Evaluating the Statistical Significance of Models Developed by Stepwise Regression

Information for evaluating the statistical significance of stepwise regression models developed with a forward selection procedure is presented. Cumulative distributions of the adjusted coefficient of determination (R²) under the null hypothesis of no relationship between the dependent variable and m potential independent variables are derived from a Monté Carlo simulation study. The study design included sample sizes of 25, 50, and 100, available independent variables of 10, 20, and 40, and three criteria for including variables in the regression model. The results reveal that the biases involved in testing statistical significance by two well-known rules are very large, thus demonstrating the desirability of using the Monté Carlo cumulative R² distributions developed by the authors. Although the results were derived under the assumption of uncorrelated predictors, the authors show that the results continue to be useful for the correlated predictor case.