Assuming that thei are independent and normally
Chapter 11, Problem 11.60(choose chapter or problem)
Assuming that the \(\epsilon_i\) are independent and normally distributed with zero means and common variance \(\sigma^2\), show that \(B_0\), the least squares estimator of \(\beta_0\) in \(\mu_Y | x = \beta_0 + \beta_1 x\), is normally distributed with mean \(\beta_0\) and variance
\(\sigma_{B_{0}}^{2}=\frac{\sum_{i=1}^{n} x_{i}^{2}}{n \sum_{i=1}^{n}\left(x_{i}-\bar{x}\right)^{2}} \sigma^{2}\).
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