Bazilevsky M.P., Karaulova A.V. Estimating the degree of nonlinearity for polynomial regression models // Informacionnye tehnologii i matematicheskoe modelirovanie v upravlenii slozhnymi sistemami: ehlektronnyj nauchnyj zhurnal [Information technology and mathematical modeling in the management of complex systems: electronic scientific journal], 2022. No. 3(15). P. 1-6. DOI: 10.26731/2658-3704.2022.3(15).1-6 [Accessed 15/10/22]
10.26731/2658-3704.2022.3(15).1-6
This article is devoted to the development of an approach to estimating the degree of nonlinearity for polynomial regression models. The non-linearity «over the area» criteria proposed earlier by the authors are limited by the fact that they are valid only for functions that do not have either extrema or inflections, therefore, when modeling, it was possible to measure the degree of non-linearity only for models that do not differ much from linear ones. In this paper, for polynomial regression models, a vector criterion for nonlinearity is proposed. A large number of components of this vector close to unity allows us to conclude that the polynomial is significantly non-linear. A straight line is characterized by a vector of one zero component. If the vector consists of several zeros, then the regression function is a broken line. The proposed approach has been successfully demonstrated on a specific example.
- Noskov S.I., Bychkov Yu.A. Vychislitel'nye eksperimenty s nepreryvnoy formoy metoda maksimal'noy soglasovannosti v regressionnom analize [Computational experiments with the continuous form of the maximum consistency method in regression analysis] // Vestnik Voronezhskogo gosudarstvennogo tekhnicheskogo universiteta – Bulletin of Voronezh state technical University. 2022. Vol. 18. No. 2. Pp. 7-12.
- Noskov S.I. Postroenie svertki kriteriev adekvatnosti regressionnykh modeley [Construction of convolution criteria for regression models] // Modeli, sistemy, seti v ekonomike, tekhnike, prirode i obshchestve – Models, systems, networks in economics, technology, nature and society. 2022. No. 1 (41). Pp. 73-81.
- Noskov S.I. Metod smeshannogo otsenivaniya parametrov lineynoy regressii: osobennosti primeneniya [Method of mixed estimation of linear regression parameters: application features] // Vestnik Voronezhskogo gosudarstvennogo universiteta. Seriya: Sistemnyy analiz i informatsionnye tekhnologii – Proceedings of Voronezh State University. Series: systems analysis and information technologies. 2021. No. 1. Pp. 126-132.
- Bazilevskiy M.P. Analiticheskie zavisimosti dlya nekotorykh kriteriev adekvatnosti modeli regressii Deminga [Analytical dependences for some adequacy criteria of Deming regression model] // Vestnik Irkutskogo gosudarstvennogo tekhnicheskogo universiteta – Proceedings of Irkutsk State Technical University. 2016. Vol. 20. No. 10 (117). Pp. 81-89.
- Bazilevskiy M.P., Noskov S.I. Programmnyy kompleks postroeniya lineynoy regressionnoy modeli s uchetom kriteriya soglasovannosti povedeniya fakticheskoy i raschetnoy traektoriy izmeneniya znacheniy ob"yasnyaemoy peremennoy [Program complex for linear regression model construction considering behavior consistency criterion of actual and calculated trajectories of explained variable value change] // Vestnik Irkutskogo gosudarstvennogo tekhnicheskogo universiteta – Proceedings of Irkutsk State Technical University. 2017. Vol. 21. No. 9 (128). Pp. 37-44.
- Bazilevskiy M.P. Svedenie zadachi otbora informativnykh regressorov pri otsenivanii lineynoy regressionnoy modeli po metodu naimen'shikh kvadratov k zadache chastichno-bulevogo lineynogo programmirovaniya [Reduction the problem of selecting informative regressors when estimating a linear regression model by the method of least squares to the problem of partial-Boolean linear programming] // Modelirovanie, optimizatsiya i informatsionnye tekhnologii – Modeling, optimization and information technology. 2018. Vol. 6. No. 1 (20). Pp. 108-117.
- Bazilevskiy M.P. Kriterii nelineynosti kvazilineynykh regressionnykh modeley [Nonlinear criteria of quasilinear regression models] // Modelirovanie, optimizatsiya i informatsionnye tekhnologii – Modeling, optimization and information technology. 2018. Vol. 6. No. 4 (23). Pp. 185-195.
- Bazilevskiy M.P., Karaulova A.V. Predvaritel'noe otsenivanie stepeni nelineynosti strukturnykh spetsifikatsiy kvazilineynykh regressiy [Preliminary estimation of non-linearity degree of quasilinear regressions structural specifications] // Matematicheskie metody v tekhnike i tekhnologiyakh - MMTT – Mathematical methods in technics and technology. 2020. Vol. 5. Pp. 49-52.
- Bazilevskiy M.P., Karaulova A.V. Vybor optimal'nogo sootnosheniya mezhdu tochnost'yu i nelineynost'yu pri postroenii kvazilineynykh regressionnykh modeley [Selecting the optimum relationship between accuracy and non-linearity in constructing quasi-linear regression models] // Vestnik kibernetiki – Proceedings in Cybernetics. 2021. No. 4 (44). Pp. 63-70.
- Karaulova A.V., Bazilevskiy M.P. Programmnyy kompleks postroeniya kvazilineynykh regressiy po kriteriyam tochnosti i nelineynosti [Software complex for constructing quasi-linear regressions according to the criteria of accuracy and non-linearity] // Ekonomika. Informatika – Economics. Information technologies. 2022. Vol. 49. No. 1. Pp. 121-133.