A comparison among Different Methods for Estimating Regression Parameters with Autocorrelation Problem under Exponentially Distributed Error

Abstract

Multiple linear regressions are concerned with studying and analyzing linear relationship between the dependent variable and a set of explanatory variables. From this relationship, the values of variables are predicted. In this paper the multiple linear regression model and three covariates were studied in the presence of the problem of auto-correlation of errors when the random error was distributed over the distribution of exponential. Three methods were compared (general least squares, M robust, and Laplace robust method). Simulation studies have been employed and calculated the statistical standard mean squares error with different sample sizes. Further the best method has been applied on real data representing the varieties of cigarettes according to the US Federal Trade Commission.