INVESTIGATION OF A TWO-FACTOR FULLY CONNECTED LINEAR REGRESSION MODEL
This paper is devoted to the study of a fully connected linear regression model, which is a synthesis of the pairing linear regression model and the Deming regression model. If multiple regression is based on the principle “independent variables influence dependent”, then the principle of fully connected regression is “all variables influence each other”. A fully connected regression is fairly simply estimated, devoid of multicollinearity effect, has a much more diverse interpretation than multiple regression, and is suitable for prediction. However, when building a fully connected regression, the ratio of error variances of independent variables remains unknown. In this paper, we find the ratio of error variances of independent variables that provides the best approximation qualities of the secondary fully connected regression model. The research results are presented in the form of a theorem. It follows from the theorem that the value of the coefficient of determination of the secondary model of a fully connected regression will be greatest either when it takes the form of a two-factor linear regression or the best one in the coefficient of determination of a single-factor linear regression. Thus, the selection of informative regressors in the regression model is carried out. It is established that the basis of such a selection is the complete consistency of the signs of the coefficients with independent variable signs of the corresponding correlation coefficients.
Keywords: :fully connected regression, multiple regression, Deming regression, EIV-model, coefficient of determination, multicollinearity, subset selection in regression