11.91772 6.726233 6.725034 2 1984
## 213 12.06968 6.558198 7.355002 3 1941
## 214 11.80485 7.102499 7.736744 4 1910
## 215 12.06105 6.639876 7.393878 2 2003
## 216 11.60368 6.796824 6.795706 2 1962
## 217 11.97666 6.923629 7.232733 2 1956
## 218 12.09737 6.613384 7.313887 3 1999
## 219 12.29683 6.913737 7.726213 3 1937
## 220 12.07539 6.639876 7.393878 2 2003
## 221 12.85579 7.576097 7.575585 2 2007
## 222 12.09514 6.672033 7.323171 3 2004
## 223 11.54733 7.048386 7.352441 2 1956
## 224 10.91509 6.584791 6.990257 2 1920
## 225 12.04355 5.953243 7.225481 3 2004
## 226 12.25248 7.349231 7.348588 2 2006
## 227 11.73206 6.705639 6.704414 2 1982
## 228 11.84510 6.458338 7.010312 3 1930
## 229 11.98293 6.398595 7.132498 2 1999
## 230 12.30727 7.172425 7.512071 3 2006
## 231 11.81229 6.947937 6.946976 3 1977
## 232 11.67844 6.549651 6.548219 2 1947
## 233 12.18485 6.665684 7.384610 3 2005
## 234 11.81303 7.094235 7.418181 3 1927
## 235 11.80485 6.645091 6.643790 2 1972
## 236 11.93164 6.947937 7.000334 3 1984
## 237 11.58058 6.963190 6.962243 2 1966
## 238 12.30138 6.965080 7.535830 3 2000
## 239 11.68604 6.597146 6.595781 2 1952
## 240 11.84940 6.837333 7.156956 3 1962
## 241 12.10016 6.511745 7.572503 3 1915
## 242 12.54966 7.561642 7.561122 2 2002
## 243 12.28995 7.266129 7.406711 3 1977
## 244 12.26670 7.208600 7.213768 2 2007
## 245 11.74404 6.437752 7.412160 3 1967
## 246 12.54522 7.227662 8.008033 3 2004
## 247 11.37366 6.816736 7.129298 2 1930
## 248 12.27932 6.629363 7.344073 3 2009
## 249 11.99843 6.698268 7.447751 4 1915
## 250 11.83501 6.665684 7.379632 4 1923
## 251 12.10800 6.562444 7.323831 3 1994
## 252 11.90497 7.037906 7.037028 3 1960
## 253 12.66033 7.613325 7.631917 3 1994
## 254 11.79056 6.725034 6.749931 2 1929
## 255 11.91505 6.511745 7.244228 3 1978
## 256 12.11997 6.734592 7.450080 3 2004
## 257 12.32163 7.204149 7.272398 2 1993
## 258 12.93603 7.533159 7.532624 2 2005
## 259 11.95118 6.898715 6.897705 3 1994
## 260 11.81303 6.580639 7.147559 4 1948
## 261 12.00762 6.823286 7.406103 4 1941
## 262 11.76368 6.859615 6.858565 3 1968
## 263 12.18842 6.758095 7.450080 3 2004
## 264 11.78295 6.601230 7.104965 3 1941
## 265 11.92504 7.104965 7.104144 2 1991
## 266 11.91772 7.072422 7.164720 2 1954
## 267 11.84868 6.569481 7.264030 4 1900
## 268 11.70148 6.796824 6.795706 2 1977
## 269 11.94471 7.128496 7.127694 3 1959
## 270 11.84868 6.886532 7.259820 3 1960
## 271 11.51293 0.000000 7.475339 4 1957
## 272 12.38839 6.811244 7.765569 5 1908
## 273 11.81303 7.028201 7.027315 3 1976
## 274 12.06681 6.610696 7.302496 3 2005
## 275 12.84397 7.602401 7.609862 3 2008
## 276 12.24047 7.217443 7.216709 2 2005
## 277 11.78295 6.900731 7.289611 3 1939
## 278 11.93164 6.398595 7.119636 2 2005
## 279 11.02679 0.000000 7.049255 2 1955
## 280 11.89894 6.274762 6.984716 2 2003
## 281 11.82774 6.965080 7.346655 3 1938
## 282 11.76368 6.580639 7.231287 2 1941
## 283 12.24289 7.303170 7.377759 2 1957
## 284 12.05815 6.823286 7.428333 3 1978
## 285 12.84793 7.675082 7.879670 3 2006
## 286 11.82774 6.844815 6.949856 2 1947
## 287 11.77529 6.663133 6.697034 2 1971
## 288 12.27839 6.690842 7.581210 3 2001
## 289 11.93819 7.020191 7.019297 3 1960
## 290 12.86100 7.519150 7.518607 0 1981
## 291 11.77529 6.878326 7.443664 3 2004
## 292 11.75194 6.224558 7.132498 3 1908
## 293 12.50618 6.993015 7.580189 3 2006
## 294 11.85652 6.996681 6.995766 2 1957
## 295 12.36734 7.625107 7.632401 3 1978
## 296 12.45644 6.838405 7.878534 5 1967
## 297 12.83468 7.667158 7.618742 3 1965
## 298 11.85652 6.660575 7.226209 3 1937
## 299 11.98293 7.018402 7.017506 3 1962
## 300 12.18075 7.418781 7.423568 3 1999
## 301 12.44902 7.392648 7.400010 3 2006
## 302 12.03469 5.953243 7.295735 3 1995
## 303 11.91772 6.983790 6.982863 3 1971
## 304 11.68688 6.776507 6.895683 3 1950
## 305 11.63514 6.511745 6.510258 2 1941
## 306 11.97666 6.912743 7.416980 3 1947
## 307 11.97666 7.105786 7.104965 3 2007
## 308 12.03172 7.130899 7.391415 3 1961
## 309 11.71178 6.783325 6.802395 3 1967
## 310 11.71382 6.842683 7.461640 2 1920
## 311 11.69525 6.837333 6.934397 2 1920
## 312 12.95098 7.299797 7.881937 4 2001
## 313 11.57965 6.318968 7.162397 3 1900
## 314 11.51293 6.597146 7.023759 3 1939
## 315 11.56172 6.357842 6.892642 2 1920
## 316 11.56076 6.573680 7.460490 4 1920
## 317 12.13886 6.270988 7.525640 3 1976
## 318 12.10901 7.141245 7.140453 3 1976
## 319 12.13940 7.254178 7.265430 3 2001
## 320 12.16525 7.266129 7.265430 3 1974
## 321 12.34583 7.308543 7.307873 3 2002
## 322 11.75979 7.067320 7.066467 3 1954
## 323 12.19096 7.129298 7.128496 1 2005
## 324 12.93603 7.515889 8.208492 5 1935
## 325 11.82012 6.850126 6.849066 2 1979
## 326 12.42922 6.925595 7.629004 3 1936
## 327 12.59811 7.486053 7.485492 3 2004
## 328 12.37370 7.469654 7.488853 3 2001
## 329 12.31493 7.520235 7.519692 3 1969
## 330 12.34801 7.137278 7.678326 3 2001
## 331 11.77529 5.953243 7.215240 3 1955
## 332 11.74006 6.776507 6.804615 3 1967
## 333 11.90158 7.136483 7.135687 3 1965
## 334 11.27720 6.300786 6.651572 3 1931
## 335 11.48247 6.182085 6.894670 2 1972
## 336 11.74006 6.689599 7.215240 2 1938
## 337 12.07824 7.217443 7.231287 3 1962
## 338 11.31447 6.175867 6.291569 1 1941
## 339 11.44035 6.150603 7.040536 3 1924
## 340 11.83501 7.097549 7.551712 3 1950
## 341 12.07824 7.032624 7.031741 2 2005
## 342 12.24529 6.350886 7.591862 3 1986
## 343 11.85652 6.762730 6.761573 3 1961
## 344 11.99535 6.517671 7.244228 3 1986
## 345 11.92834 7.050989 7.070724 3 1984
## 346 12.29608 7.355641 7.355002 3 2007
## 347 12.68386 7.237059 7.856320 4 1998
## 348 11.92504 6.228511 7.100027 3 1977
## 349 11.75587 6.740519 7.167038 3 1927
## 350 12.22096 7.190676 7.189922 3 2005
## 351 11.70355 6.842683 6.841615 2 1954
## 352 12.26905 6.608001 7.481556 3 1993
## 353 12.23077 6.825460 7.816014 5 1940
## 354 12.14950 7.113956 7.113142 2 1988
## 355 12.12811 7.023759 7.567346 3 1977
## 356 11.75979 6.350886 7.086738 3 1940
## 357 11.40756 6.867974 6.866933 3 1958
## 358 12.03112 7.208600 7.195937 2 1977
## 359 11.87060 6.744059 6.742881 1 2004
## 360 12.42922 6.960348 7.596894 3 2003
## 361 12.08954 7.119636 7.126891 1 2004
## 362 12.76569 7.183871 7.776954 3 2003
## 363 11.87409 6.493754 7.158514 3 1977
## 364 12.10349 7.261927 7.273786 3 1990
## 365 11.94795 6.966024 6.973543 3 1963
## 366 12.40901 7.251345 7.250636 1 2002
## 367 11.93819 7.180831 7.180070 3 1961
## 368 12.34583 6.912743 7.524021 3 1999
## 369 11.62625 6.705639 7.255591 3 1918
## 370 12.24289 7.181592 7.180831 2 2007
## 371 12.18075 7.255591 7.282761 2 2003
## 372 11.69941 6.762730 6.761573 3 1971
## 373 11.87757 7.003065 7.002156 3 1995
## 374 12.08051 7.042286 7.041412 1 2004
## 375 11.77529 7.094235 7.252054 3 1955
## 376 11.48247 0.000000 6.782192 2 1956
## 377 11.32660 6.182085 6.894670 2 1973
## 378 11.86358 6.816736 6.815640 3 1961
## 379 11.95054 6.595781 7.202661 3 1921
## 380 11.88449 7.455298 7.454720 6 1965
## 381 11.72723 6.248043 6.951772 2 1980
## 382 12.42922 6.855409 7.643962 4 2007
## 383 11.87060 6.950815 6.956545 3 1971
## 384 12.44902 7.046647 7.637716 3 1993
## 385 11.78866 6.867974 6.866933 2 1959
## 386 11.79434 6.907755 6.906755 3 1962
## 387 12.11121 7.139660 7.138867 3 1983
## 388 12.86618 7.541683 7.541152 2 2004
## 389 12.49874 6.999422 7.738488 4 1992
## 390 11.71178 6.529419 7.765569 4 1872
## 391 11.48247 6.304449 7.203406 3 1970
## 392 12.34148 7.094235 7.688455 4 1988
## 393 12.73670 7.158514 7.803843 3 1998
## 394 11.81303 6.493754 7.412160 3 1916
## 395 11.91170 6.517671 7.209340 4 1939
## 396 12.56024 7.426549 7.497207 3 1994
## 397 12.36414 7.202661 7.201916 2 2006
## 398 11.69107 0.000000 7.410952 4 1977
## 399 11.71994 6.762730 6.802395 3 1967
## 400 11.91170 6.628041 7.319865 3 1920
## 401 11.82041 7.513709 7.513164 4 1967
## 402 11.68688 6.437752 7.160846 3 1917
## 403 11.72804 6.511745 7.098376 3 1941
## 404 11.67844 6.899723 6.981935 2 1939
## 405 12.46844 7.466799 7.880804 3 1974
## 406 11.96400 7.061334 7.197435 2 1953
## 407 12.46844 7.161622 7.790282 4 1991
## 408 12.00762 7.104144 7.103322 2 1998
## 409 12.14153 7.282074 7.281386 3 1961
## 410 12.47991 7.008505 7.697121 4 1992
## 411 10.71442 0.000000 6.416732 1 1940
## 412 12.06105 7.090910 7.090077 3 1964
## 413 12.17561 7.215975 7.266827 2 1978
## 414 12.08954 6.562444 7.254178 3 2004
## 415 11.75979 6.511745 7.188413 3 1936
## 416 11.39639 6.424869 6.423247 2 1921
## 417 11.77529 6.762730 6.761573 3 1971
## 418 11.98293 6.822197 7.604396 3 1900
## 419 11.87060 6.878326 6.933423 2 1974
## 420 11.37366 6.641182 6.639876 2 1925
## 421 11.90834 6.910751 6.909753 3 1970
## 422 11.05089 6.373320 7.013915 4 1934
## 423 11.75979 6.948897 6.947937 3 1958
## 424 12.27373 6.796824 7.566828 4 2007
## 425 11.77414 6.842683 7.378384 3 1925
## 426 11.65269 6.762730 6.761573 3 1971
## 427 12.00457 6.776507 6.871091 2 1921
## 428 11.88449 7.195187 7.194437 2 1990
## 429 12.50987 7.109879 7.662468 3 1994
## 430 11.46163 6.424869 7.013016 3 1941
## 431 12.16525 7.241366 7.240650 2 1963
## 432 12.10625 6.665684 7.375256 3 2005
## 433 12.85055 6.591674 8.145260 4 1935
## 434 11.84940 6.280396 7.378384 3 1958
## 435 11.77913 6.645091 7.090077 3 1946
## 436 11.95118 7.003974 7.261225 3 1969
## 437 11.40199 5.768321 7.248504 3 1920
## 438 12.53358 7.271704 7.803027 3 1962
## 439 11.84940 6.811244 6.810142 3 1978
## 440 11.98293 7.125283 7.592870 5 1910
## 441 11.73607 7.202661 7.201916 4 1951
## 442 12.06393 7.064759 7.081709 2 2005
## 443 11.81303 6.883463 6.911747 2 1977
## 444 12.20607 6.918695 7.726213 4 2002
## 445 12.53538 7.833996 7.833600 4 1981
## 446 11.83428 6.752270 7.283448 3 1977
## 447 12.61154 7.387090 7.401231 2 2000
## 448 12.03765 7.388946 7.493874 3 1957
## 449 11.76912 6.816736 6.846943 3 1967
## 450 12.02575 6.645091 7.336937 3 2005
## 451 12.14153 7.224753 7.294377 3 1980
## 452 11.77452 6.705639 6.704414 2 1957
## 453 12.37159 6.957497 7.575072 3 1993
## 454 11.74006 6.641182 7.218910 3 1973
## 455 12.16525 7.057037 7.611842 4 1977
## 456 12.01673 7.001246 7.012115 1 1978
## 457 11.95118 6.918695 6.958448 3 1971
## 458 11.87757 0.000000 7.610853 4 1977
## 459 12.04942 6.573680 7.405496 4 1971
## 460 12.28765 6.749931 7.469084 3 1998
## 461 12.46844 6.976348 7.630947 3 1995
## 462 11.32055 0.000000 7.049255 2 1955
## 463 12.05525 6.665684 7.584773 4 1969
## 464 12.18075 6.742881 7.574558 4 2004
## 465 11.74800 6.978214 6.977281 2 1925
## 466 11.71178 6.830874 7.543803 4 1910
## 467 12.26905 7.333023 7.416980 3 1978
## 468 11.83501 6.680855 6.679599 2 1971
## 469 11.89819 7.030857 7.225481 3 1964
## 470 11.77529 6.881411 7.762171 4 1920
## 471 11.54248 6.532334 7.515345 4 1900
## 472 12.26905 7.396949 7.396335 3 2000
## 473 11.60824 6.829794 6.828712 3 1975
## 474 11.78676 6.946976 6.946014 3 1965
## 475 12.52453 7.334329 7.799343 4 2001
## 476 12.01673 7.243513 7.438384 4 1959
## 477 12.57764 7.061334 7.834392 4 1994
## 478 11.74404 6.796824 6.823286 2 1926
## 479 11.72804 6.947937 6.946976 3 1975
## 480 12.67608 7.422971 8.077758 5 1990
## 481 12.95984 7.590347 7.589842 2 2007
## 482 11.47730 6.645091 6.670766 2 1926
## 483 11.42846 6.665684 6.664409 2 1955
## 484 12.51539 7.516977 7.516433 3 2007
## 485 12.21019 6.755769 7.447751 3 2005
## 486 11.98293 6.891626 7.467371 4 1940
## 487 11.26446 6.391917 7.083388 3 1920
## 488 12.21503 6.762730 7.506592 4 1965
## 489 12.18332 6.741701 7.374002 3 2004
## 490 11.58525 0.000000 6.717805 2 1955
## 491 11.71178 6.867974 6.866933 2 1955
## 492 11.99535 7.094235 7.093405 2 1998
## 493 12.42922 7.239215 7.931644 5 1978
## 494 12.66981 7.447168 7.446585 2 2005
## 495 12.46844 7.333676 7.333023 3 2005
## 496 11.95118 6.591674 6.669498 1 1980
## 497 11.69525 6.979145 6.978214 3 1967
## 498 11.97666 7.016610 7.015712 3 2004
## 499 11.62625 6.426488 7.177782 2 1924
## 500 12.32829 7.282074 7.299121 3 2003
## 501 12.68850 7.481556 7.499977 3 2008
## 502 11.51192 6.762730 6.761573 2 1922
## 503 12.51172 7.292337 7.291656 2 2005
## 504 12.84133 7.465655 7.465083 3 2006
## 505 11.78295 0.000000 7.608871 4 1880
## 506 11.86710 6.762730 6.795706 3 1974
## 507 12.08069 7.181592 7.180831 3 2006
## 508 11.81303 7.412764 7.412160 4 1973
## 509 11.91839 7.561122 7.560601 4 1964
## 510 12.13350 7.100852 7.100027 3 2009
## 511 12.27839 7.379632 7.379008 3 1977
## 512 11.66135 6.532334 7.130899 3 1918
## 513 11.98605 7.081709 7.080868 2 1997
## 514 12.50432 7.063904 7.932721 6 2000
## 515 12.41710 7.221836 7.320527 2 2002
## 516 11.78600 6.762730 7.042286 3 1961
## 517 11.59910 6.705639 6.704414 2 1925
## 518 11.79434 7.046647 7.045777 3 1959
## 519 12.34801 7.249215 7.568379 3 2000
## 520 11.76679 6.957497 6.956545 2 1956
## 521 11.58432 6.734592 7.380879 3 1915
## 522 12.91164 7.340187 7.956827 4 2000
## 523 12.30138 7.145196 7.167038 2 2001
## 524 11.88380 6.991177 6.990257 3 1954
## 525 11.82774 7.055313 7.069874 3 1958
## 526 11.91772 6.752270 7.283448 3 1975
## 527 12.11724 7.264030 7.263330 4 1969
## 528 11.50791 6.823286 6.822197 2 1979
## 529 12.17819 6.904751 7.463937 3 1993
## 530 11.84582 6.682109 7.394493 4 1900
## 531 12.35017 7.050123 7.493874 3 1993
## 532 11.62178 6.844815 7.576097 4 1900
## 533 12.42521 7.309881 7.317212 3 2005
## 534 11.89819 6.937314 7.018402 3 1977
## 535 12.61653 7.594381 7.594381 2 1994
## 536 11.87757 6.734592 6.784457 2 1983
## 537 11.84582 7.041412 7.040536 3 2005
## 538 11.51791 6.182085 6.894670 2 1972
## 539 11.87757 6.932448 7.203406 2 1958
## 540 11.71994 6.964136 6.961296 2 1975
## 541 12.14950 7.282761 7.268223 3 2001
## 542 12.40287 7.155396 7.822044 4 1993
## 543 11.88449 7.417580 7.416980 4 1978
## 544 11.84223 6.996681 6.995766 3 1962
## 545 11.94194 6.549651 7.241366 3 1915
## 546 12.64433 6.925595 7.604396 3 2008
## 547 12.08673 6.613384 7.668561 4 1965
## 548 12.27839 7.149917 7.283448 2 2003
## 549 11.75979 7.074117 7.073270 2 1970
## 550 11.73767 6.916715 6.999422 3 1975
## 551 12.43321 7.309881 7.409742 2 2000
## 552 12.66033 7.516977 7.516433 2 2006
## 553 11.75194 6.629363 7.333676 3 1947
## 554 11.54733 6.880384 7.572503 4 1910
## 555 12.19349 6.660575 7.532624 4 1976
## 556 11.84940 6.660575 7.493317 4 1963
## 557 11.84940 7.007601 7.215240 3 1969
## 558 12.84265 7.484930 7.484369 2 2004
## 559 12.34583 0.000000 7.166266 2 1986
## 560 12.06105 6.864848 7.160069 2 1977
## 561 11.75194 6.630683 7.296413 4 1977
## 562 12.73670 7.365813 7.810353 4 2004
## 563 12.07254 7.303170 7.302496 3 1971
## 564 11.13459 6.255750 6.253829 1 1927
## 565 11.81303 6.591674 7.149917 3 1939
## 566 11.69525 6.760415 7.054450 3 1929
## 567 11.86005 6.796824 6.795706 2 1960
## 568 11.82408 6.762730 6.761573 3 1978
## 569 11.35627 6.304449 6.995766 3 1972
## 570 12.22588 7.307202 7.313887 3 1999
## 571 12.13619 7.276556 7.275865 3 2004
## 572 11.60368 6.716595 6.715383 2 1954
## 573 12.52453 6.965080 7.551712 3 2005
## 574 12.32829 7.257708 7.257003 3 1997
## 575 11.92338 6.969791 7.190676 3 1959
## 576 11.76757 6.816736 6.815640 3 1966
## 577 11.87757 6.762730 6.806829 3 1970
## 578 12.27373 7.119636 7.118826 1 1980
## 579 11.22524 6.304449 6.995766 3 1970
## 580 11.99535 6.584791 7.240650 3 1972
## 581 11.60824 6.993015 6.992096 2 1963
## 582 12.17045 6.728629 7.502186 3 2004
## 583 11.90497 6.986566 6.985642 3 1960
## 584 11.55694 5.579730 7.173192 3 1977
## 585 11.28351 6.304449 6.995766 3 1970
## 586 11.44572 6.437752 7.129298 2 1920
## 587 12.13270 7.218910 7.218177 2 2005
## 588 11.65269 6.677083 7.324490 3 1919
## 589 12.13296 6.723832 7.409136 3 1999
## 590 11.95118 6.785588 7.269617 3 1940
## 591 11.66135 4.663439 6.813445 3 1953
## 592 12.08391 6.629363 7.360740 3 2000
## 593 11.95118 7.103322 7.102499 3 1958
## 594 11.82774 6.331502 7.113956 2 1980
## 595 11.73607 6.816736 6.815640 3 1967
## 596 12.33710 7.350516 7.372746 3 1994
## 597 12.25486 6.820016 7.553811 4 1994
## 598 12.16003 6.781058 7.447751 2 1996
## 599 12.94324 7.441320 7.922261 4 2005
## 600 12.52453 7.469654 7.488294 3 2001
## 601 11.77529 6.762730 6.801283 3 1967
## 602 11.84582 6.916715 6.915723 3 1968
## 603 12.72189 7.461640 7.463363 3 2008
## 604 11.83501 6.898715 6.897705 3 1994
## 605 11.80932 6.830874 6.906755 3 1962
## 606 11.79810 7.007601 7.006695 3 1956
## 607 11.73206 6.948897 6.947937 3 1959
## 608 11.97980 6.486161 7.085064 3 1959
## 609 12.06105 6.683361 7.402452 3 2004
## 610 10.59663 6.476972 7.183112 3 1920
## 611 11.28978 0.000000 6.849066 3 1958
## 612 12.36734 7.330405 7.329750 3 2000
## 613 12.69158 7.023759 7.825645 4 2005
## 614 11.77144 6.645091 7.191429 3 1950
## 615 12.08954 6.609349 7.457032 3 1985
## 616 11.75194 5.710427 7.043160 3 1956
## 617 12.05815 6.593045 7.293698 3 1999
## 618 12.01309 6.889591 7.421776 3 1940
## 619 11.98293 7.080868 7.247081 3 1969
## 620 12.44804 6.974479 7.688913 4 2003
## 621 12.66033 7.591357 7.590852 3 2004
## 622 12.12811 7.025538 7.383989 3 1972
## 623 11.79056 6.511745 7.186901 4 1939
## 624 12.18587 7.238497 7.237778 2 2004
## 625 11.93819 6.900731 7.174724 2 1957
## 626 12.18075 6.723832 7.414573 3 2002
## 627 12.50987 7.358194 7.431892 3 2002
## 628 11.68688 6.785588 6.806829 2 1926
## 629 11.69441 6.677083 7.019297 3 1939
## 630 11.72804 7.368340 7.367709 4 1967
## 631 12.05234 7.170888 7.201171 2 1990
## 632 11.81303 6.480045 7.236339 3 1946
## 633 12.04355 7.237059 7.236339 2 1974
## 634 12.03765 6.821107 7.377759 3 1997
## 635 11.46163 6.529419 6.984716 3 1890
## 636 12.08673 7.090910 7.090077 3 1995
## 637 11.56172 6.783325 6.797940 2 1961
## 638 11.63514 6.677083 6.675823 2 1945
## 639 12.40901 7.355002 7.354362 3 2007
## 640 12.15478 7.325149 7.543273 2 1966
## 641 11.84940 6.753438 7.419381 3 1950
## 642 11.84940 6.825460 6.841615 0 1996
## 643 12.07824 7.192934 7.192182 3 1960
## 644 12.71890 7.196687 7.946618 3 1992
## 645 11.64395 5.849325 6.924612 2 1900
## 646 12.68850 7.450080 7.449498 1 1993
## 647 11.76757 6.947937 7.021084 3 1961
## 648 11.79434 7.009409 7.081709 3 1962
## 649 12.28535 6.758095 7.580700 4 2002
## 650 12.11176 7.062192 7.072422 2 1988
## 651 11.95761 6.898715 6.897705 3 1995
## 652 11.87235 6.889591 6.888572 3 1971
## 653 11.82774 6.841615 6.840547 3 1965
## 654 11.37366 6.580639 6.688355 2 1941
## 655 11.70767 7.239215 7.238497 3 1957
## 656 11.28978 6.447306 6.445720 1 1970
## 657 11.78295 0.000000 7.402452 3 1950
## 658 12.61487 6.961296 7.624619 3 2003
## 659 12.37582 6.836259 7.598399 4 1995
## 660 12.00151 7.217443 7.216709 3 1961
## 661 12.46844 7.338888 7.338238 3 2005
## 662 11.63514 6.601230 7.304516 3 1945
## 663 12.27139 6.845880 7.493874 3 2006
## 664 12.35017 6.683361 7.321189 3 1925
## 665 12.16785 6.728629 7.416378 3 2003
## 666 11.28853 6.398595 6.616065 1 1926
## 667 11.76757 6.935370 7.398174 3 1948
## 668 12.01974 7.074963 7.081709 3 1993
## 669 12.14950 5.953243 7.395108 3 1996
## 670 11.77144 6.311735 7.296413 4 1976
## 671 11.82408 7.163172 7.259820 3 1926
## 672 12.16785 6.842683 7.482119 3 2002
## 673 12.42922 7.358831 7.384610 3 2002
## 674 11.69107 6.660575 7.226936 3 1937
## 675 12.04355 6.716595 7.420579 4 1971
## 676 12.90917 7.611348 7.610853 3 2008
## 677 11.96400 6.575076 7.266827 3 1977
## 678 11.55215 6.995766 6.994850 2 1951
## 679 11.78295 6.968850 6.967909 3 1954
## 680 11.50791 6.437752 6.674561 2 1923
## 681 11.87060 7.398174 7.397562 4 1967
## 682 12.38798 6.984716 7.538495 3 1993
## 683 11.70251 6.932448 6.931472 3 1965
## 684 12.33929 6.694562 7.591862 3 1989
## 685 12.38839 6.947937 7.648740 4 1997
## 686 12.55673 6.906755 7.623642 3 2003
## 687 11.66565 6.248043 6.939254 2 1980
## 688 11.79056 6.437752 7.279319 3 1920
## 689 11.30220 6.796824 6.795706 2 1935
## 690 11.64395 6.617403 7.055313 3 1925
## 691 11.69941 6.762730 6.761573 3 1970
## 692 11.77529 6.762730 6.761573 2 1967
## 693 11.54636 6.182085 6.894670 2 1973
## 694 12.40901 7.071573 7.745868 4 1999
## 695 11.69525 7.043160 7.042286 3 1960
## 696 11.72804 6.933423 6.932448 3 1962
## 697 11.60824 7.073270 7.072422 2 1960
## 698 12.14153 7.053586 7.448334 3 1990
## 699 12.69772 7.283448 7.896181 4 2000
## 700 11.74324 6.935370 6.934397 3 1962
## 701 11.84223 6.705639 6.704414 2 1983
## 702 11.82774 6.916715 6.915723 2 1954
## 703 12.14420 6.781058 7.452402 3 1998
## 704 11.27085 6.447306 6.586172 1 1890
## 705 11.83501 6.270988 7.075809 3 1959
## 706 12.12811 7.108244 7.107425 2 2004
## 707 11.97035 7.028201 7.275865 3 1964
## 708 11.56647 6.725034 6.723832 2 1954
## 709 12.04942 7.237778 7.438972 3 1975
## 710 12.12269 6.626718 7.339538 3 1994
## 711 11.89683 6.937314 6.967909 3 1976
## 712 12.57764 7.050123 7.727535 4 1999
## 713 12.04297 6.920672 6.941190 3 1976
## 714 11.77529 6.799056 6.841615 3 1962
## 715 11.71994 6.796824 6.795706 2 1972
## 716 11.87687 7.039660 7.436028 3 1962
## 717 12.31717 6.825460 7.487734 3 2001
## 718 12.24047 6.746412 7.475339 3 1999
## 719 12.19854 6.734592 7.452982 3 2002
## 720 11.91405 7.113956 7.113142 3 1966
## 721 12.01370 6.523562 7.293018 3 1995
## 722 12.36734 6.679599 7.724447 3 1977
## 723 11.87409 6.858565 6.857514 2 1958
## 724 12.16395 6.762730 7.506592 3 1993
## 725 12.13886 6.820016 7.432484 3 2000
## 726 11.71587 6.656727 7.736307 4 1885
## 727 11.91036 6.313548 7.004882 2 2004
## 728 11.94146 6.963190 6.979145 3 1975
## 729 12.56024 7.074963 7.772332 4 2003
## 730 12.12540 7.175490 7.174724 1 2005
## 731 12.18332 6.831954 7.380256 3 1998
## 732 12.45877 7.332369 7.665285 4 1941
## 733 12.12811 6.804615 7.536897 4 1974
## 734 11.98293 6.903747 6.916715 3 1977
## 735 11.79434 6.815640 6.860664 3 1976
## 736 12.26434 7.305860 7.314553 1 1985
## 737 12.07824 6.562444 7.254178 3 2002
## 738 12.16525 7.136483 7.145984 2 2004
## 739 11.77529 6.946014 6.945051 2 1984
## 740 12.16525 7.286192 7.285507 3 2002
## 741 11.63956 5.081404 7.040536 2 1958
## 742 11.66993 6.726233 6.725034 2 1954
## 743 11.96718 6.916715 6.931472 2 1956
## 744 12.20607 7.248504 7.247793 2 2003
## 745 11.39639 6.182085 6.854355 2 1972
## 746 11.84940 7.065613 7.064759 3 1958
## 747 12.15478 6.762730 7.454720 3 2004
## 748 12.47419 7.170120 7.534763 3 2001
## 749 11.95761 7.104144 7.454720 3 1953
## 750 11.12879 0.000000 6.739337 1 1939
## 751 11.30590 0.000000 6.694562 1 1945
## 752 12.82126 7.583248 7.582738 3 2005
## 753 11.88793 6.939254 6.938284 2 1952
## 754 11.86358 7.133296 7.132498 3 1959
## 755 12.28303 6.703188 7.422971 3 2000
## 756 11.71994 6.947937 6.946976 3 1966
## 757 12.44863 6.899723 7.574045 3 2004
## 758 12.10071 6.844815 6.895683 1 1969
## 759 12.38839 7.364547 7.363914 3 2006
## 760 12.40082 7.092574 7.676937 4 1950
## 761 10.57898 0.000000 5.811141 1 1946
## 762 11.96718 6.580639 7.272398 4 1964
## 763 12.13886 7.123673 7.226209 3 1956
## 764 12.06105 7.080868 7.104144 3 1990
## 765 11.84223 6.274762 6.984716 2 2003
## 766 11.88793 6.960348 6.959399 3 1959
## 767 12.15478 7.520235 7.519692 3 1977
## 768 12.06681 7.225481 7.349231 2 2007
## 769 12.15478 7.305188 7.257708 2 2002
## 770 11.75979 6.693324 7.406711 4 1915
## 771 12.09369 7.226936 7.254178 2 2004
## 772 12.66033 6.749931 7.910957 3 1932
## 773 12.00151 6.762730 7.351158 2 1975
## 774 12.10349 6.639876 7.508787 3 1919
## 775 11.77144 6.896694 6.895683 3 1962
## 776 11.79810 6.947937 6.946976 3 1963
## 777 11.98916 7.100027 7.099202 3 1976
## 778 12.42118 6.881411 7.522941 3 1994
## 779 11.81303 6.762730 6.761573 3 1961
## 780 11.44945 6.645091 6.643790 1 1930
## 781 11.86780 7.455298 7.454720 6 1965
## 782 12.26904 7.306531 7.313220 3 2006
## 783 12.86424 7.780303 7.779885 3 2003
## 784 12.27256 6.964136 7.166266 1 1978
## 785 12.66033 7.293698 7.874739 4 1998
## 786 11.72804 7.043160 7.042286 3 1963
## 787 11.84582 6.930495 6.929517 3 1994
## 788 11.69941 6.608001 6.656727 2 1940
## 789 12.57764 7.125283 7.824446 4 1995
## 790 12.27839 7.161622 7.221105 2 1997
## 791 12.06681 6.655440 7.273093 2 1999
## 792 11.86429 6.960348 6.959399 3 1963
## 793 11.77529 6.979145 7.396335 3 1953
## 794 12.12269 6.934397 7.506592 4 1925
## 795 12.50432 7.063904 7.932721 6 2000
## 796 11.89478 6.591674 7.404888 3 1942
## 797 11.88449 6.759255 7.297768 3 1928
## 798 12.13886 6.848005 7.515889 3 1997
## 799 11.69441 6.762730 6.761573 3 1972
## 800 12.25486 6.548219 7.496097 3 1930
## 801 12.92999 7.360740 7.889084 3 2003
## 802 12.26905 6.814543 7.506592 3 1996
## 803 12.11176 7.482682 7.352441 3 1962
## 804 12.12811 6.729824 7.443664 3 1991
## 805 11.81303 6.955593 6.954639 3 1956
## 806 11.65703 6.768493 6.996681 2 1958
## 807 11.70767 6.979145 6.978214 2 1956
## 808 11.73607 6.555357 7.294377 3 1925
## 809 11.82408 6.957497 6.956545 3 1961
## 810 11.90497 7.042286 7.014814 3 1976
## 811 11.73607 6.796824 6.795706 3 1966
## 812 11.51092 6.570883 6.569481 2 1930
## 813 11.69525 6.762730 6.778785 3 1975
## 814 11.75194 6.762730 6.761573 3 1972
## 815 11.98293 6.861711 7.789040 3 1900
## 816 11.74086 6.347389 6.983790 2 1948
## 817 12.39669 6.373320 7.634821 4 1960
## 818 11.38793 6.304449 6.995766 