R help - Feb 2008 - lm, coefficient 'not defined because of singularities'? What does this mean?

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

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
>
> ______________________________________________
> R-help at r-project.org mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide
http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
>
-- 
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)
1 South Parks Road,                     +44 1865 272866 (PA)
Oxford OX1 3TG, UK                Fax:  +44 1865 272595

Ah yes - you're right, and its also a tiny number (10^-18)

Thanks...

Martin

Patrick Burns wrote:
> I think it is saying that there is only one (unique)
> number in 'x1'.  If that is right, then you could do:
>
> lm(y1 ~ x1 - 1)
>
> Patrick Burns
> patrick at burns-stat.com
> +44 (0)20 8525 0696
> http://www.burns-stat.com
> (home of S Poetry and "A Guide for the Unwilling S User")
>
> 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
>>
>> ______________________________________________
>> R-help at r-project.org mailing list
>> https://stat.ethz.ch/mailman/listinfo/r-help
>> PLEASE do read the posting guide 
>> http://www.R-project.org/posting-guide.html
>> and provide commented, minimal, self-contained, reproducible code.
>>
>>
>>  
>>
>
>