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MathGroup Archive 2006

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"the sum of squares removed by fitting..."?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg69919] "the sum of squares removed by fitting..."?
  • From: kj <socyl at 987jk.com.invalid>
  • Date: Wed, 27 Sep 2006 06:05:23 -0400 (EDT)

In a textbook I'm reading ("Mathematical Population Genetics, v.
1" by W. J. Ewens) there's a line I can't follow at all.  The
context is the problem of determining a certain set of coefficients,
called "average effects" and denoted $\alpha_j$ below, by performing
a constrained minimization.

I'll quote the problematic passage, even though, out of context,
some references won't mean much.  (If anyone cares to read the
preceding text, one can view the page in question using Amazon's
search feature for this book.  The passage I quoted is on p. 63.)
Using LaTeX notation:

  Standard regression theory shows that the sum of squares removed
  by fitting the $\alpha_j$ values in (2.57), that is the additive
  genetic variance $\sigma_A^2$, is given by
  \begin{equation}
  \sigma_A^2 = 2 \sum_u x_u a_u \alpha_u .
  \end{equation}

I'm hoping that the expression "sum of squares removed by fitting"
is sufficiently common that someone may be able to tell me what
the author means.

Even though the author describes the result above as "standard",
I can't find anything in my stats book that resembles it (though
it could very well be there under a different guise).  Could someone
point me to a reference that would more explicitly explain how one
derives this "sum squares removed by fitting"?

Thanks!

kj

-- 
NOTE: In my address everything before the first period is backwards;
and the last period, and everything after it, should be discarded.


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