Statistical derivation of linear regression

Shengjie Mao

doi:10.1117/12.2628017

22 April 2022 Statistical derivation of linear regression

Shengjie Mao

Proceedings Volume 12163, International Conference on Statistics, Applied Mathematics, and Computing Science (CSAMCS 2021); 121633F (2022) https://doi.org/10.1117/12.2628017
Event: International Conference on Statistics, Applied Mathematics, and Computing Science (CSAMCS 2021), 2021, Nanjing, China

Abstract

Linear regression can be used to find the influence of independent variables on dependent variable in a linear way. First, the definition, how to use the method of ordinary least squares to estimate regression coefficients, some properties of least squares estimate, and some test methods of simple linear regression model is introduced. Then, the number of independent variables is extended from simple to multiple. Not only multiple linear regression model is illustrated from the same aspects of introducing the simple linear regression, but also the situation when the ordinary least squares method has multiple solutions and collinearity test of independent variables is elaborated. Finally, to avoid the inaccuracy of least squares estimates caused by the collinearity of independent variables, the definition of ridge regression and properties of ridge estimate is stated.

Citation Download Citation

Shengjie Mao "Statistical derivation of linear regression", Proc. SPIE 12163, International Conference on Statistics, Applied Mathematics, and Computing Science (CSAMCS 2021), 121633F (22 April 2022); https://doi.org/10.1117/12.2628017

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