If you're dealing with a growth curve, is it possible that an exponential curve would fit? (I know that for some segments of an organism's history the expected growth rate follows an exponential function, which implies a constant doubling time when the predictor is the age of the organism, until constraints of available space (or of maturation, I suppose) prevent the exponential increase from continuing.)
Your predictor, I gather, is fertilizer concentration, not time; I can't tell whether an exponential (or logarithmic) function is at all reasonable, but such models might be worth trying. I'd be inclined to distrust a polynomial of any order, particularly > 2, because I should think the underlying trend should be monotonically increasing, and a polynomial is not "naturally" monotonic, so to speak: I suspect the 6th-order polynomial is useful mainly in sharpening the corner, so to speak, between slower growth rates at lower concentrations and faster growth rates at higher concentrations. (Certainly a similar effect occurred with some data I once had occasion to work with, dry mass of organism as a function of time. An exponential nicely fit the data; it took a 4th-order polynomial to represent adequately the shape of the empirical curve, mainly due to having to sharpen that lower-right corner much more than one would get from a parabola.) For fitting Y as a function of X, if the response curve is exponential, one expected form of relationship would be Y = a*e^(b*X). Taking logarithms (natural logs, here), log (Y) = log(a) + b*X which is a nicely linear function. If plotting log(Y) as a function of X does not produce a (nearly) straight line in the scatterplot, you might also try log(Y) vs. log(X) and/or Y vs. log(X). (I have no theoretical reasons for these suggestions, only looking for a functionality that looks reasonably linear: when one has found such a thing, one can then worry about whether it can be justified on grounds other than sheer empiricism.) And of course if Y vs. X is quadratic in X, you might try plotting sqrt(Y) vs. X. Good luck! -- DFB. On Tue, 23 Mar 2004 [EMAIL PROTECTED] wrote: > Hello, > > In most nutrition studies, the classical nutrient response curve is > not quadratic. And that is what my research group is encountering > now. I have 2 sets of growth response data from flowering plants. > The quadratic model is barely significant at the 10% level and the > correlation is poor. The optimum and confidence intervals it predicts > are over-estimates. Remember, I want the lowest fertilizer > concentration that generates an optimum growth response. That sounds perfectly reasonable. Only, it's not clear (to me, that is) how to recognize "an optimum growth response" if I saw one. > Just by looking at the data, I would pick that level to be about 0.25 > to 0.5 mM in both experiments. Any model that does not go this low, > does not fit the biology. > > So my question is, can we model such a curve. On the vinca data, a > 6th order polynomial generates a pretty good best fit curve. > > Can one do with higher order polynomial, or some other line model, and > do the same confidence interval determination as you showed us how to > do with quadratic? I have the data in Excel and would send it to > anyone who can help me with this question. > > Thank you, > > Carrie ------------------------------------------------------------ Donald F. Burrill [EMAIL PROTECTED] 56 Sebbins Pond Drive, Bedford, NH 03110 (603) 626-0816 . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
