R help - Dec 2006 - stat question - not R question so ignore if not interested

If do a scattrplot of data ( x and y ) and there are two clouds of
points. One cloud is in the left
bottom corner of the plot and the other cloud is in the upper right.

If I fit a regression line to this data ( or equivalently , calculate a
correlation ), then obviously, it is going to seem like
x and y are related because a line has to be connected between the 2
clouds. But, there must be a regression assumption that
is violated here because if the regressions are done separately on each
cloud, then there really isn't
a relationship between x and y. I was just wondering 1) what assumption
in regression is being violated in
the first case or 2) possibly if the regression is valid and the results
just have some different interpreation ? 
Thanks.

 
Mark
--------------------------------------------------------

This is not an offer (or solicitation of an offer) to buy/se...{{dropped}}

The missing piece is why there are two clusters.  There is
most likely a two-level factor distinguishing the groups
that was not included in the model.  It might not even have
been measured and now you need to find it.

Rich

A classic example used by my colleague Paul Rozin (when he
teaches Psych 1) is to compute the correlation between height
and number of shoes owned, in the class.  Shorter students own
more shoes.  But ...

On 12/05/06 16:34, Richard M. Heiberger wrote:
> The missing piece is why there are two clusters.  There is
> most likely a two-level factor distinguishing the groups
> that was not included in the model.  It might not even have
> been measured and now you need to find it.
> 
> Rich
-- 
Jonathan Baron, Professor of Psychology, University of Pennsylvania
Home page: http://www.sas.upenn.edu/~baron
Editor: Judgment and Decision Making (http://journal.sjdm.org)

On Dec 5, 2006, at 3:42 PM, Leeds, Mark ((IED)) wrote:
> If do a scattrplot of data ( x and y ) and there are two clouds of
> points. One cloud is in the left
> bottom corner of the plot and the other cloud is in the upper right.
>
> If I fit a regression line to this data ( or equivalently ,  
> calculate a
> correlation ), then obviously, it is going to seem like
> x and y are related because a line has to be connected between the 2
> clouds. But, there must be a regression assumption that
> is violated here because if the regressions are done separately on  
> each
> cloud, then there really isn't
> a relationship between x and y. I was just wondering 1) what  
> assumption
> in regression is being violated in
> the first case or 2) possibly if the regression is valid and the  
> results
> just have some different interpreation ?
One needs only to look at diagnostic plots:

Suppose
set.seed(2)
xy <- data.frame(y = c(rnorm(300), rnorm(300, 5)), x = c(rnorm(300),  
rnorm(300, 5)))
op <- par(mfrow = c(2,2))
plot(lm(y ~ x, xy))
par(op)

The model does not fit well because the residuals aren't flat as a  
function of fit and because homoscedasticity is violated.

When this happens we might try a different approach:
require(sm)
xy.sm <- sm.regression(xy$x, xy$y)

Whenever there's a big discrepancy between an OLS fit and a robust  
one, we should not pursue the OLS one w/o reinterpretation, which  
others have discussed in their replies.
_____________________________
Professor Michael Kubovy
University of Virginia
Department of Psychology
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