LinearModelFit with large number of coordinates

Question

I am sorry if this is on here already (or if it is really easy!) I have looked and I am not sure how to go about it. I have data that is 1000 rows and each row contains 200 columns (x1,x2,x3,...)

I am trying to do linear regression of the form $y=\sum_{i=1}^{200}a_ix_i$, however seem to be unable to input it into Mathematica, am I meant to be doing something along the lines of the following:

LinearModelFit[data, {x01, x02, x03, ..., x199, x200}, {x01, x02, x03, ..., x199, x200}]

This doesn't seem like it should be the best way to do it! Please let me know where I am going wrong...

Answer 1

Turning a great comment into an answer.

All linear models are of the form $\vec{y}=\hat{A}\vec{x}$ and $\vec{x}$ can be a long vector. While this problem can be put into a form LinearModelFit[{{x11,c12,...,y1},{x21,x22,...,y2},...},{f1,f2,...},{x1,x2,...}] it might be more useful to use another supported form LinearModelFit[{m,v}], where m is the design matrix and v is the response vector. See the examples in the LinearModelFit documentation.

You could solve your Least-Square problem directly by finding a pseudo inverse PseudoInverse[A], but LinearModelFit has useful additional features for giving you statistics of the residuals.