Correlation Coefficient Calculator
Calculate Pearson correlation coefficient (r), R-squared, and linear regression. Visualize relationships with interactive scatter plots.
Correlation Coefficient Calculator
Calculate Pearson correlation coefficient (r) and linear regression
Enter one X,Y pair per line, separated by comma, tab, or space
Formula
r = Σ((x - x̄)(y - ȳ)) / √(Σ(x - x̄)² × Σ(y - ȳ)²)Pearson's r measures the linear relationship between two variables, ranging from -1 (perfect negative) to +1 (perfect positive).
Correlation Strength Guide
±0.9 to ±1.0
Very Strong
±0.7 to ±0.9
Strong
±0.5 to ±0.7
Moderate
±0.3 to ±0.5
Weak
0 to ±0.3
None/Negligible
Correlation vs Causation
⚠️ Important: Correlation does not imply causation. Just because two variables are correlated doesn't mean one causes the other. Always consider:
- Confounding variables that might affect both
- Reverse causation (Y might cause X)
- Coincidental relationships
- Selection bias in your data
How to Use
- 1Enter data pairs — Input your X,Y data pairs, one pair per line.
- 2Calculate — Click Calculate to compute correlation and regression.
- 3View scatter plot — See your data visualized with the regression line.
- 4Interpret results — Review correlation strength, significance, and R-squared.
Frequently Asked Questions
What is Pearson correlation coefficient?
Pearson's r measures the strength and direction of the linear relationship between two variables. It ranges from -1 (perfect negative correlation) to +1 (perfect positive correlation), with 0 indicating no linear relationship.
What does R-squared (R²) mean?
R-squared represents the proportion of variance in the dependent variable (Y) that is predictable from the independent variable (X). An R² of 0.80 means 80% of the variance in Y can be explained by X.
How do I interpret correlation strength?
|r| < 0.3 is weak, 0.3-0.5 is moderate, 0.5-0.7 is strong, and > 0.7 is very strong. The sign indicates direction: positive means both variables increase together, negative means one increases as the other decreases.
What is the regression equation used for?
The regression equation (y = mx + b) allows you to predict Y values from X values. The slope (m) shows how much Y changes for each unit change in X, and the intercept (b) is the Y value when X is zero.
Does correlation imply causation?
No! Correlation only shows that two variables are related, not that one causes the other. There could be confounding variables, reverse causation, or coincidental relationships.