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