Coefficient of multiple correlation: Difference between revisions

Revision as of 16:28, 21 November 2010

Revision as of 16:53, 21 November 2010

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==Fundamental equation of multiple regression analysis==

The coefficient of multiple determination ''R''² (a [[scalar (mathematics)|scalar]]), is computed using the [[Euclidean space|vector]] ''c'' of cross-correlations between the predictor variables and the criterion variable, its [[transpose]]&nbsp;''c''', and the [[Matrix (mathematics)|matrix]] ''R''_''xx'' of inter-correlations between predictor variables. The "fundamental equation of multiple regression analysis"<ref>Visualstatistics.net [http://www.visualstatistics.net/Visual%20Statistics%20Multimedia/multiple_regression_analysis.htm]</ref> is

::''R''² = ''c''' ''R''_''xx''^&minus;1 ''c''.

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==References==

{{reflist}}

* Paul D. Allison. ''Multiple Regression: A Primer'' (1998)

* Cohen, Jacob, et al. ''Applied Multiple Regression - Correlation Analysis for the Behavioral Sciences'' (2002) (ISBN 0805822232)

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==External links==

* [http://www.amstat.org/publications/jse/v9n3/stanton.html A Brief History of Linear Regression Analysis]

* [http://www.visualstatistics.net/Visual%20Statistics%20Multimedia/multiple_regression_analysis.htm A Guide To Computing <math>R^2</math> For Multiple Correlation]

* [http://www.docstoc.com/docs/3530187/A-Derivation-of-the-Sample-Multiple-Corelation-Formula-for-Standard-Scores, "Derivations"]