R help - Mar 2005 - Surface plot for polynomial regression

Dear R-experts,

my goal is to visualize the following polynomial regression as a 3D-surface:

Z = b0 + b1*X + b2*Y + b3*XY + b4*X^2 + b5*Y^2

I believe that a solution to this problem may be of interest to a wider
range of scientists because the problem is a derivative of a more general
problem, i.e.: how to describe the relationship between one dependent
variable and the DIFFERENCE between two other variables. There are numerous
problems associated with difference scores (e.g., reliability). One
suggested alternative consists of using the components of the difference
score separately in polynomial regression. So this is how I ended up with
the above regression, which is essentially a reformulation of b1*(X-Y)^2.

After consulting the help pages and archives my best guess was that the
function scatter3d could be rewritten in part to produce the desired output.
In fact, the quadratic fit output of the scatter3d function comes closest to
what I have in mind. However, I think the XY term is missing from the
quadratic fit equation. When I use wireframe to visualize the raw data,
there is a peak of the dependent variable when both X AND Y are high. Yet
this peak does not appear in the quadratic fit of scatter3d.

Any pointers would be welcome. I should add that I am not a programmer and
mainly work with high-level functions.

Thank you very much for R and for your help

Johannes

           Dipl.-Psych. Johannes Ullrich
            Philipps-Universit?t Marburg
                                 Germany

Please note there is no `scatter3d' function in R.
There is one in John Fox's package Rcmdr: please give credit where it is 
due.

However, I think you have overlooked functions like persp, image, contour, 
cloud wireframe and levelplot (lattice), all of which can plot any 
function of two variables and whose examples (and some of the demos) show 
you how.  You might also want to look at rgl.surface (package rgl).

On Thu, 31 Mar 2005, Johannes Ullrich wrote:
> Dear R-experts,
>
> my goal is to visualize the following polynomial regression as a
3D-surface:
It is a 2D surface, by any reasonable definition of `dimension'.
> Z = b0 + b1*X + b2*Y + b3*XY + b4*X^2 + b5*Y^2
>
> I believe that a solution to this problem may be of interest to a wider
> range of scientists because the problem is a derivative of a more general
> problem, i.e.: how to describe the relationship between one dependent
> variable and the DIFFERENCE between two other variables. There are numerous
> problems associated with difference scores (e.g., reliability). One
> suggested alternative consists of using the components of the difference
> score separately in polynomial regression. So this is how I ended up with
> the above regression, which is essentially a reformulation of b1*(X-Y)^2.
>
> After consulting the help pages and archives my best guess was that the
> function scatter3d could be rewritten in part to produce the desired
output.
> In fact, the quadratic fit output of the scatter3d function comes closest
to
> what I have in mind. However, I think the XY term is missing from the
> quadratic fit equation. When I use wireframe to visualize the raw data,
> there is a peak of the dependent variable when both X AND Y are high. Yet
> this peak does not appear in the quadratic fit of scatter3d.
>
> Any pointers would be welcome. I should add that I am not a programmer and
> mainly work with high-level functions.
>
> Thank you very much for R and for your help
>
> Johannes
>
>           Dipl.-Psych. Johannes Ullrich
>            Philipps-Universit?t Marburg
>                                 Germany
>
> ______________________________________________
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http://www.R-project.org/posting-guide.html
>
-- 
Brian D. Ripley,                  ripley at stats.ox.ac.uk
Professor of Applied Statistics,  http://www.stats.ox.ac.uk/~ripley/
University of Oxford,             Tel:  +44 1865 272861 (self)
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