Construction of Two-factor Non-elementary Linear Regressions with Boolean Functions

Mikhail Bazilevskiy

Abstract


This article is devoted to the development of new structural specifications for regression models. The two-factor Leontief function, which is an integral part of non-elementary linear regressions, is considered. Based on it, a logical function of argument activation is introduced, which takes the values 0 and 1, depending on which of the arguments is activated in the min binary operation. A regression model with a logical function of argument activation is formulated. An algorithm for its approximate estimation using the ordinary least squares method is proposed. The developed regression can be used to construct models with a binary dependent variable. Two varieties of non-elementary linear regressions with a logical function of argument activation are synthesized. The proposed models are generalized to the case of many explanatory variables. With the help of regression with a logical function of argument activation, a problem with a binary dependent variable is solved. The model accurately predicted the values of the dependent variable in 76 observations out of 100. And using a non-elementary linear regression with a logical function of argument activation, the problem of modeling the gross regional product of the Irkutsk region was solved. The constructed model turned out to be better than the regression without the logical function of argument activation.


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