Covariance vs. Correlation

Covariance is a measure of how two variables change together. It is defined as

A positive covariance indicates that $X$ and $Y$ tend to move in the same direction, while a negative one indicates they move in opposite directions. However, covariance is sensitive to scale and has units, making it harder to interpret.

Correlation, on the other hand, is the normalized version of covariance:

It is dimensionless and ranges between $-1$ and $1$, making it easier to interpret and compare across datasets.