# KAJIAN REGRESI KEKAR MENGGUNAKAN METODE PENDUGA-MM DAN KUADRAT MEDIAN TERKECIL

• Khusnul Khotimah Department of Statistics, IPB University, Indonesia
• Kusman Sadik Department of Statistics, IPB University, Indonesia
• Akbar Rizki Department of Statistics, IPB University, Indonesia
Keywords: least median squares, multi-stage method, outliers, robust regression, root mean squares error

### Abstract

Regression is a statistical method that is used to obtain a pattern of relations between two or more variables presented in the regression line equation. This line equation is derived from estimation using ordinary least squares (OLS). However, OLS has limitations that are highly dependent on outliers data. One solution to the outliers problem in regression analysis is to use the robust regression method. This study used the least median squares (LMS) and multi-stage method (MM) robust regression for analysis of data containing outliers. Data analysis was carried out on generation data simulation and actual data. The simulation results of regression analysis in various scenarios are concluded that the LMS and MM methods have better performance compared to the OLS on data containing outliers. MM method has the lowest average parameter estimation bias, followed by the LMS, then OLS. The LMS has the smallest average root mean squares error (RMSE) and the highest average R2 is followed by the MM then the OLS. The results of the regression analysis comparison of the three methods on Indonesian rice production data in 2017 which contains 10% outliers were concluded that the LMS is the best method. The LMS produces the smallest RMSE of 4.44 and the highest R2 that is 98%. MM's method is in the second-best position with RMSE of 6.78 and R2 of 96%. OLS method produces the largest RMSE and lowest R2 that is 23.15 and 58% respectively.

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Published
2020-02-28
How to Cite
Khotimah, K., Sadik, K., & Rizki, A. (2020). KAJIAN REGRESI KEKAR MENGGUNAKAN METODE PENDUGA-MM DAN KUADRAT MEDIAN TERKECIL. Indonesian Journal of Statistics and Its Applications, 4(1), 97-115. https://doi.org/10.29244/ijsa.v4i1.502
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