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Transformations
Posted:
Oct 30, 1996 7:32 AM


I was asked to expand on my earlier comments, but in the meantime you have seen two excellent responses from Bruce King and James Lang. I agree with what they say.
The point is that fitting a model to transformed data and then transforming back to the original scale is not the same as fitting a model directly to the untransformed data. If SSEL denotes the sum of squared residuals for the linearized data and SSEU for the untransformed data, a technique (as used by TI in many cases) that minimizes SSEL will not, in general, simultaneously minimize SSEU. There are nonlinear techniques available to minimize SSEU, but they are beyond what is covered in an introductory course (and are computerintensive). So, r^2 does not have the same interpretation for, say, an exponential model fit by linearizing as it does for, say, a quadratic model fit by least squares, as is correctly pointed out by Bruce.
Incidentally, a LINEAR MODEL means that the model is linear in the parameters, not necessarily linear in its functional form. So, the quadratic model is still a linear model (and fit by methods of linear algebra).
Dick Scheaffer



