Sorry? The natural generalization of a mean to a 2-dimensional space
is surely the vector mean, which is a point.
-Robert Dawson
Perhaps I should be more careful with my language, but you know how mania is
<grin>. Would it help if I replaced "mean" with "least squares estimator of
individual Y given the individual's value(s) on all remaining (k-1)
variables in k-dimensional space? Or might that confuse my students? Are
there objections to the generalization in that case? In Cartesian space,
the regression LINE is that which minimizes the sum of squared deviations
(in the Y dimension) about it. If we drop the X dimension, our least
squares estimator of Y becomes the mean, the POINT which minimizes the sum
of squared deviations about it. If instead of dropping X we add X2, our
regression surface is a plane in three dimensional space, .................
In Abbot's fanciful tale, Flatland is inhabited by men, who,
according to their social status, are triangles, squares, or polygons, and
women who are straight lines. The women can makes themselves almost
invisible by rotating to the perpendicular, and in such an orientation
present a threat to any man who might run into her point. Under law, they
must wiggle their ends so that the men can see them and avoid such danger.
Silly, yes. Sexist, yes. Latest edition written in 1884. A Flatland
resident has a vision of Lineland (a one-dimensional world). Here men are
small lines and women points, but inhabitants see both as points, so mating
can be tricky. The inhabitant of Flatland is visited by an inhabitant of
(three-dimensional) Spaceland. As you can imagine, it is quite difficult
for the Flatlander to understand the Spacelander's description of his world.
============================================================
"Wuensch, Karl L." wrote (inter alia):
>
> If you have read Edwin Abbott's "Flatland," you might recognize
that the
> same concept (a mean) which looked like a point in one dimensional
space now
> looks like a line in two dimensional space. Then you would be
ready to leap
> into three dimensional space and even beyond, into hyperspace, but
you might
> want to sit down and have a good beer first. I promise that we
shall travel
> that space before the semester is out (as soon as we get started
on multiple
> regression).
Sorry? The natural generalization of a mean to a 2-dimensional space
is surely the vector mean, which is a point.
-Robert Dawson
+++++++++++++++++++++++++++++++++++++++++
Karl L. Wuensch, Department of Psychology,
East Carolina University, Greenville NC 27858-4353
Voice: 252-328-4102 Fax: 252-328-6283
[EMAIL PROTECTED] <mailto:[EMAIL PROTECTED]>
http://core.ecu.edu/psyc/wuenschk/klw.htm
<http://core.ecu.edu/psyc/wuenschk/klw.htm>
----------
From: Robert J. MacG. Dawson [SMTP:[EMAIL PROTECTED]]
Sent: Tuesday, October 10, 2000 8:01 AM
To: Wuensch, Karl L.
Cc: 'edstat'
Subject: Re: memorizing formulas
"Wuensch, Karl L." wrote (inter alia):
>
> If you have read Edwin Abbott's "Flatland," you might recognize that the
> same concept (a mean) which looked like a point in one dimensional space
now
> looks like a line in two dimensional space. Then you would be ready to
leap
> into three dimensional space and even beyond, into hyperspace, but you
might
> want to sit down and have a good beer first. I promise that we shall
travel
> that space before the semester is out (as soon as we get started on
multiple
> regression).
Sorry? The natural generalization of a mean to a 2-dimensional space
is
surely the vector mean, which is a point.
-Robert Dawson
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