Pembahasan Ujian PAI: A50 - No. 24 - Mei 2017

Pembahasan Soal Ujian Profesi Aktuaris

Institusi	:	Persatuan Aktuaris Indonesia (PAI)
Mata Ujian	:	Metoda statistika
Periode Ujian	:	Mei 2017
Nomor Soal	:	24

SOAL

Sebuah regresi linear digunakan untuk mencocokkan suatu deret waktu dengan 30 pengamatan, diketahui:
\({\widehat \varepsilon _1} = – 7\) \({\widehat \varepsilon _{30}} = 11\) \(\sum\limits_{t = 1}^{t = 30} {\widehat \varepsilon _t^2} = 2422\) \(\sum\limits_{t = 2}^{t = 30} {({{\widehat \varepsilon }_t}{\rm{ x }}{{\widehat \varepsilon }_{t – 1}})} = 801\) Hitunglah statistik Durbin-Watson

1.31
1.27
1.23
1.19
1.15

Kunci Jawaban & Pembahasan

Diketahui	\({\widehat \varepsilon _1} = – 7\) \({\widehat \varepsilon _{30}} = 11\) \(\sum\limits_{t = 1}^{t = 30} {\widehat \varepsilon _t^2} = 2422\) \(\sum\limits_{t = 2}^{t = 30} {({{\widehat \varepsilon }_t}{\rm{ x }}{{\widehat \varepsilon }_{t – 1}})} = 801\)
Rumus yang digunakan	\(d = \frac{{\sum\limits_{t = 2}^{t = 30} {{{({{\widehat \varepsilon }_t} – {{\widehat \varepsilon }_{t – 1}})}^2}} }}{{\sum\limits_{t = 1}^{t = 30} {\widehat \varepsilon _t^2} }}\)
Proses pengerjaan	\(\sum\limits_{t = 2}^{t = 30} {{{({{\widehat \varepsilon }_t} – {{\widehat \varepsilon }_{t – 1}})}^2}} = \sum\limits_{t = 2}^{t = 30} {(\widehat \varepsilon _t^2 – 2{{\widehat \varepsilon }_t}{\rm{ x }}{{\widehat \varepsilon }_{t – 1}} + \widehat \varepsilon _{t – 1}^2)} \) \(= \sum\limits_{t = 2}^{t = 30} {\widehat \varepsilon _t^2} – 2\sum\limits_{t = 2}^{t = 30} {{{\widehat \varepsilon }_t}{\rm{ x }}{{\widehat \varepsilon }_{t – 1}}} + \sum\limits_{t = 2}^{t = 30} {\widehat \varepsilon _{t – 1}^2} \) \(= (2422 – (49)) – 2(801) + (2422 – (121))\) \(= 3072\) selanjutnya \(d = \frac{{\sum\limits_{t = 2}^{t = 30} {{{({{\widehat \varepsilon }_t} – {{\widehat \varepsilon }_{t – 1}})}^2}} }}{{\sum\limits_{t = 1}^{t = 30} {\widehat \varepsilon _t^2} }} = \frac{{3072}}{{2422}} = 1.26837 = 1.27\)
Jawaban	b. 1.27

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