On Nov 21, 8:13 pm, djh <halitsk...@att.net> wrote: > In a different thread, Ray Koopman explained that if one > suspects these regressions to be dependent on the IV ?u?: > > c on u > c on e > c on (e,u) > > then under the usual initial assumption that the dependence > is linear, these three regressions should be modified to: > > c on (u, u^2) instead of c on u > c on (e, u, u*e) instead of c on e > c on (e, u, u*e, u^2) instead of c on (e,u)
In this post I want to talk about only your third case:
y = a0 + a1*x1 + a2*x2 + a3*x1*x2 + a4*x2^2.
(As before, I use the usual generic variable names so as not to get caught up in any peculiarities of your particular variables.)
One interpretation of the model is that y is a linear function of x1 and x2: y = A0 + A1*x1 + A2*x2, with A0, A1, and A2 all being linear functions of x2. (I'll let you do the algebra; it parallels that in the first two models.) Note that this model does not treat x1 and x2 symmetrically: it matters which x is 1 and which is 2.
There are two average slopes. Call them Av1 and Av2: