Method of straightening distorted due to multicollinearity coefficients in regression models

When constructing regression models, due to the strong multicollinearity of the explanatory variables, its coefficients are distorted, in particular, their signs, which negatively affects the interpretational qualities of such regression. This article is devoted to the development of a method of straightening coefficients distorted due to multicollinearity. This method is based on the property of the fully connected linear regression models proposed by the author. A nonlinear system, which is used to estimate fully connected regressions, is investigated. It is shown that the solution of this system can be obtained numerically using the method of simple iterations. A method for choosing unknown lambda-parameters in fully connected regression is proposed. It was found that in multivariate fully connected models with a strong correlation of all factors, the signs of the coefficients for the variables in the secondary equation coincide with the corresponding signs of the correlation coefficients. To straighten the distorted coefficients on the basis of this research, the “Selection B” algorithm was developed. The developed method of straightening has been successfully demonstrated by the example of modeling Russia's gross domestic product (GDP).