15.071 | Spring 2017 | Graduate

The Analytics Edge

4.2 Judge, Jury, and Classifier: An Introduction to Trees

4.2 Judge, Jury, and Classifier: An Introduction to Trees

Quick Question

Suppose that you have the following CART tree:

How many splits are in this tree?

Exercise 1

Numerical Response

For which data observations should we predict “Red”, according to this tree? Select all that apply.

Exercise 2

If X is less than 60, and Y is any value.

If X is greater than or equal to 60, and Y is greater than or equal to 20.

If X is greater than or equal to 85, and Y is less than 20.

If X is greater than or equal to 60 and less than 85, and Y is less than 20.

Explanation

This tree has three splits. The first split says to predict “Red” if X is less than 60, regardless of the value of Y. Otherwise, we move to the second split. The second split says to check the value of Y - if it is greater than or equal to 20, predict “Gray”. Otherwise, we move to the third split. This split checks the value of X again. If X is less than 85 (and greater than or equal to 60 by the first split) and Y is less than 20, then we predict “Red”. Otherwise, we predict “Gray”.