Decision Tree vs. Linear Regression

Decision Tree vs. Linear Regression

Decision trees and linear regression are both supervised machine learning techniques, but they serve different purposes and have distinct characteristics. Below is a detailed comparison:

Key Differences

1. Model Type and Assumptions

• Decision Tree: A non-parametric model that makes no assumptions about data distribution. It works by recursively splitting data based on feature thresholds.
• Linear Regression: A parametric model that assumes a linear relationship between features and the target variable. It minimizes the sum of squared errors.

2. Interpretability

• Decision Tree: Highly interpretable—rules can be visualized as a tree structure.
• Linear Regression: Coefficients provide clear insight into feature importance but assume linearity.

3. Handling Non-linearity

• Decision Tree: Naturally captures non-linear relationships and interactions.
• Linear Regression: Requires feature engineering (e.g., polynomial features) to model non-linear patterns.

4. Handling Categorical Features

• Decision Tree: Can directly handle categorical variables without encoding.
• Linear Regression: Typically requires one-hot encoding or label encoding.

5. Robustness to Outliers

• Decision Tree: Less sensitive to outliers due to splitting logic.
• Linear Regression: Highly sensitive to outliers since it minimizes squared error.

6. Overfitting

• Decision Tree: Prone to overfitting unless pruned or regularized (e.g., max_depth).
• Linear Regression: Less prone to overfitting unless high-dimensional (can use regularization like Lasso/Ridge).

7. Use Cases

• Decision Tree: Classification and regression tasks where interpretability is crucial (e.g., medical diagnosis).
• Linear Regression: Predicting continuous outcomes with linear assumptions (e.g., house price prediction).

Example Code

Decision Tree (Regression)

from sklearn.tree import DecisionTreeRegressor

model = DecisionTreeRegressor(max_depth=3)
model.fit(X_train, y_train)
predictions = model.predict(X_test)

Linear Regression

from sklearn.linear_model import LinearRegression

model = LinearRegression()
model.fit(X_train, y_train)
predictions = model.predict(X_test)

Choosing Between Them

• Use linear regression if the relationship is linear and interpretability of coefficients is needed.
• Use a decision tree if the data has complex interactions, non-linear patterns, or requires rule-based insights.

For improved performance, ensemble methods like Random Forests (based on decision trees) or advanced techniques like Gradient Boosting can be considered.