[R] Definition of t-value

Dimitrios Rizopoulos Dimitris.Rizopoulos at med.kuleuven.be
Sat Jan 13 20:14:37 CET 2007

try this

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

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

I hope it helps.


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/

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
> --
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