sibsutisВестник СибГУТИThe Herald of the Siberian State University of Telecommunications and Information Science1998-6920СибГУТИ10.55648/1998-6920-2022-16-1-89-96sibsutis-123Research ArticleСтатьиИсследование поведения относительных вкладов переменных в общую детерминацию в оцененном на основе метода выпрямления искаженных коэффициентов регрессионном уравненииResearching the behavior of variables relative contributions to the total determination in regression equation estimated using the method of distorted coefficients straighteningБазилевскийМ. П.BazilevskiyM. P.

Базилевский Михаил Павлович, к.т.н., доцент кафедры математики

664074, Иркутск, ул. Чернышевского, 15 

Mikhail P. Bazilevskiy, Candidate of technical sciences, Docent

Irkutsk

mik2178@yandex.ruИрГУПСРоссияIrkutsk State Transport UniversityRussian Federation202213052022018996Copyright © Базилевский М.П., 20222022Базилевский М.П.Bazilevskiy M.P.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://vestnik.sibsutis.ru/jour/article/view/123

Для решения проблемы мультиколлинеарности в регрессионном анализе может применяться ранее разработанный автором метод выпрямления искаженных коэффициентов, основанный на построении модели полносвязной линейной регрессии. В статье для оценки степени влияния независимых переменных на зависимую переменную в полученном с помощью этого метода регрессионном уравнении предлагается использовать относительные вклады переменных в общую детерминацию. Доказано, что в таком уравнении в случае линейной функциональной зависимости входных переменных их относительные вклады в общую детерминацию равны. Тогда при сильной корреляции входных переменных их вклады распределяются примерно одинаково. Доказано, что задача оценивания полносвязной регрессии не зависит от выбора связующей переменной. Полученные результаты успешно продемонстрированы на примере моделирования внутреннего валового продукта (ВВП) России.

To solve the problem of multicollinearity in regression analysis a distorted coefficients straightening method developed by the author and based on the construction of fully connected linear regression model can be used. In the article, to assess the degree of independent variables influence on the dependent variable in the regression equation obtained by using this method, it is proposed to use the variables relative contributions to the total determination. It is proved that in such an equation in the case of linear functional dependence of the input variables their relative contributions to the total determination are equal. Then, with a strong correlation of the input variables, their contributions are distributed approximately in the same way. It is proved that the problem of estimating a fully connected regression does not depend on the choice of connecting variable. The obtained results have been successfully demonstrated using the example of the Russia's GDP modeling.

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The authors declare that there are no conflicts of interest present.