Response Surface Regression with LTS and MM-Estimator to Overcome Outliers on Red Roselle Flowers

  • Trianingsih Eni Lestari Universitas Negeri Malang
  • Rike Desy Tri Yuansa Yuansa Universitas Negeri Malang
Keywords: Response Surface Regression, Outliers, Least Trimmed Square (LTS);, MM-estimator


The surface response method is similar to the regression analysis method which uses procedures or ways of estimating the response function regression model based on the Ordinary Least Square (OLS) method. Unfortunately, using the quadratic method has no drawbacks because it is easily sensitive to assumption deviations due to outlier cases. One of the solutions to the outlier problem is using robust regression. The method of parameters in the regression is very diverse, but the methods used in this study are the Least Trimmed Square (LTS) and MM-estimator methods because both methods have a high breakdown point of nearly 50%. The variables studied were the response variable consisting of red roselle plant height (Y1) and red roselle flower weight (Y2). While the independent variables were soil moisture factor (X1) and NPK fertilizer application factor (X2). The purpose of this study is to estimate the response surface regression parameters. using the LTS and MM-estimator methods on data that contains outliers. The resulting model in data analysis shows the same result that the best model is using the LTS estimation method. The modeling result of plant height obtained an R-Square value of 98,27% with an error is 1,243. Meanwhile, for the red rosella plant flower weight model, the R-Square value was 97,31% with an error is 0.6632.


Ajala, E. O., Aberuagba, F., Olaniyan, A. M., Ajala, M. A., & Sunmonu, M. O. (2017). Optimization of a two stage process for biodiesel production from shea butter using response surface methodology. Egyptian Journal of Petroleum, 26(4), 943–955.
Aminuddin, A., Sudarno, S. and Sugito, S. (2013). Pemilihan Model Regresi Linier Multivariat Terbaik Dengan Kriteria Mean Square Error. Jurnal Gaussian, 2(1), 11–18.
Calfee, R. and Piontkowski, D. (2016). Handbook of reading research: In Choice Reviews Online (Vol. 38, Issue 02).
Jensen, W. A. (2017). Response Surface Methodology: Process and Product Optimization Using Designed Experiments 4th edition. Journal of Quality Technology, 49(2), 186–188.
Keshani, S., Luqman Chuah, A., Nourouzi, M. M., Russly, A. R., & Jamilah, B. (2010). Optimization of concentration process on pomelo fruit juice using response surface methodology (RSM). International Food Research Journal, 17(3), 733–742.
Peroumal, D., Loganathan, Kumar, R., & Prabu, B. (2019). Determination of more influencing geometrical parameter of dent on buckling strength of thin plate under axial load using response surface regression. Materials Today: Proceedings, 16, 677–685.
Rohmawati, A., & Dwidayati, N. K. (2018). Perbandingan Metode Least Trimmed Square (LTS) dan Scale (S) Pada Response Surface Methodology. PRISMA, 1, 728–735.
Roozbeh, M., Babaie-Kafaki, S., & Naeimi Sadigh, A. (2018). A heuristic approach to combat multicollinearity in least trimmed squares regression analysis. Applied Mathematical Modelling, 57, 105–120.
Rousseeuw, P. J., & Hubert, M. (2011). Robust statistics for outlier detection. Wiley Interdisciplinary Reviews: Data Mining and Knowledge Discovery, 1(1), 73–79.
Rousseeuw, P. J., & Hubert, M. (2018). Anomaly detection by robust statistics. Wiley Interdisciplinary Reviews: Data Mining and Knowledge Discovery, 8(2), 1–14.
Sawale, P. D., Patil, G. R., Hussain, S. A., Singh, A. K., & Singh, R. R. B. (2020). Development of free and encapsulated Arjuna herb extract added vanilla chocolate dairy drink by using response surface methodology (RSM) software. Journal of Agriculture and Food Research, 2(December 2019), 100020.
Seheult, A. H., Green, P. J., Rousseeuw, P. J., & Leroy, A. M. (1989). Robust Regression and Outlier Detection. Journal of the Royal Statistical Society. Series A (Statistics in Society), 152(1), 133.
Shemi, A. P., & Procter, C. (2018). E-commerce and entrepreneurship in SMEs: case of myBot. Journal of Small Business and Enterprise Development, 25(3), 501–520.
Shodiqin, A., Aini, A. N., & Rubowo, M. R. (2018). Perbanding Dua Metode Regresi Robust yakni Metode Least Trimmed Squares (LTS) dengan metode Estimator-MM (Estmasi-MM) (Studi Kasus Data Ujian Tulis Masuk Terhadap Hasil IPK Mahasiswa UPGRIS). Jurnal Ilmiah Teknosains, 4(1), 35.
Wulandari, S., Sutarman, S., & Darnius, O. (2013). Perbandingan Metode Least Trimmed Squares Dan Penaksir M Dalam Mengatasi Permasalahan Data Pencilan. Saintia Matematika, 1(1), 73–85.
Yu, M., Wang, B., Qi, Z., Xin, G., & Li, W. (2019). Response surface method was used to optimize the ultrasonic assisted extraction of flavonoids from Crinum asiaticum. Saudi Journal of Biological Sciences, 26(8), 2079–2084.
Yuliana, S., Hasih, P., Sri Sulistijowati, H., & Twenty, L. (2014). M Estimation, S Estimation, and Mm Estimation in Robust Regression. International Journal of Pure and Applied Mathematics, 91(3), 349–360.
Zhang, W., & Ato Xu, W. (2017). Simulation-based robust optimization for the schedule of single-direction bus transit route: The design of experiment. Transportation Research Part E: Logistics and Transportation Review, 106, 203–230.
How to Cite
T. Lestari and R. D. Yuansa, “Response Surface Regression with LTS and MM-Estimator to Overcome Outliers on Red Roselle Flowers”, Jurnal Varian, vol. 4, no. 2, pp. 91 - 98, Apr. 2021.