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Performing regression using R & C

It is probably not worth trying to call R to do OLS from C.  I would 
look at GSL:

http://www.gnu.org/software/gsl/manual/gsl-ref_toc.html

GSL has a simple but elegant C interface for doing OLS and weighted 
least squares.  It will give you the covariance matrix of the model 
parameters, from which you can derive t-stats.

Jim M