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.
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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. Logistic regression T Technology > TD Environmental technology. Sanitary engineering |
| Divisions: | Faculty of Mathematics and Science > Statistics > 49101-(S2) Master Thesis |
| 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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