Ridge Regression Studio

A real 4-feature synthetic dataset — two features deliberately correlated — and a real, from-scratch closed-form ridge solve (a hand-written Gauss-Jordan matrix inverse, no linear-algebra library) recomputed live as you drag $\lambda$. Makes Ridge Regression, In Full Depth's central claim — multicollinearity makes OLS coefficients unstable, ridge fixes it at a small MSE cost — something you watch happen, not just read.

What to Try

• Set λ = 0 (plain OLS) and push Correlation up toward 0.98. Watch x1 and x2 swing apart individually — one shooting up, the other down — while x1 + x2 in the readout barely moves. That's multicollinearity: the model can't tell which of two nearly-identical features deserves the credit, so it arbitrarily splits it unstably.
• Now drag λ up from 0. Watch x1 and x2 converge toward each other instead of splitting — ridge treats correlated features symmetrically, pulling them toward sharing the credit evenly — while x3 (genuinely irrelevant, true weight 0) shrinks toward zero fastest of all.
• Watch the MSE readout while you do this: it barely moves. That's the whole trade — a large reduction in coefficient instability for a tiny cost in fit quality, exactly the bias-variance tradeoff the page describes.
• Set Correlation back to 0 and compare: with independent features, OLS is already stable, and increasing λ has nothing to fix — regularization is a solution to a specific problem, not a free improvement to apply blindly everywhere.

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