6.4 Correlation

Linear relationship between two variables

Corrleation, \(r = \frac{\sum (x_i - \bar x)(y_i - \bar y)}{\sqrt{\frac{\sum(x_i - \bar x)^2}{n}\frac{\sum(y_i - \bar y)^2}{n}}}; -1 \le r \le 1\)

• \(r = \frac{Cov(x,y)}{\sigma_x \sigma_y}\)

• Compare with \[\sigma ^2 = \sum_{i=1}^n \frac{(x_i-\bar x)^2}{n}\]