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All Journal Natural Science: Journal of Science and Technology JURNAL ILMIAH MATEMATIKA DAN TERAPAN Journal of Data Analysis BAREKENG: Jurnal Ilmu Matematika dan Terapan Jurnal Varian Inferensi DedikasiMU: Journal of Community Service Parameter: Journal of Statistics Indonesian Journal of Statistics and Its Applications
Mohammad Fajri
Department Of Statistics, Faculty Of Mathematics And Natural Sciences, Tadulako University, Indonesia
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Journal : Journal of Data Analysis

 1 
Analisis Sensitivitas Model Regresi Linier Berganda Menggunakan Pendekatan Bayesian (Distribusi Prior Normal) Junaidi Junaidi; Mohammad Fajri; Yandi Ristawan
Journal of Data Analysis Volume 3, Number 1, June 2020
Publisher : Department of Statistics, Syiah Kuala University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24815/jda.v3i1.18358

Abstract

Metode regresi linier berganda merupakan metode yang memodelkan hubungan antara peubah respon (y) dan beberapa peubah predictor (x). Pada metode Bayesian parameter yang digunakan merupakan variabel random yang dilkukan dengan mengalikan Likelihood dengan distribusi prior. Distribusi prior adalah distribusi subyektif berdasarkan pada keyakinan seseorang dan dirumuskan sebelum data sampel diambil. Tujuan penelitian ini adalah  untuk menganalisis sensitivitas dari parameter-paremeter pada model regresi linier berganda yang akan dilakukan dengan menggunakan prior berdistribusi Normal. Selanjutnya, penerapan model pada data aset bank di Indonesia dengan hasil estimasi parameter yaitu , , , , , dan , dengan selang kepercayaan 95%  untuk setiap parameter yang dihasilkan yaitu==       (-1,427 ; 3,594),  =(-5,07;0,3061), =(, , dan  = (-0,5955 ; 2,487). Nilai estimasi parameter yang diperoleh dengan pendekatan Bayesian mendekati nilai parameter yang diperoleh dengan Frequantis. Selang kepercayaan yang diperoleh juga mendekati dengan hasil frequentis yang memiliki interval lebih sempit dibandingkan nilai interval dengan metode OLS. Hal ini menunjukkan bahwa metode Bayesian merupakan suatu pendekatan yang dapat digunakan untuk mengestimasi parameter pada analisis regresi linier berganda. The multiple linear regression method is a method that models the relationship between the response variable (y) and several predictor variables (x). In the Bayesian method, the parameters used are random variables which are conducted by multiplying the likelihood with the prior distribution. The prior distribution is a subjective distribution based on a person's beliefs and is formulated before the sample data is taken. The purpose of this study is to analyze the sensitivity of the parameters in the multiple linear regression model that will be carried out using prior normal distribution. Furthermore, the application of the model to the data on bank assets in Indonesia with the results of parameter estimation is β0 = 23.06, β1 = 1.05, β2 = -2,379, β3 = -0,4786, β4 = -0.03796, and β5 = 0.9075, with a 95% confidence interval for each resulting parameter, namely β0 = (6,052; 40,200), β1 = (-1,427; 3,594), β2 = (- 5.07; 0, 3061), β3 = (0.9896; 0.03289), β4 = (- 1,224; 1.139), and β5 = (-0.5955; 2.487). The parameter estimate value obtained by the Bayesian approach is close to the parameter value obtained by Frequantis. The confidence interval obtained is also close to the frequentis result which has a narrower interval than the interval value with the OLS method. This shows that the Bayesian method is an approach that can be used to estimate parameters in multiple linear regression analysis.
Co-Authors Andri Annisa, Mufitatul Ayu Anggraeni Desy Lusiyanti Fadjriyani Gamayanti, Nurul Fiskia Hajra Rasmita Ngemba Hartayuni Sain Iman Al Fajri Iman Setiawan Insany, Annisa Nur Iut Triutami Junaidi Junaidi Lilies Handayani Margareth, Cecilia Muh. Maruf Nur?Eni, Nur?Eni Nurhidayati, Maulida Nurpati Nurpati Nurul Fiskia Gamayanti Phyta Rahima Primajati, Gilang Rais Rais Rais Rais Rais Rizwan Arisandi Shalsa Yunita Rahman Jati Siti Natazha Dg Mabaji Siti Soraya Wulansari, Eka Rizky Yandi Ristawan Yunita, Silva