Frequency of Selecting Noise Variables in Subset Regression Analysis: A Simulation Study

Abstract This article presents the results of a simulation study of variable selection in a multiple regression context that evaluates the frequency of selecting noise variables and the bias of the adjusted R 2 of the selected variables when some of the candidate variables are authentic. It is demonstrated that for most samples a large percentage of the selected variables is noise, particularly when the number of candidate variables is large relative to the number of observations. The adjusted R 2 of the selected variables is highly inflated.