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My questions stems from this answer: https://stats.stackexchange.com/a/390839/37540

I understand that we should check normality of residuals.

But regarding dependent variable, am I understand correctly all below for linear regression?

  1. We should check normality of dependent variable for each level of independent variable.
  2. We should not check normality for whole dependent variable.
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  • $\begingroup$ That is correct. The assumption is that the conditonal distribution of the outcome (conditioned on the variables) is normal. The marginal distribution could, for instance, be bimodal and we could still use linear regression. $\endgroup$
    – Demetri Pananos
    Nov 7, 2019 at 15:26
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    $\begingroup$ @DemetriPananos Is the "check normality of dependent variable for each level of independent variable" same as checking normality of residuals or it is different? $\endgroup$
    – vasili111
    Nov 7, 2019 at 15:55
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    $\begingroup$ Yes, it is equivalent. $\endgroup$
    – Demetri Pananos
    Nov 7, 2019 at 16:16
  • $\begingroup$ @DemetriPananos This is very helpful. Thank you. $\endgroup$
    – vasili111
    Nov 7, 2019 at 16:26
  • $\begingroup$ Strictly any assumptions are about the unknown errors or disturbances. In practice that can only be checked by looking at residuals, as by definition you don't know the errors. $\endgroup$
    – Nick Cox
    Nov 7, 2019 at 16:29

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