Log transformed data mean




I am struggling to decide between using log transformed data or normal data for the statistical description, especially the mean (arithmetic or geometric).
Which one is the most suitable and interesting?

For a bit of background, I want to know if there is any correlation between the Spot rate USD-CAD, and the oil price (WTI). I transformed the daily data for each into log data and then did a regression. My problem is now how to represent descriptive statistics?
Which one is more interesting and gives the most information? Descriptive statistics of normal data, or of the log data? And why?

Thanks :)


You can use the Principle of Maximum Entropy which is related to most information.
Using this principle you can identify a best distribution (given what you know) and from that you can define the best transformation.
Typically, this translates in Normal distribution being the most informative and so you would transform the data to get a distribution similar to a Normal.
Typically, for you kind of data the log follows a Normal distribution and so I would use the log. This is consistent with you using the log for linear regression.