Aplikasi Spline Truncated dalam Regresi Nonparametrik
Lampiran 1. Data
Pengaruh Waktu
Tegangan
Pengamatan
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
X
5
10
15
20
25
30
35
40
45
50
55
60
65
70
75
80
85
90
95
100
Output Sensor Polimer (milivolt)
Y
288
304
317
325
331
333
335
337
340
341
340
340
337
335
335
335
332
331
329
327
Pengamatan
(menit) Terhadap
Variabel
X
Y
Keterangan
Waktu (menit)
Tegangan output sensor polimer (mv)
Diketahui oleh
Peneliti,
Muhammad Balyan
Lampiran 2. Program Regresi Spline dengan Software Aplikasi Matlab R2007b.
Satu titik knot:
Dua titik knot:
Lampiran 3. Nilai MSE dan GCV dari Percobaan Sebanyak p
1. Nilai MSE dan GCV untuk
Knot
6
7
8
9
11
12
13
14
16
17
18
19
21
22
23
24
26
27
28
29
31
32
Untuk
MSE
62,03474
62,03474
62,03474
62,03474
48,71128
40,88988
36,44235
33,93042
26,29977
22,2521
19,75504
18,32365
14,54342
12,597
11,51147
11,06932
9,898791
9,360139
9,351772
9,758915
10,068514
10,10538
GCV
85,86123
85,86123
85,86123
85,86123
67,42046
56,59499
50,43923
46,96251
36,40106
30,79876
27,34261
25,36146
20,1293
17,4353
15,93283
15,32086
13,70075
12,95521
12,94363
13,50715
13,935659
13,98668
Knot
33
34
36
37
38
39
41
42
43
44
46
47
48
49
51
52
53
54
61
79
97
99
MSE
10,52358
11,25642
12,24826
12,59683
13,24802
14,160778
15,618948
16,223246
17,084076
18,175443
20,272874
21,315255
22,582488
24,057049
26,943135
28,384272
30,033874
31,88007
44,74032
78,763442
108,6386
108,6386
nilai terkecil MSE dan GCV terletak pada
GCV
14, 56550
15,57982
16,95261
17,43505
18,33635
19,599693
21,617922
22,454320
23,645780
25,156322
28,059342
29,502082
31,256039
33,296954
37,291537
39,286190
41,569376
44,12467
61,92431
109,01514
150,3648
150,3648
2. Nilai MSE dan GCV untuk
Knot
28, 29
28, 30
28, 35
28, 40
28, 45
28, 46
28, 50
28, 51
28, 52
28, 53
28, 54
28, 55
28, 56
28, 57
28, 58
28, 59
28, 60
28, 65
28, 70
28, 75
28, 80
28, 85
28, 90
28, 95
29, 30
29, 35
29, 40
29, 45
29, 50
29, 54
29, 60
29, 65
29, 70
29, 75
29, 80
29, 85
29, 90
29, 95
30, 31
30, 35
30, 40
MSE
9,297203
9,297209
8,609646
7,24489
5,86668
5,644039
5,06282
4,983144
4,927494
4,893864
4,879945
4,883221
4,879963
4,895349
4,928154
4,976841
5,039599
5,592334
6,104124
6,409327
6,706496
7,282747
7,810804
8,467155
9,297203
9,262144
8,064914
6,787402
6,025279
5,841572
5,963493
6,456309
6,905782
7,158316
7,402987
7,912564
8,376887
8,962803
10,03304
10,03304
8,976886
GCV
14,52688
14,52689
13,45257
11,32014
9,166688
8,81881
7,910656
7,786162
7,699209
7,646662
7,624915
7,630033
7,624942
7,648982
7,700241
7,776314
7,874373
8,738022
9,537693
10,01457
10,4789
11,37929
12,20438
13,22993
14,52688
14,4721
12,60143
10,60532
9,414498
9,127457
9,317958
10,08798
10,79028
11,18487
11,56717
12,36338
13,08889
14,00438
15,67663
15,67663
14,02638
Knot
30, 45
30, 50
30, 54
30, 55
30, 60
30, 70
30, 90
35, 36
35, 45
35, 54
35, 55
5, 54
10, 54
15, 54
20, 54
25, 54
30, 54
35, 54
40, 54
45, 54
50, 54
16, 54
17, 54
18, 54
19, 54
21, 54
22, 54
23, 54
24, 54
10, 25
10, 75
20, 21
27, 30
27, 54
55, 59
18, 19
18, 20
18, 25
18, 30
18, 35
18, 40
MSE
7,79563
7,086836
6,917464
6,917027
7,029729
7,900534
9,214444
12,20014
11,77062
11,23578
11,21786
singular
12,56436
3,889296
1,675202
3,017021
6,917464
11,23578
15,28099
18,79471
22,94303
2,469418
1,691417
1,391625
1,424361
1,408944
1,471329
1,8011
2,335583
10,48525
34,90787
11,03221
9,297204
4,067791
29,41953
17,36507
17,36507
10,86507
7,556591
4,905509
2,737569
GCV
12,18067
11,07318
10,80854
10,80786
10,98395
12,34458
14,39757
19,06272
18,39159
17,5559
17,52791
singular
19,63182
