# Assumption for valid hypothesis testing of the OLS estimators in the small samples

Please support me solve this question: In a simple regression model $$y = b_0 + b_1x + u$$ we have the five main assumptions:

1. linearity in parameters
2. random sampling
3. zero conditional mean
4. variation in x
5. homoscedasticity

IN ADDITION TO the 5 assumptions, what is the additional assumption for valid hypothesis testing of OLS estimators in the small samples?

• Several answers here list assumptions for regression. I can think of at least two additional assumptions for $u$ that are required. This sounds like a self-study question; please read information at the link relating to such questions. Commented Jul 27, 2014 at 8:39
• For example, there are assumptions you don't have in the question here. Commented Jul 27, 2014 at 8:56
• You could perhaps write an answer for this question. Commented Jul 27, 2014 at 9:21

• @SamuelBenidt Thanks. For asymptotics to definitely apply, you need $n\to\infty$. In general we have $n$ smaller than that (it's not safe to assume n is large here). Sometimes even surprisingly large $n$ can still have the asymptotic results not hold. If we assess that the distribution of residuals is perhaps not too strongly non-normal then it might be reasonable to ignore that it's not actually normal (i.e. to use the asymptotic inference that would result from applying CLT+Slutsky, say, which would for example make our t-statistics go to $z$ for a wide variety of conditional distributions). Commented Jul 31, 2014 at 3:27