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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 R<sup>2</sup> 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 R<sup>2</sup> of zero, while a regression of ''y'' on ''x'' and ''z'' will yield a strictly positive R<sup>2</sup>. This follows since the correlation of 'y' with the best predictor based on ''x'' and ''z'' must be at last as large as the correlation of 'y' with the best predictor based on ''x'' alone.
{{inline|date=April 2013}}
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