Calculator Input
Example Data Table
This sample set follows a clear power pattern and works well for testing the calculator quickly.
| Observation | X | Y |
|---|---|---|
| 1 | 1 | 2.9 |
| 2 | 2 | 8.1 |
| 3 | 3 | 14.2 |
| 4 | 4 | 21.6 |
| 5 | 5 | 30.1 |
| 6 | 6 | 39.7 |
| 7 | 7 | 50 |
| 8 | 8 | 60.6 |
Formula Used
Power regression fits the model y = a × xb. The method converts it into a straight line with natural logarithms.
The calculator reports fit quality on both the original scale and the transformed log scale for better interpretation.
How to Use This Calculator
- Enter positive X values in the first field.
- Enter matching positive Y values in the second field.
- Optionally add a forecast X value for prediction.
- Choose your preferred decimal precision.
- Click Run Power Regression to generate the equation, statistics, graph, and exportable table.
Frequently Asked Questions
1. What does this calculator estimate?
It estimates a power model in the form y = a × xb. It also reports predictions, residuals, multiple fit metrics, and graphs to help you judge how well the curve matches your data.
2. Why must all values be positive?
Power regression uses logarithms. Logarithms require values greater than zero. If your dataset contains zeros or negatives, you must transform, filter, or choose a different regression model.
3. What does the exponent b mean?
The exponent measures scaling. If b is 2, y grows roughly with x squared. If b is 0.5, y grows more slowly. Negative exponents indicate inverse relationships.
4. Why are there two R² values?
One R² is calculated using original Y values. The other uses the linearized log model. Comparing both helps you assess practical fit and transformed line quality.
5. Can I predict new values with this tool?
Yes. Enter a positive forecast X value before running the model. The calculator then returns the predicted Y value from the estimated power equation.
6. When is power regression useful?
It works well when growth is nonlinear and multiplicative. Typical examples include scaling laws, learning curves, biological relationships, cost curves, and many physical measurement patterns.
7. What do residuals tell me?
Residuals show the difference between observed and predicted values. Small, pattern free residuals usually suggest a better fit. Large structured residuals may signal outliers or a poor model choice.
8. What do the exports include?
The CSV and PDF exports include the fitted equation summary and row level output. Each row contains X, observed Y, predicted Y, residual, and absolute error values.