Pembahasan Soal Ujian Profesi Aktuaris
| Institusi | : | Persatuan Aktuaris Indonesia (PAI) |
| Mata Ujian | : | Metoda Statistika |
| Periode Ujian | : | Juni 2016 |
| Nomor Soal | : | 17 |
SOAL
Suatu studi dilakukan untuk meneliti data Indeks Prestasi Kumulatif (IPK) mahasiswa sebagai fungsi linear penghasilan orangtua. Diketahui data sebagai berikut:
| IPK (Y) | Penghasilan Orangtua (X) |
| 4,00 | 21 |
| 3,00 | 15 |
| 3,50 | 15 |
| 2,00 | 9 |
Hitunglah \({R^2}\).
- 0,98
- 0,91
- 0,87
- 0,82
- 0,7
| Diketahui | | IPK (Y) | Penghasilan Orangtua (X) | | 4,00 | 21 | | 3,00 | 15 | | 3,50 | 15 | | 2,00 | 9 |
|
| Rumus yang digunakan | \({R^2} = {\left( {\frac{{n\sum\nolimits_{i = 1}^n {{X_i}{Y_i}} – \sum\nolimits_{i = 1}^n {{X_i}} \sum\nolimits_{i = 1}^n {{Y_i}} }}{{\sqrt {n\sum\nolimits_{i = 1}^n {X_i^2} – {{\left( {\sum\nolimits_{i = 1}^n {{X_i}} } \right)}^2}} \sqrt {n\sum\nolimits_{i = 1}^n {Y_i^2} – {{\left( {\sum\nolimits_{i = 1}^n {{Y_i}} } \right)}^2}} }}} \right)^2}\) |
| Proses pengerjaan | | No | \(Y\) | \(X\) | \({Y^2}\) | \({X^2}\) | \(XY\) | | 1 | 4.00 | 21.00 | 16.00 | 441.00 | 84.00 | | 2 | 3.00 | 15.00 | 9.00 | 225.00 | 45.00 | | 3 | 3.50 | 15.00 | 12.25 | 225.00 | 52.50 | | 4 | 2.00 | 9.00 | 4.00 | 81.00 | 18.00 | | Total | 12.50 | 60.00 | 41.25 | 972.00 | 199.50 |
\({R^2} = {\left( {\frac{{n\sum\nolimits_{i = 1}^n {{X_i}{Y_i}} – \sum\nolimits_{i = 1}^n {{X_i}} \sum\nolimits_{i = 1}^n {{Y_i}} }}{{\sqrt {n\sum\nolimits_{i = 1}^n {X_i^2} – {{\left( {\sum\nolimits_{i = 1}^n {{X_i}} } \right)}^2}} \sqrt {n\sum\nolimits_{i = 1}^n {Y_i^2} – {{\left( {\sum\nolimits_{i = 1}^n {{Y_i}} } \right)}^2}} }}} \right)^2}\)
\(= {\left( {\frac{{4 \cdot 199,5 – 60 \cdot 12,5}}{{\sqrt {4 \cdot 972 – {{60}^2}} \cdot \sqrt {4 \cdot 41,25 – {{12,5}^2}} }}} \right)^2}\)
\(= 0,914286\) |
| Jawaban | b. 0,91 |
