R help - Jan 2007 - Definition of t-value

Hello,

I'd like to ask for the exact definition of the t-value, which R uses in its
summaries of a linear model for judging the importance of an independent
variable in explaining the dependent variable.
I searched the documentation, some groups, and the web for quite a long time,
but the best I could come up with is the following from

www.answers.com/topic/value 

which reads:

Measure of the statistical significance of an independent variable b in
explaining the dependent variable y. It is determined by dividing the estimated
regression coefficient b by its standard error Sb. That is

t-Value = b/Sb

Thus, the t-statistic measures how many standard errors the coefficient is away
from zero. Generally, any t-value greater than +2 or less than - 2 is
acceptable. The higher the t-value, the greater the confidence we have in the
coefficient as a predictor. Low t-values are indications of low reliability of
the predictive power of that coefficient.


My problem is that I do not know how to compute the standard error Sb of some
regression coefficient, when I have done nothing more than to use the lm command
in this manner:

Out = lm(A~ data$B + data$C + data$D)


Does anyone know in detail, how R computes the t-value displayed in summaries?


Thank you very much,

Peter
--

try this

Out <-  lm(A ~ data$B + data$C + data$D)
summary(Out)

moreover, by typing 'summary.lm' in your R console you may see how the  
t-values are computed; check also ?summary.lm.

Another way, though less efficient, to obtain the standard errors is  
the following

summ.Out <- summary(Out)
X <- model.matrix(Out) # the design matrix
var.betas <- solve(crossprod(X)) * summ.Out$sigma^2
# standard errors
sqrt(diag(var.betas))


I hope it helps.

Best,
Dimitris

----
Dimitris Rizopoulos
Ph.D. Student
Biostatistical Centre
School of Public Health
Catholic University of Leuven

Address: Kapucijnenvoer 35, Leuven, Belgium
Tel: +32/(0)16/336899
Fax: +32/(0)16/337015
Web: http://med.kuleuven.be/biostat/
      http://www.student.kuleuven.be/~m0390867/dimitris.htm


Quoting algorithms at gmx.de:
> Hello,
>
> I'd like to ask for the exact definition of the t-value, which R   
> uses in its summaries of a linear model for judging the importance   
> of an independent variable in explaining the dependent variable.
> I searched the documentation, some groups, and the web for quite a   
> long time, but the best I could come up with is the following from
>
> www.answers.com/topic/value
>
> which reads:
>
> Measure of the statistical significance of an independent variable b  
>  in explaining the dependent variable y. It is determined by  
> dividing  the estimated regression coefficient b by its standard  
> error Sb.  That is
>
> t-Value = b/Sb
>
> Thus, the t-statistic measures how many standard errors the   
> coefficient is away from zero. Generally, any t-value greater than   
> +2 or less than - 2 is acceptable. The higher the t-value, the   
> greater the confidence we have in the coefficient as a predictor.   
> Low t-values are indications of low reliability of the predictive   
> power of that coefficient.
>
>
> My problem is that I do not know how to compute the standard error   
> Sb of some regression coefficient, when I have done nothing more   
> than to use the lm command in this manner:
>
> Out = lm(A~ data$B + data$C + data$D)
>
>
> Does anyone know in detail, how R computes the t-value displayed in   
> summaries?
>
>
> Thank you very much,
>
> Peter
> --
>
> ______________________________________________
> R-help at stat.math.ethz.ch 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.
>
>


Disclaimer: http://www.kuleuven.be/cwis/email_disclaimer.htm

Thank you for the suggestion to use summary.lm. It does help.
Best Regards,
Peter
--

On Sat, 13 Jan 2007 algorithms at gmx.de wrote:
> My problem is that I do not know how to compute the standard error Sb of
some regression coefficient, when I have done nothing more than to use the lm
command in this manner:
>
> Out = lm(A~ data$B + data$C + data$D)
better make that
  Out <- lm(A ~ B + C + D, data = mydata)
and then
  summary(Out)
computes the usual t statistics. See the source code for what is exactly
computed. Several components of the summary also have their own extractor
function, e.g.
  coef(Out)
  vcov(Out)
extract the estimated coefficients and covariance matrix respectively.
Thus, you can compute the t statistics by hand via
  coef(Out) / sqrt(diag(vcov(Out)))

hth,
Z