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Just love it when R2 comes out negative

ron_horne

Super User

Joined:

Jun 23, 2011

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 R2. 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....

11843_fit Duration, distance and speed.png

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

Thanks,

Ron

1 ACCEPTED SOLUTION

Accepted Solutions
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.

14 REPLIES
jiancao

Staff

Joined:

Jul 7, 2014

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.

jenkins_macedo

Community Trekker

Joined:

Jul 13, 2015

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
ron_horne

Super User

Joined:

Jun 23, 2011

thanks for the comment jiancao

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

jiancao

Staff

Joined:

Jul 7, 2014

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

11871_pastedImage_1.png

ron_horne

Super User

Joined:

Jun 23, 2011

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

11873_fit Duration, distance and speed2.png

jiancao

Staff

Joined:

Jul 7, 2014

My apologies for missing the Fit Measured on Original Scale report. The attached table show where a negative R Square came from in this case. I saved the column 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. 

ron_horne

Super User

Joined:

Jun 23, 2011

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.

11874_pastedImage_0.png

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.

ron_horne

Super User

Joined:

Jun 23, 2011

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