Quantile Regression

4Quantile Regressions Based on (X1,Y1)

4.1 Introduction

The equation specifications (ESs) of all univariate regression models of a numerical dependent variable presented in Agung (2011a) can also be used to conduct the analysis of the quantile regression models, based on cross-section and experimental data sets. However, this chapter presents only several selected models, based on Data_Faad.wf1, motorcycle data from MASS, MCYCLE.wf1 and the National Social-Economics Survey of Indonesia, namely SUSENAS-2013.

4.2 The Simplest Quantile Regression

The simplest quantile regressions (QRs) based on (X1,Y1) can be presented using the equation specification as follows:

(4.1)

Example 4.1  An Application of the QR (4.1)

Figure 4.1 presents the statistical results of the QR (4.1) based on Data_Faad.wf1, and Figure 4.2 presents the forecast graph Y1F and its forecast evaluation. Based on these figures, the following findings and notes are presented:

1. We can easily obtain the forecast graph and evaluation in Figure 4.1 by clicking the Forecast button and then OK, without selecting any options. Then there is a question “Why the forecast graph of Y1, namely Y1F?” presents a four step function? The explanation is that Data_Faad.wf1 is sorted by the two factors A and B, which makes four different groups or sets of the values or scores of the numerical variables X1 and Y1.
2. In fact, the ...