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Regression analysis is a recognized tool for constructing mathematical models of statistical type. Methods of the regression analysis are used in various fields: in economics, technology, education, medical field, etc. The main stages in constructing the regression model are: identifying variables, collecting statistical data, specifying the model, i.e. choosing the mathematical form of the relationship between the variables, identification of model parameters, model verification. In other words, determining the degree of conformity of the constructed model to the real object of study, and interpretation of the results, consisting in forecasting, making managerial decisions, etc.

The article is devoted to the problem of choosing the structural specification of the regression model. Additive power regressions that are non-linear in the parameters are presented, representing a more flexible modeling tool than similar power models with multiplicative independent variables. To estimate the unknown parameters of the proposed additive power regressions, 3 special algorithms were developed, based on the nonlinear least squares method. Using the Gretl econometric package, a study of the developed algorithms was carried out. In this case, the Levenberg-Marquardt algorithm was used to estimate the unknown parameters of nonlinear models in Gretl. The best results were shown by an algorithm with a preliminary choice of the initial approximation. It is shown that the first few steps of this algorithm represent a one-criteria "contest" of power regression models. A numerical experiment is performed proving the rationality of using the algorithm of estimating additive power regressions with a preliminary choice of the initial approximation in organizing the "competition" of the regression models.

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