Suppose I have the following experiment set up. I'm trying to build a regression model to predict how much weight a person can bicep curl based on their bicep size. So I go ahead and have a bunch of people lift some weight, measure their bicep size and fit a regression model to the data.
Now I calculate the difference between the actual weight they lifted and the predicted weight and notice (visually)that there is a trend for my model to overestimate how much someone with a small bicep can lift (negative errors), normal biceps seem to be pretty accurate predictions and it overestimates how much someone with a large bicep can lift (positive errors).
How would I go about doing the equivalent of a one sample t-test if I violate the assumption of homogeneity?
EDIT: Will multiple Wilcoxon signed rank test with alpha correction be appropriate here?