Date: Dec 8, 2012 9:38 PM
Author: Halitsky
Subject: One other possibly worthwhile observation regarding the term u*e in<br> the regression c on (e,u,u^e,u^2)
I am hopeful that you?ll agree it?s worth compiling the ordered p

tables for the term u*e of c on (e.u,u*e,u^2), for the following

reason.

By simple rotation of coordinates, it is possible to show that

hyperbolic paraboloids not only have equations like z = y^2-x^2 but

also equations like z = xy.

http://mathworld.wolfram.com/HyperbolicParaboloid.html

Hence the term u*e in c on (e,u,u^e,u^2) can actually be interpreted

as a quadric (not quartic!) term in the same sense that the term u^2

of this regression can be interpreted as a quadratic term.

And therefore, buried inside this regression is the (c,e,u) 3-space

whose orthonormal transformation we were recently dicussing, i.e. a 3-

space that projects into a 2-space that again becomes a 3-space with

the addition of L.

So looking at u*e as a ?quadric? term may not only help elucidate the

relation of L to (c,e,u), but may also prove very useful in reducing

the arbitrarines of the way in which Bob Lewis generates quardric

surfaces from n-tuples of slopes and intercepts.

Unless, of course, there?s a statistical reason why looking at u*e as

a quadric term would throw a monkey wrench into everything.

In which case, I?d be curious to know what the monkey wrench is.