How accurate is the correlation coefficient for log-log data?

[Old Guy]

I am familiar with linear regression and the correlation coefficient. My current problem involves a data set that is pretty linear on a log-log plot. I have calculated the slope by taking logs of all my x's and y's, and doing the linear regression on the transformed data set. The resulting slope appears to be correct, and I'm happy with that.

The question is, how good a fit do I have on the data? I planned to simply calculate the correlation coefficient on the transformed data, but a coworker challenged this - said that the transformations alter the measurements in a way that makes the typical correlation coefficient calculation invalid.

Is that correct? And if it is, what is the correct measure of goodness of fit for log-log data? Thanks.

 

[SW VandeCarr]

I am familiar with linear regression and the correlation coefficient. My current problem involves a data set that is pretty linear on a log-log plot. I have calculated the slope by taking logs of all my x's and y's, and doing the linear regression on the transformed data set. The resulting slope appears to be correct, and I'm happy with that.

The question is, how good a fit do I have on the data? I planned to simply calculate the correlation coefficient on the transformed data, but a coworker challenged this - said that the transformations alter the measurements in a way that makes the typical correlation coefficient calculation invalid.

Is that correct? And if it is, what is the correct measure of goodness of fit for log-log data? Thanks.

If it's linear with a log-log transform, then the correlation is based on a log-log data set with transformed expectations. As along as it's clear what the data is, I don't see a problem.

EDIT: I forgot to answer your second question. If you have a linear plot in a standard regression on transformed data, the $$R^2$$ statistic should be appropriate for the transformed data (but only for the transformed data.)