Transformation of the response

It is much easier to interpret the parameters when parallel lines are fitted to different groups than when their slopes are different, but the data or the context may not justify such a simplification.

After a nonlinear transformation of the response, the relationships in the two groups may be closer to parallel. A transformation to reduce skewness in the reponse often works well.

Understanding the model for ln(y)

Logarithmic transformations are particularly useful because the parallel least squares lines have a simple interpretation. For the above data they are:

Female:    ln (y) = 0.391 + 0.0747 x
Male:       ln (y) = 1.192 + 0.0747 x

This means that:

ln(y) is (1.192 - 0.391) = 0.801 higher for females than for males with the same x.

We can now concisely summarise the difference between males and females:

y for females is e0.810 = 2.23 times that for males with the same x.