REGRESI LINIER NONPARA METRIK DENGAN METODE THEIL

Authors

  • Aldila Sarti

DOI:

https://doi.org/10.25077/jmu.2.3.167-174.2013

Abstract

> Analisis regresi linier adalah analisis terhadap hubungan satu variabel terikat
( y) dengan satu atau lebih variabel bebas ( x). Pendugaan parameter biasanya diselesaikan dengan Metode Kuadrat Terkecil (MKT) yang harus memenuhi asumsi-asumsi
tertentu. Salah satu asumsi yang harus dipenuhi dalam MKT adalah kenormalan dari
galat, yaitu galat berdistribusi normal dengan rata-rata nol dan simpangan baku tertentu. Jika asumsi kenormalan galat tidak dapat dipenuhi, maka MKT tidak dapat digunakan. Analisis alternatif yang dapat digunakan untuk mengatasi masalah
tersebut adalah prosedur regresi nonparametrik, salah satunya dengan metode Theil.
Metode Theil adalah metode nonparametrik yang digunakan untuk menduga parameterparameter pada model regresi linier berdasarkan data sampel yang teramati, dengan kondisi galat tidak menyebar normal. Metode Theil menduga koefisien kemiringan (slope)
sebagai median kemiringan dari seluruh pasangan garis dari titik-titik variabel x dan
y dengan syarat semua nilai x i harus berbeda. Pengujian hipotesis parameternya didasarkan pada statistik Tau Kendall. Interval kepercayaannya hanya untuk koefisien
kemiringan (slope). Penerapan Metode Theil untuk data banyak hafalan Al-Quran siswa
dengan variabel terikat y i adalah banyak hafalan Al-Quran siswa dan variabel bebas x i
adalah lama menghafal dapat disimpulkan: (1) model regresi Theil yang diperoleh adalah
yˆi = 0, 9990 + 0, 1667x i, (2) lama menghafal berpengaruh terhadap banyak hafalan AlQuran siswa, (3) selang kepercayaan koefisien slope yaitu (0.0833, 0.3).

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Published

10-09-2013

How to Cite

Sarti, A. (2013). REGRESI LINIER NONPARA METRIK DENGAN METODE THEIL. Jurnal Matematika UNAND, 2(3), 167–174. https://doi.org/10.25077/jmu.2.3.167-174.2013

Issue

Vol. 2 No. 3 (2013)

Section

Articles

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