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Topic: Interpretation of coefficients in multiple regressions which model
linear dependence on an IV

Replies: 146   Last Post: Dec 15, 2012 6:44 PM

 Messages: [ Previous | Next ]
 Halitsky Posts: 600 Registered: 2/3/09
Results of p's obtained by referring Q’s to the ch
i-square distribution.

Posted: Dec 10, 2012 11:54 PM

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, 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.

Date Subject Author
11/21/12 Halitsky
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