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More on nonlinear models
Posted:
Oct 30, 1996 1:22 AM
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One comment that Dick Scheaffer made was
>It should be pointed out to students that fitting a least squares line
>to the transformed data is not the same as fitting a nonlinear
>model directly by least squares.
If you would like an example, I have some data on Toyota Corolla prices
that I got from the Orlando Sentinel classified ads. The variables are the
age of the car and the advertised price.
Age Price
1 11500
1 12000
3 8000
5 6000
6 3500
6 3000
6 4500
6 4000
8 4000
9 2200
10 3000
12 1000
12 600
16 600
If you do a ExpReg you get y = 14837.73(0.80851^x) which has SSE = 6431130.
Using a couple data points, (1,11500) and (16,600), that appeared to be a
good visual fit to estimate a,b
I got y = 14002.35(0.82129^x) which has SSE = 6302004.
The point is that the visual fit gave a smaller SSE than the regression on
the transformed data. There is nothing special about this data. You can do
this with any data set that "appears" to be exponential but has some
deviation from the exponential model.
James Lang
Valencia Community College
Orlando, FL
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