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Multiple Regression Case

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TUGAS ANALISIS REGRESI II Pelanggaran Asumsi KetidakHomogenan Ragam Pada Analisis Regresi Berganda Disusun Oleh : Destya Kusuma G54062392 destya.kusuma@yahoo .com
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Page 1: Multiple Regression Case

TUGAS ANALISIS REGRESI II

Pelanggaran Asumsi KetidakHomogenanRagam Pada Analisis Regresi Berganda

Disusun Oleh :

Destya Kusuma G54062392

[email protected]

Page 2: Multiple Regression Case

ASUMSI-ASUMSI REGRESI LINEAR BERGANDA

KEBEBASAN

KENORMALAN

KEHOMOGENAN

MULTIKOLINEAR

Sisaan tidak saling berkorelasi cov (εi, εj) = 0

sisaan mengikuti distribusi normal 2,0 Ni

Homoskedastisitas (identik )

Tidak ada korelasi antar peubah penjelas

2 iVarians

VIF

Page 3: Multiple Regression Case

MENGATASI PELANGGARAN ASUMSI-ASUMSI REGRESI LINEAR BERGANDA

KEBEBASAN Eksplorasi plot sisaan, uji Run Test,uji Durbin Watson,penambahan komponen

KEHOMOGENAN Metode kuadrat Terkecil Terboboti atau Transformasi Y

KENORMALANEksplorasi histogram atau plot normal, Transformasi Y

MULTIKOLINIER

Sisaan sekitar nol/tidak

Lebar pita sama/tidak berpola

Plot antara sisaan tidak memiliki pola

VIF >10PCA

Page 4: Multiple Regression Case

Transformasi digunakan untuk :

Menyederhanakan hubungan peubah bebas dan peubah tak bebas

Melinierkan Model

Mengatasi Ketidakhomogenan Ragam

Penyimpangan asumsi sebaran normal

Page 5: Multiple Regression Case

Studi kasus Ketidakhomogenan :

Di bawah ini merupakan data dari 21 hari proses oksidasi NH3 ke HN03 pada tumbuhan

Keterangan :

X1 = laju proses oksidasi NH3 ke HN03

X2 = suhu air dingin di dalam penyerapan besar untuk oksidasi nitritY = Persentase hilangnya NH3 oleh tidak terserapnya oksidasi nitrit

Obs X1 X2 Y

1 80 27 42

2 80 27 37

3 75 25 37

4 62 24 28

5 62 22 18

6 62 23 18

7 62 24 19

8 62 24 20

9 58 23 15

10 58 18 14

11 58 18 14

12 58 17 13

13 58 18 11

14 58 19 12

15 50 18 8

16 50 18 7

17 50 19 8

18 50 19 8

19 50 20 9

20 56 20 15

21 70 29 15

Page 6: Multiple Regression Case

Cek Korelasi :

Correlations: Y, X1, X2

Y X1 X2X1 0.920 0.000

X2 0.740 0.820 0.000 0.000

Cell Contents: Pearson correlation P-Value

Page 7: Multiple Regression Case
Page 8: Multiple Regression Case

Regression Analysis: Y versus X1, X2

The regression equation isY = - 43.9 + 1.06 X1 - 0.119 X2

Predictor Coef SE Coef T P VIFConstant -43.878 6.338 -6.92 0.000X1 1.0584 0.1791 5.91 0.000 3.1X2 -0.1187 0.4579 -0.26 0.798 3.1

S = 4.20270 R-Sq = 84.6% R-Sq(adj) = 82.9% PRESS = 556.420 R-Sq(pred) = 73.11% Analysis of VarianceSource DF SS MS F P Regression 2 1751.31 875.65 49.58 0.000Residual Error 18 317.93 17.66Total 20 2069.24

Source DF Seq SSX1 1 1750.12X2 1 1.19

Unusual ObservationsObs X1 Y Fit SE Fit Residual St Resid 4 62.0 28.000 18.893 1.297 9.107 2.28R 21 70.0 15.000 26.767 2.424 -11.767 -3.43R

R denotes an observation with a large standardized residual.

Durbin-Watson statistic = 1.25842

HipotesisH0: βi=0 Vs H1: βi≠0 P-value < α Tolak

H0

Hipotesis

HipotesisH0: β1=β2=…=0 Vs H1: Ada min βi≠0

Ftabel(2,18) = 3.55 Fhit>Ftabel Tolak

H0

Page 9: Multiple Regression Case

PLOT Y

Page 10: Multiple Regression Case

Residual Vs Fit For Y

Page 11: Multiple Regression Case

Box-Cox Terhadap Y

Ket : ambil λ = 1/2

Page 12: Multiple Regression Case

Regression Analysis: Y1 versus X1, X2

The regression equation isY1 = - 2.78 + 0.114 X1 - 0.0019 X2

Predictor Coef SE Coef T P VIFConstant -2.7764 0.6694 -4.15 0.001X1 0.11352 0.01892 6.00 0.000 3.1X2 -0.00194 0.04836 -0.04 0.969 3.1

S = 0.443900 R-Sq = 85.8% R-Sq(adj) = 84.2%PRESS = 6.04738 R-Sq(pred) = 75.79%

Analysis of VarianceSource DF SS MS F PRegression 2 21.428 10.714 54.37 0.000Residual Error 18 3.547 0.197Total 20 24.974

