# FreeBSD Manual Pages

```r.regression.multi(1)	    GRASS GIS User's Manual	 r.regression.multi(1)

NAME
r.regression.multi  - Calculates	multiple linear	regression from	raster
maps.

KEYWORDS
raster, statistics, regression

SYNOPSIS
r.regression.multi
r.regression.multi --help
r.regression.multi  [-g]	  mapx=name[,name,...]	 mapy=name    [residu-
als=name]    [estimates=name]   [output=name]   [--overwrite]  [--help]
[--verbose]  [--quiet]  [--ui]

Flags:
-g
Print in shell script style

--overwrite
Allow output	files to overwrite existing files

--help
Print usage summary

--verbose
Verbose module output

--quiet
Quiet module	output

--ui
Force launching GUI dialog

Parameters:
mapx=name[,name,...]A [required]
Map for x coefficient

mapy=nameA [required]
Map for y coefficient

residuals=name
Map to store	residuals

estimates=name
Map to store	estimates

output=name
ASCII file for storing regression coefficients (output to screen if
file	not specified).

DESCRIPTION
r.regression.multi  calculates a	multiple linear	regression from	raster
maps, according to the formula
Y = b0 +	sum(bi*Xi) + E
where
X = {X1,	X2, ..., Xm}
m = number of explaining	variables
Y = {y1,	y2, ..., yn}
Xi = {xi1, xi2, ..., xin}
E = {e1,	e2, ..., en}
n = number of observations (cases)
In R notation:
Y ~ sum(bi*Xi)
b0 is the intercept, X0 is set to 1

r.regression.multi is designed for large	datasets that can not be  pro-
cessed  in  R.  A  p value is therefore not provided, because even very
small, meaningless effects will become significant with a large	number
of  cells.  Instead  it is recommended to judge by the estimator	b, the
amount of variance explained (R squared for a given variable)  and  the
gain in AIC (AIC	without	a given	variable minus AIC global must be pos-
itive) whether the inclusion of a  given	 explaining  variable  in  the
model is	justified.

The global model
The b coefficients (b0 is offset), R squared or coefficient of determi-
nation (Rsq) and	F are identical	to the ones  obtained  from  R-stats's
lm()  function and R-stats's anova() function. The AIC value is identi-
cal to the one obtained from R-stats's stepAIC()	function (in  case  of
backwards  stepping,  identical to the Start value). The	AIC value cor-
rected for the number of	explaining variables and the BIC (Bayesian In-
formation Criterion) value follow the logic of AIC.

The explaining variables
R squared for each explaining variable represents the additional	amount
of explained variance when including this variable compared to when ex-
cluding this variable, that is, this amount of variance is explained by
the current explaining variable after taking into consideration all the
other explaining	variables.

The  F  score for each explaining variable allows testing if the	inclu-
sion of this variable significantly increases the explaining  power  of
the model, relative to the global model excluding this explaining vari-
able.  That means that the F value for a	given explaining  variable  is
only  identical	to  the	 F  value of the R-function summary.aov	if the
given explaining	variable is the	last variable in the R-formula.	 While
R  successively includes	one variable after another in the order	speci-
fied by the formula and at each step calculates the F value  expressing
the  gain by including the current variable in addition to the previous
variables, r.regression.multi calculates	 the  F-value  expressing  the
gain  by	 including the current variable	in addition to all other vari-
ables, not only the previous variables.

The AIC value is	identical to the  one  obtained	 from  the  R-function
stepAIC()  when	excluding  this	 variable from the full	model. The AIC
value corrected for the number of  explaining  variables	 and  the  BIC
value  (Bayesian	 Information Criterion)	value follow the logic of AIC.
BIC is identical	to the R-function stepAIC with k = log(n). AICc	is not
available through the R-function	stepAIC.

EXAMPLE
Multiple	regression with	soil K-factor and elevation, aspect, and slope
(North Carolina dataset). Output	maps are the residuals and estimates:
g.region	raster=soils_Kfactor -p
r.regression.multi mapx=elevation,aspect,slope mapy=soils_Kfactor \
residuals=soils_Kfactor.resid estimates=soils_Kfactor.estim

d.correlate, r.regression.line,	r.stats

AUTHOR
Markus Metz

SOURCE CODE
Available at: r.regression.multi	source code (history)

Main index | Raster index | Topics index	| Keywords index  |  Graphical
index | Full index

A(C) 2003-2020 GRASS Development	Team, GRASS GIS	7.8.5 Reference	Manual

GRASS 7.8.5						 r.regression.multi(1)
```

NAME | KEYWORDS | SYNOPSIS | DESCRIPTION | EXAMPLE | SEE ALSO | AUTHOR | SOURCE CODE

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