## 3.4 Further Measures for Association Strength

### Coefficient of Determination; r^2

- The
**coefficient of determination**gives a quantitative way of determining how much of the variation of the response variable is explained by variation in the explanatory variable. - It is represented by a lower-case r with a 2 superscript and can be calculated by squaring the correlation coefficient:

r^{2}=\left(\frac{\sum_{i=1}^{n}\left(x_{i}-\bar{x}\right)\left(y_{i}-\bar{y}\right)}{(n-1) s_{x} s_{y}}\right)^{2}

- When calculating the coefficient of determination, you will get a decimal answer, however, when interpreting the value, you should convert it into a percentage (multiply by 100).