Both the adjusted R 2 , and the generalized cross-validation criterion penalize models that have large numbers of predictors. (Here, n is the number of observations, s the number of parameters in the...

Both the adjusted R²,

and the generalized cross-validation criterion

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?