SUBSET SELECTION IN REGRESSION MODELS WITH CONSIDERING MULTICOLLINEARITY AS A TASK OF MIXED 0-1 INTEGER LINEAR PROGRAMMING

The article is devoted to the problem of subset selection in linear regression model, the exact solution of which guarantees either a full search of all possible regressions or a solution of a specially formulated mathematical programming problem with Boolean variables. Often the problem of subset selection is solved using only one criterion of adequacy, for example, only model errors are minimized. But in the case of estimating regression using ordinary least squares, it is necessary to strive not only to increase the quality of the approximation, but also to observe the conditions of the Gauss-Markov theorem, one of which is the absence of a linear dependence between the explanatory variables. If this condition is not satisfied, then it is said that multicollinearity takes place. Thus, when selecting informative regressors, it is expedient to solve the two-criteria problem - to strive to maximize the quality of approximation and at the same time minimize the multicollinearity between explanatory variables. Since there are no exact quantitative criteria for determining the presence / absence of multicollinearity, in this paper, based on the wellknown recommendation, a criterion for the upper bound of multicollinearity is formulated. Using this criterion, four possible statements of the two-criteria problem of subset selection are proposed, each of which is reduced to task of mixed 0-1 integer linear programming. To demonstrate the proposed mathematical apparatus, a trial version of a specialized software package was developed, with the help of which the task of modeling the freight turnover of the Krasnoyarsk railroad was solved.

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