Correlation Coefficient Calculator - Free Pearson's r Calculator
Correlation Coefficient Calculator
Calculate the Pearson correlation coefficient (r) to measure the linear relationship between two variables. Values range from -1 to +1.
Enter Your Data
Format: x, y (comma-separated pairs)
Correlation Analysis Results
Correlation Coefficient (r)
Coefficient of Determination (r²)
Explained variance
Scatter Plot with Regression Line
Linear Regression Equation
X Variable Statistics
Y Variable Statistics
Calculation Details
| i | X | Y | (X - X̄) | (Y - Ȳ) | (X - X̄)(Y - Ȳ) |
|---|
How to use this calculator
📊 How to Use This Calculator
- Choose your input method: paired data or separate lists
- Enter your X and Y values (minimum 2 pairs)
- Optionally label your variables (e.g., Height, Weight)
- Click "Calculate Correlation" to see results
- Review the correlation coefficient, scatter plot, and regression line
📐 Understanding Correlation
Correlation Coefficient (r)
Measures the strength and direction of linear relationship between two variables. Ranges from -1 to +1.
- • r = +1: Perfect positive correlation
- • r = -1: Perfect negative correlation
- • r = 0: No linear correlation
Interpreting Correlation Strength
- • |r| ≥ 0.7: Strong correlation
- • 0.3 ≤ |r| < 0.7: Moderate correlation
- • |r| < 0.3: Weak correlation
Coefficient of Determination (r²)
Represents the proportion of variance in Y explained by X. If r² = 0.64, then 64% of Y's variation is explained by X.
🌟 Real-World Examples
Example 1: Height vs Weight
Typically shows r ≈ 0.7 (strong positive correlation)
Taller people tend to weigh more
Example 2: Study Time vs Test Score
Often shows r ≈ 0.5 to 0.7 (moderate to strong positive)
More study time generally leads to better scores
Example 3: Temperature vs Ice Cream Sales
Usually shows r ≈ 0.8 (strong positive correlation)
Higher temperatures increase ice cream sales
💡 Pro Tips
- • Correlation does not imply causation
- • Check scatter plot for outliers that might affect correlation
- • Pearson correlation assumes linear relationship
- • For non-linear relationships, consider Spearman correlation
- • Always visualize your data with a scatter plot
- • r² is often more interpretable than r
⚠️ Common Mistakes to Avoid
- • Don't assume causation from correlation alone
- • Be aware of restricted range effects
- • Check for non-linear relationships in scatter plot
- • Don't ignore outliers - they can greatly affect r
- • Ensure you have enough data points (n ≥ 30 preferred)
- • Remember correlation only measures linear relationships
About this calculator
Calculate Pearson correlation coefficient (r) between two variables. Includes scatter plot, regression line, and coefficient of determination (r²).
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