Coefficient of multiple correlation: Difference between revisions

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{{Expert-subject|statistics|date=November 2008}}
 
In [[statistics]], [[regression analysis]] is a method for explanation of phenomena and prediction of future events. In the regression analysis, a [[correlation coefficient|coefficient of correlation]] ''r'' between [[random variable]]s ''X'' and ''Y'' is a quantitative index of association between these two variables. In its squared form, as a [[coefficient of determination]] ''r''<sup>2</sup>, indicates the amount of [[variance]] in the criterion variable ''Y'' that is accounted for by the variation in the predictor variable ''X''. In the multiple regression analysis, the set of predictor variables ''X''<sub>1</sub>, ''X''<sub>2</sub>, ... is used to explain variability of the criterion variable ''Y''. A multivariate counterpart of the coefficient of determination ''r''<sup>2</sup> is the ''coefficient of multiple determination'', ''R''<sup>2</sup>. The [[square root]] of the coefficient of multiple determination is the '''coefficient of '''multiple correlation''', '''''R'''''.
 
==Conceptualization of multiple correlation==