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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.

Oiko
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  • This is called "controlling for" study time. Ordinarily one just includes group and study time in the same multiple regression model, but sometimes separate models are run as a way to handle heteroscedasticity. Searching for threads on both regression and multiple regression might turn up a few of these discussions. – whuber Jul 06 '21 at 14:01
  • @whuber Thanks for your reply. I'm still not sure I understand... How am I controlling for the independent variable by testing differences between groups in the residuals of the model (same independent variable and e.g. grades). Sorry. I'm probably missing something obvious – Oiko Jul 06 '21 at 15:25
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    The residuals are what's left after you account for relationships with study time. Here's a highly-voted thread on the subject: https://stats.stackexchange.com/questions/17336. Here's one that clarifies a possible misconception: https://stats.stackexchange.com/questions/78828. They are two out of the thousands of related posts found by [searching our site for control regression](https://stats.stackexchange.com/search?tab=votes&q=control%20regression). – whuber Jul 06 '21 at 15:26
  • Thank you very much! I'll have a look at this post – Oiko Jul 06 '21 at 15:28

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