Choosing the best set of variables in regression analysis using integer programming

Authors:
Hiroshi Konno;Rei Yamamoto
Affiliations:
Department of Industrial and Systems Engineering, Chuo University, Tokyo, Japan 112-8551;Department of Industrial and Systems Engineering, Chuo University, Tokyo, Japan 112-8551 and Mitsubishi UFJ Trust Investment Technology Institute Co., Ltd, Tokyo, Japan 105-0014
Venue:
Journal of Global Optimization
Year:
2009

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Abstract

This paper is concerned with an algorithm for selecting the best set of s variables out of k( s) candidate variables in a multiple linear regression model. We employ absolute deviation as the measure of deviation and solve the resulting optimization problem by using 0-1 integer programming methodologies. In addition, we will propose a heuristic algorithm to obtain a close to optimal set of variables in terms of squared deviation. Computational results show that this method is practical and reliable for determining the best set of variables.