A Procedure for Optimal Stepwise MSAE Regression Analysis

This paper brings together two topics from regression analysis. One is the topic of stepwise regression, a set of commonly used procedures for exploring alternative formulations of the regression model. The other topic is regression by minimizing the sum of the absolute errors about the regression line (MSAE). This technique has been found, in a variety of circumstances, to be more attractive than the traditional least-squares method. The paper presents a procedure for selecting from among m regressors the best sets of k, k + 1, … and m regressors according to the MSAE criterion (k ≦ m). Building upon the well known linear-programming formulation of the MSAE problem, the paper develops a partial enumerative search scheme, in which a set of distinct, but related, combinatorial optimization problems (corresponding to determination of “best k,” “best k + 1,” etc.) are, in effect, solved simultaneously.