= Unpenalized intercept in ridge regression
{title2=$\widehat\alpha=\overline Y-\overline x^T\widehat\beta$}
In <ridge regression>, penalize slopes but ordinarily leave the <regression intercept> free. Centering gives $\widehat\beta=(X_c^TX_c+\lambda I)^{-1}X_c^TY_c$ and $\widehat\alpha=\overline Y-\overline x^T\widehat\beta$. An exactly centered predictor matrix has $\widehat\alpha=\overline Y$ for every penalty. A table with a penalty-dependent intercept therefore cannot arise from exactly centered columns under this convention.
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