What does covariance measure in statistics?

Covariance measures the strength and direction of a linear relationship between two variables. It indicates how much the two variables change together; if one variable increases while the other tends to increase as well, the covariance will be positive. Conversely, if one variable increases while the other decreases, the covariance will be negative. The magnitude of the covariance gives insights into the strength of that relationship, although the value itself can be difficult to interpret directly without further analysis or normalization, such as in correlation.

In a statistical context, understanding covariance is crucial for various analytical approaches, especially in regression and portfolio theory. It essentially lays the groundwork for identifying whether a relationship exists and whether it is positive or negative, which is foundational for further statistical analysis and hypothesis testing.