Timeline for Why in Box-Cox method we try to make x and y normally distributed, but that's not an assumption for linear regression?
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
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| Oct 30, 2017 at 2:49 | vote | accept | Andre | ||
| Jan 4, 2019 at 6:35 | |||||
| Oct 28, 2017 at 6:16 | vote | accept | Andre | ||
| Oct 28, 2017 at 6:16 | |||||
| Oct 27, 2017 at 21:33 | comment | added | Andre | @AdamO yes, I know the assumptions. But it seems in practice we still want our data to “look better”, i.e. making x and y more symmetric or normally distributed. And my original question is basically asking reason for that. | |
| Oct 27, 2017 at 21:03 | comment | added | AdamO | The assumptions for the classical linear model are simply that $Y = a + b X + \epsilon$ and that $\epsilon$ has a IID normal mean-zero distribution. $X$ can be anything, and $Y$ will consequentially be a linear combination of that and the error. In that case, CIs and p-values are exact rather than merely approximate. | |
| Oct 27, 2017 at 19:56 | comment | added | Andre | @AdamO I’m sorry I didn’t make it clear. You make a good point in explaining. But the “data” in my answer actually refers to predictors and response variables. Would you also comment on this? | |
| Oct 27, 2017 at 19:53 | history | edited | Andre | CC BY-SA 3.0 |
added 29 characters in body
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| Oct 27, 2017 at 19:50 | comment | added | AdamO | However if you have small samples and need exact inference, you can relax the need for normally distributed residuals by using resampling statistics (like the permutation test). | |
| Oct 27, 2017 at 19:48 | comment | added | AdamO | The answer to your question: "why do we want our data [you mean residuals] to be symmetric or normally distributed?" is that we don't. The rationale for applying power transforms to an outcome is because it addresses a scientific question of interest. It happens that linear regression is an exact (not asymptotic) procedure when residuals are normally distributed (and identically independently distributed). It turns out you need relatively few observations to enjoy very good approximations to asymptotic test statistic distributions, CIs, and p-values. | |
| Oct 27, 2017 at 19:30 | history | answered | Andre | CC BY-SA 3.0 |