Piece-linear convolution of options of the object regression model

Abstract

The paper provides a brief overview of the results on the application of regression analysis methods in the study of complex systems: the power of wind turbines in Brazil and wind speed forecasting, the assessment of the calorific value of biomass briquettes when they are used as an efficient combustible fuel, the study of the problem of utilization of plant residues in northern China, the analysis development of small and medium-sized businesses in the Republic of Kazakhstan, development of necessary measures to stimulate the growth of wheat production in South Africa. The case is considered when, for various reasons, when constructing a regression model of a complex object, several of its alternative variants are constructed, each of which is acceptable both in terms of the signs of the estimated parameters and in terms of the values of the adequacy criteria. These reasons may, in particular, include: the use of various types of approximating functions, the use of several methods for identifying model parameters, varying the set of independent variables, including through their transformations - inverse, exponentiation, multiplicative, logarithmic, exponential, trigonometric, logistics, etc. A rule is proposed for choosing a model variant from several alternative ones, formalized by developing an algorithm for constructing a piecewise linear convolution of these variants in the form of a risk function, the problem of estimating the parameters of which is reduced to a linear Boolean programming problem. With the help of this algorithm, a piecewise-linear reconciliation of three variants of the regression model of the cargo turnover of the Krasnoyarsk railway is built - one linear and two linear-multiplicative. As a dependent variable, the freight turnover of the road is taken, while the independent variables are the reception of loaded cars, the reception of empty cars, the dynamic load, and the transfer at the joints of trains.