## Power regression

Purpose

Description

Macro Synopsis

Modules

Related Functions

References

### Purpose

Power regression.

### Description

"Power regression", also known as log-log regression, takes the input signal and fits a function

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

Return parameters of Power regression are:

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

Besides *a* and *b*, the corresponding uncertainties *sigma a* and *sigma b* and the correlation coefficient *r*, will 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.

**Warning:** *Make sure that the input signal does not cross any of the axes x=0 or y=0. Otherwise an error will be produced.*

### Macro Synopsis

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

signal x,y;

float a,b;

### Modules

Statistics

### Related Functions

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

### References

Graybill [12]