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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

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 Ray Koopman Posts: 3,383 Registered: 12/7/04
Re: Average Slope SEs for a1_N_1_S and a1_N_1_C (and some questions
regarding them ...)

Posted: Dec 2, 2012 1:27 AM
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On Nov 30, 8:37 pm, Ray Koopman <koop...@sfu.ca> wrote:
> On Nov 29, 8:29 am, djh <halitsk...@att.net> wrote:
>

>> Here are the SE?s for average slopes for a1_N_1_S and a1_N_1_C:
>>
>> a1_N_1_S:
>>
>> Len
>> ID obsN Avg Slope Avg slope SE
>>
>> 1 215 -4.805470268 0.950050755
>> 2 314 -2.595530566 0.959429879
>> 3 311 -2.291065716 1.024763870
>> 4 210 -2.389119127 1.471966277
>> 5 256 -1.215695376 1.398629841
>> 6 246 -0.262323729 1.643926445
>> 7 226 1.363522805 1.611512322
>> 8 278 -0.560630170 1.620693559
>> 9 246 2.374377463 1.847997565
>> 10 211 -0.816451823 2.632764400
>> 11 194 -0.499208768 2.855882984
>> 12 234 1.968865343 2.864247061
>>
>> a1_N_1_C:
>>
>> Len
>> ID obsN Avg Slope Avg slope SE
>> 1 166 -2.225882168 0.813316857
>> 2 265 -2.315512399 0.693531939
>> 3 258 -0.769858117 0.939333935
>> 4 188 -1.697049757 1.291121211
>> 5 243 -2.069842267 1.245969677
>> 6 228 -4.427566827 1.508641800
>> 7 219 -0.941379623 1.493402326
>> 8 263 -2.069096413 1.534849449
>> 9 233 -1.620229799 1.518979934
>> 10 199 -3.764328472 2.294575586
>> 11 185 -7.882327621 2.694025880
>> 12 232 -11.82556530 3.055385684
>>
>> You?ll see that:
>>
>> a) for a1_N_1_S, going to the bounds implied by the SE will not change
>> the sign of the average slope only up to length interval 4 ? after
>> that the SE generally will;
>>
>> b) for a1_N_1_C, the SE will only change the sign of the average slope
>> in two cases out of the 12: length intervals 3 and 7;
>>
>> c) in both cases, SE increases considerably with length but ?much more
>> so? (?) for a1_N_1_C than for a1_N_1_S.
>>
>> If it?s legit to draw conclusions from comparative behavior of SE?s in
>> contrasting sets of results like these, then interesting scientific
>> interpretations can be made of the above SE behaviors. But I?ve
>> learned not to jump the gun by making such interpretations based on
>> illegitimate interpretations of statistical behaviors. So, guidance
>> please, when you have a chance.
>>
>> Also, regarding point (c) above, if it?s legitimate in general to look
>> at SE behavior in such results sets, is there a legitimate way to show
>> that the SE?s for a1_N_1_C really do increase significantly MORE with
>> increasing length interval than SE?s for a1_N_1_S? Or not? Again,
>> guidance please.
>>
>> And thanks again as always for your continued consideration of these
>> matters.

>
> SE's of slopes depend on n, the distribution of the predictors,
> and the standard error of prediction, only the last of which is a
> "structural parameter", something that is intrinsic to the phenomenon
> being studied. The other two are "design parameters" that are to some
> extent arbitrary and therefore not proper objects of hypotheses.
>
> It is legitimate to compare standard errors of prediction, but it's
> harder than comparing means or slopes. I would steer clear unless you
> have nothing else to keep you busy.

Nevertheless, plots of SE*sqrt[n] against the width of the length
interval are close enough to linear to make me wonder if we should
revert to equal-width intervals. (The current equal-ratio intervals
were designed for logging.)

Date Subject Author
11/21/12 Halitsky
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