ANALISIS REGRESI ROBUST ESTIMASI M PEMBOBOT WELSCH DAN ESTIMASI LTS (Studi kasus: Faktor yang mempengaruhi angka kasus tuberkulosis di Jawa Timur tahun 2023)

Ade Suryanti, NIM.: 21106010076 (2025) ANALISIS REGRESI ROBUST ESTIMASI M PEMBOBOT WELSCH DAN ESTIMASI LTS (Studi kasus: Faktor yang mempengaruhi angka kasus tuberkulosis di Jawa Timur tahun 2023). Skripsi thesis, UNIVERSITAS ISLAM NEGERI SUNAN KALIJAGA.

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Abstract

Regression analysis is a statistical analysis method that examines the causal relationship between one dependent variable and one or more independent variables. The commonly used method is Ordinary Least Squares (OLS). The data are analyzed under the classical assumptions of linear regression, including tests for homoskedasticity, normality, autocorrelation, and multicollinearity. However, in certain cases and conditions, violations of these assumptions may occur, leading to inaccurate results. Therefore, outlier detection is necessary using leverage, DFFITS, and R-student measures. Robust regression is a method used in regression analysis that accounts for the presence of outliers. In this study, the robust regression models employed are M-estimation withWelsch weighting and Least Trimmed Squares (LTS) estimation. This study aims to obtain the best model by comparing the Residual Standard Error (RSE) and the coefficient of determination from the estimation results. The case study in this research focuses on the factors affecting the tuberculosis (TB) rate (Y), with HIV (X1), general hospitals (X2), access to improved water sources (X3), healthcare workers (X4), and the open unemployment rate (X5) as independent variables, based on regencies and cities in East Java Province in 2023. The results show that M-estimation with Welsch weighting is the best method for modeling TB data, as it produces the smallest Residual Standard Error (RSE) of 9.007 and the highest coefficient of determination of 0.8623. This indicates that the resulting model is able to explain 86.23% of the variation in the number of TB cases, while the remaining variation is explained by other factors outside the model. Furthermore, all independent variables used in this study namely HIV (X1), general hospitals (X2), access to improved water sources (X3), healthcare workers (X4), and the open unemployment rate (X5) have a significant effect on the number of TB cases (Y). The regression model obtained using the M-estimation method in this study can be expressed as follows: ˆ Y = 2,159 + 0,034X1 + 2,855X2 + 1,092X3 − 0,008X4 − 6,255X5

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