The Use of an F -Statistic in Stepwise Regression Procedures

This is an expository paper, pointing out explicitly the pseudoness of the "F-statistic" used in stepwise procedures for determining the independent variables to be used in a linear prediction equation. Unfortunately this pseudoness prevents one from obtaining any probabilistic measure of the goodness of the final prediction equation. The use of the distribution of an order statistic is discussed as an aid to understanding the problem as well as furnishing a "better" (although still unsatisfactory) approach.