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 = ax^{b}

**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.