Implement ridge with an unpenalised intercept

Question

Implement Python ridge regression for a finite two-dimensional design matrix X and one-dimensional target y, with positive penalty and an unpenalised intercept. Explain why you avoid an explicit matrix inverse.

Short answer

Centre X and y, solve the penalised normal system, then restore the intercept. Positive penalty ensures invertibility of the centred system, although QR/SVD formulations can offer better numerical conditioning.

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Lessons behind this question

The Supervised Learning Problem and the ML Pipeline
Simple Linear Regression: OLS Estimators and Geometry
Multiple Linear Regression

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