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Feb 19, 2009 8:29 AM
(695 views)

I am doing least squares fits, up to cubic with 15 X's. Only the 1st several ever turn out "significant", so those at the "bottom" with small p values could be removed...one at a time...as long as R^2 doesn't go down. This would be a slow iterative process, but would result in a much shorter equation. I know of one other tool that will do this.

Can JMP?

Thanks,

Dave

10 REPLIES

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Feb 19, 2009 1:27 PM
(595 views)

What it sounds like you want to do is fit a large model, and then remove insignificant terms one-by-one. You can do this in JMP using the Fit Model platform using Backward selection.

On the Fit Model dialog, enter the model terms and response, change the Personality to Stepwise, then click Run Model. A Stepwise dialog opens. Change the Direction to Backward, and change the Prob to Leave to 0.05 (or whatever significance level you want). Click the Enter All button.

At this point, you can either click the Go button or Step button. The Go button tells JMP to remove insignificant terms until all terms in the model are significant. If you want to watch each step of that process, use the Step button.

Once the process is finished, click the Make Model button. This opens the Fit Model dialog and populates it with the final model. Click Run Model to fit it.

Also of interest to you may be the All Possible Models and Model Averaging features found on the Stepwise dialog popup menu. See JMP Documentation for complete explanations of these items.

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Feb 19, 2009 5:18 PM
(595 views)

The Stepwise options seems real picky about missing terms, or terms out of order. There was no way to rearrange them in the fit window, even if I knew what order it wanted, so I recreated my terms again. After the backward was complete, that model gave a lower R^2 than the previous model with the same terms all left in (0.9867 vs. 0.9932). So I believe I am trading accuracy for a shorter equation, basically. Correct?

Dave

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Feb 20, 2009 8:44 AM
(595 views)

Now, about your question: "I believe I am trading accuracy for a shorter equation, basically. Correct?" You are the one who brought this up first, you wanted to remove insignificant terms from a model. You get a shorter equation, yes, at the expense of a lower R-squared. However, I wouldn't say you have less accuracy here when you remove terms like this ... you have reduced the precision (increased the variance) of the estimates of predicted value, within the level of noise.

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Feb 20, 2009 10:03 AM
(595 views)

So I wouldn't rule out the shortened equation.

Thanks for your patience with the "new guy" :)

Dave

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Feb 20, 2009 10:50 AM
(595 views)

X Y

1 0.28248748

2 0.90870512

3 0.50182335

4 0.12685357

5 0.32946774

6 0.14868958

7 0.53642655

8 0.40279645

9 0.35250681

10 0.37013588

fitting an ordinary least squares model of y=x produces an R^2 of .04 indicating, as it should, that there is no relationship between Y and X.

Now consider the same data, but with 10 indicator variables, one for each row. Fitting a model with Y = X1 - X10 produces an R^2 of 1. Sounds like a perfect model! The problem is that the number of obs is the same as predictors and that will always generate an R^2 of 1. Of course JMP also will report Singularity Details. Meaning that there is no noise left once all the Xs are included.

Y X1 X2 X3 X4 X5 X6 X7 X8 X9 X10

0.28248748 1 0 0 0 0 0 0 0 0 0

0.90870512 0 1 0 0 0 0 0 0 0 0

0.50182335 0 0 1 0 0 0 0 0 0 0

0.12685357 0 0 0 1 0 0 0 0 0 0

0.32946774 0 0 0 0 1 0 0 0 0 0

0.14868958 0 0 0 0 0 1 0 0 0 0

0.53642655 0 0 0 0 0 0 1 0 0 0

0.40279645 0 0 0 0 0 0 0 1 0 0

0.35250681 0 0 0 0 0 0 0 0 1 0

0.37013588 0 0 0 0 0 0 0 0 0 1

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Apr 3, 2009 12:48 PM
(595 views)

Thanks....

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Apr 6, 2009 5:38 AM
(595 views)

You have discovered the difficulties of doing backwards stepwise modeling. This is one of the many reasons why many statisticians advise people to avoid backwards (and all forms of stepwise) modeling. See the comments regarding stepwise regression in this FAQ

Message was edited by: Paige

Message was edited by: Paige

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Feb 20, 2009 11:04 AM
(595 views)

I don't know the context of the situation, or any details of the model, but maybe a difference of 0.99 vs 0.98 may not be important. I don't know. You have to make that judgement.

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Feb 20, 2009 11:27 AM
(595 views)

Thanks again,

Dave