If we fit the following model with n observations where i = 1,...,n and 's are...

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If we fit the following model with n observations

$y_{i} = \beta_{0} + \beta_{1}x_{1i} + \beta_{2}x_{2i} + \epsilon_{i}$

where i = 1,...,n

and $\epsilon$ 's are identically and independently distributed as a normal random variable with a mean of zero and a variance $\sigma^{2}$ , and all the x's are fixed.

How can I show that the point estimator of the mean response and its residuals are statistically independent normal random variables?

math Statistics-And-Probability

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