Correlation Math Example 1

Solution

1. 1
   Compute means: $\bar{x} = 3$, $\bar{y} = 4$.
2. 2
   Compute $\sum(x_i - \bar{x})(y_i - \bar{y})$: $(-2)(-2) + (-1)(0) + (0)(1) + (1)(0) + (2)(1) = 4 + 0 + 0 + 0 + 2 = 6$.
3. 3
   Compute $\sum(x_i - \bar{x})^2 = 4 + 1 + 0 + 1 + 4 = 10$ and $\sum(y_i - \bar{y})^2 = 4 + 0 + 1 + 0 + 1 = 6$.
4. 4
   $r = \frac{6}{\sqrt{10 \times 6}} = \frac{6}{\sqrt{60}} = \frac{6}{7.746} \approx 0.775$.