Pembahasan Soal Ujian Profesi Aktuaris
SOAL
Sebuah regresi linier digunakan untuk mencocokkan suatu deret waktu dengan 30 pengamatan. Diketahui:
\({{\hat \varepsilon }_1} = – 8\) \({{\hat \varepsilon }_{30}} = 10\) \(\sum\limits_{t = 1}^{30} {\hat \varepsilon _t^2} = 3200\) \(\sum\limits_{t = 2}^{30} {\left( {{{\hat \varepsilon }_t}{{\hat \varepsilon }_{t – 1}}} \right)} = 760\)Hitunglah statistik Durbin-Watson (dibulatkan 2 desimal).
- 1,27
- 1,37
- 1,47
- 1,57
- 1,67
| Diketahui | regresi linier digunakan untuk mencocokkan suatu deret waktu dengan 30 pengamatan \({{\hat \varepsilon }_1} = – 8\) \({{\hat \varepsilon }_{30}} = 10\) \(\sum\limits_{t = 1}^{30} {\hat \varepsilon _t^2} = 3200\) \(\sum\limits_{t = 2}^{30} {\left( {{{\hat \varepsilon }_t}{{\hat \varepsilon }_{t – 1}}} \right)} = 760\) |
| Rumus yang digunakan | \(d = \frac{{\sum\limits_{t = 2}^n {{{\left( {{{\hat \varepsilon }_t} – {{\hat \varepsilon }_{t – 1}}} \right)}^2}} }}{{\sum\limits_{t = 1}^n {{{\hat \varepsilon }_t}^2} }}\) \(= \frac{{\sum\limits_{t = 1}^n {{{\hat \varepsilon }_t}^2} + \sum\limits_{t = 2}^n {{{\hat \varepsilon }_{t – 1}}^2} – 2\sum\limits_{t = 2}^n {\left( {{{\hat \varepsilon }_t}{{\hat \varepsilon }_{t – 1}}} \right)} }}{{\sum\limits_{t = 1}^n {{{\hat \varepsilon }_t}^2} }}\) |
| Proses pengerjaan | \(d = \frac{{\sum\limits_{t = 1}^{30} {{{\hat \varepsilon }_t}^2} + \sum\limits_{t = 2}^{30} {{{\hat \varepsilon }_{t – 1}}^2} – 2\sum\limits_{t = 2}^{30} {\left( {{{\hat \varepsilon }_t}{{\hat \varepsilon }_{t – 1}}} \right)} }}{{\sum\limits_{t = 1}^{30} {{{\hat \varepsilon }_t}^2} }}\) \(= \frac{{3200 + \left( {3200 – {{\left( { – 8} \right)}^2} – {{10}^2}} \right) – 2\left( {760} \right)}}{{3200}}\) \(= 1,47375\) |
| Jawaban | c. 1,47 |