library(ISLR)
names(Hitters)
dim(Hitters)
sum(is.na(Hitters$Salary))
Hitters=na.omit(Hitters)
dim(Hitters)
sum(is.na(Hitters))

1. 'AtBat'
2. 'Hits'
3. 'HmRun'
4. 'Runs'
5. 'RBI'
6. 'Walks'
7. 'Years'
8. 'CAtBat'
9. 'CHits'
10. 'CHmRun'
11. 'CRuns'
12. 'CRBI'
13. 'CWalks'
14. 'League'
15. 'Division'
16. 'PutOuts'
17. 'Assists'
18. 'Errors'
19. 'Salary'
20. 'NewLeague'

1. 322
2. 20

59

1. 263
2. 20

0

library(leaps)
regfit.full=regsubsets(Salary~.,Hitters)
summary(regfit.full)

Subset selection object
Call: regsubsets.formula(Salary ~ ., 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 CRBI
1  ( 1 ) " "   " "  " "   " "  " " " "   " "   " "    " "   " "    " "   "*" 
2  ( 1 ) " "   "*"  " "   " "  " " " "   " "   " "    " "   " "    " "   "*" 
3  ( 1 ) " "   "*"  " "   " "  " " " "   " "   " "    " "   " "    " "   "*" 
4  ( 1 ) " "   "*"  " "   " "  " " " "   " "   " "    " "   " "    " "   "*" 
5  ( 1 ) "*"   "*"  " "   " "  " " " "   " "   " "    " "   " "    " "   "*" 
6  ( 1 ) "*"   "*"  " "   " "  " " "*"   " "   " "    " "   " "    " "   "*" 
7  ( 1 ) " "   "*"  " "   " "  " " "*"   " "   "*"    "*"   "*"    " "   " " 
8  ( 1 ) "*"   "*"  " "   " "  " " "*"   " "   " "    " "   "*"    "*"   " " 
         CWalks LeagueN DivisionW PutOuts Assists Errors NewLeagueN
1  ( 1 ) " "    " "     " "       " "     " "     " "    " "       
2  ( 1 ) " "    " "     " "       " "     " "     " "    " "       
3  ( 1 ) " "    " "     " "       "*"     " "     " "    " "       
4  ( 1 ) " "    " "     "*"       "*"     " "     " "    " "       
5  ( 1 ) " "    " "     "*"       "*"     " "     " "    " "       
6  ( 1 ) " "    " "     "*"       "*"     " "     " "    " "       
7  ( 1 ) " "    " "     "*"       "*"     " "     " "    " "       
8  ( 1 ) "*"    " "     "*"       "*"     " "     " "    " "       

regfit.full=regsubsets(Salary~.,data=Hitters,nvmax=19)
reg.summary=summary(regfit.full)
names(reg.summary)
reg.summary$rsq

1. 'which'
2. 'rsq'
3. 'rss'
4. 'adjr2'
5. 'cp'
6. 'bic'
7. 'outmat'
8. 'obj'

1. 0.321450088667894
2. 0.425223746466778
3. 0.451429415717957
4. 0.475406653394787
5. 0.490803615963518
6. 0.508714557358996
7. 0.514122682361273
8. 0.528556860302574
9. 0.534612447792431
10. 0.540494950940798
11. 0.54261532542542
12. 0.543630208632163
13. 0.544457014231977
14. 0.545216356301489
15. 0.545469230681164
16. 0.54576555748528
17. 0.545951808076699
18. 0.546094522341906
19. 0.546115861912532

par(mfrow=c(2,2))
plot(reg.summary$rss,xlab="Number of Variables",ylab="RSS",type="l")
plot(reg.summary$adjr2,xlab="Number of Variables",ylab="Adjusted RSq",type="l")
which.max(reg.summary$adjr2)
points(11,reg.summary$adjr2[11], col="red",cex=2,pch=20)
plot(reg.summary$cp,xlab="Number of Variables",ylab="Cp",type='l')
which.min(reg.summary$cp)
points(10,reg.summary$cp[10],col="red",cex=2,pch=20)
which.min(reg.summary$bic)
plot(reg.summary$bic,xlab="Number of Variables",ylab="BIC",type='l')
points(6,reg.summary$bic[6],col="red",cex=2,pch=20)

