On 04/12/2013 1:30 PM, David Winsemius wrote:
On Dec 4, 2013, at 8:56 AM, Duncan Murdoch wrote:
On 04/12/2013 11:36 AM, Jun Shen wrote:
Hi,
I have a dataset with two independent variables (x, y) and a response
variable (z). I was hoping to generate a response surface by
plotting x, y,
z on a three dimensional plot. I can plot the data with rgl.points(x, y,
z). I understand I may not have enough data to generate a surface.
Is there
a way to smooth out the data points to generate a surface? Thanks a lot.
There are many ways to do that. You need to fit a model that
predicts z from (x, y), and then plot the predictions from that model.
An example below follows yours.
Jun
===========================
An example:
x<-runif(20)
y<-runif(20)
z<-runif(20)
library(rgl)
rgl.points(x,y,z)
Don't use rgl.points, use points3d() or plot3d(). Here's the full
script:
x<-runif(20)
y<-runif(20)
z<-runif(20)
library(rgl)
plot3d(x,y,z)
fit <- lm(z ~ x + y + x*y + x^2 + y^2)
Newcomers to R may think they would be getting a quadratic in x and
y. But R's formula interpretation will collapse x^2 to just x and then
it becomes superfluous and is discarded. The same result is obtained
with z ~ (x + y)^2). I would have thought that this would have been
the code:
fit <- lm(z ~ poly(x,2) +poly(y,2) + x:y )
Oops, thanks for the correction. I had intended the full 2nd order
polynomial.
Duncan Murdoch
xnew <- seq(min(x), max(x), len=20)
ynew <- seq(min(y), max(y), len=20)
df <- expand.grid(x = xnew,
y = ynew)
df$z <- predict(fit, newdata=df)
surface3d(xnew, ynew, df$z, col="red")
With the modified fitting formula one sees a nice saddle (for that
particular random draw) using rgl.snapshot().
The result with the earlier formula is a more restrained:
Continued thanks to you Duncan for making this great tool available.
--
David.
Duncan Murdoch
David Winsemius
Alameda, CA, USA
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