Russian Federation
This article provides a probabilistic justification of the least squares method through the principle of maximum likelihood. A statistical interpretation of linear regression is considered, where observations are treated as realizations of random variables, and errors are modeled by normal distribution. It is shown that under the normality assumption, maximization of the likelihood function is equivalent to minimization of the sum of squared residuals. The classical formula for regression parameter estimation is derived, and the equivalence of LSM and MLE methods is proved.
linear regression, least squares method, maximum likelihood estimation, normal distribution, parameter estimation
1. Zhaksybaev, D. O. Algoritmy klassifikacii tekstovyh dokumentov s uchetom blizosti v priznakovom prostranstve / D. O. Zhaksybaev, M. N. Bakiev // Modelirovanie sistem i processov. – 2022. – T. 15, № 1. – S. 36–43. – DOIhttps://doi.org/10.12737/2219-0767-2022-15-1-36-43.
2. Sazonova, S. A. Modelirovanie processa diagnostiki utechek na osnove dvuhal'ternativnoy gipotezy s uchetom pomeh ot stohastichnosti potrebleniya v gidravlicheskoy sisteme / S. A. Sazonova, I. V. Scherbakova, G. I. Smetankina // Modelirovanie sistem i processov. – 2024. – T. 17, № 1. – S. 111–120. – DOIhttps://doi.org/10.12737/2219-0767-2024-17-1-111-120.
3. Spesivcev, G. A. Osnovy lineynoy regressii / G. A. Spesivcev // Mezhotraslevye issledovaniya. Bezbar'ernaya sreda nauchnoy deyatel'nosti : sb. st. Mezhdunar. nauch.-prakt. konf. – Ekaterinburg, 2025. – S. 73–82.
