Covariance

Topics: Measure of Association - Statistics

---

(definition)

Let $(x_1,y_1),\dots ,(x_n,y_n)$ be observations of the variables $(X,Y)$. The covariance between the variables $(X,Y)$ is defined as:

$$S_{XY}=\frac{1}{n}\sum _{i=1}^n\left[\left(x_i-\overline{X}\right)\left(y_i-\overline{Y}\right)\right]$$

Meaning §

Covariance quantifies the joint variability of both variables.

When it’s positive, the greater values of one variable correspond to greater values of the other; when it’s negative, the greater values of one correspond to the lesser values of the other: