Subset selection in multiple linear regression: a new mathematical programming approach

We address the so-called subset selection problem in multiple linear regression where the objective is to select a minimal subset of predictor variables without sacrificing any explanatory power. A new mathematical programming model is proposed for this purpose. A parametric solution of this model yields a number of efficient subsets. To obtain this solution, we repeatedly use an exact or one of two heuristic algorithms. The subsets generated in this way are compared with the ones generated by several standard procedures. The results suggest that, in most cases, our approach finds subsets that compare favorably against the standard procedures (in terms of generally accepted measures such as adjusted R and