```Date: Dec 5, 2012 11:52 PM
Author: Ray Koopman
Subject: Re: Holy Moly, were you right about covariances for Rub and Rubq !!!!

On Dec 5, 7:08 am, djh <halitsk...@att.net> wrote:> Here is the table for the covariances AubC and AubqC for the> regressions Rub = c on (u,e,u*e) and Rubq = c on (e,u,u*e,u^2)> respectively.>            a1   a3   b1  b47   c1   c2  "H-L>           C S  C S  c S  c S  C S  C S   Het">> N1 AubC   H L  H L  H L  H L  H L  H L    6>    AubqC  H L  H L  H L  H L  H L  H L    6>> N2 AubC   H L  H L  H L  H L  H L  H L    6>    AubqC  H L  H L  H L  H L  H L  H L    6>> N3 AubC   L L  L L  H H  H L  H H  H L    2>    AubqC  L L  H H  L H  L L  H H  H L    1>> R1 AubC   L H  L L  L L  H H  H L  H H    1>    AubqC  L H  L L  L L  H H  H L  H H    1>> R2 AubC   L H  L L  H L  L H  H L  H H    2>    AubqC  L H  H L  L L  L H  H L  H H    2>> R3 AubC   L H  H L  L H  L L  H H  H L    2>    AubqC  L H  H L  L H  L H  H H  L H    1>> Note that this time, the ?het? singularity is ?H-L Het-ness?, rather> than ?L-H Hetness?, as was the case for the average slopes Auq, Aubu,> Aubqu in the last table posted.>> Quite a remarkable result, at least in my naive and ignorant opinion.Sometimes the easiest way to answer such questions is via simulationinstead of analysis. Here is a Monte Carlo estimate, based on 10^6trials, of the distribution of "Het" when all 12! orderings of the12 sample values are equally likely:Het   Prob 0  .021822 1   0 2  .389284 3   0 4  .519354 5   0 6  .069540Here is an estimate of the distribution of "L-H Het" and "H-L Het",again based on 10^6 trials:Het   Prob 0  .152731 1  .331035 2  .308409 3  .151769 4  .048634 5  .006345 6  .001077
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