方法对比

	多元回归的功效分析	多元线性回归
领域	统计学	统计学
方法族	Hypothesis test	Regression model
起源年份	1988	1886
提出者	Jacob Cohen	Francis Galton; formalized by Karl Pearson
类型	A priori sample size determination	Parametric linear model
开创性文献	Cohen, J. (1988). Statistical Power Analysis for the Behavioral Sciences (2nd ed.). Lawrence Erlbaum Associates. ISBN: 978-0805802832	Galton, F. (1886). Regression towards mediocrity in hereditary stature. Journal of the Anthropological Institute of Great Britain and Ireland, 15, 246–263.
别名	regression power analysis, sample size estimation regression, f² power analysis, Güç Analizi — Regresyon	MLR, OLS regression, multiple regression, linear regression with multiple predictors
相关	4	8
摘要	Power analysis for multiple regression is a pre-study procedure, formalised by Jacob Cohen (1988), that calculates the minimum sample size needed to detect a regression effect of a given size with adequate statistical power. It uses the anticipated R² (or the equivalent Cohen's f² effect size) and the number of predictors to determine how many observations must be collected before data collection begins.	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.