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Abstract
This study investigates the determinants of per capita expenditure in 154 regencies and cities across Sumatra Island. The use of the Ordinary Least Squares method is deemed inappropriate due to violations of classical assumptions and the presence of outliers within the dataset. To address these issues, robust regression approaches are applied, specifically M-estimation and Least Trimmed Squares (LTS). The dependent variable in the analysis is per capita expenditure, while the explanatory variables include poverty line, human development index, average years of schooling, and expected years of schooling. The estimation procedures are performed using both raw and standardized data. The empirical results demonstrate that each independent variable significantly influences per capita expenditure under both robust estimation techniques. To determine the most reliable method, the residual standard error is used as the evaluation criterion. The outcomes indicate that the LTS estimator applied to standardized data provides the lowest error value, suggesting that it is the most suitable approach for estimating the regression parameters associated with per capita expenditure in Sumatra.
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Copyright (c) 2025 Andro Kurniawan, Cinta Rizki Oktarina, Sabarinsyah
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References
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References
I. Ghozali, Multivariate Analysis Application with IBM SPSS 19 Program. Semarang: UNDIP, 2011.
K. Sambell, L. McDowell, and C. Montgomery, Assessment for learning in higher education. Abingdon: Routledge, 2012. doi: 10.4324/9780203818268.
N. Nurdin, A. Islamiyati, and Raupong, "The Use of Robust Regression on Data Containing Outliers Using the Moment Method," JMSK J. Mat. Stat. dan Komputasi, vol. 10, no. 2, pp. 114–123, 2014, [Online]. Available at: journal.unhas.ac.id/index.php/jmsk
Soemartini, Outliers. Bandung: Unpad Press, 2007.
S. Wijaya, “Parameter Estimation in Robust Regression Models Using Huber Functions,” University of Indonesia, 2009. [Online]. Available at: https://lib.ui.ac.id/file?file=digital/old23/20181962-010-09-Taksiran parameter.pdf
M. H. Kutner and Christopher J. Nachtsheim, Applied Linear Statistical Models, vol. 29, no. 2. New York: New York: Mc.Graw-Hill Companies, 1997. doi: 10.1080/00224065.1997.11979760.
D. Intan Perihatini, "COMPARISON OF LTS ESTIMATION, M ESTIMATION, AND S ESTIMATION METHODS IN ROBUST REGRESSION (Case Study: Car Financing at Company 'X' in 2016)," 2018.
N. Draper and H. Smith, Applied Regression Analysis (Second Edition, translated by Gramedia). Jakarta: PT. Gramedia Pustaka Utama, 1992.
S. Yuliana, P. Hasih, H. Sri Sulistijowati, and L. Twenty, “M Estimation, S Estimation, and MM Estimation in Robust Regression,” Int. J. Pure Appl. Math., vol. 91, no. 3, pp. 349–360, 2014.
D. C. Montgomery and E. A. Peck, Introduction to Linear Regression Analysis. New York: John Wiley & Sons, 1992.
Y. D. K. Setyo Wira Rizki, “Robust M-Estimation Regression Analysis Using Tukey and Welsch Bisquare Weighting to Overcome Outlier Data,” Bimaster Bul. Ilm. Mat. Stat. dan Ter., vol. 8, no. 4, pp. 799–804, 2019, doi: 10.26418/bbimst.v8i4.36199.
M. Y. Matdoan, "ROBUST LEAST TRIMMED SQUARE (LTS) REGRESSION MODELING (Case Study: Factors Factors Affecting the Spread of Malaria in Indonesia),” Euclid, vol. 7, no. 2, pp. 77, 2020, doi: 10.33603/e.v7i2.2926.
Dina Rohmah, Y. Susanti, and E. Zukhronah, “Comparison of Robust Regression Models: M Estimation and Least Trimmed Squares (LTS) Estimation on the Number of Tuberculosis Cases in Indonesia,” vol. 4, no. 2, pp. 136–146, 2020