Sorry I was not clearer, but I was asking an R programming question not a 
theory question. I will try to clarify. If I did this analysis with a dataset 
involving  just one subject the summary command on the lm object would give me 
a significance test on each parameter fit. The question in this cSe, is the 
cubic parameter significant? When I try to do this for each subject separately 
in a larger dataset using the by command, I get the parameter estimate but 
can't find a significance test. I apologize again for my poor explanation 
originally, 

> On Jan 24, 2015, at 10:04 PM, Jeff Newmiller <jdnew...@dcn.davis.ca.us> wrote:
> 
> R-square is often a poor indicator of whether a model is appropriate or not. 
> While it is possible that there exists a package that implements your 
> algorithm (which you might find using the sos package), I would recommend 
> that you get some advice from an expert on how to approach this subject, and 
> this list is not a good place for studying statistics theory (read the 
> Posting Guide). You might try stats.stackexchange. com. 
> ---------------------------------------------------------------------------
> Jeff Newmiller                        The     .....       .....  Go Live...
> DCN:<jdnew...@dcn.davis.ca.us>        Basics: ##.#.       ##.#.  Live Go...
>                                      Live:   OO#.. Dead: OO#..  Playing
> Research Engineer (Solar/Batteries            O.O#.       #.O#.  with
> /Software/Embedded Controllers)               .OO#.       .OO#.  rocks...1
> --------------------------------------------------------------------------- 
> Sent from my phone. Please excuse my brevity.
>> .
> 

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