Date: Nov 27, 2012 3:22 PM
Author: Ray Koopman
Subject: Re: OK – I think I’m set, at least till we get t<br> o c on (e, u, u*e).
On Nov 27, 6:19 am, djh <halitsk...@att.net> wrote:
> You wrote:
> ?slope = dy/dx = a1 + 2*a2*x?
> Oh! That slope! (Of the tangent to the quadratic at x = 0.) Duh!
> I was construing ?slope? as just a alternative term for ?coefficient?
> ? don?t know why. Someday I?ll learn if that if I can?t make sense
> of something you?ve written, then I?ve construed something wrongly.
> When I re-run the analysis, I will use (u/1+u) instead of u. So I
> assume I would use ln(u/(1+u)), and (ln(u+(1/u)))^2, parallel to
> ln(u) and (ln(u))^2? (Unless you don?t want me to take logs ? please
> clarify here.)
I intended no logs. Also, I worry when I see u/1+u and u+(1/u),
neither of which equals u/(1+u).
> 3. You wrote:
> ?For instance, you might get the slope at each data point and then
> use their literal average, a1 + 2*a2*mean_x. But what if cells with
> different x-means give the same a1 and a2? Should their "average
> slope" measures be the same or different? That's the kind of question
> you have to ask yourself.?
> Since I can?t think that far ahead in the abstract (as you can), I
> will use ?a1 + 2*a2*mean_x? initially, and see if any peculiarities
> arise of the sort you mention (or others.)
Here's a f'rinstance. First, remember that a quadratic can always be
written as A + B*(x - C)^2. Next, suppose that two cells have the
same A,B,C, but mean_x is < C in one cell and > C in the other, so
that their average slopes differ. Then, if the difference in mean_x
is an intrinsic property of the cells then the average slope is
appropriate, but if the difference in mean_x is arbitrary, a result
of experimenter whim, then the average slope is not appropriate.
I'll respond to 4 later.