R help - Feb 2016 - multiple linear regression with quadratic function

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

-- 
This e-mail and any attachments may contain confidential...{{dropped:16}}

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).

-pd

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
> 
> -- 
> This e-mail and any attachments may contain confidential...{{dropped:16}}
> 
> ______________________________________________
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> PLEASE do read the posting guide
http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
-- 
Peter Dalgaard, Professor,
Center for Statistics, Copenhagen Business School
Solbjerg Plads 3, 2000 Frederiksberg, Denmark
Phone: (+45)38153501
Office: A 4.23
Email: pd.mes at cbs.dk  Priv: PDalgd at gmail.com

Inline.

-- 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
>
> --
> This e-mail and any attachments may contain confidenti...{{dropped:8}}