OK, a simple answer:
Given heteroscedastic data, the least-squares method will put
undue emphasis on trying to fit the line to the widely-scattered part
of the plot.
This is especially troublesome when:
(a) the wide scattering occurs near one or both ends
(b) the sample size is small
(c) the assumption of a linear fit is not perfectly satisfied.
(there may be other danger signs I can't think of atthe moment,
but these will do.)
(a) is the most usual form of heteroscedasticity. However, when
the data are plentiful throughout the range, we can hope for decent
results even in such a situation.
Similarly, _if_ you have a "bulge in the middle" - _not_ the usual
rotundity of the bivariate normal (or similar) scatterplot that
reflects only a higher density of X values near the middle - you may
be comparatively safe, as it is harder to translate a fit line than it
is to twist it.
In the presence of nonlinearity, you will almost always have
problems. There may be situations where the Right Thing To Do is
indeed to fit a straight line to nonlinear data - say in a situation
where simplicity counts for more than accuracy. But usually
nonlinearity means "find the right model and start again."
-Robert Dawson
===========================================================================
This list is open to everyone. Occasionally, less thoughtful
people send inappropriate messages. Please DO NOT COMPLAIN TO
THE POSTMASTER about these messages because the postmaster has no
way of controlling them, and excessive complaints will result in
termination of the list.
For information about this list, including information about the
problem of inappropriate messages and information about how to
unsubscribe, please see the web page at
http://jse.stat.ncsu.edu/
===========================================================================
