Correlation Calculator

The Pearson correlation coefficient (r) measures the strength and direction of a linear relationship between two variables. It ranges from -1 to +1. Values close to +1 indicate a strong positive relationship (as X increases, Y increases), values close to -1 indicate a strong negative relationship (as X increases, Y decreases), and values near 0 indicate no linear relationship. Interpretation: |r| > 0.7 is strong, 0.5-0.7 is moderate, 0.3-0.5 is weak, and < 0.3 is very weak or no correlation.

R-squared (r²) is the coefficient of determination, calculated by squaring the correlation coefficient. It represents the percentage of variance in Y that is explained by X. For example, r² = 0.64 means that 64% of the variation in Y can be explained by its linear relationship with X. The remaining 36% is due to other factors or random variation. R-squared always ranges from 0 to 1, regardless of whether the correlation is positive or negative.

Correlation measures the statistical association between two variables—when one changes, the other tends to change. Causation means one variable directly causes the other to change. A high correlation does NOT prove causation. For example, ice cream sales and drowning deaths are correlated (both increase in summer), but ice cream doesn't cause drowning—hot weather is a confounding variable affecting both. To establish causation, you need controlled experiments or rigorous causal analysis methods.

Use Pearson correlation when: both variables are continuous and approximately normally distributed, the relationship is linear, and there are no extreme outliers. Use Spearman correlation for ordinal data, non-linear monotonic relationships, or when outliers are present (it's based on ranks, not raw values). Use Kendall's tau for small sample sizes or when there are many tied ranks. For categorical variables, use chi-square or Cramér's V instead of correlation.

The linear regression equation y = mx + b describes the best-fit line through your data points. The slope (m) tells you how much Y changes for each one-unit increase in X. For example, m = 2.5 means Y increases by 2.5 for every 1-unit increase in X. The y-intercept (b) is the predicted value of Y when X = 0. You can use this equation to predict Y for any X value, but only within the range of your original data (extrapolation beyond this range is unreliable).