= Lack-of-fit F-test
{c}
{title2=$F=\frac{(\mathrm{RSS}-\mathrm{SS}_{\mathrm{PE}})/(g-p)}{\mathrm{SS}_{\mathrm{PE}}/(n-g)}$}
For $n$ independent normal responses of common <variance> at $g$ distinct predictor settings, a rank-$p$ <normal linear model> has residual degrees $n-p$. The saturated setting-mean model has $g$ parameters and <pure error> degrees $n-g$. Splitting orthogonal residual spaces gives <lack of fit> degrees $g-p$. Under the fitted mean model, the two squared lengths divided by the common variance are independent <chi-squared> variables; their ratio of mean squares has the <F-distribution> shown. This test is unavailable without repeated settings or positive lack-of-fit degrees.
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