When would it be appropriate to perform a non-linear transformation on your data?

1 Answer
Jul 23, 2015

Answer:

(1) When your data is obviously non linear.

and/or

(2) When your model is obviously non-linear.

Explanation:

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 #y = a*b^x# then try linear regression on #x# vs #log(y)#.

If you suspect a power relationship like #y = ax^b# then try linear regression on #log(x)# vs #log(y)#.

If you suspect a polynomial relationship like #y = ax^2+bx+c# and you have data points at regular #x# intervals (e.g. periodic samples), then you can use the differences between successive pairs of samples as a new sample to reduce the degree by #1#. Repeat as necessary until the resulting data looks linear.