## Exponential regression

Purpose

Description

Macro Synopsis

Modules

Related Functions

References

### Purpose

Exponential regression

### Description

"Exponential regression" takes the input signal and fits an exponential
function

to it where *t* is the variable along the x-axis.
The function is based on the function Linear regression, with the y-axis scaled logarithmically.

Return parameters of "Exponential regression" are:

- the amplitude
*a* and
- the exponent
*b* of the exponential fitting function.

Besides *a* and *b*, the corresponding uncertainties *sigma a* and *sigma b* and the linear correlation coefficient *r* appear in the message window. This coefficent is given by

where the overline denotes mean values.
Values of r near 0 indicate poor fitting, whereas good fitting is indicated by values of r near +1 or -1, depending on whether the exponent b of the fitting function is positive or negative.

### Macro Synopsis

`y = ExpRegress(x,&a,&b);`

signal x,y;

float a,b;

### Modules

Statistics

### Related Functions

Linear regression, Multilinear regression,
Power regression, Remove DC, Remove trend,
Long term correlation analysis (LTCA), Principal component analysis (PCA), R/S statistics, Box-Cox transform, Detrended fluctuation analysis (DFA).

### References

Graybill [12]