Pembahasan Soal Ujian Profesi Aktuaris
| Institusi | : | Persatuan Aktuaris Indonesia (PAI) |
| Mata Ujian | : | Metoda Statistika |
| Periode Ujian | : | Mei 2017 |
| Nomor Soal | : | 24 |
SOAL
Sebuah regresi linear digunakan untuk mencocokkan suatu deret waktu dengan 30 pengamatan.
Diketahui:
\({{\hat \varepsilon }_1} = – 7\)
\({{\hat \varepsilon }_{30}} = 11\)
\(\sum\limits_{t = 1}^{t = 30} {\hat \varepsilon _t^2} = 2422\)
\(\sum\limits_{t = 2}^{t = 30} {\left( {{{\hat \varepsilon }_t} \times {{\hat \varepsilon }_{t – 1}}} \right)} = 801\)
Hitunglah statistik Durbin-Watson (dibulatkan 2 desimal)
- 1,31
- 1,27
- 1,23
- 1,19
- 1,15
| Diketahui | Sebuah regresi linear digunakan untuk mencocokkan suatu deret waktu dengan 30 pengamatan.
Diketahui:
\({{\hat \varepsilon }_1} = – 7\)
\({{\hat \varepsilon }_{30}} = 11\)
\(\sum\limits_{t = 1}^{t = 30} {\hat \varepsilon _t^2} = 2422\)
\(\sum\limits_{t = 2}^{t = 30} {\left( {{{\hat \varepsilon }_t} \times {{\hat \varepsilon }_{t – 1}}} \right)} = 801\) |
| 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 | \(d = \frac{{\sum\limits_{t = 1}^{30} {{{\hat \varepsilon }_t}^2} + \sum\limits_{t = 2}^{30} {{{\hat \varepsilon }_{t – 1}}^2} – 2\sum\limits_{t = 2}^{30} {\left( {{{\hat \varepsilon }_t}{{\hat \varepsilon }_{t – 1}}} \right)} }}{{\sum\limits_{t = 1}^{30} {{{\hat \varepsilon }_t}^2} }}\)
\(d = \frac{{2422 + \left( {2422 – {{\left( { – 7} \right)}^2} – {{11}^2}} \right) – 2\left( {801} \right)}}{{2422}}\)
\(d = 1.268373\) |
| Jawaban | B. 1,27 |
