 AIC deletion threshold in a normal linear model

Deleting $q$ fitted mean parameters improves the Akaike information criterion exactly when the displayed condition holds, since the criterion difference is $n\log ({\mathrm{RSS}}_{\mathrm{reduced}}/{\mathrm{RSS}}_{\mathrm{full}})-2q$. For one parameter, the equivalent partial F-test statistic is below $(n-p)(e^{2/n}-1)$, where $p$ is the full mean-model dimension. This is not the usual fixed-level significance-test cutoff. Fits must use the same observations and response transformation.