Effrihan, - (2017) Simulasi Analisis Multikolinieritas Pada Regresi Linier Berganda Menggunakan Metode Ridge Bayesian. Sarjana thesis, Universitas Brawijaya.
Abstract
Suatu kajian atau analisis yang melibatkan satu atau lebih variabel prediktor dan satu variabel respon disebut analisis regresi, dengan tujuan untuk memprediksi nilai rata-rata dari variabel respon dengan nilai variabel prediktor yang telah diketahui. Terdapat beberapa asumsi yang melandasi dalam analisis regresi yaitu non- multikolinieritas, normalitas, non-autokorelasi, dan homoskedastisitas. Banyak kasus tidak terpenuhinya asumsi non-multikolinieritas, sehingga perlu adanya penanganan kasus tersebut. Salah satu metode yang dapat digunakan dalam pendugaan parameter regresi ridge selain dengan Metode Kuadrat Terkecil (MKT) yaitu dengan metode Bayesian. Pada penelitian ini, metode Bayesian diterapkan pada data simulasi dengan berbagai ukuran sampel dan korelasi. Hasil yang didapatkan berupa penduga parameter, standard error (SE), R2adjusted, dan Kuadrat Tengah Galat (KTG). Berdasarkan hasil simulasi regresi ridge dengan metode Bayesian didapatkan bahwa pendugaan parameter regresi ridge bayesian mempunyai hasil yang serupa dengan MKT. Standard error (SE) penduga regresi ridge bayesian memiliki pola yang sama dengan MKT di mana SE menurun seiring bertambahnya ukuran sampel. Metode Bayesian sangat baik digunakan pada ukuran sampel yang kecil (n=20) karena menghasilkan nilai SE penduga parameter yang kecil. R2adjusted untuk ridge bayesian meningkat dan cenderung semakin stabil seiring bertambahnya ukuran sampel. Sedangkan KTG regresi ridge bayesian yang dihasilkan semakin kecil seiring bertambahnya ukuran sampel.
English Abstract
A study or an analysis that involves one or more predictor variables and one response variable is called as regression analysis, which is aimed to predict the average value of the response variable with the predictor variable value. There are several underlying assumptions in regression analysis that are non-multicollinearity, normality, non-autocorrelation, and homoscedasticity. A lot of cases do not meet the assumption of non-multicollinearity, thus there is a need to solve this problem. One of the methods that can be used in estimation of ridge regression parameters beside the Ordinary Least Square (OLS) is Bayesian method. In this study, Bayesian method was applied to simulation data with various sample size and correlation. The results obtained were parameter estimators, standard error (SE), R2adjusted, and Mean Square Error (MSE). Based on the result of simulation of ridge regression using Bayesian method, it was found that the estimation of Bayesian ridge regression parameter had similar result with OLS. Standard error (SE) Bayesian ridge regression estimators had the same pattern as OLS in which the SE decreased as the sample size increased. The Bayesian method is best used on small sample sizes (n = 20) because it resulted a low value of the parameter estimator SE. In addition, R2adjusted for Bayesian ridge increased and tended to be more stable as the sample size increased. Meanwhile, Bayesian ridge regression’s MSE obtained was becoming lower as the sample size increased.
| Item Type: | Thesis (Sarjana) |
|---|---|
| Identification Number: | SKR/FMIPA/2017/261/051705760 |
| Uncontrolled Keywords: | Regresi Ridge Bayesian, Simulasi, Gibbs Sampling, Ridge Trace |
| Subjects: | 500 Natural sciences and mathematics > 519 Probabilities and applied mathematics > 519.5 Statistical mathematics > 519.53 Descriptive statistics, multivariate analysis, analysis of variance and covariance > 519.536 Regression analysis |
| Divisions: | Fakultas Matematika dan Ilmu Pengetahuan Alam > Statistika |
| Depositing User: | Nur Cholis |
| Date Deposited: | 24 Oct 2017 01:34 |
| Last Modified: | 24 Nov 2021 02:40 |
| URI: | http://repository.ub.ac.id/id/eprint/4230 |
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