CART Regression

Introduction
When you think of machine learning models for regression, linear or polynomial regression might come to mind. But what if your data doesn’t follow a linear pattern? That’s where CART Regression (Classification and Regression Trees) comes into play. It’s a powerful, intuitive, and non-linear way to make predictions using decision trees.

In this post, you'll learn:

What CART Regression is

How it works under the hood

A Python implementation using scikit-learn

When to use it (and when not to)

What is CART Regression?
CART stands for Classification and Regression Trees. It’s a type of decision tree algorithm that works for both classification (predicting categories) and regression (predicting continuous values).

When used for regression, the tree splits the dataset into smaller and smaller groups based on feature values, minimizing the Mean Squared Error (MSE) at each step. The final prediction is the average of the target values in a leaf node.

How CART Regression Works
Here’s the step-by-step breakdown:

Start with all the data at the root.

At each step, CART finds the best feature and threshold that minimizes MSE.

Split the data into two branches.

Repeat the process recursively on each branch (subtree).

Stop splitting when a stopping criterion is met (like max_depth or min_samples_split).

Advantages of CART Regression
✅ Handles non-linear relationships well.

✅ Easy to interpret and visualize.

✅ No need for feature scaling.

✅ Handles both numerical and categorical data.

** Limitations to Watch For**
❌ Prone to overfitting, especially with deep trees.

❌ Small changes in data can result in a different tree (high variance).

❌ Not great at extrapolation (predicting outside of the training range).

You can reduce overfitting using pruning, setting max_depth, or using ensemble models like Random Forests or Gradient Boosting.
Real-World
Predicting house prices based on features like size, location, and age

Estimating customer spending from demographics and purchase history

Forecasting sales based on seasonality and marketing data
Final Thoughts
CART Regression is a simple yet powerful way to model complex, non-linear relationships in data. It’s a great baseline model and forms the building block of more advanced tree-based algorithms like Random Forests and XGBoost.