Analysis of regressionis one technique that is often used in statistical analysis. There are three regression analysis approaches, such as parametric regression, nonparametric regression and semiparametric regression. Semiparametric regression consists of parametric components and nonparametric components. Parametric component that used such as linear estimator and nonparametric component by using a Fourier series estimator. Semiparametric regression approach that use Fourier series, have an advantages which is can resolve oscillation data pattern. This study compares the three Fourier series estimators such as sine, cosine, and combination between cosine and sine or complete estimator for longitudinal data. Longitudinal data can explain more complete information than cross section data or time series data. The purpose of this study is to introduce another Fourier series for the application of electricity consumption in Madura island. The results of this study indicated the optimal model in predicting electricity consumption in Madura island. The best estimator is the Fourier series estimator with the smallest Generalized Cross Validation (GCV) and Mean Square Error (MSE), and the biggest determination coefficient values by considering the parsimony of the model.

Regression modelling is one Statistical methods that be used to investigate the relationship between predictor variable and response variable. In regression modelling can be estimated with three approaches, such as parametric, nonparametric and semiparametric regression. In this case, we concentrated to elaborate semiparametric regression. Semiparametric regression consists of parametric and nonparametric component. This research examined semiparametric regression model with Fourier series estimator for longitudinal data. By minimizing Weighted Least Square (WLS), the Fourier series estimator depends on the oscillation parameter. The result is the estimator for parameter and curve regression, that be used to model with real data. The optimal model is selected based on minimum Generalized Cross Validation (GCV) which affects the small value of Mean Square Error (MSE) and high determination coefficient so that the model can be used further as estimation and prediction.

Madura is an area in Indonesia that is still far behind compared to other regions, especially in the field of education. The education system in Madura is dominated by boarding school where boarding school has become a distinctive culture that is still maintained by the Madura community, especially among adolescents who are deciding the future of a country to receive education, it can be a motivation to improve the education system in Madura. In addition there are many things that are the reason for the Madura community that causes the education system in Madura is unstable so it needs to be further analyzed factors that influence the motivation of adolescents to improve education. For this purpose, collected through a survey of adolescents in Madura who became the sample. The survey was conducted online related to the reasons for the interruption of adolescent education in Madura including motivation, environment and poverty data obtained and then processed using Structural Equation Modeling. The method has the advantage of being able to analyze latent variables or variables that cannot be measured such as motivation. Based on the results of the study, it can be seen that the factors that influence motivation to improve education are motivation and poverty. Environmental factors do not affect the improvement of adolescent education in Madura.

No abstract