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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.
vasili111
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  • 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. – Demetri Pananos Nov 07 '19 at 15:26
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    @DemetriPananos Is the "check normality of dependent variable for each level of independent variable" same as checking normality of residuals or it is different? – vasili111 Nov 07 '19 at 15:55
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    Yes, it is equivalent. – Demetri Pananos Nov 07 '19 at 16:16
  • @DemetriPananos This is very helpful. Thank you. – vasili111 Nov 07 '19 at 16:26
  • 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. – Nick Cox Nov 07 '19 at 16:29
  • Actually, no, checking normality of residuals is not equivalent to checking normality of $Y$ at each level of $X$. You can have a normal error distribution when the conditionals are non-normal. See https://stats.stackexchange.com/a/486951/102879 – BigBendRegion Sep 13 '20 at 12:34

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