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STATISTIKA INDUSTRI 2
TIN 4004
Pertemuan 8
• Outline: – Multiple Linear Regression and Correlation
– Non Linear Regression
• Referensi: – Montgomery, D.C., Runger, G.C., Applied Statistic
and Probability for Engineers, 5th Ed. John Wiley & Sons, Inc., 2011.
– Walpole, R.E., Myers, R.H., Myers, S.L., Ye, K., Probability & Statistics for Engineers & Scientists , 9th Ed. Prentice Hall, 2012.
Multiple Linear Regression
• Terdiri atas lebih dari satu independent variable
• Metode yang digunakan untuk estimasi koefisien: – Least square estimation (metode kuadarat
terkecil)
– Normal equation (Persamaan Normal)
– Matrix approach (Sistem Matriks)
Multiple Linear Regression Penentuan Koefisien
• Least square estimation (metode kuadarat terkecil)
Multiple Linear Regression Least square estimation
• Persamaan least square:
• Least square normal equations:
LEAST SQUARE ESTIMATOR
Multiple Linear Regression Least square estimation
• Contoh soal:
Multiple Linear Regression Least square estimation
Multiple Linear Regression Least square estimation
• Contoh soal:
Multiple Linear Regression Penentuan Koefisien
• Matrix approach (Sistem Matriks)
Model umum:
Normal Equations :
Least square Estimate of β :
Multiple Linear Regression Matrix approach
p x p p x 1 p = k + 1
• Contoh soal
Multiple Linear Regression Matrix approach
• Contoh soal
Multiple Linear Regression Matrix approach
Multiple Linear Regression Estimator of Variance
• Residual:
– the difference between the observation 𝑦𝑖 dengan nilai 𝑦 𝑖
–
Multiple Linear Regression Estimator of Variance
• Residual:
– Contoh soal:
Multiple Linear Regression Estimator of Variance
• Variance Estimator
Error atau Residual Sum of Squares
Multiple Linear Regression Estimator of Variance
• Variance Estimator
Contoh soal:
𝜎 2 = 𝑠2 =? ? ? ?
Multiple Linear Regression Uji Hipotesa
• Uji Nilai Individu Koefisien Regresi
– Area Penolakan:
Partial / Marginal Test
Multiple Linear Regression Uji Hipotesa
– Contoh Soal:
– Kesimpulan: ???
Pertemuan 10 - Persiapan
• Materi – Uji hipotesa serentak MLR
– ANOVA
– Confident Interval MLR
– Regresi Nonlinier
