[R] lm, coefficient 'not defined because of singularities'? What does this mean?

[Prof Brian Ripley]

Hint:

x1 <- rep(pi, 283)
y1 <- rnorm(283)
summary(lm(y1 ~ x1))

More generally, see ?alias.

The idea of singularity is a linear model is a statistical one, so it may 
be time to revisit your statistical education or read a good book on the 
subject (MASS comes to mind in this context).


On Thu, 14 Feb 2008, Martin Waller wrote:

> Hello,
>
> I'm doing an lm(y1~x1), no NAs in them, both of length 283.
>
> I get out however and 'NA' for the estimate of x1 and summary gives:
>
> Residuals:
> 	Min	1Q	Median	3Q	Max
> -0.1998309 -0.0447269 -0.0006252  0.0390933  0.3141687
>
> Coefficients: (1 not defined because of singularities)
> 	Estimate Std. Error t value Pr(>|t|)
> (Intercept) -0.021291   0.003994   -5.331 2.01e-07 ***
> x1                  NA        NA       NA       NA
> ---
> Signif. codes: 0 .***. 0.001 .**. 0.01 .*. 0.05 '.' 0.1 ' ' 1
>
> Residual standard error: 0.06719 on 282 degrees of freedom
>
>
> I don't understand why x1 can't be defined because of singularities - is
> it trying to tell me something about the data and what can I do about it?
>
> Thanks for any help,
>
> Martin
>
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-- 
Brian D. Ripley,                  ripley at stats.ox.ac.uk
Professor of Applied Statistics,  http://www.stats.ox.ac.uk/~ripley/
University of Oxford,             Tel:  +44 1865 272861 (self)
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