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.
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.
Exponential Regression Equation:
y = Aebx
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 response variable \(Y\) changes exponentially with respect to the predictor variable \(X\). 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 requires the response values to be transformed using natural logs. Make sure your response values are all positive.
- Outliers: Significant outliers can greatly impact the fit of the model and the correlation coefficient.
- Non-Exponential Relationships: This model works best for data that follows an exponential trend. If your data does not follow such a pattern, the model may not be accurate.