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- Just love it when R2 comes out negative

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Jun 19, 2016 10:58 AM
(1271 views)

Hi all,

Does anyone know what JMP does in the bivariate fit platform when calculating the “fit measured on original scale”? I just got a negative R^{2}. Does it estimate a model without the intercept?

I know the data is peculiar and when using the log-log transformation I have many missing observations but still, something must be going on....

Attached is the data table with a script to reproduce the results I got.

Thanks,

Ron

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Solution

Two modes, one fit to the original data and the other to the log-log transformed data, are different models. Anti-logs won't make summary of fit statistics from the log linear model identical to the results from the original linear fit.

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Jun 22, 2016 12:10 PM
(849 views)

Your R Square is actually positive, but it is close to zero. When this happens, adjusted R square maybe slightly negative. This is how adjusted R square formula is built to work. In fact, if R Square is <k/(n-1) , R Square Adj will be negative.

In your case, a negative R Square Adj. will occur when R Square <0.0013568. What a negative R square Adj. means is that the model terms do not help predict the response.

Does it estimate a model without the intercept?

No, it includes an intercept by default.

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Jun 22, 2016 12:32 PM
(849 views)

I would add that what a negative R Square Adj means is that the portion of variability of the predictors do not help predict the expected response. Thus, the R Square should not be used exclusively as the iron-fist to judge a model's anticipated performance. But it is also good for the R Square and the associated R Square Adj. to be positive.

Jenkins Macedo

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Jun 22, 2016 4:45 PM
(849 views)

thanks for the comment jiancao

I must be missing something. where exactly does it say adjusted in the output?

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Jun 23, 2016 4:15 AM
(849 views)

R Square Adj is the original R^2 adjusted for # of model terms in regression

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Jun 23, 2016 4:27 AM
(849 views)

sorry for the misunderstanding. i was referring to the R2 marked below.

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Jun 23, 2016 6:16 AM
(849 views)

**Residuals Speed** from the model fit (Notice that that it is calculated by taking Exp to back transform to the original scale). Then I calculated two Sum of Squares columns: **SS of Total** (SST) and **SS of Error** (SSE), for the R Square formula used by JMP, which is 1- SSE/SST=1- 164569257/115933657=-0.41951234. So, the back transformation gives rise to a negative R Square.

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Jun 23, 2016 7:24 AM
(849 views)

Thank you jiancao,

that did reproduce the negative figure. yet i would expect the figure to be identical to the outcome of fitting a line to the same data as in the picture.

but if i just run this with a fit line i do not get the same R2.

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Jun 23, 2016 9:40 AM
(849 views)

I see, so how can i make use of the anti-log results? what are they comparable to?