11

10

6

plot(regfit.full,scale="r2")

plot(regfit.full,scale="adjr2")

plot(regfit.full,scale="Cp")

plot(regfit.full,scale="bic")

coef(regfit.full,6)

(Intercept)

91.5117981171539

AtBat

-1.86858923135561

Hits

7.60439763117204

Walks

3.69764677424139

CRBI

0.643016935097332

DivisionW

-122.95153377292

PutOuts

0.264307605461511

# Forward and Backward Stepwise Selection

regfit.fwd=regsubsets(Salary~.,data=Hitters,nvmax=19,method="forward")
summary(regfit.fwd)

Subset selection object
Call: regsubsets.formula(Salary ~ ., data = Hitters, nvmax = 19, method = "forward")
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 19
Selection Algorithm: forward
          AtBat Hits HmRun Runs RBI Walks Years CAtBat CHits CHmRun CRuns CRBI
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 ) "*"   "*"  "*"   "*"  "*" "*"   "*"   "*"    "*"   "*"    "*"   "*" 
          CWalks LeagueN DivisionW PutOuts Assists Errors NewLeagueN
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 ) "*"    "*"     "*"       "*"     "*"     "*"    "*"       

regfit.bwd=regsubsets(Salary~.,data=Hitters,nvmax=19,method="backward")
summary(regfit.bwd)

Subset selection object
Call: regsubsets.formula(Salary ~ ., data = Hitters, nvmax = 19, method = "backward")
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 19
Selection Algorithm: backward
          AtBat Hits HmRun Runs RBI Walks Years CAtBat CHits CHmRun CRuns CRBI
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 ) "*"   "*"  "*"   "*"  "*" "*"   "*"   "*"    "*"   "*"    "*"   "*" 
          CWalks LeagueN DivisionW PutOuts Assists Errors NewLeagueN
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 ) "*"    "*"     "*"       "*"     "*"     "*"    "*"       

coef(regfit.full,7)

(Intercept)

79.4509472435319

Hits

1.28335125463328

Walks

3.22742638972714

CAtBat

-0.375235019565453

CHits

1.49570730989869

CHmRun

1.44205381889666

DivisionW

-129.986643165116

PutOuts

0.236681317525621

coef(regfit.fwd,7)

(Intercept)

109.787306240078

AtBat

-1.95888512315655

Hits

7.44987721841218

Walks

4.91314009272066

CRBI

0.853762209061578

CWalks

-0.305307000381738

DivisionW

-127.122392777488

PutOuts

0.253340431147386

coef(regfit.bwd,7)

(Intercept)

105.648748778828

AtBat

-1.97628381026618

Hits

6.75749144281392

Walks

6.05586912154598

CRuns

1.12930946903271

CWalks

-0.71633458662198

DivisionW

-116.16921690431

PutOuts

0.302884743257576

# Choosing Among Models

set.seed(1)
train=sample(c(TRUE,FALSE), nrow(Hitters),rep=TRUE)
test=(!train)
regfit.best=regsubsets(Salary~.,data=Hitters[train,],nvmax=19)
test.mat=model.matrix(Salary~.,data=Hitters[test,])
val.errors=rep(NA,19)
for(i in 1:19){
   coefi=coef(regfit.best,id=i)
   pred=test.mat[,names(coefi)]%*%coefi
   val.errors[i]=mean((Hitters$Salary[test]-pred)^2)
}
val.errors

1. 220968.010570781
2. 169157.080938694
3. 178518.155945132
4. 163426.079195481
5. 168418.096758255
6. 171270.594721366
7. 162377.082699745
8. 157909.280553932
9. 154055.716825013
10. 148162.052539399
11. 151156.401317955
12. 151742.451908185
13. 152214.450874715
14. 157358.654080678
15. 158541.407297311
16. 158743.3209425
17. 159972.673927589
18. 159859.793366072
19. 160105.640513861

which.min(val.errors)

10

coef(regfit.best,10)

(Intercept)