Source DF Seq SSX1 1 21.427X2 1 0.000

Unusual Observations

Obs X1 Y1 Fit SE Fit Residual St Resid 4 62.0 5.2915 4.2152 0.1370 1.0763 2.55R 21 70.0 3.8730 5.1137 0.2560 -1.2407 -3.42RR denotes an observation with a large standardized residual.Durbin-Watson statistic = 1.38728

Y1 Transformasi Y1/2

Page 13: Multiple Regression Case

Output minitab sebelum Transformasi

Regression Analysis: Y versus X1, X2

The regression equation isY = - 43.9 + 1.06 X1 - 0.119 X2

Predictor Coef SE Coef T P VIFConstant -43.878 6.338 -6.92 0.000X1 1.0584 0.1791 5.91 0.000 3.1X2 -0.1187 0.4579 -0.26 0.798 3.1

S = 4.20270 R-Sq = 84.6% R-Sq(adj) = 82.9% PRESS = 556.420 R-Sq(pred) = 73.11% Analysis of VarianceSource DF SS MS F P Regression 2 1751.31 875.65 49.58 0.000Residual Error 18 317.93 17.66Total 20 2069.24

Output Minitab sesudah transformasi

Regression Analysis: Y1 versus X1, X2

The regression equation isY1 = - 2.78 + 0.114 X1 - 0.0019 X2

Predictor Coef SE Coef T P VIFConstant -2.7764 0.6694 -4.15 0.001X1 0.11352 0.01892 6.00 0.000 3.1X2 -0.00194 0.04836 -0.04 0.969 3.1

S = 0.443900 R-Sq = 85.8% R-Sq(adj) = 84.2%PRESS = 6.04738 R-Sq(pred) = 75.79%

Analysis of VarianceSource DF SS MS F PRegression 2 21.428 10.714 54.37 0.000Residual Error 18 3.547 0.197Total 20 24.974

Ket : Kedua output masih terdapat pencilan pada obs 4 dan 21

Page 14: Multiple Regression Case

Plot Y1

Page 15: Multiple Regression Case

Residual Vs Fit for Y1

Plot dengan Obs 4 dan 21

Page 16: Multiple Regression Case

Regression Analysis: Y1 versus X1, X2

The regression equation isY1 = - 3.39 + 0.101 X1 + 0.0630 X2

Predictor Coef SE Coef T P VIFConstant -3.3945 0.2934 -11.57 0.000X1 0.101216 0.008413 12.03 0.000 3.3X2 0.06296 0.02426 2.59 0.020 3.3

S = 0.183645 R-Sq = 97.7% R-Sq(adj) = 97.4%PRESS = 0.808714 R-Sq(pred) = 96.53%

Analysis of VarianceSource DF SS MS F PRegression 2 22.783 11.391 337.77 0.000Residual Error 16 0.540 0.034Total 18 23.322

Ket : Regresi dilakukan setelah menghilangkan pencilan obs 4 dan 21

Source DF Seq SSX1 1 22.555X2 1 0.227

Unusual ObservationsObs X1 Y1 Fit SE Fit Residual St Resid 2 80.0 6.0828 6.4028 0.1023 -0.3200 -2.10RR denotes an observation with a large standardized residual.Durbin-Watson statistic = 1.97080

Page 17: Multiple Regression Case

OutPut Minitab data lengkap Transformasi Y1

The regression equation is Y1 = - 2.78 + 0.114 X1 - 0.0019 X2

Predictor Coef SE Coef T P VIFConstant -2.7764 0.6694 -4.15 0.001X1 0.11352 0.01892 6.00 0.000 3.1X2 -0.00194 0.04836 -0.04 0.969 3.1

S = 0.443900 R-Sq = 85.8% R-Sq(adj) = 84.2%PRESS = 6.04738 R-Sq(pred) = 75.79%

Analysis of VarianceSource DF SS MS F PRegression 2 21.428 10.714 54.37 0.000Residual Error 18 3.547 0.197Total 20 24.974

Output Minitab data tanpa obs 4 dan 21 Terhadap Y1

The regression equation isY1 = - 3.39 + 0.101 X1 + 0.0630 X2

Predictor Coef SE Coef T P VIFConstant -3.3945 0.2934 -11.57 0.000X1 0.101216 0.008413 12.03 0.000 3.3X2 0.06296 0.02426 2.59 0.020 3.3

S = 0.183645 R-Sq = 97.7% R-Sq(adj) = 97.4%PRESS = 0.808714 R-Sq(pred) = 96.53%

Analysis of VarianceSource DF SS MS F PRegression 2 22.783 11.391 337.77 0.000Residual Error 16 0.540 0.034Total 18 23.322

Ternyata dengan menghilangkan obs 4 dan 21, R-sq(adj) membesar, S mengecil Dan PRESS mengecil , R-sq(pred) membesar, parameter nyata (p-value < α), model layak dari annova dihasilkan p-value < α

Page 18: Multiple Regression Case

Plot Y1 tanpa obs 4 dan 21

Page 19: Multiple Regression Case

Kesimpulan : Lebar pita sama HOMOGEN

Plot Y dengan sisaan

Page 20: Multiple Regression Case

TERIMA KASIH


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