6,077025
2,617503
4,714095
10,80854
17,5559
23,87655
29,36673
35,84849
3,858465
2,642838
2,174414
2,225563
2,201475
2,298952
2,814219
3,649349
16,38321
54,54355
17,23782
14,52688
6,355924
45,96801
27,13293
27,13293
16,97667
11,80717
7,664858
4,277451
Knot
18, 45
18, 46
18, 47
18, 48
18, 49
18, 50
18, 51
18, 52
18, 53
18, 54
18, 55
18, 60
18, 65
18, 70
18, 75
18, 80
18, 85
18, 90
18, 95
16, 44
16, 46
16, 47
16, 48
16, 51
16, 52
16, 53
16, 56
16, 59
16, 63
17, 44
17, 46
17, 47
17, 48
17, 49
17, 51
17, 52
Untuk
MSE
1,166259
0,953165
0,820099
0,760617
0,767362
0,832516
0,881851
0,994521
1,166193
1,391625
1,664974
3,129685
5,295891
7,393356
9,094503
10,74159
12,83809
14,81428
17,00132
1,494867
1,279263
1,21626
1,24048
1,644091
1,849394
2,126546
3,150378
4,385161
6,419073
1,266005
0,962125
0,855381
0,82777
0,871426
1,05797
1,206776
GCV
1,82228
1,489321
1,281405
1,188464
1,199004
1,300806
1,377892
1,553939
1,822177
2,174414
2,601522
4,890132
8,27483
11,55212
14,21016
16,78373
20,05952
23,14731
26,56456
2,335729
1,998849
1,900406
1,938251
2,568892
2,889678
3,322728
4,922466
6,851814
10,0298
1,978133
1,50332
1,336533
1,29339
1,361603
1,653079
1,885588
Knot
17, 56
17, 61
17, 66
19, 44
19, 46
19, 47
19, 48
19, 49
19, 51
21, 44
21, 48
21, 49
21, 51
21, 52
21, 53
21, 58
22, 44
22, 48
22, 51
22, 52
22, 58
23, 44
23, 48
23, 52
23, 58
24, 44
24, 48
24, 58
26, 44
26, 48
26, 54
26, 58
27, 44
27, 48
27, 54
27, 58
MSE
2,239646
4,085548
6,490843
1,542564
1,159343
1,011839
0,934225
0,919416
0,990924
2,01813
1,271026
1,203431
1,168547
1,203927
1,285529
2,019348
2,325936
1,515191
1,332038
1,338755
1,932688
2,794305
1,956167
1,715002
2,163695
3,389111
2,549413
2,637102
4,603941
3,778402
3,43777
3,598719
5,270571
4,465654
4,067791
4,15795
nilai terkecil MSE dan GCV terletak pada
GCV
3,499447
6,383668
10,14194
2,410256
1,811473
1,580998
1,459727
1,436587
1,548319
3,153329
1,985978
1,880361
1,825855
1,881137
2,00864
3,155231
3,634276
2,367485
2,081309
2,091805
3,019825
4,366101
3,05651
2,67969
3,380774
5,295486
3,983458
4,120473
7,193657
5,903754
5,371515
5,622998
8,235268
6,977585
6,355924
6,496797
dan
Lampiran 4. Uji Simultan Model Regresi Spline Truncated Linier Terbaik dengan
Menggunakan SPSS 16.0
Input data variabel dari knot optimal
Variabel
,
diberi label X
Variabel
diberi label XK
Variabel
diberi label XK2
Variabel
dan
diberi label Y
Kemudian klik Analyze > Regression > Linear sehingga muncul kotak
kerja Linear Regression
Kemudian masukkan variabel X, XK, XK2 ke dalam kotak Independent,
variabel Y ke dalam kotak Dependent
Klik Statistic sehingga muncul kotak kerja Linear Regression: Statistics
Klik Estimates, Model Fit
Lalu klik Continue > OK
Ouputnya,
Lampiran 5. Uji Normalitas dengan Uji Kolmogorov-Smirnov
Input data dari knot optimal
dan
,
Kemudian klik Analyze > Nonparametric Test > 1-Sample K-S
sehingga muncul kotak kerja One-Sample Kolmogorov-Smirnov Test
Kemudian masukkan variabel e dan masukkan ke kotak kerja Test
Variable List
Klik Normal pada kotak kerja Test Distribution
Klik OK
Outputnya,
Pengaruh Waktu
Tegangan
Pengamatan
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
X
5
10
15
20
25
30
35
40
45
50
55
60
65
70
75
80
85
90
95
100
Output Sensor Polimer (milivolt)
Y
288
304
317
325
331
333
335
337
340
341
340
340
337
335
335
335
332
331
329
327
Pengamatan
(menit) Terhadap
Variabel
X
Y
Keterangan
Waktu (menit)
Tegangan output sensor polimer (mv)
Diketahui oleh
Peneliti,
Muhammad Balyan
Lampiran 2. Program Regresi Spline dengan Software Aplikasi Matlab R2007b.
