Covariance

What is Covariance?

Covariance measures how two variables move in tandem. Covariance is the most common statistical measure of association.

To calculate the covariance between two variables, X and Y, we multiply together each variable's deviation from its mean value at the same point in the process and take the average.

$$q_{xy}=\frac1 n \underset{i=0}{\overset{n}{\sum}}(x_i-\mu_x)(y_i-\mu_y)$$

A positive covariance means that the two variables move together.
A negative covariance means that the two variables vary inversely.
A covariance equal to (or close to) zero means that the two variables move independently.
The covariance between a variable and itself is simply its variance - the sum of the squared deviations from its mean.

$$Larger\; Positive\; Covariance\;$$

$$Smaller\; Positive\; Covariance\;$$