手法を比較

	Canonical Correlation Analysis	Multiple Linear Regression
分野	統計学	統計学
系統	Latent structure	Regression model
提唱年	1936	1886
提唱者	Harold Hotelling	Francis Galton; formalized by Karl Pearson
種類	Multivariate linear dimension reduction and association	Parametric linear model
原典	Hotelling, H. (1936). Relations between two sets of variates. Biometrika, 28(3–4), 321–377.	Galton, F. (1886). Regression towards mediocrity in hereditary stature. Journal of the Anthropological Institute of Great Britain and Ireland, 15, 246–263.
別名	CCA, canonical variate analysis, canonical analysis, multiple canonical correlation	MLR, OLS regression, multiple regression, linear regression with multiple predictors
関連	4	8
概要	Canonical Correlation Analysis (CCA) is a multivariate statistical method that identifies pairs of linear combinations — one from each of two variable sets — such that the correlation between each pair is maximised. Introduced by Harold Hotelling in his landmark 1936 Biometrika paper, CCA provides the most general linear framework for studying the association between two multivariate batteries of measurements, and many classical procedures (multiple regression, MANOVA, discriminant analysis) are special cases of it.	Multiple linear regression (MLR) is a parametric regression model that expresses a continuous outcome as a weighted linear combination of two or more predictor variables plus a random error term. The unknown weights (regression coefficients) are estimated by ordinary least squares (OLS), which minimises the sum of squared residuals. The method traces to Francis Galton's 1886 work on hereditary stature and was placed on firm mathematical footing by Karl Pearson; Draper and Smith's 1966 textbook established it as the standard framework for applied regression.