[R] multiple linear regression with quadratic function

peter dalgaard pdalgd at gmail.com
Tue Feb 23 11:59:10 CET 2016

That's pretty standard. Some call it "response surface analysis". Of course you need to check assumptions like homoscedasticity on the log scale, etc.

It's not really an R question, specifically; so stats.stackexchange.com is a better avenue for more detailed discussions. As far as R goes, you just need to be aware that, due to an ancien misfeature, terms like x^2 need to be protected by writing I(x^2). 


On 23 Feb 2016, at 11:42 , <james.foadi at diamond.ac.uk> <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.
> 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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Peter Dalgaard, Professor,
Center for Statistics, Copenhagen Business School
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