The accompanying data set contains three predictor variables, x₁, x₂, and x₃, and one numerical target variable, y. A regression tree will be constructed using the data set.

a. Which split on x₁ will generate the smallest MSE? 

b. Which split on x₂ will generate the smallest MSE?

c. Which split on x₃ will generate the smallest MSE? 

d. Which variable and split value should be used to create the root node if a regression tree is constructed using the accompanying data set? 

e. State the rules generated from this split.