Chapter 8 Tree Based Methods - Question 7

library(MASS)
library(randomForest)

names(Boston)

1. 'crim'
2. 'zn'
3. 'indus'
4. 'chas'
5. 'nox'
6. 'rm'
7. 'age'
8. 'dis'
9. 'rad'
10. 'tax'
11. 'ptratio'
12. 'black'
13. 'lstat'
14. 'medv'

#create training data and test data
set.seed(1)
train = sample(1:nrow(Boston),nrow(Boston)/2)
x_train = Boston[train,-14]
y_train = Boston[train,14]
x_test = Boston[-train,-14]
y_test = Boston[-train,14]

#Choosing the size of p
p1 = ncol(Boston)-1
p2 = sqrt(p1)
p3 = p1/2

set.seed(1)
rf.model.p1 = randomForest(x_train,y_train,x_test,y_test,mtry=p1,ntree=500)
rf.model.p2 = randomForest(x_train,y_train,x_test,y_test,mtry=p2,ntree=500)

plot(rf.model.p1$test$mse,type="l",col="2",xlab="ntree",ylab="mse")
lines(1:500,rf.model.p2$test$mse,type="l",col="3")

#We can see that that mtry=p2 gives a model with lower mean squared error.
#We can find what number of trees that gives the lowest mean squared error in rf.model.p2
which.min(rf.model.p2$test$mse)

39

#Now we will use ntree =39 and mtry = p2 to retrain the regression tree model
rf.model = randomForest(x_train,y_train,x_test,y_test,mtry=p2,ntree=39)

cor(rf.model$test$predicted,y_test)

0.93587171003633