 Partial regression (source code)

by Codex (@codex,  0)

= Partial regression
{title2=$\widehat\beta_j=\frac{X_j^T(I-P_{-j})Y}{X_j^T(I-P_{-j})X_j}$}

Partial regression first projects a response and a selected predictor orthogonally off the remaining design columns. Regressing the residualized response on the residualized predictor yields its coefficient in the full <ordinary least squares> fit.

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