I've been analysing a dataset and a colleague suggested something I don't seem to understand and I feel might be wrong.
For example, start by testing if two groups (e.g. male vs female) differ on two variable (e.g. grades and study time) and find no significant differences between groups on either.
Run a linear regression with grades as dependent variable and study time as independent variable and, once again find no significant effect. Keep in mind that I aggregate the data across males and females (i.e. one model only was ran)
My colleague suggested me to test the difference of residuals of this regression between male and females. The goal here would be to test if residuals are different between groups.
What would be the purpose of such a test and what is the correct interpretation of it? To me it seems wrong to infer differences between groups (on either variable) based on such a test, which seems to be the interpretation my colleague favoured.
Any insight is very welcome.