> I do plan to non-linear curve fitting since modeling data with linear, > exponential and quadratic functions is becoming a "typical" focus of many > Algebra series. I have done this modeling with modest academic students > with amazing success, particularly with the support of graphing > calculators and their regression capabilities. Restricting AP Stats > students to deal only with linear regression is unrealistic and > imprudent, I think...
Here's my worry, NOT exhaustively thought out. I wonder what others (with more statistical experience than I) feel...
I've seen some new snippets of curriculum (and can't find them right now to complain more precisely) that use nonlinear fitting on graphing calculators. To me it looks as if the designers are asking kids to try lots of functions (especially polynomials of higher degree) in order to get a better fit.
I remember a relationship between two variables in a Census dataset that gave a better fit with a cubic than with a quadratic, and much better than with a linear function. Unfortunately, there was no reason why the variables should be be related that way.
Using a cubic in that situation might help interpolate expected values, but it probably doesn't illuminate the relationship between the variables, and, importantly, it will not help extrapolate to values beyond the range of the data. Therefore it may give students a false sense of what good data analysis is.
On the other hand, if there is an a priori reason to expect a type of function -- exponential for population growth, quadratic for falling bodies -- I see no problem with fitting that nonlinear function to the data. Then the resultant coefficients are meaningful in terms of the problem rather than simple parameters that "look good."
Another strategy, of course, is to fit linear functions to transformed data, in the same way that in the olden days we used semilog and log-log graph paper when appropriate. What do you think? It THAT a good skill for the AP students? It seems to me it may be more useful, though conceptually difficult.