3 1970
## 819 12.16003 7.205635 7.315884 2 2005
## 820 11.90497 6.769642 6.817831 2 1996
## 821 12.05757 6.860664 7.416980 3 2000
## 822 12.32163 6.740519 7.675082 5 1964
## 823 11.96400 7.268920 7.268223 4 1974
## 824 11.84940 6.726233 6.800170 3 1968
## 825 12.11997 6.701960 7.329750 3 1997
## 826 11.28978 6.722630 6.778785 2 1936
## 827 12.07254 6.593045 7.276556 3 1996
## 828 12.11121 7.043160 7.264730 3 1960
## 829 12.66271 7.229839 7.782390 3 1996
## 830 11.88449 6.744059 6.742881 1 2004
## 831 11.97035 6.498282 7.209340 4 1969
## 832 11.95761 6.790097 6.815640 2 1978
## log.X2nd.Flr.SF...1. log.Lot.Area. Overall.Cond Overall.Qual .fitted
## 1 0.000000 8.973351 6 6 11.66286
## 2 0.000000 8.351139 5 5 11.74831
## 3 0.000000 8.709465 9 5 11.76563
## 4 5.777652 9.005282 8 4 11.45514
## 5 6.752270 9.035987 6 8 12.37515
## 6 7.264030 8.895767 5 7 12.05763
## 7 0.000000 8.699515 4 4 11.44432
## 8 0.000000 9.425048 6 5 11.79858
## 9 0.000000 8.209308 5 6 11.90238
## 10 0.000000 8.738735 5 8 12.31697
## 11 6.478510 9.256747 5 5 11.86785
## 12 0.000000 8.909776 6 4 11.39708
## 13 0.000000 9.159047 5 6 11.99206
## 14 0.000000 9.119868 5 7 12.30106
## 15 6.678342 9.045466 5 6 12.11229
## 16 0.000000 9.017726 3 3 11.12432
## 17 0.000000 9.268892 7 6 12.26976
## 18 0.000000 8.949755 5 6 11.94811
## 19 0.000000 8.914761 5 7 12.27008
## 20 6.304449 7.297768 9 6 11.75564
## 21 7.186144 9.367344 7 7 12.12004
## 22 6.342121 7.426549 5 5 11.45329
## 23 0.000000 9.096612 5 8 12.38079
## 24 6.690842 7.657755 5 6 11.91834
## 25 6.891626 9.247829 6 7 12.33751
## 26 0.000000 9.644134 5 10 12.87446
## 27 0.000000 8.662851 8 5 11.61937
## 28 0.000000 9.825202 5 6 12.22077
## 29 6.679599 9.476773 7 6 12.00485
## 30 0.000000 8.978534 6 5 11.86414
## 31 0.000000 9.383957 5 7 12.27743
## 32 6.795706 9.134754 5 7 12.26078
## 33 0.000000 8.965718 5 3 10.95198
## 34 6.816736 9.396488 6 6 12.21225
## 35 0.000000 8.874868 6 5 11.71939
## 36 6.461468 9.305651 5 9 12.57798
## 37 0.000000 9.125545 5 6 11.91170
## 38 0.000000 9.337413 7 7 12.16266
## 39 0.000000 9.063926 6 5 11.73189
## 40 6.664409 9.287301 9 5 11.81541
## 41 7.014814 9.375516 5 7 12.33574
## 42 6.343880 9.342158 4 5 11.83154
## 43 0.000000 8.408494 7 5 11.53321
## 44 6.308098 9.253400 6 5 11.60056
## 45 0.000000 9.047821 5 7 12.25192
## 46 6.463029 9.283498 4 5 11.85757
## 47 0.000000 9.287301 7 5 11.95119
## 48 6.997596 9.263123 5 7 12.45551
## 49 6.660575 9.388403 8 7 12.44115
## 50 0.000000 9.051813 4 4 11.15329
## 51 6.459904 9.260273 6 6 12.02182
## 52 0.000000 9.273315 6 5 11.75001
## 53 0.000000 9.413281 6 5 11.93765
## 54 0.000000 8.738735 5 8 12.30854
## 55 6.618739 9.173469 7 6 12.11598
## 56 6.925595 9.175749 5 8 12.49311
## 57 6.447306 9.495519 5 7 12.16613
## 58 0.000000 9.236398 5 7 12.32441
## 59 0.000000 9.632728 5 8 12.44955
## 60 6.775366 9.088173 6 7 11.94560
## 61 0.000000 9.190138 5 5 11.56135
## 62 0.000000 9.312897 6 6 12.02902
## 63 0.000000 8.987197 6 5 11.85467
## 64 0.000000 9.287301 6 5 11.70643
## 65 0.000000 8.889033 5 5 11.68386
## 66 0.000000 9.559235 8 6 12.16560
## 67 6.376727 8.699515 6 6 11.75539
## 68 0.000000 8.878497 6 6 11.89058
## 69 6.437752 9.088173 7 6 11.80915
## 70 0.000000 8.840870 5 5 11.69240
## 71 6.553933 9.534595 5 5 12.08568
## 72 0.000000 9.239414 6 4 11.69586
## 73 6.469250 9.101529 6 6 11.78788
## 74 0.000000 9.401622 4 4 11.72889
## 75 6.629363 8.005701 5 6 11.98696
## 76 0.000000 9.210340 6 5 11.91769
## 77 0.000000 8.853665 6 5 11.45470
## 78 0.000000 7.330405 8 4 11.36329
## 79 0.000000 9.121509 5 6 11.99169
## 80 0.000000 8.238008 5 8 12.13350
## 81 0.000000 9.076809 5 7 12.22431
## 82 0.000000 9.209340 5 4 12.05283
## 83 0.000000 9.495519 7 5 11.81808
## 84 0.000000 9.317220 5 9 12.86428
## 85 6.774224 10.880064 5 6 12.45024
## 86 0.000000 9.455011 8 6 11.99804
## 87 0.000000 7.293018 6 4 11.24324
## 88 0.000000 7.307202 6 4 11.25340
## 89 0.000000 9.186355 5 7 12.36249
## 90 6.214608 9.271624 3 5 11.42890
## 91 6.643790 9.249561 6 7 12.34504
## 92 6.658011 9.249561 5 6 12.04188
## 93 0.000000 9.517825 6 5 11.79815
## 94 6.886532 9.287301 8 7 12.21896
## 95 0.000000 8.812546 5 8 12.29053
## 96 5.808142 9.169518 7 5 11.83018
## 97 0.000000 9.058703 6 4 11.56116
## 98 0.000000 8.949365 8 6 11.98936
## 99 0.000000 10.138006 5 4 11.75399
## 100 6.626718 8.940105 5 7 12.20216
## 101 6.368187 8.836665 7 6 11.74007
## 102 0.000000 9.354960 9 5 11.98861
## 103 0.000000 8.551595 8 5 11.67568
## 104 5.937536 8.546752 7 4 11.37983
## 105 0.000000 9.254740 6 6 11.89190
## 106 0.000000 9.002701 5 6 12.21204
## 107 0.000000 9.323848 5 8 12.38212
## 108 0.000000 9.323669 3 5 11.76553
## 109 0.000000 9.901385 8 6 12.46544
## 110 6.431331 9.305469 5 5 11.81700
## 111 6.846943 9.076695 5 7 12.33293
## 112 6.727432 9.274910 6 7 12.29262
## 113 6.698268 9.370502 7 6 12.07226
## 114 0.000000 9.271247 5 7 12.11372
## 115 0.000000 9.035987 5 5 11.73011
## 116 0.000000 9.091219 5 4 11.69864
## 117 0.000000 9.249753 5 7 12.20616
## 118 0.000000 9.035987 5 4 11.57904
## 119 6.848005 9.506734 5 7 12.36002
## 120 0.000000 8.641886 5 8 12.40902
## 121 0.000000 8.924523 7 5 11.98819
## 122 0.000000 9.248503 5 8 12.57086
## 123 6.291569 8.827761 7 6 11.78379
## 124 5.609472 8.854808 8 4 11.26424
## 125 0.000000 8.839856 5 6 12.15117
## 126 0.000000 9.430359 5 8 12.47541
## 127 0.000000 9.311452 5 8 12.33673
## 128 0.000000 8.209308 5 6 11.90238
## 129 0.000000 8.719317 7 5 11.61675
## 130 6.572283 8.881836 7 6 12.02002
## 131 0.000000 9.059982 7 5 11.86217
## 132 0.000000 9.613336 5 8 12.40366
## 133 0.000000 9.310186 5 5 11.72872
## 134 0.000000 9.937551 5 7 12.33940
## 135 0.000000 9.525443 5 7 12.35128
## 136 6.714171 9.317759 5 8 12.46361
## 137 0.000000 9.215328 6 5 11.91108
## 138 6.823286 9.017968 7 6 11.99924
## 139 7.193686 9.411402 7 6 12.49075
## 140 0.000000 8.818186 6 5 11.44336
## 141 0.000000 8.636397 7 5 11.51882
## 142 0.000000 9.250522 5 4 11.93788
## 143 5.883322 8.600799 8 4 11.53367
## 144 0.000000 8.794825 5 5 11.59276
## 145 0.000000 9.214034 5 8 12.38922
## 146 0.000000 9.204121 5 7 12.31376
## 147 0.000000 9.267949 5 7 12.36587
## 148 0.000000 8.852665 7 5 11.88432
## 149 6.677083 8.875287 5 6 12.05380
## 150 0.000000 9.116030 6 5 11.60114
## 151 6.803505 8.529517 5 7 12.23627
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## 592 6.690842 7.657755 5 6 11.91834
## 593 0.000000 9.425452 7 6 12.03499
## 594 6.505784 7.305188 6 6 11.73567
## 595 0.000000 9.050289 5 5 11.63859
## 596 0.000000 9.386560 5 8 12.41492
## 597 6.883463 9.076809 5 7 12.24382
## 598 6.694562 9.076809 5 7 12.27383
## 599 6.944087 9.521788 5 9 12.76593
## 600 0.000000 9.601098 5 8 12.54405
## 601 0.000000 8.961879 7 5 11.73227
## 602 0.000000 9.434923 7 5 11.87014
## 603 0.000000 9.246383 5 9 12.60338
## 604 0.000000 8.996157 5 5 11.79531
## 605 0.000000 9.230633 5 5 11.69571
## 606 0.000000 9.251962 5 5 11.73815
## 607 0.000000 9.169518 6 5 11.76091
## 608 0.000000 9.094930 6 6 11.91044
## 609 6.736967 9.031931 5 6 12.13818
## 610 6.505784 9.047821 4 4 11.41710
## 611 0.000000 9.351406 5 4 11.36927
## 612 0.000000 9.116030 5 7 12.28775
## 613 7.223296 9.323490 5 9 12.66691
## 614 6.329721 8.699515 7 5 11.77315
## 615 6.628041 9.127611 5 6 12.10317
## 616 0.000000 8.948976 7 5 11.79801
## 617 6.593045 8.080237 5 6 11.92901
## 618 6.490724 8.699515 7 6 11.96475
## 619 0.000000 9.501741 5 5 11.96981
## 620 7.018402 9.420115 5 8 12.49985
## 621 0.000000 9.725377 5 9 12.72826
## 622 0.000000 9.337678 7 7 12.33835
## 623 6.049733 8.738735 8 5 11.74536
## 624 0.000000 8.362175 5 7 12.19140
## 625 0.000000 9.072457 7 5 11.97304
## 626 6.721426 9.097731 5 7 12.23799
## 627 0.000000 9.492884 5 8 12.49740
## 628 0.000000 8.699515 7 6 11.66442
## 629 5.786897 8.961879 7 5 11.66680
## 630 0.000000 9.098738 5 5 11.94796
## 631 0.000000 9.227787 5 7 12.22104
## 632 6.526495 8.125039 8 7 11.94137
## 633 0.000000 9.211340 5 5 11.99307
## 634 6.529419 9.079434 5 6 12.10722
## 635 5.983936 8.685078 9 5 11.51472
## 636 0.000000 9.328035 5 6 12.05352
## 637 0.000000 9.360655 6 5 11.74150
## 638 0.000000 9.045466 6 5 11.55836
## 639 0.000000 9.230731 5 8 12.43813
## 640 0.000000 9.710631 6 6 12.35820
## 641 6.322565 9.169518 8 6 12.12147
## 642 0.000000 8.811354 5 6 11.96052
## 643 0.000000 9.416134 6 7 12.13158
## 644 7.175490 9.307921 5 8 12.63919
## 645 5.733341 9.120744 7 5 11.48672
## 646 0.000000 9.291552 5 8 12.53059
## 647 0.000000 8.849371 5 4 11.62279
## 648 0.000000 8.952605 6 5 11.82683
## 649 7.003974 8.968396 5 6 12.18471
## 650 0.000000 8.463792 5 8 12.12530
## 651 0.000000 9.515469 5 5 11.86650
## 652 0.000000 9.261984 5 6 11.81917
## 653 0.000000 9.512369 6 5 11.76307
## 654 0.000000 8.517193 6 5 11.47815
## 655 0.000000 9.336180 6 5 11.95560
## 656 0.000000 7.297768 4 4 11.12863
## 657 0.000000 9.969743 5 5 11.83632
## 658 6.884487 8.988446 5 8 12.44897
## 659 6.952729 9.328123 5 7 12.30654
## 660 0.000000 9.229849 5 6 11.97836
## 661 0.000000 9.087834 5 8 12.40128
## 662 6.536692 9.075780 4 6 11.78243
## 663 6.755769 9.131838 5 7 12.30939
## 664 6.572283 8.937087 9 8 12.16325
## 665 6.720220 9.455167 5 7 12.28952
## 666 0.000000 8.669914 5 4 11.28011
## 667 6.408529 9.380168 7 5 11.98324
## 668 0.000000 8.888757 5 6 11.98305
## 669 6.508769 9.035987 5 7 12.17369
## 670 6.311735 7.887959 7 5 11.78792
## 671 0.000000 8.885026 5 5 11.72113
## 672 6.734592 9.547241 5 7 12.33954
## 673 0.000000 9.364262 5 7 12.36162
## 674 6.391917 9.059517 6 6 11.81969
## 675 6.716595 9.499646 6 7 12.18006
## 676 0.000000 9.421411 5 9 12.71818
## 677 6.575076 9.022323 7 5 11.96688
## 678 0.000000 8.962007 5 6 11.80530
## 679 0.000000 9.003070 7 6 11.87974
## 680 0.000000 9.050172 8 5 11.57481
## 681 0.000000 10.126631 4 5 12.04167
## 682 6.685861 9.264829 5 7 12.30397
## 683 0.000000 9.476697 6 5 11.81526
## 684 6.694562 9.331407 6 7 12.37669
## 685 6.961296 9.145802 5 7 12.32446
## 686 6.947937 9.270965 5 7 12.39138
## 687 6.248043 7.538495 6 6 11.66271
## 688 6.580639 8.584852 8 7 11.91608
## 689 0.000000 9.798127 4 3 11.39144
## 690 6.023448 8.923458 8 5 11.67773
## 691 0.000000 8.847935 6 4 11.55775
## 692 0.000000 8.872067 6 5 11.68116
## 693 6.224558 7.426549 5 6 11.53333
## 694 6.993933 9.673823 5 7 12.46197
## 695 0.000000 9.116030 5 5 11.75950
## 696 0.000000 8.853665 5 5 11.66535
## 697 0.000000 9.016756 6 6 11.95591
## 698 6.274762 9.529376 5 7 12.27937
## 699 7.108244 9.450931 5 8 12.62261
## 700 0.000000 8.987197 5 5 11.68380
## 701 0.000000 9.360913 7 5 11.83280
## 702 0.000000 9.343559 6 5 11.78418
## 703 6.739337 9.096500 5 7 12.24514
## 704 0.000000 9.287301 5 3 11.10246
## 705 0.000000 8.987197 5 5 11.73606
## 706 0.000000 8.922658 5 7 12.18231
## 707 0.000000 9.400547 6 6 12.10018
## 708 0.000000 8.885579 6 6 11.69624
## 709 0.000000 9.719985 5 5 12.14182
## 710 6.668228 9.117018 5 7 12.16034
## 711 0.000000 9.335474 5 6 11.89812
## 712 7.009409 9.372799 7 8 12.61764
## 713 0.000000 9.419628 5 6 11.89258
## 714 0.000000 8.818778 5 5 11.60283
## 715 0.000000 8.881836 5 5 11.66696
## 716 0.000000 9.523178 5 5 12.05473
## 717 6.765039 9.328123 5 7 12.30953
## 718 6.778785 9.366489 5 8 12.38732
## 719 6.786717 9.076695 5 7 12.25760
## 720 0.000000 9.052985 6 5 11.87822
## 721 6.673298 9.004423 5 6 12.02814
## 722 6.679599 9.720706 7 7 12.51328
## 723 0.000000 8.988446 9 6 11.98252
## 724 6.803505 9.359880 5 6 12.19815
## 725 6.621406 9.157678 5 6 12.16115
## 726 6.951772 9.336092 6 4 11.71081
## 727 6.313548 8.537976 5 7 11.96523
## 728 0.000000 9.224243 6 5 11.85361
## 729 7.039660 9.392579 5 8 12.54863
## 730 0.000000 8.541300 5 6 12.12999
## 731 6.520621 9.162725 5 6 12.12405
## 732 6.812345 9.254549 6 7 12.18596
## 733 6.839476 9.118225 6 6 12.12250
## 734 0.000000 9.181941 7 5 11.87518
## 735 0.000000 9.285448 5 5 11.73320
## 736 0.000000 8.827615 5 8 12.35282
## 737 6.562444 8.955448 5 7 12.12149
## 738 0.000000 8.065265 5 8 12.18647
## 739 0.000000 8.260751 6 5 11.78767
## 740 0.000000 9.076695 5 7 12.26336
## 741 0.000000 9.104980 6 6 11.88168
## 742 0.000000 8.594154 7 5 11.62594
## 743 0.000000 9.262268 6 6 11.88244
## 744 0.000000 8.083946 5 7 12.15757
## 745 6.144186 7.426549 5 6 11.50621
## 746 0.000000 8.897682 6 5 11.79464
## 747 6.762730 9.139167 5 7 12.27617
## 748 6.352629 9.383032 5 8 12.45118
## 749 0.000000 9.400878 6 5 12.07209
## 750 0.000000 9.311723 4 2 11.06348
## 751 0.000000 8.719317 6 5 11.37370
## 752 0.000000 9.345483 5 8 12.58727
## 753 0.000000 8.939319 8 5 11.85299
## 754 0.000000 9.279960 6 6 11.98151
## 755 6.758095 8.922658 5 7 12.21098
## 756 0.000000 9.365376 4 5 11.69952
## 757 6.863803 9.437635 5 7 12.38843
## 758 0.000000 9.973620 5 6 11.98911
## 759 0.000000 9.491979 5 7 12.38260
## 760 0.000000 9.442642 7 6 12.30388
## 761 0.000000 8.517193 3 1 10.28874
## 762 6.580639 9.143132 6 5 11.83238
## 763 0.000000 9.559235 5 5 11.91192
## 764 0.000000 9.205026 5 7 12.11595
## 765 6.311735 8.399985 5 7 11.93014
## 766 0.000000 9.211040 7 5 11.83105
## 767 0.000000 9.371694 6 6 12.31018
## 768 0.000000 8.211754 5 7 12.25045
## 769 0.000000 9.079434 5 6 12.19842
## 770 6.693324 8.833171 4 6 11.64592
## 771 0.000000 8.030084 5 7 12.15796
## 772 7.072422 9.265775 8 8 12.52375
## 773 0.000000 9.570111 6 5 12.15564
## 774 6.639876 9.511555 6 6 11.96703
## 775 0.000000 9.116030 4 5 11.61864
## 776 0.000000 8.922658 5 5 11.68750
## 777 0.000000 9.477922 5 6 11.99944
## 778 6.770789 10.307585 6 7 12.48694
## 779 0.000000 8.999619 8 5 11.74612
## 780 0.000000 8.746875 6 6 11.57013
## 781 0.000000 9.480444 5 5 11.95977
## 782 0.000000 9.077951 5 8 12.38833
## 783 0.000000 9.508369 5 10 12.90522
## 784 0.000000 8.253228 6 8 12.20884
## 785 7.057037 9.126959 5 8 12.56067
## 786 0.000000 9.127393 5 5 11.77346
## 787 0.000000 9.562194 5 5 11.88824
## 788 0.000000 8.839277 6 5 11.49753
## 789 7.131699 9.386728 7 8 12.66107
## 790 0.000000 8.856518 5 7 12.21387
## 791 6.519147 7.880426 5 8 12.11759
## 792 0.000000 9.017968 7 5 11.82278
## 793 0.000000 10.029768 5 5 12.05723
## 794 6.533789 9.118225 6 7 11.99926
## 795 7.390181 9.380505 5 7 12.45060
## 796 6.629363 9.156940 7 5 11.92047
## 797 6.398595 8.747034 7 7 11.93551
## 798 6.799056 9.024493 5 6 12.17961
## 799 0.000000 8.881836 8 5 11.77673
## 800 6.548219 9.561701 7 6 12.06789
## 801 7.000334 9.524275 5 9 12.77682
## 802 6.814543 9.310186 5 7 12.29665
## 803 0.000000 9.365548 5 5 11.99758
## 804 6.755769 9.551587 5 6 12.17676
## 805 0.000000 9.225426 5 5 11.70221
## 806 0.000000 9.049702 6 4 11.71573
## 807 0.000000 9.166493 5 5 11.75108
## 808 6.447306 9.169518 8 5 11.84444
## 809 0.000000 9.274160 6 5 11.78813
## 810 0.000000 8.976768 7 6 11.99805
## 811 0.000000 8.867005 5 5 11.59831
## 812 0.000000 9.250522 8 3 11.38906
## 813 0.000000 9.177301 6 5 11.72238
## 814 0.000000 8.879055 7 5 11.71876
## 815 6.475433 9.287301 4 5 11.82822
## 816 6.137727 8.554489 5 7 11.72489
## 817 0.000000 10.227381 7 7 12.49172
## 818 6.304449 7.549609 4 4 11.31800
## 819 0.000000 8.065265 5 7 12.20278
## 820 0.000000 9.087721 5 5 11.80586
## 821 6.568078 9.002209 5 6 12.13375
## 822 7.177782 9.082507 7 6 12.16806
## 823 0.000000 9.230143 5 6 12.02297
## 824 0.000000 9.035987 6 5 11.68666
## 825 6.569481 9.016513 5 6 12.06649
## 826 0.000000 8.560253 3 5 11.34805
## 827 6.576470 9.992963 5 7 12.24446
## 828 0.000000 9.587749 6 6 12.10150
## 829 6.923629 9.374753 5 7 12.47992
## 830 0.000000 8.395252 5 6 11.83721
## 831 6.536692 9.144628 7 6 11.96268
## 832 0.000000 8.927977 6 6 11.85823
## .se.fit .resid .hat .sigma .cooksd
## 1 0.011005683 0.0811725699 0.008392862 0.1201723 4.329950e-04
## 2 0.009795475 0.0975082292 0.006648551 0.1201575 4.932161e-04
## 3 0.014717096 -0.0303643419 0.015007912 0.1202012 1.098035e-04
## 4 0.014696048 0.1888113912 0.014965014 0.1200227 4.233151e-03
## 5 0.010566211 -0.0424476480 0.007735966 0.1201968 1.089936e-04
## 6 0.029394685 0.1409176054 0.059870607 0.1200990 1.035625e-02
## 7 0.011577096 -0.0039649350 0.009286997 0.1202059 1.145210e-06
## 8 0.011356814 0.0328013142 0.008936944 0.1202005 7.537069e-05
## 9 0.010464398 -0.0529868593 0.007587603 0.1201916 1.665291e-04
## 10 0.010190111 -0.0178641052 0.007195051 0.1202043 1.793503e-05
## 11 0.011921775 -0.0474442584 0.009848224 0.1201945 1.740825e-04
## 12 0.010031716 -0.1072970004 0.006973109 0.1201473 6.267771e-04
## 13 0.007575660 -0.0153991368 0.003976647 0.1202048 7.318200e-06
## 14 0.007905604 -0.0273316057 0.004330581 0.1202022 2.512347e-05
## 15 0.008846359 -0.1107868662 0.005422570 0.1201435 5.180099e-04
## 16 0.018151492 -0.0118680625 0.022829727 0.1202052 2.592707e-05
## 17 0.010433575 -0.0389904162 0.007542968 0.1201982 8.963304e-05
## 18 0.007791584 -0.1632493261 0.004206565 0.1200705 8.704130e-04
## 19 0.008547491 -0.1638251313 0.005062363 0.1200694 1.056711e-03
## 20 0.020426768 -0.2629180642 0.028911816 0.1198452 1.631670e-02
## 21 0.019875785 0.3711324641 0.027373139 0.1194872 3.068482e-02
## 22 0.015348205 0.1131744750 0.016322672 0.1201400 1.663476e-03
## 23 0.010128873 -0.1697312548 0.007108833 0.1200590 1.599382e-03
## 24 0.014592371 0.1683883316 0.014754611 0.1200602 3.318153e-03
## 25 0.008412164 -0.1314356829 0.004903334 0.1201181 6.585990e-04
## 26 0.016266923 0.1425469367 0.018335252 0.1201012 2.976527e-03
## 27 0.012473538 -0.1974602482 0.010780908 0.1200063 3.307221e-03
## 28 0.010278460 -0.0172010563 0.007320355 0.1202044 1.692223e-05
## 29 0.011125573 0.2356213139 0.008576712 0.1199223 3.729626e-03
## 30 0.007840545 0.0870363818 0.004259597 0.1201675 2.505598e-04
## 31 0.008772265 0.0239498532 0.005332115 0.1202030 2.380031e-05
## 32 0.008593403 -0.0749123805 0.005116893 0.1201774 2.233588e-04
## 33 0.017274031 0.0748113037 0.020675852 0.1201770 9.289203e-04
## 34 0.009046801 -0.0314922929 0.005671084 0.1202009 4.379737e-05
## 35 0.007922101 0.0501117645 0.004348673 0.1201932 8.481158e-05
## 36 0.012830878 0.0030975545 0.011407456 0.1202059 8.622349e-07
## 37 0.008285146 -0.1061095788 0.004756379 0.1201487 4.162558e-04
## 38 0.010103845 -0.0291547775 0.007073745 0.1202016 4.695355e-05
## 39 0.007204052 0.0699700726 0.003596083 0.1201811 1.365265e-04
## 40 0.016156470 0.0895593399 0.018087103 0.1201646 1.158453e-03
## 41 0.010263785 -0.0573481424 0.007299467 0.1201892 1.875542e-04
## 42 0.011710354 -0.0485840733 0.009502023 0.1201939 1.760071e-04
## 43 0.011593019 0.0704725471 0.009312561 0.1201806 3.628017e-04
## 44 0.013451337 0.0076795933 0.012537385 0.1202057 5.838155e-06
## 45 0.008080108 -0.1534309964 0.004523872 0.1200862 8.273864e-04
## 46 0.011874177 -0.0081771556 0.009769742 0.1202056 5.129190e-06
## 47 0.008946910 -0.0228451273 0.005546541 0.1202033 2.253585e-05
## 48 0.010432834 0.2841234514 0.007541898 0.1197936 4.758871e-03
## 49 0.014002381 -0.0738072802 0.013585632 0.1201780 5.855891e-04
## 50 0.015292194 0.0311360543 0.016203755 0.1202010 1.249586e-04
## 51 0.007406041 -0.0771127365 0.003800566 0.1201757 1.753240e-04
## 52 0.010084409 0.0113328339 0.007046557 0.1202053 7.066913e-06
## 53 0.008070733 0.0327039120 0.004513381 0.1202005 3.750284e-05
## 54 0.010219622 0.1365534143 0.007236785 0.1201109 1.054127e-03
## 55 0.013858135 -0.0783296528 0.013307168 0.1201745 6.456656e-04
## 56 0.009220777 0.0653830653 0.005891299 0.1201842 1.962038e-04
## 57 0.013154765 -0.0407203008 0.011990636 0.1201975 1.568107e-04
## 58 0.007748307 -0.0506770501 0.004159965 0.1201929 8.294051e-05
## 59 0.010913774 0.1033723147 0.008253268 0.1201514 6.903454e-04
## 60 0.013446692 -0.0680357630 0.012528727 0.1201822 4.578952e-04
## 61 0.011623830 -0.4414629386 0.009362128 0.1192063 1.431419e-02
## 62 0.006743087 -0.1240552270 0.003150602 0.1201278 3.756627e-04
## 63 0.007711067 0.1219943912 0.004120074 0.1201303 4.759971e-04
## 64 0.010716443 -0.0111825482 0.007957513 0.1202053 7.784521e-06
## 65 0.008619201 0.1284309131 0.005147663 0.1201220 6.604889e-04
## 66 0.016394254 -0.0374936359 0.018623418 0.1201987 2.092843e-04
## 67 0.011413506 0.0389528352 0.009026391 0.1201982 1.073746e-04
## 68 0.008329098 0.0954673561 0.004806977 0.1201596 3.405655e-04
## 69 0.010886676 0.2045540484 0.008212334 0.1199923 2.689546e-03
## 70 0.013162862 -0.1794787670 0.012005401 0.1200409 3.050192e-03
## 71 0.013315315 0.0685773862 0.012285107 0.1201819 4.559436e-04
## 72 0.010313369 -0.0705034313 0.007370164 0.1201806 2.862573e-04
## 73 0.012305134 0.0966069127 0.010491769 0.1201582 7.699453e-04
## 74 0.014569368 -0.0504451180 0.014708131 0.1201929 2.968243e-04
## 75 0.013753817 0.0327835787 0.013107579 0.1202004 1.113600e-04
## 76 0.008007164 -0.0127186488 0.004442562 0.1202051 5.582341e-06
## 77 0.027598332 0.0481706569 0.052776639 0.1201936 1.050838e-03
## 78 0.019058430 -0.0011878834 0.025168092 0.1202059 2.877213e-07
## 79 0.007767417 0.0220089279 0.004180511 0.1202035 1.572170e-05
## 80 0.014941760 0.1284831631 0.015469616 0.1201211 2.028370e-03
## 81 0.007782386 0.0305552311 0.004196638 0.1202012 3.041999e-05
## 82 0.016748470 0.2864658594 0.019436870 0.1197817 1.277187e-02
## 83 0.010155342 -0.0275199060 0.007146036 0.1202021 4.226899e-05
## 84 0.015921800 0.1919471683 0.017565494 0.1200160 5.162381e-03
## 85 0.019714250 -0.0618467855 0.026930012 0.1201861 8.375605e-04
## 86 0.012641829 -0.0696981982 0.011073779 0.1201811 4.234915e-04
## 87 0.016561404 -0.0450256754 0.019005109 0.1201955 3.082413e-04
## 88 0.016550649 -0.0215124837 0.018980432 0.1202036 7.026926e-05
## 89 0.013764778 0.3443546511 0.013128480 0.1195964 1.230662e-02
## 90 0.018309795 0.1563438290 0.023229669 0.1200793 4.581979e-03
## 91 0.008288016 -0.2169269673 0.004759674 0.1199665 1.740932e-03
## 92 0.008624920 -0.0272737766 0.005154496 0.1202022 2.982628e-05
## 93 0.008096584 -0.0620811090 0.004542340 0.1201864 1.360149e-04
## 94 0.019847610 -0.2391582755 0.027295590 0.1199080 1.270384e-02
## 95 0.010160989 -0.1870457100 0.007153984 0.1200275 1.954849e-03
## 96 0.011756613 0.1527455082 0.009577243 0.1200867 1.753758e-03
## 97 0.009300322 0.0380176553 0.005993382 0.1201986 6.749904e-05
## 98 0.013042774 -0.0511688505 0.011787344 0.1201925 2.433100e-04
## 99 0.013374351 0.0384607573 0.012394285 0.1201984 1.447183e-04
## 100 0.009218252 -0.0745865209 0.005888073 0.1201776 2.551860e-04
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## 564 0.015203249 0.0019600720 0.016015808 0.1202059 4.892718e-07
## 565 0.009074274 0.1089751470 0.005705580 0.1201455 5.276650e-04
## 566 0.010781648 -0.0163057152 0.008054644 0.1202046 1.675653e-05
## 567 0.010584875 0.2147295119 0.007763320 0.1199706 2.799200e-03
## 568 0.013897502 0.0260005001 0.013382878 0.1202025 7.155651e-05
## 569 0.018441322 0.0601151460 0.023564604 0.1201872 6.876611e-04
## 570 0.007599773 -0.0640103695 0.004002002 0.1201851 1.272608e-04
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## 573 0.009906308 0.0685637227 0.006799856 0.1201820 2.494873e-04
## 574 0.007791030 0.1043454703 0.004205967 0.1201506 3.555556e-04
## 575 0.008505841 0.0511230798 0.005013148 0.1201927 1.018928e-04
## 576 0.009974221 0.0233671636 0.006893408 0.1202032 2.938244e-05
## 577 0.013191958 0.0372649081 0.012058535 0.1201988 1.320887e-04
## 578 0.015058052 0.1405827605 0.015711354 0.1201043 2.467552e-03
## 579 0.015550524 -0.1570492862 0.016755836 0.1200790 3.291159e-03
## 580 0.009617102 -0.0274002665 0.006408620 0.1202021 3.752252e-05
## 581 0.010737770 -0.1289647227 0.007989218 0.1201211 1.039554e-03
## 582 0.009349581 -0.1489155520 0.006057039 0.1200930 1.046770e-03
## 583 0.008746247 -0.0131366267 0.005300532 0.1202051 7.117655e-06
## 584 0.012921735 -0.1215386887 0.011569582 0.1201303 1.346753e-03
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## 587 0.008453559 -0.1150139122 0.004951710 0.1201387 5.093322e-04
## 588 0.010257581 -0.1174599397 0.007290646 0.1201356 7.858413e-04
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## 590 0.008752206 0.0595144475 0.005307758 0.1201879 1.462891e-04
## 591 0.012397903 0.0246815683 0.010650562 0.1202028 5.103312e-05
## 592 0.014592371 0.1655674553 0.014754611 0.1200651 3.207912e-03
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## 596 0.009800242 -0.0778145123 0.006655025 0.1201751 3.144157e-04
## 597 0.009300122 0.0110421381 0.005993125 0.1202053 5.693961e-06
## 598 0.011323367 -0.1138057623 0.008884382 0.1201398 9.018631e-04
## 599 0.011723003 0.1773018461 0.009522562 0.1200452 2.349225e-03
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## 601 0.010160513 0.0430204089 0.007153315 0.1201965 1.034012e-04
