Multi-criteria approach to pair-multiple linear regression models constructing
A pair-multiple linear regression model which is a synthesis of Deming regression and multiple linear regression model is considered. It is shown that with a change in the type of minimized distance, the pair-multiple regression model transforms smoothly from the pair model into the multiple linear...
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| Format: | Article |
| Language: | English |
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Saratov State University
2021-03-01
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| Series: | Известия Саратовского университета. Новая серия. Серия Математика. Механика. Информатика |
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| Online Access: | https://mmi.sgu.ru/sites/mmi.sgu.ru/files/text-pdf/2021/02/mmi_2021_1_88-99.pdf |
| _version_ | 1818910479191375872 |
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| author | Bazilevskiy, Mikhail P. |
| author_facet | Bazilevskiy, Mikhail P. |
| author_sort | Bazilevskiy, Mikhail P. |
| collection | DOAJ |
| description | A pair-multiple linear regression model which is a synthesis of Deming regression and multiple linear regression model is considered. It is shown that with a change in the type of minimized distance, the pair-multiple regression model transforms smoothly from the pair model into the multiple linear regression model. In this case, pair-multiple regression models retain the ability to interpret the coefficients and predict the values of the explained variable. An aggregated quality criterion of regression models based on four well-known indicators: the coefficient of determination, Darbin – Watson, the consistency of behaviour and the average relative error of approximation is proposed. Using this criterion, the problem of multi-criteria construction of a pair-multiple linear regression model is formalized as a nonlinear programming problem. An algorithm for its approximate solution is developed. The results of this work can be used to improve the overall qualitative characteristics of multiple linear regression models. |
| first_indexed | 2024-12-19T22:43:27Z |
| format | Article |
| id | doaj.art-2c0ec978c466413e8fd0deb745b4283e |
| institution | Directory Open Access Journal |
| issn | 1816-9791 2541-9005 |
| language | English |
| last_indexed | 2024-12-19T22:43:27Z |
| publishDate | 2021-03-01 |
| publisher | Saratov State University |
| record_format | Article |
| series | Известия Саратовского университета. Новая серия. Серия Математика. Механика. Информатика |
| spelling | doaj.art-2c0ec978c466413e8fd0deb745b4283e2022-12-21T20:03:00ZengSaratov State UniversityИзвестия Саратовского университета. Новая серия. Серия Математика. Механика. Информатика1816-97912541-90052021-03-01211889910.18500/1816-9791-2021-21-1-88-99Multi-criteria approach to pair-multiple linear regression models constructingBazilevskiy, Mikhail P.0Irkutsk State Transport University, 15 Chernyshevskogo St., Irkutsk 664074, RussiaA pair-multiple linear regression model which is a synthesis of Deming regression and multiple linear regression model is considered. It is shown that with a change in the type of minimized distance, the pair-multiple regression model transforms smoothly from the pair model into the multiple linear regression model. In this case, pair-multiple regression models retain the ability to interpret the coefficients and predict the values of the explained variable. An aggregated quality criterion of regression models based on four well-known indicators: the coefficient of determination, Darbin – Watson, the consistency of behaviour and the average relative error of approximation is proposed. Using this criterion, the problem of multi-criteria construction of a pair-multiple linear regression model is formalized as a nonlinear programming problem. An algorithm for its approximate solution is developed. The results of this work can be used to improve the overall qualitative characteristics of multiple linear regression models.https://mmi.sgu.ru/sites/mmi.sgu.ru/files/text-pdf/2021/02/mmi_2021_1_88-99.pdfdeming regressionpair-multiple linear regression modelmulti-criteria approachaggregate criterionnonlinear programming |
| spellingShingle | Bazilevskiy, Mikhail P. Multi-criteria approach to pair-multiple linear regression models constructing Известия Саратовского университета. Новая серия. Серия Математика. Механика. Информатика deming regression pair-multiple linear regression model multi-criteria approach aggregate criterion nonlinear programming |
| title | Multi-criteria approach to pair-multiple linear regression models constructing |
| title_full | Multi-criteria approach to pair-multiple linear regression models constructing |
| title_fullStr | Multi-criteria approach to pair-multiple linear regression models constructing |
| title_full_unstemmed | Multi-criteria approach to pair-multiple linear regression models constructing |
| title_short | Multi-criteria approach to pair-multiple linear regression models constructing |
| title_sort | multi criteria approach to pair multiple linear regression models constructing |
| topic | deming regression pair-multiple linear regression model multi-criteria approach aggregate criterion nonlinear programming |
| url | https://mmi.sgu.ru/sites/mmi.sgu.ru/files/text-pdf/2021/02/mmi_2021_1_88-99.pdf |
| work_keys_str_mv | AT bazilevskiymikhailp multicriteriaapproachtopairmultiplelinearregressionmodelsconstructing |