I used to assume that formal tests were the way to go. Say the ADF for stationarity. But I was reading through an author I have a lot of respect for, and he focused on graphs to make these decisions not the formal tests. Of course there are well known problems with stationarity tests, but I am curious what people think. Are graphical methods or formal tests generally better for testing violations of assumptions in regression and time series.

I always thought tests were more scientific than looking at a graph of say residuals That they only used graphical methods before something better (and better computers) came along. But I am not so sure now.