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

Mallows’ CpCp plot is a useful tool for variable selection in linear regression. Though not as popular as the CpCp plot, Spjotvoll’s FpFp and PpPp plots are also used in the variable selection procedure. The CpCp, FpFp and PpPp 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 CpCp or FpFp plot is used. If a formal testing procedure is to be performed, then a PpPp 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.