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where ''c'' ' is the [[transpose]] of ''c'', and ''R''<sub>''xx''</sub><sup>−1</sup> is [[Matrix inversion|inverse]] of the matrix ''R''<sub>''xx''</sub>.
If all the predictor variables are uncorrelated, the matrix ''R''<sub>''xx''</sub> is the identity matrix and ''R''<sup>2</sup> simply equals ''c''' ''c'', the sum of the squared cross-correlations with the dependent variable. If there is cross-correlation among the predictor variables, the inverse of the cross-correlation matrix accounts for this.
The coefficient of multiple correlation can also be computed as the fraction of variance of the dependent variable that is explained by the independent variables, which in turn is 1 minus the unexplained fraction. The unexplained fraction can be computed as the [[sum of squared residuals]]—that is, the sum of the squares of the prediction errors—divided by the [[Total sum of squares|sum of the squared deviations of the values of the dependent variable]] from its [[expected value]].
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