I cannot wrap my head around what does it mean that the OLS estimators are being normally distributed.

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    $\begingroup$ This is really too broad. What details confuses you? Just what this means? Why you would bother to check or assume this? What the consequences are of it not being true? Something else? $\endgroup$ – Matthew Drury Aug 26 '17 at 17:00

Say you have a population of 100m people of a particular state and you want to carry out a survey with 1k participants chosen randomly from this state. For some reason, you want to analyse the survey findings with a regression model. If you were doing this survey again and again and again with randomly chosen 1k people and fitted your regression model each time, you would get a lot of OLS estimates for your variable of interest. These OLS estimates for your variable of interest would be normally distributed.

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    $\begingroup$ I have edited estimators to estimates. This is more than a cosmetic edit, since estimators were incorrect in this context, but I hope this is fine with you. $\endgroup$ – Richard Hardy Aug 26 '17 at 18:01
  • $\begingroup$ Of course it should be "estimate" and not "estimator". Well spotted Richard! $\endgroup$ – Tom Pape Aug 26 '17 at 18:26
  • $\begingroup$ This is okay but we should keep in mind the distinction between a model and reality -- the example population of 100 million people can't leave you with an exactly normal distribution of the population and hence the estimator won't in turn be quite normal either. To actually get a normal distribution out you would require an infinite population, which itself possesses a conditionally-normal distribution for the response variable. $\endgroup$ – Glen_b -Reinstate Monica Aug 27 '17 at 3:01

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