Thanks for giving me (offline) your permission to reopen this thread with a new reply to your post of 8/13@4:42/
1. Possible value of ?simple regression vs multiple regression comparison?
When you responded (in your post of 8/13@4:42) to my proposal involving comparison of a simple and a multiple regression, you wrote:
?The comparison you want to make can (probably) be done, but not with the two-stage heterocscedastic t-test that I described. A different procedure will be needed. [. . .] Moreover, even if a proper test can be devised, it's still not obvious to me that the comparison makes sense. What do you think it will tell you??
To answer your question about what we?ll learn, I?m assuming that by comparing:
ln(c/L) on ln(c/e) with ln(c/L) on (ln(c/e),ln(c/u)) ln(c/L) on ln(c/u) with ln(c/L) on (ln(c/e, ln(c/u))
we MAY learn something about when dipeptide concentration is:
i) more a function of energy concentration ii) more a function of dicodon concentation iii) more a function of both energy concentration AND dicodon concentration.
So, would you have the time to devise the ?different procedure? you mention?
If so, I would like to perform it AS I collect the data for the ?closeness analysis? we?re discussing in the other thread. That way, I won?t have to revisit the same file more than once.
2. Regressions when L held constant.
In your post of 8:13@4:42, you also wrote:
?A more fundamental problem relates to the length intervals. I assume that you are using intervals, instead of doing everything at each actual length, because the N at each length is too small to support analysis. However, that shouldn't stop you from asking what you would get if you had enough data to analyze each length separately. In the regressions mentioned above, L would become a constant; the intercept would be an obvious direct function of L, but the slope would involve L only indirectly, to the extent that the relations among c,e,u change as a function of L. I'm not sure how this should be approached, but I suspect that both the current and previous regressions are not quite right.?
I agree that when L is held constant, it may be more appropriate to investigate regressions like:
a) ln(c) on ln(e) b) ln(c) on ln(u) c) ln(c) on (ln(e),ln(u))
And if the data from:
d) ln(c/L) on ln(c/e) e) ln(c/L) on ln(c/u) f) ln(c/L) on (ln(c/e),ln(c/u))
are empirically ?interesting?, then I will investigate (a-c) as well as (d-f). But again, if comparing (d) with (f) and (e) with (f) suggest nothing of empirical interest, then there?s no sense looking at (a-c).