topic Just love it when R2 comes out negative in Discussions

Just love it when R2 comes out negative

ron_horne — Wed, 19 Oct 2016 03:08:09 GMT

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....

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

Thanks,

Ron

Re: Just love it when R2 comes out negative

jiancao — Wed, 22 Jun 2016 19:10:57 GMT

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.

Re: Just love it when R2 comes out negative

jenkins_macedo — Wed, 22 Jun 2016 19:32:17 GMT

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.

Re: Just love it when R2 comes out negative

ron_horne — Wed, 22 Jun 2016 23:45:49 GMT

thanks for the comment jiancao

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

Re: Just love it when R2 comes out negative

jiancao — Wed, 19 Oct 2016 03:10:26 GMT

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

Re: Just love it when R2 comes out negative

ron_horne — Wed, 19 Oct 2016 03:10:35 GMT

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

Re: Just love it when R2 comes out negative

jiancao — Thu, 23 Jun 2016 13:16:59 GMT

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.

Re: Just love it when R2 comes out negative

ron_horne — Wed, 19 Oct 2016 03:10:54 GMT

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.

Re: Just love it when R2 comes out negative

jiancao — Thu, 23 Jun 2016 16:35:12 GMT

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.

Re: Just love it when R2 comes out negative

ron_horne — Thu, 23 Jun 2016 16:40:10 GMT

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

Re: Just love it when R2 comes out negative

jiancao — Thu, 23 Jun 2016 17:04:08 GMT

Unfortunately their usefulness and comparability is limited IMHO.

Additional note--if you want to make predictions on the original scale from a log linear model , then anti log is necessary. However, you would also need to apply an adjustment by adding s²/2, i.e., y* = exp[log(y*) + (s²/2)]. This blog post explains why: Econometrics Beat: Dave Giles' Blog: Forecasting From Log-Linear Regressions.

Re: Just love it when R2 comes out negative

ron_horne — Thu, 23 Jun 2016 17:33:34 GMT

Thank you very much, this is all relevant and interesting.

Re: Just love it when R2 comes out negative

ron_horne — Thu, 23 Jun 2016 21:43:53 GMT

in this case i would like to ask whether you know if JMP uses this correction (or any other) when asking predicted values from the fit model platform (after transforming on the fly)? what about the prediction profiler?

Re: Just love it when R2 comes out negative

jiancao — Fri, 24 Jun 2016 14:17:53 GMT

Only in Bivariate/Fit Special in Fit Y by X will JMP back transform the predicted values to the original scale, but it doesn't make adjustment with the anti-log transformation as referenced in the above-mentioned literature. When you use a transformed response with Fit Model or Fit Y by X (except Fit Special) the prediction is made on the transformed response, so does the Prediction Profiler.

Re: Just love it when R2 comes out negative

ron_horne — Fri, 24 Jun 2016 21:27:30 GMT

thanks for he clarification.