Enter Paired Values
Use one pair per line. Separate X and Y with a comma, space, semicolon, or tab.
Example Data Table
This sample shows a positive linear pattern that works well for testing regression and correlation output.
| Point | Study Hours (X) | Score Gain (Y) |
|---|---|---|
| 1 | 1 | 2 |
| 2 | 2 | 3 |
| 3 | 3 | 5 |
| 4 | 4 | 4 |
| 5 | 5 | 6 |
| 6 | 6 | 8 |
| 7 | 7 | 7 |
| 8 | 8 | 9 |
Formula Used
1) Mean of X and Y
x̄ = Σx / n and ȳ = Σy / n
2) Sample Covariance
Cov(x,y) = Σ[(xi − x̄)(yi − ȳ)] / (n − 1)
3) Correlation Coefficient
r = Cov(x,y) / (sx × sy)
4) Linear Regression Slope
b1 = Σ[(xi − x̄)(yi − ȳ)] / Σ[(xi − x̄)²]
5) Intercept
b0 = ȳ − b1x̄
6) Fitted Line
ŷ = b0 + b1x
7) Coefficient of Determination
R² = 1 − (SSE / SST)
8) Root Mean Squared Error
RMSE = √(SSE / n)
How to Use This Calculator
- Enter one X,Y pair per line in the paired values box.
- Set the chart title, axis labels, decimals, and marker size.
- Add an optional X value when you want a predicted Y output.
- Choose whether to display the regression trendline.
- Press Generate Scatter Plot to calculate statistics and draw the graph.
- Review the metrics, equation, processed data table, and chart.
- Use the CSV button for data export and the PDF button for a printable report.
FAQs
1) What does a scatter plot show?
A scatter plot displays paired numeric observations as points. It helps you see direction, clustering, spread, unusual values, and whether a linear relationship may exist.
2) What is correlation in this tool?
Correlation measures the strength and direction of a linear relationship between X and Y. Values near 1 or -1 show stronger linear patterns, while values near 0 show weak linear association.
3) Why is the regression line useful?
The regression line summarizes the linear trend across the points. It can estimate Y from X, compare datasets, and reveal whether the average response rises or falls as X changes.
4) What does R² mean?
R² shows how much variation in Y is explained by the fitted line. Higher values indicate a tighter linear fit, though a high R² does not automatically prove causation.
5) Can I use negative and decimal values?
Yes. The parser accepts negative numbers, decimals, and zero. Each valid line must still contain exactly one X value and one Y value.
6) Why am I seeing an error about X values?
Regression needs variation in X. If every X value is identical, the slope cannot be calculated because the denominator in the slope formula becomes zero.
7) What does RMSE tell me?
RMSE measures the typical size of prediction errors from the fitted line. Smaller RMSE values indicate that the line tracks the observed points more closely.
8) What is included in the CSV and PDF exports?
The CSV export includes the summary metrics and processed point table. The PDF export captures the result section, including the equation, metric cards, and plotted chart.