Interpretation of Parameter Estimates for Fully connected Linear Regression Models

Abstract

This article is devoted to the study of interpretation questions of parameter estimates for fully connected linear regression models. In such models, all observed variables contain errors, and true variables are interconnected by linear functional dependencies. A special case of fully connected regression is the well-studied Deming regression. Previously, a weighted total least squares method was used to estimate fully connected regressions. In this article, it is established that the estimates of fully connected linear regression obtained by this method coincide with the estimates of the maximum likelihood method. It was found that it is impossible to interpret fully connected regressions by analogy with multiple regressions, since the former are construct on the assumption that all variables are strongly correlated with each other. A theorem is proved according to which a simultaneous increase in the values of the observed variables in the estimated model of a fully connected linear regression by certain values leads to an increase in the estimates of the true values of the variables by the same values. Using this fact, any model of fully connected linear regression can be interpreted, which is demonstrated by the example of modeling such macroeconomic indicators of the Irkutsk region as the turnover of wholesale and retail trade, as well as agricultural products.