Both the adjusted R2, Re2 1 # n # 1 n # s RSS TSS and the generalized cross-validation criterion GCV n

Both the adjusted R2, Re2 ¼ 1 # n # 1 n # s

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RSS TSS and the generalized cross-validation criterion GCV ¼ n · RSS ð Þ n # s 2 penalize models that have large numbers of predictors. (Here, n is the number of observations, s the number of parameters in the model, RSS the residual sum of squares under the model, and TSS the total sum of squares.) Do these two criteria necessarily rank a set of models in the same order? That is, if one model has a larger Re2 than another, does it necessarily also have a smaller GCV?