# Linear Regression Assumptions of Homoskedasticity

When I studied linear regression analysis, one of the assumptions taught was that of homoskedatiscity. I understood that homoskedasticity was required for significance testing on the coefficients. Then in my econometrics class, my professor said that we actually don't need homogeneity assumption since it was too strong. Instead, in order to conduct hypothesis testing on the coefficients, we could use "t-robust test" or Wald test.

So then why is homoskedasticity still widely assumed and taught in linear regression class? How do I reconcile these?

• Hi: it's taught that way because getting involved in teaching the wald lrt, lm tests and other robust tests iis a more advanced topic. for large n, the latter tests are better than the standard inference procedures ( like t-tests ) but not optimal theoretically so there are more difficulties teaching those topics. Oct 18, 2018 at 17:50
• I see. Whenever I look up "assumptions behind linear regression" online, the "homogeneity" assumption shows up. Is this because the default in statistical packages is to use t test? Oct 18, 2018 at 20:20
• That's probably largely the reason. But even the test of homog has its issues too. So, you have to test whether a test is valid, yet the former test probably has its own issues. So, it might be best to assume heteroscedasticity.. Usually, regression estimates are robust to heterosced. So, if you're really worried about the homog assumption, I would suggest dropping it and then either using 1) bootstrapping or 2) Halbert White's results for constructing a heterosced consistent covar estimate when there is heterosced. If you're interested in 1) or 2) I can try to think of references. Oct 19, 2018 at 6:30
• Re the meaning of homogeneity in a regression context, this question on Cross Validated SE is relevant, especially answer by gung. Oct 19, 2018 at 12:36
• My bad. it should be homoskedatiscity. Oct 20, 2018 at 1:39