Re: Re: st: about residuals and coefficients

[David Hoaglin <dchoaglin@gmail.com>]

Charley,

I usually suggest the following wording: The coefficient of Xj is the
average change in Y per unit increase in Xj after adjusting for
simultaneous linear change in the other predictors in the model in the
data at hand.  It would be nice to have something simpler, but in
general nothing simpler will do.  I suggest "per unit increase in Xj"
because the coefficient is a sort of slope, and a change of one unit
may not be meaningful in the particular set of data.

Once people (e.g., students) have absorbed that wording, it often
suffices to shorten it to "the contributions of the other predictors"
and omit the reminder "in the data at hand."

Language that uses "held constant" and "controlling for"
oversimplifies the interpretation and is often incorrect.

A search for causal associations is one purpose of regression, but by
no means the only purpose.

David Hoaglin

On Fri, Sep 6, 2013 at 6:17 PM, Charley Greenwood
<Charley.Greenwood@coffey.com> wrote:
> I wonder if people think this is a reasonable description of the interpretation of regression coefficients:
>
> - The difference in Y associated with a unit increase in X, adjusted for Y's associations (likewise adjusted) with "any other Xs in our model that tend to change at the same time as X (according to our data)".
>
> It's not very catchy, but it's consistent with using regression coefficients to look for good candidates for causal associations which I think is what most people who ask for a definition are interested in doing.
>
> A problem with shorter formulations may be that people tend to hear 'effects' and 'contributions' as implying causality even when they are being used as shorthands for associations.
*
*   For searches and help try:
*   http://www.stata.com/help.cgi?search
*   http://www.stata.com/support/faqs/resources/statalist-faq/
*   http://www.ats.ucla.edu/stat/stata/