A Method for Constructing Nonelementary Linear Regressions Based on Mathematical Programming

Abstract. This paper is devoted to constructing nonelementary linear regressions consisting of explanatory variables and all possible combinations of their pairs transformed using binary minimum and maximum operations. Such models are formalized through a 0-1 mixed integer linear programming problem. By adjusting the constraints on binary variables, we control the structural specification of a nonelementary linear regression, namely, the number of regressors, their types, and the composition of explanatory variables. In this case, the model parameters are approximately estimated using the ordinary least squares method. The formulated problem has advantages: the number of constraints does not depend on the sample size, and the signs of the estimates for the explanatory variables are consistent with the signs of their correlation coefficients with the dependent variable. Regressors are eliminated at the initial stage to reduce the time for solving the problem and make the model quite interpretable. A nonelementary linear regression of rail freight in Irkutsk oblast is constructed, and its interpretation is given.

Keywords: nonelementary linear regression, ordinary least squares method, 0-1 mixed integer linear programming problem, subset selection, coefficient of determination, interpretation, rail freight.