Pembahasan Soal Ujian Profesi Aktuaris
SOAL
Sebuah model \(Y_i = \beta_1 + \beta_2 X_{2i} + \beta_3 X_{3i} + \beta_4 X_{4i} + \varepsilon_i\)
i. \(N = 15\) dan \(ESS = 282{,}82\)
ii. \((X’X)^{-1} = \begin{bmatrix} 13{,}66 & -0{,}33 & 2{,}05 & -6{,}31 \\ -0{,}33 & -0{,}03 & 0{,}11 & 0{,}00 \\ 2{,}05 & 0{,}11 & 2{,}14 & -2{,}52 \\ -6{,}31 & 0{,}00 & -2{,}52 & 4{,}32 \end{bmatrix}\)
Hitunglah standard error dari \(\hat{\beta}_3 – \hat{\beta}_2\)
a. 6,4
b. 6,8
c. 7,1
d. 7,5
e. 7,8
| Diketahui | \(Y_i = \beta_1 + \beta_2 X_{2i} + \beta_3 X_{3i} + \beta_4 X_{4i} + \varepsilon_i\) i. \(N = 15\) dan \(ESS = 282{,}82\) ii. \((X’X)^{-1} = \begin{bmatrix} 13{,}66 & -0{,}33 & 2{,}05 & -6{,}31 \\ -0{,}33 & -0{,}03 & 0{,}11 & 0{,}00 \\ 2{,}05 & 0{,}11 & 2{,}14 & -2{,}52 \\ -6{,}31 & 0{,}00 & -2{,}52 & 4{,}32 \end{bmatrix}\) |
| Rumus yang digunakan | Formula,
|
| Proses pengerjaan |
\(\sigma_{\hat{\beta}_3 – \hat{\beta}_2} = 7{,}080687 \approx \mathbf{7{,}1}\) |
| Jawaban | c. 7,1 |