Software complex for constructing quasi-linear regressions according to the criteria of accuracy and non-linearity
DOI:
https://doi.org/10.52575/2687-0932-2022-49-1-121-133Keywords:
regression model, quasi-linear regression, coefficient of determination, criterion of non-linearity, Student's t-test, interpretation, freight rail transportationAbstract
This article is devoted to the problem of choosing structural specifications for quasi-linear regression models. Such regressions are fairly easy to estimate, but the presence of non-linear transformations of variables in them makes it difficult to interpret their estimates. Previously, the authors formulated a two-criterion problem of choosing the specification for quasi-linear regression, which consists in maximizing the coefficient of determination and simultaneously minimizing the general criterion of nonlinearity. For a large number of variables, such a formulation turns into a complex computational problem. In this paper, we describe for the first time a software complex developed by us that fully automates the solution of a two-criteria problem. It provides work in two modes. In the first of them, a Pareto set is formed, with the help of which the user can visually trace the sequential transformation of a linear regression into a nonlinear model and choose the most acceptable alternative. In the second mode, all significantly non-linear regressions are first automatically excluded, and the best one according to the determination criterion is selected from the remaining ones. In both modes, it is possible to exclude models with coefficients that are insignificant according to Student's t-test. With the help of the software complex, the problem of modeling freight rail transportation in the Irkutsk region was successfully solved.
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