[R] Regression w/ interactions

Frank E Harrell Jr f.harrell at Vanderbilt.Edu
Thu Apr 15 14:26:18 CEST 2010

Michael Dykes wrote:
> I have a project due in my Linear Regression class re: regression on a data
> set & my professor gave us a hint that there were *exactly *2 sig
> interactions. The data set is attached. We have to find which predictors are
> significant, & which 2 interactions are sig. Also, I nedd some guidance for
> this & selecting the best model. I tried the `full' model, that being:
> z=lm(y~x1+x2+x3+x4+x1*x2+x2*x3...+x3*x4). I then ran an anova(z), &
> summary(z). My R^2 & R^2_a were *really* low. I am not sure how to do PRESS,
> AIC & Cp in R yet though. Any help would be appreciated.

Michael this is not really the place for help on homework other than 
perhaps on technical roadblocks.  Note that the strategy you are being 
told to follow is one whose statistical properties have been severely 
criticized in the statistical literature.  Only with a very high signal 
to noise ratio (e.g., high true R^2) can torturing data lead to a 
confession to something other than what the analyst wants to hear.  I 
suppose that in simulated data there is a "true" model out there waiting 
to be found, but beware of using this approach with real data with low 
signal to noise ratios.


Frank E Harrell Jr   Professor and Chairman        School of Medicine
                      Department of Biostatistics   Vanderbilt University

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