Pemodelan Hubungan Kepadatan Penduduk dan Indeks KualitasUdara (IKU) di Indonesia Menggunakan Regresi Kuantil Smoothing Splines

Abstract

The level of pollution in Indonesia is in the top 10 worst in the world. Judging from the Air Quality Index (IKU), there are 9 provinces that have KPI values ​​below the expected target. This paper aims to perform IKU modelling using the population density variable as a predictor variable. Modelling using linear regression in the parametric method cannot be used because the model residuals are not normally distributed, so a nonparametric smoothing splines approach is carried out. However, the presence of outliers in the smoothing splines residual model causes the residuals of the model to be too large so that it affects the prediction accuracy, so the smoothing splines quantile regression is used in the IKU modelling. Apart from using the median (quantile τ = 0.5), the quantiles of 0.2 were also used; 0.4; 0.6; and 0.8 to generate models at various quantiles. The results of the analysis using the R package quantreg Software prove that the smoothing splines (median) quantile regression model is more robust against the presence of outliers seen from the lower RMSE value than the smoothing splines regression model (mean). In addition, it is concluded that there are 5 provinces that are below the quantile 0.2, which means that the IKU level is very low or there is very high pollution based on the level of population density. Likewise, there are 3 provinces with KPI values ​​above the quantile of 0.8, which means they have very high IKU levels or areas with low levels of pollution.