Timeline for What if residuals are normally distributed, but y is not?
Current License: CC BY-SA 3.0
11 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 26, 2023 at 13:36 | comment | added | gung - Reinstate Monica | @24n8, to be more technical, the errors need to be normally distributed, not the residuals. But we don't have access to the errors & the residuals are an estimate of them. It is common for people to talk about the residuals. | |
| Nov 25, 2023 at 18:06 | comment | added | 24n8 | Also, when you say "residuals being normally distributed for p-values to be correct," I thought the underlying hypothesis test assumes that the unobserved errors (not residuals) are normally distributed? | |
| Nov 14, 2023 at 12:39 | comment | added | gung - Reinstate Monica | @24n8, the residuals are the distribution of Y conditioned on X. Regarding the assumptions of an OLS regression model, it is only the distribution of the residuals that matters. Nonetheless, people often look at the marginal distribution of Y, which is perfectly fine, it just doesn't matter if it's normal. That is the whole point of this thread. | |
| Nov 14, 2023 at 1:44 | comment | added | 24n8 | "However, even if the residuals are normally distributed, that doesn't guarantee that 𝑌 will be (not that it matters... ); it depends on the distribution of 𝑋". hmm, if we condition on $X$ as is done typically doesn't that remove $X$ from consideration. i thought in most cases of interest, we want to know the distribution of $Y$ when conditoined on $X$ | |
| Feb 20, 2015 at 2:31 | comment | added | gung - Reinstate Monica | @loganecolss, that might be better as a new question. At any rate, yes it has to do w/ whether the p-values are correct. If your residuals are sufficiently non-normal & your N is low, then the sampling distribution will differ from how it is theorized to be. Since the p-value is how much of that sampling distribution is beyond your test statistic, the p-value will be wrong. | |
| Feb 20, 2015 at 2:26 | comment | added | avocado | So the assumption of residuals being normally distributed is only for p-values to be correct? Why the p-values might go wrong if residual is not normal? | |
| Oct 21, 2014 at 13:35 | history | edited | gung - Reinstate Monica | CC BY-SA 3.0 |
added 50 characters in body
|
| Jul 30, 2012 at 18:43 | history | edited | gung - Reinstate Monica | CC BY-SA 3.0 |
deleted 9 characters in body
|
| Jul 30, 2012 at 17:43 | history | edited | gung - Reinstate Monica | CC BY-SA 3.0 |
added 172 characters in body
|
| Jul 30, 2012 at 17:37 | history | edited | gung - Reinstate Monica | CC BY-SA 3.0 |
added 1369 characters in body
|
| Jul 30, 2012 at 4:20 | history | answered | gung - Reinstate Monica | CC BY-SA 3.0 |