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.
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.
