Excellent suggestion statdad. Sometimes it's easy to overlook established methods. I see a lot of students have an aha moment after they calculate the estimated confidence bands that increase in width as the data limits are approached. Cheers!
Wow - lots of options here. If standard methods are not sufficient, there are many ways to approximate data fit so that you can consider complex transformation for testing and estimation. Currently, the R language might be most amenable to this sort of modeling. You might start with some spline...
R is certainly a useful skill to have if in the scientific field. The learning curve is steeper than traditional statistics packages such as SAS and SPSS. But it can be worth the investment. And the new techniques are commonly implemented first in R.
Jack Dagg