Modeling the Percentage of Poor People in West Nusa Tenggara Using Truncated Spline Nonparametric Regression

Abstract

Nonparametric regression approaches have received significant attention due to their high flexibility and ability to model data without relying on specific functional form assumptions. One widely applied method is the truncated spline, which effectively handles data behavior changes within specific sub-intervals. This study aims to model the Percentage of Poor People in West Nusa Tenggara Province from 2017 to 2025 using independent variables Average Years of Schooling (X1), Open Unemployment Rate (X2), Per Capita Expenditure (X3), and Life Expectancy (X4). The best model selection was performed by evaluating combinations of 1 to 3 knot points, using the minimum Generalized Cross Validation (GCV) as the primary criterion. Based on the analysis, the optimal truncated spline nonparametric regression model utilizes 1 knot point and degree 1, yielding a GCV value of 12.34126 and a coefficient of determination (R²) of 59.38%. The identified optimal knot points are 8.015 for X1; 3.07 for X2; 10310.5 for X3; and 68.095 for X4.