MATHEMATICAL MODELLING OF FACTORS FOR MEDICAL INSURANCE COST IN THE UNITED STATES USING ROBUST REGRESSION

Abstract

The rising cost of medical insurance in the United States requires a thorough understanding of the factors influence it. Many factors can affect the cost of medical insurance, including age, sex, BMI, smoking habits and number of children. Problems arise when analysing data that contain outliers, as individual observations can a large impact on results. Robust regression is one of the useful methods in decreasing the effect of outliers in modelling. Hence, this paper aims to determine the best estimator between three estimators and to test the robustness of the best estimator when the data contaminated with outliers. We then applied to the dataset collected from the US Census Bureau published by Brett Lantz in 2013.  The findings showed that R² of LTS-estimator, MM-estimator and S-estimator were 0.9813, 0.6735 and 0.9728 respectively.  When the data was contaminated with 10%, 20% and 30% of outliers the R² values of LTS-estimator were 0.9399, 0.9030 and 0.8678. Thus, it can be concluded that the LTS-estimator can help in producing results that are resistant to outliers.