This calculator performs **Exponential Regression** and produces an equation for the line of best fit for the provided predictor and response values. It also calculates the **correlation coefficient**.

The equation takes the form: \( y = A \cdot B^x \)

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 "Do Exponential Regression" button.

**Exponential Regression Equation:**

y = A · B^{x}

**Correlation Coefficient (r):**

## Exponential Regression and Correlation Coefficient

The **Exponential Regression** finds the best-fit equation in the form:

This regression is useful for modeling relationships where the change in \(Y\) is proportional to \(B^x\). 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:**Exponential regression typically involves log transformation of the response values (Y), assuming all Y values are positive. This transformation linearizes the exponential relationship, allowing for easier calculation of the regression parameters.**Outliers:**Large outliers can significantly distort the regression equation and the correlation coefficient.**Non-Linear Relationships:**Exponential regression is only suitable for relationships that follow the exponential pattern. Other relationships may not fit well.