題組內容

8. (20%) Given are following observations collected in a regression study on two variables. Consider the linear regression model $$Y = \beta_0 + \beta_1 X + \varepsilon$$ | $$x_t$$ | 2 | 3 | 4 | 5 | 6 | | --- | --- | --- | --- | --- | --- | | $$y_t$$ | 3 | 7 | 5 | 11 | 14 |

(d) (5%) Use F test to test the hypotheses \( H_0 \): \( \beta_1 = 0 \) vs. \( H_a \): \( \beta_1 \neq 0 \) at 0.05 level of significance.