Thanks, Milo! I agree with everything you write, with the exception of
(essentially) one matter of fact, as noted below.
On Fri, 21 Jan 2000, Milo Schield wrote in part:
> Consider the Minitab PULSE dataset.
> Pulse1 is first measurement of pulse (beats per minute)
> Pulse2 is second measurement of pulse (bpm)
> RAN, SEX and SMOKES are binary.
> RAN =1: subject ran in place between pulse measurements
> RAN =0: subject did not run/exercise between pulse measurements
> Thus, we might expect if RAN = 0 (simple test-retest)
> a = 0 and b1 = 1.
> -------------------------------------------------------------------
> In doing the actual regression, I obtained:
> PULSE2 = 17.3 + 0.763 PULSE1 + 36.2 RAN + 1.17 SMOKES - 1.04 SEX
> - 8.03 Ran*Sex - 20.6 Ran*Smokes
Milo, are you sure you've got the interactions correctly labelled? My
results (on the Minitab web site) are essentially the same (except that
I coded SEX as (1 = F, 0 = M) and I think you coded it the other way
round), but the value of the Ran*Sex coefficient was 20.6 and the value
for Ran*Smoke was -8.03. (Similarly in the other regression analysis
you report below.)
> Predictor Coef StDev T P
> Constant 17.332 6.009 2.88 0.005
> PULSE1 0.76297 0.07786 9.80 0.000
> RAN 36.249 3.005 12.06 0.000
> SMOKES 1.169 2.325 0.50 0.616
> SEX -1.036 2.137 -0.48 0.629
> Ran*Sex -8.030 3.567 -2.25 0.027
> Ran*Smok -20.649 3.510 -5.88 0.000
>
> If I eliminate the two non-significant terms, I got:
> PULSE2 = 16.4 + 0.773 PULSE1 + 36.4 RAN - 6.89 Ran*Sex - 21.6 Ran*Smokes
>
> Predictor Coef StDev T P
> Constant 16.352 5.556 2.94 0.004
> PULSE1 0.77275 0.07546 10.24 0.000
> RAN 36.450 2.733 13.34 0.000
> Ran*Sex -6.893 2.707 -2.55 0.013
> Ran*Smok -21.582 2.869 -7.52 0.000
>
> S = 7.566 R-Sq = 81.3% R-Sq(adj) = 80.4%
> --------------------------------------------------------------------------
> Using the last model, I would say that running (RAN=1)
> * adds 36.45 beats per minute to one's pulse rate (if female non-smoker).
> * adds 29... beats per minute to one's rest pulse rate (if male non-smoker)
> * adds 17 beats per minute to one's pulse rate (if female smoker)
> * adds 8... beats per minute to one's pulse rate (if male smoker).
My results, with "Ran*Sex"and "Ran*Smok" interchanged, were
adds 36.45 bpm (if female non-smoker), as you say;
adds 29.56 bpm (if female smoker);
adds 14.87 bpm (if male non-smoker);
adds 7.97 bpm (if male smoker).
> =================
> Interpretation requires a knowledge of the subject matter -- not just
> p-values.
> One should look for plausible explanations for the coefficients:
> 1. Why is the constant positive? (2nd measurement effect?)
> 2. Why is the coefficient for PULSE1 different from 1? (regression effect?)
Partly because the slope is an average of several slopes that do
not differ significantly, but the slope for RAN=0 (when the two
groups are segregated) is steeper than 0.77 and (I think, but
analysis is not at hand) is not different from 1.
The variable (Pulse2-Pulse1) for those who did not run has mean
-0.105 and 95% C.I. = (-1.209, +0.999).
> 3. Why does running in place (RAN=1) increase the 2nd pulse measure?
> 4. Why is the increase somewhat less for males than for females?
> 5. Why is the increase much less for smokers than for non-smokers?
>
> Plausibility is a sign of a good model.
>
> Of course, one may wonder if all running subjects ran at the same pace.
> Perhaps females ran slower than males.
^^^^^^
Don't you mean "faster"?
> Perhaps smokers ran slower than non-smokers.
> This lack of control might give the observed results, but a totally
> different interpretation.
>
> Milo
> ==================================================
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Donald F. Burrill [EMAIL PROTECTED]
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