Estimation of a Multiple Linear Regression Model Using Some Robust Methods

Abstract

The multiple linear regression modelsare one of the important models in regression because it is used in analyzing a lot of data in various economic, medical and social fields. The relationship between the dependent variable and the interpreted variables in the form of an equation by estimating its parameters, we infer the strength and importance of this relationship. Inefficient and gives biased capabilities in the event that one of its basic hypotheses is not available. Therefore, in this research, robust methods were used instead of them because of the problem of outliers, which are observations that go out of the data pattern and that have a significant impact on the non-fulfillment of the hypothesis of a normal distribution, and this contradicts one of the basic assumptions on which multiple linear regression is based. One of the most important methods used in this research is the MM-Estimation, S-Estimation and M-Estimation method, through an applied study of a data set to study the impact of exchange rates and oil on gold prices. It was found through the results that the exchange rate variable had a more significant effect on the dependent variable than the oil price, except in the S method. It was found that the exchange rate variable did not have a significant effect on the price of gold, and based on the MSE comparison standard, it was found that the best method is the M method, followed by the S method and then the MM method.