Summary points

In lecture 5, we met

• The population and sample correlation coefficient

\[\begin{aligned} r &=\frac{S_{xy}}{\sqrt{S_{xx}S_{yy}}}\\ &=\frac{\sum_{i=1}^n(x_i-\bar{x})(y_i-\bar{y})}{\sqrt{\sum_{i=1}^n(x_i-\bar{x})^2\sum_{i=1}^n(y_i-\bar{y})^2}}\end{aligned}.\]

• The mechanisms to test the hypothesis \[H_0:\rho= 0 \mbox{ vs } H_1:\rho \neq 0\]