Pembahasan Soal Ujian Profesi Aktuaris
| Institusi | : | Persatuan Aktuaris Indonesia (PAI) |
| Mata Ujian | : | Metoda Statistika |
| Periode Ujian | : | November 2017 |
| Nomor Soal | : | 27 |
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 |
