I'm doing some exploratory data analysis of x and y variables on a scatterplot.
I log transformed the x axis and had a better linear fit:
From just playing around I tried log(log(x)):
My end goal is to build a linear regression model. From here it looks like y is related to x via log(log(x)) transformation.
My question is, does this 'type' of relationship have a name, other than just log log x?
Is it possible to rewrite it using the properties of logs in some other form? I gave it a try and could not, it seems it's just log(log(x)) is the only way to write it. Is that right?