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curve fitting
Posted:
Jun 12, 1996 11:14 AM


> > 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.
This is all true, but if the only thing you ever fit is LINES, you give the impression that lines fit EVERYTHING! (They won't all be economics majors!) > > 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 loglog 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. This is what the graphing calculators actually do!

_   Robert W. Hayden   Department of Mathematics /  Plymouth State College   Plymouth, New Hampshire 03264 USA  *  Rural Route 1, Box 10 /  Ashland, NH 032179702  ) (603) 9689914 (home) L_____/ hayden@oz.plymouth.edu fax (603) 5352943 (work)