## 602 0.009984667 -0.0243212542 0.006907855 0.1202029 3.189845e-05
## 603 0.012386718 0.1185049207 0.010631353 0.1201341 1.174299e-03
## 604 0.009792673 0.0397024334 0.006644748 0.1201979 8.172165e-05
## 605 0.008481112 0.1136118348 0.004984041 0.1201403 5.002674e-04
## 606 0.007886237 0.0599498429 0.004309389 0.1201877 1.202753e-04
## 607 0.007274651 -0.0288530425 0.003666911 0.1202017 2.367599e-05
## 608 0.007260862 0.0693634265 0.003653023 0.1201815 1.363094e-04
## 609 0.010123159 -0.0771300047 0.007100815 0.1201756 3.298968e-04
## 610 0.014166732 -0.8204647960 0.013906421 0.1167004 7.411951e-02
## 611 0.026938878 -0.0794922648 0.050284604 0.1201723 2.712260e-03
## 612 0.007808653 0.0795923032 0.004225016 0.1201738 2.078172e-04
## 613 0.012063423 0.0246681704 0.010083637 0.1202028 4.820894e-05
## 614 0.009213463 -0.0017166506 0.005881957 0.1202059 1.350340e-07
## 615 0.008217846 -0.0136270845 0.004679420 0.1202050 6.753136e-06
## 616 0.009590655 -0.0460671732 0.006373420 0.1201951 1.054734e-04
## 617 0.011507939 0.1291429290 0.009176375 0.1201207 1.200199e-03
## 618 0.009607348 0.0483478157 0.006395626 0.1201941 1.165852e-04
## 619 0.008424816 0.0131168904 0.004918095 0.1202051 6.579223e-06
## 620 0.010504735 -0.0518114384 0.007646210 0.1201923 1.604715e-04
## 621 0.012498264 -0.0679290888 0.010823692 0.1201823 3.929824e-04
## 622 0.009751516 -0.2102340344 0.006589012 0.1199806 2.271967e-03
## 623 0.012831004 0.0451996993 0.011407680 0.1201955 1.835978e-04
## 624 0.010678354 -0.0055251889 0.007901048 0.1202058 1.886698e-06
## 625 0.011237731 -0.0348471703 0.008750509 0.1201998 8.325991e-05
## 626 0.008975224 -0.0572382908 0.005581702 0.1201893 1.423755e-04
## 627 0.009552009 0.0124763877 0.006322160 0.1202052 7.673359e-06
## 628 0.011918585 0.0224594287 0.009842954 0.1202034 3.898955e-05
## 629 0.009559836 0.0276181834 0.006332526 0.1202021 3.766332e-05
## 630 0.012389925 -0.2199252785 0.010636859 0.1199583 4.046558e-03
## 631 0.007863055 -0.1687044937 0.004284091 0.1200612 9.468356e-04
## 632 0.014201191 -0.1283366440 0.013974156 0.1201214 1.822569e-03
## 633 0.010750919 0.0504802227 0.008008796 0.1201930 1.596716e-04
## 634 0.009173531 -0.0695638085 0.005831082 0.1201813 2.198007e-04
## 635 0.016290452 -0.0530885344 0.018388331 0.1201914 4.140930e-04
## 636 0.007928619 0.0332014605 0.004355832 0.1202004 3.729158e-05
## 637 0.008586090 -0.1797835233 0.005108188 0.1200414 1.284247e-03
## 638 0.009197630 0.0767827520 0.005861759 0.1201759 2.692125e-04
## 639 0.009674295 -0.0291127351 0.006485070 0.1202016 4.287118e-05
## 640 0.014120386 -0.2034181502 0.013815582 0.1199934 4.525492e-03
## 641 0.011341301 -0.2720737720 0.008912546 0.1198274 5.171121e-03
## 642 0.016581155 -0.1111232758 0.019050466 0.1201422 1.882157e-03
## 643 0.009214633 -0.0533375546 0.005883451 0.1201915 1.303939e-04
## 644 0.011606950 0.0797108082 0.009334955 0.1201735 4.652930e-04
## 645 0.014255824 0.1572317737 0.014081882 0.1200790 2.757358e-03
## 646 0.015235022 0.1579059873 0.016082820 0.1200777 3.189157e-03
## 647 0.010084266 0.1447790667 0.007046356 0.1200991 1.153325e-03
## 648 0.007348603 -0.0324952948 0.003741843 0.1202006 3.064900e-05
## 649 0.010934904 0.1006357916 0.008285258 0.1201543 6.568572e-04
## 650 0.012121225 -0.0135418331 0.010180500 0.1202050 1.467052e-05
## 651 0.011171879 0.0911101868 0.008648255 0.1201636 5.623936e-04
## 652 0.010256865 0.0531732391 0.007289627 0.1201915 1.610200e-04
## 653 0.009784660 0.0646659050 0.006633879 0.1201847 2.164378e-04
## 654 0.009237627 -0.1044905062 0.005912851 0.1201504 5.029620e-04
## 655 0.008246575 -0.2479346987 0.004712195 0.1198930 2.251303e-03
## 656 0.017831636 0.1611526263 0.022032229 0.1200715 4.605934e-03
## 657 0.029470801 -0.0533656883 0.060181073 0.1201906 1.493927e-03
## 658 0.009199164 0.1658947418 0.005863714 0.1200658 1.257129e-03
## 659 0.009316012 0.0692787031 0.006013622 0.1201815 2.249098e-04
## 660 0.007563302 0.0231444587 0.003963684 0.1202032 1.647693e-05
## 661 0.009851602 0.0671568123 0.006724961 0.1201830 2.366815e-04
## 662 0.011700122 -0.1472892626 0.009485425 0.1200951 1.614770e-03
## 663 0.009099357 -0.0380008325 0.005737166 0.1201986 6.452304e-05
## 664 0.018225844 0.1869188885 0.023017138 0.1200249 6.486603e-03
## 665 0.010402284 -0.1216734589 0.007497793 0.1201305 8.675524e-04
## 666 0.013270321 0.0084188319 0.012202222 0.1202056 6.824016e-06
## 667 0.010704411 -0.2156738225 0.007939654 0.1199685 2.889042e-03
## 668 0.007831938 0.0366968646 0.004250250 0.1201991 4.444322e-05
## 669 0.008860073 -0.0241841767 0.005439396 0.1202030 2.476192e-05
## 670 0.016022619 -0.0164884133 0.017788652 0.1202046 3.859441e-05
## 671 0.012778704 0.1029518875 0.011314873 0.1201517 9.445737e-04
## 672 0.010313151 -0.1716869847 0.007369853 0.1200556 1.697431e-03
## 673 0.007892357 0.0676000657 0.004316080 0.1201827 1.531702e-04
## 674 0.008890468 -0.1286186187 0.005476780 0.1201218 7.052395e-04
## 675 0.010704798 -0.1365095135 0.007940228 0.1201109 1.157488e-03
## 676 0.012147807 0.1909947904 0.010225200 0.1200193 2.931404e-03
## 677 0.011655791 -0.0028767572 0.009413682 0.1202059 6.112443e-07
## 678 0.008786193 -0.2531507638 0.005349060 0.1198795 2.667646e-03
## 679 0.009338277 -0.0967881515 0.006042401 0.1201583 4.411149e-04
## 680 0.012430903 -0.0669008774 0.010707335 0.1201831 3.769893e-04
## 681 0.013887931 -0.1710735530 0.013364451 0.1200558 3.093406e-03
## 682 0.008239345 0.0840049373 0.004703937 0.1201701 2.579883e-04
## 683 0.008383310 -0.1127526121 0.004869755 0.1201413 4.813201e-04
## 684 0.008755054 -0.0373961369 0.005311213 0.1201988 5.779713e-05
## 685 0.009130265 0.0639305121 0.005776207 0.1201852 1.838757e-04
## 686 0.009454639 0.1653518190 0.006193926 0.1200667 1.320122e-03
## 687 0.013977517 0.0029377446 0.013537425 0.1202059 9.243500e-07
## 688 0.014578848 -0.1255212269 0.014727278 0.1201250 1.840253e-03
## 689 0.015866825 -0.0892315398 0.017444404 0.1201649 1.107675e-03
## 690 0.011595393 -0.0337748262 0.009316375 0.1202001 8.336750e-05
## 691 0.010440875 0.1416516867 0.007553528 0.1201036 1.184712e-03
## 692 0.007519413 0.0941248248 0.003917815 0.1201609 2.693367e-04
## 693 0.015060029 0.0130334263 0.015715480 0.1202051 2.121471e-05
## 694 0.010152329 -0.0529565643 0.007141795 0.1201917 1.564250e-04
## 695 0.007579095 -0.0642534394 0.003980254 0.1201850 1.275267e-04
## 696 0.008387989 0.0626855190 0.004875192 0.1201860 1.489377e-04
## 697 0.007038899 -0.3476789517 0.003433092 0.1195906 3.217088e-03
## 698 0.009153740 -0.1378333216 0.005805949 0.1201092 8.591576e-04
## 699 0.010080430 0.0751062495 0.007040997 0.1201772 3.101396e-04
## 700 0.008150371 0.0594387113 0.004602892 0.1201880 1.263602e-04
## 701 0.012514114 0.0094266300 0.010851162 0.1202055 7.587512e-06
## 702 0.007771137 0.0435589610 0.004184516 0.1201963 6.164190e-05
## 703 0.008433689 -0.1009430156 0.004928460 0.1201541 3.904709e-04
## 704 0.017980656 0.1683965082 0.022402015 0.1200591 5.117598e-03
## 705 0.007701055 0.0989463405 0.004109382 0.1201562 3.123102e-04
## 706 0.008086074 -0.0541986896 0.004530556 0.1201910 1.033967e-04
## 707 0.006870705 -0.1298323709 0.003270986 0.1201203 4.272913e-04
## 708 0.009964311 -0.1297734825 0.006879717 0.1201201 9.044246e-04
## 709 0.011452791 -0.0924022524 0.009088635 0.1201623 6.084539e-04
## 710 0.009139365 -0.0376537799 0.005787728 0.1201987 6.391467e-05
## 711 0.008938357 -0.0012923595 0.005535941 0.1202059 7.198027e-08
## 712 0.012015965 -0.0400013852 0.010004454 0.1201978 1.257507e-04
## 713 0.009679031 0.1503810430 0.006491422 0.1200907 1.145028e-03
## 714 0.009270490 0.1724595475 0.005954995 0.1200545 1.379994e-03
## 715 0.007801651 0.0529809777 0.004217442 0.1201917 9.191652e-05
## 716 0.011015906 -0.1778524084 0.008408460 0.1200444 2.082590e-03
## 717 0.009226603 0.0076370451 0.005898746 0.1202057 2.680296e-06
## 718 0.010733027 -0.1468488167 0.007982160 0.1200959 1.346654e-03
## 719 0.008778420 -0.0590592448 0.005339600 0.1201882 1.449334e-04
## 720 0.007433536 0.0358228316 0.003828837 0.1201994 3.811995e-05
## 721 0.009236700 -0.0144438808 0.005911664 0.1202049 9.608622e-06
## 722 0.012232410 -0.1459369483 0.010368122 0.1200970 1.735868e-03
## 723 0.014735563 -0.1084290439 0.015045601 0.1201455 1.403790e-03
## 724 0.009885721 -0.0342048448 0.006771622 0.1202000 6.183057e-05
## 725 0.009776760 -0.0222891392 0.006623171 0.1202034 2.567190e-05
## 726 0.018241051 0.0050569352 0.023055564 0.1202058 4.756027e-06
## 727 0.013136550 -0.0548733983 0.011957454 0.1201905 2.839518e-04
## 728 0.007786596 0.0878442270 0.004201181 0.1201667 2.517028e-04
## 729 0.010014770 0.0116175782 0.006949571 0.1202053 7.322850e-06
## 730 0.014384671 -0.0045860964 0.014337582 0.1202058 2.389678e-06
## 731 0.009462707 0.0592625823 0.006204500 0.1201881 1.698664e-04
## 732 0.010518632 0.2728129823 0.007666455 0.1198258 4.461109e-03
## 733 0.008581298 0.0056123882 0.005102488 0.1202058 1.250127e-06
## 734 0.010115676 0.1077494937 0.007090321 0.1201468 6.428511e-04
## 735 0.009399806 0.0611411721 0.006122290 0.1201869 1.783812e-04
## 736 0.014357576 -0.0884795826 0.014283620 0.1201658 8.860414e-04
## 737 0.010258418 -0.0432523734 0.007291835 0.1201964 1.065730e-04
## 738 0.013146592 -0.0212230738 0.011975741 0.1202036 4.254194e-05
## 739 0.010540368 -0.0123823037 0.007698172 0.1202052 9.228614e-06
## 740 0.007905104 -0.0981117152 0.004330033 0.1201570 3.236947e-04
## 741 0.009777269 -0.2421187749 0.006623861 0.1199070 3.029523e-03
## 742 0.009013140 0.0439879916 0.005628961 0.1201961 8.480727e-05
## 743 0.007941683 0.0847443366 0.004370198 0.1201695 2.437588e-04
## 744 0.012571423 0.0484985872 0.010950776 0.1201939 2.027220e-04
## 745 0.015278739 -0.1098233250 0.016175253 0.1201439 1.551809e-03
## 746 0.007508746 0.0547589234 0.003906707 0.1201907 9.089797e-05
## 747 0.009061822 -0.1213910321 0.005689932 0.1201309 6.529353e-04
## 748 0.009776211 0.0230064725 0.006622428 0.1202033 2.734778e-05
## 749 0.011723617 -0.1144777692 0.009523559 0.1201390 9.794603e-04
## 750 0.029518891 0.0653157030 0.060377637 0.1201830 2.246147e-03
## 751 0.027582270 -0.0677977455 0.052715223 0.1201814 2.078926e-03
## 752 0.010052018 0.2339853165 0.007001362 0.1199266 2.992926e-03
## 753 0.011463692 0.0349426949 0.009105945 0.1201997 8.718001e-05
## 754 0.006865296 -0.1179238142 0.003265838 0.1201353 3.519431e-04
## 755 0.008538522 0.0720535134 0.005051745 0.1201795 2.039784e-04
## 756 0.010645829 0.0204179698 0.007852989 0.1202038 2.560599e-05
## 757 0.009858794 0.0602015075 0.006734783 0.1201875 1.904765e-04
## 758 0.015570765 0.1116009425 0.016799483 0.1201418 1.666407e-03
## 759 0.008239856 0.0057910704 0.004704520 0.1202058 1.226203e-06
## 760 0.015002685 0.0969414752 0.015596028 0.1201576 1.164448e-03
## 761 0.031330599 0.2902413943 0.068016367 0.1197477 5.078660e-02
## 762 0.010051859 0.1347993650 0.007001141 0.1201133 9.933002e-04
## 763 0.008521168 0.2269446220 0.005031231 0.1199437 2.015249e-03
## 764 0.009033951 -0.0549050741 0.005654986 0.1201906 1.327443e-04
## 765 0.013273388 -0.0879080745 0.012207863 0.1201664 7.443884e-04
## 766 0.008658105 0.0568860645 0.005194236 0.1201895 1.307647e-04
## 767 0.010600604 -0.1554054760 0.007786410 0.1200827 1.470595e-03
## 768 0.013084449 -0.1836442926 0.011862792 0.1200331 3.154575e-03
## 769 0.009763804 -0.0436398945 0.006605629 0.1201963 9.814580e-05
## 770 0.016920028 0.1138656441 0.019837102 0.1201390 2.061108e-03
## 771 0.013035830 -0.0642695699 0.011774796 0.1201848 3.834298e-04
## 772 0.017100565 0.1365754569 0.020262684 0.1201096 3.031493e-03
## 773 0.013374804 -0.1541341225 0.012395124 0.1200842 2.324425e-03
## 774 0.011510603 0.1364579679 0.009180623 0.1201108 1.340647e-03
## 775 0.010974473 0.1527988709 0.008345327 0.1200868 1.525444e-03
## 776 0.008121633 0.1106078980 0.004570491 0.1201437 4.344578e-04
## 777 0.007618221 -0.0102846404 0.004021455 0.1202054 3.301376e-06
## 778 0.015041800 -0.0657549125 0.015677459 0.1201837 5.386303e-04
## 779 0.012711273 0.0669095234 0.011195774 0.1201830 3.946780e-04
## 780 0.014182184 -0.1206784453 0.013936775 0.1201312 1.607110e-03
## 781 0.021922980 -0.0919676613 0.033302377 0.1201617 2.320586e-03
## 782 0.009993714 -0.1192827291 0.006920379 0.1201334 7.686885e-04
## 783 0.015777622 -0.0409752551 0.017248810 0.1201973 2.308601e-04
## 784 0.015105887 0.0637183843 0.015811333 0.1201851 5.102404e-04
## 785 0.010117584 0.0996572618 0.007092995 0.1201553 5.501283e-04
## 786 0.007481763 -0.0454241121 0.003878680 0.1201955 6.209632e-05
## 787 0.010916713 -0.0424197084 0.008257714 0.1201968 1.163138e-04
## 788 0.009429967 0.2018744371 0.006161641 0.1199983 1.957317e-03
## 789 0.011852043 -0.0834353649 0.009733353 0.1201704 5.319760e-04
## 790 0.008172386 0.0645213286 0.004627791 0.1201848 1.497073e-04
## 791 0.013894611 -0.0507747927 0.013377312 0.1201927 2.727699e-04
## 792 0.008795068 0.0415033224 0.005359872 0.1201972 7.184916e-05
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## 794 0.013015773 0.1234328464 0.011738591 0.1201279 1.409832e-03
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## .std.resid
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## 828 0.081033719
## 829 1.527411491
## 830 0.395506473
## 831 0.064203018
## 832 0.829087062## log.price. log.Total.Bsmt.SF...1. log.area. Bedroom.AbvGr Year.Built
## 1 12.63101 7.601402 7.600902 3 2004
## 2 12.45877 7.298445 7.516977 3 1957
## 3 11.66135 6.580639 6.782192 2 1952
## 4 11.87374 6.816736 7.049255 3 1968
## 5 12.53358 7.353722 7.353082 2 2005
## 6 12.20607 6.867974 7.382124 3 1999
## 7 11.56172 6.606650 7.201916 2 1939
## 8 12.22588 6.569481 7.712891 3 1980
## 9 12.44902 7.161622 7.792349 4 1954
## 10 11.96081 6.329721 7.432484 4 1910
## 11 11.36210 6.270988 6.405228 2 1920
## 12 12.39214 6.831954 7.541152 3 2003
## 13 12.49874 7.704361 7.703910 4 1970
## 14 12.40492 7.314553 7.313887 2 1987
## 15 11.95118 6.546785 7.255591 3 1999
## 16 11.88103 7.104144 7.330405 4 1957
## 17 11.71587 6.641182 7.218910 2 1971
## 18 11.85652 6.744059 6.742881 1 2004
## 19 11.78295 6.762730 6.804615 2 1983
## 20 12.34583 6.675823 7.324490 3 1929
## 21 12.67608 7.421776 7.718685 3 2002
## 22 12.13296 6.647688 7.366445 3 2004
## 23 11.77529 6.437752 7.160069 3 1992
## 24 12.14420 7.126891 7.212294 3 1977
## 25 11.75587 6.785588 7.220374 3 1931
## 26 12.14685 6.728629 7.020191 2 2004
## 27 12.20657 6.677083 7.496652 4 1920
## 28 11.90834 6.752270 7.273093 3 1978
## 29 11.82774 6.834109 7.560080 4 1948
## 30 11.96400 7.575585 7.575072 6 1977
## 31 11.32055 6.759255 6.758095 1 1940
## 32 12.03172 7.080868 7.270313 3 1956
## 33 11.58989 6.628041 7.319865 4 1940
## 34 12.08743 6.955593 7.454720 3 1956
## 35 12.36734 6.880384 7.501634 3 2002
## 36 11.95118 6.639876 7.393878 2 2003
## 37 11.58989 6.725034 7.198184 3 1956
## 38 11.95118 6.398595 7.090077 2 2004
## 39 12.07254 6.555357 7.463363 3 1968
## 40 12.80078 7.116394 7.761745 4 1993
## 41 12.12757 7.070724 7.090077 2 2003
## 42 11.81303 6.740519 6.794587 2 1949
## 43 11.91839 6.538140 7.351158 3 1939
## 44 12.18075 7.044033 7.135687 1 2008
## 45 12.25486 6.645091 7.371489 3 2008
## 46 11.79810 6.645091 6.643790 2 1972
## 47 12.56549 7.446001 7.445418 3 2002
## 48 11.69441 6.645091 6.766192 2 1971
## 49 12.15478 7.393263 7.366445 4 1964
## 50 11.82774 6.928538 7.564238 4 1910
## 51 11.65269 6.708084 7.109879 3 1926
## 52 11.63956 6.265301 6.995766 3 1973
## 53 12.02874 7.145984 7.142037 3 1960
## 54 12.72189 7.007601 7.688913 3 2008
## 55 11.84940 6.591674 7.211557 3 1941
## 56 12.07824 6.593045 7.284821 2 1999
## 57 11.73607 6.855409 6.854355 2 1952
## 58 11.56172 6.329721 7.137278 2 1939
## 59 11.77721 6.844815 6.843750 3 1975
## 60 12.25914 6.971669 7.625107 4 1996
## 61 11.71178 6.877296 6.876265 3 1975
## 62 12.83468 7.700295 7.832808 1 2004
## 63 12.52453 7.436617 7.436028 3 2008
## 64 11.07442 6.487684 6.875232 4 1927
## 65 11.87757 6.820016 7.062192 3 1920
## 66 12.05234 6.705639 7.455877 3 1992
## 67 11.59451 6.867974 6.866933 2 1920
## 68 12.40656 6.940222 7.784473 4 1940
## 69 12.18587 7.057037 7.424165 3 1977
## 70 11.41861 6.915723 6.981935 3 1922
## 71 12.45683 7.201916 7.528869 3 2007
## 72 12.01370 7.070724 7.284821 3 1967
## 73 11.54248 6.660575 7.096721 2 1925
## 74 11.87060 7.102499 7.101676 3 1967
## 75 12.56375 7.374002 7.373374 0 2001
## 76 11.74404 7.353082 7.352441 4 1968
## 77 11.98262 6.932448 6.990257 3 1966
## 78 11.85474 6.605298 7.293018 2 1922
## 79 12.50618 6.803505 7.492760 3 2006
## 80 11.68267 6.705639 6.704414 3 1990
## 81 11.60824 6.580639 7.157735 2 1947
## 82 11.71994 6.182085 7.263330 3 1915
## 83 11.68688 6.856462 6.855409 2 1924
## 84 11.74543 7.058758 7.058758 3 1955
## 85 11.79056 6.705639 7.109879 3 1948
## 86 11.90497 7.085901 7.085064 3 1959
## 87 11.80932 6.850126 6.849066 2 1967
## 88 11.80881 0.000000 7.370231 4 1959
## 89 12.28690 7.528869 7.515345 3 2004
## 90 12.23999 6.859615 7.655391 4 1969
## 91 11.60733 7.087574 7.086738 2 1916
## 92 11.76757 6.945051 6.944087 2 1974
## 93 11.79810 6.584791 6.642487 1 1998
## 94 12.50618 7.259116 7.301822 1 1977
## 95 11.73607 7.060476 7.059618 3 1950
## 96 12.36947 6.896694 7.535297 3 1999
## 97 11.65269 6.248043 6.939254 2 1980
## 98 11.73607 6.993933 6.993015 3 1954
## 99 12.61087 7.041412 7.906547 4 1976
## 100 11.81303 7.034388 7.113956 3 1956
## 101 11.84940 7.022868 7.021976 2 2003
## 102 11.23849 6.665684 6.664409 2 1928
## 103 12.72189 7.551187 7.550661 3 1959
## 104 12.01974 6.814543 7.233455 4 1952
## 105 11.84582 6.916715 6.915723 2 1952
## 106 12.42078 7.417580 7.427739 1 1997
## 107 11.98293 7.132498 7.131699 3 1964
## 108 12.03172 6.693324 7.360104 3 1995
## 109 12.49500 6.936343 7.804659 4 1998
## 110 11.75587 6.947937 6.946976 2 1925
## 111 12.22955 6.715383 7.487734 3 1997
## 112 11.98293 7.044033 7.043160 2 2006
## 113 12.19096 6.771936 7.554335 4 2002
## 114 11.92768 6.849066 7.832411 5 1973
## 115 10.98529 6.033086 6.395262 2 1940
## 116 11.89136 6.690842 7.344719 3 1976
## 117 12.14153 6.539586 7.311886 3 1995
## 118 12.20607 7.003974 7.724888 4 1918
## 119 11.66565 6.755769 6.754604 2 1958
## 120 12.27839 6.890609 7.543803 3 2000
## 121 12.27839 7.305860 7.305188 3 1968
## 122 12.63460 7.430707 7.434848 3 2004
## 123 12.50618 6.916715 7.733246 4 2003
## 124 12.28765 7.299797 7.309212 3 1997
## 125 11.59451 6.493754 6.762730 2 1920
## 126 11.69525 0.000000 7.200425 3 1957
## 127 11.85652 6.597146 7.288928 4 1968
## 128 12.44114 7.015712 7.586296 3 2005
## 129 12.06681 6.555357 7.300473 3 1994
## 130 11.60824 6.785588 7.225481 3 1938
## 131 12.10349 7.262629 7.261927 3 1964
## 132 11.84940 6.744059 6.742881 1 2003
## 133 12.47717 7.297091 7.753194 4 1990
## 134 11.75979 6.447306 7.143618 2 1980
## 135 12.21850 7.223296 7.222566 2 2006
## 136 11.64833 6.816736 6.815640 2 1958
## 137 12.20607 6.345636 7.434848 3 1997
## 138 11.72804 6.796824 6.979145 2 1956
## 139 12.07767 6.638568 7.411556 3 1993
## 140 12.35234 6.871091 7.491088 3 2001
## 141 12.28765 6.858565 7.483807 3 1999
## 142 11.97980 6.538140 7.262629 3 1977
## 143 13.04332 7.482682 7.927324 4 2007
## 144 11.94471 6.590301 7.349874 4 1968
## 145 12.90669 7.288244 7.935230 4 1995
## 146 12.15478 7.126087 7.158514 3 1977
## 147 11.35627 6.089045 6.767343 2 1923
## 148 11.84940 6.807935 7.312553 3 1946
## 149 11.98293 6.532334 7.564238 5 1916
## 150 12.49313 7.050123 7.757906 4 1941
## 151 12.66033 7.497762 7.768533 3 1971
## 152 12.30592 7.358194 7.357556 3 2001
## 153 12.61154 7.316548 7.333676 2 2006
## 154 11.54248 6.746412 6.866933 2 1926
## 155 12.01974 7.239215 7.238497 3 1957
## 156 11.88449 6.378426 7.037028 3 1958
## 157 11.82701 6.902743 7.525640 4 1954
## 158 12.48200 7.068172 7.710653 3 1993
## 159 11.84940 6.947937 7.216709 3 1957
## 160 12.23077 6.859615 7.502186 3 2002
## 161 12.59473 7.293698 8.158516 3 1880
## 162 11.94406 6.776507 7.255591 4 1915
## 163 11.97351 6.997596 6.996681 3 1966
## 164 11.77529 6.695799 6.977281 2 1940
## 165 11.47210 6.182085 6.894670 2 1971
## 166 11.71178 0.000000 7.232010 2 1954
## 167 12.66508 7.403670 7.403061 3 2008
## 168 12.19349 7.057898 7.230563 3 1972
## 169 12.25486 7.341484 7.636752 3 1978
## 170 12.29911 6.685861 7.461640 3 1940
## 171 11.79810 6.818924 6.817831 3 1970
## 172 11.27720 6.350886 6.999422 2 1924
## 173 11.74404 6.759255 7.250636 3 1938
## 174 11.95118 7.016610 7.015712 3 2003
## 175 11.99535 6.961296 6.966967 1 1990
## 176 12.14420 6.728629 7.436028 3 2003
## 177 12.90421 7.396335 7.803027 4 1994
## 178 12.33929 7.008505 7.507690 4 1984
## 179 12.04355 6.411818 7.241366 3 2007
## 180 12.10071 7.136483 7.135687 3 1986
## 181 11.99381 6.536692 7.238497 3 1977
## 182 11.49170 6.437752 6.841615 3 1948
## 183 12.26434 6.765039 7.477604 3 2007
## 184 11.71913 6.511745 6.828712 3 1949
## 185 12.75996 7.242082 7.779885 3 1997
## 186 12.05525 7.128496 7.127694 3 1964
## 187 11.75979 6.973543 6.972606 2 1950
## 188 12.33271 7.361375 7.360740 3 2002
## 189 11.98293 5.973810 7.434848 3 1994
## 190 12.04355 7.208600 7.191429 2 1959
## 191 11.97035 7.172425 7.171657 3 1964
## 192 12.03053 6.614726 7.306531 3 2005
## 193 11.81229 6.818924 6.817831 2 1979
## 194 12.15478 6.753438 7.061334 2 2005
## 195 12.16598 6.597146 7.516433 4 2005
## 196 11.91371 6.744059 6.742881 1 2004
## 197 11.79056 6.816736 6.839476 2 1964
## 198 12.10625 7.205635 7.315884 1 2005
## 199 12.42320 7.387709 7.387090 3 2007
## 200 12.30818 7.375256 7.374629 2 2005
## 201 12.08391 6.734592 7.426549 4 1915
## 202 12.19096 6.715383 8.033334 5 1920
## 203 11.82774 6.447306 7.185387 3 1993
## 204 11.90158 6.705639 7.116394 3 1916
## 205 11.86005 6.833032 7.338888 3 1936
## 206 12.54254 7.515889 7.515345 3 2004
## 207 11.91839 6.934397 6.933423 3 1977
## 208 12.33138 6.765039 7.477604 3 2005
## 209 11.93819 6.932448 7.460490 3 1935
## 210 12.31940 7.167809 7.402452 3 1954
## 211 12.79386 7.459915 7.459339 3 2008
## 212 12.76569 7.288244 7.707063 4 2004
## 213 11.58525 6.902743 7.771489 4 1892
## 214 12.26905 7.391415 7.390799 3 1975
## 215 12.15214 6.852243 7.382746 3 1997
## 216 11.95118 7.149917 7.149132 2 1960
## 217 11.99226 5.953243 7.232733 3 1997
## 218 11.97035 7.070724 7.084226 3 1975
## 219 12.56024 7.178545 7.177782 1 2001
## 220 12.41044 7.435438 7.434848 3 2008
## 221 12.16525 6.660575 7.565275 4 1979
## 222 12.27839 6.985642 7.412160 3 1960
## 223 11.84223 7.087574 7.086738 2 1956
## 224 11.66993 6.186209 7.399398 2 1910
## 225 11.94471 7.051856 7.050989 3 1966
## 226 11.61729 6.762730 6.854355 3 1954
## 227 11.60824 6.565265 7.092574 3 1950
## 228 12.44863 6.956545 7.557995 3 1998
## 229 11.73607 6.641182 7.218910 3 1970
## 230 12.20607 6.758095 7.455298 3 2002
## 231 12.00089 6.725034 7.416980 4 1976
## 232 11.01863 6.527958 6.806829 1 1922
## 233 12.40901 7.329750 7.329094 3 1979
## 234 12.10071 7.155396 7.154615 2 1992
## 235 11.60824 0.000000 7.231287 1 1949
## 236 11.84940 5.888878 7.502186 4 1900
## 237 11.95118 7.021976 7.028201 3 1963
## 238 12.06047 6.613384 7.345365 3 1999
## 239 12.12269 6.670766 7.306531 3 2004
## 240 12.03573 6.605298 7.307202 3 2006
## 241 12.45254 7.029088 7.736307 4 2002
## 242 12.61487 7.315218 7.912057 4 1986
## 243 12.28765 7.344073 7.343426 3 2005
## 244 11.83863 6.796824 6.795706 3 1965
## 245 11.89819 6.511745 7.203406 3 1920
## 246 12.77705 7.036148 7.811163 4 2004
## 247 11.81303 7.100852 7.419381 3 1948
## 248 11.98293 6.437752 7.299121 3 1926
## 249 11.75194 6.952729 6.951772 3 1963
## 250 12.30134 7.239933 7.362645 2 2004
## 251 12.36734 7.379632 7.132498 1 1960
## 252 12.84113 7.561642 7.561122 3 2005
## 253 11.98418 7.044033 7.043160 2 2005
## 254 12.63134 7.441320 7.440734 3 2007
## 255 12.15478 6.678342 7.322510 3 2000
## 256 12.27373 6.734592 7.470224 3 1999
## 257 11.80560 6.859615 7.099202 3 1968
## 258 12.04355 6.347389 7.560080 4 1968
## 259 12.15478 7.130099 7.841493 6 1969
## 260 12.10016 7.106606 7.142827 3 1965
## 261 11.62625 0.000000 7.550661 4 1978
## 262 11.84940 6.511745 7.203406 3 1929
## 263 12.35879 6.863803 7.642044 4 2004
## 264 12.08108 6.613384 7.313887 3 1999
## 265 12.20857 6.690842 7.427739 3 1998
## 266 12.36734 6.511745 7.605392 4 1928
## 267 11.84940 7.102499 7.101676 2 1965
## 268 12.16264 7.155396 7.154615 2 1992
## 269 12.15478 6.716595 7.597396 4 1971
## 270 12.61818 7.404888 7.508787 2 1971
## 271 11.97035 7.040536 7.039660 3 1967
## 272 12.13886 6.725034 7.444249 3 1993
## 273 11.91772 6.398595 7.109062 2 2005
## 274 11.68826 6.687109 7.412160 2 1940
## 275 11.87060 6.947937 7.520776 3 1949
## 276 11.83501 6.916715 7.041412 2 1928
## 277 12.04355 6.867974 7.368970 3 1999
## 278 11.51293 0.000000 7.416980 4 1965
## 279 11.94471 6.966967 6.966024 3 1968
## 280 12.38422 6.883463 7.575585 3 1997
## 281 11.41311 6.304449 6.995766 3 1970
## 282 11.81303 6.816736 6.829794 3 1965
## 283 11.95118 6.629363 7.516977 4 1966
## 284 12.30592 7.309881 7.309212 3 2002
## 285 12.34583 6.812345 7.735433 4 1977
## 286 11.87757 7.087574 7.086738 3 1968
## 287 12.24047 7.237778 7.237059 3 2003
## 288 11.76757 6.224558 7.288928 3 1910
## 289 12.19400 7.039660 7.808323 3 1952
## 290 12.54254 6.991177 7.562162 3 1998
## 291 12.22163 6.049733 7.409742 3 1994
## 292 11.99843 7.083388 7.082549 2 1989
## 293 11.49272 0.000000 6.921658 2 1956
## 294 12.36734 6.900731 7.531016 3 2000
## 295 11.96400 6.391917 7.474205 