Problem $2.$ Greedy Heuristic for Decision Trees

$15$ Points

Consider the following data set that contains $100$ training examples $(50$ labeled as positive class while the remainder labeled as negative class$).$

Build a two$-$level decision tree using gini index as the criterion for splitting.

You need to show your computations for each candidate splitting attribute at each level clearly to obtain full credit. What is the overall training error rate of the induced tree? Note: we consider a tree with only $1$ internal node and two leaf nodes as a one$-$level decision tree.

Use variable X as the first splitting attribute, then choose the best available splitting attribute at each of the two successor nodes. What is the training error rate of the induced tree?

Discuss the results obtained in parts $($a$)$ and $($b$)$ above. Comment on the suitability of the greedy heuristic used as the splitting attribute selection.