Calculator
Paste pairs as x,y (one per line) or upload a CSV. Then select the model and chart options.
Example data table
Use these sample pairs to test the chart and statistics.
| X | Y |
|---|---|
| 1 | 2 |
| 2 | 3 |
| 3 | 5 |
| 4 | 4 |
| 5 | 7 |
| 6 | 8 |
| 7 | 9 |
| 8 | 10 |
| 9 | 12 |
| 10 | 13 |
Formula used
These calculations use standard summary statistics and least-squares fitting.
- x̄ = (Σx)/n and ȳ = (Σy)/n (means).
- Cov(X,Y) = Σ((x−x̄)(y−ȳ)) / (n−1) (sample covariance).
- r = Σ((x−x̄)(y−ȳ)) / √(Σ(x−x̄)² Σ(y−ȳ)²) (Pearson correlation).
- Linear fit: m = Sxy/Sxx, b = ȳ − m x̄, so ŷ = mx + b.
- Quadratic fit solves normal equations for ŷ = ax² + bx + c.
- R² = 1 − SSE/SST, where SSE = Σ(y−ŷ)² and SST = Σ(y−ȳ)².
- Outliers: standardized residual z = (y−ŷ)/s, where s = √(SSE/df).
How to use this calculator
- Enter paired values in the textarea, one pair per line.
- Or upload a CSV with two numeric columns.
- Pick a model (linear or quadratic) and set labels.
- Optionally set axis bounds and the outlier threshold.
- Press Submit to view the chart and statistics.
- Use Download CSV or Download PDF to export results.
FAQs
1) What does a scatter plot show?
It displays paired measurements as points on an X–Y plane. Clusters, slopes, and gaps help you spot relationships, variability, and unusual observations quickly.
2) What is Pearson correlation r?
Pearson r measures linear association from −1 to +1. Values near ±1 indicate a strong linear link, while values near 0 suggest little linear relationship.
3) Why also calculate Spearman ρ?
Spearman ρ works on ranks, so it detects monotonic trends even when the relationship is not strictly linear. It is also less sensitive to extreme values.
4) When should I use a quadratic model?
Use it when the cloud curves, such as accelerating growth or diminishing returns. A quadratic can capture one bend, but it can overfit if data are noisy or sparse.
5) What does R² mean here?
R² is the fraction of Y variation explained by the chosen model, compared to using the mean only. Higher values indicate a better fit on this dataset.
6) How are outliers flagged?
The calculator computes residuals (y−ŷ), scales them by the residual standard deviation, and flags points whose absolute standardized residual meets your threshold.
7) Can I use negative numbers or decimals?
Yes. Enter values like −3.2 or 4.75. The parser accepts commas, spaces, tabs, or semicolons between the two numbers on each line.
8) Why do axis bounds matter?
Fixed bounds make charts comparable across datasets. If bounds are too tight, points may clip; if too wide, detail can be hard to see. Leaving them blank uses automatic scaling.