[R] Seemingly simple "lm" giving unexpected results

[Berend Hasselman]

On 13-04-2012, at 22:20, Gene Leynes wrote:

> I can't figure out why this is returning an NA for the slope in one case,
> but not in the other.
> 
> I can tell that R thinks the first case is singular, but why isn't the
> second?
> 
> ## Define X and Y
> ## There are two versions of x
> ##     1) "as is"
> ##     2) shifted to start at 0
> y  = c(58, 57, 57, 279, 252, 851, 45, 87, 47)
> x1 = c(1334009411.437, 1334009411.437, 1334009411.437, 1334009469.297,
>        1334009469.297, 1334009469.297, 1334009485.697, 1334009485.697,
> 1334009485.697)
> x2 = x1 - min(x1)
> 
> ## Why doesn't the LM model work for the "as is" x?
> lm(y~x1)
> lm(y~x2)


With your data  the matrix t(X)%*%X is extremely ill-conditioned for the case with x1.
See

http://en.wikipedia.org/wiki/Condition_number
http://mathworld.wolfram.com/ConditionNumber.html
http://en.wikipedia.org/wiki/Numerical_methods_for_linear_least_squares

You can check it with

makeXX <- function(x) {
    matrix(data=c(x,rep(1,length(x))),nrow=length(x), byrow=FALSE)
}

X1 <- makeXX(x1)
(XTX1 <- t(X1) %*% X1)
svd(XTX1)

and similar for x2.

Berend