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

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

Is it too important to have normality on the residuals?

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 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.