An R-square coefficient based on final prediction error

Abstract In this paper, we propose an R 2 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 R FPE 2 , is a reparametrization of the FPE criterion in use for model selection, such that maximizing R FPE 2 over a set of candidate models is the same as minimizing FPE. Thus, R FPE 2 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.

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