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The paper discusses a synthesis of multiple linear regression and Deming regression model’s, which gives countless different and previously unknown estimates of unknown parameters in framework of ordinary least squares. Using example of railway freight turnover modeling for synthesized regression, for the first time, dependences of parameter estimates and adequacy criteria on a ratio of error variances of variables are obtained. It is shown that using the considered synthesis it is possible to reduce the approximation qualities of the classical multiple linear regression model for the sake of improving some of its other important characteristics. Also, the synthesized model can act as a tool for solving the problem of subset selection in regression.

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