Coefficient of multiple correlation: Difference between revisions

Revision as of 22:51, 26 March 2009

Revision as of 15:55, 26 July 2009

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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''^ 2, 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''₁, ''X''₂, ... is used to explain variability of the criterion variable ''Y''. A multivariate counterpart of the coefficient of determination ''r''^ 2 is the ''coefficient of multiple determination'', ''R''^ 2. The [[square root]] of the coefficient of multiple determination is the '''coefficient of multiple correlation''',  '''''R'''''.

==Conceptualization of multiple correlation==

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==Fundamental equation of multiple regression analysis==

Initially, a [[matrix (mathematics)|matrix]] of correlations ''R'' is computed for all variables involved in the analysis. This matrix can be conceptualized as a supermatrix, consisting of the [[Euclidean space|vector]] of cross-correlations between the predictor variables and the criterion variable ''c'', its [[transpose]]  ''c''’ and the matrix of intercorrelations between predictor variables  ''R''_''xx''. The fundamental equation of the multiple regression analysis is

::''R''² = ''c''' ''R''_''xx''^−1 ''c''.

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* Timothy Z. Keith. '' Multiple Regression and Beyond'' (2005)

* Fred N. Kerlinger, Elazar J. Pedhazur, ''Multiple Regression in Behavioral Research.'' (1973)

==External links==