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The way I see it, in OLS, we are geometrically fitting a line of best fit to some data. Unlike MLE (even though OLS and MLE give the same regression estimates for simple linear regression), there are no underlying probability distributions.

So for simple linear regression in OLS, why do we still check if the residuals are Normally Distributed even though OLS does not use probability distributions?

kjetil b halvorsen
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Uk rain troll
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    Tests and CIs are not distribution free (though the significance level and coverage will be approximately correct in large samples under iid errors, under some modest conditions). Prediction intervals are a different matter. – Glen_b Mar 04 '24 at 08:13
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    @Glen_b +1. Do you want to make this an answer? It's very close to one now, even though it's short. – Peter Flom Mar 04 '24 at 10:23
  • If you have extreme outlier residuals, you might choose to use something other than OLS, such as quantile regression. – BigBendRegion Mar 04 '24 at 20:21

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