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Re: st: coefficient interpretation in OLS


From   Clive Nicholas <clivelists@googlemail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: coefficient interpretation in OLS
Date   Sun, 19 Aug 2012 07:36:56 +0100

David Hoaglin replied to Lynn Lee:

> In interpreting the coefficients in a multiple regression, two facts
> are important.
>
> 1. The definition of each coefficient includes the set of other
> predictors in the model.
>
> 2. The coefficient of a predictor, say X1, tells how Y changes in
> response to change in X1 after adjusting for the contributions of the
> other predictors in the model (in the data at hand).  A coefficient is
> a slope, so it gives change in Y per unit increase in X1, not
> necessarily the change in Y when X1 is increased by 1 unit (unless the
> values of X1 are only 0 and 1).  Some textbooks, unfortunately,
> interpret the coefficient of X1 as telling how Y changes with an
> increase of 1 unit in X1 when the other predictors are held fixed, but
> that is simply not how OLS works; that interpretation is
> oversimplified and often incorrect.
>
> Terry Speed's column in the current issue of the IMS Bulletin
> discusses both of these points.

I've had time to read Speed's article. The key quotation, on page 13,
appears to be:

"A lengthy but basically correct interpretation goes like this:
{b}_{12.3} tells us how X1 responds, on average, to change in X2,
after allowing for simultaneous linear change in X3 in the data at
hand."

This may well be right, but it reads and sounds like utter waffle.
Would you seriously explain an effect, as explained by its
coefficient, of a continuous variable on another continuous variable
in front of an audience in this way? I wouldn't, and nor would anyone
else I know. There has to be a simpler way of saying this that is also
correct.

If it has to be like this, I'd think I'd advise Lynn simply to say the
effect of this or that continuous variable is positive or negative and
leave it at that.

-- 
Clive Nicholas

[Please DO NOT mail me personally here, but at
<clivenicholas@hotmail.com>. Please respond to contributions I make in
a list thread here. Thanks!]

"My colleagues in the social sciences talk a great deal about
methodology. I prefer to call it style." -- Freeman J. Dyson
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