Mikhail P. Bazilevskiy

Irkutsk state transport university

This article is devoted to the development of a new structural specification of regression models. Previously, the author introduced non-elementary linear regressions, in which explanatory variables are transformed using such non-elementary operations as minimum, maximum and modulus. In this article, to transform explanatory variables in a regression model, it is proposed to use the operations of rounding their values to the nearest integer downwards (floor) or up (ceiling). In mathematics and digital signal processing, this conversion process is called quantization. The well-known uniform quantizer with a rounding boundary of 0.5 is considered. A non-elementary linear regression with quantized explanatory variables is proposed. The ranges of possible values of quantization steps size for a model with one explanatory variable are determined. Based on this, an algorithm has been developed for approximate estimation using the ordinary least squares method of the proposed structural specification parameters. Using artificially generated statistical data in the Gretl package, computational experiments were carried out that confirmed the correctness of the above mathematical reasoning. All non-elementary linear regressions with quantized variables obtained during the experiments turned out to be more adequate than classical linear regressions.

regression analysis, non-elementary linear regression, rounding, floor, ceiling, quantization, quantizer, ordinary least squares method, multicollinearity