# What happens if you reject normality of residuals when estimating with least squares?

What happens if you reject normality of residuals when estimating with least squares?

Is it too important to have normality on the residuals?

• in what way are the residuals non-normal? – Macro Jun 3 '12 at 0:55
• and how did you decide to reject normality? – John Jun 3 '12 at 2:07
• And how many observations do you have? – jbowman Jun 3 '12 at 18:31

The $t$-statistic is assumed to be distributed asymptotically normally for hypothesis tests. If your residuals are severely non-normal, your $t$-statistics, $p$-values, and hypothesis tests will be meaningless.
Your $\hat{\beta}$ estimates are still okay, but you cannot express confidence in the $\beta$s.
You can try and use some form of robust standard error that controls for non-normality. Alternatively, if your dataset is very large and your $\hat{\beta}$ estimates are very far from zero, you might be able to get away with it.
• I believe that statistic inference is destroyed more than implied above. And non-normality of residuals is sometimes indicative of not having the best transformation of $Y$. – Frank Harrell Mar 7 '14 at 13:23