ch8

# Chapter 8 page 332: 3,8,9

# 3

p=seq(0,1,0.01)
gini.index=2*p*(1-p)
class.error=1-pmax(p,1,-p)
cross.entropy=-(p*log(p)+(1-p)*log(1-p))
matplot(p,cbind(gini.index,class.error,cross.entropy),col=c("pink","yellow","blue"))

# 8
library(MASS)

## Warning: package 'MASS' was built under R version 4.1.3

library(ISLR)

## Warning: package 'ISLR' was built under R version 4.1.3

set.seed(1)
train=sample(1:nrow(Carseats),nrow(Carseats)/2)
Carseats.train=Carseats[train,]
Carseats.test=Carseats[-train,]
library(tree)

## Warning: package 'tree' was built under R version 4.1.3

## Registered S3 method overwritten by 'tree':
##   method     from
##   print.tree cli

tree.carseats=tree(Sales~.,data=Carseats.train)
summary(tree.carseats)

## 
## Regression tree:
## tree(formula = Sales ~ ., data = Carseats.train)
## Variables actually used in tree construction:
## [1] "ShelveLoc"   "Price"       "Age"         "Advertising" "CompPrice"  
## [6] "US"         
## Number of terminal nodes:  18 
## Residual mean deviance:  2.167 = 394.3 / 182 
## Distribution of residuals:
##     Min.  1st Qu.   Median     Mean  3rd Qu.     Max. 
## -3.88200 -0.88200 -0.08712  0.00000  0.89590  4.09900

plot(tree.carseats)
text(tree.carseats,pretty=0)

yhat=predict(tree.carseats,newdata=Carseats.test)
mean((yhat-Carseats.test$Sales)^2)

## [1] 4.922039

cv.carseats=cv.tree(tree.carseats)
plot(cv.carseats$size,cv.carseats$dev,type="b")
tree.min=which.min(cv.carseats$dev)
points(tree.min,cv.carseats$dev[tree.min],col="pink",cex=2,pch=20)

prune.carseats=prune.tree(tree.carseats,best=8)
plot(prune.carseats)
text(prune.carseats,pretty=0)

yhat=predict(prune.carseats,newdata=Carseats.test)
mean((yhat-Carseats.test$Sales)^2)

## [1] 5.113254

# 9

set.seed(1)
train=sample(1:nrow(OJ),800)
OJ.train=OJ[train, ]
OJ.test=OJ[-train, ]
tree.oj=tree(Purchase~.,data=OJ.train)
summary(tree.oj)

## 
## Classification tree:
## tree(formula = Purchase ~ ., data = OJ.train)
## Variables actually used in tree construction:
## [1] "LoyalCH"       "PriceDiff"     "SpecialCH"     "ListPriceDiff"
## [5] "PctDiscMM"    
## Number of terminal nodes:  9 
## Residual mean deviance:  0.7432 = 587.8 / 791 
## Misclassification error rate: 0.1588 = 127 / 800

plot(tree.oj)
text(tree.oj,pretty=0)

tree.pred=predict(tree.oj,OJ.test,type="class")
table(tree.pred,OJ.test$Purchase)

##          
## tree.pred  CH  MM
##        CH 160  38
##        MM   8  64

cv.oj=cv.tree(tree.oj,FUN=prune.misclass)
cv.oj

## $size
## [1] 9 8 7 4 2 1
## 
## $dev
## [1] 150 150 149 158 172 315
## 
## $k
## [1]       -Inf   0.000000   3.000000   4.333333  10.500000 151.000000
## 
## $method
## [1] "misclass"
## 
## attr(,"class")
## [1] "prune"         "tree.sequence"

plot(cv.oj$size,cv.oj$dev,type="b",xlab="Tree size",ylab="Deviance")

prune.oj=prune.misclass(tree.oj,best=2)
plot(prune.oj)
text(prune.oj,pretty=0)

summary(tree.oj)

## 
## Classification tree:
## tree(formula = Purchase ~ ., data = OJ.train)
## Variables actually used in tree construction:
## [1] "LoyalCH"       "PriceDiff"     "SpecialCH"     "ListPriceDiff"
## [5] "PctDiscMM"    
## Number of terminal nodes:  9 
## Residual mean deviance:  0.7432 = 587.8 / 791 
## Misclassification error rate: 0.1588 = 127 / 800

summary(prune.oj)

## 
## Classification tree:
## snip.tree(tree = tree.oj, nodes = 3:2)
## Variables actually used in tree construction:
## [1] "LoyalCH"
## Number of terminal nodes:  2 
## Residual mean deviance:  0.9768 = 779.5 / 798 
## Misclassification error rate: 0.205 = 164 / 800

prune.pred=predict(prune.oj,OJ.test,type="class")
table(prune.pred,OJ.test$Purchase)

##           
## prune.pred  CH  MM
##         CH 142  24
##         MM  26  78