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 $\mathbf{X}$.