Correlation Calculator - Pearson r & R-Squared 2025
Free correlation coefficient calculator. Calculate Pearson correlation (r), R-squared, linear regression equation, and covariance. Interactive scatter plot with trend line visualization.
Quick Answer
Pearson correlation coefficient (r) measures the linear relationship between two variables, ranging from -1 to +1. r = +1 means perfect positive correlation (both increase together), r = -1 means perfect negative correlation (one increases as other decreases), r = 0 means no linear relationship. Formula: r = Sum[(x-mean_x)(y-mean_y)] / sqrt[Sum(x-mean_x)^2 x Sum(y-mean_y)^2]. R-squared (r^2) shows proportion of variance explained.
Key Facts
- r ranges from -1 (perfect negative) to +1 (perfect positive)
- r = 0 indicates no linear relationship
- R-squared (r^2) = proportion of variance explained (0 to 1)
- |r| > 0.7 typically indicates strong correlation
- |r| between 0.3-0.7 indicates moderate correlation
- |r| < 0.3 indicates weak correlation
- Correlation does not imply causation
- Linear regression finds best fit line: y = mx + b
Common Applications
Finance
Stock correlations for portfolio diversification, beta coefficient calculation, risk analysis.
Healthcare
Relationship between risk factors and health outcomes, drug dosage vs. effectiveness.
Education
Study time vs. test scores, class size vs. student performance, attendance vs. grades.
Marketing
Advertising spend vs. sales, price vs. demand, customer satisfaction vs. retention.
Frequently Asked Questions
Frequently Asked Questions
The Pearson correlation coefficient (r) measures the strength and direction of the linear relationship between two continuous variables. It ranges from -1 to +1. A value of +1 indicates a perfect positive linear relationship (both variables increase together), -1 indicates a perfect negative linear relationship (one increases as the other decreases), and 0 indicates no linear relationship.
R-squared (coefficient of determination) is the square of the correlation coefficient. It represents the proportion of variance in the dependent variable (Y) that is predictable from the independent variable (X). For example, R-squared = 0.64 means 64% of the variance in Y is explained by X. Higher R-squared indicates a better fit of the regression line to the data.
Correlation strength is typically interpreted as: |r| >= 0.9 is very strong, |r| 0.7-0.9 is strong, |r| 0.5-0.7 is moderate, |r| 0.3-0.5 is weak, and |r| < 0.3 is very weak or negligible. However, these are general guidelines and interpretation depends on context. In some fields like physics, r > 0.9 is expected, while in social sciences, r > 0.3 may be meaningful.
No, correlation does not imply causation. Two variables can be correlated without one causing the other. They might both be influenced by a third variable (confounding), the relationship might be coincidental, or the causation might be reversed. To establish causation, you need controlled experiments or rigorous causal analysis methods.
Both measure the relationship between two variables, but covariance is scale-dependent (measured in units of X times Y) while correlation is standardized (unitless, ranging -1 to +1). Correlation is covariance divided by the product of standard deviations, making it easier to interpret and compare across different datasets.