A Note on Stagewise Regression

Suppose one estimates the coefficient β2 in E[Y] = β0 + β1 X 1 + β2 X 2 by stagewise regression. That is, first the model E[Y] ≌ β0 + β1 X 1 is fit using simple linear regression followed by a simple linear regression of the residuals from this model on X 2 to yield the estimator β2. The ratio of the squared t statistic for the estimate b 2 from multiple regression to the squared t statistic for β2 is greater than or equal to 1.0 and is shown to be a convenient function of correlation coefficients among Y, X 1, and X 2. Examination of stagewise regression can provide useful insights when introducing concepts of multiple regression.