Scatter Plot & Correlation
A scatter plot shows x,y pairs. Pearson correlation r measures linear relationship (-1 to 1). The best-fit line y=mx+b minimizes squared errors; R² = r².
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r = 1: perfect positive correlation; r = -1: perfect negative. R² is the proportion of variance in y explained by x. Correlation does not imply causation.
Ready to run the numbers?
Why: Scatter plots reveal relationships—height vs weight, study time vs grade, price vs demand.
How: Enter x,y pairs; the calculator computes Pearson r, best-fit line, and R².
Run the calculator when you are ready.
Scatter Plot — Correlation & Regression
Enter x,y data pairs. Get scatter plot, Pearson correlation, best-fit line, and R². Comma or space separated.
Quick Examples — Click to Load
Input — X,Y Data Pairs
One pair per line or comma/space separated. Format: x,y (e.g. 1,3 or 1 3)
For educational and informational purposes only. Verify with a qualified professional.
🧮 Fascinating Math Facts
Pearson r measures linear relationship; r=0 means no linear correlation.
R² = r²—the proportion of variance in y explained by x.
Key Takeaways
- • Scatter plots visualize the relationship between two variables (x and y)
- • Pearson r ranges from -1 (perfect negative) to +1 (perfect positive); 0 means no linear correlation
- • R² (coefficient of determination) = proportion of variance in y explained by x
- • Best-fit line: y = mx + b (least squares regression)
Did You Know?
How It Works
Enter x,y pairs (one per line or comma-separated). The calculator computes Pearson correlation, fits a least-squares regression line, and reports R². Outliers are detected using distance from the regression line (mean + 2×SD).
Pearson r formula
r = [nΣxy − ΣxΣy] / √[(nΣx² − (Σx)²)(nΣy² − (Σy)²)]
Best-fit line
Slope m = [nΣxy − ΣxΣy] / [nΣx² − (Σx)²], Intercept b = (Σy − mΣx) / n
Expert Tips
Data format
Use x,y per line: 1,3 or 1 3. Multiple formats: 1,3 2,5 3,7 or one pair per line.
Outliers
Points far from the regression line may be outliers. Verify they are not data errors before removing.
Non-linear data
Pearson r measures linear correlation. For curved relationships, consider polynomial or other models.
Sample size
At least 10–30 points recommended for reliable correlation. Small samples can produce misleading r.
Correlation Strength Comparison
| |r| Range | Interpretation |
|---|---|
| 0.9 – 1.0 | Very strong |
| 0.7 – 0.9 | Strong |
| 0.5 – 0.7 | Moderate |
| 0.3 – 0.5 | Weak |
| 0.0 – 0.3 | Very weak / None |
FAQ
What data format do I use?
Enter x,y pairs. One pair per line (e.g. 1,3) or comma/space separated (e.g. 1,3 2,5 3,7).
What does R² mean?
R² is the proportion of variance in y explained by x. R²=0.9 means 90% of y variation is explained by the linear fit.
Does correlation imply causation?
No. Correlation shows association, not cause. A third variable or coincidence can produce correlation.
How are outliers detected?
Points with distance from the regression line greater than mean + 2×SD of distances are flagged as potential outliers.
When is Pearson r appropriate?
For linear relationships with roughly normal distributions. For non-linear or ordinal data, consider Spearman correlation.
Infographic Stats
Official Sources
- Calculator Soup — Correlation coefficient reference
- Math Is Fun — Correlation explained
Disclaimer: This tool is for educational and exploratory analysis. Correlation does not imply causation. For formal statistical inference, consult a statistician or use specialized software.
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