4 1920
## 296 11.87060 6.752270 7.283448 4 1975
## 297 11.91839 6.897705 7.605392 4 1939
## 298 12.32386 6.945051 7.750184 4 1999
## 299 11.69316 6.825460 6.860664 2 1938
## 300 12.34148 6.511745 7.619233 3 1996
## 301 12.00151 7.140453 7.139660 3 1958
## 302 11.98293 7.063904 7.079184 3 1992
## 303 12.06393 6.605298 7.297091 3 2005
## 304 11.84223 5.921578 7.011214 3 1971
## 305 11.96400 7.134094 7.133296 2 1960
## 306 12.85970 7.484369 7.844241 4 1997
## 307 11.85652 0.000000 7.711101 5 1979
## 308 11.84940 6.511745 7.301148 4 1925
## 309 12.50618 7.631917 7.896181 4 1994
## 310 12.30138 7.207119 7.213768 1 2002
## 311 12.79386 7.548029 7.572503 3 2003
## 312 11.95761 6.539586 7.280697 3 1999
## 313 12.25961 6.678342 7.493317 3 1998
## 314 11.81673 6.888572 6.887553 3 1967
## 315 12.97154 8.071219 8.079618 4 1992
## 316 12.92391 7.250636 8.032035 4 1998
## 317 11.73607 6.716595 6.715383 2 1955
## 318 12.05234 6.599870 7.249926 3 2005
## 319 12.14420 6.651572 7.413367 3 1995
## 320 12.62807 7.301822 7.724005 4 2003
## 321 11.68688 7.350516 7.349874 4 1960
## 322 12.19552 7.427144 7.452402 3 1967
## 323 12.08954 6.985642 7.028201 2 1966
## 324 11.91839 6.859615 7.366445 3 1938
## 325 12.42922 7.374629 7.406103 2 2004
## 326 12.07824 6.645091 7.336937 3 2005
## 327 12.00151 6.781058 7.477604 2 1914
## 328 12.36734 7.028201 7.653495 4 1935
## 329 12.31043 6.717805 7.474205 3 2002
## 330 12.65396 7.273093 7.674617 3 2000
## 331 11.95118 6.814543 7.509883 4 1915
## 332 11.57119 6.182085 6.894670 2 1970
## 333 12.17045 7.209340 7.215975 3 2007
## 334 11.08214 6.385194 6.761573 3 1920
## 335 11.89819 7.035269 7.095893 3 1962
## 336 12.12269 7.248504 7.198184 2 1999
## 337 11.76174 6.814543 7.268920 3 1950
## 338 11.41861 6.137727 6.895683 2 1973
## 339 11.85083 6.880384 7.363280 3 1939
## 340 11.89819 6.690842 7.344719 3 1978
## 341 11.65269 6.799056 7.203406 3 1936
## 342 12.29911 6.751101 7.598399 4 2002
## 343 12.10071 7.169350 7.168580 3 1985
## 344 11.87060 6.478510 7.301148 3 1920
## 345 12.30592 7.086738 7.516977 4 1998
## 346 11.94146 6.923629 6.932448 3 1976
## 347 11.87060 6.828712 6.827629 2 1980
## 348 12.71289 7.450661 7.450080 3 2008
## 349 11.87060 6.680855 7.216709 1 1993
## 350 12.39255 6.996681 7.346010 2 2006
## 351 11.81857 6.859615 6.858565 2 1956
## 352 11.63071 6.783325 6.782192 3 1972
## 353 12.23539 6.701960 7.417580 3 2007
## 354 11.89136 6.898715 6.897705 3 1994
## 355 12.07254 7.239215 7.252762 3 1988
## 356 12.45293 7.415175 7.414573 3 2007
## 357 11.76757 7.043160 7.042286 3 1956
## 358 11.88449 6.898715 6.897705 3 1994
## 359 11.91036 6.762730 7.021084 3 1966
## 360 11.40199 6.182085 6.894670 2 1971
## 361 12.02575 5.953243 7.225481 3 2004
## 362 11.96972 7.274480 7.273786 4 1958
## 363 12.08673 6.648985 7.309212 3 1942
## 364 12.05234 7.087574 7.153834 3 1977
## 365 11.60733 0.000000 6.946976 2 1950
## 366 12.12269 7.382124 7.409136 3 1986
## 367 12.12540 6.516193 7.536364 3 1975
## 368 12.71890 7.444833 7.444249 2 2007
## 369 12.59134 7.325808 7.337588 3 2006
## 370 12.57764 6.836259 7.894691 4 1990
## 371 11.81303 6.848005 7.293018 4 1954
## 372 12.43718 6.972606 7.776954 4 1998
## 373 12.50618 7.422971 7.422374 3 2000
## 374 12.52453 7.463363 7.462789 2 1985
## 375 12.20607 7.373374 7.409742 3 1959
## 376 12.45254 7.377134 7.381502 3 2006
## 377 12.20607 6.912743 6.927558 1 1988
## 378 12.17819 6.569481 7.546974 3 1994
## 379 12.01673 6.900731 7.415175 3 1955
## 380 12.14153 6.831954 7.380256 3 1997
## 381 12.32386 7.387090 7.386471 3 2005
## 382 11.51293 6.916715 7.126891 3 1920
## 383 12.08391 6.799056 7.556428 3 1928
## 384 12.30138 6.751101 7.596392 3 1932
## 385 12.32341 7.408531 7.415175 3 1998
## 386 11.96081 7.228388 7.227662 3 1960
## 387 11.84223 6.705639 7.356280 5 1924
## 388 11.93819 7.168580 7.167809 3 1954
## 389 11.38509 6.304449 6.995766 3 1970
## 390 11.65269 0.000000 7.479300 3 1960
## 391 11.51293 7.100852 7.238497 3 1915
## 392 12.18075 6.706862 7.346010 3 1920
## 393 12.05525 7.243513 7.242798 2 1990
## 394 12.46458 7.508239 7.507690 3 2005
## 395 11.40756 0.000000 7.167038 2 1967
## 396 12.22047 6.875232 7.553811 4 2002
## 397 12.23563 6.624065 7.633854 3 1974
## 398 12.31043 6.781058 7.426549 3 1988
## 399 12.05525 6.954639 6.987490 2 1976
## 400 11.84142 6.617403 7.486613 4 1914
## 401 11.84223 6.495266 7.130899 3 1910
## 402 12.53538 7.531552 7.512071 2 1967
## 403 12.42521 6.950815 7.890957 4 1980
## 404 11.82408 6.985642 7.299797 4 1951
## 405 11.07442 6.928538 6.927558 2 1918
## 406 11.91839 7.310550 7.309881 3 1989
## 407 12.32386 6.799056 7.604894 3 1948
## 408 11.44999 6.304449 6.995766 3 1970
## 409 11.77529 7.083388 7.093405 2 1987
## 410 12.34583 7.181592 7.180831 2 2007
## 411 11.72804 6.331502 7.113956 2 1980
## 412 11.89068 7.149132 7.696213 4 1900
## 413 11.65269 6.338594 7.103322 3 1920
## 414 12.38631 7.029088 7.610853 3 1995
## 415 12.10625 6.947937 7.177019 3 1974
## 416 12.07254 6.255750 7.288928 3 1963
## 417 11.91505 6.790097 7.581720 4 1915
## 418 12.50618 7.388328 7.395722 3 2002
## 419 11.88449 6.475433 6.866933 0 1965
## 420 12.39462 7.234177 7.217443 2 1954
## 421 11.63071 6.834109 6.833032 3 1957
## 422 11.93164 6.814543 7.351158 4 1950
## 423 12.13619 6.842683 7.491088 3 2000
## 424 12.12811 7.274480 7.273786 2 1970
## 425 12.40492 7.654917 7.654443 3 1968
## 426 11.31904 6.285998 7.203406 3 1915
## 427 12.04942 6.755769 7.447751 4 1962
## 428 12.30138 7.486053 7.485492 3 1979
## 429 11.72804 6.816736 6.815640 3 1964
## 430 11.64395 6.424869 7.116394 3 1910
## 431 11.76679 6.804615 7.228388 3 1935
## 432 11.80186 6.725034 7.286876 4 1949
## 433 12.14950 6.418365 7.863651 4 1921
## 434 11.57119 6.745236 7.667626 2 1898
## 435 12.82799 7.522400 7.932362 4 1993
## 436 12.06105 6.665684 7.397562 4 1969
## 437 11.99843 7.117206 7.116394 3 1984
## 438 12.15478 7.313887 7.313220 3 2004
## 439 11.76757 6.762730 6.761573 3 1950
## 440 11.83138 7.050123 7.049255 3 1953
## 441 11.89136 6.875232 7.207860 3 1954
## 442 12.01067 7.196687 7.195937 3 1967
## 443 12.08954 6.695799 7.373374 3 1992
## 444 12.50061 6.994850 7.702556 3 1999
## 445 12.85448 7.696667 7.696213 3 2003
## 446 11.72804 6.947937 6.946976 3 1978
## 447 12.07824 7.121252 7.133296 3 1995
## 448 11.66135 6.204558 6.937314 3 1972
## 449 12.43718 7.389564 7.388946 2 2004
## 450 12.34583 6.883463 7.736744 4 1999
## 451 11.75587 6.751101 7.153052 4 1954
## 452 11.91839 7.126891 7.126087 3 1957
## 453 12.12269 7.180831 7.822044 5 1890
## 454 11.56172 6.762730 6.761573 3 1962
## 455 11.87409 7.145984 7.145196 3 1977
## 456 11.19821 6.523562 6.638568 2 1925
## 457 11.77529 5.484797 7.174724 3 1910
## 458 12.07824 6.725034 7.589842 4 1968
## 459 11.88449 6.947937 6.946976 3 1968
## 460 12.07539 7.125283 7.124478 3 1973
## 461 12.03469 6.629363 7.321189 2 2000
## 462 11.84940 6.846943 7.374629 2 1940
## 463 12.83201 7.491645 7.491088 2 2003
## 464 12.12269 6.587550 7.299121 4 1972
## 465 12.25248 7.349231 7.348588 2 2006
## 466 11.82041 7.042286 7.041412 3 1959
## 467 11.83501 6.830874 7.342132 3 1890
## 468 12.14950 6.591674 7.283448 3 2005
## 469 12.58861 7.364547 7.379008 3 2007
## 470 12.10349 7.050123 7.049255 3 1964
## 471 12.27373 7.229114 7.228388 2 2004
## 472 12.37582 6.848005 7.511525 3 2003
## 473 11.73527 6.993015 7.533159 2 1890
## 474 12.06105 6.685861 7.397562 4 1966
## 475 12.46844 7.305860 7.305188 2 2004
## 476 12.12811 7.198931 7.198184 3 2003
## 477 11.98916 6.762730 7.299121 5 1969
## 478 11.46058 6.137727 6.895683 1 1973
## 479 12.51319 7.677400 7.694393 3 1990
## 480 12.27607 6.739337 7.665753 5 1916
## 481 12.61154 7.374629 7.406103 2 2004
## 482 12.17045 6.733402 7.373374 3 2004
## 483 12.59134 7.084226 7.681099 3 1974
## 484 12.32386 7.219642 7.344719 2 2004
## 485 11.89751 6.580639 7.176255 3 1969
## 486 11.77529 6.776507 6.810142 3 1977
## 487 12.47801 7.358194 7.676010 3 1968
## 488 12.45293 7.354362 7.356918 2 1966
## 489 11.99535 6.969791 7.160069 3 1959
## 490 12.02575 6.916715 7.305188 3 1964
## 491 11.77529 6.884487 7.443078 3 2004
## 492 11.95118 7.198931 7.198184 2 2001
## 493 12.42118 6.877296 7.734121 4 2000
## 494 12.27839 7.301822 7.309212 3 1998
## 495 12.50432 7.063904 7.932721 6 2000
## 496 12.36094 7.279319 7.472501 3 1992
## 497 12.12811 6.725034 7.448916 3 1998
## 498 11.85652 6.762730 6.761573 2 1951
## 499 12.06681 6.903747 7.156177 3 1978
## 500 11.88449 6.900731 6.899723 3 1967
## 501 12.25486 7.282761 7.298445 3 1991
## 502 11.79810 6.744059 6.742881 1 2003
## 503 11.88449 7.003974 7.003065 3 1996
## 504 11.80560 6.878326 7.443664 3 2004
## 505 12.53897 7.259116 7.556951 3 2004
## 506 11.76757 6.842683 6.841615 2 1956
## 507 11.77529 6.892642 6.856462 2 1953
## 508 12.45410 7.356918 7.377759 3 2007
## 509 11.86358 7.016610 7.015712 3 2004
## 510 12.37792 7.095064 7.657755 4 1970
## 511 12.14791 6.573680 7.414573 3 1934
## 512 12.07767 7.234898 7.358194 1 2007
## 513 11.92172 6.947937 6.946976 3 1977
## 514 12.54219 7.023759 7.818430 5 2003
## 515 12.10071 7.287561 7.450661 3 1968
## 516 11.80932 6.916715 6.915723 2 1953
## 517 12.04942 6.478510 7.355002 3 1980
## 518 11.83501 6.705639 6.704414 2 1982
## 519 12.33271 7.370860 7.370231 3 2006
## 520 11.90834 6.962243 6.961296 2 1977
## 521 11.34451 6.447306 6.445720 1 1970
## 522 11.91170 6.580639 7.565275 4 1927
## 523 12.16707 7.138867 7.210080 2 1979
## 524 12.05525 7.192934 7.192182 3 1958
## 525 12.01612 6.616065 7.412160 3 2003
## 526 12.12811 7.059618 7.422971 4 1918
## 527 11.78980 6.680855 6.679599 2 1972
## 528 12.27135 7.217443 7.317212 2 2005
## 529 12.53177 7.054450 7.631432 3 1988
## 530 12.45877 7.387090 7.413367 3 2008
## 531 11.04105 6.762730 6.761573 3 1965
## 532 12.52198 7.011214 7.648263 3 1998
## 533 11.97035 6.958448 7.055313 3 1968
## 534 11.57590 0.000000 6.782192 3 1959
## 535 12.42922 7.333676 7.333023 3 2007
## 536 12.21850 6.609349 7.738052 5 1963
## 537 11.68182 6.920672 6.919684 2 1920
## 538 11.89136 6.762730 7.090077 1 1965
## 539 11.75194 6.959399 6.958448 3 1963
## 540 12.29911 6.742881 7.564238 4 2003
## 541 11.26446 5.379897 6.841615 2 1916
## 542 11.31447 0.000000 6.850126 2 1952
## 543 12.38422 6.859615 7.760041 4 1932
## 544 11.96049 6.805723 6.830874 2 1977
## 545 11.80560 7.041412 7.040536 3 1976
## 546 12.27793 6.706862 7.546446 4 2002
## 547 10.85900 5.602119 6.591674 2 1935
## 548 11.00210 5.673323 6.082219 1 1920
## 549 11.89819 6.842683 6.903747 2 1992
## 550 11.72400 7.003974 7.550661 4 1923
## 551 12.37582 7.029088 7.616284 3 2002
## 552 11.33857 0.000000 6.739337 3 1957
## 553 12.38212 7.224753 7.277939 2 2006
## 554 11.86005 6.373320 7.269617 3 1921
## 555 11.83863 6.517671 7.275865 3 1900
## 556 11.84868 6.660575 7.255591 3 1948
## 557 12.02575 7.324490 7.323831 3 1964
## 558 12.11997 6.909753 7.169350 2 1979
## 559 12.42922 7.044033 7.695303 4 2000
## 560 12.08391 6.927558 7.213032 2 1959
## 561 11.75194 6.762730 6.761573 3 1972
## 562 12.01370 6.888572 6.927558 3 1964
## 563 12.56724 6.962243 7.724447 3 2001
## 564 12.72784 7.133296 7.768533 3 1999
## 565 12.44114 7.430114 7.429521 2 2006
## 566 11.82041 6.947937 6.946976 3 1953
## 567 12.20607 7.172425 7.171657 1 2005
## 568 12.20607 7.130099 7.876259 6 1969
## 569 11.81229 6.549651 7.069874 2 1937
## 570 11.22524 6.350886 6.349139 2 1925
## 571 12.24047 6.835185 7.535297 3 1988
## 572 11.91772 7.290975 7.290293 3 1959
## 573 11.37939 0.000000 6.946976 2 1949
## 574 12.14420 6.836259 7.470224 4 1930
## 575 12.26905 6.742881 7.593878 4 2003
## 576 11.58989 6.458338 7.197435 3 1920
## 577 11.93819 7.016610 7.015712 3 2003
## 578 11.91772 6.893656 6.892642 3 1977
## 579 12.77987 7.063904 7.824046 5 2005
## 580 11.35041 6.930495 6.929517 2 1910
## 581 12.17922 7.217443 7.216709 2 2005
## 582 11.83790 6.834109 7.336937 4 1930
## 583 12.24289 6.762730 7.454720 3 2003
## 584 12.58622 7.259116 7.951559 4 1978
## 585 11.90497 7.012115 7.051856 3 1961
## 586 12.12269 7.039660 7.442493 3 1978
## 587 11.83138 6.845880 7.321850 4 1920
## 588 11.60368 6.645091 6.674561 2 1924
## 589 12.25961 6.742881 7.574558 4 2003
## 590 11.93492 6.551080 7.331060 3 1948
## 591 12.12323 6.013715 7.257708 3 2002
## 592 11.96400 6.716595 7.311218 3 1937
## 593 12.29225 7.271009 7.270313 3 1976
## 594 11.65269 6.913737 6.912743 2 1955
## 595 12.35449 7.413367 7.419381 3 2003
## 596 11.69525 6.983790 7.221105 3 1950
## 597 11.95118 7.034388 7.497207 3 1957
## 598 11.66135 6.827629 6.826545 2 1957
## 599 11.96718 6.916715 6.999422 3 1978
## 600 12.38839 7.029973 7.752335 4 2003
## 601 12.15452 6.816736 7.262629 3 1918
## 602 11.82408 7.074963 7.434848 4 1925
## 603 11.97666 7.104144 7.796469 4 1985
## 604 11.79810 6.799056 7.491088 4 1974
## 605 11.75194 6.856462 7.009409 3 1967
## 606 11.58989 6.904751 6.903747 3 1940
## 607 11.75194 6.862758 6.861711 3 1966
## 608 11.54829 6.511745 7.221836 3 1925
## 609 11.06664 6.683361 6.733402 2 1920
## 610 12.03765 6.575076 7.607878 5 1900
## 611 11.61729 6.523562 7.215240 2 1910
## 612 12.45683 7.063904 7.747165 4 1950
## 613 12.09458 7.320527 7.319865 3 1967
## 614 12.09458 6.989335 7.537430 4 1974
## 615 11.51293 6.705639 6.704414 2 1938
## 616 12.51356 7.366445 7.378384 3 2001
## 617 11.40756 0.000000 6.946976 2 1949
## 618 12.02874 6.591674 7.610358 3 1910
## 619 11.84940 6.842683 6.841615 2 1980
## 620 11.31447 6.582025 6.734592 2 1950
## 621 11.77529 6.796824 6.795706 3 1967
## 622 12.03172 7.113956 7.261225 2 1921
## 623 12.33050 7.249215 7.370860 2 2003
## 624 12.53897 6.874198 7.463363 0 1976
## 625 11.24505 6.591674 7.174724 3 1940
## 626 11.51192 6.675823 6.674561 2 1958
## 627 12.12811 6.890609 6.941190 1 1989
## 628 12.48749 7.142827 7.759614 3 1996
## 629 11.98916 7.132498 7.267525 3 1961
## 630 11.82408 6.629363 6.966024 1 1925
## 631 11.84223 6.875232 7.401231 4 1957
## 632 12.34126 7.313220 7.487734 3 1965
## 633 12.42922 6.961296 7.883823 4 1968
## 634 12.71640 7.239933 7.862882 4 1999
## 635 11.75587 6.680855 7.383368 3 1910
## 636 12.14950 6.725034 7.412764 3 1994
## 637 11.75979 6.892642 6.891626 3 1963
## 638 12.03765 6.896694 7.004882 2 1980
## 639 11.81303 6.523562 7.068172 2 1900
## 640 12.10016 6.563856 7.255591 3 1968
## 641 12.30138 6.817831 7.660114 4 1996
## 642 11.90429 7.001246 7.000334 3 1996
## 643 11.96400 6.994850 6.993933 2 2005
## 644 11.76757 6.796824 6.795706 3 1968
## 645 11.89819 6.752270 7.186901 3 1974
## 646 11.91170 6.720220 6.783325 2 1992
## 647 12.12215 6.539586 7.280697 3 1999
## 648 12.01370 6.705639 7.589336 4 1964
## 649 11.91505 6.398595 7.090077 2 2004
## 650 11.93819 7.025538 7.024649 3 1956
## 651 11.38509 6.755769 6.754604 3 1971
## 652 12.70685 7.189922 7.839132 4 1996
## 653 12.67576 7.385851 7.385231 2 2006
## 654 12.08391 6.629363 7.329750 3 2000
## 655 12.10071 6.664409 7.319202 3 2003
## 656 11.73607 6.961296 6.982863 3 1925
## 657 11.98916 6.378426 7.418181 3 1925
## 658 12.07824 7.137278 7.143618 3 2005
## 659 11.50791 6.255750 6.815640 2 1930
## 660 11.98449 7.185387 7.224753 3 1978
## 661 11.93164 7.047517 7.387709 3 1926
## 662 12.16525 6.850126 7.401231 3 1998
## 663 11.72804 6.838405 6.837333 2 1950
## 664 11.65269 5.579730 7.173192 3 1976
## 665 12.66033 5.634790 7.910591 2 1986
## 666 11.80186 6.867974 6.950815 3 1976
## 667 11.88103 6.498282 6.979145 3 1950
## 668 11.70355 6.424869 7.149132 3 1910
## 669 12.03172 6.821107 7.462789 4 1882
## 670 11.75194 6.922644 7.046647 3 1960
## 671 12.10625 6.735780 7.423568 3 1999
## 672 11.77452 6.762730 6.761573 3 1958
## 673 11.82704 7.427144 7.426549 4 1976
## 674 11.90834 6.276643 7.001246 2 1930
## 675 11.40199 0.000000 6.905753 3 1945
## 676 11.82041 6.985642 6.984716 3 1958
## 677 11.77144 6.740519 6.739337 2 1982
## 678 12.46844 7.458763 7.458186 3 2005
## 679 12.34583 6.851185 7.517521 3 2001
## 680 12.01370 6.988413 7.044033 3 1963
## 681 11.64837 6.529419 7.221105 3 1910
## 682 11.61277 7.006695 7.005789 2 1925
## 683 12.56024 7.428927 7.962764 4 1992
## 684 11.67844 6.762730 6.761573 3 1959
## 685 12.11997 7.057037 7.063904 3 1993
## 686 11.49272 6.762730 6.761573 2 1925
## 687 12.06105 6.821107 7.400010 3 1996
## 688 11.71994 6.816736 6.815640 3 1962
## 689 11.56172 6.645091 7.226936 3 1941
## 690 11.94146 7.121252 7.198184 2 1998
## 691 11.66135 6.475433 7.019297 2 1920
## 692 12.55673 7.380256 7.362011 2 2003
## 693 12.41187 7.387090 7.386471 3 2005
## 694 12.72487 7.111512 7.867871 4 1998
## 695 11.91839 6.875232 7.169350 3 1954
## 696 11.72481 6.898715 6.897705 3 1994
## 697 12.16003 6.778785 7.433667 3 1997
## 698 11.95118 6.329721 7.034388 3 1936
## 699 11.69525 6.816736 6.815640 2 1958
## 700 12.00762 6.327937 7.468513 4 1988
## 701 11.92437 7.455298 7.454720 4 1976
## 702 12.15214 6.767343 7.396335 3 2004
## 703 12.02754 7.370231 7.369601 3 1971
## 704 11.93819 7.053586 7.326466 3 1955
## 705 12.34583 7.019297 7.591357 4 1978
## 706 12.11176 6.626718 7.383368 3 1995
## 707 12.38839 5.849325 7.726654 3 1890
## 708 11.71994 6.411818 7.184629 3 1953
## 709 12.52453 7.374629 7.406103 2 2004
## 710 12.02455 7.241366 7.358831 3 1958
## 711 11.89136 7.048386 7.047517 3 1961
## 712 11.81303 7.023759 7.591357 4 1928
## 713 11.32055 6.042633 6.562444 2 1940
## 714 11.95761 5.953243 7.265430 3 1999
## 715 11.67844 6.720220 7.374002 3 1910
## 716 11.95118 6.690842 7.344719 3 1976
## 717 10.86857 6.542472 6.541030 2 1941
## 718 11.77529 6.831954 7.182352 3 1929
## 719 12.27373 6.900731 7.630461 3 1999
## 720 12.01370 6.513230 7.231287 3 2000
## 721 12.12811 7.130099 7.272398 2 1959
## 722 12.06681 6.529419 7.352441 3 2005
## 723 11.91839 7.156177 7.390181 3 1976
## 724 13.05301 7.876259 7.875879 2 2001
## 725 12.50540 7.019297 7.607381 3 1996
## 726 11.94730 6.617403 7.401842 3 1946
## 727 11.61954 6.762730 6.761573 3 1972
## 728 11.63071 6.842683 6.891626 2 1954
## 729 12.01370 6.716595 7.635787 4 1956
## 730 12.77987 7.396335 7.813996 4 1998
## 731 12.10625 6.831954 7.380256 3 1997
## 732 12.10071 7.574558 7.699389 3 1970
## 733 12.14950 6.962243 7.520235 3 1992
## 734 11.99535 6.493754 7.185387 3 2003
## 735 12.38003 7.007601 7.662468 4 1991
## 736 11.56172 6.220590 6.911747 2 1930
## 737 11.92504 6.398595 7.090077 2 2004
## 738 11.61729 6.182085 6.894670 2 1973
## 739 11.79056 6.964136 6.963190 3 1962
## 740 11.47210 0.000000 7.036148 4 1947
## 741 11.76368 6.879356 6.878326 3 1969
## 742 12.32386 6.700731 7.696213 4 1993
## 743 11.63514 6.901737 6.954639 2 1922
## 744 11.76718 6.857514 7.110696 3 1959
## 745 11.88103 6.744059 6.742881 1 2004
## 746 12.47801 7.356918 7.356280 3 2008
## 747 11.69107 6.852243 6.851185 2 1973
## 748 11.60368 6.665684 6.664409 2 1924
## 749 11.70355 6.331502 7.113956 2 1980
## 750 12.60149 7.441907 7.448916 3 2007
## 751 10.97678 6.437752 6.704414 2 1910
## 752 11.94146 0.000000 7.111512 2 1951
## 753 12.01733 6.548219 7.313887 3 1993
## 754 11.57119 6.580639 6.740519 2 1920
## 755 12.54687 6.998510 7.816820 4 2005
## 756 11.51293 6.876265 6.875232 2 1923
## 757 11.99226 7.224753 7.201916 3 1967
## 758 12.01370 6.401917 7.314553 3 1923
## 759 12.17045 7.262629 7.261927 3 1998
## 760 11.86005 6.350886 7.198184 3 1950
## 761 11.58989 6.265301 6.995766 3 1972
## 762 12.38422 7.223296 7.872455 4 1918
## 763 12.03112 6.660575 7.384610 4 1964
## 764 12.08391 7.248504 7.198184 2 1997
## 765 11.71178 6.496775 7.188413 3 1920
## 766 12.33929 7.158514 7.682022 3 2002
## 767 12.07254 6.595781 7.477604 3 1937
## 768 11.72804 6.880384 7.383989 4 1938
## 769 12.16003 7.292337 7.299121 3 1999
## 770 11.75587 6.975414 6.974479 2 1977
## 771 11.49272 0.000000 7.332369 4 1945
## 772 11.96081 6.255750 7.198931 2 1983
## 773 12.24047 7.288928 7.288244 3 1998
## 774 11.77913 6.587550 7.299121 3 1976
## 775 11.81303 6.629363 7.292337 3 1906
## 776 11.94665 7.008505 7.729296 5 1960
## 777 12.35449 7.388328 7.387709 3 2005
## 778 11.71994 6.755769 6.770789 3 1971
## 779 12.22096 7.316548 7.315884 3 1996
## 780 12.16003 6.779922 7.492760 3 2005
## 781 11.81303 7.380879 7.380256 4 1958
## 782 12.10625 6.723832 7.413970 3 2004
## 783 12.13216 7.306531 7.305860 3 1968
## 784 11.57119 6.447306 7.171657 3 1970
## 785 11.52288 6.274762 7.013016 3 1920
## 786 12.61154 7.057037 7.711549 3 2000
## 787 11.84223 7.123673 7.397562 3 1958
## 788 12.46844 6.982863 7.942362 4 1995
## 789 11.73126 6.958448 6.957497 3 1966
## 790 11.88449 6.963190 6.962243 3 1955
## 791 11.83138 6.878326 7.443664 3 2004
## 792 11.96718 0.000000 7.294377 2 1959
## 793 12.31043 6.872128 7.712444 4 1997
## 794 12.07254 6.860664 7.406711 3 1999
## 795 12.10293 6.672033 7.289611 3 1998
## 796 11.58989 0.000000 7.026427 2 1949
## 797 11.83138 6.693324 7.259820 3 1951
## 798 11.47210 6.858565 7.216709 4 1920
## 799 12.38839 7.444833 7.444249 3 2004
## 800 11.75194 6.934397 7.433075 3 1924
## 801 11.95118 6.493754 7.206377 3 1966
## 802 11.86710 6.967909 6.961296 2 1978
## 803 11.94471 6.639876 7.393878 2 2003
## 804 12.36521 7.348588 7.347944 3 2003
## 805 12.07539 7.260523 7.259820 3 1981
## 806 11.74006 6.434547 7.217443 3 1910
## 807 12.54076 6.970730 7.661527 4 1996
## 808 12.20607 7.217443 7.641084 3 2003
## 809 11.87583 6.744059 6.742881 1 2003
## 810 11.37366 6.511745 6.733402 3 1930
## 811 12.76359 7.047517 7.840313 4 2005
## 812 12.06681 7.173958 7.427739 3 1970
## 813 12.17561 6.804615 7.448334 2 1940
## log.X2nd.Flr.SF...1. log.Lot.Area. Overall.Cond Overall.Qual .fitted
## 1 0.000000 9.248214 5 8 12.57861
## 2 0.000000 9.577896 7 6 12.31285
## 3 0.000000 9.354960 6 5 11.67848
## 4 0.000000 9.367344 6 6 11.96454
## 5 0.000000 8.897409 5 9 12.49452
## 6 6.470800 7.880426 5 8 12.14892
## 7 6.150603 8.699515 5 6 11.77415
## 8 6.760415 9.194109 8 6 12.41142
## 9 0.000000 9.447071 7 6 12.42189
## 10 6.634633 8.881836 9 7 12.03010
## 11 0.000000 9.115810 7 4 11.24803
## 12 6.767343 8.853665 5 7 12.29013
## 13 0.000000 9.671871 6 8 12.58611
## 14 0.000000 8.307459 6 7 12.21530
## 15 6.580639 7.852439 5 7 11.96911
## 16 0.000000 9.055089 6 5 11.95701
## 17 6.398595 7.560080 5 5 11.68312
## 18 0.000000 8.395252 5 6 11.80737
## 19 0.000000 9.092120 5 5 11.73225
## 20 6.587550 9.344434 7 8 12.11775
## 21 6.335054 9.521495 5 8 12.58689
## 22 6.700731 9.026418 5 7 12.19726
## 23 6.498282 9.252346 5 5 11.87639
## 24 0.000000 9.677653 6 6 12.14816
## 25 6.013715 8.738735 6 6 11.78233
## 26 0.000000 9.693939 5 7 12.18352
## 27 6.804615 8.934323 6 7 11.97471
## 28 6.375025 7.735870 6 6 11.86498
## 29 6.900731 9.336532 5 5 11.95199
## 30 0.000000 9.016149 4 5 12.02659
## 31 0.000000 9.420763 5 4 11.53562
## 32 0.000000 9.559235 6 5 12.00921
## 33 6.628041 9.114270 5 4 11.65649
## 34 0.000000 9.510075 6 5 12.11711
## 35 6.733402 9.044286 5 8 12.36925
## 36 6.760415 7.803027 5 7 12.10299
## 37 6.226537 9.033842 5 4 11.67267
## 38 6.398595 8.075583 5 7 11.94146
## 39 6.555357 9.367344 6 6 12.13178
## 40 7.002156 9.483645 5 8 12.52187
## 41 0.000000 9.218606 5 7 12.18014
## 42 0.000000 9.169518 7 5 11.70840
## 43 6.538140 8.764990 6 5 11.79935
## 44 0.000000 8.346879 5 6 12.07712
## 45 6.690842 9.104980 5 8 12.30806
## 46 0.000000 9.041330 7 5 11.67826
## 47 0.000000 9.727347 5 8 12.52291
## 48 0.000000 9.038959 6 5 11.70306
## 49 0.000000 10.505068 5 5 12.13538
## 50 6.928538 9.120634 8 6 12.02480
## 51 6.008813 8.281471 8 6 11.73632
## 52 6.342121 7.698483 6 6 11.64958
## 53 0.000000 9.137770 5 5 11.84535
## 54 6.961296 9.333266 5 9 12.62943
## 55 6.390241 8.735686 5 5 11.66843
## 56 6.593045 8.080237 5 6 11.96815
## 57 0.000000 9.301095 6 6 11.81098
## 58 6.329721 9.111624 5 6 11.76954
## 59 0.000000 9.126959 6 5 11.74808
## 60 6.892642 9.977342 5 7 12.41640
## 61 0.000000 9.245321 6 5 11.78376
## 62 0.000000 8.895082 5 8 12.76075
## 63 0.000000 9.323133 5 8 12.49131
## 64 0.000000 9.287301 6 4 11.47955
## 65 0.000000 9.074635 5 5 11.62963
## 66 6.800170 8.949365 6 6 12.16770
## 67 0.000000 8.699515 4 4 11.36556
## 68 7.087574 10.089552 7 7 12.42124
## 69 0.000000 10.433616 6 5 12.28594
## 70 0.000000 9.188708 4 3 11.38543
## 71 6.255750 9.190240 5 8 12.43908
## 72 0.000000 9.162725 5 5 11.96265
## 73 0.000000 8.738735 5 4 11.57784
## 74 0.000000 9.245225 5 5 11.85637
## 75 0.000000 8.501673 5 8 12.43561
## 76 0.000000 9.067393 5 5 11.97160
## 77 0.000000 9.503010 5 5 11.80611
## 78 6.401917 9.264829 7 6 11.93157
## 79 6.787845 9.268892 5 8 12.40125
## 80 0.000000 9.379323 5 6 11.77326
## 81 6.336826 8.160518 7 5 11.72402
## 82 6.532334 8.661294 7 6 11.76463
## 83 0.000000 8.699515 7 5 11.60445
## 84 0.000000 8.669056 8 3 11.69709
## 85 6.013715 8.995165 8 6 11.90030
## 86 0.000000 9.077951 6 6 11.92943
## 87 0.000000 9.035749 5 5 11.69827
## 88 6.150603 9.748003 4 4 11.57142
## 89 0.000000 9.116030 5 7 12.42245
## 90 6.928538 9.312446 5 6 12.17116
## 91 0.000000 8.476371 7 4 11.62070
## 92 0.000000 9.282754 5 5 11.81663
## 93 0.000000 8.308446 5 7 11.78954
## 94 0.000000 9.906583 7 7 12.44165
## 95 0.000000 9.294682 5 5 11.77160
## 96 6.786717 9.289152 5 7 12.32454
## 97 