I'm wondering if anyone could provide some code (preferably in R) which demonstrates violated assumptions leading to type 1 errors. Some concrete examples of errors arising from assumption violations would be useful teaching tools.
I've generated 10,000s of null regression models (slope 0), with major violations of some of the assumptions---such as non-independent residuals, or serious heteroskedacity---but my type 1 error rate never rises above .05. As far as I can tell regression (at least simple regression) seems to be totally 'robust' to assumption violations. Please somebody show me how things can go wrong!