When would it be appropriate to perform a non-linear transformation on your data?
(1) When your data is obviously non linear.
(2) When your model is obviously non-linear.
There seem to me to be two main reasons to try a non-linear transformation on your data:
(1) The data itself is obviously non-linear. e.g. When plotted on a linear scale, the points follow a non-linear curve.
(2) The data pertains to a non-linear system. e.g. population growth.
If you suspect an exponential relationship like
If you suspect a power relationship like
If you suspect a polynomial relationship like