What Correlation Measures

Variables moving together

Correlation summarizes the strength and direction of association between two variables. Pearson correlation ranges from -1 to 1 and describes linear co-movement: positive values mean they tend to rise together, negative values mean one tends to fall as the other rises, and values near zero mean little linear relationship.

r near +1: points cluster around an upward line
r near -1: points cluster around a downward line
r near  0: no strong straight-line pattern

Near zero does not mean unrelated: a U-shaped relationship can be strong while positive and negative slopes cancel. Outliers can also create or destroy a correlation. Always inspect a scatter plot and understand the measurement process before trusting one coefficient.

Warning: Correlation does not tell you which variable caused the other, whether a third variable caused both, or whether the association will continue outside the observed range.

Tip: Calculate correlation only after checking units, missingness, repeated observations, and time order. A clean number can summarize a dirty process.