6.248043 7.457609 6 6 11.64772
## 98 0.000000 8.914626 6 5 11.74651
## 99 7.340187 9.100860 9 8 12.69795
## 100 0.000000 9.749170 6 4 11.84637
## 101 0.000000 9.053219 5 4 11.86471
## 102 0.000000 9.104980 3 6 11.42423
## 103 0.000000 9.769956 8 7 12.50558
## 104 6.165418 9.050172 4 5 11.68442
## 105 0.000000 9.455480 6 5 11.78658
## 106 0.000000 8.742574 5 8 12.44924
## 107 0.000000 9.082507 6 6 11.97960
## 108 6.642487 9.246094 5 6 12.10454
## 109 7.125283 9.694370 5 8 12.58467
## 110 0.000000 8.881836 7 6 11.77460
## 111 6.782192 9.141740 5 6 12.18001
## 112 0.000000 8.071843 5 7 12.02615
## 113 6.945051 9.074062 5 7 12.28025
## 114 7.115582 8.285009 4 6 12.09034
## 115 0.000000 8.594154 5 2 10.97992
## 116 6.613384 7.744137 5 6 11.84969
## 117 6.694562 9.475086 5 6 12.09477
## 118 7.060476 8.956093 8 6 12.13818
## 119 0.000000 8.882808 7 5 11.68282
## 120 6.782192 9.066239 5 6 12.22375
## 121 0.000000 9.979476 6 6 12.21570
## 122 0.000000 9.218705 5 8 12.46349
## 123 7.151485 9.375177 5 8 12.51905
## 124 0.000000 9.130864 5 6 12.17567
## 125 4.836282 9.214532 8 6 11.64661
## 126 0.000000 9.111624 6 5 11.68294
## 127 6.597146 9.084097 6 5 11.86834
## 128 6.755769 9.177301 5 7 12.37035
## 129 6.659294 9.002701 5 6 12.02955
## 130 6.093570 9.133459 4 5 11.67381
## 131 0.000000 9.227689 5 6 12.03461
## 132 0.000000 8.397283 5 6 11.80394
## 133 6.682109 9.379154 5 7 12.41979
## 134 6.456770 8.988696 5 6 11.91164
## 135 0.000000 8.770594 5 8 12.31204
## 136 0.000000 9.225229 5 5 11.66500
## 137 6.734592 9.025696 5 7 12.20481
## 138 0.000000 8.915969 5 5 11.72526
## 139 6.794587 9.210340 5 6 12.12203
## 140 6.721426 9.428270 5 7 12.31995
## 141 6.720220 9.504948 5 7 12.31654
## 142 6.591674 8.980927 6 6 11.99030
## 143 6.886532 9.565003 5 9 12.78574
## 144 6.590301 9.367344 6 6 12.02393
## 145 7.173958 9.624963 5 8 12.65986
## 146 0.000000 9.171600 7 6 12.10402
## 147 0.000000 8.682708 7 4 11.43365
## 148 6.390241 9.104980 6 5 11.85100
## 149 6.888572 8.865312 8 5 11.88472
## 150 7.050123 9.109636 9 7 12.39629
## 151 0.000000 9.775484 9 7 12.73703
## 152 0.000000 8.879055 5 8 12.36101
## 153 0.000000 9.293946 5 9 12.53096
## 154 0.000000 8.850518 7 5 11.63318
## 155 0.000000 9.384294 5 6 12.01154
## 156 0.000000 9.257415 8 6 11.99166
## 157 6.461468 9.161675 4 6 11.97397
## 158 6.925595 9.366660 5 8 12.51104
## 159 0.000000 9.153770 5 4 11.79373
## 160 6.758095 8.922658 5 7 12.27069
## 161 7.506042 9.819345 9 7 12.54947
## 162 6.293419 9.446598 8 5 11.80405
## 163 0.000000 9.281544 7 6 11.96898
## 164 0.000000 8.881836 8 5 11.80640
## 165 6.224558 7.426549 5 6 11.53134
## 166 0.000000 9.657267 5 4 11.65889
## 167 0.000000 9.579349 5 9 12.58282
## 168 0.000000 9.144201 7 6 12.12626
## 169 0.000000 9.486076 6 6 12.40757
## 170 6.660575 9.482274 6 7 12.12803
## 171 0.000000 8.977146 5 5 11.64540
## 172 6.263398 9.169518 5 6 11.63488
## 173 6.308098 8.738735 5 6 11.77304
## 174 0.000000 9.524786 5 6 12.04697
## 175 0.000000 9.285262 6 7 12.14353
## 176 6.759255 9.221280 5 6 12.17903
## 177 6.637258 10.749120 7 8 12.81294
## 178 6.576470 10.082470 5 6 12.23154
## 179 6.670766 9.311904 5 6 12.07075
## 180 0.000000 9.812742 5 6 12.09891
## 181 6.556778 9.296518 7 6 12.06166
## 182 5.746203 8.847360 7 4 11.48971
## 183 6.805723 9.284427 5 8 12.39555
## 184 5.533389 8.995165 7 5 11.59141
## 185 6.893656 9.153982 5 8 12.55120
## 186 0.000000 9.449357 5 6 11.97040
## 187 0.000000 9.169518 7 4 11.74976
## 188 0.000000 9.190954 5 7 12.31963
## 189 6.647688 9.224933 5 6 12.12240
## 190 0.000000 9.735365 6 5 12.03067
## 191 0.000000 9.143132 7 6 12.06296
## 192 6.614726 9.095827 5 6 12.08719
## 193 0.000000 8.846497 7 5 11.79800
## 194 0.000000 9.168163 5 7 12.15278
## 195 7.007601 9.995611 5 5 12.20090
## 196 0.000000 8.395252 5 6 11.80737
## 197 0.000000 9.246286 7 6 11.88721
## 198 0.000000 8.065265 5 7 12.23725
## 199 0.000000 9.142597 5 8 12.43366
## 200 0.000000 9.103534 5 8 12.44944
## 201 6.734592 9.653487 7 6 11.96433
## 202 6.906755 9.671745 3 7 12.21928
## 203 6.538140 8.192017 5 6 11.85564
## 204 0.000000 9.056490 8 6 11.87567
## 205 6.159095 8.719317 6 5 11.79000
## 206 0.000000 9.338030 5 8 12.53166
## 207 0.000000 9.631679 8 5 11.97354
## 208 6.805723 9.190444 5 7 12.29355
## 209 6.388561 8.855093 5 5 11.83062
## 210 0.000000 9.600895 7 6 12.22711
## 211 0.000000 9.356862 5 9 12.59458
## 212 6.637258 9.086363 5 9 12.57505
## 213 6.902743 8.794825 4 5 11.77119
## 214 0.000000 9.145588 7 5 12.16706
## 215 6.498282 9.228082 5 6 12.13140
## 216 0.000000 9.594241 4 5 11.89002
## 217 6.447306 9.090656 5 6 11.99063
## 218 0.000000 9.310186 5 7 12.04845
## 219 0.000000 8.420242 5 9 12.34236
## 220 0.000000 9.256747 5 8 12.48276
## 221 6.740519 9.336003 5 7 12.23268
## 222 0.000000 10.366278 5 6 12.23998
## 223 0.000000 9.104980 5 6 11.90933
## 224 6.453625 8.577347 8 6 11.91005
## 225 0.000000 9.305651 6 5 11.87517
## 226 0.000000 9.231613 5 4 11.55432
## 227 5.416100 8.855806 4 5 11.60235
## 228 6.781058 9.310186 5 8 12.42355
## 229 6.398595 7.769801 6 5 11.71738
## 230 6.768493 9.006754 5 7 12.24710
## 231 6.725034 9.224243 5 7 12.11622
## 232 0.000000 9.212338 1 1 11.02005
## 233 0.000000 9.916897 6 7 12.34842
## 234 0.000000 8.531096 5 8 12.18707
## 235 0.000000 9.375855 7 4 11.74208
## 236 6.660575 8.939843 9 5 11.86255
## 237 0.000000 9.071078 6 5 11.82119
## 238 6.675823 7.731931 5 6 11.92958
## 239 6.555357 9.641083 5 7 12.23363
## 240 6.625392 9.027979 5 7 12.16656
## 241 7.040536 9.328123 5 8 12.51703
## 242 7.071573 9.247636 5 7 12.48654
## 243 0.000000 9.371609 5 7 12.34013
## 244 0.000000 9.041922 8 5 11.76808
## 245 6.511745 9.277064 7 5 11.74416
## 246 7.195187 9.400878 5 8 12.57882
## 247 6.093570 9.169518 6 5 11.94776
## 248 6.602588 8.853665 8 7 11.99087
## 249 0.000000 8.979165 6 6 11.84302
## 250 0.000000 8.278936 5 7 12.25353
## 251 0.000000 9.510445 7 6 12.14515
## 252 0.000000 9.557964 5 9 12.67546
## 253 0.000000 8.065265 5 7 12.02171
## 254 0.000000 9.348187 5 8 12.49374
## 255 6.545350 9.039908 5 6 12.07556
## 256 6.820016 9.155673 5 6 12.17791
## 257 0.000000 9.017968 5 5 11.82388
## 258 6.549651 9.229358 6 7 12.21827
## 259 7.167809 9.176887 5 6 12.20774
## 260 0.000000 9.143132 8 5 12.01181
## 261 6.371612 9.097172 5 6 11.89395
## 262 6.511745 8.648221 6 7 11.82150
## 263 7.029088 9.224440 5 7 12.36308
## 264 6.613384 7.731931 5 6 11.91032
## 265 6.778785 9.076809 5 6 12.13701
## 266 6.511745 9.900984 7 6 12.15084
## 267 0.000000 9.123693 7 5 11.96973
## 268 0.000000 8.518193 5 8 12.18556
## 269 6.799056 9.602585 5 6 12.17243
## 270 0.000000 11.653982 5 7 12.62615
## 271 0.000000 9.169518 7 5 11.90473
## 272 6.778785 9.136801 5 6 12.13737
## 273 6.436150 7.841493 5 7 11.92936
## 274 6.331502 8.939581 6 4 11.82247
## 275 6.520621 9.258750 6 6 12.09948
## 276 0.000000 8.869398 7 5 11.75976
## 277 6.437752 7.880426 5 8 12.14097
## 278 0.000000 9.192685 5 5 11.77459
## 279 0.000000 9.017484 8 5 11.89059
## 280 6.883463 8.909100 5 7 12.29674
## 281 6.304449 7.568379 7 4 11.50725
## 282 0.000000 9.002701 7 5 11.73649
## 283 6.670766 8.948976 5 6 12.02515
## 284 0.000000 9.457435 5 7 12.31620
## 285 6.880384 9.530538 7 7 12.45874
## 286 0.000000 9.214731 6 5 11.89587
## 287 0.000000 9.083643 5 7 12.22768
## 288 6.552508 9.200290 8 5 11.79258
## 289 6.278521 9.182352 7 5 12.25724
## 290 6.732211 9.393578 5 8 12.43776
## 291 6.629363 9.885578 6 7 12.31949
## 292 0.000000 8.270525 5 8 12.09720
## 293 0.000000 8.959954 5 5 11.47010
## 294 6.773080 9.241451 5 7 12.32021
## 295 6.639876 8.881836 7 7 11.99651
## 296 6.400257 7.744137 6 6 11.82518
## 297 6.639876 8.738735 5 7 12.05098
## 298 7.159292 9.430279 5 7 12.43881
## 299 0.000000 8.749098 7 5 11.66390
## 300 6.601230 9.263028 5 7 12.35394
## 301 0.000000 9.118225 6 6 11.96714
## 302 0.000000 9.164925 5 7 12.09032
## 303 6.605298 9.063347 5 6 12.07718
## 304 6.280396 9.259131 7 5 11.78997
## 305 0.000000 9.298351 5 6 11.97787
## 306 6.650279 9.408453 5 8 12.59729
## 307 7.033506 9.164820 6 5 11.92877
## 308 6.511745 9.405496 8 6 11.93700
## 309 6.411818 9.480978 5 8 12.63603
## 310 0.000000 9.313619 5 8 12.39079
## 311 0.000000 9.423676 5 9 12.65925
## 312 6.606650 8.234300 5 7 12.02923
## 313 6.818924 9.162305 5 6 12.18794
## 314 0.000000 9.185023 5 5 11.70554
## 315 0.000000 9.448727 5 8 12.84324
## 316 7.249926 9.264544 5 9 12.77193
## 317 0.000000 9.016149 7 5 11.66108
## 318 6.514713 8.856946 5 5 11.94029
## 319 6.786717 8.987197 5 6 12.10495
## 320 6.660575 9.412791 5 8 12.53685
## 321 0.000000 9.049232 5 5 11.93842
## 322 0.000000 9.790935 5 6 12.23856
## 323 0.000000 9.339613 8 6 12.08098
## 324 6.378426 8.719317 6 5 11.81284
## 325 0.000000 8.245647 5 7 12.28183
## 326 6.645091 9.233764 5 6 12.12333
## 327 6.790097 9.287301 7 7 12.10697
## 328 6.771936 9.527193 7 6 12.17697
## 329 6.785588 9.203316 5 7 12.28061
## 330 6.519147 9.310186 5 9 12.60299
## 331 6.814543 7.824046 8 7 11.93820
## 332 6.224558 7.533159 6 6 11.58957
## 333 0.000000 9.172327 5 7 12.23832
## 334 6.070738 9.104980 6 4 11.31055
## 335 0.000000 9.160099 5 6 11.90585
## 336 0.000000 8.675564 5 7 12.17685
## 337 6.265301 9.068085 6 5 11.83539
## 338 6.137727 7.375256 5 4 11.36569
## 339 6.406880 8.769507 5 6 11.85490
## 340 6.613384 7.768110 5 6 11.85982
## 341 6.107023 8.738735 4 5 11.60647
## 342 7.031741 9.075665 5 7 12.30672
## 343 0.000000 9.323669 5 6 12.06013
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## 775 6.570883 9.241839 7 6 11.83227
## 776 7.064759 9.358760 5 5 12.07413
## 777 0.000000 9.069698 5 7 12.33455
## 778 0.000000 9.023288 5 4 11.53867
## 779 0.000000 9.382864 5 7 12.28996
## 780 6.821107 9.139489 5 7 12.29755
## 781 0.000000 9.020027 5 5 11.94808
## 782 6.720220 9.385973 5 7 12.27192
## 783 0.000000 9.122165 7 6 12.16529
## 784 6.511745 7.608871 5 5 11.61103
## 785 6.274762 8.881836 7 5 11.57174
## 786 6.937314 9.163773 5 8 12.51302
## 787 0.000000 9.169518 6 6 12.13730
## 788 7.451242 9.187174 5 6 12.43207
## 789 0.000000 9.185945 5 5 11.74895
## 790 0.000000 10.453053 5 5 11.86004
## 791 6.606650 7.832808 5 7 12.11581
## 792 0.000000 9.363061 5 7 11.93364
## 793 7.126087 9.473166 5 7 12.41044
## 794 6.543912 8.976768 5 6 12.12430
## 795 6.517671 9.036225 5 6 12.04695
## 796 0.000000 9.079890 5 4 11.44172
## 797 5.834811 9.423434 5 5 11.82721
## 798 5.932245 8.929303 5 4 11.51265
## 799 0.000000 9.402447 5 7 12.40778
## 800 6.501290 8.517193 6 5 11.78124
## 801 6.535241 8.934587 5 6 11.85851
## 802 0.000000 7.742402 7 7 11.92905
## 803 6.760415 7.803027 5 7 12.10299
## 804 0.000000 9.075208 5 7 12.30116
## 805 0.000000 9.400134 6 6 12.16511
## 806 6.434547 8.954157 7 4 11.59354
## 807 6.967909 9.304741 5 7 12.35993
## 808 6.580639 9.343647 5 7 12.42648
## 809 0.000000 8.397283 5 6 11.80394
## 810 0.000000 8.386629 7 5 11.46454
## 811 7.228388 9.419628 5 8 12.60322
## 812 0.000000 9.249561 6 7 12.29525
## 813 6.385194 9.425452 6 5 11.98921
## .se.fit .resid .hat .sigma .cooksd
## 1 0.010334407 0.0524036340 0.007905651 0.1162871 1.814172e-04
## 2 0.011060025 0.1459211226 0.009054798 0.1161869 1.614878e-03
## 3 0.009275501 -0.0171393937 0.006368560 0.1163004 1.558495e-05
## 4 0.007545586 -0.0908021019 0.004214562 0.1162576 2.882284e-04
## 5 0.012580869 0.0390513183 0.011716227 0.1162937 1.504596e-04
## 6 0.012814479 0.0571509295 0.012155376 0.1162842 3.346276e-04
## 7 0.011503120 -0.2124347454 0.009794849 0.1160577 3.707853e-03
## 8 0.015504606 -0.1855419280 0.017794590 0.1161142 5.222656e-03
## 9 0.015944314 0.0271324087 0.018818204 0.1162979 1.183532e-04
## 10 0.016516605 -0.0692852774 0.020193336 0.1162757 8.304877e-04
## 11 0.014411072 0.1140696174 0.015373016 0.1162312 1.696991e-03
## 12 0.008050771 0.1020051578 0.004797792 0.1162460 4.145597e-04
## 13 0.013386703 -0.0873686791 0.013265199 0.1162605 8.553589e-04
## 14 0.011527121 0.1896193813 0.009835766 0.1161074 2.966765e-03
## 15 0.012014181 -0.0179318446 0.010684515 0.1163002 2.887082e-05
## 16 0.011719622 -0.0759706772 0.010167021 0.1162707 4.925903e-04
## 17 0.014989138 0.0327469746 0.016631056 0.1162961 1.516887e-04
## 18 0.012013204 0.0491454907 0.010682778 0.1162889 2.168225e-04
## 19 0.009068551 0.0507065982 0.006087547 0.1162881 1.303164e-04
## 20 0.015418103 0.2280828833 0.017596583 0.1160181 7.801139e-03
## 21 0.009610839 0.0891829105 0.006837370 0.1162591 4.534565e-04
## 22 0.008603682 -0.0642993987 0.005479428 0.1162797 1.883846e-04
## 23 0.011212755 -0.1011005387 0.009306602 0.1162467 7.971564e-04
## 24 0.007597907 -0.0039667501 0.004273212 0.1163019 5.577862e-07
## 25 0.008999968 -0.0264600307 0.005995817 0.1162982 3.494432e-05
## 26 0.011463715 -0.0366684354 0.009727859 0.1162947 1.097026e-04
## 27 0.013405113 0.2318622688 0.013301710 0.1160099 6.041195e-03
## 28 0.012185424 0.0433597888 0.010991267 0.1162918 1.737584e-04
## 29 0.009699660 -0.1242583379 0.006964333 0.1162187 8.968606e-04
## 30 0.023322478 -0.0625877860 0.040263903 0.1162801 1.408365e-03
## 31 0.014629389 -0.2150679000 0.015842324 0.1160501 6.222497e-03
## 32 0.008386418 0.0225106973 0.005206183 0.1162992 2.192579e-05
## 33 0.010966746 -0.0666033969 0.008902707 0.1162780 3.306787e-04
## 34 0.010878042 -0.0296831052 0.008759272 0.1162972 6.460295e-05
## 35 0.009040819 -0.0019079980 0.006050371 0.1163019 1.833720e-07
## 36 0.013418921 -0.1518046907 0.013329126 0.1161768 2.595084e-03
## 37 0.010479577 -0.0827866177 0.008129316 0.1162650 4.657879e-04
## 38 0.012138222 0.0097216126 0.010906281 0.1163014 8.665675e-06
## 39 0.007428261 -0.0592361137 0.004084518 0.1162831 1.188483e-04
## 40 0.009465520 0.2789085068 0.006632168 0.1158819 4.300142e-03
## 41 0.008545400 -0.0525707064 0.005405443 0.1162871 1.242083e-04
## 42 0.009248314 0.1046280115 0.006331282 0.1162430 5.773356e-04
## 43 0.008181820 0.1190384942 0.004955259 0.1162257 5.832838e-04
## 44 0.013848188 0.1036382176 0.014195555 0.1162436 1.290431e-03
## 45 0.010724724 -0.0531930426 0.008514101 0.1162867 2.015577e-04
## 46 0.011619984 0.1198428737 0.009994880 0.1162243 1.204623e-03
## 47 0.010079480 0.0425832217 0.007520431 0.1162922 1.138677e-04
## 48 0.008603335 -0.0086501132 0.005478986 0.1163015 3.409101e-06
## 49 0.014111582 0.0194024828 0.014740693 0.1162999 4.701705e-05
## 50 0.012604188 -0.1970659616 0.011759701 0.1160914 3.846080e-03
## 51 0.012473608 -0.0836350089 0.011517300 0.1162641 6.781297e-04
## 52 0.013105858 -0.0100258858 0.012714445 0.1163014 1.078404e-05
## 53 0.007827585 0.1833857955 0.004535468 0.1161209 1.265977e-03
## 54 0.011465270 0.0924561570 0.009730497 0.1162557 6.976280e-04
## 55 0.008747498 0.1809720769 0.005664143 0.1161255 1.543175e-03
## 56 0.012242406 0.1100884862 0.011094304 0.1162363 1.130832e-03
## 57 0.009701249 -0.0749128197 0.006966615 0.1162717 3.260847e-04
## 58 0.012624172 -0.2078276806 0.011797020 0.1160677 4.291516e-03
## 59 0.009475295 0.0291269418 0.006645872 0.1162974 4.699564e-05
## 60 0.010970156 -0.1572617945 0.008908244 0.1161683 1.844738e-03
## 61 0.009252329 -0.0719882820 0.006336780 0.1162740 2.735507e-04
## 62 0.020840711 0.0739353933 0.032150782 0.1162717 1.543138e-03
## 63 0.009448611 0.0332131348 0.006608494 0.1162960 6.075826e-05
## 64 0.013402162 -0.4051290611 0.013295854 0.1154079 1.843542e-02
## 65 0.011753487 0.2479350196 0.010225863 0.1159690 5.277491e-03
## 66 0.008963202 -0.1153657957 0.005946931 0.1162302 6.587973e-04
## 67 0.014358860 0.2289431076 0.015261822 0.1160166 6.784908e-03
## 68 0.012213631 -0.0146769749 0.011042212 0.1163008 2.000312e-05
## 69 0.014014738 -0.1000728181 0.014539064 0.1162475 1.233144e-03
## 70 0.014745586 0.0331881458 0.016094985 0.1162960 1.506171e-04
## 71 0.008855860 0.0177515124 0.005805345 0.1163003 1.522229e-05
## 72 0.008757960 0.0510539659 0.005677700 0.1162879 1.231122e-04
## 73 0.012883154 -0.0353606997 0.012286011 0.1162952 1.295132e-04
## 74 0.007580374 0.0142272412 0.004253513 0.1163009 7.141929e-06
## 75 0.019595683 0.1281399726 0.028424139 0.1162114 4.066559e-03
## 76 0.012042366 -0.2275594342 0.010734706 0.1160214 4.671736e-03
## 77 0.008658263 0.1765090035 0.005549170 0.1161341 1.437868e-03
## 78 0.012767665 -0.0768292190 0.012066725 0.1162700 6.002208e-04
## 79 0.009823957 0.1049258484 0.007143966 0.1162426 6.562295e-04
## 80 0.014408270 -0.0905896260 0.015367038 0.1162573 1.069849e-03
## 81 0.012142726 -0.1157861248 0.010914375 0.1162294 1.230178e-03
## 82 0.010960499 -0.0446856230 0.008892566 0.1162912 1.486775e-04
## 83 0.009957211 0.0824319340 0.007339085 0.1162653 4.162508e-04
## 84 0.018079012 0.0483360296 0.024194458 0.1162891 4.882646e-04
## 85 0.011087713 -0.1097435998 0.009100190 0.1162369 9.180649e-04
## 86 0.007324433 -0.0244603744 0.003971134 0.1162987 1.969794e-05
## 87 0.008123995 0.1110487112 0.004885464 0.1162356 5.003924e-04
## 88 0.025761925 0.2373926277 0.049127324 0.1159842 2.518470e-02
## 89 0.009529803 -0.1355455214 0.006722555 0.1162029 1.029645e-03
## 90 0.008199767 0.0688345753 0.004977021 0.1162765 1.959027e-04
## 91 0.014034907 -0.0133707312 0.014580942 0.1163010 2.207893e-05
## 92 0.008452138 -0.0490651493 0.005288100 0.1162890 1.058218e-04
## 93 0.014108643 0.0085690339 0.014734553 0.1163016 9.166808e-06
## 94 0.016134815 0.0645238854 0.019270565 0.1162792 6.860583e-04
## 95 0.008359022 -0.0355332433 0.005172225 0.1162952 5.427194e-05
## 96 0.008236753 0.0449257229 0.005022022 0.1162911 8.421041e-05
## 97 0.014154877 0.0049711690 0.014831283 0.1163018 3.105979e-06
## 98 0.007643686 -0.0104408067 0.004324862 0.1163014 3.911371e-06
## 99 0.016918312 -0.0870767308 0.021187542 0.1162605 1.379145e-03
## 100 0.010711529 -0.0333357166 0.008493162 0.1162960 7.896262e-05
## 101 0.014082671 -0.0153160645 0.014680356 0.1163007 2.917431e-05
## 102 0.021283048 -0.1857367049 0.033530045 0.1161107 1.018537e-02
## 103 0.013120114 0.2163057656 0.012742121 0.1160479 5.030842e-03
## 104 0.011891782 0.3353224075 0.010467919 0.1156920 9.886663e-03
## 105 0.008716322 0.0592376019 0.005623841 0.1162831 1.641537e-04
## 106 0.014708522 -0.0284599514 0.016014174 0.1162975 1.101842e-04
## 107 0.006848914 0.0033243109 0.003472241 0.1163019 3.178032e-07
## 108 0.008791883 -0.0728210957 0.005721769 0.1162734 2.524369e-04
## 109 0.010065784 -0.0896647460 0.007500008 0.1162586 5.034637e-04
## 110 0.010887914 -0.0187298239 0.008775176 0.1163001 2.576932e-05
## 111 0.008961815 0.0495304782 0.005945090 0.1162887 1.213967e-04
## 112 0.011232465 -0.0432196826 0.009339350 0.1162919 1.462022e-04
## 113 0.008899821 -0.0892911454 0.005863123 0.1162590 3.890249e-04
## 114 0.017250995 -0.1626617907 0.022029002 0.1161570 5.012310e-03
## 115 0.015197325 0.0053680428 0.017096247 0.1163018 4.194061e-06
## 116 0.012209370 0.0416737592 0.011034508 0.1162926 1.611536e-04
## 117 0.010139570 0.0467637993 0.007610366 0.1162902 1.389904e-04
## 118 0.013550969 0.0678945269 0.013592746 0.1162769 5.296491e-04
## 119 0.009307286 -0.0171711533 0.006412283 0.1163004 1.575154e-05
## 120 0.009666437 0.0546403675 0.006916706 0.1162859 1.722183e-04
## 121 0.008984738 0.0626949610 0.005975542 0.1162808 1.955115e-04
## 122 0.009487214 0.1711151414 0.006662602 0.1161440 1.626115e-03
## 123 0.009560307 -0.0128697303 0.006765660 0.1163011 9.342640e-06
## 124 0.008114149 0.1119862635 0.004873629 0.1162345 5.076326e-04
## 125 0.016352174 -0.0521013466 0.019793268 0.1162871 4.599430e-04
## 126 0.025613870 0.0123029051 0.048564274 0.1163011 6.678783e-05
## 127 0.009397389 -0.0118200503 0.006537036 0.1163012 7.610973e-06
## 128 0.008554958 0.0707900791 0.005417541 0.1162750 2.257301e-04
## 129 0.008300193 0.0372579477 0.005099680 0.1162945 5.882279e-05
## 130 0.011863032 -0.0655783663 0.010417366 0.1162787 3.762695e-04
## 131 0.007570434 0.0688740476 0.004242366 0.1162764 1.669306e-04
## 132 0.011949353 0.0454557937 0.010569519 0.1162908 1.834793e-04
## 133 0.008372556 0.0573755325 0.005188988 0.1162842 1.419642e-04
## 134 0.010596774 -0.1518577618 0.008312159 0.1161774 1.603104e-03
## 135 0.009953487 -0.0935420560 0.007333596 0.1162547 5.356094e-04
## 136 0.009193715 -0.0166701159 0.006256747 0.1163005 1.448110e-05
## 137 0.007812268 0.0012583841 0.004517736 0.1163019 5.937507e-08
## 138 0.007924239 0.0027722306 0.004648166 0.1163019 2.965590e-07
## 139 0.008527016 -0.0443594914 0.005382210 0.1162914 8.805322e-05
## 140 0.008946492 0.0323846326 0.005924778 0.1162963 5.171726e-05
## 141 0.009217262 -0.0288908289 0.006288838 0.1162975 4.372140e-05
## 142 0.007299294 -0.0105029527 0.003943921 0.1163014 3.606678e-06
## 143 0.011514003 0.2575809314 0.009813393 0.1159427 5.461809e-03
## 144 0.008678168 -0.0792238953 0.005574714 0.1162682 2.910145e-04
## 145 0.010181058 0.2468284569 0.007672772 0.1159728 3.904424e-03
## 146 0.008720106 0.0507566426 0.005628725 0.1162881 1.206209e-04
## 147 0.010170649 -0.0773824862 0.007657092 0.1162696 3.829567e-04
## 148 0.007716543 -0.0016027971 0.004407700 0.1163019 9.395720e-08
## 149 0.015619205 0.0982053358 0.018058611 0.1162494 1.485619e-03
## 150 0.015035116 0.0968392578 0.016733241 0.1162509 1.334948e-03
## 151 0.018854161 -0.0767058593 0.026313640 0.1162696 1.343148e-03
## 152 0.010251229 -0.0550924494 0.007778904 0.1162856 1.972466e-04
## 153 0.012676992 0.0805781317 0.011895945 0.1162668 6.506568e-04
## 154 0.009500776 -0.0906975310 0.006681664 0.1162576 4.581658e-04
## 155 0.008165930 0.0082040972 0.004936030 0.1163016 2.759697e-06
## 156 0.011332069 -0.1071745198 0.009505718 0.1162398 9.153519e-04
## 157 0.010836950 -0.1469685838 0.008693219 0.1161852 1.571583e-03
## 158 0.009372429 -0.0290460794 0.006502357 0.1162974 4.571262e-05
## 159 0.010878718 0.0556634422 0.008760359 0.1162852 2.272106e-04
## 160 0.007814720 -0.0399204429 0.004520572 0.1162934 5.979205e-05
## 161 0.024221739 0.0452626918 0.043428731 0.1162905 7.997371e-04
## 162 0.012231909 0.1400072371 0.011075287 0.1161958 1.825801e-03
## 163 0.009203375 0.0045307065 0.006269901 0.1163018 1.071963e-06
## 164 0.011022746 -0.0311131903 0.008993860 0.1162967 7.291326e-05
## 165 0.014562571 -0.0592336199 0.015697937 0.1162829 4.675697e-04
## 166 0.026329360 0.0528888976 0.051315327 0.1162862 1.311766e-03
## 167 0.012934918 0.0822617834 0.012384939 0.1162653 7.067058e-04
## 168 0.008580562 0.0672303808 0.005450019 0.1162776 2.048330e-04
## 169 0.012144733 -0.1527061760 0.010917983 0.1161757 2.140499e-03
## 170 0.010451930 0.1710762045 0.008086479 0.1161439 1.978404e-03
## 171 0.009740747 0.1527082851 0.007023458 0.1161761 1.366225e-03
## 172 0.015623353 -0.3576795042 0.018068204 0.1156023 1.971807e-02
## 173 0.009781687 -0.0290020193 0.007082621 0.1162974 4.969907e-05
## 174 0.010100980 -0.0957915903 0.007552549 0.1162524 5.787050e-04
## 175 0.012367094 -0.1481799594 0.011321444 0.1161830 2.091677e-03
## 176 0.009647083 -0.0348366772 0.006889038 0.1162954 6.972049e-05
## 177 0.016673204 0.0912682619 0.020578069 0.1162564 1.469699e-03
## 178 0.011721261 0.1077521419 0.010169864 0.1162391 9.912190e-04
## 179 0.011182305 -0.0271920408 0.009256124 0.1162980 5.734743e-05
## 180 0.009188737 0.0017990610 0.006249973 0.1163019 1.684766e-07
## 181 0.010171690 -0.0678543830 0.007658658 0.1162771 2.945170e-04
## 182 0.012069222 0.0019913401 0.010782638 0.1163019 3.593821e-07
## 183 0.010080401 -0.1312054923 0.007521806 0.1162091 1.081205e-03
## 184 0.012068652 0.1277187705 0.010781620 0.1162136 1.478200e-03
## 185 0.009470004 0.2087608582 0.006638452 0.1160668 2.411428e-03
## 186 0.008071939 0.0848514492 0.004823055 0.1162632 2.883793e-04
## 187 0.011189976 0.0100265790 0.009268828 0.1163014 7.808052e-06
## 188 0.007888666 0.0130769806 0.004606527 0.1163010 6.539176e-06
## 189 0.008730882 -0.1394680438 0.005642645 0.1161972 9.130008e-04
## 190 0.010808672 0.0128850021 0.008647910 0.1163011 1.201568e-05
## 191 0.008168006 -0.0926104426 0.004938540 0.1162558 3.518380e-04
## 192 0.009669935 -0.0566627658 0.006921713 0.1162846 1.853387e-04
## 193 0.010453412 0.0142868725 0.008088772 0.1163009 1.380179e-05
## 194 0.008753703 0.0020027312 0.005672182 0.1163019 1.892606e-07
## 195 0.015038577 -0.0349234007 0.016740946 0.1162953 1.737005e-04
## 196 0.012013204 0.1063433049 0.010682778 0.1162407 1.015213e-03
## 197 0.009888482 -0.0966540152 0.007238119 0.1162516 5.642861e-04
## 198 0.015721465 -0.1309992036 0.018295848 0.1162083 2.679493e-03
## 199 0.009593726 -0.0104668577 0.006813042 0.1163014 6.223514e-06
## 200 0.009851893 -0.1412583062 0.007184654 0.1161943 1.196247e-03
## 201 0.011883921 0.1195705207 0.010454085 0.1162246 1.255412e-03
## 202 0.021920754 -0.0283259907 0.035569477 0.1162975 2.523654e-04
## 203 0.009946603 -0.0279004557 0.007323455 0.1162978 4.758248e-05
## 204 0.012701702 0.0259168684 0.011942365 0.1162983 6.757948e-05
## 205 0.008388004 0.0700517535 0.005208153 0.1162755 2.124131e-04
## 206 0.009609248 0.0108852890 0.006835106 0.1163013 6.753151e-06
## 207 0.014187599 -0.0551449669 0.014899933 0.1162854 3.840249e-04
## 208 0.008521903 0.0378313215 0.005375758 0.1162942 6.396591e-05
## 209 0.010515641 0.1075714375 0.008185364 0.1162395 7.919448e-04
## 210 0.009534004 0.0922954091 0.006728483 0.1162560 4.778211e-04
## 211 0.012305801 0.1992751495 0.011209500 0.1160867 3.744622e-03
## 212 0.011955785 0.1906366129 0.010580902 0.1161051 3.230716e-03
## 213 0.020269832 -0.1859398345 0.030413526 0.1161109 9.199464e-03
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## 313 0.009155187 0.0716770988 0.006204416 0.1162743 2.654554e-04
