Joint Regression Modeling of Location and Scale Parameters of the Skew Distribution with Application in Soil Chemistry Data

In regression model applications, the errors may frequently present a symmetric shape. In such cases, the normal and Student distributions are commonly used. In this paper, we shall be concerned only to model heavy-tailed, skewed errors and absence of variance homogeneity with two regression structures based on the skew distribution. We consider a classic analysis for the parameters of the proposed model. We perform a diagnostic analysis based on global influence and quantile residuals. For different parameter settings and sample sizes, various simulation results are obtained and compared to evaluate the performance of the skew regression. Further, we illustrate the usefulness of the new regression by means of a real data set (amount of potassium in different soil areas) from a study carried out at the Department of Soil Science of the Luiz de Queiroz School of Agriculture, University of São Paulo.