ESTIMASI PARAMETER DAN PENGUJIAN HIPOTESIS PADA MODEL REGRESI GAMMA

NASUTION, ALVI SAHRIN (2016) ESTIMASI PARAMETER DAN PENGUJIAN HIPOTESIS PADA MODEL REGRESI GAMMA. Masters thesis, Institut Teknologi Sepuluh Nopember.

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Abstract

Analisis regresi merupakan metode statistik yang berguna untuk memodelkan hubungan antara variabel respon dan variabel prediktor. Model regresi pada umumnya dibangun berdasarkan asumsi residualnya Normal, tapi secara empirik asumsi sering terlanggar. Dalam kasus pencemaran sungai Surabaya, tingginya nilai Biochemical Oxygen Demand (BOD) di sungai Surabaya berdasarkan laporan Badan Lingkungan Hidup Surabaya Tahun 2013 membuat pola data mengikuti distribusi Gamma. Penelitian ini menentukan estimasi parameter dan pengujian hipotesis dari model regresi Gamma menggunakan Maximum Likelihood Estimation (MLE) dan Weighted Least Square (WLS). Estimator yang diperoleh pada model regresi Gamma ini adalah vektor g gradien dengan variabel k yaitu g(β) = l β   . Karena hasil yang diperoleh tidak close form, maka untuk menentukan estimatornya harus menggunakan metode iterasi. Metode iterasi yang digunakan adalah metode iterasi Newton- Raphson sehingga memerlukan turunan pertama dan turunan kedua terhadap parameter untuk membentuk matriks Hessian. Sementara dalam pengujian hipotesis menggunakan Likelihood Ratio Test (LRT) digunakan adalah uji serentak dan uji parsial dengan uji statistik distribusi Chi-square. Pada pengujian hipotesis parsial metode MLE dan WLS menunjukkan variabel prediktor yang berpengaruh terhadap variabel respon kecepatan air sungai. Sedangkan untuk pemilihan model berdasarkan nilai AIC diperoleh adalah metode estimasi WLS. ===================================================================================================== Regression analysis is a statistical method that is useful to model the relationship between the response variable and the predictor variable. Regression models are built on the assumption residual Normal, but by empirical assumptions are often violated. In the case of river pollution Surabaya, the high value of Biochemical Oxygen Demand (BOD) in the river Surabaya based on the report of the Environment Agency in Surabaya in 2013 to make the data patterns following the Gamma distribution. This study determines the parameter estimation and hypothesis testing of Gamma regression model using Maximum Likelihood Estimation (MLE) and Weighted Least Square (WLS). Estimator obtained in Gamma regression model is the gradient vector g k variables, namely g(β) = l β   . Due to the results obtained do not close the form, then to determine estimatornya should use iteration method. Iteration method used is the Newton-Raphson iteration method that requires the first derivative and the second derivative of the parameters to form the Hessian matrix. While in hypothesis testing provided by Likelihood Ratio Test (LRT) used simultaneously test and partial test with statistical test Chi-square distribution. In the partial hypothesis testing methods MLE and WLS show predictor variables that influence the response variable speed river water. As for the model selection is based on the value of AIC acquired WLS estimation method.

Item Type: Thesis (Masters)
Additional Information: RTSt 519.544 Nas e
Uncontrolled Keywords: Biochemical Oxygen Demand, Regresi Gamma, Maximum Likelihood Estimation, Weighted Least Square, Newton Raphson.
Subjects: Q Science > QA Mathematics
Q Science > QA Mathematics > QA278.2 Regression Analysis
T Technology > TD Environmental technology. Sanitary engineering
Divisions: Faculty of Mathematics and Science > Statistics > (S2) Master Theses
Depositing User: Mr. Tondo Indra Nyata
Date Deposited: 09 Jan 2017 08:07
Last Modified: 27 Dec 2018 03:04
URI: http://repository.its.ac.id/id/eprint/1416

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