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Oct 30, 2019 at 15:50 comment added mlofton Okay. So, if it's non-random, then there's no variance ( much less any covariance ) and the OP's issue is hopefully straightened out now.
Oct 29, 2019 at 18:24 history edited Jesper for President CC BY-SA 4.0
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Oct 29, 2019 at 9:29 comment added Jesper for President Yes $x_0$ is treated as non-random.
Oct 29, 2019 at 9:23 history edited Jesper for President CC BY-SA 4.0
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Oct 29, 2019 at 9:04 history edited Jesper for President CC BY-SA 4.0
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Oct 29, 2019 at 7:56 history edited Jesper for President CC BY-SA 4.0
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Oct 29, 2019 at 5:31 comment added mlofton But I think that study_meow is saying ( albeit in a slightly different way): "How can be $\hat\beta$ and $\beta$ be independent since $\hat\beta$ is the estimate of $\beta$ !!!!!. To me, it's a great question and not intuitive. I think the best way to think about it is to NOT THINK of $x_{0}^{\prime} \beta$ as a random variable. Think of it as a constant which therefore is not a random variable. But that's just me. I'm not sure what the correct interpretation is.
Oct 29, 2019 at 3:47 history answered Jesper for President CC BY-SA 4.0