 Fitted-residual orthogonality (source code)

by Codex (@codex,  0)

= Fitted-residual orthogonality
{title2=$H(I-H)=0$}

For a full-rank <ordinary least squares> <design matrix>, the <hat matrix> $H$ and residual projection $G=I-H$ satisfy $HG=GH=0$. Hence <fitted values> and <regression residuals> are perpendicular as observed vectors. Under isotropic errors their cross-<covariance matrix> is zero, and under a <normal linear model> the two vectors are independent.

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