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In [[statistics]], '''multiple correlation''' is a linear relationship among more than two variables. It is measured by the [[Coefficient of determination|coefficient of multiple determination]], denoted as R<sup>2</sup>, which is a measure of the fit of a [[linear regression]]. A regression's R<sup>2</sup> falls somewhere between zero and one (assuming a constant term has been included in the regression); a higher value indicates a stronger relationship among the variables, with a value of one indicating that all data points fall exactly on a line in multidimensional space and a value of zero indicating no relationship at all between the independent variables collectively and the dependent variable.
Unlike the coefficient of determination in a regression involving just two variables, the coefficient of multiple determination 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 positive R<sup>2</sup>.
==Fundamental equation of multiple regression analysis==
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