-----Original Message-----

From: jsm_44092 [mailto:

tpr42345@...]

Sent: Monday, March 29, 2004 9:38 AM

because I don't have time, but when I see your discussions of the

regressions that you have run I am reminded of the fact that

regression coefficients really don't have any meaning for

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

nonorthogonal data, which of course is the type of data with which

^^^^^^^^^^^^^^^^^^

you are working. I believe there is a better approach. I see

that the UNC-G library has a copy of my regression book ("Modern

Regression Methods") and I suggest that you look at pages 472-475 of

my book. Some programming work would certainly be required,

especially for the number of predictors that you are using, but I

believe that the project would be doable. We can discuss this if you

want to go in that direction.

*** Our library does not have a copy of _Modern Regression Methods_

so I'm going to have to ask for clarification on this.

If by non-orthogonal data, you mean that some of the explanatory

variables are correlated with each other, then practically every

regression that's ever been run has non-orthogonal data.

And I don't understand how the coefficients don't have any meaning.

They have meaning in terms of marginal effects, holding all other

variables constant. If you mean that it's dangerous to extrapolate

from them, that's correct -- e.g. to apply them as average effects

would require strong assumptions about linearity. And to try to

assign percent of variation explained to individual explanatory

variables is also futile with non-orthogonal variables. But the

coefficients still have meaning.

Or maybe your comment is refering to a key assumption of the standard

least squares regression model: that the explanatory variables are

non-stochastic. When they do have randomness in them, things can

get bad, and when that randomness is correlated with the residual

term (or error term), then things get worse -- we have endogeneity,

aka simultaneity bias. But there are regression techniques for

dealing with these, if they truly are a problem (quite often they

are not, even when the explanatory variables do come from some

stochastic process).

I haven't had time to look in detail at DanR's regression results,

but regardless of what's in his results, I don't understand the

highlighted comment. Taken at face value, what you're doing is

trashing about a century of statistical work.

--MKT