Generalization of a method for straightening coefficients distorted due to multicollinearity in regression models with different degrees of explanatory variables correlation

When constructing regression models, one of the main problems is multicollinearity. This negative phenomenon leads to distortion of the regression coefficients, in particular, their signs. Earlier, to solve the problem of multicollinearity, a method for straightening distorted coefficients was developed which is based on the construction of a fully connected linear regression model. One of the conditions for its applicability is a close correlation of absolutely all pairs of explanatory variables. But when solving real applied problems, this condition is rarely met. Most often, explanatory variables correlate with each other in different ways. The authors propose a new iterative algorithm for the method of straightening distorted coefficients. A feature of the algorithm is that it combines the advantages of both traditional multiple models and new fully connected regressions. The developed algorithm is universal and can be used to construct a regression equation with any structure of the correlation matrix. The new algorithm has been successfully applied to simulate freight transportation by rail in the Irkutsk region.