Pembahasan Soal Ujian Profesi Aktuaris
SOAL
Dalam sebuah regresi model diberikan untuk resitricted model
\(ES{S_{UR}} = 90\)
\(TS{S_{UR}} = 190\)
Untuk restricted model
\(ES{S_R} = 40\)
\(TS{S_R} = 60\)
Hitunglah statistik \({F_{1,98}}\)
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| Diketahui | \(ES{S_{UR}} = 90\) \(TS{S_{UR}} = 190\) \(ES{S_R} = 40\) \(TS{S_R} = 60\) |
| Rumus yang digunakan | \(R_{UR}^2 = 1 – \frac{{ES{S_{UR}}}}{{TS{S_{UR}}}}\) \(R_R^2 = 1 – \frac{{ES{S_R}}}{{TS{S_R}}}\) \({F_{q,N – k}} = \frac{{(R_{UR}^2 – R_R^2)/q}}{{(1 – R_{UR}^2)/(N – k)}}\) |
| Proses pengejaan | \(R_{UR}^2 = 1 – \frac{{ES{S_{UR}}}}{{TS{S_{UR}}}} = 1 – \frac{{90}}{{190}} = \frac{{100}}{{190}}\) \(R_R^2 = 1 – \frac{{ES{S_R}}}{{TS{S_R}}} = 1 – \frac{{40}}{{60}} = \frac{{20}}{{60}}\) \({F_{1,98}} = \frac{{(R_{UR}^2 – R_R^2)/1}}{{(1 – R_{UR}^2)/(98)}}\) \(= \frac{{(\frac{{100}}{{190}} – \frac{{20}}{{60}})/1}}{{(1 – \frac{{100}}{{190}})/(98)}}\) \(= 39.925\) \(= 40\) |
| Jawaban | a. 40 |