Date: Dec 8, 2012 9:38 PM
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
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.
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.