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## 315 0.017446535 0.1283006635 0.022531228 0.1162118 3.192720e-03
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## 318 0.011788864 0.1120512463 0.010287513 0.1162340 1.084550e-03
## 319 0.008287023 0.0392479950 0.005083509 0.1162937 6.506528e-05
## 320 0.009400106 0.0912147981 0.006540816 0.1162571 4.535096e-04
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## 325 0.013004335 0.1473887409 0.012518226 0.1161841 2.293703e-03
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## 329 0.008295472 0.0298242718 0.005093880 0.1162972 3.764854e-05
## 330 0.011277496 0.0509693347 0.009414383 0.1162879 2.049981e-04
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## 334 0.013768057 -0.2284033236 0.014031749 0.1160183 6.193195e-03
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## 337 0.007451784 -0.0736488806 0.004110427 0.1162728 1.848932e-04
## 338 0.016145068 0.0529268775 0.019295066 0.1162867 4.622172e-04
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## 342 0.008785047 -0.0076153882 0.005712874 0.1163016 2.756380e-06
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## 347 0.008887873 0.0609081237 0.005847392 0.1162820 1.805222e-04
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## 350 0.010638426 0.1479297748 0.008377631 0.1161837 1.533429e-03
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## 352 0.010286232 0.0052094510 0.007832116 0.1163018 1.775892e-06
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## 357 0.007158849 -0.0488233353 0.003793612 0.1162891 7.494336e-05
## 358 0.010095732 0.0793893202 0.007544702 0.1162679 3.970712e-04
## 359 0.009111018 0.0174964123 0.006144694 0.1163003 1.566304e-05
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## 380 0.008401516 0.0310301303 0.005224946 0.1162968 4.181415e-05
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## 382 0.009220293 -0.1331881444 0.006292974 0.1162063 9.298103e-04
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## 388 0.007763147 0.0582810956 0.004461102 0.1162837 1.257491e-04
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## 399 0.009954610 0.0452365727 0.007335252 0.1162909 1.252891e-04
## 400 0.012476918 0.0495489866 0.011523414 0.1162887 2.381452e-04
## 401 0.011060487 0.3099314489 0.009055554 0.1157818 7.285707e-03
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## 403 0.011399153 -0.1339239202 0.009618595 0.1162050 1.446595e-03
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## 408 0.017028513 0.0223999108 0.021464459 0.1162992 9.250885e-05
## 409 0.012855639 -0.3151770469 0.012233587 0.1157623 1.024421e-02
## 410 0.009262729 0.1714485625 0.006351034 0.1161435 1.555142e-03
## 411 0.016056043 0.0031125952 0.019082862 0.1163019 1.580331e-06
## 412 0.014172947 -0.0524263354 0.014869172 0.1162870 3.463554e-04
## 413 0.009795551 0.0550258808 0.007102712 0.1162856 1.794211e-04
## 414 0.008784363 -0.0487105833 0.005711984 0.1162892 1.127543e-04
## 415 0.006485450 0.0505399826 0.003113484 0.1162882 6.581871e-05
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## 418 0.009857317 0.0336269783 0.007192567 0.1162959 6.786620e-05
## 419 0.024409571 -0.0149327017 0.044104895 0.1163007 8.852523e-05
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## 422 0.009926636 0.0784866188 0.007294082 0.1162687 3.750116e-04
## 423 0.009491264 -0.0729979992 0.006668292 0.1162732 2.961910e-04
## 424 0.008735975 -0.0384338885 0.005649230 0.1162940 6.941649e-05
## 425 0.011817332 -0.0024249493 0.010337258 0.1163019 5.104582e-07
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## 427 0.007437218 0.0092855207 0.004094374 0.1163015 2.927438e-06
## 428 0.008844752 -0.0630470188 0.005790790 0.1162805 1.915294e-04
## 429 0.009278190 0.0552059969 0.006372253 0.1162855 1.617864e-04
## 430 0.011079575 0.0930804730 0.009086836 0.1162551 6.594512e-04
## 431 0.011673921 -0.0819096608 0.010087883 0.1162657 5.680689e-04
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## 433 0.014250498 0.0900129590 0.015032340 0.1162579 1.032563e-03
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## 436 0.011104119 0.0499711618 0.009127140 0.1162885 1.909245e-04
## 437 0.007348178 -0.0715739223 0.003996923 0.1162744 1.697611e-04
## 438 0.008094479 -0.1233456959 0.004850028 0.1162201 6.128288e-04
## 439 0.012767001 0.0961164763 0.012065471 0.1162519 9.393071e-04
## 440 0.007196346 0.0237499687 0.003833457 0.1162989 1.792160e-05
## 441 0.010707540 0.1175996754 0.008486838 0.1162273 9.819406e-04
## 442 0.008461924 -0.1233251546 0.005300353 0.1162201 6.701132e-04
## 443 0.008253483 -0.0037115352 0.005042443 0.1163019 5.771160e-07
## 444 0.009192794 -0.0116500163 0.006255494 0.1163012 7.071135e-06
## 445 0.011119279 0.1705077310 0.009152078 0.1161448 2.229040e-03
## 446 0.008426536 -0.0407085106 0.005256112 0.1162930 7.239966e-05
## 447 0.008767381 -0.0368921216 0.005689921 0.1162946 6.442491e-05
## 448 0.015419788 0.0225998128 0.017600431 0.1162992 7.660915e-05
## 449 0.011059588 -0.0868606749 0.009054082 0.1162612 5.721566e-04
## 450 0.008869452 -0.0408412221 0.005823178 0.1162930 8.082659e-05
## 451 0.011705493 0.0026168031 0.010142521 0.1163019 5.829974e-07
## 452 0.007325372 -0.0679524481 0.003972152 0.1162771 1.520607e-04
## 453 0.018785257 -0.0174620522 0.026121659 0.1163003 6.907261e-05
## 454 0.010078013 -0.0515641457 0.007518243 0.1162876 1.669133e-04
## 455 0.010473770 -0.1342767868 0.008120310 0.1162046 1.223997e-03
## 456 0.013350545 -0.1455726514 0.013193636 0.1161869 2.361480e-03
## 457 0.013294581 0.0216881953 0.013083254 0.1162994 5.196675e-05
## 458 0.008491962 -0.1155052795 0.005338049 0.1162301 5.920511e-04
## 459 0.009737837 0.0675857142 0.007019263 0.1162773 2.674507e-04
## 460 0.008777287 -0.0261995015 0.005702787 0.1162983 3.256602e-05
## 461 0.014657780 0.0883651718 0.015903873 0.1162595 1.054664e-03
## 462 0.012006666 -0.0880073546 0.010671153 0.1162600 6.945315e-04
## 463 0.012750215 0.1957163574 0.012033764 0.1160942 3.884146e-03
## 464 0.016545768 -0.0624112823 0.020264708 0.1162807 6.763524e-04
## 465 0.011509520 -0.1045370973 0.009805752 0.1162429 8.988868e-04
## 466 0.007922299 0.0632854738 0.004645890 0.1162804 1.544706e-04
## 467 0.014105778 0.1493943346 0.014728571 0.1161806 2.785102e-03
## 468 0.009442624 0.0036629930 0.006600120 0.1163019 7.380739e-07
## 469 0.009544118 0.1506280837 0.006742766 0.1161796 1.275412e-03
## 470 0.009533249 0.1582406360 0.006727418 0.1161669 1.404338e-03
## 471 0.011229815 0.0102704478 0.009334943 0.1163014 8.252029e-06
## 472 0.008971887 0.0186427480 0.005958460 0.1163001 1.723728e-05
## 473 0.018257674 -0.0919239581 0.024675013 0.1162556 1.802769e-03
## 474 0.012056848 -0.0571803073 0.010760540 0.1162843 2.956978e-04
## 475 0.010333780 0.2254841964 0.007904691 0.1160273 3.358414e-03
## 476 0.008334906 -0.0685847128 0.005142425 0.1162766 2.010133e-04
## 477 0.013980321 0.1673557112 0.014467743 0.1161497 3.431343e-03
## 478 0.019028925 0.0094209093 0.026803717 0.1163015 2.065874e-05
## 479 0.013361899 -0.1320141293 0.013216087 0.1162074 1.945466e-03
## 480 0.014151351 0.2695367429 0.014823894 0.1159065 9.126295e-03
## 481 0.012960226 0.2450918175 0.012433450 0.1159758 6.298549e-03
## 482 0.009099833 0.0616221465 0.006129617 0.1162815 1.938079e-04
## 483 0.011064931 0.0996082375 0.009062832 0.1162483 7.531581e-04
## 484 0.013510841 0.1115474117 0.013512362 0.1162344 1.420990e-03
## 485 0.008896825 0.0472916842 0.005859177 0.1162899 1.090522e-04
## 486 0.013634889 0.0755402773 0.013761624 0.1162710 6.640290e-04
## 487 0.012655935 -0.1049414435 0.011856459 0.1162423 1.099849e-03
## 488 0.013943400 0.1199748100 0.014391427 0.1162237 1.753877e-03
## 489 0.008960492 0.0425990252 0.005943336 0.1162922 8.977001e-05
## 490 0.007005919 -0.0767419495 0.003633262 0.1162703 1.772752e-04
## 491 0.010480946 -0.3741462496 0.008131439 0.1155439 9.516252e-03
## 492 0.010984123 -0.1063279544 0.008930942 0.1162409 8.454897e-04
## 493 0.009427586 -0.0778591958 0.006579115 0.1162693 3.323875e-04
## 494 0.008544716 -0.0503770882 0.005404577 0.1162883 1.140404e-04
## 495 0.017960720 0.0687456912 0.023878881 0.1162760 9.741403e-04
## 496 0.010399310 0.0377051778 0.008005261 0.1162943 9.512239e-05
## 497 0.008122986 -0.1251844846 0.004884250 0.1162176 6.357344e-04
## 498 0.013513580 0.2629639187 0.013517842 0.1159261 7.900329e-03
## 499 0.006669012 0.0084089064 0.003292225 0.1163016 1.927334e-06
## 500 0.009955598 0.0658963595 0.007336707 0.1162785 2.659158e-04
## 501 0.007582068 0.0165035713 0.004255414 0.1163005 9.614480e-06
## 502 0.011949353 -0.0058375007 0.010569519 0.1163018 3.025956e-06
## 503 0.010904541 -0.0881343719 0.008801998 0.1162600 5.723676e-04
## 504 0.012348248 -0.3102195288 0.011286965 0.1157797 9.139005e-03
## 505 0.009567330 0.0552487693 0.006775604 0.1162855 1.724338e-04
## 506 0.008900015 0.0576931184 0.005863378 0.1162840 1.624156e-04
## 507 0.010066982 0.0731498307 0.007501793 0.1162731 3.351631e-04
## 508 0.009889279 -0.0217789338 0.007239286 0.1162994 2.865522e-05
## 509 0.011021243 -0.0979379707 0.008991407 0.1162501 7.222690e-04
## 510 0.013999372 -0.0167804741 0.014507201 0.1163004 3.459467e-05
## 511 0.009191070 0.1209924091 0.006253147 0.1162231 7.624078e-04
## 512 0.015791445 -0.2104661771 0.018459087 0.1160601 6.980428e-03
## 513 0.010412692 0.0527528060 0.008025878 0.1162869 1.866840e-04
## 514 0.012317344 0.0855171891 0.011230539 0.1162623 6.909416e-04
## 515 0.011576762 -0.0375059032 0.009920663 0.1162943 1.170911e-04
## 516 0.008602410 0.0116472766 0.005477807 0.1163012 6.179461e-06
## 517 0.007134263 -0.0163559520 0.003767599 0.1163005 8.352549e-06
## 518 0.014234445 0.0587874247 0.014998491 0.1162832 4.394067e-04
## 519 0.009575485 -0.0938967217 0.006787160 0.1162544 4.989170e-04
## 520 0.012873551 0.0216701553 0.012267702 0.1162994 4.856604e-05
## 521 0.015499120 0.0759487520 0.017781998 0.1162705 8.744401e-04
## 522 0.011925827 0.0134268752 0.010527943 0.1163010 1.594448e-05
## 523 0.007920115 0.0760656154 0.004643329 0.1162708 2.230349e-04
## 524 0.007404682 0.0004964971 0.004058628 0.1163020 8.296009e-09
## 525 0.008132698 -0.1829363728 0.004895937 0.1161218 1.360890e-03
## 526 0.012840943 0.0984442192 0.012205633 0.1162494 9.970838e-04
## 527 0.013509364 0.0490309264 0.013509407 0.1162889 2.744825e-04
## 528 0.013329086 0.0752802391 0.013151257 0.1162712 6.294367e-04
## 529 0.009095987 0.1477740732 0.006124437 0.1161843 1.113583e-03
## 530 0.009488906 -0.0056273079 0.006664979 0.1163018 1.759271e-06
## 531 0.010675857 -0.5534560138 0.008436688 0.1146361 2.161829e-02
## 532 0.009219954 0.0894378409 0.006292511 0.1162588 4.192504e-04
## 533 0.007728048 0.1318557262 0.004420853 0.1162084 6.377882e-04
## 534 0.026641348 0.1130103012 0.052538646 0.1162298 6.147746e-03
## 535 0.013360725 -0.0868258569 0.013213765 0.1162610 8.414001e-04
## 536 0.011460020 -0.0124857427 0.009721588 0.1163011 1.271087e-05
## 537 0.014099365 0.0266294535 0.014715181 0.1162981 8.840779e-05
## 538 0.016495180 -0.1460118358 0.020140980 0.1161854 3.678354e-03
## 539 0.009762081 -0.0821781881 0.007054257 0.1162655 3.974087e-04
## 540 0.008994249 0.0176568127 0.005988201 0.1163003 1.554039e-05
## 541 0.015105505 0.0515424703 0.016890286 0.1162875 3.818453e-04
## 542 0.026207750 0.1392446692 0.050842390 0.1161925 8.999750e-03
## 543 0.012739229 0.0884047603 0.012013035 0.1162596 7.910895e-04
## 544 0.008952991 0.0880836200 0.005933389 0.1162602 3.831653e-04
## 545 0.010507983 0.0621842041 0.008173447 0.1162811 2.642518e-04
## 546 0.009233863 -0.0251237295 0.006311511 0.1162986 3.318371e-05
## 547 0.011987864 -0.3156019705 0.010637758 0.1157617 8.903132e-03
## 548 0.020048598 0.2195260872 0.029753257 0.1160357 1.252756e-02
## 549 0.008654989 -0.0684894472 0.005544974 0.1162767 2.163219e-04
## 550 0.012675002 -0.0689149825 0.011892210 0.1162762 4.757789e-04
## 551 0.008783634 -0.0836472928 0.005711037 0.1162643 3.324432e-04
## 552 0.027180513 0.1541789285 0.054686710 0.1161672 1.196477e-02
## 553 0.009704905 0.0168862340 0.006971866 0.1163004 1.658118e-05
## 554 0.009840512 0.0432526799 0.007168065 0.1162919 1.118924e-04
## 555 0.014056146 -0.0465249303 0.014625105 0.1162902 2.681584e-04
## 556 0.008012261 -0.0531913034 0.004752003 0.1162867 1.116399e-04
## 557 0.007415291 -0.0978819124 0.004070267 0.1162504 3.233660e-04
## 558 0.007922136 -0.0051095857 0.004645699 0.1163018 1.006911e-06
## 559 0.009981124 -0.0836048183 0.007374378 0.1162642 4.302700e-04
## 560 0.009282095 -0.0394713921 0.006377618 0.1162936 8.277604e-05
## 561 0.010598158 0.1481436692 0.008314330 0.1161834 1.526052e-03
## 562 0.012798302 0.1017577980 0.012124706 0.1162458 1.058099e-03
## 563 0.009202672 0.0514026489 0.006268944 0.1162877 1.379595e-04
## 564 0.009421631 0.1818668245 0.006570806 0.1161236 1.811239e-03
## 565 0.010327837 -0.0809126062 0.007895602 0.1162666 4.319434e-04
## 566 0.009742686 -0.0322563127 0.007026255 0.1162963 6.098202e-05
## 567 0.014406900 0.1218073775 0.015364117 0.1162212 1.933871e-03
## 568 0.017979671 0.0380908139 0.023929299 0.1162940 2.997312e-04
## 569 0.014769423 -0.0685048551 0.016147064 0.1162764 6.438725e-04
## 570 0.015838704 0.0281340516 0.018569738 0.1162976 1.255092e-04
## 571 0.007302636 -0.0180225939 0.003947534 0.1163002 1.062967e-05
## 572 0.011617109 -0.0496346072 0.009989933 0.1162886 2.065269e-04
## 573 0.025423982 0.1246668245 0.047846880 0.1162145 6.746303e-03
## 574 0.011663033 0.3848217496 0.010069074 0.1154983 1.251477e-02
## 575 0.008907470 -0.0333902049 0.005873206 0.1162959 5.449465e-05
## 576 0.010449111 -0.0251218315 0.008082118 0.1162985 4.263834e-05
## 577 0.010760745 -0.0139588177 0.008571388 0.1163009 1.397493e-05
## 578 0.013583521 0.0414662245 0.013658130 0.1162926 1.985406e-04
## 579 0.012917614 0.2110967650 0.012351825 0.1160601 4.641023e-03
## 580 0.016265466 -0.1255274062 0.019583915 0.1162159 2.640461e-03
## 581 0.009342718 0.0231349254 0.006461197 0.1162991 2.881400e-05
## 582 0.011056925 0.1577195039 0.009049722 0.1161675 1.885499e-03
## 583 0.009426748 0.0671927906 0.006577946 0.1162776 2.475096e-04
## 584 0.012098486 -0.0125453940 0.010834990 0.1163011 1.433454e-05
## 585 0.008899910 -0.0085834934 0.005863240 0.1163016 3.594989e-06
## 586 0.008529575 -0.0812763491 0.005385442 0.1162664 2.957768e-04
## 587 0.012256470 0.0503013091 0.011119809 0.1162883 2.366424e-04
## 588 0.012542365 0.0245425857 0.011644622 0.1162987 5.905596e-05
## 589 0.009011012 -0.0234500394 0.006010542 0.1162990 2.751448e-05
## 590 0.010151245 -0.1687139031 0.007627902 0.1161483 1.813350e-03
## 591 0.012240654 -0.0549786053 0.011091129 0.1162856 2.819516e-04
## 592 0.008451428 0.0658189436 0.005287212 0.1162786 1.903957e-04
## 593 0.014253310 0.1367754544 0.015038272 0.1162002 2.385061e-03
## 594 0.010147711 0.0139179163 0.007622592 0.1163009 1.233165e-05
## 595 0.009461054 -0.1011041241 0.006625911 0.1162468 5.645230e-04
## 596 0.008533968 -0.1861384394 0.005390989 0.1161153 1.552958e-03
## 597 0.013156765 -0.0972127421 0.012813409 0.1162507 1.021966e-03
## 598 0.008995673 -0.0028490511 0.005990097 0.1163019 4.047407e-07
## 599 0.009090330 0.0315002691 0.006116822 0.1162966 5.053679e-05
## 600 0.009102360 -0.0545937774 0.006133021 0.1162859 1.522048e-04
## 601 0.013381333 0.1886987589 0.013254558 0.1161086 3.986732e-03
## 602 0.012013837 -0.0360273639 0.010683903 0.1162949 1.165330e-04
## 603 0.018269346 -0.0744359182 0.024706572 0.1162715 1.183671e-03
## 604 0.009605415 -0.1782617596 0.006829655 0.1161305 1.809638e-03
## 605 0.007504549 -0.0573836542 0.004168844 0.1162842 1.138530e-04
## 606 0.009773129 -0.1185329898 0.007070233 0.1162262 8.287034e-04
## 607 0.010129878 -0.0044614710 0.007595825 0.1163018 1.262635e-06
## 608 0.010006788 -0.2043112308 0.007412349 0.1160766 2.583013e-03
## 609 0.014915878 -0.1188573637 0.016468883 0.1162250 1.978172e-03
## 610 0.015639647 0.1440022051 0.018105911 0.1161888 3.202974e-03
## 611 0.014719813 0.0584725956 0.016038772 0.1162833 4.658476e-04
## 612 0.012857888 0.2349422549 0.012237868 0.1160024 5.694391e-03
## 613 0.009555400 0.0501402624 0.006758717 0.1162884 1.416615e-04
## 614 0.007981972 -0.0386137720 0.004716142 0.1162939 5.838502e-05
## 615 0.009766276 0.0458414583 0.007060322 0.1162906 1.237712e-04
## 616 0.009588006 0.0846572131 0.006804921 0.1162633 4.066361e-04
## 617 0.024573118 0.0397570491 0.044697891 0.1162931 6.367337e-04
## 618 0.014235604 -0.1620606736 0.015000933 0.1161591 3.339842e-03
## 619 0.008249631 0.1264846224 0.005037738 0.1162158 6.696098e-04
## 620 0.011979588 -0.1064795654 0.010623075 0.1162406 1.012006e-03
## 621 0.011062604 0.0324018091 0.009059021 0.1162963 7.966145e-05
## 622 0.014736328 -0.0689394376 0.016074780 0.1162761 6.490532e-04
## 623 0.012996868 0.0012843853 0.012503854 0.1163019 1.739753e-07
## 624 0.022412622 -0.0598223843 0.037183633 0.1162821 1.180637e-03
## 625 0.020781179 -0.1493290747 0.031967365 0.1161786 6.256617e-03
## 626 0.012389866 0.1813203128 0.011363176 0.1161238 3.143714e-03
## 627 0.013888655 0.0420643920 0.014278641 0.1162923 2.138611e-04
## 628 0.009748302 0.0319154756 0.007034358 0.1162965 5.976991e-05
## 629 0.008506419 0.0072941772 0.005356241 0.1163017 2.369199e-06
## 630 0.014851388 0.1684855919 0.016326781 0.1161473 3.939566e-03
## 631 0.008628044 -0.1052956208 0.005510502 0.1162422 5.080839e-04
## 632 0.027349198 -0.0650278667 0.055367600 0.1162780 2.158008e-03
## 633 0.012778726 0.0156386615 0.012087643 0.1163006 2.491311e-05
## 634 0.011852861 0.0074647974 0.010399511 0.1163017 4.866908e-06
## 635 0.013396779 -0.0978991655 0.013285176 0.1162499 1.075638e-03
## 636 0.009919977 -0.1085226571 0.007284300 0.1162384 7.159833e-04
## 637 0.008882468 0.0742446807 0.005840281 0.1162723 2.679021e-04
## 638 0.007450932 0.0318554061 0.004109488 0.1162965 3.458238e-05
## 639 0.014327210 0.1586613510 0.015194616 0.1161650 3.243808e-03
## 640 0.008290096 0.1009130542 0.005087279 0.1162471 4.304615e-04
## 641 0.008427835 -0.0560791691 0.005257734 0.1162850 1.374373e-04
## 642 0.011137742 -0.0452529262 0.009182497 0.1162909 1.575400e-04
## 643 0.010539387 0.0500609893 0.008222374 0.1162884 1.723025e-04
## 644 0.010153948 0.1330497342 0.007631965 0.1162064 1.128347e-03
## 645 0.011851043 0.1483171013 0.010396320 0.1161829 1.920718e-03
## 646 0.010177491 0.1292485433 0.007667396 0.1162118 1.069815e-03
## 647 0.009970616 0.0939490148 0.007358859 0.1162543 5.421686e-04
## 648 0.007495020 -0.1258248602 0.004158264 0.1162168 5.459946e-04
## 649 0.012883996 0.0009761926 0.012287617 0.1163019 9.871921e-08
## 650 0.008092152 0.0430816182 0.004847241 0.1162920 7.471763e-05
## 651 0.012399731 -0.0913988015 0.011381277 0.1162567 8.000891e-04
## 652 0.009523042 0.1670956146 0.006713019 0.1161514 1.562509e-03
## 653 0.012427878 0.1449698955 0.011433006 0.1161881 2.022218e-03
## 654 0.013648436 0.1681511293 0.013788984 0.1161484 3.296979e-03
## 655 0.008725241 -0.0587991131 0.005635357 0.1162833 1.620674e-04
## 656 0.009579351 0.0167309540 0.006792642 0.1163004 1.585347e-05
## 657 0.015280956 -0.0676574484 0.017284927 0.1162770 6.738567e-04
## 658 0.008999877 -0.0749580921 0.005995696 0.1162717 2.804298e-04
## 659 0.009354229 -0.0977719317 0.006477129 0.1162504 5.159162e-04
## 660 0.009095056 0.0453897159 0.006123183 0.1162909 1.050391e-04
## 661 0.009947593 0.0214463424 0.007324913 0.1162995 2.812022e-05
## 662 0.008614213 0.0329378765 0.005492850 0.1162961 4.955610e-05
## 663 0.010697000 0.0179417830 0.008470138 0.1163002 2.281046e-05
## 664 0.012457914 -0.0345395727 0.011488337 0.1162955 1.153590e-04
## 665 0.018555640 -0.0860538435 0.025486981 0.1162613 1.634585e-03
## 666 0.008924150 -0.0581319652 0.005895222 0.1162838 1.658020e-04
## 667 0.009758358 -0.0094785496 0.007048878 0.1163015 5.282895e-06
## 668 0.010694109 0.0946469248 0.008465560 0.1162536 6.344203e-04
## 669 0.022337274 -0.1188400971 0.036934042 0.1162234 4.625565e-03
## 670 0.009586180 -0.0071070427 0.006802329 0.1163017 2.864759e-06
## 671 0.013863218 -0.1560888614 0.014226386 0.1161696 2.933648e-03
## 672 0.010968647 0.1946416252 0.008905793 0.1160971 2.825128e-03
## 673 0.012514748 -0.3061456235 0.011593397 0.1157932 9.147861e-03
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## .std.resid
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## 804 0.552401538
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## 806 1.266260801
## 807 1.559731080
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## 810 -0.786626814
## 811 1.384507835
## 812 -1.970505483
## 813 1.615216386## P(B != 0 | Y) model 1 model 2
## Intercept 1.00000000 1.0000 1.0000000
## log(Garage.Area + 1) 0.03855625 0.0000 0.0000000
## log(Total.Bsmt.SF + 1) 1.00000000 1.0000 1.0000000
## Garage.Cars 0.99996052 1.0000 1.0000000
## log(area) 1.00000000 1.0000 1.0000000
## Full.Bath 0.04897608 0.0000 0.0000000
## Half.Bath 0.04306068 0.0000 0.0000000
## Bedroom.AbvGr 0.99999409 1.0000 1.0000000
## Year.Built 1.00000000 1.0000 1.0000000
## log(X1st.Flr.SF) 0.85638295 1.0000 0.0000000
## log(X2nd.Flr.SF + 1) 0.18067164 0.0000 1.0000000
## log(Lot.Area) 1.00000000 1.0000 1.0000000
## Overall.Cond 1.00000000 1.0000 1.0000000
## Overall.Qual 1.00000000 1.0000 1.0000000
## BF NA 1.0000 0.1766875
## PostProbs NA 0.7160 0.1265000
## R2 NA 0.9033 0.9029000
## dim NA 10.0000 10.0000000
## logmarg NA -1047.2501 -1048.9834280
## model 3 model 4 model 5
## Intercept 1.000000e+00 1.000000e+00 1.000000e+00
## log(Garage.Area + 1) 0.000000e+00 0.000000e+00 0.000000e+00
## log(Total.Bsmt.SF + 1) 1.000000e+00 1.000000e+00 1.000000e+00
## Garage.Cars 1.000000e+00 1.000000e+00 1.000000e+00
## log(area) 1.000000e+00 1.000000e+00 1.000000e+00
## Full.Bath 1.000000e+00 0.000000e+00 0.000000e+00
## Half.Bath 0.000000e+00 1.000000e+00 0.000000e+00
## Bedroom.AbvGr 1.000000e+00 1.000000e+00 1.000000e+00
## Year.Built 1.000000e+00 1.000000e+00 1.000000e+00
## log(X1st.Flr.SF) 1.000000e+00 1.000000e+00 1.000000e+00
## log(X2nd.Flr.SF + 1) 0.000000e+00 0.000000e+00 1.000000e+00
## log(Lot.Area) 1.000000e+00 1.000000e+00 1.000000e+00
## Overall.Cond 1.000000e+00 1.000000e+00 1.000000e+00
## Overall.Qual 1.000000e+00 1.000000e+00 1.000000e+00
## BF 5.142395e-02 4.658921e-02 4.518892e-02
## PostProbs 3.680000e-02 3.340000e-02 3.240000e-02
## R2 9.034000e-01 9.034000e-01 9.034000e-01
## dim 1.100000e+01 1.100000e+01 1.100000e+01
## logmarg -1.050218e+03 -1.050316e+03 -1.050347e+03## P(B != 0 | Y) model 1 model 2 model 3
## Intercept 1.0000000 1.0000 1.000000e+00 1.000000e+00
## log(Total.Bsmt.SF + 1) 1.0000000 1.0000 1.000000e+00 1.000000e+00
## log(area) 1.0000000 1.0000 1.000000e+00 1.000000e+00
## Bedroom.AbvGr 0.9999798 1.0000 0.000000e+00 1.000000e+00
## Year.Built 1.0000000 1.0000 1.000000e+00 1.000000e+00
## log(X2nd.Flr.SF + 1) 1.0000000 1.0000 1.000000e+00 0.000000e+00
## log(Lot.Area) 1.0000000 1.0000 1.000000e+00 1.000000e+00
## Overall.Cond 1.0000000 1.0000 1.000000e+00 1.000000e+00
## Overall.Qual 1.0000000 1.0000 1.000000e+00 1.000000e+00
## BF NA 1.0000 2.015475e-05 7.279329e-13
## PostProbs NA 1.0000 0.000000e+00 0.000000e+00
## R2 NA 0.8940 8.902000e-01 8.855000e-01
## dim NA 9.0000 8.000000e+00 8.000000e+00
## logmarg NA -999.7468 -1.010559e+03 -1.027695e+03
## model 4 model 5
## Intercept 1.000000e+00 1.000000e+00
## log(Total.Bsmt.SF + 1) 0.000000e+00 0.000000e+00
## log(area) 1.000000e+00 1.000000e+00
## Bedroom.AbvGr 1.000000e+00 0.000000e+00
## Year.Built 1.000000e+00 1.000000e+00
## log(X2nd.Flr.SF + 1) 1.000000e+00 1.000000e+00
## log(Lot.Area) 1.000000e+00 1.000000e+00
## Overall.Cond 1.000000e+00 1.000000e+00
## Overall.Qual 1.000000e+00 1.000000e+00
## BF 8.091495e-16 5.777938e-19
## PostProbs 0.000000e+00 0.000000e+00
## R2 8.835000e-01 8.805000e-01
## dim 8.000000e+00 7.000000e+00
## logmarg -1.034497e+03 -1.041742e+030.0.0.13 Part 4 Final Model Assessment
statistical assumptions are violated, you may: (1) systematically over- or under-estimate coefficients (2) have large standard errors (3) have inaccurate statistical significance. There are two types of diagnostics: 1.those that are used to evaluate model fit. 2.and those that identify where (which data points) the model fits poorly. Model fit reflects whether the appropriate link function and structural model (i.e., relevant predictors are included, predictors are not correlated and irrelevant predictors are excluded) have been specified.
