I tried using prcomp():

library(compositions)
library(rgl)
x <- rnorm(100)
y <- rnorm(100)
z <- rnorm(100)
mat<-cbind(x,y,z)
plot3D(mat,col=3,bbox=F)
pr<-prcomp(mat)
planes3d(pr$rotation[3,1]*sign(pr$rotation[3,1]),pr$rotation[3,2]*sign(pr$rotation[3,2]),pr$rotation[3,3]*sign(pr$rotation[3,3]),alpha=0.5,col=3,bbox=F)
decorate3d()

It seems fine; any advice is welcome
best
paolo


________________________________________
Da: R-sig-ecology <r-sig-ecology-boun...@r-project.org> per conto di Paolo 
Piras <paolo.pi...@uniroma3.it>
Inviato: martedì 19 gennaio 2016 14.46
A: r-sig-ecology@r-project.org
Oggetto: [R-sig-eco] 3d fitting plane

Hi folks,
I look for a fast way to estimate a 3d fitting plane to my 3d data.
I do not want z~y+x as this is a regression model.
I just want the equation of the best plane that fits the data in 3d. Maybe 
using princomp() and Total least squares?
Looking around I found some solutions but nothing definitive.
Thanks in advance for any suggestion.
best
paolo

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