A Comparison between Nonparametric Approach: Smoothing Spline and B-Spline to Analyze The Total of Train Passangers in Sumatra Island

Abstract

he train is one of the means of land transportation of the most desirable communities other than ground transportation such as bus or car. This is because the rail has an advantage that is free from congestion. Increasing mobility of people, means of transportation that is free from congestion increasingly in demand. In Indonesia, the only railway in Java and Sumatra. Either in Java or Sumatra Island train passenger numbers have increased every year. Based on data from BPS-Statistics, the number of train passengers in Sumatra during the last five years has increased an average of 14.8 percent per year. Noparametric regression model that can be used to describe the pattern of data on the number of train passengers in Sumatra Island is smoothing spline regression and B-spline regression. The purpose of this study is to find the most nonparametric regression model to describe the pattern of the relationship between the time and number of train passengers on Sumatra Island. Smoothing spline and B-spline models were compared by looking at the regression curve and the value of Mean Square Error (MSE). The results of this study indicate that smoothing spline model is more appropriate to see the pattern of the relationship between the time and number of train passengers in Sumatra Island. This can be seen from the MSE of smoothing spline models 2,742.801 smaller than the MSE of B-spline models 3,847.657.