Re: efficient computation of many univariate least squares fits
- From: Paul Rubin <rubin@xxxxxxx>
- Date: Wed, 15 Apr 2009 19:36:13 -0400
john.tramuta@xxxxxxxxxxxxxx wrote:
How would I use the QR to efficiently compute *all* the p times q
univariate regressions, with a t-test for each?
For each X variable, compute M'M, factor it, then for each Y solve (M'M)B=M'Y for B using the factored form of M'M (unless MATLAB, or whatever you're using, automatically solves inconsistent systems using L2 approximation -- see my response to Greg). Since M'M is 2x2, though, I'm not sure factorization really is necessary.
To do the t-tests, you need the diagonal entries of the inverse of M'M.
The suggestion in a different subthread to use the master correlation matrix may be a good alternative, particularly if (a) you're using something that has a built-in (efficient) routine for calculating correlations and (b) it has a built-in t-test (z-test?) for the significance of the correlations. The one caveat there is that if you ask for the correlation matrix of the nx(p+q) matrix of X's and Y's, you'll get (and pay for) the p(p-1) correlations of X's with other X's and the q(q-1) correlations of Y's with other Y's, which do not benefit you at all. If there's a routine that will compute the pxq matrix of X-Y correlations only (and test them), that's a good choice.
/Paul
.
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- From: john.tramuta@xxxxxxxxxxxxxx
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- From: Paul Rubin
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- Re: efficient computation of many univariate least squares fits
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