## table of contents

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

# 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*
[**residuals**=*name*] [**estimates**=*name*]
[**output**=*name*] [--**overwrite**] [--**help**]
[--**verbose**] [--**quiet**] [--**ui**]

## Flags:¶

## Parameters:¶

**mapx**=*name[,**name*,...]**[required]**-

Map for x coefficient **mapy**=*name***[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 processed 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 positive) 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 determination (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 identical to the one obtained from R-stats’s stepAIC()
function (in case of backwards stepping, identical to the Start value). The
AIC value corrected for the number of explaining variables and the BIC
(Bayesian Information 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 excluding 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
inclusion of this variable significantly increases the explaining power of
the model, relative to the global model excluding this explaining variable.
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 specified 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 variables, 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

# SEE ALSO¶

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

# AUTHOR¶

Markus Metz

# SOURCE CODE¶

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

Accessed: Saturday Jul 27 17:08:19 2024

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