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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