Satu titik knot:
Dua titik knot:
Lampiran 3. Nilai MSE dan GCV dari Percobaan Sebanyak p
1. Nilai MSE dan GCV untuk
Knot
6
7
8
9
11
12
13
14
16
17
18
19
21
22
23
24
26
27
28
29
31
32
Untuk
MSE
62,03474
62,03474
62,03474
62,03474
48,71128
40,88988
36,44235
33,93042
26,29977
22,2521
19,75504
18,32365
14,54342
12,597
11,51147
11,06932
9,898791
9,360139
9,351772
9,758915
10,068514
10,10538
GCV
85,86123
85,86123
85,86123
85,86123
67,42046
56,59499
50,43923
46,96251
36,40106
30,79876
27,34261
25,36146
20,1293
17,4353
15,93283
15,32086
13,70075
12,95521
12,94363
13,50715
13,935659
13,98668
Knot
33
34
36
37
38
39
41
42
43
44
46
47
48
49
51
52
53
54
61
79
97
99
MSE
10,52358
11,25642
12,24826
12,59683
13,24802
14,160778
15,618948
16,223246
17,084076
18,175443
20,272874
21,315255
22,582488
24,057049
26,943135
28,384272
30,033874
31,88007
44,74032
78,763442
108,6386
108,6386
nilai terkecil MSE dan GCV terletak pada
GCV
14, 56550
15,57982
16,95261
17,43505
18,33635
19,599693
21,617922
22,454320
23,645780
25,156322
28,059342
29,502082
31,256039
33,296954
37,291537
39,286190
41,569376
44,12467
61,92431
109,01514
150,3648
150,3648
2. Nilai MSE dan GCV untuk
Knot
28, 29
28, 30
28, 35
28, 40
28, 45
28, 46
28, 50
28, 51
28, 52
28, 53
28, 54
28, 55
28, 56
28, 57
28, 58
28, 59
28, 60
28, 65
28, 70
28, 75
28, 80
28, 85
28, 90
28, 95
29, 30
29, 35
29, 40
29, 45
29, 50
29, 54
29, 60
29, 65
29, 70
29, 75
29, 80
29, 85
29, 90
29, 95
30, 31
30, 35
30, 40
MSE
9,297203
9,297209
8,609646
7,24489
5,86668
5,644039
5,06282
4,983144
4,927494
4,893864
4,879945
4,883221
4,879963
4,895349
4,928154
4,976841
5,039599
5,592334
6,104124
6,409327
6,706496
7,282747
7,810804
8,467155
9,297203
9,262144
8,064914
6,787402
6,025279
5,841572
5,963493
6,456309
6,905782
7,158316
7,402987
7,912564
8,376887
8,962803
10,03304
10,03304
8,976886
GCV
14,52688
14,52689
13,45257
11,32014
9,166688
8,81881
7,910656
7,786162
7,699209
7,646662
7,624915
7,630033
7,624942
7,648982
7,700241
7,776314
7,874373
8,738022
9,537693
10,01457
10,4789
11,37929
12,20438
13,22993
14,52688
14,4721
12,60143
10,60532
9,414498
9,127457
9,317958
10,08798
10,79028
11,18487
11,56717
12,36338
13,08889
14,00438
15,67663
15,67663
14,02638
Knot
30, 45
30, 50
30, 54
30, 55
30, 60
30, 70
30, 90
35, 36
35, 45
35, 54
35, 55
5, 54
10, 54
15, 54
20, 54
25, 54
30, 54
35, 54
40, 54
45, 54
50, 54
16, 54
17, 54
18, 54
19, 54
21, 54
22, 54
23, 54
24, 54
10, 25
10, 75
20, 21
27, 30
27, 54
55, 59
18, 19
18, 20
18, 25
18, 30
18, 35
18, 40
MSE
7,79563
7,086836
6,917464
6,917027
7,029729
7,900534
9,214444
