Covariance

Measures how two variables vary with each other.

Given two variables $X$ and $Y$:

$$Cov(X,Y)=E[(X-{\mu }_X)(Y-{\mu }_Y)]$$

For two samples of data:

$$Cov(X,Y)=\frac{1}{n-1}\sum _{i=1}^n(x_i-\bar{x})(y_i-\bar{y})$$

What it tells us

• Positive tells us that when one variable goes up, the other variable tends to go up
• Negative tells us that as one variable goes up, the other tends to go down
• Zero tells us that there is no linear relationship between the two variables

It DOES NOT tell us if two variables are connected in some way, its just used to make a simple observation.

Limitations

Covariance can be heavily skewed if the two variables have different scales. To counteract this, you can either normalize the data (partially the reasoning behind Normalization techniques), or compute Correlation. #probability