On Nov 27, 6:19 am, djh <halitsk...@att.net> wrote: > 1. > > 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. > > 2. > > 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.