Which statistic indicates whether two variables increase or decrease together?

The statistic that indicates whether two variables increase or decrease together is covariance. Covariance measures the degree to which two variables change in tandem. A positive covariance suggests that as one variable increases, the other variable tends to also increase, while a negative covariance indicates that one variable tends to decrease when the other increases. This characteristic makes it a valuable metric in understanding relationships between variables in multivariate analysis.

Covariance provides a foundational understanding of the relationship, but it is often used in conjunction with other statistics like correlation, which standardizes the measure and allows for easier interpretation. Unlike standard deviation, which measures the dispersion of a single variable around its mean, covariance specifically focuses on the mutual relationship between two variables. Trend analysis, on the other hand, looks at patterns over time rather than the direct relationship between the two variables at a specific point.