Date: Dec 11, 2012 5:58 PM
Author: Ray Koopman
Subject: Re: Results of p's obtained by referring Q’s to th<br>	e chi-square distribution.

On Dec 10, 8:54 pm, djh <> wrote:
> I am sending off-line 2 files:
> Cubque2.csv: u*e p?s from referral of Q?s to chi-square dist
> Cubquq2.csv: u^2 p?s from referral of Q?s to chi-square dist
> They both have the column headers:
> Set 1,2,3
> Fold a1,a3,b1,b47,c1,c2
> Coeff ?Cubquq? (u^2) or ?Cubque? (u*e)
> Qdf df | set, fold
> Q_nS Q for S,N | set, fold
> Qp_nS p for S,N | set, fold
> Q_nC Q for C,N | set, fold
> Qp_nC p for C,N | set, fold
> Q_rS Q for S,R | set, fold
> Qp_rS p for S,R | set, fold
> Q_rC Q for C,R | set, fold
> Qp_rC p for C,R | set, fold
> With respect to these files, suppose we agree that a p for S,N is
> ?acceptable? only if it is < .05 AND it is also less than all three of
> p for C,N, p for S,R, and p for C,R for the same set and fold.

Are you saying that you want the coefficients to be nonzero for C,N
and either smaller or (preferably) zero in the three other cells?
If so then you need to look at the coefficients, as well as the Qp's.
Q is the test statistic for the hypothesis that all the coefficients
are zero. A small Qp says only that the data are not consistent with
that hypothesis. Comparing Qp's doesn't tell you anything interesting.

> Then if you examine the files Cubque2.csv and Cubquq2.csv, you?ll see
> that the only fold x set pairs that satisfy this condition for both
> u^2 and u^e are:
> p for S,N
> Fold Set u*e u^2
> a1 1 .007 8.70E-10
> c1 1 .017 2.87E-03
> Please let me know if you are prepared to warrant these results,
> because if you are, then I am prepared to start discussing them
> scientifically with Jacques and Arthur (whom I believe will find the
> results of more than passing interest for various reasons that I won?t
> go into now.)
> Also, if you are prepared to warrant these results, then I would like
> to start discussing:
> i) the slopes of the tangents to THREE parabolas implicitly defined
> by your regression c on (e,u,u*e,u^2).
> ii) the slopes of the tangents to many hyperbolae implicitly defined
> by your regression c on (e,u,u*e,u^2).
> One of these parabolas, of course, is the parabola defined by the
> quadratic equation whose square term is u^2.
> The other two parabolas result from the fact I mentioned earlier ?
> namely, that z = u*e is the equation of the quadric surface termed a
> hyperbolic paraboloid. As a ?locus?, a hyperboloc paraboloid is the
> surface swept out by a parabola whose apex is traversing another
> parabola normal to it ? hence two parabolas.
> And the hyperbolae arise from the fact that slicing a hyperbolic
> paraboloid with a plane at the correct angle always yields a
> hyperbola.
> I strongly suspect that the slopes of these various tangents can be
> ?successfully? regressed on one another in at least some combinations,
> and that such regressions will allow us to extend the results obtained
> above for a1 and c1 to the other four folds as well.
> If you need further clarification before forming a reaction to this
> suggestion, I will of course be happy to provide.

You lose me when you start talking about that stuff. I don't see
how or why the regressions should relate to anything. It seems like
the geometric equivalent of numerology. (That's a little strong,
but it has the right flavor.)

> In any event, thank you very much for getting us this far, Ray. This
> is now as much your "idea" as Jacques, Arthur's, or my own.