Selection of informative regressors significant by Student’s t-test in regression models estimated using ols as a partial boolean linear programming problem

Abstract

This article is devoted to the problem of selecting a fixed number of informative regressors in linear regression models estimated using ordinary least squares method. In modern scientific works, the apparatus of integer mathematical programming, which has been well developed in recent years, is used to solve this problem. In most of these works, the problem of subset selection is formalized in the form of partial-quadratic linear programming problems. Relatively recently, articles began to appear in which the authors strive to formulate a unified problem of mathematical programming, which, in parallel with the selection of factors, guarantees the construction of a regression that satisfies various statistical tests. This work is a logical continuation of the previous articles of the author, in which the problem of subset selection is formalized as a partial Boolean linear, not quadratic, programming problem. Methods of control in this problem of the degree of multicollinearity have already been considered. In this article, using the well-known approach to determining the values of Student’s t-tests, based on the calculation of partial F-tests, linear constraints on the degree of significance of the regression coefficients were integrated into the mentioned problem of partial-Boolean linear programming. A two-criteria problem is formulated, which allows to build a model from the perspective of the ratio «quality —significance», and a three-criteria problem, which constructs a regression from the position of the relationship «quality — multicollinearity — significance».