Question

(Based on Stock & Watson "Introduction to Econometrics" 6th ed., Exercise 5.8.) Suppose that \(\left(Y_{i}, X_{i}\right)\) satisfy the simple linear regression assumptions. In addition, \(u_{i}\) is \(N\left(0, \sigma_{u}^{2}\right)\) and is independent of \(X_{i}\). A sample of size \(n=30\) yields

$$ \hat{Y}_{i}=43.2+61.5 X_{i}, n=30, R^{2}=0.54 . $$

$$ (10.2)(7.4) $$

(a) Construct a \(95 \%\) confidence in

(a) Construct a \(95 \%\) confidence interval for \(\beta_{0}\).

(b) Test \(H_{0}: \beta_{1}=55\) v.s. \(H_{1}: \beta_{1} \neq 55\) at the significance level \(5 \%\).

(c) Test \(H_{0}: \beta_{1}=55\) v.s. \(H_{1}: \beta_{1}>55\) at the \(5 \%\) level.

Answer 1