How princomp() works?

Question

I always used lm() to check the linear regression for two series. That function returns a coefficient(beta) that i can use doing:

y = beta*x

Today I found the princomp() function, that calculate the Total Least Squares.

It should be good for me (more accurate). I've done some tests using princomp(), like:

r <- princomp( ~ x + y)

My problem is: How to interpret its results.

How can I get the coefficient? (with "coefficient" i mean, the number that i have to use to multiply the X value to give a numer similar to y)

Could someone help me?

(I'm using R)

THANK YOU!

Answer 1

princomp is running principal component analysis instead of total least squares regression. As far as I know there is no R function nor package that does TLS; at most there is Deming regression in MethComp.
Yet, please treat this as a suggestion that it is most likely not worth it.

Answer 2

Based on the naive GNU Octave implementation found here, something like this might (grain of salt, it's late) work.

tls <- function(A, b){

  n <- ncol(A)
  C <- cbind(A, b)

  V <- svd(C)$v
  VAB <- V[1:n, (n+1):ncol(V)]
  VBB <- V[(n+1):nrow(V), (n+1):ncol(V)]
  return(-VAB/VBB)
}