Multi-criteria approach to pair-multiple linear regression models constructing
M. P. Bazilevskiy
Irkutsk State Transport University, 15 Chernyshevskogo St., Irkutsk 664074, Russia
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.
Deming regression, pair-multiple linear regression model, multi-criteria approach, aggregate criterion, nonlinear programming.
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M. P. Bazilevskiy, “Multi-criteria approach to pair-multiple linear regression models constructing”, Izv. Saratov Univ. Math. Mech. Inform., 21:1 (2021), 88–99
Citation in format AMSBIB
\paper Multi-criteria approach to pair-multiple linear regression models constructing
\jour Izv. Saratov Univ. Math. Mech. Inform.
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