Asymptotic Validity of F Tests for the Ordinary Linear Model and the Multiple Correlation Model

In this article we establish under fairly general conditions that the F tests used in the linear model and the correlation model are asymptotically valid in the presence of nonnormality, in that their sizes are unaffected, asymptotically, by this nonnormality. Similar results could be derived for Scheffé-type simultaneous confidence intervals as well as the one-sided t tests used in these models. Finally, we find the asymptotic distribution of the sample variance and show why the size of a χ2 test about the variance for the linear model is not asymptotically valid in the presence of nonnormal errors.