# distribution of errors in simple linear regression

I just started learning about simple linear regression, and I have a question about one of its assumptions.

One of the assumptions is that the errors are normally distributed. Does this mean that if I get every $y-\hat{y}$ point, those points should be distributed as a mound shape?

• The normality assumption only means that the MLE is the least squares solution. Without normality the least squares estimate can still be BLUE (best linear unbiased estimate). – Michael R. Chernick Nov 24 '17 at 23:54
• It means that if you fit all of the signal and none of the noise (i.e. have a perfect model) then $y -/hat{y}$ should be distributed as gaussian. – David Kozak Nov 25 '17 at 0:52

• Actually, no. Consider $\hat{y}=0 \forall x$. It's a badly misspecified model but it is one. And it does not satisfy $\hat{\epsilon} \sim N(0,\sigma^2)$ in general. – David Kozak Nov 25 '17 at 3:19