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Topic: Transformations
Replies: 2   Last Post: Oct 30, 1996 11:16 AM

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Richard Scheaffer

Posts: 440
Registered: 12/6/04
Transformations
Posted: Oct 30, 1996 7:32 AM
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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 non-linear
techniques available to minimize SSEU, but they are beyond what
is covered in an introductory course (and are computer-intensive).
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






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