STATISTIKA INDUSTRI 2

TIN 4004

Pertemuan 10

• Outline: – Multiple Linear Regression and Correlation – Non Linear Regression – ANOVA

• 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 Uji Hipotesa

• Uji Nilai Individu Koefisien Regresi

– Area Penolakan:

Partial / Marginal Test

Multiple Linear Regression Uji Hipotesa

– Contoh Soal:

– Kesimpulan: ???

Multiple Linear Regression Uji Hipotesa

• Uji Kesesuaian Model (Fitted Model Hypothesis Testing) – The ability of the entire function to predict the

true response in the range of the variables considered

– Reject 𝐻0interpret at least one regressor variable contributes significantly to the model

Multiple Linear Regression Uji Hipotesa

• Uji Kesesuaian Model (Fitted Model Hypothesis Testing)

– Menggunakan uji F

– Area Penolakan: 𝒇 > 𝒇𝜶(𝒗𝟏=𝒌,𝒗𝟐=𝒏−𝒑)

𝒇 =𝑺𝑺𝑹/𝒌

𝑺𝑺𝑬/(𝒏 − 𝒑)=

𝑺𝑺𝑹/𝒌

𝒔𝟐

Multiple Linear Regression Uji Hipotesa

• Uji Kesesuaian Model (Fitted Model Hypothesis Testing)

– Format ANOVA

Multiple Linear Regression Confident Interval

• CI on Individual Regression Coefficients

– Contoh:

Multiple Linear Regression Confident Interval

• CI on Mean Response

– Contoh:

Multiple Linear Regression Correlation

• Coefficient of multiple determination 𝑅2

• Adjoint 𝑅2

Multiple Linear Regression Multicollinearity

• strong dependencies among regressor variables 𝑥𝑗 – The estimates of the regression coefficients are

very imprecise and affects the stability of the regression coefficients.

– To detect: • Variance inflation factors > 1

• Significant F-test of significance of regression, but tests on the individual regression coefficients are not significant

NONLINEAR REGRESSION

Nonlinear Regression

Beberapa Jenis Nonlinear Regression:

• Polynomial Regression Models

– Bersifat curvilinear

• Logistic Regression

– For non normal distribution data, binary responses

ANOVA

ANOVA konsep dasar

• Digunakan untuk menganalisa dan mengintrepertasikan pengamatan/observasi pada multiple populasi – Pengujian rata-rata beberapa populasi (3 atau lebih) – Versatile statistical tool (alat statistik serbaguna)

• Asumsi pada ANOVA – Tiap populasi berdistribusi normal – Standar deviasi tiap populasi sama

• Membagi total variasi set data berdasarkan sumber variasinya: – Antar populasi – Dalam populasi

What does ANOVA do?

At its simplest (there are extensions) ANOVA tests the following hypotheses:

H0: The means of all the factors / treatments are equal.

H1: Not all the means are equal • doesn’t say how or which ones differ.

• Can follow up with “multiple comparisons”

Note: we usually refer to the sub-populations as “treatments” when doing ANOVA.

ANOVA jenis

• One-way ANOVA

– Equal sample size

– Unequal sample size

• Two-way ANOVA

– Without Interaction

– With Interaction

One-way ANOVA Equal Sample Size: data

𝑎 = 𝑗𝑢𝑚𝑙𝑎ℎ 𝑓𝑎𝑐𝑡𝑜𝑟 𝑡𝑟𝑒𝑎𝑡𝑚𝑒𝑛𝑡 𝑛 = 𝑗𝑢𝑚𝑙𝑎ℎ 𝑜𝑏𝑠𝑒𝑟𝑣𝑎𝑠𝑖 𝑆𝑆 = 𝑆𝑢𝑚 𝑆𝑞𝑢𝑎𝑟𝑒 𝑀𝑆 = 𝑀𝑒𝑎𝑛 𝑆𝑞𝑢𝑎𝑟𝑒

One-way ANOVA Equal Sample Size: format

One-way ANOVA Equal Sample Size: Uji Hipotesa

• Contoh Soal

One-way ANOVA Equal Sample Size: Uji Hipotesa

• Contoh Soal

KESIMPULAN???

Hardwood concentration berpengaruh pada rata-rata kekuatan kertas

One-way ANOVA Unequal Sample Size: format

Two-way ANOVA w/o interaction vs w/ interaction

(a) No interaction (b) Interact

Two-way ANOVA data

𝑎 = 𝑗𝑢𝑚𝑙𝑎ℎ 𝑓𝑎𝑐𝑡𝑜𝑟 𝑡𝑟𝑒𝑎𝑡𝑚𝑒𝑛𝑡 𝑏 = 𝑗𝑢𝑚𝑙𝑎ℎ 𝑏𝑙𝑜𝑐𝑘 𝑛 = 𝑗𝑢𝑚𝑙𝑎ℎ 𝑜𝑏𝑠𝑒𝑟𝑣𝑎𝑠𝑖 𝑆𝑆 = 𝑆𝑢𝑚 𝑆𝑞𝑢𝑎𝑟𝑒 𝑀𝑆 = 𝑀𝑒𝑎𝑛 𝑆𝑞𝑢𝑎𝑟𝑒

𝑁𝑂𝑇𝐸! 𝑏𝑙𝑜𝑐𝑘 ≠ 𝑓𝑎𝑐𝑡𝑜𝑟

Two-way ANOVA format

Two-way ANOVA Uji Hipotesa

• Contoh:

Two-way ANOVA Uji Hipotesa

• Contoh:

KESIMPULAN???

Two-way ANOVA Uji Hipotesa

Two-Factor ANOVA data

𝑎 = 𝑗𝑢𝑚𝑙𝑎ℎ 𝑓𝑎𝑐𝑡𝑜𝑟 𝑡𝑟𝑒𝑎𝑡𝑚𝑒𝑛𝑡 𝐴 𝑏 = 𝑗𝑢𝑚𝑙𝑎ℎ 𝑓𝑎𝑐𝑡𝑜𝑟 𝑡𝑟𝑒𝑎𝑡𝑚𝑒𝑛𝑡 𝐵 𝑛 = 𝑗𝑢𝑚𝑙𝑎ℎ 𝑟𝑒𝑝𝑙𝑖𝑘𝑎𝑠𝑖

Two-Factor ANOVA format

Two-Factor ANOVA format

Two-Factor ANOVA Uji Hipotesa

Two-Factor ANOVA Uji Hipotesa

• Contoh

Two-Factor ANOVA Uji Hipotesa

• Contoh

Two-Factor ANOVA Uji Hipotesa

• Contoh

Two-Factor ANOVA Uji Hipotesa

• Contoh

Two-Factor ANOVA Uji Hipotesa

• Contoh

Pertemuan 11 & 12 - Persiapan

• Materi – Nonparametric Statistic