Application of the cubic spline nonparametric regression model to human development index data in Indonesia

The most popular measurement in determining the success of human development is known as the Human Development Index (HDI). The HDI calculation is based on four influencing indicators, namely life expectancy, expected years of schooling, mean years of schooling, and adjusted per capita expenditure. The effect of indicators on HDI can be determined by using a cubic spline nonparametric regression model. Cubic spline regression is used because it can eliminate curves that exceed the limit and the error is large enough to fit the data characteristics. The best cubic spline nonparametric regression model is influenced by the optimal knot point selection. The selection of the optimal knot point is based on the minimum generalized cross validation (GCV) value. In this article, a cubic spline nonparametric regression model is applied to the HDI data in Indonesia. Based on the results, it was obtained that the best cubic spline nonparametric regression model on HDI data in Indonesia with GCV value=0.003539 and 3 optimal knot points for each independent variable. The results show that indicators of life expectancy, expected years of schooling, mean years of schooling, and adjusted per capita expenditure are indicators that influence HDI in Indonesia.