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I am supposed to conduct a regression analysis on my multivariate data. But my data is not normally distributed, so I was considering doing a principal component regression. Therefore, I would like to confirm: what are the assumptions of principal component regression?

Is normality one of them?

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    $\begingroup$ The comments and answer to your previous (apparently related) question stats.stackexchange.com/questions/248168/… appear to address this, but to be perfectly clear no form of regression assumes normality of all the variables. $\endgroup$
    – whuber
    Commented Nov 28, 2016 at 19:01
  • $\begingroup$ To add to what whuber said, for simple linear regression the assumed model is $Y=aX+b+\epsilon$ where $\epsilon$ is a normally distributed noise and X can have any distribution. $\endgroup$
    – Hugh
    Commented Nov 28, 2016 at 19:34
  • $\begingroup$ My answer here stats.stackexchange.com/questions/169664 is very much related. $\endgroup$
    – amoeba
    Commented Nov 28, 2016 at 19:37
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    $\begingroup$ @Hugh, normality assumption is unnecessary even in regression models, except for the ability to use the standard critical values for $t$ and $F$ tests in small samples. For example, OLS estimator is consistent and efficient regardless of normality, and $t$ and $F$ tests work well in asymptotics regardless of normality as well. This has been discussed many times before. $\endgroup$ Commented Nov 28, 2016 at 19:55
  • $\begingroup$ Thanks @RichardHardy that hadn't occurred to me for applying a t test. But I thought that the F test was sensitive to non-normal residuals, if residuals are non-normal does it also work well asymptotically? $\endgroup$
    – Hugh
    Commented Nov 28, 2016 at 20:05

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