Correlation coefficient
Also known as: pearson correlation coefficient, r value
A correlation coefficient, written r, measures the strength and direction of the linear relationship between two variables. It always falls between −1 and +1, where values near ±1 indicate a strong linear relationship and values near 0 indicate almost none.
The correlation coefficient reduces a scatterplot to a single number between −1 and +1. The sign gives direction: a positive r means the two variables tend to rise together, while a negative r means one tends to fall as the other rises. The magnitude gives strength: the closer |r| is to 1, the more tightly the points cluster around a straight line.
Reading specific values makes this concrete. An r of 0.9 describes a strong positive linear relationship — as one variable increases, the other increases in a nearly straight-line pattern with modest scatter. An r of −0.9 is equally strong but runs the other direction. An r of 0.1 means the points are scattered with almost no linear trend. Squaring the coefficient gives r², the proportion of variation in one variable explained by the linear relationship, so r = 0.9 corresponds to r² = 0.81.
Two cautions matter. First, correlation is not causation: a strong r shows that two variables move together, not that one causes the other, since a third variable may drive both. Second, r measures only linear association. Data following a perfect U-shaped curve can produce an r near zero even though the relationship is exact, which is why you should always look at the scatterplot alongside the number.
The correlation coefficient shows up across very different exams. Praxis Core Math asks you to interpret scatterplots and estimate the direction and strength of association. The CIMA Certificate in Business Accounting covers correlation as part of inter-relationships between variables. On the Series 6, correlation is the basis for portfolio analysis, where combining assets with low or negative correlation is what reduces overall portfolio risk.
Key takeaways
- The correlation coefficient r measures the strength and direction of a linear relationship and always lies between −1 and +1.
- The sign indicates direction; the absolute value indicates strength, with |r| near 1 meaning a tight linear pattern.
- r² gives the proportion of variation explained by the linear relationship — an r of 0.9 means r² = 0.81.
- Correlation does not prove causation, and r only detects linear relationships.