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Science Forum Index » Statistics - Math Forum » regression model selection
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| Beliavsky |
 Posted: Wed Dec 27, 2006 4:38 pm |
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If I have N candidate predictors and search all possible to subsets to
find M <= N predictors to use in a multiple linear regression model,
and I also include an intercept, effectively how many parameters do I
have in the model? The coefficients of predictors not selected are set
to zero. Only M+1 coefficients are estimated in the final model, but
there were N+1 potential coefficients in the model.
I want to plug in the # of parameters into an information criterion
such as AIC in order to choose a model, after having found the best
models with 1, 2, ..., N predictors. |
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| Gordon Sande |
| Posted: Wed Dec 27, 2006 4:51 pm |
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On 2006-12-27 16:38:49 -0400, "Beliavsky" <beliavsky@aol.com> said:
Quote: If I have N candidate predictors and search all possible to subsets to
find M <= N predictors to use in a multiple linear regression model,
and I also include an intercept, effectively how many parameters do I
have in the model? The coefficients of predictors not selected are set
to zero. Only M+1 coefficients are estimated in the final model, but
there were N+1 potential coefficients in the model.
I want to plug in the # of parameters into an information criterion
such as AIC in order to choose a model, after having found the best
models with 1, 2, ..., N predictors.
If one of your predictors had been the constant then there would be no
need for the intercept. Otherwise said, the intercept is just an convenient
algebraic way of representing the constant predictor.
The rest is left as an exercise. If the difference of two of your predictors
is the constant then the exercise is not totally vacuous. In this last case
one would expect the intercept coefficient to be zero. |
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