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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?

Richard Hardy
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user52882
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  • 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](http://stats.stackexchange.com/tags/self-study/info) question; please read information at the link relating to such questions. – Glen_b Jul 27 '14 at 08:39
  • For example, there are assumptions you don't have in the question [here](http://stats.stackexchange.com/questions/55113/where-do-the-assumptions-for-linear-regression-come-from). – Glen_b Jul 27 '14 at 08:56
  • You could perhaps write an answer for this question. – Glen_b Jul 27 '14 at 09:21

1 Answers1

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In the absence of a followup answer from the OP, I'll post an answer to hopefully save yet another question going unanswered.

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

As indicated at the link I mentioned in comments, independence, normality and homoskedasticity of errors are all necessary for the usual normal-theory inference (i.e. confidence intervals, prediction intervals and hypothesis tests).

So that's at least three assumptions you need. Of those, the normality assumption is the easiest one to avoid (e.g. by using inferential procedures that don't assume it), so if I had to nominate only two, I'd have to go with independence and homoskedasticity of errors.

Glen_b
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  • Independence and homoskedasticity of the errors are all that are required for inference based on asymptotic normal theory to apply. For the exact small-sample theory to apply you need the errors to be normally distributed. – Samuel Benidt Jul 31 '14 at 03:13
  • @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). – Glen_b Jul 31 '14 at 03:27