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, fold, and method.
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.
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.