Coefficient of Determination

$R^{2} = \frac{Sample variance of \hat{Y}}{Sample variance of Y} = \frac{\sum_{i = 1}^{n} ({\hat{Y}}_{i} - \bar{Y})^{2}}{\sum_{i = 1}^{n} (Y_{i} - \bar{Y})^{2}}$
- $0 \leq R^{2} \leq 1$
the proportion of the total variance in Y that can be attributed to the linear relationship with X
for simple linear regression models, $R^{2} = r^{2}$