# Re: st: Interaction term in OLS regression

 From Robert A Yaffee To statalist@hsphsun2.harvard.edu Subject Re: st: Interaction term in OLS regression Date Sun, 08 Feb 2009 11:46:59 -0500

```Antonio,
If scatterrplots reveal that the functional form of these variables
are linear, then there is no need to include polynomial terms.
The main effect may not be statistically significant, owing to the
ratio of the contribution to the R^2 contributed by the c not being at least
1.96 times its std error.  The interaction with the f variable means that
the joint (multiplicative) effect of c*f over and above the individual main
effects (c and f taken separately) is significantly different at different levels of
c.
These joint effects exhibit sufficiently large differences in their contribution to
the slope (trend) over their standard error to obtain statistical significance.
Plotting different  levels of the c or f against the other interacting variable
should reveal this phenomenon.
Regards,
Bob

Robert A. Yaffee, Ph.D.
Research Professor
Silver School of Social Work
New York University

Biosketch: http://homepages.nyu.edu/~ray1/Biosketch2008.pdf

CV:  http://homepages.nyu.edu/~ray1/vita.pdf

----- Original Message -----
From: Antonio Silva <asilva100@live.com>
Date: Sunday, February 8, 2009 9:00 am
Subject: st: Interaction term in OLS regression
To: Stata list <statalist@hsphsun2.harvard.edu>

> List: sorry for the earlier post that did not have a subject line. My
> mistake. Here is the original post:
>  Hello Statlist:
>
> I have an OLS model that looks like this: y = constant + b + c + d + e
> + f. c is the variable in which I am most interested.
> In the basic model, c turns out NOT to be significant (it is not even
> close). However, when I include an interaction term in the model, c*f,
> c turns out to be highly significant.
> So the new model looks like this: y = constant + b + c + d + e + f +
> c*f. The interaction term, c*f, is highly significant as well (though
> in many versions f is NOT significant). My question is this: Is it
> defensible JUST to report the results of the fully specified
> model--that is, the one with the interaction? I kind of feel bad
> knowing that the first model does not produce the results I desire (I
> am very happy c ends up significant in the full model--it helps
> support my hypothesis). I have heard from others that if the variable
> of interest is NOT significant without the interaction term in the
> model but IS significant WITH the interaction term, I should either a)
> report the results of both models; or b) assume the data are screwy
> and back away... What do you all think?Thanks so much.Antonio Silva
> Anyway, I received several good responses. And here are my responses
> to those responses. Any further feedback is appreciated.
> First, OLS seems appropriate, though I udnerstand the desire to do
> something more. The DV is a continuous variable that is normally distributed.
> Diagnostics show the model works well... So I really don't think any
> other method makes sense here.
> Second, the interaction is exactly what the theory holds, which is
> nice. I guess my confusion lies here...why would the variable not
> be significant without the interaction term included? Th etheory holds
> that c would affect everyone, but would affect
> different values of f differently. So I would expect that the model
> without the interaction would also produce some good
> results on c, but it does not.
>
> Thanks again...
>
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