Researching the behavior of variables relative contributions to the total determination in regression equation estimated using the method of distorted coefficients straightening
https://doi.org/10.55648/1998-6920-2022-16-1-89-96
Abstract
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.
About the Author
M. P. Bazilevskiy
Irkutsk State Transport University
Russian Federation
Russian Federation
Mikhail P. Bazilevskiy, Candidate of technical sciences, Docent
Irkutsk
References
1. Arkes J. Regression analysis: a practical introduction. Routledge, 2019, 362 p.
2. Westfall P. H., Arias A. L. Understanding regression analysis: a conditional distribution approach. Chapman and Hall/CRC, 2020, 514 p.
3. Thompson C.G., Kim R.S., Aloe A.M., Becker B.J. Extracting the variance inflation factor and other multicollinearity diagnostics from typical regression results. Basic and Applied Social Psychology. 2017, vol. 39, no. 2, pp. 81-90.
4. Yoo C., Cho E. Effect of multicollinearity on the bivariate frequency analysis of annual maximum rainfall events. Water. 2019, vol. 11, no. 5, pp. 905.
5. Lindner T., Puck J., Verbeke A. Misconceptions about multicollinearity in international business research: Identification, consequences, and remedies. Journal of International Business Studies. 2020, vol. 51, pp. 283-298.
6. Giacalone M., Panarello D., Mattera R. Multicollinearity in regression: an efficiency comparison between Lp-norm and least squares estimators. Quality & Quantity: International Journal of Methodology. 2018, vol. 52, no. 4, pp. 1831-1859.
7. Babaie-Kafaki S., Roozbeh M. A revised Cholesky decomposition to combat multicollinearity in multiple regression models. Journal of Stat. Comp. and Simul. 2017, vol. 87, pp. 2298-2308.
8. Dawoud I. A new improved estimator for reducing the multicollinearity effects. Communication in Statistics - Simulation and Computation. 2021, pp. 1-12.
9. Bazilevskiy M. P. Multifactor fully connected linear regression models without constraints to the ratios of variables errors variances. Inform. and its Applic. 2020, vol. 14, no. 2, pp. 92-97.
10. Bazilevskiy M. P. Method of straightening distorted due to multicollinearity coefficients in regression models. Informatics and its Applications. 2021, vol. 15, no. 2, pp. 60-65.
Review
For citations:
Bazilevskiy M.P. Researching the behavior of variables relative contributions to the total determination in regression equation estimated using the method of distorted coefficients straightening. The Herald of the Siberian State University of Telecommunications and Information Science. 2022;(1):89-96. (In Russ.) https://doi.org/10.55648/1998-6920-2022-16-1-89-96
Views:
3522
Email this article 
