Regression: Model Comparison

Compare how different feature engineering choices affect a linear regression model fitted to the classic Advertising dataset. Toggle options below and watch the coefficients and fit metrics update instantly.

Dataset from Chapter 3 of Introduction to Statistical Learning (James et al.)

Controls

Residual Analysis

Coefficients

Interpreting the Results

How to read the residual plot

• Random scatter around zero: The model captures the relationship well
• Curved pattern: A nonlinear relationship exists — try polynomial features
• Funnel shape: Heteroscedasticity — variance changes with fitted values
• Large outliers: Individual points the model struggles to predict

Try toggling the interaction term — notice how the residual pattern changes when TV × Radio synergy is captured by the model.

What do the coefficients mean?

• Coefficients represent the change in sales for a one-unit change in the feature
• When features are normalized, coefficients reflect relative importance
• The intercept captures baseline sales when all features are zero
• Interaction terms capture synergy — does TV advertising work better in markets with high radio spend?

Why normalize features?

Without normalization, coefficient magnitudes depend on feature scales. TV ranges from 0-300 while Radio ranges from 0-50, so raw TV coefficients appear smaller. Normalization puts all features on the same scale, making coefficients directly comparable.