# Transformation between log and reciprocal powers for regression

Left shows the response transformed with $\frac{1}{gestation^{1/4}}$ and right shows the natural log of gestation. (Original graph of gestation vs age looked just like the transformed graph with the log on right)

It looks like that I need a transformation with a strength between reciprocal powers and log; anyone know one?. So that they might show a more linear and homogeneous relationship for multiple regression

My advice is that the search for a transformation here is largely futile here, and unnecessary too. Although logarithms and some other functions sometimes (indeed often) aid interpretation, I doubt that log of gestation length matches any medical or other interpretation of pregnancy or birth, and I assert that $1/y^{1/4}$ doesn't have any other discernible advantages (it also inverts the scale: negation solves that). The same logic applies to nearby standard transformations.