Robust Regression Analysis Study for Data with Outliers at Some Significance Levels

Waego Hadi Nugroho,Ni Wayan Surya Wardhani,Adji Achmad Rinaldo Fernandes,Solimun Solimun

doi:10.13189/ms.2020.080401

Waego Hadi Nugroho, Ni Wayan Surya Wardhani + Show 2 more

Open Access

https://doi.org/10.13189/ms.2020.080401

Copy DOI

Abstract

Robust regression analysis is an analysis that is used if there is an outlier in a regression model. Outliers cause data to be abnormal. The most commonly used parameter estimation method is Ordinary Least Squares (OLS). However, outliers in models cause the estimator of the least-squares in the model to be biased, so handling of outliers is required. One of the regressions used for outliers is robust regression. Robust regression method that can be used is M-Estimation. By using Tukey's Bisquare weighted function, a robust M-estimation method can estimate parameters in a model, for example in malnutrition data in East Java Province 2017 to 2012. This study aims to compare the robust method of M-estimation and OLS method on data with several different levels of significance, which is 1%, 5%, and 10%. The predictor variables used in this study were the percentage of poor society, population density, and some health facilities. R2 is used to compare the OLS method and the robust method of M-estimation. The results obtained that robust regression is the best method to handle the model if there are outliers in the data. It was supported by almost all results of the value of R^2 on each data that M-estimation has a higher value than the OLS method.

Highlights

Regression analysis is a statistical analysis that is used to determine the relationship between response variables and predictor variables, both and more
If there is more than one predictor variable, the analysis can be said as multiple linear regression analysis (Fernandes et al, 2018)
Based on the results of the analysis it can be concluded that, the model with parameter estimators obtained from the M-Estimator method can be effectively used to predict Malnutrition in East Java Province

Summary

Introduction

Regression analysis is a statistical analysis that is used to determine the relationship between response variables and predictor variables, both and more. According to (Draper & Smith, 1992), regression analysis is used to determine conclusions from data that has a related relationship between response and predictors variables. If there is more than one predictor variable, the analysis can be said as multiple linear regression analysis (Fernandes et al, 2018). There are several methods to predict the parameters in regression, one of the methods is Ordinary Least Square (OLS) (Hidayat et al, 2019). OLS must fulfill some prescribed assumptions, with errors mutually independent and normal with a middle value 0 and variance 2 (Fernandes et al, 2014). Multiple regression analysis must fulfill several other assumptions namely the assumption of normality, multicollinearity, heteroscedasticity, and autocorrelation (Gujarati, 2003)

Objectives

Methods

Discussion

Conclusion