Comparasion of The M, MM and S Estimator in Robust Regression Analysis on Indonesian Literacy Index Data 2018

Ditya Anggraheni Rahayu (Mathematics Department Ahmad Dahlan University, Jl. Ringroad Selatan, Kragilan, Tamanan, Kec. Banguntapan, Kabupaten Bantul, Daerah Istimewa Yogyakarta 55191)
Ummu Fitrotin Nursholihah (Mathematics Department Ahmad Dahlan University, Jl. Ringroad Selatan, Kragilan, Tamanan, Kec. Banguntapan, Kabupaten Bantul, Daerah Istimewa Yogyakarta 55191)
Galang Suryaputra (Mathematics Department Ahmad Dahlan University, Jl. Ringroad Selatan, Kragilan, Tamanan, Kec. Banguntapan, Kabupaten Bantul, Daerah Istimewa Yogyakarta 55191)
Sugiyarto Surono (Mathematics Department Ahmad Dahlan University, Jl. Ringroad Selatan, Kragilan, Tamanan, Kec. Banguntapan, Kabupaten Bantul, Daerah Istimewa Yogyakarta 55191)

EKSAKTA: Journal of Sciences and Data Analysis
VOLUME 4, ISSUE 1, February 2023

Regression analysis is a method used to determine the relationship between one dependent variable and one or more independent variables. However, the existence of outliers in the 2018 Community Literacy Development Index data led to the application of statistical methods not sensitive to pencils for analysis. This was the reason for adopting robust regression methods, including the M, S, and MM estimations. Therefore, this research aims to compare these three estimates and select the one with the best estimate based on the parameter estimation model associated with the RSE and R2 values. Descriptive and inferential analysis with robust regression was used due to several outlier data and to provide good regression model results with unbiased values. It was discovered that the S-estimator and MM-estimator are the best methods because they have the most minor Residual Standard Error (RSE) of 1.856 and R2 of 0.9778.