Allow me to add to Michael's and Clifford's responses.

If you fit the same regression model for each group, then you are also
fitting a standard deviation parameter for each model.  The solution
proposed by Michael and Clifford is a good one, but the solution assumes
that the standard deviation parameter is the same for all three models.

You may want to consider the degree by which the standard deviation
estimates differ for the three separate models.  If they differ wildly, the
method described by Michael and Clifford may not be the best.  Rather, you
may want to consider gls() in the nlme package to explicitly allow the
variance parameters to vary.

-tgs

On Mon, Sep 13, 2010 at 4:52 PM, Doug Adams <fog0@gmx.com> wrote:

> Hello,
>
> We've got a dataset with several variables, one of which we're using
> to split the data into 3 smaller subsets.  (as the variable takes 1 of
> 3 possible values).
>
> There are several more variables too, many of which we're using to fit
> regression models using lm.  So I have 3 models fitted (one for each
> subset of course), each having slope estimates for the predictor
> variables.
>
> What we want to find out, though, is whether or not the overall slopes
> for the 3 regression lines are significantly different from each
> other.  Is there a way, in R, to calculate the overall slope of each
> line, and test whether there's homogeneity of regression slopes?  (Am
> I using that phrase in the right context -- comparing the slopes of
> more than one regression line rather than the slopes of the predictors
> within the same fit.)
>
> I hope that makes sense.  We really wanted to see if the predicted
> values at the ends of the 3 regression lines are significantly
> different... But I'm not sure how to do the Johnson-Neyman procedure
> in R, so I think testing for slope differences will suffice!
>
> Thanks to any who may be able to help!
>
> Doug Adams
>
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