Your national pride does you credit. Gauss was one
of the greats, and he may have used "eigenvalue"
or its equivalent, but I don't know for sure -- do
you really, or are you guessing?
It is hard to be certain with Gauss, because of
his brilliance, but I doubt that he used the
general linear model as we now know it, and
although he did solve least squares equations, he
may not have have invented the technique --
Legendre was the first to publish in 1809. No one
has been able to verify Gauss' use of least
squares before Legendre, because he either made
calculational errors in his analysis or used
something other than least squares. Gauss often
said in his later years upon being shown a new
technique, that he had used it himself but had not
published. Who is to say.
However, your 10DM bill to the contrary, Gauss was
not the first to use the normal distribution:
DeMoivre used it as an approximation the the
binomial about 50 years before Gauss was born.
The thrust of Fisher's ANOVA was in the
partitioning of sums of squares and in the use of
significant tests there upon -- brilliant ideas.
The fact that some of the computations can be done
with linear models does not make the procedures
equivalent, and Fisher's early papers clearly show
that he was well aware of the connection.
Calculation was no great problem. Pearson once
said, while twiddling the handle of his
calculator, that he had never encountered a
calculation too difficult for him; and his tables
of various functions are still as extensive and as
accurate as any produced by modern computers.
I can't find a paper by anyone named Cohen with a
title resembling what you give in CIS. Perhaps you
can improve the citation.
<Karl,
<yes it is as German as your name.Value means
"Wert" and eigenvalue means "Eigenwert" and I
<guess it goes back to Carl Friedrich Gauss
<who provided us with many math concepts,i.e.
matrix algebra among many others.
<In Germany we honor him very much.His portrait is
on our 10 DM bill,with the normal curve <and its
equation. In teaching statistics, I always
<use that bill to remind my students where all
this stuff comes from.
<If we had had computers earlier, Sir Ronald
Fisher would probably not have to develop <ANOVA,
because of the general linear model Gauss
<developed,but inverting the
<correlation matrix to get the effects was too
complicated to compute by hand,so Sir Ronald
<developed the ANOVA shortcut. Later Jack
<Cohen showed in his seminal paper " Multiple
regression as a general data analytic system"
<that using the general linear model does the
<job.
<I'm always teasing my colleagues and students, if
you spent one year learning ANOVA and one <year
multiple regression you've wasted
<almost one year of your life.
<Cordially yours
<Werner
<Werner W. Wittmann; University of Mannheim;
Germany;
<e-mail: [EMAIL PROTECTED]
--
Bob Wheeler --- (Reply to: [EMAIL PROTECTED])
ECHIP, Inc.
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