What Does Correlation Measure?

Correlation studies and measures the direction and the intensity of the relationship among variables. It tells us both which way two variables move relative to each other and how closely they move together.

A crucial caution runs through the whole idea: correlation measures covariation, not causation. The presence of correlation between two variables should never, by itself, be interpreted as implying a cause-and-effect relationship. Two variables can be strongly correlated because one genuinely affects the other, because both are driven by some third factor, or simply by coincidence — and correlation alone cannot distinguish between these.

What, then, does it mean to say two variables $X$ and $Y$ are correlated? It means that when the value of one variable is found to change in one direction, the value of the other is found to change too — either in the same direction (a positive change) or in the opposite direction (a negative change) — but in a definite, regular way rather than randomly. It is this definite pattern of joint movement that correlation captures. …