Re: st: about residuals and coefficients

[Ronan Conroy <rconroy@rcsi.ie>]

On 2013 MFómh 7, at 01:25, David Hoaglin wrote:

> 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.

Or, if writing for people who think in language: The coefficient of the predictor variable is the change we expect associated with a one-unit increase in the predicted variable, after we adjusted for the expected effect that this change will have on the other predictor variables in the model. 

Or can someone suggest a better way of phrasing this?

Purely pragmatically, I tend to teach the 'other things held constant' interpretation because it's a good first-pass in understanding multivariate models, and it's not doing any real-life violence to the interpretation of the data that I can see (has anyone examples where it's plain misleading?).



Ronán Conroy
rconroy@rcsi.ie
Associate Professor
Division of Population Health Sciences
Royal College of Surgeons in Ireland
Beaux Lane House
Dublin 2


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