A Comparison between Linear Regression and Lasso Quantile regression methods in Variables Selection

One of the main topics in the development of predictive models is the identification of variables which are predictors of a given outcome. Automated model selection methods, such as backward or forward stepwise regression, are classical solutions to this problem, but are generally based on strong assumptions about the functional form of the model or the distribution of residuals. The quantile regression can give complete information about the relationship between the response variable and covariates on the entire conditional distribution, and has no distributional assumption about the error term in the model. This study evaluates the performance of the Lasso regression as a good alternative to Ordinary least squares and least absolute value regression methods when used to estimate the regression coefficients. The efficiency of the Lasso regression when used to select subset of variables is demonstrated. The study presents a data analysis to demonstrate the efficiency of the Lasso quantile regression when different quantile regression values are used to select subset of variables and estimation regression coefficients. Kruskal-Wallis test as a goodness of fit test is applied to confirm the efficiency of the methods in which it may be many researches have praised the efficiency simulated but separate in many research. All methods used to estimate linear regression equation. The study results showed that Lasso quantile regression is an appropriate model for estimating the parameters and selection of variables.