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A new uncertain linear regression model based on equation deformation

  • Mathematical methods in data science
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Abstract

When the observed data are imprecise, the uncertain regression model is more suitable for the linear regression analysis. Least squares estimation can fully consider the given data and minimize the sum of squares of residual error and can effectively solve the linear regression equation of imprecisely observed data. On the basis of uncertainty theory, this paper presents an equation deformation method for solving unknown parameters in uncertain linear regression equations. We first establish the equation deformation method of one-dimensional linear regression model and then extend it to the case of multiple linear regression model. We also combine the equation deformation method with Cramer’s rule and matrix and propose the Cramer’s rule and matrix elementary transformation method to solve the unknown parameters of the uncertain linear regression equation. Numerical example show that the equation deformation method can effectively solve the unknown parameters of the uncertain linear regression equation.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (No. 11701338) and the Natural Science Foundation of Shandong Province (No. ZR2014GL002).

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Authors and Affiliations

  1. School of Information Engineering, Shandong Youth University of Political Science, No. 31699, Jingshi East Road, Jinan, China

    Shuai Wang & Yufu Ning

  2. Key Laboratory of Information Security and Intelligent Control in Universities of Shandong, Jinan, 250100, China

    Shuai Wang & Yufu Ning

  3. School of Information Science and Engineering, Shandong Agricultural and Engineering University, No. 866, Nongganyuan Road, Licheng District, Jinan, China

    Hongmei Shi

Authors
  1. Shuai Wang
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  2. Yufu Ning
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  3. Hongmei Shi
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Contributions

Shuai Wang contributed to the conception of the study. Hongmei Shi contributed significantly to analysis and manuscript preparation; Shuai Wang performed the data analyses and wrote the manuscript; Yufu Ning helped perform the analysis with constructive discussions.

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Correspondence to Hongmei Shi.

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Wang, S., Ning, Y. & Shi, H. A new uncertain linear regression model based on equation deformation. Soft Comput 25, 12817–12824 (2021). https://doi.org/10.1007/s00500-021-06030-7

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  • DOI: https://doi.org/10.1007/s00500-021-06030-7

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