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Calculate the Pearson correlation coefficient (r) between two data sets. Find the strength and direction of linear relationships, coefficient of determination (R²), and regression line equation.
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Please enter at least 2 data points
This calculator computes the Pearson correlation coefficient for linear relationships. Results assume bivariate normal distribution of data.
Correlation does not imply causation. Statistical significance depends on sample size. For critical research decisions, consult a statistician.
Correlation measures the strength and direction of the linear relationship between two variables. The Pearson correlation coefficient (r) ranges from -1 to +1, where +1 indicates a perfect positive linear relationship, -1 indicates a perfect negative linear relationship, and 0 indicates no linear relationship. Correlation is fundamental in statistics for understanding how variables move together and for predictive modeling.
Understanding correlation strength helps interpret your results:
Strong correlation (|r| > 0.7): Variables are closely related, moving together predictably. One variable explains most of the variance in the other.
Moderate correlation (0.4 < |r| ≤ 0.7): Variables are related but other factors also influence them. Useful for identifying trends.
Weak correlation (|r| ≤ 0.4): Variables have limited relationship. Other factors dominate the variation.
r = Σ[(xi - x̄)(yi - ȳ)] / √[Σ(xi - x̄)² × Σ(yi - ȳ)²]Where xi and yi are data points, x̄ and ȳ are means. This measures the linear relationship strength.
R² = r²R² indicates the proportion of variance in Y explained by X. An R² of 0.81 means 81% of variance is explained.
A 'good' correlation depends on your field. In physics, r > 0.9 might be expected. In social sciences, r > 0.5 is often considered strong. In finance, even r = 0.3 can be meaningful. Context matters more than arbitrary thresholds.
Correlation (r) measures the strength and direction of a linear relationship (-1 to +1). R² is r squared (0 to 1) and represents the proportion of variance explained. For example, r = 0.9 means R² = 0.81, so 81% of variance is explained by the relationship.
Yes, negative correlation means variables move in opposite directions. When one increases, the other decreases. For example, price and demand often show negative correlation. A correlation of -0.8 is just as strong as +0.8, but in the opposite direction.
Mathematically, you need at least 2 points, but for reliable results, more is better. With less than 10 points, correlation can be highly variable. For statistical significance testing, sample size directly affects p-values. General guideline: 30+ points for reliable estimates.
Statistical significance (p < 0.05) indicates the correlation is unlikely to be due to random chance. However, significance depends on sample size. Large samples can show 'significant' but weak correlations. Always consider both the p-value and the correlation magnitude.
The regression line (y = mx + b) predicts Y values from X values. The slope (m) shows how much Y changes per unit change in X. The intercept (b) is the predicted Y when X = 0. Use this for making predictions within your data range.
Pearson correlation only measures linear relationships. If your data has a curved pattern (quadratic, exponential), the linear correlation may be near zero even though the variables are clearly related. Consider non-linear correlation methods like Spearman's rank correlation.
Key limitations: (1) Only measures linear relationships, (2) Sensitive to outliers, (3) Doesn't prove causation, (4) Assumes continuous variables, (5) Can be misleading with small samples. Always combine correlation analysis with domain knowledge and data visualization.