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	ベイズ線形回帰（単純）	単回帰分析
分野	統計学	統計学
系統	Regression model	Regression model
提唱年	Early 19th century; textbook synthesis 2013	1805
提唱者	Laplace, P.-S. (early 19th c.); modern treatment: Gelman et al.	Adrien-Marie Legendre (least squares, 1805); Francis Galton (regression concept, 1886)
種類	Bayesian linear regression	Parametric bivariate regression
原典	Gelman, A., Carlin, J. B., Stern, H. S., Dunson, D. B., Vehtari, A., & Rubin, D. B. (2013). Bayesian Data Analysis (3rd ed.). CRC Press. ISBN: 978-1439840955	Legendre, A. M. (1805). Nouvelles méthodes pour la détermination des orbites des comètes. Firmin Didot, Paris. [Appendix: Sur la méthode des moindres quarrés, pp. 72–80]
別名	Bayesian SLR, Bayesian univariate regression, probabilistic simple linear regression, Bayesian linear model	SLR, ordinary least squares regression, OLS regression, bivariate regression
関連	6	7
概要	Bayesian Simple Linear Regression models the relationship between a continuous outcome and a single predictor by combining a Gaussian likelihood with prior distributions over the intercept, slope, and error variance. The result is a full posterior distribution over all parameters, providing probabilistic uncertainty quantification rather than a single point estimate.	Simple linear regression is the foundational parametric method for modelling a straight-line relationship between one continuous predictor and one continuous outcome, estimating the slope and intercept by ordinary least squares (OLS). The least squares principle was first published by Adrien-Marie Legendre in 1805, and Francis Galton introduced the concept of regression to the mean in 1886, coining the term that names the entire family of methods.