I need a good algorithm! (Regression related)

[CallMeIshmael]

Ive got a bunch of data, in the form

[ a1 a2 a3 .. an a(n+1)]
[ b1 b2 b3 .. bn b(n+1)]
[ c1 c2 c3 .. cn c(n+1)]
...

I want to find the best set of n coefficients so that the sum of (coefficient*letter) for the first n terms predicts the last term. Im not really sure what the name for this is, but its some kind of regression.


Does anyone have any suggestion for places to look for an algorithm for this type of problem? Or some other point in the right direction?


To note: Im looking at a lot of data here, so Im thinking the slower stuff like matlab/R (despite the built in functions for this) wont do it fast enough, and I'll be looking to do it in C.