Pembahasan Soal Ujian Profesi Aktuaris
| Institusi |
: |
Persatuan Aktuaris Indonesia (PAI) |
| Mata Ujian |
: |
Metoda Statistika |
| Periode Ujian |
: |
November 2017 |
| Nomor Soal |
: |
24 |
SOAL
Sebuah model regresi linier \(Y = \alpha + \beta X + \varepsilon \) digunakan untuk mengestimasikan 8 data pengamatan.
Diketahui:
- \(\hat \beta = 2,075\)
- \(\sum {{{\left( {{X_i} – \bar X} \right)}^2}} = 38\)
- \(\sum {{{\left( {{Y_i} – \bar Y} \right)}^2}} = 185\)
Hitunglah \({R^2}\) (dibulatkan 3 desimal).
- 0,584
- 0,684
- 0,784
- 0,884
- 0,984
| Diketahui |
- \(\hat \beta = 2,075\)
- \(\sum {{{\left( {{X_i} – \bar X} \right)}^2}} = 38\)
- \(\sum {{{\left( {{Y_i} – \bar Y} \right)}^2}} = 185\)
|
| Rumus yang digunakan |
\({R^2} = \hat \beta _2^2\left( {\frac{{\sum {{{\left( {{X_2} – {{\bar X}_2}} \right)}^2}} }}{{\sum {{{\left( {Y – \bar Y} \right)}^2}} }}} \right)\) |
| Proses pengerjaan |
\({R^2} = \hat \beta _2^2\left( {\frac{{\sum {{{\left( {{X_2} – {{\bar X}_2}} \right)}^2}} }}{{\sum {{{\left( {Y – \bar Y} \right)}^2}} }}} \right)\)
\(= {\left( {2,075} \right)^2}\left( {\frac{{38}}{{185}}} \right)\)
\(= 0,884399\) |
| Jawaban |
d. 0,884 |
