Pembahasan Soal Ujian Profesi Aktuaris
| Institusi |
: |
Persatuan Aktuaris Indonesia (PAI) |
| Mata Ujian |
: |
Metoda Statistika |
| Periode Ujian |
: |
November 2017 |
| Nomor Soal |
: |
21 |
SOAL
Sebuah regresi 2 variabel dicocokkan ke dalam 5 observasi sebagai berikut:
| \(i\) |
1 |
2 |
3 |
4 |
| \({X_i}\) |
7 |
12 |
15 |
21 |
| \({\hat \varepsilon _i}\) |
1,017 |
0,409 |
-0,557 |
-2,487 |
Berapakah nilai \({X_5}\)?
- 26
- 27
- 28
- 29
- 30
| Diketahui |
| \(i\) |
1 |
2 |
3 |
4 |
| \({X_i}\) |
7 |
12 |
15 |
21 |
| \({\hat \varepsilon _i}\) |
1,017 |
0,409 |
-0,557 |
-2,487 |
|
| Rumus yang digunakan |
Sifat pada residual
- Zero mean : \(\sum\nolimits_{i = 1}^n {{{\hat \varepsilon }_i}} = 0\)
- Orthogonality : \(\sum\nolimits_{i = 1}^n {{{\hat \varepsilon }_i}} {X_i} = 0\)
|
| Proses pengerjaan |
\(\sum\nolimits_{i = 1}^n {{{\hat \varepsilon }_i}} = 0\)
\(1,017 + 0,409 – 0,557 – 2,487 + {{\hat \varepsilon }_5} = 0\)
\({{\hat \varepsilon }_5} = 1,618\) |
| \(\sum\nolimits_{i = 1}^n {{{\hat \varepsilon }_i}} {X_i} = 0\)
\(1,017\left( 7 \right) + 0,409\left( {12} \right) – 0,557\left( {15} \right) – 2,487\left( {21} \right) + 1,618\left( {{X_5}} \right) = 0\)
\({X_5} = 30,009271\) |
| Jawaban |
e. 30 |
