Coefficient of multiple correlation: Difference between revisions

Revision as of 10:03, 5 April 2013

Revision as of 12:32, 5 April 2013

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==Properties==

The coefficient of multiple correlation is not computationally [[commutative]]: a regression of ''y'' on ''x'' and ''z'' will in general have a different R² than will a regression of ''z'' on ''x'' and ''y''. For example, suppose that in a particular sample the variable ''z'' is [[Correlation and dependence|uncorrelated]] with both ''x'' and ''y'', while ''x'' and ''y'' are linearly related to each other. Then a regression of ''z'' on ''y'' and ''x'' will yield an R² of zero, while a regression of ''y'' on ''x'' and ''z'' will generally yield a positive R².

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