Robust regression analysis study for data with outliers at some significance levels

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 R² on each data that M-estimation has a higher value than the OLS method.