# How to interpret cubed root transformation?

I did a cubed root transformation of one of my predictors in multiple linear regression. How can I interpret this predictor now that it is transformed and my model is fit with it?

• Usually there is little difficulty with interpretation when a predictor is transformed--certainly not in comparison to interpreting a transformed predictand. If you read these threads related to interpreting transformations, you might learn all you need for understanding your own situation.
– whuber
Nov 25 '13 at 18:47

Probably the best way to gain an understanding is through graphs and through example computations. You don't say how many other variables you have in the model, nor whether they are continuous or categorical or what, but....

Suppose you have a model:

$Y = 12 + 3x_1^{\frac{1}{3}} + 2x_2$

You could calculate predicted Y at various typical levels of $x_1$ and $x_2$, you could also graph how predicted Y changes: One such graph would have $x_1$ (not transformed) on the x-axis, predicted Y on the y-axis, and a line for the result at each of (say) three levels of $x_2$. If you have many x variables, you might need to just use their median levels in the plot, or make multiple plots.