[R] multiple linear regression with quadratic function

[james.foadi at diamond.ac.uk]

Dear R community,
this is probably a well-known topic to some of you, but I am not well into it
and would like some clarifications or even jus some suggestions.

I have a quadratic scalar field:

        F(x,y)=K*exp(-(a*x^2+b*y^2+c*x*y))

I also have a random set of positive x,y values and related F(x,y) values.
It seems reasonable to estimate the parameters K, a, b, c with a linear regression,
using the log of both sides of the equation.

What worries me, though, is the interaction term, c*x*y.

Are there well-known issues on the application of linear regression to cases like this one?

Thanks in advance for your answers.

James

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