ISYE 6501 — Introduction to Analytics
Module 10, Lesson 1: Introduction to CART
Classification and Regression Trees
1. Overview
Tree-based methods extend regression (and classification) by splitting the dataset into subsets
and fitting a separate, simpler model to each subset. The general framework is called CART —
Classification And Regression Trees.
What problem does CART solve?
A single global regression model assumes the same coefficients apply to all observations. But
real-world relationships often differ across subgroups. For example, the effect of a marketing
email on customer spending may vary strongly by age. CART lets the model capture these
interactions naturally by partitioning the data.
2. How Trees Work in Regression
Basic Concept
Start with all training data at the root node. Split into branches based on the value of one
predictor variable at a time. Each branch can be split again, creating a tree structure. The
endpoints of the tree are called leaves (or leaf nodes). A separate model is fit to the data within
each leaf.
Example: Marketing Email Study
Suppose we model the impact of a marketing email on website spending using:
• Demographic factors: age, sex, number of children, annual income
• Purchasing factor: average monthly spend on the website
• Treatment indicator: binary variable for whether a marketing email was received
A tree might branch as follows:
• Root split: Age ≤ 25 vs. Age ≥ 26
• Second split (within Age ≥ 26): Age 26–50 vs. Age ≥ 51
• Third split (within Age 26–50): No children vs. At least one child
