# TUBERCULOSIS CASE MODEL USING GCV AND UBR KNOT SELECTION METHODS IN TRUNCATED SPLINE NONPARAMETRIC REGRESSION

• Sitti Anggraeni Statistical Study Program, Faculty of Mathematics and Natural Sciences, Mulawarman University, Indonesia
• Sifriyani Sifriyani Statistical Study Program, Faculty of Mathematics and Natural Sciences, Mulawarman University, Indonesia
• Qonita Qurrota A'yun Mathematics Study Program, Faculty of Mathematics and Natural Sciences, Mulawarman University, Indonesia
Keywords: Nonparametric Regression, Truncated Spline, GCV, UBR, Tuberculosis

### Abstract

The nonparametric regression approach is used when the shape of the regression curve is not known. The advantage of nonparametric regression is that it has a high degree of flexibility. The truncated spline is a method in the nonparametric regression approach, which can overcome changing data patterns at certain sub-intervals with the help of knot points. The purpose of this research is to obtain the best truncated spline nonparametric regression model estimates based on the GCV and UBR knot point selection methodsThe data used in this study came from the publications of the Indonesian Ministry of Health and BPS Indonesia. The response variable used is the percentage of successful treatment of tuberculosis patients in Indonesia with predictor variables namely the percentage of people who smoke over the age of 15 years, the percentage of households that have access to proper sanitation, the percentage of poor people, the percentage of food processing establishments that meet the standard requirements , national health insurance membership coverage and percentage of accredited hospitals. The results showed that the best model came from the GCV method using three knots. This model produces an MSE value of 3.65 with  value of 97.04. The value indicates that the predictor variable used in this study affects the response variable by 97.04% while the other 2.96% is influenced by other variables that are not included in this study.

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Published
2023-09-30
How to Cite
[1]
S. Anggraeni, S. Sifriyani, and Q. A’yun, “TUBERCULOSIS CASE MODEL USING GCV AND UBR KNOT SELECTION METHODS IN TRUNCATED SPLINE NONPARAMETRIC REGRESSION”, BAREKENG: J. Math. & App., vol. 17, no. 3, pp. 1565-1574, Sep. 2023.
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Articles