With more than two variables being related to each other, the value of the coefficient of multiple correlation depends on the choice of dependent variable: a regression of ''<math>y''</math> on ''<math>x''</math> and ''<math>z''</math> will in general have a different ''<math>R''</math> than will a regression of ''<math>z''</math> on ''<math>x''</math> and ''<math>y''</math>. For example, suppose that in a particular sample the variable ''<math>z''</math> is [[Correlation and dependence|uncorrelated]] with both ''<math>x''</math> and ''<math>y''</math>, while ''<math>x''</math> and ''<math>y''</math> are linearly related to each other. Then a regression of ''<math>z''</math> on ''<math>y''</math> and ''<math>x''</math> will yield an ''<math>R''</math> of zero, while a regression of ''<math>y''</math> on ''<math>x''</math> and ''<math>z''</math> will yield a strictly positive ''<math>R''</math>. This follows since the correlation of ''<math>y''</math> with the best predictor based on ''<math>x''</math> and ''<math>z''</math> is in all cases at least as large as the correlation of ''<math>y''</math> with the best predictor based on ''<math>x''</math> alone, and in this case with ''<math>z''</math> providing no explanatory power it will be exactly as large.
