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From: "Bruno Luong" <brunoluong@yahoo.com>
Newsgroups: comp.soft-sys.matlab
Subject: Re: Is this kind of regression possible?
Date: Sat, 1 Dec 2007 21:24:23 +0000 (UTC)
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I'm not following this thread very closely (read diagonally,
it seems more to be a formalism problem rather than
mathematics or MATLAB).

But in case of over-determine system (more unknown than
data), using the backslash operator is rather risky. In
fact, the solution returned by "\" will have appropriate
number of zeros (number of unknown minus matrix rank), and
the position of these zeros are rather randomly set.

In the case of overdertermine linear system, using pinv() is
a better choice, because W=pinv(M)*Y is well defined. It's
the unique solution that verifies the two following conditions:

(i) M*W = Y
(ii) |W| is minimum among all W that satisfied (i).

Bruno