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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
Response to your last of 12/7 at 12:17am
Posted: Dec 7, 2012 3:18 AM

I.
You wrote:

?1. Het = 3 (posted 12/5 @ 12:00) is impossible. Check your data.?

Thanks. ?Het? is 4 for R1 Aubqe:

a1 a3 b1 b47 c1 c2
C S C S c S c S C S C S "Het"
Aubqe H L H H H L H L L L L H 4

II.

You wrote:

?2. Why do you present results from the regressions of c on
both(u,e,u*e) and (u,e,u*e,u^2) for the same data? It is unusual to
consider the results of both analyses, except for the purpose of
deciding which model to use. Have you checked the significance of the
quadratic term? Does its inclusion reduce the Standard Error of
Prediction (SEP) substantially? (Those are two conceptually separate
issues.)?

I presented results from both out of ignorance, i.e. not knowing
whether the similarity of ?het?, ?L-H?, and ?H-L? results for both
regressions would be relevant to your consideration of the entire
matter.

But re actual comparison of the two regressions, consider for the sake
of discussion just the average slopes Aubu and Aubqu for c on
(u,e,u*e) and c on (u,e,u*e,u^2) respectively.

For these two average slopes the ?2-way? data for Subset x MoSS |
(Fold x Set x Length) = (a1,1,24) are:

Aubu Aubqu

t 0.297413484 0.274819583
df 133.708200500 128.3098338
2-tailed p 0.766614886 0.783897935
N for 1S 47 47
N for 1C 36 36
N for R1S 41 41
N for R1C 34 34
1S Coeff -1.952726236 -4.174717322
IC Coeff -4.009830911 -4.280992887
R1S Coeff 0.060946658 -0.901924172
R1C Coeff -0.84027985 -2.098708096
Var for 1S 3.881459118 4.222990696
Var for 1C 2.589180286 2.578813072
Var for R1S 4.019024218 3.952029957
Var for R1C 4.61471327 4.991890592

based on the underlying data:

Method N N R R
Subset S C S C

obsN 47 36 41 34
Mean u 0.615 0.501 0.540 0.558
Mean u^2 0.394 0.293 0.315 0.335

Aubu -1.953 -4.010 0.061 -0.840
Aubqu -4.175 -4.281 -0.902 -2.099

AubuSE 1.970 1.609 2.005 2.148
AubquSE 2.055 1.606 1.988 2.234

And speaking from my usual complete ignorance, I would say that the
similarity of t,df,p for Aubu and Aubqu at the ?2-way? level is
sufficient to:

a) rule out any need for further analysis at the ?underlying? level;

b) motivate the choice of c on (u,e,u*e) over c on (u,e,u*e,u^2)
because complicating the regression by addition of u^2 doesn?t seem to
make any appreciable difference, at least not at the ?2-way level?.

But if these conclusions are incorrect, I await your guidance and
instructions.

III.

You wrote:

?3. What does "Het" *mean*? I'm always suspicious of anything that
starts with arbitrary dichotomization. What are you trying to show??

I will make a separate post in response to this question.

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