Pembahasan Soal Ujian Profesi Aktuaris
SOAL
Model dengan 48 observasi yang anda miliki, sesuai dengan model berikut:
\(Y = {\beta _1} + {\beta _2}{X_2} + {\beta _3}{X_3} + {\beta _4}{X_4} + \varepsilon \)
Jika diberikan:
| Sumber variasi | Derajat Kebebasan | Sum of Square |
| Regresi | 3 | 103.658 |
| Error | 44 | 69.204 |
Hitunglah nilai \({\bar R^2}\)
- 0,57
- 0,58
- 0,59
- 0,60
- 0,61
| Diketahui | RSS = 69,204 ESS = 103,658 n = 48 k = 4 karena \(Y = {\beta _1} + {\beta _2}{X_2} + {\beta _3}{X_3} + {\beta _4}{X_4} + \varepsilon \) memiliki 4 parameter |
| Rumus yang digunakan | \(TSS = ESS + RSS\) \({R^2} = \frac{{ESS}}{{TSS}}\) \({\bar R^2} = 1 – \frac{{\left( {1 – {R^2}} \right)\left( {n – 1} \right)}}{{\left( {n – k} \right)}}\) |
| Proses pengerjaan | \(TSS = ESS + RSS\) \(= 69,204 + 103,658\) \(= 172,862\) |
| \({R^2} = \frac{{ESS}}{{TSS}}\) \(= \frac{{103,658}}{{172,862}}\) \(= 0,599658\) | |
| \({{\bar R}^2} = 1 – \frac{{\left( {1 – {R^2}} \right)\left( {n – 1} \right)}}{{\left( {n – k} \right)}}\) \(= 1 – \frac{{\left( {1 – 0,599658} \right)\left( {47} \right)}}{{44}}\) \(= 0,572362\) | |
| Jawaban | a. 0,57 |