Correlation

Correlation describes the strength and direction of the relationship between two quantitative variables. When two variables tend to rise and fall together — like height and shoe size — they are positively correlated. When one tends to rise as the other falls — like a car's age and its resale value — they are negatively correlated. When knowing one tells you nothing about the other, the variables are uncorrelated.

The relationship is quantified by the correlation coefficient, usually written r, which always falls between −1 and +1. Values near the extremes indicate a strong linear relationship; values near 0 indicate a weak one. An r of 0.9 between study hours and test scores signals a strong positive association, while an r of −0.2 signals a weak negative one. On a scatterplot, strong correlation appears as points clustered tightly around a line, and the sign of r matches the direction of the line's slope.

The most important caveat: correlation does not imply causation. Ice cream sales and drowning deaths are positively correlated, but one does not cause the other — both rise in summer. Correlation also captures only linear relationships; a strong curved pattern can produce an r near zero. In finance, correlation drives diversification: combining assets with low or negative correlation reduces portfolio risk, because losses in one holding are offset by gains in another.

Correlation appears across several exams. The Praxis Core math test covers interpreting scatterplots and describing associations, the CGMA business economics syllabus tests correlation between economic variables, and the Series 6 exam applies correlation to portfolio analysis and diversification.