## Linear regression

Purpose

Description

Macro Synopsis

Modules

Related Functions

References

### Purpose

Linear regression

### Description

"Linear regression" takes the input signal and fits a linear function

to it where *t* is the variable along the x-axis.
Return parameters are:

- the offset a and
- the slope b of the linear fitting function.

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

where the overline stands for the mean values of x and y, respectively. If all values lie on a straight line (complete positive or complete negative correlation), *r* will be -1 or +1, depending on whether the slope of the line is positive or negative. Values of *r* near 0 indicate uncorrelated variables x and y.

### Macro Synopsis

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

signal x,y;

float a,b;

### Modules

Statistics

### Related Functions

Multilinear regression, Exponential regression,
Power 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]