Stepwise Least Squares: Residual Analysis and Specification Error

Abstract A stepwise procedure for estimating the parameters of the multiple linear regression model y = X 1β1 + X 2β2 + e is often used. Two articles in the March 1961 issue of this Journal focussed on the connection between the stepwise and the direct estimator of β2. The present paper spells out the connection between the stepwise and the direct estimator of β1, as a special case of Theil's analysis of specification error. A unified treatment of the two stepwise estimators is also provided.