[R] Call the Standard Error and t-test probability in linear regression

[Martin Maechler]

> On 02-Mar-2012 IOANNA wrote:
> > Hello, 
> > I run a linear regression I get the summary, e.g.:
> > 
> >>  
> >    Call: 
> >    lm(formula = signal ~ conc) 
> >    Residuals: 
> >       1        2     3      4      5  
> >      0.4  -1.0   1.6  -1.8    0.8  
> >    Coefficients: 
> >                   Estimate Std.  Error    t value    Pr(>|t|)     
> >      (Intercept)  3.60000    1.23288    2.92     0.0615 .   
> >      conc          1.94000     0.05033   38.54  3.84e-05 *** 
> >    --- 
> >    Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1  
> >    Residual standard error: 1.592 on 3 degrees of freedom 
> >    Multiple R-Squared: 0.998,      Adjusted R-squared: 0.9973  
> >    F-statistic:  1486 on 1 and 3 DF,  p-value: 3.842e-0
> > 
> > I would like to call the probability of the t-test only in order
> > to use it separately. For example I 'd like to get: 
> > Pr<-3.84e-05 
> > 
> > Similarly I want to call the standard error of the parameters
> > and the function:
> > SEconc<-0.05033
> > 
> > I don't know how to do this. Any help?
> > 
> > Regards, 
> > Ioanna

> Hi Ioanna,
> If you look at '?summary.lm' and read the section "Value",
> you will see that the returned value is a list with several
> components, one of which is:

>   coefficients: a p x 4 matrix with columns for the
>     estimated coefficient, its standard error,
>     t-statistic and corresponding (two-sided) p-value.
>     Aliased coefficients are omitted.

> This is effectively as displayed by summary(lm...)).
> So your 

>   Coefficients: 
> >               Estimate  Std. Error  t value  Pr(>|t|)     
> >   (Intercept)  3.60000     1.23288     2.92    0.0615 .   
> >          conc  1.94000     0.05033    38.54  3.84e-05 *** 

> (apart from the significance codes "." and "***") are the
> elements in this p=2 x 4 matrix.

indeed.

> Hence

>   summary(lm.r)$coef

> would give the full 4x4 matrix (you can abbreviate "coefficients"
> to "coef"), 

Yes.  In the present case, I tell all my "students" (:= everyone
who wants to learn .. ;-) to use

  coef(summary(lm.r))
instead of
  summary(lm.r)$coef

because using the coef() [or coefficients()] method will work
with many more models and situations, notably also for cases
where the (summary of the) fitted model is not a list (but e.g. a S4 class,
reference class, ..), or does not store these in exactly this location.

Martin

> and so

>   summary(lm.r)$coef[2,4]

> will give you the P-value for "conc", and

>   summary(lm.r)$coef[2,2]

> will give the SE of the estimate of "conc". And so on.

> Ted.

> -------------------------------------------------
> E-Mail: (Ted Harding) <Ted.Harding at wlandres.net>
> Date: 02-Mar-2012  Time: 13:09:03
> This message was sent by XFMail

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