Slide10 - Analisis Korelasi dan Regresi ESL/11...Title Microsoft PowerPoint - Slide10 - Analisis...
Transcript of Slide10 - Analisis Korelasi dan Regresi ESL/11...Title Microsoft PowerPoint - Slide10 - Analisis...
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Metode StatistikaPertemuan XII
Analisis Korelasi dan Regresi
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Analisis HubunganJenis/tipe hubungan
Skala pengukuran variabel
Ukuran Keterkaitan
Pemodelan Keterkaitan
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Relationship vs Causal Relationship
Tidak semua hubungan (relationship) berupa hubungan sebab-akibat
Penentuan suatu hubungan bersifat sebab-akibat memerlukan well-argued position dari bidang ilmu terkait
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Alat Analisis Keterkaitan
Ditentukan oleh:1. Skala pengukuran data/variabel2. Jenis hubungan antar variabel
Relationship Numerik Kategorik
Numerik Korelasi Pearson, Spearman Tabel Ringkasan
Kategorik Tabel Ringkasan Spearman (ordinal),
Chi Square
Causal relationship
X
YNumerik Kategorik
Numerik Regresi Linier ANOVA
Kategorik Regresi Logistik Regresi Logistik
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• Apa itu analisis regresi?
• Apa bedanya dengan korelasi?
Analisis Regresi Analisis statistika yang memanfaatkan hubungan antara dua atau lebih peubah kuantitatif sehingga salah satu peubah dapat diramalkan dari peubah lainnya.
Korelasi mengukur keeratan HUBUNGAN LINEAR dari dua variabel
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Korelasi
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Korelasi
r = 1 r = 0
r = 0 r = 0
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Korelasi
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Koefisien Korelasi tidak menggambarkan hubungan sebab
akibat nilainya berkisar antara -1 dan 1 tanda (+) / (-) arah hubungan
– (+) searah; – (-) beralawanan arah
Pearson’s Coef of Correlation linear relationship
Spearman’n Coef of Correlation (rank correlation) trend relationship
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Koefisien Korelasi Pearson (r)
1
)(dan
1
)(
1
1
1
))((
22
n
yyS
n
xxS
n
yxyx
nn
yyxxS
SS
Sr
iy
ix
iiii
iixy
yx
xyxy
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Korelasi !!!
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Analisis Regresi
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Definisi
Linear : linear dalam parameter
Sederhana : hanya satu peubah penjelas
Berganda : lebih dari satu peubah penjelas
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Simple Linear Regression
Peubah penjelas
satu
> satu
Multiple Linear Regression
Hubungan parameter
linear
non linear
Regresi non linear
Regresi Linear
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ANALISIS REGRESI
• Hubungan Antar Peubah:
• Fungsional (deterministik) Y=f(X) ; misalnya: Y=10X
• Statistik (stokastik) amatan tidak jatuh pas pada kurva
Mis: IQ vs Prestasi, Berat vs Tinggi, Dosis Pupuk vs Produksi
• Model regresi linear sederhana:
niXY iii ,...,2,1 ; 10
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Regresi
Makna 0 & 1 ?
0 adalah nilai Y ketika X = 0, sedangkan 1 adalah perubahan nilai Y untuk setiap perubahan 1 satuan X.
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Regresi
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Analisis Regresi• Pendugaan terhadap koefisien regresi:
b0 penduga bagi 0 dan b1 penduga bagi 1
Bagaimana Pengujian terhadap model regresi ??• parsial (per koefisien) uji-t• bersama uji-F (Anova)
Bagaimana menilai kesesuaian model ??R2 (Koef. Determinasi: % keragaman Y yang mampu dijelaskan oleh X)
xbybn
xx
n
yxxy
b
10
22
1 )(
))((
Metode Kuadrat Terkecil
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2
1
(Re )100%
( )
b100%
Sxy
yy
JK gresiR x
JK Total
Sx
Koefisien Determinasi
Koefisien determinasi sebesar 80% menjelaskan bahwa sebesar 80% keragaman dari Y dapat dijelaskan oleh Xdalam hubungan linier, sisanya oleh faktor-faktor lain
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catatan2
12
1
n
ini
ii
Y
Syy Yn
2
12
1
n
ini
ii
X
Sxx Xn
1 1
1
n n
i ini i
i ii
X Y
Sxy X Yn
Keterangan :Syy = Jumlah Kuadrat Terkoreksi variabel YSxx = Jumlah Kuadrat Terkoreksi variabel XSxy = Jumlah Kuadrat Terkoreksi variabel XY
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Metoda Kuadrat Terkecil Pendugaan parameter pada regresi didapat
dengan meminimumkan jumlah kuadrat galat.
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Keragaman yang dapat dijelaskan dan yang tidak
dapat dijelaskan
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Contoh DataJarak Emisi31 55338 59048 60852 68263 75267 72575 83484 75289 84599 960
Percobaan dalam bidang lingkungan
Apakah semakin tua mobil semakin besar juga emisi HC yang dihasilkan?
