Exponential Regression Calculator
Provide positive-valued observations to estimate the exponential growth or decay model, review R-squared, and forecast new outcomes.
All y values must be positive to support the logarithmic transformation.
Regression equation
y = 1.8640 * exp(0.5257 * x)
R-squared = 0.9947
| x | Actual y | Predicted y | Residual |
|---|---|---|---|
| 0 | 2.0000 | 1.8640 | 0.1360 |
| 1 | 3.0000 | 3.1533 | -0.1533 |
| 2 | 5.0000 | 5.3345 | -0.3345 |
| 3 | 9.0000 | 9.0246 | -0.0246 |
| 4 | 16.0000 | 15.2671 | 0.7329 |
How to Use This Calculator
- Enter paired observations (x, y) with y greater than zero.
- Review the estimated parameters a and b for the exponential model y = a * exp(b * x).
- Inspect residuals to evaluate how well the model fits your data.
- Use the prediction input to forecast y for new x values within the observed range.
Formulas
Transform y using natural log: Y = ln(y)
Fit linear model Y = ln(a) + b * x via least squares
Back-transform parameters: a = exp(ln(a)), predicted y-hat = a * exp(b * x)
R-squared = 1 - SS_res / SS_tot (computed on original y values)
Full Description
Exponential regression models multiplicative change by log-transforming the response. Least-squares estimation on the transformed data provides growth or decay parameters that are easy to interpret.
Always verify assumptions, inspect residuals for systematic patterns, and be cautious when extrapolating beyond the observed data range.
Frequently Asked Questions
Why must y be positive?
The natural logarithm is only defined for positive values. Exponential regression relies on log-transforming y.
Can the model handle zero or negative y values?
No. Consider shifting the response or using an alternative regression technique designed for non-positive data.
How do I interpret the parameter b?
The parameter b represents the rate of growth (b greater than 0) or decay (b less than 0) for each unit increase in x.
Is extrapolation reliable?
Predictions outside the observed x range can change quickly for exponential models, so use caution when extrapolating.