-80.2751498545584

AtBat

-1.46838155352597

Hits

7.16253138932867

Walks

3.64303449365111

CAtBat

-0.185569803428967

CHits

1.10532384927797

CHmRun

1.38448634401015

CWalks

-0.74831695417675

LeagueN

84.5576102976496

DivisionW

-53.0289658320235

PutOuts

0.238166218963617

predict.regsubsets=function(object,newdata,id,...){
  form=as.formula(object$call[[2]])
  mat=model.matrix(form,newdata)
  coefi=coef(object,id=id)
  xvars=names(coefi)
  mat[,xvars]%*%coefi
  }
regfit.best=regsubsets(Salary~.,data=Hitters,nvmax=19)

coef(regfit.best,10)

(Intercept)

162.535442040545

AtBat

-2.16865005340437

Hits

6.91801749476659

Walks

5.7732246470264

CAtBat

-0.130079783913646

CRuns

1.40824900877044

CRBI

0.774312153250204

CWalks

-0.830826351501743

DivisionW

-112.380057493543

PutOuts

0.297372596603942

Assists

0.283168028635278

k=10
set.seed(1)
folds=sample(1:k,nrow(Hitters),replace=TRUE)
cv.errors=matrix(NA,k,19, dimnames=list(NULL, paste(1:19)))
for(j in 1:k){
  best.fit=regsubsets(Salary~.,data=Hitters[folds!=j,],nvmax=19)
  for(i in 1:19){
    pred=predict(best.fit,Hitters[folds==j,],id=i)
    cv.errors[j,i]=mean( (Hitters$Salary[folds==j]-pred)^2)
    }
  }
mean.cv.errors=apply(cv.errors,2,mean)
mean.cv.errors

1

160093.486398318

2

140196.773091529

3

153116.968353284

4

151159.338649923

5

146841.301803275

6

138302.632366087

7

144346.225347738

8

130207.693625525

9

129459.613710927

10

125334.660569683

11

125153.816649585

12

128273.547905646

13

133461.030824061

14

133974.608481698

15

131825.723993328

16

131882.769468209

17

132750.868578319

18

133096.230787088

19

132804.718368856

par(mfrow=c(1,1))
plot(mean.cv.errors,type='b')
reg.best=regsubsets(Salary~.,data=Hitters, nvmax=19)

coef(reg.best,11)

(Intercept)

135.751219457458

AtBat

-2.12774819603869

Hits

6.92369939666552

Walks

5.62027551957861

CAtBat

-0.138991434861849

CRuns

1.45533103037942

CRBI

0.785252782049429

CWalks

-0.822855923951907

LeagueN

43.1116151638512

DivisionW

-111.14602518374

PutOuts

0.289408680295373

Assists

0.26882769003494

# Chapter 6 Lab 2: Ridge Regression and the Lasso

x=model.matrix(Salary~.,Hitters)[,-1]
y=Hitters$Salary

# Ridge Regression

library(glmnet)
grid=10^seq(10,-2,length=100)
ridge.mod=glmnet(x,y,alpha=0,lambda=grid)

Loading required package: Matrix
Loading required package: foreach
Loaded glmnet 2.0-5

dim(coef(ridge.mod))
ridge.mod$lambda[50]

1. 20
2. 100

11497.5699539774

coef(ridge.mod)[,50]

(Intercept)

407.356050200416

AtBat

0.0369571817501359

Hits

0.138180343807892

HmRun

0.524629975886911

Runs

0.230701522621179

RBI

0.239841458504058

Walks

0.289618741049884

Years

1.10770292908555

CAtBat

0.00313181522151328

CHits

0.0116536373557531

CHmRun

0.0875456697555949

CRuns

0.0233798823693758

CRBI

0.0241383203685686

CWalks

0.0250154205993732

LeagueN

0.0850281135625444

DivisionW

-6.21544097273146

PutOuts

0.0164825767604547

Assists

0.00261298804528183

Errors

-0.0205026903654579

NewLeagueN

0.301433531372699

sqrt(sum(coef(ridge.mod)[-1,50]^2))

6.36061242142791

ridge.mod$lambda[60]

705.480231071865

coef(ridge.mod)[,60]

(Intercept)

54.3251995018372

AtBat

0.112111145878249

Hits

0.656224085323628

HmRun

1.17980909638777

Runs

0.937697128927054

RBI

0.847185458771521

Walks

1.31987948048781

Years

2.59640424574253

CAtBat

0.0108341254432856

CHits

0.0467455700054452

CHmRun

0.337773183143353

CRuns

0.0935552830000676

CRBI

0.0978040232271687

CWalks

0.0718961166304866

LeagueN

13.6837019095343

DivisionW

-54.658777504592

PutOuts

0.118522894134745

Assists

0.01606037317599

Errors

-0.703586547290985

NewLeagueN

8.61181213448926

sqrt(sum(coef(ridge.mod)[-1,60]^2))

