Return to a Note on Screening Regression Equations

Abstract

We revisit an article by D. A. Freedman on screening variables for regression models. After summarizing his asymptotic results we show that the theory does not entirely explain the results of computer simulations of his model. We demonstrate that this is due to the random correlation between simulated independent random variables. Finally, we explore some consequences of the asymptotic results. In the case of uncorrelated variables using the proposed two-stage screening procedure, it is possible to obtain significance tests for the final F statistic and t statistic that have the correct Type I error rates.

Key Words:

• F statistic
• Multiple correlation coefficient
• Significance levels
• Variable selection