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 |
