題組內容

1. You have data $(x_t \quad y_t)$, $t = 1, \dots, T$. Suppose that the model
$y_t = \alpha + \beta x_t + \varepsilon_t$
satisfies Gauss-Markov conditions Let $x_B$ be the biggest x, $x_S$ be the smallest x, and $y_B$, $y_S$ are the values corresponding to $x_B$, $x_S$. (Note: $y_B$ may or may not be the largest y; it is the y corresponding to the largest x. Similarly for $y_S$.)

1-2 (10 分) Please calculate $\text{var}(\tilde{\beta})$. Whether $\tilde{\beta}$ is efficiency?     (7)