# curve fitting - growth modelling - (Jan/11/2012 )

hi guys,

I'm just wondering, has any of you done any statistical modeling of plant growth? I know, plants normally have a s-shape growth pattern, but under certain conditions (e.g. disease, drought) they don't follow this kind of growth curves.

My data shows more of a parabolic curve, does any of you have idea how to fit a parabolic equation to describe that curve? Thanks in advance.

tj.

Your growth curves look like a U shape? Typical parabolas have the equation y=ax^{2} + bx + c, however, it has been too many years since I last did them (at least 15), so I can't remember how to derive them, other than that the crossing point on the y axis is determined by the lower limit of the graph (position c) and the size of x.

If you have prism graph or some other program (even excel) I can help more.

hi bob. I do not have prism to try to adjust the curve to my data, however I do have excel. was having a look earlier and apparently sigmaplot can also adjust curves of many different kinds.

indeed my growth curves look like a u shape. mathematically I find it quite interesting. I'm just trying to sort out the way to explain this process in a biological context

thanks for your input. cheers.

tj

right, so I did adjust the data to a curve with a nonlinear regression equation. the most similar option to the growth curve was a a gaussian distribution. it provided many parameters, said the normality test (shapiro-wilk) passed successfully and then a long report with stuff like the Rsqr of (0.9213), analysis of variance and an equation that was:

Equation: Peak, Gaussian, 3 Parameter

f=a*exp(-.5*((x-x0)/^2)

but anyway, I don't even know whether it is methodologically correct to adjust curves to data this way. would you agree bob?

Statistically what you would do is perform a regression analysis with the most simple line and work your way up to more complex, looking at what are known as "residual plots" and looking for the type of curve that produces the "least squares". If a line does not fit the curve, the residuals will show a non-random distribution, and the squares will be large.

It sounds like what you have done in sigmaplot is probably OK, though without actually examining the data it is pretty hard to tell. It may be that there is a simpler curve that fits your data just as well, but I doubt it will make much difference, unless you are looking to extrapolate from your curve.