Estimation of linear regression parameters by minimizing the sum of the excesses of the approximation error modules relative to a given level

Objective . Development of an algorithmic method for estimating the parameters of a linear regression model based on minimizing the sum of excesses of absolute deviations of the calculated values of the dependent variable from the real ones relative to some predetermined level. Methods . The least absolute values method based on minimizing the city (Manhattan) distance between the vectors of calculated and specified values of the dependent variable is used as a basic method for identifying unknown parameters of the regression equation. Implementation of the method is reduced to a linear programming problem. The problem of minimizing the sum of excesses of absolute deviations of the calculated values of the dependent variable from the real ones relative to some predetermined level is reduced to this problem by introducing some additional constraints and replacing the objective function. Result . Three alternative, highly adequate, versions of a regression single-factor model for the development of the Russian industrial sector engaged in the production of electrical, electronic and optical equipment are constructed. The volume of investments in the industry is used as an independent variable. Conclusion . A criterion for the adequacy of regression models is proposed, which is a modification of the loss function used in the least absolute value method.