Coding cubic and quadratic regression with 2 variables

[Medel Valiente]

Variables: fingerlings (number), credit, equity
If quadratic regression is coded as

regress fingerlings credit credit2

where, credit2 is credit*credit
And cubic regression is coded as

regress fingerlings credit credit2 credit3

where credit3 is credit*credit2

How should i code quadratic and cubic regression with both credit and equity in play.

Thanks.

[Clyde Schechter]

It isn't clear what you want when you speak of "equity in play." But first, let me suggest you use factor-variable notation instead of creating higher-order terms. Your cubic model shown in #1 can be more compactly handled as:

regress fingerlings c.credit##c.credit##c.credit

Returning to "equity in play," I don't grasp whether you just want to add a polynomial involving equity, or if you also want cross-product terms between equity and credit. If you just want to add an equity polynomial (and go up to 4th degree in both variables):

regress fingerlings c.credit##c.credit##c.credit##c.credit c.equity##c.equity##c.equity##c.equity

does that.

If you want all possible crossproduct terms between credit and equity as well:

regress fingerlings c.(credit equity)##c.(credit equity)##c.(credit equity)##c.(credit equity)

All of that said, before you proceed, I suggest you consult with an expert in your discipline about this model. There are very few things in the real world that follow high-degree polynomials. Even quadratic models are usually very crude approximations used just for their mathematical simplicity; usually they are mediocre descriptions of the actual data generating process, or worse. (Motion of a particle in a constant force field is the rare exception to this rule.) So I would discuss this with somebody very knowledgeable in your discipline to verify that a model of this nature is plausible.