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One of the assumptions of the OLS is that observations of the error terms should not be correlated with each other. This assumption is often denoted as $\text{Corr}(\epsilon_i,\epsilon_j) = 0$.

The confusion I have is the following: if $\epsilon_i$ and $\epsilon_j$ are errors, this should mean that they are numbers, and therefore their correlation should always be zero. If I got it wrong and $\epsilon_i$ and $\epsilon_j$ are random variables, please explain why they are.

Richard Hardy
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Антон Бугаев
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  • Residuals are numbers. Errors are random variables. It is a slang to use those words interchangeably. Cross Validated must have a good post about residuals vs errors. I’ll see if I can find one. – Dave Jun 12 '22 at 12:48
  • This was the top hit on Google. – Dave Jun 12 '22 at 12:57
  • I am confused about your confusion. What do you mean with "this should mean that they are numbers, and therefore their correlation should always be zero". Why should numbers not be able to be correlated? E.g the number of ice cream sales in an ice cream stand on the beach and the number of people/visitors on that beach are numbers: are they not correlated? In a game roulette, the number of time we have red and the number of times we have black are numbers: are they not (negatively) correlated? – Sextus Empiricus Jun 12 '22 at 13:05

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