Calculator Inputs
Enter paired x and y values. Then add the x value you want to predict.
Plotly Graph
The chart shows observed points, the fitted line, and your predicted point.
Example Data Table
This sample shows how paired values can build a trend line.
| Point | X | Y |
|---|---|---|
| 1 | 1 | 2.2 |
| 2 | 2 | 2.9 |
| 3 | 3 | 3.8 |
| 4 | 4 | 4.4 |
| 5 | 5 | 5.1 |
| 6 | 6 | 6.2 |
Formula Used
Simple linear regression predicts y from x with a best fit line.
Slope: m = [nΣxy − (Σx)(Σy)] / [nΣx² − (Σx)²]
Intercept: b = [Σy − mΣx] / n
Prediction: y = mx + b
Fit quality: R² = 1 − SSE / SST
This method works best when the relationship is roughly linear.
How to Use This Calculator
- Enter all x values in the first field.
- Enter the matching y values in the second field.
- Make sure both lists have the same length.
- Type the x value you want to test.
- Click Predict Y to generate the output.
- Review the equation, R², and residual table.
- Use the graph to inspect the trend visually.
- Download CSV or PDF for reporting or revision.
FAQs
1. What does this calculator do?
It estimates a y value from a chosen x value. It uses paired observations and builds a straight best fit line from the supplied dataset.
2. Which method is used for prediction?
The tool uses simple linear regression. It calculates slope and intercept, then applies the line equation to the target x value.
3. What if my data is not linear?
The estimate may be weaker. Check the scatter plot and R² value. Curved patterns often need polynomial or other non linear models.
4. Why must x and y lists match?
Each x value needs one paired y value. Without matching pairs, the regression line cannot represent the relationship correctly.
5. What does R² mean here?
R² shows how much variation in y is explained by the fitted line. Values closer to 1 usually indicate a stronger linear fit.
6. What are residuals?
Residuals are the differences between observed y values and fitted y values. They help reveal errors, outliers, and model weakness.
7. Can I predict outside my data range?
Yes, but caution is important. Predictions beyond the observed x range are extrapolations and can become much less reliable.
8. What do the export buttons include?
The CSV and PDF files include the prediction summary and regression table. They are useful for homework, reports, and quick sharing.