Model Selection
library(ISLR)## Warning: package 'ISLR' was built under R version 3.1.2summary(Hitters)## AtBat Hits HmRun Runs
## Min. : 16.0 Min. : 1 Min. : 0.00 Min. : 0.00
## 1st Qu.:255.2 1st Qu.: 64 1st Qu.: 4.00 1st Qu.: 30.25
## Median :379.5 Median : 96 Median : 8.00 Median : 48.00
## Mean :380.9 Mean :101 Mean :10.77 Mean : 50.91
## 3rd Qu.:512.0 3rd Qu.:137 3rd Qu.:16.00 3rd Qu.: 69.00
## Max. :687.0 Max. :238 Max. :40.00 Max. :130.00
##
## RBI Walks Years CAtBat
## Min. : 0.00 Min. : 0.00 Min. : 1.000 Min. : 19.0
## 1st Qu.: 28.00 1st Qu.: 22.00 1st Qu.: 4.000 1st Qu.: 816.8
## Median : 44.00 Median : 35.00 Median : 6.000 Median : 1928.0
## Mean : 48.03 Mean : 38.74 Mean : 7.444 Mean : 2648.7
## 3rd Qu.: 64.75 3rd Qu.: 53.00 3rd Qu.:11.000 3rd Qu.: 3924.2
## Max. :121.00 Max. :105.00 Max. :24.000 Max. :14053.0
##
## CHits CHmRun CRuns CRBI
## Min. : 4.0 Min. : 0.00 Min. : 1.0 Min. : 0.00
## 1st Qu.: 209.0 1st Qu.: 14.00 1st Qu.: 100.2 1st Qu.: 88.75
## Median : 508.0 Median : 37.50 Median : 247.0 Median : 220.50
## Mean : 717.6 Mean : 69.49 Mean : 358.8 Mean : 330.12
## 3rd Qu.:1059.2 3rd Qu.: 90.00 3rd Qu.: 526.2 3rd Qu.: 426.25
## Max. :4256.0 Max. :548.00 Max. :2165.0 Max. :1659.00
##
## CWalks League Division PutOuts Assists
## Min. : 0.00 A:175 E:157 Min. : 0.0 Min. : 0.0
## 1st Qu.: 67.25 N:147 W:165 1st Qu.: 109.2 1st Qu.: 7.0
## Median : 170.50 Median : 212.0 Median : 39.5
## Mean : 260.24 Mean : 288.9 Mean :106.9
## 3rd Qu.: 339.25 3rd Qu.: 325.0 3rd Qu.:166.0
## Max. :1566.00 Max. :1378.0 Max. :492.0
##
## Errors Salary NewLeague
## Min. : 0.00 Min. : 67.5 A:176
## 1st Qu.: 3.00 1st Qu.: 190.0 N:146
## Median : 6.00 Median : 425.0
## Mean : 8.04 Mean : 535.9
## 3rd Qu.:11.00 3rd Qu.: 750.0
## Max. :32.00 Max. :2460.0
## NA's :59
There are some missing values here,so before we proceed we will remove them:
Hitters<- span=""> na.omit(Hitters)
with(Hitters,sum(is.na(Salary)))## [1] 0Best Subset regression
We will now use the package
leaps to evaluate all the best-subset models.library(leaps)
regfit.full<- span=""> regsubsets(Salary~.,data=Hitters)
summary(regfit.full)## Subset selection object
## Call: regsubsets.formula(Salary ~ ., data = Hitters)
## 19 Variables (and intercept)
## Forced in Forced out
## AtBat FALSE FALSE
## Hits FALSE FALSE
## HmRun FALSE FALSE
## Runs FALSE FALSE
## RBI FALSE FALSE
## Walks FALSE FALSE
## Years FALSE FALSE
## CAtBat FALSE FALSE
## CHits FALSE FALSE
## CHmRun FALSE FALSE
## CRuns FALSE FALSE
## CRBI FALSE FALSE
## CWalks FALSE FALSE
## LeagueN FALSE FALSE
## DivisionW FALSE FALSE
## PutOuts FALSE FALSE
## Assists FALSE FALSE
## Errors FALSE FALSE
## NewLeagueN FALSE FALSE
## 1 subsets of each size up to 8
## Selection Algorithm: exhaustive
## AtBat Hits HmRun Runs RBI Walks Years CAtBat CHits CHmRun CRuns
## 1 ( 1 ) " " " " " " " " " " " " " " " " " " " " " "
## 2 ( 1 ) " " "*" " " " " " " " " " " " " " " " " " "
## 3 ( 1 ) " " "*" " " " " " " " " " " " " " " " " " "
## 4 ( 1 ) " " "*" " " " " " " " " " " " " " " " " " "
## 5 ( 1 ) "*" "*" " " " " " " " " " " " " " " " " " "
## 6 ( 1 ) "*" "*" " " " " " " "*" " " " " " " " " " "
## 7 ( 1 ) " " "*" " " " " " " "*" " " "*" "*" "*" " "
## 8 ( 1 ) "*" "*" " " " " " " "*" " " " " " " "*" "*"
## CRBI CWalks LeagueN DivisionW PutOuts Assists Errors NewLeagueN
## 1 ( 1 ) "*" " " " " " " " " " " " " " "
## 2 ( 1 ) "*" " " " " " " " " " " " " " "
## 3 ( 1 ) "*" " " " " " " "*" " " " " " "
## 4 ( 1 ) "*" " " " " "*" "*" " " " " " "
## 5 ( 1 ) "*" " " " " "*" "*" " " " " " "
## 6 ( 1 ) "*" " " " " "*" "*" " " " " " "
## 7 ( 1 ) " " " " " " "*" "*" " " " " " "
## 8 ( 1 ) " " "*" " " "*" "*" " " " " " "
It gives by default best-subsets up to size 8; lets increase that to 19, i.e. all the variables
regfit.full<- span=""> regsubsets(Salary~.,data=Hitters,nvmax=19)
reg.summary<- span=""> summary(regfit.full)
names(reg.summary)## [1] "which" "rsq" "rss" "adjr2" "cp" "bic" "outmat" "obj"plot(reg.summary$cp,xlab='Number of Variables',ylab='Cp')
which.min(reg.summary$cp)## [1] 10points(10,reg.summary$cp[10],pch=20,col='red')
There is a plot method for the regsubsetsobjectplot(regfit.full,scale='Cp')
coef(regfit.full,10)## (Intercept) AtBat Hits Walks CAtBat
## 162.5354420 -2.1686501 6.9180175 5.7732246 -0.1300798
## CRuns CRBI CWalks DivisionW PutOuts
## 1.4082490 0.7743122 -0.8308264 -112.3800575 0.2973726
## Assists
## 0.2831680