R help - Oct 2009 - lm output

Hi All

I am running a linear regression using the lm object.

In the event that my independent variable is the same across all
observations the regression slope is returned as an NA.

For example, if I have the following 

y=c(10,12,17)
x=c(5,5,5)

lm = lm(y~x)
produces the following 

Coefficients:
(Intercept)            x  
      13           NA  

Other than post-processing the results, is there a way to output the
slope as 0 rather than NA?

Thanks

Pete 


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That comes out as an NA because X'X is not invertible because it is not full
rank (one row/column is a linear combination of the other(s)). And that
means there is no unique solution to the system.

y=c(10,12,17)
x=c(5,5,5)
X=cbind(1,x)

X
t(X)%*%X
solve(t(X)%*%X)

Therefore, nope, there is now way to make this come out as a zero, because
it fails the very assumptions of regression analysis.

HTH,
Daniel

-------------------------
cuncta stricte discussurus
-------------------------

-----Urspr?ngliche Nachricht-----
Von: r-help-bounces at r-project.org [mailto:r-help-bounces at r-project.org] Im
Auftrag von Brecknock, Peter
Gesendet: Friday, October 09, 2009 5:12 PM
An: r-help at r-project.org
Betreff: [R] lm output

Hi All

I am running a linear regression using the lm object.

In the event that my independent variable is the same across all
observations the regression slope is returned as an NA.

For example, if I have the following 

y=c(10,12,17)
x=c(5,5,5)

lm = lm(y~x)
produces the following 

Coefficients:
(Intercept)            x  
      13           NA  

Other than post-processing the results, is there a way to output the slope
as 0 rather than NA?

Thanks

Pete 


This e-mail may contain confidential or proprietary information belonging to
the BP group and is intended only for the use of the recipients named above.
If you are not the intended recipient, please immediately notify the sender
and either delete this email or return to the sender immediately.  You may
not review, copy or distribute this email.  Within the bounds of law, this
part of BP retains all emails and IMs and may monitor them to ensure
compliance with BP's internal policies and for other legitimate business
purposes.


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On 09-Oct-09 21:12:18, Brecknock, Peter wrote:
> Hi All
> I am running a linear regression using the lm object.
> 
> In the event that my independent variable is the same across all
> observations the regression slope is returned as an NA.
> 
> For example, if I have the following 
> 
> y=c(10,12,17)
> x=c(5,5,5)
> 
> lm = lm(y~x)
> produces the following 
> 
> Coefficients:
> (Intercept)            x  
>       13           NA  
> 
> Other than post-processing the results, is there a way to output the
> slope as 0 rather than NA?
> 
> Thanks
> Pete
You should post-process! To incorporate such a thing into the
function lm() itself would be an arbitrary resolution of an
indeterminate situation, and would not be appropriate for a
general-purpose function. Your situation is, graphically,


17 +    *
   |
15 +
   |
   |
12 +    *
   |
10 +    *
   |
   |
   |
   |
 5 +----+----+
   0    5    10

Any line whatever through the point (5,13) will fit the three
points as well as any other, so the slope is indeterminate.[*]
You have decided that you would like it to be zero, but that
is an arbitrary decision!

[*] Note that a vertical line (with slope +/- Inf) does not
resolve the indeterminacy, since, although it goes through all
three points, you do not know which point[s] on the line to
use in evaluating the error -- the difference between a point
on the line with given value of x and "the" y-value on the line
corresponding to x -- because all points on the line qualify
as potential y values, since they all have the same value of x.

Since the slope is indeterminate, it is NA (that is what NA means).
It arises numerically because the calculation of the slope is

  (N*sum(x*y) - sum(x)*sum(y))/(N*sum(x^2) - sum(x)^2)

which is 0/0 -- likewise NA.

Hoping this helps,
Ted.

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Date: 09-Oct-09                                       Time: 22:41:37
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