"...the sum of squares removed by fitting..."
- From: kj <socyl@xxxxxxxxxxxxxxxxx>
- Date: Tue, 26 Sep 2006 18:58:18 +0000 (UTC)
On p. 63 of W. J. Ewens' "Mathematical Population Genetics, v. 1",
the author uses the phrase "the sum of squares removed by fitting",
which I don't understand. FWIW here's the full sentence, rendered
in bright LaTeX:
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}
The context is the computation of a set of coefficients $\alpha_1,
...., \alpha_k$, called the "average effects", by a least-squares procedure.
I can *guess* possible meanings for what the author's phrase, but
in any can't figure out how to derive the expression above. The
author says this stuff is standard, but I can't find it in my stats
book (it could be there under a different guise, though). Where
can I find a more explicit derivation of this "sum of squares
removed by fitting"?
TIA!
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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