No, this is not right.

This is how it works. 
You start with a mental and mathematical model.
In this case I want to create a model that uses the log of price and the log of time as measured from the Genesis Block means I want to create a power law model. 

Period.

Now you can use a dozen different types of regression. They will give you slightly different results if the underlying phenomenon is real. 

In fact, all these regressions are basically consistent with some slight differences (in particular in how to deal with the bubbles).