Estimates of cross-validity for stepwise regression and with predictor selection

The effects of preselection of predictors (e.g., stepwise regression) on fo rmula estimates of cross-validity were examined. Three actual data sets wer e used to generate populations of varying sample size, population validity, and number of predictors. No formula estimate provided an unbiased estimat e of the population cross-validity, although some formula estimates were le ss biased than others. More important, having an adequate sample size (rela tive to number of predictors) was the issue most affecting the utility of t he formula estimates. Another conclusion was that adjusted R-2 provided by at least some popular software programs can provide gross overestimates of cross-validity and should not be used as such.