This calculator performs Power Regression and produces an equation for the line of best fit for the provided predictor and response values. It also calculates the correlation coefficient.
To use the calculator, provide a list of values for the predictor and the response, ensuring they are the same length, and then click the "Calculate and Plot" button.
Power Regression Equation:
y = axb
Correlation Coefficient (r):
Power Regression and Correlation Coefficient
The Power Regression finds the best-fit equation in the form:
This regression is useful for modeling relationships where the change in \(Y\) is proportional to \(X^b\). The correlation coefficient \(r\) tells us how well the model fits the data.
Correlation Coefficient Interpretation
You can interpret the correlation coefficient \(r\) as follows:
- 0.7 < |r| ≤ 1 — Strong correlation
- 0.4 < |r| < 0.7 — Moderate correlation
- 0.2 < |r| < 0.4 — Weak correlation
- 0 ≤ |r| < 0.2 — No correlation
Caveats and Conditions
- Log Transformation: Power regression requires log transformation of the data, which assumes all predictor and response values are positive.
- Outliers: Large outliers can significantly distort the regression equation and the correlation coefficient.
- Non-Linear Relationships: Power regression is suitable only for relationships that follow the power-law pattern. If the relationship is non-linear but not of this form, the fit may be poor.
Further Reading
Suf is a senior advisor in data science with deep expertise in Natural Language Processing, Complex Networks, and Anomaly Detection. Formerly a postdoctoral research fellow, he applied advanced physics techniques to tackle real-world, data-heavy industry challenges. Before that, he was a particle physicist at the ATLAS Experiment of the Large Hadron Collider. Now, he’s focused on bringing more fun and curiosity to the world of science and research online.