## part (a)
library(mclust)
library(tree)

### Fit tree
### Say you have the data frame named precip_dt
#### with variables, Y, X1, X2, X3

tree.precip = tree(Y ~ X1+X2+X3, data = precip_dt)
summary(tree.precip)

## unpruned tree

plot(tree.precip)

### treeFun below
treeFit = treeFun(precip_dt, toPlot=T, title="Burnt Area Tree")

  #Use tree to predict original data
  treePred <- predict(treeFit)
  treeResid <- resid(treeFit)
  myRange <- range(treePred, precipData$precip)
  
  #Plot observed vs predicted
  plot(precipData$precip, treePred, xlim = myRange, ylim = myRange, xlab="True value", ylab="Prediction",
       main = paste("Pred vs True for", title))
  lines(precipData$precip, precipData$precip, col = "red")


part(b)
#### #############################
#### Fit a Random Forest ####
#############################

# Fit random forest and plot
forest.precip = randomForest(Y ~ X1+X2+X3, data = precip_dt)
summary(forest.precip)
plot(forest.precip)

rforestpred = predict(forest.precip)

### compare the predicted values with the observed..

### similarly apply bagging and other trees.

##########

### Function to prune the tree

treeFun <- function(precip_dt, toPlot = F, title = ""){
  
  #Create Complex Tree - or full tree
  myTree <- tree(Y ~ X1+X2+X3, data = precipData, model = T)
  
  #Perform CV on tree object
  cvTree <- cv.tree(myTree)
  optTree <- which.min(cvTree$dev)
  bestTree <- cvTree$size[optTree]
  
  #prune Tree based on CV results
  pruneTree <- prune.tree(myTree, best = bestTree)
  
  #If plotting is selected
  if(toPlot){
    
    #Plot unpruned Tree
    plot(myTree)
    text(myTree, cex = .75)
    title(main = paste("Unpruned Tree for", title))
    
    #Plot CV
    plot(cvTree$size, cvTree$dev, type = "b", 
         main = paste("Cross Validation for", title))
    
    #Plot Prunned Tree
    plot(pruneTree)
    text(pruneTree, cex = .75)
    title(main = paste("Pruned Tree for", title))
  } 
  return(pruneTree)
}