Open AccessMulti-criteria approach to pair-multiple linear regression models constructing
Author(s) -
Mikhail Pavlovich Bazilevskiy
Publication year - 2021
Publication title -
izvestiâ saratovskogo universiteta. novaâ seriâ. seriâ matematika. mehanika. informatika
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.255
H-Index - 4
eISSN - 2541-9005
pISSN - 1816-9791
DOI - 10.18500/1816-9791-2021-21-1-88-99
Subject(s) - proper linear model , linear regression , linear predictor function , mathematics , polynomial regression , regression diagnostic , segmented regression , regression analysis , local regression , nonlinear regression , linear model , regression , principal component regression , statistics , multivariate adaptive regression splines
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.