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

Jul 23, 2015

(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 $y = a \cdot {b}^{x}$ then try linear regression on $x$ vs $\log \left(y\right)$.

If you suspect a power relationship like $y = a {x}^{b}$ then try linear regression on $\log \left(x\right)$ vs $\log \left(y\right)$.

If you suspect a polynomial relationship like $y = a {x}^{2} + b x + c$ 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.