Asmin, Sufri (2009) Pemodelan Nilai UNAS IPA Dengan Pendekatan Regresi Semiparametrik Spline Di SMAN 1 Grati Pasuruan. Masters thesis, Institut Teknologi Sepuluh November.
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Abstract
UNAS sebagai salah satu indikator peningkatan mutu pendidikan dilihat dari beberapa aspek, yaitu nilai tryout, nilai UAS, nilai rapor, nilai UNAS SMP, jarak tempuh,penghasilan orang tua, dan jumlah saudara. Aspek-aspek inilah yang dipakai sebagai variabel prediktor. Metode statistika yang digunakan adalah analisis regresi semiparametrik spline. Penelitian ini bertujuan mengkaji estimator model regresi semiparametrik spline dengan menggunakan least square dan penerapannya pada data nilai UNAS. Model regresi semiparametrik dinyatakan y_i = x'_i β + f(t_i) + ε_i, i = 1,2,...,n, dengan error random diasumsikan berdistribusi normal dengan mean nol dan varians σ². Jika f(t_i) didekati dengan fungsi spline univariabel: f(t) = ∑{j=0}^{m} γ_j t^j + ∑{k=1}^{N} δ_k (t - K_k)_+^m, maka diperoleh model regresi y_i = x'i β + ∑{j=0}^{m} γ_j t_i^j + ∑{k=1}^{N} δ_k (t_i - K_k)+^m + ε_i. Estimator yang diperoleh dengan metode least square adalah ŷ = A(K_1,...,K_N) y. Apabila model regresi semiparametrik y_i = x'i β + f(t{1i}, t_{2i}, ..., t_{pi}) + ε_i didekati dengan fungsi spline multivariable f(t_{ji}) = ∑{k=1}^{m} ϕ{jk} t_{ji}^k + ∑{l=1}^{N} ω{jl} (t_{ji} - K_{jl})+^m, maka diperoleh model regresi y_i = x'i β + f(t{ji}) = ∑{k=1}^{m} ϕ_{jk} t_{ji}^k + ∑{l=1}^{N} ω{jl} (t_{ji} - K_{jl})_+^m + ε_i. Selanjutnya diperoleh estimasi kurva regresi dengan metode least square adalah ŷ = B(K_11,...,K_N1 ; ... ; K_1p,...,K_Np) y. Selanjutnya estimator regresi semiparametrik spline diaplikasikan pada data Nilai UNAS SMAN 1 Grati Pasuruan, diperoleh hasil bahwa nilai tryout, nilai UAS, nilai rapor, nilai UNAS SMP, jarak tempuh, penghasilan orang tua, dan jumlah saudara memberikan pengaruh yang berarti terhadap nilai UNAS SMAN 1 Grati.
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UNAS as one of improvement indicator quality of education seen from some aspects, tryout score, school examination score, rapor score, UNAS SMP score, distance, parent salary, and number of yous. These aspects was used as predictor variables. Statistical methods applied is spline semiparametric regression analysis. This research is aim to study spline semiparametric regression estimator by using least square and applied to data of UNAS score. Semiparametric regression model expressed as y_i = x'_i β + f(t_i) + ε_i, i = 1,2,...,n, with error random assumed distributed normal with zero mean and variance σ². If f(t_i) approximately by univariable spline function: f(t) = ∑{j=0}^{m} γ_j t^j + ∑{k=1}^{N} δ_k (t - K_k)_+^m, then we have regression model y_i = x'i β + ∑{j=0}^{m} γ_j t_i^j + ∑{k=1}^{N} δ_k (t_i - K_k)+^m + ε_i. Estimator obtained with least square method is ŷ = A(K_1,...,K_N) y. If semiparametric regression model y_i = x'i β + f(t{1i}, t_{2i}, ..., t_{pi}) + ε_i, closed to multivariable spline function f(t_{ji}) = ∑{k=1}^{m} ϕ{jk} t_{ji}^k + ∑{l=1}^{N} ω{jl} (t_{ji} - K_{jl})+^m, then we have regression model y_i = x'i β + f(t{ji}) = ∑{k=1}^{m} ϕ_{jk} t_{ji}^k + ∑{l=1}^{N} ω{jl} (t_{ji} - K_{jl})_+^m + ε_i. Thus we have regression curve estimation with least square method is ŷ = B(K_11,...,K_N1 ; ... ; K_1p,...,K_Np) y. Thus spline semiparametric regression estimator applied to data Nilai UNAS SMAN 1 Grati Pasuruan, obtained result that tryout score, school examination score, rapor score, UNAS SMP score, distance, parent salary, and number of yous gives influence meaning to UNAS score of SMAN 1 Grati.
| Item Type: | Thesis (Masters) |
|---|---|
| Additional Information: | 519.536 Asm p |
| Uncontrolled Keywords: | Regresi Semiparametrik, Spline Univariabel, Spline Multivariabel, Titik Knot, Semiparametric regression, Univariable spline, Multivariable spline, knots points. |
| Subjects: | Q Science > QA Mathematics > QA278.2 Regression Analysis. Logistic regression |
| Divisions: | Faculty of Mathematics and Science > Statistics > 49101-(S2) Master Thesis |
| Depositing User: | magang . |
| Date Deposited: | 02 Oct 2026 02:15 |
| Last Modified: | 02 Oct 2026 02:15 |
| URI: | http://repository.its.ac.id/id/eprint/145158 |
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