[R] formula used by R to compute the t-values in a linear regression

[David Winsemius]

On Aug 1, 2011, at 9:27 AM, Samuel Le wrote:

> Hello,
>
>
> I was wondering if someone knows the formula used by the function lm  
> to compute the t-values.
>
> I am trying to implement a linear regression myself. Assuming that I  
> have K variables, and N observations, the formula I am using is:
>
> For the k-th variable, t-value= b_k/sigma_k
>
> With b_k is the coefficient for the k-th variable, and sigma_k  
> =(t(x) x )^(-1) _kk is its standard deviation.
>
> I find sigma_k = sigma * n/(n*Sum x_{k,i}^2 -(sum x_{k,i}^2))
>
> With sigma: the estimated standard deviation of the residuals,
>
> Sigma = sqrt(1/(N-K-1)*Sum epsilon_i^2)
>
> With:
>
> N: number of observations
>
> K: number of variables
>
> This formula comes from my old course of econometrics.
>
> For some reason it doesn't match the t-value produced by R (I am off  
> by about 1%). I can match the other results produced by R  
> (coefficients of the regression, r squared, etc.).

Usually such a small difference results from using different degrees  
of freedom. Have you reduced the df's appropriately after considering  
the number of other estimated parameters? Just quoting code from you  
econometrics reference is not enough to answer the question. We would  
need to see code... as the message states at the end of every posting.)

>
> I would be grateful if someone could provide some clarifications.
>
>
>
> Samuel
>
>
> 	[[alternative HTML version deleted]]
>
> ______________________________________________
> 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.

David Winsemius, MD
West Hartford, CT