Thanks to Berwin and Peter for their replies. The following code
clarifies what's going on in Peter's example. I shall upodate my
intuition!
x1 <- runif(100,8,10)
x2 <- x1^2
y <- (x1-9)^2+rnorm(100,sd=.1)
opar <- par(mfrow=c(2,2), las=1)
plot(x1, y, main="x1 Only")
plot(residuals(lm(x1~x2)), residuals(lm(y~x2)),
main="Added-Variable Plot for x1")
plot(x2, y, main="x2 Only")
plot(residuals(lm(x2~x1)), residuals(lm(y~x1)),
main="Added-Variable Plot for x2")
par(opar)
## Using Lattice graphics
require(lattice)
cloud(y ~ x1 * x2)
## Using RGL graphics (with brute force scaling)
require(rgl)
rgl.clear("all")
rgl.bg(sphere = TRUE, color = c("black", "green"),
lit = FALSE, size=2, alpha=0.2, back = "lines")
rgl.light()
rgl.bbox()
x1 <- runif(100,8,10) * 10
x2 <- (x1/10)^2
esty <- ((x1/10-9)^2 + rnorm(100,sd=.1)) * 20
rgl.spheres(x1, esty, x2,
color="gray", radius=0.5,
specular="green",
texture=system.file("textures/bump_dust.png",package="rgl"),
texmipmap=T, texminfilter="linear.mipmap.linear")
Cheers
Andrew
On Fri, Mar 31, 2006 at 12:09:14PM +0200, Peter Dalgaard wrote:
> Berwin A Turlach <[EMAIL PROTECTED]> writes:
>
> > Don't know if the following example, which shows the same behaviour,
> > leads to any insight.
> >
> > > n <- 100
> > > x1 <- runif(n, -1,1)
> > > x2 <- runif(n, -1,1)
> > > y <- x1*x1*x2 + rnorm(n, sd=0.05)
> > > y <- y - mean(y)
> > > anova(lm(y~x1+x2))
>
> Here's another (paraphrased from the Pixel data in nlme, which have
> similar behaviour)
>
> x1 <- runif(100,8,10)
> x2 <- x1^2
> y <- (x1 - 9)^2 + rnorm(100, sd=.1)
> plot(x1, y)
> anova(lm(y ~ x1 + x2))
> anova(lm(y ~ x2 + x1))
> summary(lm(y ~ x1))
> summary(lm(y ~ x2))
> summary(lm(y ~ x1 + x2))
>
>
> --
> O__ ---- Peter Dalgaard ?ster Farimagsgade 5, Entr.B
> c/ /'_ --- Dept. of Biostatistics PO Box 2099, 1014 Cph. K
> (*) \(*) -- University of Copenhagen Denmark Ph: (+45) 35327918
> ~~~~~~~~~~ - ([EMAIL PROTECTED]) FAX: (+45) 35327907
--
Andrew Robinson
Department of Mathematics and Statistics Tel: +61-3-8344-9763
University of Melbourne, VIC 3010 Australia Fax: +61-3-8344-4599
Email: [EMAIL PROTECTED] http://www.ms.unimelb.edu.au
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