Problems in the data can be: 1.typos 2.outliers 3.influential data points 4.aspects of the data set that affect model performance, such as sparse data and zero cell counts.
Because methods of evaluating logistic regression models are limited, special attentions should be paid to the effects of data problems.
0.0.0.13.1 Section 4.1 Final Model Residual
For your final model, create and briefly interpret an informative plot of the residuals.
Final.lm <- lm(log(price) ~log(Total.Bsmt.SF + 1) + log(area)+ Bedroom.AbvGr + Year.Built + log(X1st.Flr.SF) +
log(Lot.Area) + Overall.Cond+Overall.Qual,
data =na.omit(train),pior="BIC")
predict.Final <- exp(predict(Final.lm, train))
resid.Final <- train$price - predict.Final
plot(resid(Final.lm))
plot(Final.lm)
model.resid<-Final.lm$residuals
plot(model.resid, main="Residuals",pch=20)
abline(0,0, lwd=2, col="blueviolet")
qqnorm(residuals(Final.lm))
qqline(residuals(Final.lm)
BIC.bas <- bas.lm(log(price) ~log(Garage.Area + 1) +
log(Total.Bsmt.SF + 1) + Garage.Cars + log(area) +
Full.Bath + Half.Bath +
Bedroom.AbvGr + Year.Built + log(X1st.Flr.SF) +
log(X2nd.Flr.SF + 1) +
log(Lot.Area) + Overall.Cond+Overall.Qual,
data =na.omit(train), prior="BIC",
modelprior=uniform())
summary(BIC.bas)
image(BIC.bas, rotate = F)
coef(BIC.bas)
plot(BIC.bas)
library(BAS)
train.ZS = bas.lm(log(price) ~ log(Garage.Area + 1) +
log(Total.Bsmt.SF + 1) + Garage.Cars + log(area) +
Full.Bath + Half.Bath +
Bedroom.AbvGr + Year.Built + log(X1st.Flr.SF) +
log(X2nd.Flr.SF + 1) +
log(Lot.Area) + Overall.Cond+Overall.Qual,
data =na.omit(train),prior="ZS-null",
modelprior=uniform(), initprobs="eplogp")
plot(train.ZS, ask=F)
train.ZS
options(width = 80)
summary(train.ZS)
image(train.ZS, rotate=F)
coef.ZS = coef(train.ZS)
plot(coef.ZS, subset=c(5:6), ask=F)
plot(coef.ZS, ask=FALSE)
confint(coef.ZS)
plot(confint(coef.ZS, parm=2:9))
muhat.BMA = fitted(train.ZS, estimator="BMA")
BMA = predict(train.ZS, estimator="BMA")
par(mar=c(9, 9, 3, 3))
plot(muhat.BMA, BMA$fit,
pch=16,
xlab=expression(hat(mu[i])), ylab=expression(hat(Y[i])))
abline(0,1)
BPM = predict(train.ZS, estimator="BPM")
(train.ZS$namesx[attr(BPM$fit, 'model') +1])[-1]
library(GGally)
BPM = predict(Final.ZS, estimator="BPM", se.fit=TRUE)
Final.conf.fit = confint(BPM, parm="mean")
Final.conf.pred = confint(BPM, parm="pred")
cbind(Final.conf.fit, Final.conf.pred)
plot(Final.conf.fit)
#new.pred = predict(Final.ZS, newdata=test, estimator="MPM")
Final.ZS = bas.lm(price ~ .,
data=test,
prior="ZS-null",
modelprior=uniform(),
method = "MCMC", MCMC.iterations = 10^6)
diagnostics(Final.ZS, type="model", pch=16)
data("test")
test$out.ind = diag(nrow(test))
## Error: <text>:16:1: unexpected symbol
## 15:
## 16: BIC.bas
## ^The RMSE for final model has been computed and compared.
0.0.0.13.2 Section 4.2 Final Model RMSE
predict.Final <- exp(predict(Final.lm, train))
resid.Final <- train$price - predict.Final
rmse.Final <- sqrt(mean(resid.Final^2))
rmse.Final## [1] 22160.99The RMSE of the final model is lower as compared to BIC/AIC but higher than model with transformed variables.Initial model has lowest rsme.
0.0.0.14 Section 4.3 Final Model Evaluation
What are some strengths and weaknesses of your model?
Although I started with maximum mixed variables for modeling,the final model contains only 8 variables giving largest Adjusted R-Squared,least possible RMSE and AIC/BIC lowest. The residuals are minimum and outliers still exist in the model as it appears in plots. There is no one magic procedure to remove all the overfitings and underfittings.By using ‘BAS’ with “BIC”as prior model is taking care overfiting and it seems to me the best model selection.
0.0.0.15 Final Model Validation
Testing your final model on a separate, validation data set is a great way to determine how your model will perform in real-life practice.
You will use the ames_validation dataset to do some additional assessment of your final model. Discuss your findings, be sure to mention: What is the RMSE of your final model when applied to the validation data? How does this value compare to that of the training data and/or testing data? What percentage of the 95% predictive confidence (or credible) intervals contain the true price of the house in the validation data set?
From this result, does your final model properly reflect uncertainty?
0.0.0.15.1 Section 4.4 Final Model Validation
validata=validation
val.ZS = bas.lm(log(price) ~ log(Garage.Area + 1) +
log(Total.Bsmt.SF + 1) + Garage.Cars + log(area) +
Full.Bath + Half.Bath +
Bedroom.AbvGr + Year.Built + log(X1st.Flr.SF) +
log(X2nd.Flr.SF + 1) +
log(Lot.Area) + Overall.Cond+Overall.Qual,
data =na.omit(validata),prior="ZS-null",
modelprior=uniform(), initprobs="eplogp")
plot(val.ZS, ask=F) 
val.ZS ##
## Call:
## bas.lm(formula = log(price) ~ log(Garage.Area + 1) + log(Total.Bsmt.SF + 1) + Garage.Cars + log(area) + Full.Bath + Half.Bath + Bedroom.AbvGr + Year.Built + log(X1st.Flr.SF) + log(X2nd.Flr.SF + 1) + log(Lot.Area) + Overall.Cond + Overall.Qual, data = na.omit(validata), prior = "ZS-null", modelprior = uniform(), initprobs = "eplogp")
##
##
## Marginal Posterior Inclusion Probabilities:
## Intercept log(Garage.Area + 1) log(Total.Bsmt.SF + 1)
## 1.00000 0.14919 1.00000
## Garage.Cars log(area) Full.Bath
## 0.95656 1.00000 0.21066
## Half.Bath Bedroom.AbvGr Year.Built
## 0.04592 1.00000 1.00000
## log(X1st.Flr.SF) log(X2nd.Flr.SF + 1) log(Lot.Area)
## 0.98802 0.05379 1.00000
## Overall.Cond Overall.Qual
## 1.00000 1.00000options(width = 80)
summary(val.ZS)## P(B != 0 | Y) model 1 model 2 model 3
## Intercept 1.00000000 1.0000 1.0000000 1.0000000
## log(Garage.Area + 1) 0.14918653 0.0000 0.0000000 1.0000000
## log(Total.Bsmt.SF + 1) 0.99999997 1.0000 1.0000000 1.0000000
## Garage.Cars 0.95656219 1.0000 1.0000000 1.0000000
## log(area) 1.00000000 1.0000 1.0000000 1.0000000
## Full.Bath 0.21065759 0.0000 1.0000000 0.0000000
## Half.Bath 0.04592006 0.0000 0.0000000 0.0000000
## Bedroom.AbvGr 0.99999974 1.0000 1.0000000 1.0000000
## Year.Built 1.00000000 1.0000 1.0000000 1.0000000
## log(X1st.Flr.SF) 0.98802490 1.0000 1.0000000 1.0000000
## log(X2nd.Flr.SF + 1) 0.05379060 0.0000 0.0000000 0.0000000
## log(Lot.Area) 1.00000000 1.0000 1.0000000 1.0000000
## Overall.Cond 1.00000000 1.0000 1.0000000 1.0000000
## Overall.Qual 1.00000000 1.0000 1.0000000 1.0000000
## BF NA 1.0000 0.2826422 0.1316314
## PostProbs NA 0.5985 0.1692000 0.0788000
## R2 NA 0.9077 0.9082000 0.9080000
## dim NA 10.0000 11.0000000 11.0000000
## logmarg NA 869.1325 867.8689721 867.1047959
## model 4 model 5
## Intercept 1.00000000 1.00000000
## log(Garage.Area + 1) 1.00000000 0.00000000
## log(Total.Bsmt.SF + 1) 1.00000000 1.00000000
## Garage.Cars 0.00000000 1.00000000
## log(area) 1.00000000 1.00000000
## Full.Bath 0.00000000 0.00000000
## Half.Bath 0.00000000 1.00000000
## Bedroom.AbvGr 1.00000000 1.00000000
## Year.Built 1.00000000 1.00000000
## log(X1st.Flr.SF) 1.00000000 1.00000000
## log(X2nd.Flr.SF + 1) 0.00000000 0.00000000
## log(Lot.Area) 1.00000000 1.00000000
## Overall.Cond 1.00000000 1.00000000
## Overall.Qual 1.00000000 1.00000000
## BF 0.05600208 0.05186174
## PostProbs 0.03350000 0.03100000
## R2 0.90700000 0.90780000
## dim 10.00000000 11.00000000
## logmarg 866.25017920 866.17337163image(val.ZS, rotate=F)
coef.ZS = coef(val.ZS)
plot(coef.ZS, subset=c(5:6), ask=F)
plot(coef.ZS, ask=FALSE)
confint(coef.ZS)## 2.5 % 97.5 % beta
## Intercept 11.9794921980 1.199512e+01 1.198732e+01
## log(Garage.Area + 1) 0.0000000000 1.172718e-02 1.340049e-03
## log(Total.Bsmt.SF + 1) 0.0163865777 3.032417e-02 2.344725e-02
## Garage.Cars 0.0129466002 5.960215e-02 3.796716e-02
## log(area) 0.4042874091 5.100059e-01 4.596646e-01
## Full.Bath -0.0304862800 2.101493e-06 -4.612937e-03
## Half.Bath 0.0000000000 0.000000e+00 3.951411e-04
## Bedroom.AbvGr -0.0522246635 -2.743234e-02 -3.908616e-02
## Year.Built 0.0035916727 4.354177e-03 3.983426e-03
## log(X1st.Flr.SF) 0.0806088573 1.621433e-01 1.202322e-01
## log(X2nd.Flr.SF + 1) -0.0003402053 2.208892e-04 9.036425e-06
## log(Lot.Area) 0.0987815541 1.376707e-01 1.182626e-01
## Overall.Cond 0.0560402120 7.155483e-02 6.373253e-02
## Overall.Qual 0.0741037327 9.280277e-02 8.356774e-02
## attr(,"Probability")
## [1] 0.95
## attr(,"class")
## [1] "confint.bas"plot(confint(coef.ZS, parm=2:9))## Warning in arrows(x, ci[, 1], x, ci[, 2], code = 3, angle = 90, length = 0.05, :
## zero-length arrow is of indeterminate angle and so skipped
## NULLmuhat.BMA = fitted(val.ZS, estimator="BMA")
BMA = predict(val.ZS, estimator="BMA")
par(mar=c(9, 9, 3, 3))
plot(muhat.BMA, BMA$fit,
pch=16,
xlab=expression(hat(mu[i])), ylab=expression(hat(Y[i])))
abline(0,1)
BPM = predict(val.ZS, estimator="BPM")
(val.ZS$namesx[attr(BPM$fit, 'model') +1])[-1]## [1] "log(Total.Bsmt.SF + 1)" "Garage.Cars" "log(area)"
## [4] "Bedroom.AbvGr" "Year.Built" "log(X1st.Flr.SF)"
## [7] "log(Lot.Area)" "Overall.Cond" "Overall.Qual"train.ZS = bas.lm(log(price) ~ log(Garage.Area + 1) +
log(Total.Bsmt.SF + 1) + Garage.Cars + log(area) +
Full.Bath + Half.Bath +
Bedroom.AbvGr + Year.Built + log(X1st.Flr.SF) +
log(X2nd.Flr.SF + 1) +
log(Lot.Area) + Overall.Cond+Overall.Qual,
data =na.omit(train),prior="ZS-null",
modelprior=uniform(), initprobs="eplogp")
plot(train.ZS, ask=F) 
train.ZS ##
## Call:
## bas.lm(formula = log(price) ~ log(Garage.Area + 1) + log(Total.Bsmt.SF + 1) + Garage.Cars + log(area) + Full.Bath + Half.Bath + Bedroom.AbvGr + Year.Built + log(X1st.Flr.SF) + log(X2nd.Flr.SF + 1) + log(Lot.Area) + Overall.Cond + Overall.Qual, data = na.omit(train), prior = "ZS-null", modelprior = uniform(), initprobs = "eplogp")
##
##
## Marginal Posterior Inclusion Probabilities:
## Intercept log(Garage.Area + 1) log(Total.Bsmt.SF + 1)
## 1.00000 0.03801 1.00000
## Garage.Cars log(area) Full.Bath
## 0.99995 1.00000 0.04810
## Half.Bath Bedroom.AbvGr Year.Built
## 0.04234 0.99999 1.00000
## log(X1st.Flr.SF) log(X2nd.Flr.SF + 1) log(Lot.Area)
## 0.85339 0.18294 1.00000
## Overall.Cond Overall.Qual
## 1.00000 1.00000options(width = 80)
summary(train.ZS)## P(B != 0 | Y) model 1 model 2 model 3
## Intercept 1.00000000 1.0000 1.0000000 1.00000000
## log(Garage.Area + 1) 0.03801088 0.0000 0.0000000 0.00000000
## log(Total.Bsmt.SF + 1) 1.00000000 1.0000 1.0000000 1.00000000
## Garage.Cars 0.99995243 1.0000 1.0000000 1.00000000
## log(area) 1.00000000 1.0000 1.0000000 1.00000000
## Full.Bath 0.04809873 0.0000 0.0000000 1.00000000
## Half.Bath 0.04234305 0.0000 0.0000000 0.00000000
## Bedroom.AbvGr 0.99999244 1.0000 1.0000000 1.00000000
## Year.Built 1.00000000 1.0000 1.0000000 1.00000000
## log(X1st.Flr.SF) 0.85339147 1.0000 0.0000000 1.00000000
## log(X2nd.Flr.SF + 1) 0.18294415 0.0000 1.0000000 0.00000000
## log(Lot.Area) 1.00000000 1.0000 1.0000000 1.00000000
## Overall.Cond 1.00000000 1.0000 1.0000000 1.00000000
## Overall.Qual 1.00000000 1.0000 1.0000000 1.00000000
## BF NA 1.0000 0.1807785 0.05015929
## PostProbs NA 0.7160 0.1294000 0.03590000
## R2 NA 0.9033 0.9029000 0.90340000
## dim NA 10.0000 10.0000000 11.00000000
## logmarg NA 934.3534 932.6428674 931.36079871
## model 4 model 5
## Intercept 1.00000000 1.00000000
## log(Garage.Area + 1) 0.00000000 0.00000000
## log(Total.Bsmt.SF + 1) 1.00000000 1.00000000
## Garage.Cars 1.00000000 1.00000000
## log(area) 1.00000000 1.00000000
## Full.Bath 0.00000000 0.00000000
## Half.Bath 1.00000000 0.00000000
## Bedroom.AbvGr 1.00000000 1.00000000
## Year.Built 1.00000000 1.00000000
## log(X1st.Flr.SF) 1.00000000 1.00000000
## log(X2nd.Flr.SF + 1) 0.00000000 1.00000000
## log(Lot.Area) 1.00000000 1.00000000
## Overall.Cond 1.00000000 1.00000000
## Overall.Qual 1.00000000 1.00000000
## BF 0.04550812 0.04415973
## PostProbs 0.03260000 0.03160000
## R2 0.90340000 0.90340000
## dim 11.00000000 11.00000000
## logmarg 931.26348567 931.23340830image(train.ZS, rotate=F)
coef.ZS = coef(train.ZS)
plot(coef.ZS, subset=c(5:6), ask=F)
plot(coef.ZS, ask=FALSE)
confint(coef.ZS)## 2.5 % 97.5 % beta
## Intercept 11.984595888 12.000695275 11.9927955455
## log(Garage.Area + 1) 0.000000000 0.000000000 -0.0000905138
## log(Total.Bsmt.SF + 1) 0.019371953 0.035064508 0.0274699188
## Garage.Cars 0.026119801 0.056977955 0.0416022903
## log(area) 0.381181885 0.586104179 0.4487503776
## Full.Bath 0.000000000 0.000000000 -0.0004871403
## Half.Bath 0.000000000 0.000000000 0.0003368691
## Bedroom.AbvGr -0.052264476 -0.025055018 -0.0384568100
## Year.Built 0.003513717 0.004314618 0.0039140509
## log(X1st.Flr.SF) 0.000000000 0.163564234 0.1127059426
## log(X2nd.Flr.SF + 1) -0.013489804 0.000000000 -0.0019530958
## log(Lot.Area) 0.099073093 0.136476515 0.1172359369
## Overall.Cond 0.049580122 0.065819895 0.0579234923
## Overall.Qual 0.076658768 0.096575459 0.0862000785
## attr(,"Probability")
## [1] 0.95
## attr(,"class")
## [1] "confint.bas"plot(confint(coef.ZS, parm=2:9))## Warning in arrows(x, ci[, 1], x, ci[, 2], code = 3, angle = 90, length = 0.05, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ci[, 1], x, ci[, 2], code = 3, angle = 90, length = 0.05, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ci[, 1], x, ci[, 2], code = 3, angle = 90, length = 0.05, :
## zero-length arrow is of indeterminate angle and so skipped
## NULLmuhat.BMA = fitted(train.ZS, estimator="BMA")
BMA = predict(train.ZS, estimator="BMA")
par(mar=c(9, 9, 3, 3))
plot(muhat.BMA, BMA$fit,
pch=16,
xlab=expression(hat(mu[i])), ylab=expression(hat(Y[i])))
abline(0,1)
BPM = predict(train.ZS, estimator="BPM")
(train.ZS$namesx[attr(BPM$fit, 'model') +1])[-1]## [1] "log(Total.Bsmt.SF + 1)" "Garage.Cars" "log(area)"
## [4] "Bedroom.AbvGr" "Year.Built" "log(X1st.Flr.SF)"
## [7] "log(X2nd.Flr.SF + 1)" "log(Lot.Area)" "Overall.Cond"
## [10] "Overall.Qual"test.ZS = bas.lm(log(price) ~ log(Garage.Area + 1) +
log(Total.Bsmt.SF + 1) + Garage.Cars + log(area) +
Full.Bath + Half.Bath +
Bedroom.AbvGr + Year.Built + log(X1st.Flr.SF) +
log(X2nd.Flr.SF + 1) +
log(Lot.Area) + Overall.Cond+Overall.Qual,
data =na.omit(test),prior="ZS-null",
modelprior=uniform(), initprobs="eplogp")
plot(test.ZS, ask=F) 
test.ZS ##
## Call:
## bas.lm(formula = log(price) ~ log(Garage.Area + 1) + log(Total.Bsmt.SF + 1) + Garage.Cars + log(area) + Full.Bath + Half.Bath + Bedroom.AbvGr + Year.Built + log(X1st.Flr.SF) + log(X2nd.Flr.SF + 1) + log(Lot.Area) + Overall.Cond + Overall.Qual, data = na.omit(test), prior = "ZS-null", modelprior = uniform(), initprobs = "eplogp")
##
##
## Marginal Posterior Inclusion Probabilities:
## Intercept log(Garage.Area + 1) log(Total.Bsmt.SF + 1)
## 1.00000 0.05072 1.00000
## Garage.Cars log(area) Full.Bath
## 0.99993 1.00000 0.04157
## Half.Bath Bedroom.AbvGr Year.Built
## 0.04097 0.99995 1.00000
## log(X1st.Flr.SF) log(X2nd.Flr.SF + 1) log(Lot.Area)
## 0.83417 0.20685 1.00000
## Overall.Cond Overall.Qual
## 1.00000 1.00000options(width = 80)
summary(test.ZS)## P(B != 0 | Y) model 1 model 2 model 3
## Intercept 1.00000000 1.0000 1.0000000 1.00000000
## log(Garage.Area + 1) 0.05072284 0.0000 0.0000000 1.00000000
## log(Total.Bsmt.SF + 1) 1.00000000 1.0000 1.0000000 1.00000000
## Garage.Cars 0.99992848 1.0000 1.0000000 1.00000000
## log(area) 1.00000000 1.0000 1.0000000 1.00000000
## Full.Bath 0.04156831 0.0000 0.0000000 0.00000000
## Half.Bath 0.04097406 0.0000 0.0000000 0.00000000
## Bedroom.AbvGr 0.99995255 1.0000 1.0000000 1.00000000
## Year.Built 1.00000000 1.0000 1.0000000 1.00000000
## log(X1st.Flr.SF) 0.83417493 1.0000 0.0000000 1.00000000
## log(X2nd.Flr.SF + 1) 0.20684523 0.0000 1.0000000 0.00000000
## log(Lot.Area) 1.00000000 1.0000 1.0000000 1.00000000
## Overall.Cond 1.00000000 1.0000 1.0000000 1.00000000
## Overall.Qual 1.00000000 1.0000 1.0000000 1.00000000
## BF NA 1.0000 0.2105989 0.05269758
## PostProbs NA 0.6914 0.1456000 0.03640000
## R2 NA 0.8993 0.8989000 0.89940000
## dim NA 10.0000 10.0000000 11.00000000
## logmarg NA 896.0631 894.5053273 893.11994135
## model 4 model 5
## Intercept 1.00000000 1.0000000
## log(Garage.Area + 1) 0.00000000 0.0000000
## log(Total.Bsmt.SF + 1) 1.00000000 1.0000000
## Garage.Cars 1.00000000 1.0000000
## log(area) 1.00000000 1.0000000
## Full.Bath 0.00000000 0.0000000
## Half.Bath 0.00000000 1.0000000
## Bedroom.AbvGr 1.00000000 1.0000000
## Year.Built 1.00000000 1.0000000
## log(X1st.Flr.SF) 1.00000000 1.0000000
## log(X2nd.Flr.SF + 1) 1.00000000 0.0000000
## log(Lot.Area) 1.00000000 1.0000000
## Overall.Cond 1.00000000 1.0000000
## Overall.Qual 1.00000000 1.0000000
## BF 0.05136128 0.0439293
## PostProbs 0.03550000 0.0304000
## R2 0.89940000 0.8994000
## dim 11.00000000 11.0000000
## logmarg 893.09425642 892.9379533image(test.ZS, rotate=F)
coef.ZS = coef(test.ZS)
plot(coef.ZS, subset=c(5:6), ask=F)
plot(coef.ZS, ask=FALSE)
confint(coef.ZS)## 2.5 % 97.5 % beta
## Intercept 1.201501e+01 12.0305983703 12.0229743189
## log(Garage.Area + 1) -7.568026e-06 0.0002629514 0.0001999572
## log(Total.Bsmt.SF + 1) 2.618871e-02 0.0403233876 0.0333637807
## Garage.Cars 3.284622e-02 0.0632837120 0.0483176580
## log(area) 4.152515e-01 0.6227373346 0.4894501096
## Full.Bath 0.000000e+00 0.0000000000 -0.0002771239
## Half.Bath 0.000000e+00 0.0000000000 0.0002645275
## Bedroom.AbvGr -4.788604e-02 -0.0219689039 -0.0343854345
## Year.Built 3.016973e-03 0.0038004798 0.0034093993
## log(X1st.Flr.SF) 0.000000e+00 0.1573291656 0.1073573398
## log(X2nd.Flr.SF + 1) -1.356369e-02 0.0000000000 -0.0022428171
## log(Lot.Area) 8.997306e-02 0.1257335113 0.1084441826
## Overall.Cond 4.157699e-02 0.0574503468 0.0497381466
## Overall.Qual 6.714401e-02 0.0864748907 0.0770966161
## attr(,"Probability")
## [1] 0.95
## attr(,"class")
## [1] "confint.bas"plot(confint(coef.ZS, parm=2:9))## Warning in arrows(x, ci[, 1], x, ci[, 2], code = 3, angle = 90, length = 0.05, :
## zero-length arrow is of indeterminate angle and so skipped
## Warning in arrows(x, ci[, 1], x, ci[, 2], code = 3, angle = 90, length = 0.05, :
## zero-length arrow is of indeterminate angle and so skipped
## NULLmuhat.BMA = fitted(test.ZS, estimator="BMA")
BMA = predict(test.ZS, estimator="BMA")
par(mar=c(9, 9, 3, 3))
plot(muhat.BMA, BMA$fit,
pch=16,
xlab=expression(hat(mu[i])), ylab=expression(hat(Y[i])))
abline(0,1)
BPM = predict(test.ZS, estimator="BPM")
(test.ZS$namesx[attr(BPM$fit, 'model') +1])[-1]## [1] "log(Total.Bsmt.SF + 1)" "Garage.Cars" "log(area)"
## [4] "Bedroom.AbvGr" "Year.Built" "log(X1st.Flr.SF)"
## [7] "log(X2nd.Flr.SF + 1)" "log(Lot.Area)" "Overall.Cond"
## [10] "Overall.Qual"Principal Component Regression A model validation was caried out by using a PSL. Compared the Prediction and RMSE. Partial Least Square Regression Method,seful when the data has highly-correlated predictors.
