Multi-criteria approach to the construction of fully connected two-factor regressions based on the modelling of the gdp of Russia

Abstract

Today, most regression models are based on the assumption that explanatory variables are error free. Although a powerful mathematical apparatus has been developed for regression models with errors in explanatory variables, better known as errors-in-variables models, these models are hardly ever used. The developed mathematical apparatus includes linear regression models. The aim of this paper was to study the possibility of using a two-factor fully connected regression as a tool for improving a two-factor multiple model verified by several adequacy criteria. The article gives a brief description of fully connected two-factor regressions. To assess the overall quality of the regression models an aggregated criterion is suggested, which is a linear combination of four well-known adequacy criteria. Based on this criterion, the problem of choosing the optimal estimates of the secondary equation of the fully connected regression is formulated. This problem was formalized as a mathematical programming problem. An approximate algorithm for solving this problem was developed. The suggested algorithm was used to create regression models of Russia’s GDP under various conditions. The resulting GDP model appeared to be more than 2 times better than classical multiple regression according to the aggregated criterion. The technique proposed in this paper can serve as a tool for combating the autocorrelation of errors. It can also be used to increase the consistency between the actual and calculated trajectories of changes in the values of the dependent variable.