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 abso...
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| Format: | Article |
| Language: | Russian |
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Dagestan State Technical University
2025-04-01
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| Series: | Вестник Дагестанского государственного технического университета: Технические науки |
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| Online Access: | https://vestnik.dgtu.ru/jour/article/view/1704 |
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| author | S. I. Noskov S. V. Belyaev |
| author_facet | S. I. Noskov S. V. Belyaev |
| author_sort | S. I. Noskov |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-2744203a9ef045a0b60dc28416911cd1 |
| institution | DOAJ |
| issn | 2073-6185 2542-095X |
| language | Russian |
| publishDate | 2025-04-01 |
| publisher | Dagestan State Technical University |
| record_format | Article |
| series | Вестник Дагестанского государственного технического университета: Технические науки |
| spelling | doaj-art-2744203a9ef045a0b60dc28416911cd12025-08-20T03:21:03ZrusDagestan State Technical UniversityВестник Дагестанского государственного технического университета: Технические науки2073-61852542-095X2025-04-0152110511210.21822/2073-6185-2025-52-1-105-112961Estimation of linear regression parameters by minimizing the sum of the excesses of the approximation error modules relative to a given levelS. I. Noskov0S. V. Belyaev1Irkutsk State Transport UniversityIrkutsk State Transport UniversityObjective. 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.https://vestnik.dgtu.ru/jour/article/view/1704regression modelparameter estimationleast absolute values methodlinear programmingerror levelelectronics manufacturing |
| spellingShingle | S. I. Noskov S. V. Belyaev Estimation of linear regression parameters by minimizing the sum of the excesses of the approximation error modules relative to a given level Вестник Дагестанского государственного технического университета: Технические науки regression model parameter estimation least absolute values method linear programming error level electronics manufacturing |
| title | Estimation of linear regression parameters by minimizing the sum of the excesses of the approximation error modules relative to a given level |
| title_full | Estimation of linear regression parameters by minimizing the sum of the excesses of the approximation error modules relative to a given level |
| title_fullStr | Estimation of linear regression parameters by minimizing the sum of the excesses of the approximation error modules relative to a given level |
| title_full_unstemmed | Estimation of linear regression parameters by minimizing the sum of the excesses of the approximation error modules relative to a given level |
| title_short | Estimation of linear regression parameters by minimizing the sum of the excesses of the approximation error modules relative to a given level |
| title_sort | estimation of linear regression parameters by minimizing the sum of the excesses of the approximation error modules relative to a given level |
| topic | regression model parameter estimation least absolute values method linear programming error level electronics manufacturing |
| url | https://vestnik.dgtu.ru/jour/article/view/1704 |
| work_keys_str_mv | AT sinoskov estimationoflinearregressionparametersbyminimizingthesumoftheexcessesoftheapproximationerrormodulesrelativetoagivenlevel AT svbelyaev estimationoflinearregressionparametersbyminimizingthesumoftheexcessesoftheapproximationerrormodulesrelativetoagivenlevel |