Donald Burrill wrote: > 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.
Don't forget reciprocal relationships: y = a/x (or y = a/(x-b) ). The latter is tricky because if you have to estimate b from the data, you no longer have a linear relationship in the coefficients, but the former can be used in the straightforward manner. . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
