Re: st: about residuals and coefficients

[David Hoaglin <dchoaglin@gmail.com>]

Ronan,

I continue to prefer "per unit increase" since a regression
coefficient is a type of slope.  In a particular application an actual
increase of one unit may be too large or too small to be meaningful.
The exception, of course, arises when the predictor is an indicator,
whose values are only 0 and 1.

The language about the expected effect of the change on the other
predictors in the model may not reflect the associations among the
predictors.

I do not understand teaching the "other things held constant"
interpretation.  First impressions are often powerful.  It seems a
disservice to students to teach them an interpretation that is flawed.
 It simply does not reflect the way that multiple regression works.

David Hoaglin

On Sat, Sep 7, 2013 at 7:16 AM, Ronan Conroy <rconroy@rcsi.ie> wrote:
> 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

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