Answer: Reference
Chapter 11, Problem 21E(choose chapter or problem)
Under the assumptions of Exercise 11.20, find \(\operatorname{Cov}\left(\widehat{\left.\beta_{0}, \tilde{\beta_{1}}\right)}\right.\). Use this answer to show that βˆ0 and βˆ1 are independent if \(\sum_{i=1}^{N} \bar{X}_{1}=0\). [Hint: \(=\operatorname{cov}\left(\bar{Y}-\tilde{\beta_{1}} \bar{x}, \tilde{\beta_{1}}\right)\). Use Theorem 5.12 and the results of this section.]
Equation transcription:
Text transcription:
{Cov}(\widehat{.\beta{0},beta{1)}
\sum_{i=1}^{N} \bar{X}_{1}=0
={cov}(\bar{Y}-{\beta{1}} \bar{x}, \tilde{\beta{1}})
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