DIMENSIONAL REDUCTION OF LINEAR REGRESSION TAKING INTO ACCOUNT A GIVEN LEVEL OF APPROXIMATION ERRORS

Abstract

Background. Quite often, when constructing regression models for real complex objects, it becomes necessary to reduce their dimension in order to eliminate the multicollinearity of variables or exclude statistically insignificant factors. Usually, the main component methods are used, as well as various step procedures and their modifications. The purpose of this work is to develop an algorithmic way to reduce the dimension of linear regression by solving linear-Boolean programming problems. Materials and methods. To achieve this goal, the mathematical apparatus for solving linear-Boolean programming problems was used. Results. Two methods have been developed to reduce the dimensionality of the linear regression model. The first, empirical, assumes that the researcher himself, based on the values of the adequacy criteria (the sum of the modules of the approximation errors, the average relative error and the average percentage error) and his experience and knowledge, decides how justified a reduction in the dimension of the model is at one step or another of the organized iterative process. The second, algorithmic one is based on setting the acceptable error level. Conclusions. Both methods involve solving linear-Boolean programming problems. The regression model of the Severstal steel and mining company has been clarified. It turned out that the best is the four-factor version of the model, in which the average percentage error is 9,39 %.