# Lab5

## Insurance data
## Importare dati

TL <- read.csv("TL.csv", header=TRUE, sep=",", row.names=1)
dim(TL)
LFACE <- log(TL$FACE)
LINCOME <- log(TL$INCOME)

TL2 <- TL[, -c(5,6)]
TL2$LINCOME <- with (TL2, LINCOME)
TL2$LFACE <- with(TL2, LFACE)
library(tree)

## create trainig and test set
set.seed(2)
train <- sample(1:nrow(TL2), nrow(TL2)/2)

## fit regression tree
tree.tl <- tree(LFACE ~ ., TL2, subset = train)
summary(tree.tl)
plot(tree.tl)
text(tree.tl, pretty = 0)

## pruning tree
cv.tl <- cv.tree(tree.tl)
plot(cv.tl$size, cv.tl$dev, type= "b")

prune.tl <- prune.tree(tree.tl, best = 3)
plot(prune.tl)
text(prune.tl, pretty = 0)

## predictions
yhat <- predict(tree.tl, newdata = TL2[-train,])
tl.test <- TL2[-train, "LFACE"]
plot(yhat, tl.test)
abline(0,1)
mean((yhat-tl.test)^2)

## new plot (similar to plot 8.5 of ISL)
yhat.tr <- matrix(NA, length(train), 8)
yhat.test <- matrix(NA, length(TL2[-train,1]),8)
MSE.tr <- c()
MSE.test <- c()
for (j in 2:8){
  tree.sized <- prune.tree(tree.tl, best = j)
  a<-summary(tree.sized)
  newTL2 <- as.data.frame(TL2[, as.character(a$used)])
  colnames(newTL2) <- as.character(a$used)
  tree.chosen <- tree(LFACE ~  ., newTL2, subset = train)
  yhat.tr[,j] <- predict(tree.chosen, newdata=TL2[train, ])
  yhat.test[,j] <- predict(tree.chosen, newdata=TL2[-train, ])
  MSE.tr[j] <- (1/length(train))*sum((TL2$LFACE[train]-yhat.tr[,j])^2)
  MSE.test[j] <- (1/length(TL2[-train,1]))*sum((TL2$LFACE[-train]-yhat.test[,j])^2)
}

plot((2:8), MSE.tr[2:8], type="b", xlab = "Tree size", col="black", ylim=c(1,4))
lines(2:8, MSE.test[2:8], type="b", col= "orange")

## per la consegna

library(ISLR2)
library(dplyr)
newHitters <- Hitters %>% filter(!is.na(Salary))
newHitters$Salary <- log(newHitters$Salary)
data(Hitters)