## The optional tolerance argument [Design Issues]

Hi Hötzi,

» » » For observation 8 we have -3.608225e-16, I think,
» » I think, is around the "effective zero" for fits in R at default settings on 64- and 32-bit systems.
»
» Yes, it is. »

x    <- -3.608225e-16» zero <- .Machine$double.eps» all.equal(x, zero)»  TRUE» zero»  2.220446e-16 This comparison in your context is just a test if the difference is less than about 10-8 since there is an implied tolerance argument for all.equal, the square root of .Machine$double.eps

Effective zero residuals will be somewhat better than 10-8 in practice. They will depend on the approach used to find the solution; in lm I believe the approach is via a qr decomposition of the model matrix, and R by defualt has a tol argument in that function of 10-7 which lm may be leaning on.

Here's an example of a perfect fit, therefore having effective zero residuals:

a=c(rep(1,5), rep(2,5), rep(3,5)) b=c(rep("A",5), rep("B",5), rep("C",5)) M=lm(a~0+b) resid(M)

It may actually not be the best example since the dependents are all representable inernally in R's (and computer's) binary.

Perhaps this makes a better point:

a=c(rep(pi,5), rep(sin(1.5+pi),5), rep(log(pi),5)) b=c(rep("A",5), rep("B",5), rep("C",5)) M=lm(a~0+b) resid(M)

I could be wrong, but...

Best regards,
ElMaestro

No, of course you do not need to audit your CRO if it was inspected in 1968 by the agency of Crabongostan. Ing. Helmut Schütz 