Simulating Data with predefined reg-coefficients and R2

Try this:


# generate x's

x1 <- sample(100, 100, TRUE)
x2 <- sample(100, 100, TRUE)

# generate yhat with b0=1, b1=2, b2=3

yhat <- 1 + 2*x1 + 3*x2

# compute ssr

ssr <- sum( (yhat-mean(yhat))^2 )

# generate errors

e <- rnorm(100)
e <- resid( lm( e ~ x1 + x2 ) )

# to get R^2 of 0.8, ssr/(ssr+sse)=0.8 so sse=0.2/0.8*ssr

e <- e* sqrt(0.2/0.8*ssr/(sum(e^2)))

# now for y

y <- yhat + e

# put into a data frame and test

mydata <- data.frame( y=y, x1=x1, x2=x2 )
fit <- lm(y ~ x1 + x2, data=mydata )
summary(fit)


Now just change the values that you want changed to match your  
situation.  It does not matter how the x's are generated, so  
include more, include polynomials, include interactions, etc.

Hope this helps,


--
Gregory (Greg) L. Snow Ph.D.
Statistical Data Center
Intermountain Healthcare
greg.snow at imail.org
801.408.8111

-----Original Message-----
From: r-sig-teaching-bounces at r-project.org [mailto:r-sig-teaching-
bounces at r-project.org] On Behalf Of markus
Sent: Wednesday, November 19, 2008 1:19 AM
To: r-sig-teaching at r-project.org
Subject: [R-sig-teaching] Simulating Data with predefined reg-
coefficients and R2

Hi all at the R-teaching mailing list,
I am currently preparing my first  R-based  regression  course. Along
this way I encountered the following problem:

I want to simulate multivariate data that has some specific  
predefined
attributes. For example I want to produce a Predictor-matrix (X)
and a response-vector (y) that will yield a given vector of  
regression
coefficients (b) and a given R2 when I perform a multivariate linear
Regression
on the dataset. This would be best described by the well known  
equation
y=X*b+e.
In some next step I also want to simulate polynomic relationships,  
but
I
think that should work not very different.

I already searched the web and found some hints, but no clear answer.
There is a pdf out there from John H. Walker (Teaching Regression  
with
simulation)
which does however not discuss this special topic. I also have a  
Paper
from K.Baumann 'Chance Correlation in variable subset regression:
Influence of the objective function, selection mechanism and Ensemble
averaging' QCS, 2005. There an 'Autoregressive process' is used to
simulate such data.

Now my question is:
Is it really that difficult to simulate such data? Is there perhaps a
package in R facilitating at least parts of this work?

Thanks in advance for the help,
Markus