[R] multiple linear regression with quadratic function

Bert Gunter bgunter.4567 at gmail.com
Tue Feb 23 17:05:54 CET 2016


-- Bert

Bert Gunter

"The trouble with having an open mind is that people keep coming along
and sticking things into it."
-- Opus (aka Berkeley Breathed in his "Bloom County" comic strip )

On Tue, Feb 23, 2016 at 2:42 AM,  <james.foadi at diamond.ac.uk> wrote:
> 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.

Not necessarily. It depends on how the error term enters the model.

I suggest you consult with a local statistician or post as Peter
suggested. You appear to be out of your statistical depth here.

> 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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