57.110014262533

predict(ridge.mod,s=50,type="coefficients")[1:20,]

(Intercept)

48.7661032921608

AtBat

-0.358099859376738

Hits

1.96935928646357

HmRun

-1.27824798145678

Runs

1.14589163211962

RBI

0.803829228437672

Walks

2.71618579623371

Years

-6.21831921727865

CAtBat

0.00544783719814918

CHits

0.10648951402342

CHmRun

0.624485956082661

CRuns

0.221498463760022

CRBI

0.218691380321248

CWalks

-0.150024548516927

LeagueN

45.9258855144158

DivisionW

-118.201136816368

PutOuts

0.250232154092559

Assists

0.121566461346767

Errors

-3.27859954463555

NewLeagueN

-9.4966803100264

set.seed(1)
train=sample(1:nrow(x), nrow(x)/2)
test=(-train)
y.test=y[test]
ridge.mod=glmnet(x[train,],y[train],alpha=0,lambda=grid, thresh=1e-12)
ridge.pred=predict(ridge.mod,s=4,newx=x[test,])
mean((ridge.pred-y.test)^2)
mean((mean(y[train])-y.test)^2)

101036.832669597

193253.113067991

ridge.pred=predict(ridge.mod,s=1e10,newx=x[test,])
mean((ridge.pred-y.test)^2)

193253.05679545

ridge.pred=predict(ridge.mod,s=0,newx=x[test,],exact=T)
mean((ridge.pred-y.test)^2)

114783.077172766

lm(y~x, subset=train)
predict(ridge.mod,s=0,exact=T,type="coefficients")[1:20,]

Call:
lm(formula = y ~ x, subset = train)

Coefficients:
(Intercept)       xAtBat        xHits       xHmRun        xRuns         xRBI  
  299.42849     -2.54027      8.36682     11.64512     -9.09923      2.44105  
     xWalks       xYears      xCAtBat       xCHits      xCHmRun       xCRuns  
    9.23440    -22.93673     -0.18154     -0.11598     -1.33888      3.32838  
      xCRBI      xCWalks     xLeagueN   xDivisionW     xPutOuts     xAssists  
    0.07536     -1.07841     59.76065    -98.86233      0.34087      0.34165  
    xErrors  xNewLeagueN  
   -0.64207     -0.67442  

(Intercept)

299.428835955511

AtBat

-2.54014665070144

Hits

8.36611719216035

HmRun

11.6440071973906

Runs

-9.09877718514622

RBI

2.44152119069374

Walks

9.23403909103472

Years

-22.9358444150819

CAtBat

-0.181608426793676

CHits

-0.115614963792392

CHmRun

-1.33836534074527

CRuns

3.32817776511616

CRBI

0.0751177103859102

CWalks

-1.07828646608209

LeagueN

59.7652905857257

DivisionW

-98.8599658984281

PutOuts

0.340864001788611

Assists

0.341656051135429

Errors

-0.642058388019889

NewLeagueN

-0.676063138728381

set.seed(1)
cv.out=cv.glmnet(x[train,],y[train],alpha=0)
plot(cv.out)

bestlam=cv.out$lambda.min
bestlam

211.741584781282

ridge.pred=predict(ridge.mod,s=bestlam,newx=x[test,])
mean((ridge.pred-y.test)^2)
out=glmnet(x,y,alpha=0)
predict(out,type="coefficients",s=bestlam)[1:20,]

96015.5127255327

(Intercept)

