ANALISIS REGRESI LINEAR SEDERHANA DENGAN ERROR BERDISTRIBUSI UNIFORM

MONA ULYASARI, . (2026) ANALISIS REGRESI LINEAR SEDERHANA DENGAN ERROR BERDISTRIBUSI UNIFORM. Sarjana thesis, UNIVERSITAS NEGERI JAKARTA.

	Text COVER.pdf Download (727kB)
	Text BAB 1.pdf Download (345kB)
	Text BAB 2.pdf Restricted to Registered users only Download (935kB) | Request a copy
	Text BAB 3.pdf Restricted to Registered users only Download (325kB) | Request a copy
	Text BAB 4.pdf Restricted to Registered users only Download (875kB) | Request a copy
	Text BAB 5.pdf Restricted to Registered users only Download (326kB) | Request a copy
	Text Daftar Pustaka.pdf Download (230kB)
	Text Lampiran.pdf Restricted to Registered users only Download (447kB) | Request a copy

Abstract

Regresi linear sederhana merupakan metode statistika yang digunakan untuk memodelkan hubungan linear antara variabel bebas dan variabel terikat serta mengestimasi pengaruh variabel bebas terhadap variabel terikat. Model ini umumnya mengasumsikan bahwa galat berdistribusi normal, namun asumsi tersebut tidak selalu terpenuhi dalam data empiris. Salah satu alternatif adalah mengasumsikan galat berdistribusi uniform pada interval (-a,a), misalnya ketika galat memiliki batas bawah dan batas atas yang diketahui, seperti kesalahan pengukuran yang dibatasi oleh toleransi alat atau proses pengukuran yang menghasilkan penyimpangan dalam rentang tertentu. Penelitian ini bertujuan untuk menganalisis estimator parameter regresi, mengkaji sifat-sifat estimator, serta membandingkan hasil teoritis dengan simulasi. Metode yang digunakan meliputi metode kuadrat terkecil dan metode maksimum likelihood dengan pendekatan minimax yang diselesaikan secara numerik menggunakan metode optimasi Nelder-Mead. Hasil penelitian menunjukkan bahwa estimator β₀ dan β₁ yang diperoleh dengan metode kuadrat terkecil pada model regresi yang mengasumsikan galat berdistribusi uniform memiliki bentuk yang sama seperti pada asumsi galat normal, bersifat tak bias, serta memenuhi sifat Best Linear Unbiased Estimator (BLUE). Estimasi menggunakan metode maksimum likelihood menghasilkan estimator melalui pendekatan minimax, yaitu dengan meminimumkan nilai maksimum galat absolut. Parameter a yang menyatakan batas distribusi galat uniform dapat diestimasi menggunakan metode kuadrat terkecil dan metode maksimum likelihood. Hasil simulasi Monte Carlo menunjukkan bahwa estimator memiliki bias yang kecil dan mendekati nilai parameter sebenarnya sehingga sejalan dengan hasil teoritis. Kata Kunci: regresi linear sederhana, distribusi uniform, metode kuadrat terkecil, metode maksimum likelihood, minimax, Nelder-Mead. ***** MONA ULYASARI. Simple Linear Regression Analysis with Uniformly Distributed Error. Undergraduate Thesis, Statistics Study Program, Faculty of Mathematics and Natural Sciences, Universitas Negeri Jakarta, July 2026. Simple linear regression is a statistical method used to model the linear relationship between an independent variable and a dependent variable, as well as to estimate the effect of the independent variable on the dependent variable. This model generally assumes that the error term follows a normal distribution; however, this assumption is not always satisfied in empirical data. An alternative assumption is that the error term follows a uniform distribution over the interval (-a,a), for example, when the error has known lower and upper bounds, such as measurement errors limited by instrument tolerance or measurement processes that produce deviations within a specified range. This study aims to analyze the estimators of the regression parameters, examine their statistical properties, and compare the theoretical results with simulation results. The methods employed are the ordinary least squares method and the maximum likelihood method using a minimax approach, which is solved numerically through the Nelder–Mead optimization method. The results show that the estimators of β₀ and β₁ obtained by the ordinary least squares method under the assumption of uniformly distributed errors have the same form as those derived under the normal error assumption, are unbiased, and satisfy the properties of the Best Linear Unbiased Estimator (BLUE). Estimation using the maximum likelihood method produces estimators through the minimax approach by minimizing the maximum absolute error. The parameter a, which represents the bound of the uniform error distribution, can be estimated using both the ordinary least squares and maximum likelihood methods. Monte Carlo simulation results indicate that the estimators have small biases and are close to the true parameter values, confirming the theoretical results. Keywords: simple linear regression, uniform distribution, ordinary least squares, maximum likelihood estimation, minimax, Nelder-Mead.

Item Type:	Thesis (Sarjana)
Additional Information:	1). Prof. Dr. Suyono, M.Si. 2). Siti Rohmah Rohimah, S.Pd., M.Si.
Subjects:	Sains > Statistika
Divisions:	FMIPA > S1 Statistika
Depositing User:	Mona Ulyasari .
Date Deposited:	18 Aug 2026 03:31
Last Modified:	18 Aug 2026 03:31
URI:	http://repository.unj.ac.id/id/eprint/71147

Actions (login required)

View Item