Pembahasan Soal Ujian Profesi Aktuaris
| Institusi | : | Persatuan Aktuaris Indonesia (PAI) |
| Mata Ujian | : | Metoda Statistika |
| Periode Ujian | : | Juni 2016 |
| Nomor Soal | : | 26 |
SOAL
Diketahui hasil dari regresi linier sebagai berikut:
| \(t\) | Aktual
(actual) | Penyesuaian
(fitted) |
| 1 | 74,0 | 75,0 |
| 2 | 69,0 | 70,6 |
| 3 | 72,0 | 70,9 |
| 4 | 74,0 | 74,0 |
| 5 | 65,0 | 66,0 |
Hitunglah estimasi koefisien korelasi deret lag 1 (lag 1 serial correlation coefficient) untuk residual, menggunakan statistik Durbin-Watson!
- 0,1456
- 0,1026
- 0.082
- -0,023
- -0,071
| Diketahui | | \(t\) | Aktual
(actual) | Penyesuaian
(fitted) | | 1 | 74,0 | 75,0 | | 2 | 69,0 | 70,6 | | 3 | 72,0 | 70,9 | | 4 | 74,0 | 74,0 | | 5 | 65,0 | 66,0 |
|
| Rumus yang digunakan | \(d = \frac{{\sum\limits_{t = 2}^n {{{\left( {{{\hat \varepsilon }_t} – {{\hat \varepsilon }_{t – 1}}} \right)}^2}} }}{{\sum\limits_{t = 1}^n {{{\hat \varepsilon }_t}^2} }}\) dengan \({\hat \varepsilon _t} = \) nilai aktual – nilai penyesuaian
\(\hat \rho = 1 – \frac{d}{2}\) dengan \(\hat \rho \) merupakan estimasi koefisien kolerasi deret lag 1 untuk residual |
| Proses Pengerjaan | | \(t\) | Aktual | Penyesuaian | \({\hat \varepsilon _t}\) | \({\hat \varepsilon _t}^2\) | \({\left( {{{\hat \varepsilon }_t} – {{\hat \varepsilon }_{t – 1}}} \right)^2}\) | | 1 | 74.00 | 75.00 | -1.00 | 1.00 | 0.00 | | 2 | 69.00 | 70.60 | -1.60 | 2.56 | 0.36 | | 3 | 72.00 | 70.90 | 1.10 | 1.21 | 7.29 | | 4 | 74.00 | 74.00 | 0.00 | 0.00 | 1.21 | | 5 | 65.00 | 66.00 | -1.00 | 1.00 | 1.00 | | Total | 354.00 | 356.50 | -2.50 | 5.77 | 9.86 |
\(d = \frac{{\sum\limits_{t = 2}^n {{{\left( {{{\hat \varepsilon }_t} – {{\hat \varepsilon }_{t – 1}}} \right)}^2}} }}{{\sum\limits_{t = 1}^n {{{\hat \varepsilon }_t}^2} }}\)
\(= \frac{{9,86}}{{5,77}}\)
\(= 1,708839\)
\(\hat \rho = 1 – \frac{d}{2}\)
\(= 1 – \frac{{1,708839}}{2}\)
\(= 0,145581\) |
| Jawaban | a. 0,1456 |