9.88487156523819

AtBat

0.0314399123075993

Hits

1.00882875071523

HmRun

0.139276236015288

Runs

1.11320780992504

RBI

0.873189900643772

Walks

1.80410229199678

Years

0.130743811114436

CAtBat

0.0111397797786966

CHits

0.0648984331610168

CHmRun

0.451585462080598

CRuns

0.12900049045775

CRBI

0.13737711633305

CWalks

0.0290857160383186

LeagueN

27.1822753486268

DivisionW

-91.6341129943135

PutOuts

0.191492519898057

Assists

0.0425453623726451

Errors

-1.81244470270312

NewLeagueN

7.2120838996523

# The Lasso

lasso.mod=glmnet(x[train,],y[train],alpha=1,lambda=grid)
plot(lasso.mod)

set.seed(1)
cv.out=cv.glmnet(x[train,],y[train],alpha=1)
plot(cv.out)

bestlam=cv.out$lambda.min
lasso.pred=predict(lasso.mod,s=bestlam,newx=x[test,])
mean((lasso.pred-y.test)^2)
out=glmnet(x,y,alpha=1,lambda=grid)
lasso.coef=predict(out,type="coefficients",s=bestlam)[1:20,]
lasso.coef
lasso.coef[lasso.coef!=0]

100743.446221539

(Intercept)

18.5394843700404

AtBat

0

Hits

1.87353897868797

HmRun

0

Runs

0

RBI

0

Walks

2.21784439442808

Years

0

CAtBat

0

CHits

0

CHmRun

0

CRuns

0.207125172948793

CRBI

0.413013208899728

CWalks

0

LeagueN

3.26666772880497

DivisionW

-103.484545814138

PutOuts

0.220428413476128

Assists

0

Errors

0

NewLeagueN

0

(Intercept)

18.5394843700404

Hits

1.87353897868797

Walks

2.21784439442808

CRuns

0.207125172948793

CRBI

0.413013208899728

LeagueN

3.26666772880497

DivisionW

-103.484545814138

PutOuts

0.220428413476128

# Chapter 6 Lab 3: PCR and PLS Regression

# Principal Components Regression

library(pls)
set.seed(2)
pcr.fit=pcr(Salary~., data=Hitters,scale=TRUE,validation="CV")
summary(pcr.fit)

Attaching package: ‘pls’

The following object is masked from ‘package:stats’:

    loadings

Data: 	X dimension: 263 19 
	Y dimension: 263 1
Fit method: svdpc
Number of components considered: 19

VALIDATION: RMSEP
Cross-validated using 10 random segments.
       (Intercept)  1 comps  2 comps  3 comps  4 comps  5 comps  6 comps
CV             452    348.9    352.2    353.5    352.8    350.1    349.1
adjCV          452    348.7    351.8    352.9    352.1    349.3    348.0
       7 comps  8 comps  9 comps  10 comps  11 comps  12 comps  13 comps
CV       349.6    350.9    352.9     353.8     355.0     356.2     363.5
adjCV    348.5    349.8    351.6     352.3     353.4     354.5     361.6
       14 comps  15 comps  16 comps  17 comps  18 comps  19 comps
CV        355.2     357.4     347.6     350.1     349.2     352.6
adjCV     352.8     355.2     345.5     347.6     346.7     349.8

TRAINING: % variance explained
        1 comps  2 comps  3 comps  4 comps  5 comps  6 comps  7 comps  8 comps
X         38.31    60.16    70.84    79.03    84.29    88.63    92.26    94.96
Salary    40.63    41.58    42.17    43.22    44.90    46.48    46.69    46.75
        9 comps  10 comps  11 comps  12 comps  13 comps  14 comps  15 comps
X         96.28     97.26     97.98     98.65     99.15     99.47     99.75
Salary    46.86     47.76     47.82     47.85     48.10     50.40     50.55
        16 comps  17 comps  18 comps  19 comps
X          99.89     99.97     99.99    100.00
Salary     53.01     53.85     54.61     54.61

validationplot(pcr.fit,val.type="MSEP")

set.seed(1)
pcr.fit=pcr(Salary~., data=Hitters,subset=train,scale=TRUE, validation="CV")
validationplot(pcr.fit,val.type="MSEP")

pcr.pred=predict(pcr.fit,x[test,],ncomp=7)
mean((pcr.pred-y.test)^2)

96556.2191395342

pcr.fit=pcr(y~x,scale=TRUE,ncomp=7)
summary(pcr.fit)

Data: 	X dimension: 263 19 
	Y dimension: 263 1
Fit method: svdpc
Number of components considered: 7
TRAINING: % variance explained
   1 comps  2 comps  3 comps  4 comps  5 comps  6 comps  7 comps
X    38.31    60.16    70.84    79.03    84.29    88.63    92.26
y    40.63    41.58    42.17    43.22    44.90    46.48    46.69