For citation:
Bazilevskiy M. P. Multi-criteria approach to pair-multiple linear regression models constructing. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2021, vol. 21, iss. 1, pp. 88-99. DOI: 10.18500/1816-9791-2021-21-1-88-99, EDN: AVRVDN
Multi-criteria approach to pair-multiple linear regression models constructing
A pair-multiple linear regression model which is a synthesis of Deming regression and multiple linear regression model is considered. It is shown that with a change in the type of minimized distance, the pair-multiple regression model transforms smoothly from the pair model into the multiple linear regression model. In this case, pair-multiple regression models retain the ability to interpret the coefficients and predict the values of the explained variable. An aggregated quality criterion of regression models based on four well-known indicators: the coefficient of determination, Darbin – Watson, the consistency of behaviour and the average relative error of approximation is proposed. Using this criterion, the problem of multi-criteria construction of a pair-multiple linear regression model is formalized as a nonlinear programming problem. An algorithm for its approximate solution is developed. The results of this work can be used to improve the overall qualitative characteristics of multiple linear regression models.
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