題組內容

5. Consider \( Y = \beta_0 + \beta_1 X + \varepsilon \) with \( E(\varepsilon) = 0 \), \( \text{Var}(\varepsilon) = \sigma^2 \) and \( \varepsilon \) are uncorrelated.

(b)Show that \( \text{cov}(\bar{y}, \hat{\beta}_1) = 0 \) (5 分)