# What is the reasoning behind expecting residuals in OLS regression to be normally distributed?

There are a lot of similar questions here but I have not found an answer to this specific question.

Source: for example in https://peopleanalytics-regression-book.org/linear-reg-ols.html#norm-dist-assum the author (a mathematician) says:

In an appropriate model we expect our errors to be random, so we would therefore expect our residuals to be normally distributed over sufficient numbers of observations.

The author then goes on to apply qqnorm(newmodel\$residuals) to the data for diagnostics.

If you plot a model in R (plot(mymodel)), you get a bunch of diagnostic plots, the second of which is standardized residuals plotted against the theoretical quantiles - so essentially the same.

But why? What is the reasoning behind the residuals being normally distributed, and not just randomly, without having a recognised distribution at all, or some other distribution? Stats textbooks treat this as if it was obvious - could someone explain, please?

• The author made the same common mistake about the central limit theorem that I discuss here.
– Dave
Jun 5, 2022 at 15:17
• @Dave - that's a great thread (+1). Jun 5, 2022 at 15:32
• Thanks to all who took the time/trouble to respond. @Dave, I will look at the thread in a little while. Just to emphasize that since one of the R built-in diagnostic plots is also checking the residuals against theoretical quantiles, I thought there was some reasoning behind it...? Jun 5, 2022 at 15:42
• Nope, just mistaken reasoning. The reason for checking the residuals etc. Is that if the residuals are far enough away from Normality, maybe you should try a different estimation procedure that might be better (like a robust one), or check outlying data points to make sure you understand them, for example. Maybe your model is incomplete and that shows up as a patch of outliers. Lots of possibilities. Jun 5, 2022 at 17:49
• I once answered a why-Normal-errors question, where many other answers focused on why empirical variables are Normal. I'm not sure the points I summarized there explain why residuals are Normal, so I'm following this question in the hopes someone provides a basis specifically for expecting that third idea.
– J.G.
Jun 6, 2022 at 6:25