Pembahasan Soal Ujian Profesi Aktuaris
| Institusi |
: |
Persatuan Aktuaris Indonesia (PAI) |
| Mata Ujian |
: |
Metoda Statistika |
| Periode Ujian |
: |
Mei 2018 |
| Nomor Soal |
: |
19 |
SOAL
Diketahui dari 50 pengamatan
\(\sum {{\varepsilon ^2} = 100} \)
\(\sum {({Y_i} – \overline Y } {)^2} = 200\)
Hitunglah nilai \({\overline R ^2}\) untuk \(k = 1\)
- 0.34
- 0.44
- 0.5
- 0.54
- 0.64
| Diketahui |
\(n = 50,{\rm{ }}k = 1\)
\(\sum {{{\widehat \varepsilon }^2} = 100} \)
\(\sum {({Y_i} – \overline Y } {)^2} = 200\) |
| Rumus yang digunakan |
\({R^2} = 1 – \frac{{\sum {{{\widehat \varepsilon }^2}} }}{{\sum {({Y_i} – \overline Y } {)^2}}}\)
\({\overline R ^2} = 1 – \frac{{\left( {1 – {R^2}} \right)\left( {n – 1} \right)}}{{\left( {n – k} \right)}}\) |
| Proses pengerjaan |
\({R^2} = 1 – \frac{{\sum {{{\widehat \varepsilon }^2}} }}{{\sum {({Y_i} – \overline Y } {)^2}}}\)
\(= 1 – \frac{{100}}{{200}}\)
\(= 0.5\)
\({\overline R ^2} = 1 – \frac{{\left( {1 – {R^2}} \right)\left( {n – 1} \right)}}{{\left( {n – k} \right)}}\)
\(= 1 – \frac{{\left( {1 – 0.5} \right)\left( {50 – 1} \right)}}{{(50 – 1)}}\)
\(= 0.5\) |
| Jawaban |
c. 0.5 |
