# Chapter 8 Lab: Decision Trees

# Fitting Classification Trees

library(tree)
library(ISLR)
attach(Carseats)
?Carseats
fix(Carseats)
#Dichotomize Sales
High=ifelse(Sales<=8,"No","Yes")
Carseats=data.frame(Carseats,High)
#syntax of tree function is similar to lm function
tree.carseats=tree(High~.-Sales,Carseats)
#variables used in tree construction, #of nodes, error rate
#a small deviance indicates good fit to the training data
summary(tree.carseats)
#plot the tree structure
plot(tree.carseats)
#display node labels
text(tree.carseats,pretty=0)
#We see the most important predictor of sales is shelving location 

#display split criterion (e.g. Price<92.5), the
#number of observations in that branch, the deviance, the overall prediction
#for the branch (Yes or No), and the fraction of observations in that branch
#that take on values of Yes and No
tree.carseats

#we should use test error to evaluate the performance of a tree
set.seed(2)
train=sample(1:nrow(Carseats), 200)
Carseats.test=Carseats[-train,]
High.test=High[-train]
tree.carseats=tree(High~.-Sales,Carseats,subset=train)
tree.pred=predict(tree.carseats,Carseats.test,type="class")
table(tree.pred,High.test)
(86+57)/200  #correct prediction

#pruning the tree via cross validation
set.seed(3)
#FUN.prune.misclass: use classification error rate in the pruning process
#default is deviance
cv.carseats=cv.tree(tree.carseats,FUN=prune.misclass)
#size: number of terminal nodes (leaves)
#k: alpha in the slides
#dev: cross-validation error rate
cv.carseats
#The tree with 9 terminal nodes results in the lowest
#cross-validation error rate, with 50 cross-validation errors
#We plot the error rate as a function of both size and k
par(mfrow=c(1,2))
plot(cv.carseats$size,cv.carseats$dev,type="b")
plot(cv.carseats$k,cv.carseats$dev,type="b")
#We now apply the prune.misclass() function in order to prune the tree to prune.
#obtain the nine-node tree.
prune.carseats=prune.misclass(tree.carseats,best=9)
plot(prune.carseats)
text(prune.carseats,pretty=0)
#Compute test error rate
tree.pred=predict(prune.carseats,Carseats.test,type="class")
table(tree.pred,High.test)
(94+60)/200 # correct prediction


# Fitting Regression Trees to the boston data

library(MASS)
?Boston
#split half to be training data
set.seed(1)
train = sample(1:nrow(Boston), nrow(Boston)/2)
#grow a large tree using training data
#medv: median value of homes in $1000
tree.boston=tree(medv~.,Boston,subset=train)
summary(tree.boston)
#only 3 variables were used
#plot the tree.  
plot(tree.boston)
text(tree.boston,pretty=0)
#Pruning the tree
cv.boston=cv.tree(tree.boston)
plot(cv.boston$size,cv.boston$dev,type='b')
#the most complex tree is selected by cross-validation

#we use the unpruned tree to make predictions on the test set
yhat=predict(tree.boston,newdata=Boston[-train,])
boston.test=Boston[-train,"medv"]
plot(yhat,boston.test)
abline(0,1)
sqrt(mean((yhat-boston.test)^2))
#this model leads to test predictions that are within around $5, 005 of
#the true median home value for the suburb.