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Using a p-value to make any kind of decision is questionable to begin with, and especially unreliable in choosing covariates in regression. Old studies, e.g. by Walls and Weeks and by Bendel and Afifi, have shown that if predictive ability is the criterion of interest and one wishes to use p-values for deciding whether to include a covariate, one should set the p-value bar very large, at 0.25 and even 0.40. By contrast, methods such as AIC are aimed at avoiding overfitting, by penaliz...