7.9 Correlation Coefficient

The correlation coefficient \(\rho\) (Section 5.6) measures the strength of association between \(X\) and \(Y\) in the population.

It also has a second interpretation as the Coefficient of Determination: \(100\rho^{2}\) = % of variance of \(Y\) associated with \(\mathbf{X}\) or explained by \(\mathbf{X}\) (the model).

In other words, \(\rho^{2}\) is reduction in variance of Y associated with knowledge of \(\mathbf{X}\).