Exponential regression#

The Exponential model is

where $a$ is the model value at $x=0$ and $b$ controls exponential growth or decay. It describes a multiplicative change in Y as X changes, not merely a curve that happens to rise or fall quickly.

Domain#

All points selected by the Fit range must have $y>0$. GraphX rejects a fit containing zero or negative selected Y values and reports the incompatible count; it does not discard those points behind the scenes. An invalid point outside the selected range is irrelevant until the range includes it.

Unlike the fit range, the display range has no positive-X restriction for this model. The model can be evaluated at finite X values when its numerical result remains finite.

Fitting method#

GraphX linearises the model by taking the natural logarithm of Y:

It performs ordinary least squares on that transformed relationship, then recovers the displayed scale coefficient as

The method shown in the editor is Least squares on ln(Y).

Two R² values#

The primary R² compares the observed Y values with exponential predictions after transforming back to original Y-space. GraphX also shows R² (ln Y), calculated in the log-Y space that was used for the linear least-squares estimate.

These figures answer related but different questions and are not generally identical. The transformed value describes agreement after taking logarithms; the primary value describes residuals in the units of the original Y data. Neither is automatically the more important statistic without considering the use of the model. See Understanding R².

Use Fit and display ranges to distinguish the observations that set the coefficients from the interval over which the curve is drawn.