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I'm trying to work out how you do this from first principles. The Wikipedia page on linear regression gives me enough to solve it with matrix operations through the origin but I can't find much literature on implementing an algorithm for an OLS fit returning coefficients, a t-statistic and an $r^2$ value for the fit

Can anyone point me to good reference?

Thanks

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    $\begingroup$ Is the question about understanding the mathematics and/or mathematical formulas behind the mentioned quantities or is it about numerical algorithms to actually compute them? Strangely enough, they're very different questions. $\endgroup$ – cardinal Nov 5 '11 at 21:43
  • $\begingroup$ Both really. I'm primarily in need of implementing it, but I would like to understand the maths properly too. $\endgroup$ – Chris Nov 5 '11 at 22:38
  • $\begingroup$ Let me ask a question so that I understand yours better: Why do you need to implement it yourself? There are (many!) very good reasons not to do so, and instead to rely on available libraries and/or software packages with many tens (or hundreds) of thousands of man-hours already put into them. $\endgroup$ – cardinal Nov 5 '11 at 22:58
  • $\begingroup$ For the mathematical and statistical background of linear regression, any good linear-regression theory text will do. Here is a recent question where three are mentioned. $\endgroup$ – cardinal Nov 5 '11 at 23:03
  • $\begingroup$ Well, one because I feel implementing anything is a great way to understand it properly, and two because I can't find an existing implementation for the platform I require it. $\endgroup$ – Chris Nov 6 '11 at 10:28
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There are quite a few books that cover this.

My personal favourite is "Solving least squares problems" by Charles L. Lawson and Richard J. Hanson.

A more recent work is "Numerical methods for least squares problems" By Åke Björck.

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