Prediction the number of students in Indonesia who study in tutoring agency and their motivations based on fourier series estimator and structural equation modelling

In Indonesia, tutoring agencies are supporting students in learning outside the school especially close to examinations times. The predictions of the number of students who study in tutoring agencies are important as a recommendation for regulations in the field of education. The number of students who study in a tutoring agency demonstrates a seasonal pattern with an increasing trend, so the Fourier series estimator is used to predict this event. Monthly data on the number of students who enrolled in three tutoring agencies during five years is collected. After obtaining the prediction model based on the best Fourier series estimator for longitudinal data, data exploration is then preceded based on the questionnaire to find out the significant motivation factors from students along with their supporting dimensions related to the reasons for using a tutoring agency. Structural Equation Modelling (SEM) was used to analyse the motivation. The results show that there were three motivation factors for students in joining the tutoring agencies such as reliability, guarantee, and empathy. These results can be used as material for evaluating the education process in Indonesia.