Correlation Calculator

The Pearson correlation coefficient is the covariance of the two variables divided by the product of their standard deviations: r = Σ[(x−x̄)(y−ȳ)] ÷ √[Σ(x−x̄)² × Σ(y−ȳ)²]. It always falls between −1 and +1.

r = +1 is a perfect positive relationship (as one variable rises, so does the other, exactly proportionally). r = −1 is a perfect negative relationship (as one rises, the other falls proportionally). r = 0 means no linear relationship. Values near ±0.7 to ±1.0 are usually considered strong, ±0.3 to ±0.7 moderate, and below ±0.3 weak.

No — correlation only measures whether two variables move together, not why. Two variables can be strongly correlated because one causes the other, because both are caused by a third factor, or purely by coincidence. "Correlation does not imply causation" is one of the most important rules in statistics.

R² is simply the correlation coefficient squared. It represents the proportion of variance in one variable that's statistically explained by the other — an r of 0.8 gives an R² of 0.64, meaning 64% of the variation is explained by the linear relationship.

It's the best-fit straight line through your data (y = mx + b), found using the same least-squares method as the correlation itself. You can use it to estimate a y value for any new x value, though the estimate is only as reliable as how strong your correlation is.