Definition

Correlation

A standardized measure (−1 to +1) of how strongly two variables move together. Association, not causation.

Pearson’s r captures linear association: +1 is a perfect positive relationship, −1 perfect negative, 0 none. Spearman’s version works on ranks, tolerating outliers and monotonic-but-curved relationships. Squaring r gives the share of variance the variables share.

Correlation cannot say which variable drives which, or whether a third variable drives both (confounding). The inference from association to cause requires design — experiments, instrumental variables, longitudinal ordering — not a bigger r.