Classification Using CART Models

Classification and Regression Trees (CART) are often used in data mining with the goal of creating a model that predicts the value of a response (or dependent) variable given the values of input (or independent) variables. This Pull-Out is an introduction to binary CART models used for classification. In Activity 1, students are introduced to decision trees and how to read decision rules from the trees. Activity 2 focuses on creating CART models. Students use the Gini Index to determine which input variable they should use for the first split in their decision trees. Once students understand how models are built, Activity 3 discusses how to compute the accuracy of a CART model as a measure of its performance.

In Activity 4, students use CART models to make predictions. Students create confusion matrices to examine the types of errors that arise from predicting with CART models.

The activities in this Pull-Out address Mathematical Practices #4 Model with mathematics and #7 Look for and make use of structure from the Common Core State Standards for High School Mathematics.

For more information about CART models, please see Classification and Regression Trees by Leo Breiman, Jerome Friedman, Richard Olshen, and Charles Stone (Chapman & Hall/CRC Press, Boca Raton FL, 1984). For more information about decision trees and other classification techniques, please see Data Mining and Predictive Analytics by Daniel T. Larose and Chantal D. Larose (John Wiley & Sons Inc, Hoboken NJ, 2015).

Mathematics prerequisites and discussion:
Students should have an elementary knowledge of probability. It would be helpful if they have seen a tree diagram (of any sort) before. Students should be able to convert proportions to percentages. In addition, they should be familiar with averages, so that they are ready for the concept of weighted averages.

Materials needed:
No additional materials are needed.