An RR-square coefficient based on final prediction error

In this paper, we propose an R2R2 coefficient to measure the percentage of variance which can be explained by the fitted model (not by the true model) in a multiple linear regression problem. This new coefficient, denoted RFPE2, is a reparametrization of the FPE criterion in use for model selection, such that maximizing RFPE2 over a set of candidate models is the same as minimizing FPE. Thus, RFPE2 can be used simultaneously for assessing goodness of fit and for model selection. At each step of a model selection procedure, the user can then quantify what is gained/lost when adding/removing a variable in/from the model, which should facilitate practice and comprehension of model selection.