A geometric interpretation of Mallows’ Cp statistic and an alternative plot in variable selection

Abstract

Mallows’ C p plot is a useful tool for variable selection in linear regression. Though not as popular as the C p plot, Spjotvoll’s F p and P p plots are also used in the variable selection procedure. The C p , F p and P p plots are useful in their own right. If the interest is the direct measure of the amount of bias of the submodels and a distributional assumption is not made about the error term, a C p or F p plot is used. If a formal testing procedure is to be performed, then a P p plot is employed. A geometrical approach is used in order to propose an alternative plot that unifies all the information in these three plots, and that has some advantages over them. A Mathematica package has been written to implement the approach.