Construction of quite interpretable linear regression models using the method of successive increase the absolute contributions of variables to the general determination

Abstract

This article is devoted to the problem of constructing quite interpretable linear regression models estimated using the ordinary least squares. Linear regression is called quite interpretable if the signs of its coefficients correspond to the physical meaning of the factors included in the equation, and the eff ect of multicollinearity is insignificant. At the same time, it is desirable that the model has a high quality of approximation, and all its coefficients are significant. In this article, for the fi rst time, the problem of mixed 0-1 integer linear programming was formulated to select the optimal number of variables in linear regression, the signs of the coefficients for which are consistent with the signs of the corresponding coefficients of their correlation with the dependent variable, and the absolute contributions of the variables to the general determination are not less than a given number. The efficiency of solving this problem is due to the presence of restrictions on the consistency of the model coeffi cients signs, and restrictions on the absolute contributions of the variables make it possible to control the multicollinearity. A method has been developed for successive increase the absolute contributions of variables to the general determination, which guarantees the construction of quite interpretable linear regression. To solve the formulated tasks, the program ВИнтер-1 was developed. At first, using it on an ordinary personal computer, a rather complex computational problem was solved, the solution of which by the exhaustive search method requires the estimation of approximately 16.5 quadrillion models. The ВИнтер-1 program completed this task in about 293 seconds, which confirms its effectiveness. In addition, with the help of ВИнтер-1, a quite interpretable model of rail freight transportation in the Irkutsk region was construct.