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    $\begingroup$ Is it possible that last formula is giving the population standard error. $\sigma$ has no hat. $\hat{\sigma}$ would denote an estimated standard deviation, $\sigma$ could denote the population (true / unknown) standard error). $\endgroup$ Commented Dec 2, 2019 at 14:24
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    $\begingroup$ Please say more about where you found the second formula, with a link to it if possible. It looks like the formula for the standard error of the mean of $n$ observations rather than the standard error for a coefficient in linear regression. $\endgroup$ Commented Dec 2, 2019 at 14:55
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    $\begingroup$ @Edm yes, the second formula represents the standard error of the mean. I was wondering if there is any relation between the two. $\endgroup$ Commented Dec 2, 2019 at 14:59