Pembahasan Soal Ujian Profesi Aktuaris
| Institusi | : | Persatuan Aktuaris Indonesia (PAI) |
| Mata Ujian | : | Metoda Statistika |
| Periode Ujian | : | November 2017 |
| Nomor Soal | : | 29 |
SOAL
Anda mengestimasikan model regresi linear sederhana berdasarkan pengamatan atas 8 data harian berikut ini:
| Hari | \(Y\) | \(X\) |
| 1 | 11 | 2 |
| 2 | 20 | 2 |
| 3 | 30 | 3 |
| 4 | 39 | 3 |
| 5 | 51 | 4 |
| 6 | 59 | 4 |
| 7 | 70 | 5 |
| 8 | 80 | 5 |
Dengan menggunakan metode least square, Anda menentukan estimasi regresi linier sebagai \(\hat Y = – 25 + 20X\)
Hitunglah nilai dari statistik Durbin Watson (dibulatkan 2 desimal).
- 2,60
- 2,82
- 3,04
- 3,26
- 3,48
| Diketahui | | Hari | \(Y\) | \(X\) | | 1 | 11 | 2 | | 2 | 20 | 2 | | 3 | 30 | 3 | | 4 | 39 | 3 | | 5 | 51 | 4 | | 6 | 59 | 4 | | 7 | 70 | 5 | | 8 | 80 | 5 |
Dengan estimasi regresi linier \(\hat Y = – 25 + 20X\) |
| 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 \({\hat \varepsilon _t} = {Y_t} – {\hat Y_t}\) |
| Proses pengerjaan | | Hari | \(Y\) | \(X\) | \(\hat Y\) | \(\hat \varepsilon \) | \({\hat \varepsilon ^2}\) | \({\left( {{{\hat \varepsilon }_t} – {{\hat \varepsilon }_{t – 1}}} \right)^2}\) | | 1 | 11 | 2 | 15 | -4 | 16 | 0 | | 2 | 20 | 2 | 15 | 5 | 25 | 81 | | 3 | 30 | 3 | 35 | -5 | 25 | 100 | | 4 | 39 | 3 | 35 | 4 | 16 | 81 | | 5 | 51 | 4 | 55 | -4 | 16 | 64 | | 6 | 59 | 4 | 55 | 4 | 16 | 64 | | 7 | 70 | 5 | 75 | -5 | 25 | 81 | | 8 | 80 | 5 | 75 | 5 | 25 | 100 | | Total | 164 | 571 |
\(d = \frac{{\sum\limits_{t = 2}^n {{{\left( {{{\hat \varepsilon }_t} – {{\hat \varepsilon }_{t – 1}}} \right)}^2}} }}{{\sum\limits_{t = 1}^n {{{\hat \varepsilon }_t}^2} }}\)
\(= \frac{{571}}{{164}}\)
\(= 3,481707\) |
| Jawaban | e. 3,48 |
