## Multilinear regression

Purpose

Description

Example

Macro Synopsis

Modules

Related Functions

References

### Purpose

Multilinear regression

### Description

"Multilinear regression" fits a linear combination of the components of a multi-channel signal x to a single-channel signal y and returns the residual (i.e. the difference signal)

of the multilinear regression

where are the channels of the multichannel
signal.

The computed coefficients and *b* are displayed in the message window.

### Example

Use the macro `LinComb.dpm` to create a linear combination `z`
of two input signals `x` and `y`. Then generate a multichannel signal
`s` out of `x` and `y` using Merge.
Applying "Multilinear regression" to `s` and `z` will recover the coefficients
you used in the first step and yield a residual near 0 (the small
fluctuations are due to roundoff errors).

### Macro Synopsis

`r = MultiLinRegress([x,y]);`

signal r,x,y;
Note that x is a multi-channel signal.

### Modules

Statistics

### Related Functions

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

### References

Graybill [12]