0.0.0.15.2 Fit models using pcr and validating prediction error.
library(pls)##
## Attaching package: 'pls'## The following object is masked from 'package:crossval':
##
## crossval## The following object is masked from 'package:bootstrap':
##
## crossval## The following object is masked from 'package:corrplot':
##
## corrplot## The following object is masked from 'package:stats':
##
## loadingsvalidata[is.na(validata)] <- 0
fvalid <- pcr(price~., data=na.omit(validata), validata="CV")
ftrain<- pcr(price~., data=na.omit(train), train="CV")
ftest <- pcr(price~., data=na.omit(test), test="CV")
summary(fvalid)## Data: X dimension: 762 26
## Y dimension: 762 1
## Fit method: svdpc
## Number of components considered: 26
## TRAINING: % variance explained
## 1 comps 2 comps 3 comps 4 comps 5 comps 6 comps 7 comps 8 comps
## X 97.51 98.65 99.62 99.79 99.89 99.95 99.96 99.97
## price 10.40 62.63 64.44 65.19 69.55 70.52 71.89 71.92
## 9 comps 10 comps 11 comps 12 comps 13 comps 14 comps 15 comps
## X 99.98 99.99 99.99 100.00 100.00 100.00 100.00
## price 72.07 72.07 72.57 73.67 79.34 79.86 85.99
## 16 comps 17 comps 18 comps 19 comps 20 comps 21 comps 22 comps
## X 100.00 100.00 100.00 100.00 100.00 100.00 100.00
## price 86.14 87.23 87.29 87.97 87.97 87.99 87.99
## 23 comps 24 comps 25 comps 26 comps
## X 100.00 100 100.00 100.00
## price 87.99 88 88.21 88.24summary(ftrain)## Data: X dimension: 832 26
## Y dimension: 832 1
## Fit method: svdpc
## Number of components considered: 26
## TRAINING: % variance explained
## 1 comps 2 comps 3 comps 4 comps 5 comps 6 comps 7 comps 8 comps
## X 99.301 99.67 99.91 99.95 99.97 99.99 99.99 99.99
## price 6.687 68.07 72.93 73.86 75.89 76.49 77.30 77.31
## 9 comps 10 comps 11 comps 12 comps 13 comps 14 comps 15 comps
## X 100.00 100.00 100.00 100.00 100.00 100.00 100.00
## price 77.31 77.37 77.69 77.95 82.77 82.85 86.75
## 16 comps 17 comps 18 comps 19 comps 20 comps 21 comps 22 comps
## X 100.00 100.0 100.00 100.00 100.0 100.0 100.00
## price 86.86 88.1 88.71 88.97 89.2 89.2 89.24
## 23 comps 24 comps 25 comps 26 comps
## X 100.00 100.00 100.00 100.00
## price 89.25 89.26 89.26 89.42summary(ftest)## Data: X dimension: 813 26
## Y dimension: 813 1
## Fit method: svdpc
## Number of components considered: 26
## TRAINING: % variance explained
## 1 comps 2 comps 3 comps 4 comps 5 comps 6 comps 7 comps 8 comps
## X 98.87 99.41 99.85 99.91 99.95 99.98 99.99 99.99
## price 6.66 62.38 71.34 72.54 75.61 75.63 75.92 75.92
## 9 comps 10 comps 11 comps 12 comps 13 comps 14 comps 15 comps
## X 99.99 100.00 100.0 100.0 100.00 100.00 100.00
## price 76.54 76.64 78.2 81.9 82.01 82.06 85.68
## 16 comps 17 comps 18 comps 19 comps 20 comps 21 comps 22 comps
## X 100.00 100.0 100.00 100.00 100.0 100.00 100.00
## price 85.68 87.4 87.98 88.15 88.2 88.31 88.31
## 23 comps 24 comps 25 comps 26 comps
## X 100.00 100.00 100.0 100.00
## price 88.31 88.35 88.4 88.66predictions1 <- predict(fvalid, validata, ncomp=6)
predictions2 <- predict(ftrain,train, ncomp=6)
predictions3 <- predict(ftest,test, ncomp=6)0.0.0.15.3 summarize accuracy
vrmse <- mean(validata$price - predictions1)^2
trrmse <- mean(train$price - predictions2)^2
termse <- mean(test$price - predictions3)^2
vrmse## [1] 1.336108e-21trrmse## [1] 9.43363e-21termse ## [1] 1.393866e-220.0.0.15.4 Neural Network modeling and prediction-Train Dataset
library(nnet)
train=na.omit(train)
Xtr = train
X1 = X[1:832, ] # X1 is the training data
fitnn = nnet(price ~ log(area)+Overall.Qual + Overall.Cond + Year.Built + Year.Remod.Add +Total.Bsmt.SF + X1st.Flr.SF + X2nd.Flr.SF +
TotRms.AbvGrd + Central.Air + Lot.Area + Full.Bath,
X1[, 1:27,], size = 3, skip = TRUE, linout = TRUE)
summary(fitnn)
P = dollar(predict(fitnn, Xtr[1:832, 1:27]))
pred = data.frame(predicted = P, actual =Xtr[1:832, 2])
head(pred,2)
par(mfrow=c(1,1))
l = 1:200
plot(NA, xlim = c(1, length(pred[l, 1])), ylim = c(0, max(pred[, 2])), xlab = "Testing Cases",
ylab = "Price",main="Actual vs Predicted Prices-Train Data")
lines(pred[l, 1], col = "red")
lines(pred[l, 2])
legend("topleft", cex = 0.75, lty = 1, c("Predicted Price", "True Price"), col = c("red",
"black"))
rm(fitnn)
rm(pred)
rm(P)
rm(X)
rm(X1)
#Summary: Training Neural Network
# weights: 55
#initial value 26187404141688.628906
#iter 10 value 1923513771818.957764
#iter 20 value 724545492912.327637
#iter 30 value 707041721954.710693
#iter 40 value 706960994991.794556
#iter 50 value 499624323882.398315
#iter 60 value 465879328691.385010
#iter 70 value 461107765914.030029
#iter 80 value 448338999224.494507
#final value 447361855603.966797
#converged
# summary(fitnn)
#pred = data.frame(predicted = P, actual =Xtr[1:832, 2])
#head(pred,2)
predicted Actual
#1 $118,067 $126000
#2 $120,617 $139500 
0.0.0.15.5 Neural Network modeling and predition-Test Dataset
testdata = na.omit(test)
X = testdata
X1 = X[1:813, ] # X1b is the test data
fitnn = nnet(price ~ log(area)+Overall.Qual + Overall.Cond + Year.Built + Year.Remod.Add +
Total.Bsmt.SF + X1st.Flr.SF + X2nd.Flr.SF +
TotRms.AbvGrd + Central.Air + Lot.Area + Full.Bath,
X1[, 1:27,], size = 3, skip = TRUE, linout = TRUE)
summary(fitnn)
P = dollar(predict(fitnn, X1[1:813, 1:27]))
pred = data.frame(predicted = P, actual = X1[1:813, 2])
head(pred)
par(mfrow=c(1,1))
l = 1:200
plot(NA, xlim = c(1, length(pred[l, 1])), ylim = c(0, max(pred[, 2])), xlab = "Testing Cases",
ylab = "Price",main="Actual vs Predicted Prices-Test Data")
lines(pred[l, 1], col = "red")
lines(pred[l, 2])
legend("topleft", cex = 0.75, lty = 1, c("Predicted Price", "True Price"), col = c("red",
"black"))
rm(fitnn)
rm(pred)
rm(P)
rm(X)
rm(X1)
# Summary For Testa dataset
# weights: 55
#initial value 30877867087849.433594
#iter 10 value 1932574618040.414551
#iter 20 value 489858386966.532837
#final value 477319528059.363586
#converged
#pred = data.frame(predicted = P, actual = X1[1:813, 2])
#head(pred)
# predicted Actual price
#1 $294,175 $305900
#2 $223,209 $257500
#3 $112,493 $116000
#4 $152,488 $143450
#5 $262,113 $277500
#6 $211,622 $200000
0.0.0.15.6 Neural Network modeling and prediction-Validation Dataset
validata = na.omit(validation)
X = validata
X1 = X[1:761, ] # X1c is the validation data
library(nnet)
fitnn = nnet(price ~ log(area)+Overall.Qual + Overall.Cond + Year.Built + Year.Remod.Add +
Total.Bsmt.SF + X1st.Flr.SF + X2nd.Flr.SF +
TotRms.AbvGrd + Central.Air + Lot.Area + Full.Bath,
X1[, 1:27,], size = 3, skip = TRUE, linout = TRUE)
summary(fitnn)
P = dollar(predict(fitnn, X1[1:761, 1:27]))
pred = data.frame(predicted = P, actual = X1[1:761, 2])
head(pred)
par(mfrow=c(1,1))
l = 1:200
plot(NA, xlim = c(1, length(pred[l, 1])), ylim = c(0, max(pred[, 2])), xlab = "Testing Cases",
ylab = "Price",main="Actual versus Predicted Prices-Validation set")
lines(predv[l, 1], col = "red")
lines(predv[l, 2])
legend("topleft", cex = 0.75, lty = 1, c("Predicted Price", "True Price"), col = c("red",
"black"))
# Summary of Validation dataset
# weights: 55
#initial value 24424403372139.093750
#iter 10 value 2946017378475.332031
#final value 451816598680.519104
#converged
#pred = data.frame(predicted = P, actual = X1[1:761, 2])
#head(pred)
#predicted Actual price
#1 $151,823 $194000
#2 $121,623 $117600
#3 $138,035 $156000
#4 $207,115 $183000
#5 $159,301 $147000
#6 $136,702 $117000 
0.0.0.15.7 Model Assessment-Using different methods
Final.tr <- lm(log(price) ~log(Total.Bsmt.SF + 1) + area+ Bedroom.AbvGr + Year.Built + log(X1st.Flr.SF) +
log(Lot.Area) + Overall.Cond+Overall.Qual+TotRms.AbvGrd+
Bsmt.Full.Bath+Garage.Cars+Garage.Area+Year.Remod.Add+
Kitchen.AbvGr+Fireplaces+MS.SubClass+Half.Bath+Full.Bath,
data =na.omit(train))
hpr1 <- predict(Final.tr,data.frame(train),
interval = "confidence")
fit.price = dollar(as.numeric(hpr1[1]))
lower.fit = dollar(as.numeric(hpr1[2]))
upper.fit = dollar(as.numeric(hpr1[3]))
hpcb1 <- cbind.data.frame(lower.fit, fit.price, upper.fit)
head(hpcb1)## lower.fit fit.price upper.fit
## 1 $11.76 $11.74 $11.74Final.ts <- lm(log(price) ~log(Total.Bsmt.SF + 1) + area+ Bedroom.AbvGr + Year.Built + log(X1st.Flr.SF) +
log(Lot.Area) + Overall.Cond+Overall.Qual+TotRms.AbvGrd+
Bsmt.Full.Bath+Garage.Cars+Garage.Area+Year.Remod.Add+
Kitchen.AbvGr+Fireplaces+MS.SubClass+Half.Bath+Full.Bath,
data =na.omit(test))
hpr2 <- predict(Final.ts, data.frame(test),
interval = "confidence")
fit.price1 = dollar(as.numeric(hpr2[1]))
lower.fit1 = dollar(as.numeric(hpr2[2]))
upper.fit1 = dollar(as.numeric(hpr2[3]))
hpcb2 <- cbind.data.frame(lower.fit1, fit.price1, upper.fit1)
head(hpcb2)## lower.fit1 fit.price1 upper.fit1
## 1 $12.35 $12.58 $11.68Final.val <- lm(log(price) ~log(Total.Bsmt.SF + 1) + area+ Bedroom.AbvGr + Year.Built + log(X1st.Flr.SF) +
log(Lot.Area) + Overall.Cond+Overall.Qual+TotRms.AbvGrd+
Bsmt.Full.Bath+Garage.Cars+Garage.Area+Year.Remod.Add+
Kitchen.AbvGr+Fireplaces+MS.SubClass+Half.Bath+Full.Bath,
data =na.omit(validation))
hpr3 <- predict(Final.val, data.frame(validation),
interval = "confidence")
fit.price2 = dollar(as.numeric(hpr3[1]))
lower.fit2 = dollar(as.numeric(hpr3[2]))
upper.fit2 = dollar(as.numeric(hpr3[3]))
hpcb3 <- cbind.data.frame(lower.fit2, fit.price2, upper.fit2)
head(hpcb3)## lower.fit2 fit.price2 upper.fit2
## 1 $11.69 $11.91 $11.91Regression with leaps is best model selection method.
library(leaps)
library(MPV)##
## Attaching package: 'MPV'## The following object is masked from 'package:MASS':
##
## cement## The following object is masked from 'package:datasets':
##
## stacklosslibrary(DAAG)
data(train)## Warning in data(train): data set 'train' not foundfull.lm <- lm(log(price) ~ ., data=train)
press(full.lm)## [1] 10.10884aov(full.lm)## Call:
## aov(formula = full.lm)
##
## Terms:
## area MS.SubClass Lot.Area Overall.Qual Overall.Cond
## Sum of Squares 65.07093 1.66326 0.44099 27.34524 0.13186
## Deg. of Freedom 1 1 1 1 1
## Year.Built Year.Remod.Add Total.Bsmt.SF Central.Air X1st.Flr.SF
## Sum of Squares 8.18921 0.06448 3.02457 0.40969 0.10734
## Deg. of Freedom 1 1 1 1 1
## X2nd.Flr.SF Bsmt.Full.Bath Bsmt.Half.Bath Full.Bath Half.Bath
## Sum of Squares 0.02195 1.15518 0.04914 0.04120 0.00115
## Deg. of Freedom 1 1 1 1 1
## Bedroom.AbvGr Kitchen.AbvGr TotRms.AbvGrd Fireplaces
## Sum of Squares 0.20582 0.01334 0.04474 0.22572
## Deg. of Freedom 1 1 1 1
## Garage.Cars Garage.Area Wood.Deck.SF Open.Porch.SF
## Sum of Squares 0.49123 0.06947 0.00238 0.00801
## Deg. of Freedom 1 1 1 1
## Enclosed.Porch Screen.Porch Pool.Area Residuals
## Sum of Squares 0.04433 0.07498 0.12147 9.24401
## Deg. of Freedom 1 1 1 805
##
## Residual standard error: 0.1071599
## Estimated effects may be unbalancedX <- model.matrix(full.lm)[,-1]0.0.0.15.8 R^2 – all subsets
r2.leaps <- leaps(X, train$price, nbest=3, method='r2')
plot(r2.leaps$size, r2.leaps$r2, pch=23, bg='blue', cex=2)
best.model.r2 <- r2.leaps$which[which((r2.leaps$r2 == max(r2.leaps$r2))),]
print(best.model.r2)## 1 2 3 4 5 6 7 8 9 A B C D E F G
## TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
## H I J K L M N O P Q
## TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE0.0.0.15.9 Adjusted R^2 – all subsets
adjr2.leaps <- leaps(X, train$price, nbest=3, method='adjr2')
plot(adjr2.leaps$size, adjr2.leaps$adjr2, pch=23, bg='blue', cex=2)
best.model.adjr2 <- adjr2.leaps$which[which((adjr2.leaps$adjr2 == max(adjr2.leaps$adjr2))),]
print(best.model.adjr2)## 1 2 3 4 5 6 7 8 9 A B C D
## TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE FALSE
## E F G H I J K L M N O P Q
## TRUE FALSE TRUE TRUE TRUE TRUE FALSE TRUE TRUE FALSE FALSE FALSE TRUE0.0.0.15.10 Cp – all subsets
Cp.leaps <- leaps(X, train$price, nbest=3, method='Cp')
plot(Cp.leaps$size, Cp.leaps$Cp, pch=23, bg='blue', cex=2)
best.model.Cp <- Cp.leaps$which[which((Cp.leaps$Cp == min(Cp.leaps$Cp))),]
print(best.model.Cp)## 1 2 3 4 5 6 7 8 9 A B C D
## TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE FALSE
## E F G H I J K L M N O P Q
## FALSE FALSE TRUE TRUE TRUE TRUE FALSE TRUE TRUE FALSE FALSE FALSE TRUE0.0.0.15.11 Final Regression Models with k-10 fold validation.
0.0.0.15.12 Training,Test and Validation datasets models comparison
library(broom)
set.seed(10)
folds<-sample(rep(1:10, length=nrow(train)))
table(folds)## folds
## 1 2 3 4 5 6 7 8 9 10
## 84 84 83 83 83 83 83 83 83 83cv.train.errors<-matrix(NA, nrow=10,ncol=2)
for(k in 1:10)
{
train.fit<-lm(log(price) ~log(Garage.Area + 1) +
log(Total.Bsmt.SF + 1) + Garage.Cars + log(area) +
Full.Bath + Half.Bath +
Bedroom.AbvGr + Year.Built + log(X1st.Flr.SF) +
log(X2nd.Flr.SF + 1) +log(Lot.Area) + Central.Air + Overall.Cond+Overall.Qual, data=train[folds!=k,])
pred1<-predict(train.fit, train[folds==k,])
cv.train.errors[k,1]<-sqrt(mean((train$price[folds==k]-pred1)^2, na.rm=T))
cv.train.errors[k,2]<-summary(train.fit)$adj.r.squared
}
cv.train.errors#RMSE of each fold## [,1] [,2]
## [1,] 187236.9 0.9043629
## [2,] 177892.3 0.9008857
## [3,] 196398.4 0.9042077
## [4,] 190682.0 0.9047987
## [5,] 179759.2 0.9030512
## [6,] 184102.1 0.9003970
## [7,] 173825.5 0.9027575
## [8,] 184121.2 0.9041747
## [9,] 188594.9 0.9054040
## [10,] 205914.2 0.9043325mean(cv.train.errors[,1])#Average RMSE## [1] 186852.7mean(cv.train.errors[,2])#Average adj.R.Squared## [1] 0.9034372plot(cv.train.errors[,1], pch=19, ylab="RMSE", xlab="K-Fold")#Distribution of RMSE by fold
layout(matrix(c(1,2,3,4), 2, 2, byrow = TRUE))
plot(train.fit)#plotting one of the folds
glance(train.fit)## r.squared adj.r.squared sigma statistic p.value df logLik AIC
## 1 0.9061231 0.9043325 0.1142284 506.0535 0 15 569.7879 -1107.576
## BIC deviance df.residual
## 1 -1033.676 9.57733 734predtrain=pred1
library(broom)
set.seed(10)
folds<-sample(rep(1:10, length=nrow(test)))
table(folds)## folds
## 1 2 3 4 5 6 7 8 9 10
## 82 82 82 81 81 81 81 81 81 81cv.test.errors<-matrix(NA, nrow=10,ncol=2)
for(k in 1:10)
{
test.fit<-lm(log(price) ~log(Garage.Area + 1) +
log(Total.Bsmt.SF + 1) + Garage.Cars + log(area) +
Full.Bath + Half.Bath +
Bedroom.AbvGr + Year.Built + log(X1st.Flr.SF) +
log(X2nd.Flr.SF + 1) +log(Lot.Area) + Central.Air + Overall.Cond+Overall.Qual, data=test[folds!=k,])
pred2<-predict(test.fit, test[folds==k,])
cv.test.errors[k,1]<-sqrt(mean((test$price[folds==k]-pred2)^2, na.rm=T))
cv.test.errors[k,2]<-summary(test.fit)$adj.r.squared
}
cv.test.errors#RMSE of each fold## [,1] [,2]
## [1,] 178695.5 0.8978333
## [2,] 191809.2 0.8968327
## [3,] 191293.9 0.8996986
## [4,] 192580.4 0.8970725
## [5,] 186206.1 0.9024052
## [6,] 194137.7 0.8932473
## [7,] 191586.9 0.8989962
## [8,] 189422.2 0.8989738
## [9,] 184142.0 0.8997203
## [10,] 189765.3 0.8983212mean(cv.test.errors[,1])#Average RMSE## [1] 188963.9plot(cv.test.errors[,1], pch=19, ylab="RMSE", xlab="K-Fold")#Distribution of RMSE by fold
layout(matrix(c(1,2,3,4), 2, 2, byrow = TRUE))
plot(test.fit)#plotting one of the folds
visreg(test.fit)
glance(test.fit)## r.squared adj.r.squared sigma statistic p.value df logLik AIC
## 1 0.9002686 0.8983212 0.1130923 462.3077 0 15 564.3463 -1096.693
## BIC deviance df.residual
## 1 -1023.16 9.170334 717predtest = pred2
validation[is.na(validation)] <- 0
set.seed(10)
folds<-sample(rep(1:10, length=nrow(validation)))
table(folds)## folds
## 1 2 3 4 5 6 7 8 9 10
## 77 77 76 76 76 76 76 76 76 76cv.valid.errors<-matrix(NA, nrow=10,ncol=2)
for(k in 1:10)
{
valid.fit<-lm(log(price) ~log(Garage.Area + 1) +
log(Total.Bsmt.SF + 1) + Garage.Cars + log(area) +
Full.Bath + Half.Bath +
Bedroom.AbvGr + Year.Built + log(X1st.Flr.SF) +
log(X2nd.Flr.SF + 1) +log(Lot.Area) + Central.Air + Overall.Cond+Overall.Qual, data=validation[folds!=k,])
pred3<-predict(valid.fit, validation[folds==k,])
cv.valid.errors[k,1]<-sqrt(mean((validation$price[folds==k]-pred3)^2, na.rm=T))
cv.valid.errors[k,2]<-summary(valid.fit)$adj.r.squared
}
cv.valid.errors#RMSE of each fold## [,1] [,2]
## [1,] 202200.2 0.9030862
## [2,] 180727.2 0.9050697
## [3,] 167247.3 0.9071745
## [4,] 182512.5 0.9087530
## [5,] 192624.2 0.9093541
## [6,] 160872.5 0.9137843
## [7,] 183778.7 0.9068475
## [8,] 192058.0 0.9088324
## [9,] 186127.9 0.9083859
## [10,] 186454.6 0.9017523mean(cv.valid.errors[,1])#Average RMSE## [1] 183460.3mean(cv.valid.errors[,2])#Average adj.R.Squared## [1] 0.907304plot(cv.valid.errors[,1], pch=19, ylab="RMSE", xlab="K-Fold")#Distribution of RMSE by fold
layout(matrix(c(1,2,3,4), 2, 2, byrow = TRUE))
plot(valid.fit)#plotting one of the folds
visreg(valid.fit)
glance(valid.fit)## r.squared adj.r.squared sigma statistic p.value df logLik AIC
## 1 0.9037603 0.9017523 0.1103768 450.0838 0 15 546.0361 -1060.072
## BIC deviance df.residual
## 1 -987.5781 8.17482 671plot(train.fit)
plot(test.fit)
plot(valid.fit) 
predval=pred3
summary(predtrain)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 10.72 11.78 11.98 12.02 12.32 12.89summary(predtest)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 11.07 11.73 12.05 12.03 12.31 12.64summary(predval)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 10.76 11.75 12.00 11.97 12.23 12.83cat('Training dataset-Avg.AdjR^2',mean(cv.train.errors[,2]))## Training dataset-Avg.AdjR^2 0.9034372cat('Test dataset-Avg.AdjR^2',mean(cv.test.errors[,2]))## Test dataset-Avg.AdjR^2 0.8983101cat('validation dataset-Avg.AdjR^2',mean(cv.valid.errors[,2]))## validation dataset-Avg.AdjR^2 0.907304cat('Train dataset-Avg.RMSE',mean(cv.train.errors[,1])) ## Train dataset-Avg.RMSE 186852.7cat('Test dataset-Avg.RMSE',mean(cv.test.errors[,1]))## Test dataset-Avg.RMSE 188963.9cat('validation dataset-Avg.RMSE',mean(cv.valid.errors[,1]))## validation dataset-Avg.RMSE 183460.3
0.0.0.15.13 Concluding Assessments
library(BMS)
vars1 <- names(train) %in% c("price","area","Lot.Area","Overall.Qual", "Overall.Cond","Year.Built","Total.Bsmt.SF", "Bedroom.AbvGr","X2nd.Flr.SF")
traindata=train[vars1]
vars2 <- names(test) %in% c("price","area","Lot.Area","Overall.Qual", "Overall.Cond","Year.Built","Total.Bsmt.SF", "Bedroom.AbvGr","X2nd.Flr.SF")
testdata=test[vars2]
vars3 <- names(validation) %in% c("price","area","Lot.Area","Overall.Qual", "Overall.Cond","Year.Built","Total.Bsmt.SF", "Bedroom.AbvGr","X2nd.Flr.SF")
validata=validation[vars3]
mflstr = bms(traindata, burn=100000, iter=200000, g="BRIC", mprior="uniform", nmodel=2000, mcmc="bd", user.int=FALSE)
mflste = bms(testdata, burn=100000, iter=200000, g="BRIC", mprior="uniform", nmodel=2000, mcmc="bd", user.int=FALSE)
mflsval = bms(validata, burn=100000, iter=200000, g="BRIC", mprior="uniform", nmodel=2000, mcmc="bd", user.int=FALSE)
print(mflstr);(mflste);(mflsval)## PIP Post Mean Post SD Cond.Pos.Sign Idx
## price 1.000000 3.555236e-03 0.0001638338 1 1
## Overall.Cond 1.000000 -3.848014e+01 5.9079844386 0 4
## Year.Built 1.000000 -3.007947e+00 0.2704158302 0 5
## Total.Bsmt.SF 1.000000 2.459069e-01 0.0257142382 1 6
## X2nd.Flr.SF 1.000000 5.544080e-01 0.0215865686 1 7
## Bedroom.AbvGr 1.000000 1.185460e+02 9.0470436004 1 8
## Lot.Area 0.038210 -7.392461e-06 0.0001254588 0 2
## Overall.Qual 0.032945 -2.907956e-02 1.4064204761 0 3
##
## Mean no. regressors Draws Burnins Time
## "6.0712" "2e+05" "1e+05" "32.59873 secs"
## No. models visited Modelspace 2^K % visited % Topmodels
## "5176" "256" "2022" "100"
## Corr PMP No. Obs. Model Prior g-Prior
## "1.0000" "832" "uniform / 4" "BRIC"
## Shrinkage-Stats
## "Av=0.9988"## PIP Post Mean Post SD Cond.Pos.Sign Idx
## price 1.00000 3.936201e-03 0.0001824949 1 1
## Overall.Cond 1.00000 -4.053904e+01 6.3283146352 0 4
## Year.Built 1.00000 -3.048361e+00 0.2938689327 0 5
## Total.Bsmt.SF 1.00000 2.031340e-01 0.0266271494 1 6
## X2nd.Flr.SF 1.00000 5.088609e-01 0.0226248149 1 7
## Bedroom.AbvGr 1.00000 1.048265e+02 9.6799973376 1 8
## Lot.Area 0.09758 1.238036e-04 0.0004583181 1 2
## Overall.Qual 0.05850 -5.032461e-01 2.8544024400 0 3
##
## Mean no. regressors Draws Burnins Time
## "6.1561" "2e+05" "1e+05" "33.2992 secs"
## No. models visited Modelspace 2^K % visited % Topmodels
## "11645" "256" "4549" "100"
## Corr PMP No. Obs. Model Prior g-Prior
## "1.0000" "813" "uniform / 4" "BRIC"
## Shrinkage-Stats
## "Av=0.9988"## PIP Post Mean Post SD Cond.Pos.Sign Idx
## price 1.00000 0.003636972 2.451457e-04 1 1
## Lot.Area 1.00000 0.010069991 1.550348e-03 1 2
## Overall.Cond 1.00000 -42.803870807 6.918551e+00 0 4
## Year.Built 1.00000 -2.891288573 3.303762e-01 0 5
## Total.Bsmt.SF 1.00000 0.197978575 2.645327e-02 1 6
## X2nd.Flr.SF 1.00000 0.546371764 2.558785e-02 1 7
## Bedroom.AbvGr 1.00000 107.570269781 1.038308e+01 1 8
## Overall.Qual 0.26538 -5.219176249 9.876577e+00 0 3
##
## Mean no. regressors Draws Burnins Time
## "7.2654" "2e+05" "1e+05" "34.65611 secs"
## No. models visited Modelspace 2^K % visited % Topmodels
## "19917" "256" "7780" "100"
## Corr PMP No. Obs. Model Prior g-Prior
## "1.0000" "762" "uniform / 4" "BRIC"
## Shrinkage-Stats
## "Av=0.9987"0.0.0.15.14 Some Important Regression Methods-RMSE and R-Squared
library(dplyr)
library(purrr)
library(caret)
library(knitr)
set.seed(1234)
setwd("C:/Users/Tahir Hussain/Desktop/CapstoneProject")
load("C:/Users/Tahir Hussain/Desktop/CapstoneProject/ames_train.RData")
ames_train <- ames_train %>%
filter(Sale.Condition == "Normal" & price < 500001 & area < 4001)
vars <- names(ames_train) %in% c("price","area","MS.SubClass","Lot.Area","Overall.Qual","Overall.Cond",
"Year.Built","Year.Remod.Add","Total.Bsmt.SF","Bsmt.Half.Bath","Central.Air",
"Bsmt.Full.Bath","Half.Bath","Full.Bath","Bedroom.AbvGr","Kitchen.AbvGr",
"TotRms.AbvGrd","Fireplaces","Garage.Cars","Garage.Area", "X1st.Flr.SF", "X2nd.Flr.SF","Wood.Deck.SF","Open.Porch.SF","Enclosed.Porch","Screen.Porch",
"Pool.Area","Bsmt.Full.Bath")
train <- ames_train[vars]
raw_data <- train
raw_x <- raw_data
raw_x$price <- NULL
target <- raw_data$price
nrows <- nrow(raw_x)
x_data <- raw_x
sum(is.na(x_data))
model1 <- train(x = num_data, y = target, method = "glm", trControl = my_contrl, preProcess = c("center", "scale"))
model2 <- train(x = num_data, y = target, tuneGrid = glmnet_grid, method = "glmnet",trControl = my_contrl)
model3 <- train(x = num_data, y = target, method = "ranger", trControl = my_contrl)
model4 <- train(x = num_data, y = target, tuneGrid = enet_grid,
method = "enet",trControl = my_contrl)
model5 <- train(x = num_data, y = target, method = "leapBackward",
trControl = my_contrl,
preProcess = c("center", "scale"))
model6 <- train(x = num_data, y = target, tuneGrid = rrf_grid,
method = "RRFglobal",trControl = my_contrl)
model7 <- train(x = num_data, y = target, method = "svmLinear2",
trControl = my_contrl,preProcess = c("center", "scale"))
model8 <- train(x = num_data, y = target, method = "brnn",
trControl = my_contrl)
model_list <- list(mod_glm = model1, mod_glmnet = model2, mod_tree = model3,
mod_elastic = model4, mod_leap_back = model5, mod_reg_rf = model6,
mod_svm = model7,mod_bnet = model8)
mod_resamples <- resamples(model_list)
print(summary(mod_resamples))
dotplot(mod_resamples, metric = "Rsquared")
dotplot(mod_resamples, metric = "RMSE")
##### print(summary(mod_resamples))
#Call:
#summary.resamples(object = mod_resamples)
#Models: mod_glm, mod_glmnet, mod_tree, mod_elastic, mod_leap_back, mod_reg_rf, #mod_svm, mod_bnet
#Number of resamples: 10
#RMSE
#Min. 1st Qu. Median Mean 3rd Qu. Max. NA's
#mod_glm 26770 28710 29320 30400 30090 39140 0
#mod_glmnet 25170 26740 27570 28360 29420 34690 0
#mod_tree 26360 28520 29400 30150 31040 36810 0
#mod_elastic 27350 27380 27420 27420 27450 27480 8
#mod_leap_back 28590 30500 31400 33660 34420 50920 0
#mod_reg_rf 25740 28140 29010 29540 30380 36800 0
#mod_svm 26590 70480 71130 62550 71410 73080 0
#mod_bnet 23120 23740 24370 24370 24990 25620 8
#Rsquared
#Min. 1st Qu. Median Mean 3rd Qu. Max. NA's
#mod_glm 0.7558 0.8156 0.8293 0.8241 0.8409 0.8568 0
#mod_glmnet 0.7936 0.8314 0.8454 0.8419 0.8565 0.8717 0
#mod_tree 0.7680 0.8199 0.8321 0.8328 0.8537 0.8701 0
#mod_elastic 0.8430 0.8445 0.8460 0.8460 0.8475 0.8490 8
#mod_leap_back 0.6378 0.7673 0.8058 0.7833 0.8153 0.8275 0
#mod_reg_rf 0.7768 0.8403 0.8482 0.8430 0.8600 0.8760 0
#mod_svm 0.7626 0.7943 0.8062 0.8091 0.8250 0.8585 0
#mod_bnet 0.8639 0.8711 0.8782 0.8782 0.8853 0.8924 80.0.0.15.15 Plots for RMSE and Rsquared
```
0.0.0.16 Part 5 Conclusion
I have trained,tested and validated different regression methods.The methods ranged from simple linear to regsubset and then stepwise multiple regression.
I tried bayesian regression models with BMA and BAS
There are no standard diagnostics and cross validation methods applicable to every method. Even for the bayesian criteria AIC and BIC have different values.
Neither AIC nor BIC have a rigorous theoretical justification applicable to a wide variety of models. Both were derived for special classes of models that were easy to analyze and both involve some approximations. Neither can be claimed to be the right thing (nor can anything else).
As the Bayesian in BIC indicates, the BIC criterion is intended to approximate using Bayes tests instead of frequentist tests(although its approximation to true Bayes tests isfairly crude). Note that BIC penalizes models with more parameters more strongly than AIC (p logn versus 2p).So BIC always selects a larger model than AIC. This gives us four criteria for model selection. There are arguments in favor of each.None of the arguments are completely convincing.All are widely used. As for the frequentist based regression is concerned the bench marking values differ. Every model with Cp < p, corresponding to the dots below the line is’good’. There are a huge number of perfectly acceptable models, because for the larger p there are many more than 10 good models, which are not shown. The best model according to the Cp criterion is one with p = 12, so 11 nonconstant predictors, which happen to be x1 through x5 (the truly significant predictors) plus x8, x10, x11, x12, x14, and x20. I choose the highest Adjusted R-squared model with lowest RMSE and p-values less than 0.05.
I tried to count the outliers and tried to get rid of them by removing extreme observations. I tried to transform response variables in order to make the distribution mean close to zero. Tried to get rid of missing values by selecting variables with missing value less than 5%. or to replace them with zero.
There is no uniformity in Cross validation in different modeling methods.
Overfiting and underfiting is taken care of bayesian methods(BIC). but manual verification is a must.
The model testing criteria are different. Non information based criteria depend on the magnitude of variable selected. Optimal selection can not be ensured unless partition the dataset and testing for consistency. Boruta,PSL,PCA and earth package can be used to give an automatic optimal selection of variables.
A ‘good model’ can be selected only by first tidying the datasets, transformation of variables,conversions and removal or replacing missing values. Exploratory analysis helps to do all above.
Extracting records by creating subsets of necessary variables with useful range helps a lot.
There is no magic method to ensure all assumptions of ‘best model’. A lot of time is required to train,test and validate the model. The model must agree/disagree with all subsets with valid applicable conditions and supported by justifications.
I agree the model should be simple and support all possible assumptions. I found 8 mixed variables, numeric and categorical provided a ‘good’ model. Bayesian selections are the best.
I could get Adjusted R-squared close to 0.8983 i.e 89 % correlation of model to dependent variable(price).
There is a difference between predicted price and actual which means predictive regression modeling is not perfect.With training dataset we can have an optimum prediction of prices
Final Words on Modeling for Predictions
K-10 figures
Training dataset : Adj.R^2:0.9034,RMSE:186852,Avg.Pred.Price:11.972
Test dataset : Adj.R^2:0.8983,RMSE:188963,Avg.Pred.Price:12.022
Validation dataset: Adj.R^2:0.9073,RMSE:183460,Avg.Pred.Price:12.025
training is (BIC) underestimate,test and validation are overfit. Probably this is due to influencial extreme outliers. If we filter records for 1 storey houses and suitable neighborhood we could minimize them.
1.Bias \[Avg(yhat-y)\] -positive indicates overestimate -Negative indicates underestimate
2.Max.Deviation: \[max(y-yhat)\] -indicates worst Prediction.
3.Mean absolute deviation: \[Avg |y-yhat|\] -This is average error. 4.Mean square error : \[Avg(y-yhat)\] - This compares with least square regression.
5.With various combinations of variables,transformations and methods we can obtain optimum performance from model.The best method is regsubsets leaps and bayesian ‘BAS’ method. These methods allow validation and cross validations and bootstrap