APPROXIMATE LEAST SQUARES ESTIMATION OF ONE FORM OF NON-ELEMENTARY MODULAR LINEAR REGRESSIONS

Abstract

Background. The problem of finding new structural specifications of regression models with interesting interpretive properties is currently relevant. The purpose of the study is to formalize a new structural specification,based on a symbiosis of previously proposed non-elementary and modular linear regressions, to develop an algorithm for its approximate estimation using the ordinary least squares method and to demonstrate its effectiveness using the example of modeling the consumer price index in the Altai Republic. Materials and methods. To estimate the regression models, the ordinary least squares method was used in combination with the «all possible regressions» method. Results. A new structural specification of regression models is formulated – non-elementary modular linear regression, which generalizes many well-known models. An algorithm for its approximate estimation is proposed. The non-elementary modular linear regression constructed using it turned out to be 39.3 % better in terms of the approximation quality of non-elementary regression without modules, and 63.7 % better than linear regression. Conclusions. Using the proposed models of non-elementary modular linear regression, one can successfully solve forecasting problems, as well as the problem of identifying new knowledge about the object of study.

Keywords

• linear regression
• non-elementary regression
• modular regression
• leontief function
• ordinary least squares method
• multicollinearity
• consumer price index