Diambil contoh 10 mobil secara acak, kemudian dicatat jarak tempuh yang sudah dijalani mobil (dalam ribu kilometer) dan diukur Emisi HC-nya (dalam ppm)
Emisi = 382 + 5.39 Jarak
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Analisis Regresi
10090807060504030
950
850
750
650
550
Jarak
Em
isi
Plot antara Emisi Hc (ppm) dg Jarak Tempuh Mobil (ribu kilometer)
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Analisis RegresiContoh output regresi dengan Minitab (1)
Regression Analysis (Emisi Hc vs Jarak Tempuh Mobil)
The regression equation is Emisi = 382 + 5.39 Jarak
Predictor Coef StDev T PConstant 381.95 42.40 9.01 0.000Jarak 5.3893 0.6233 8.65 0.000
S = 42.01 R-Sq = 90.3% R-Sq(adj) = 89.1%
Analysis of Variance
Source DF SS MS F PRegression 1 131932 131932 74.76 0.000Error 8 14118 1765Total 9 146051
Unusual ObservationsObs Jarak Emisi Fit StDev Fit Residual St Resid8 84.0 752.0 834.7 18.0 -82.7 -2.18R
R denotes an observation with a large standardized residual
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Analisis Regresi
Bagaimana Pengujian terhadap model regresi ??• parsial (per koefisien) uji-t• bersama uji-F (Anova)
Bagaimana menilai kesesuaian model ??R2 Koef. Determinasi
(% keragaman Y yang mampu dijelaskan oleh X)
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Uji Hipotesis (Simultan)
n
iii
n
ii
n
ii yyyyyy
1
2
1
2
1
2 )ˆ()ˆ()(
H0 : 1=0 vs H1: 10
ANOVA (Analysis of Variance) Uji F
JK total = JK regresi + JK galat
Keragaman total = keragaman yang dapat dijelaskan oleh model + keragaman yang tidak dapat dijelaskan oleh model
Sumber db JK KT F
Regresi 1 JKR KTR KTR/KTE
Galat n - 2 JKG KTG
Total n - 1 JKT
Anova
F ~ F (1,n-2)
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Catatan
1(Regresi) b
S
(Regresi)
xy
yy
JK S
JK Total
JKG JK Total JK
(Regresi)
(G)
(Regresi)(Regresi)
JKKT
db
JKGKTG
db
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Uji Hipotesis (parsial)H0 : 1≤0 vs H1: 1>0 atau
Uji Parsial
Statistik uji:1
1
1
2
21
( )
ˆ( )
2 2
b
bi xx
yy xyi i
bT
S
s KTGS
x x S
S b Sy ys KTG
n n
H0 : 1≥0 vs H1: 1<0 atau
H0 : 1=0 vs H1: 1≠0
Satu arah
dua arah
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Uji Parsial (lanjutan) Kriteria Penolakan dan Penerimaan H0 :
(tergantung H1)
Tolak Hipotesis Nol (H0) jika : thitung > t(, n-2) atau
Tolak Hipotesis Nol (H0) jika : thitung < - t(, n-2) atau
Tolak Hipotesis Nol (H0) jika : |thitung|| > t(/2, n-2)
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Diskusi (1) Berapa emisi HC yang dihasilkan jika
jarak tempuh sekitar 70 ribu km?759,3 ppm
Berapa emisi HC yang dihasilkan jika jarak tempuh sekitar 110 ribu km? apakah hasil dugaan ini valid? Kenapa? 974,9 ppm
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Diskusi (2) Berapa emisi HC yang dihasilkan jika jarak
tempuh sekitar 70 ribu km? Tentukan selang kepercayaan 95% bagi
emisi HC jika waktu tempuhnya sekitar 70 ribu km? predictiction interval
Tentukan selang kepercayaan 95% bagi rata-rata emisi HC jika waktu tempuhnya sekitar 70 ribu km? confidence interval
Lebih lebar mana selang interval antara prediction intervaldengan confidence interval? Kenapa?
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Jarak
Emis
i
10090807060504030
1100
1000
900
800
700
600
500
400
S 42.0096R-Sq 90.3%R-Sq(adj) 89.1%
Regression95% CI95% PI
Fitted Line PlotEmisi = 382.0 + 5.389 Jarak
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Diskusi (3) Tentukan formula untuk prediction
interval dan confidence interval!
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Keterbatasan Korelasi dan Regresi Linear
Korelasi dan Regresi Linear hanya menggambarkan hubungan yang linear
Korelasi dan metode kuadrat terkecil pada regresi linear tidak resisten terhadap pencilan
Prediksi di luar selang nilai X tidak diperkenankan karena kurang akurat
Hubungan antara dua variabel bisa dipengaruhi oleh variabel lain di luar model
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‘All models are wrong, but some are useful’
(G. E. P. Box)