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$\begingroup$ I see your point here, but I expected to see how it fit with the covariance of the sum of the variable and the sum of the covariance. I think something like that stats.stackexchange.com/questions/390609/… $\endgroup$
– Kernel
Commented Oct 16, 2023 at 13:58
$\begingroup$ @Kernel I really don't understand what you are getting at. The least squares linear regression formula does involve the covariance matrix $X^\top X$. We never change $X$ in your question. $\endgroup$
– Steven Gubkin
Commented Oct 16, 2023 at 15:32
$\begingroup$ I did not get your point, yet, I agree with the last point; we do have only one predictor. $\endgroup$
– Kernel
Commented Oct 16, 2023 at 18:29

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