Multifactor fully connected linear regression models without constraints to the ratios of variables errors variances

The article is devoted to the problem of constructing errors-in-variables regression models. Currently, such models are not widely used because they are not suitable for forecasting and interpretation, they are difficult to estimate, and the variables errors variances are unknown. To eliminate these shortcomings, the author developed and investigated two-factor fully connected linear regression models. Such models are easily estimated, they can be used for forecasting, and they lack the effect of multicollinearity. In this paper, for the first time, multifactor fully connected linear regression models are considered. It is proved that in the case of removing the restrictions, on the ratio of variables errors variances, there are the one estimates of a fully connected regression, in which the approximation qualities of its secondary equation and the classical multiple linear regression model, estimated using the ordinary least squares, coincide.