Ridge regression is an L2-regularized linear model that penalizes squared coefficient magnitudes. It shrinks coefficients toward zero, giving larger coefficients stronger penalties without usually removing features entirely. section 4.3.2
Ridge is especially useful when predictors overlap:
- Keeps multicollinear, predictive features in the model with generally similar-sized coefficients. section 4.3.2
- Attenuates coefficients proportionally rather than selecting features as L1 regularization does. section 4.3.2
A regularized polynomial pipeline
A Scikit-learn workflow expands degree-two features, standardizes them, and fits Ridge(alpha=2500.0). Five-fold cross-validation reports an RMSE of 33.738 with a 0.275 standard deviation, alongside fit and prediction timings.

