## 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 $$\mathbf{X}$$.