How does covariance show the direction of a relationship between two random variables?

In statistics, covariance indicates the direction of a relationship between two random variables through its sign rather than its magnitude.1

The direction is determined as follows:

• Positive Covariance: Indicates a positive association, meaning that greater values of one variable tend to occur alongside greater values of the other.1
• Negative Covariance: Indicates an inverse relationship, where greater values of one variable tend to correspond with smaller values of the other.1
• Zero Covariance: Suggests that the variables do not have a linear relationship in the same way, though it does not necessarily imply that the variables are independent.1

While covariance identifies the direction of an association, it is often considered less informative than correlation. Because covariance is expressed in the product of the variables' units, its magnitude is difficult to interpret, whereas correlation provides a standardized measure of association that also indicates the strength of the relationship.1