In my previous post, I was looking for correlation ratio (η or η²) routines in R. I was surprised by the fact that no one uses η for linearity checking in the GLM procedures.

Let's start form a simple example: how do you check linearity of bivariate correlation? Solely with scatterplot?

There are several ways of doing this, one way is to compare linear and non-linear model R², then to apply F test to seek for significant difference between them.

Finally, the question is: How do you check linearity, the "non-grafical" way?