Exponential regression calculator
Fit y = a·e^(bx) to positive Y values by linearising ln(Y).
Fit on the original scale
| Row | X | Y | Fitted value | Residual |
|---|---|---|---|---|
| Fill in the fields above — the result is computed on this page. | ||||
How to use this page
- Paste X and positive Y values.
- Read a, b and the factor e^b.
- Review R-squared, RMSE and residuals on the Y scale.
What this page does not do: Every Y value must be positive. Log linearisation minimises errors in the log scale; it is not identical to nonlinear least squares that minimises errors directly on the Y scale.
Further reading
Exponential regression suits processes where change is proportional to the current level. The calculator fits a line to ln(Y) and transforms the coefficients back to y = a·e^(bx).
e^b is the factor associated with a one-unit increase in X. Positive b describes growth and negative b decay. R-squared and RMSE on this page are calculated after returning to the original Y scale.
Frequently asked questions
Why can Y not equal zero?
The model uses ln(Y), which is not defined for zero or negative real values.
What does e^b = 1.05 mean?
The fitted Y is multiplied by 1.05, an increase of about 5%, when X increases by one.
See also
Beta distribution calculator
Calculate beta density, CDF, upper tail and quantile together with its mean and variance.
Chi-square test calculator
Calculate chi-square goodness of fit, independence, or a chi-square critical value.
Continuous uniform distribution calculator
Calculate density, CDF, upper tail, quantile, mean and variance for U(a,b).