12,20014
11,77062
11,23578
11,21786
singular
12,56436
3,889296
1,675202
3,017021
6,917464
11,23578
15,28099
18,79471
22,94303
2,469418
1,691417
1,391625
1,424361
1,408944
1,471329
1,8011
2,335583
10,48525
34,90787
11,03221
9,297204
4,067791
29,41953
17,36507
17,36507
10,86507
7,556591
4,905509
2,737569
GCV
12,18067
11,07318
10,80854
10,80786
10,98395
12,34458
14,39757
19,06272
18,39159
17,5559
17,52791
singular
19,63182
6,077025
2,617503
4,714095
10,80854
17,5559
23,87655
29,36673
35,84849
3,858465
2,642838
2,174414
2,225563
2,201475
2,298952
2,814219
3,649349
16,38321
54,54355
17,23782
14,52688
6,355924
45,96801
27,13293
27,13293
16,97667
11,80717
7,664858
4,277451
Knot
18, 45
18, 46
18, 47
18, 48
18, 49
18, 50
18, 51
18, 52
18, 53
18, 54
18, 55
18, 60
18, 65
18, 70
18, 75
18, 80
18, 85
18, 90
18, 95
16, 44
16, 46
16, 47
16, 48
16, 51
16, 52
16, 53
16, 56
16, 59
16, 63
17, 44
17, 46
17, 47
17, 48
17, 49
17, 51
17, 52
Untuk
MSE
1,166259
0,953165
0,820099
0,760617
0,767362
0,832516
0,881851
0,994521
1,166193
1,391625
1,664974
3,129685
5,295891
7,393356
9,094503
10,74159
12,83809
14,81428
17,00132
1,494867
1,279263
1,21626
1,24048
1,644091
1,849394
2,126546
3,150378
4,385161
6,419073
1,266005
0,962125
0,855381
0,82777
0,871426
1,05797
1,206776
GCV
1,82228
1,489321
1,281405
1,188464
1,199004
1,300806
1,377892
1,553939
1,822177
2,174414
2,601522
4,890132
8,27483
11,55212
14,21016
16,78373
20,05952
23,14731
26,56456
2,335729
1,998849
1,900406
1,938251
2,568892
2,889678
3,322728
4,922466
6,851814
10,0298
1,978133
1,50332
1,336533
1,29339
1,361603
1,653079
1,885588
Knot
17, 56
17, 61
17, 66
19, 44
19, 46
19, 47
19, 48
19, 49
19, 51
21, 44
21, 48
21, 49
21, 51
21, 52
21, 53
21, 58
22, 44
22, 48
22, 51
22, 52
22, 58
23, 44
23, 48
23, 52
23, 58
24, 44
24, 48
24, 58
26, 44
26, 48
26, 54
26, 58
27, 44
27, 48
27, 54
27, 58
MSE
2,239646
4,085548
6,490843
1,542564
1,159343
1,011839
0,934225
0,919416
0,990924
2,01813
1,271026
1,203431
1,168547
1,203927
1,285529
2,019348
2,325936
1,515191
1,332038
1,338755
1,932688
2,794305
1,956167
1,715002
2,163695
3,389111
2,549413
2,637102
4,603941
3,778402
3,43777
3,598719
5,270571
4,465654
4,067791
4,15795
nilai terkecil MSE dan GCV terletak pada
GCV
3,499447
6,383668
10,14194
2,410256
1,811473
1,580998
1,459727
1,436587
1,548319
3,153329
1,985978
1,880361
1,825855
1,881137
2,00864
3,155231
3,634276
2,367485
2,081309
2,091805
3,019825
4,366101
3,05651
2,67969
3,380774
5,295486
3,983458
4,120473
7,193657
5,903754
5,371515
5,622998
8,235268
6,977585
6,355924
6,496797
dan
Lampiran 4. Uji Simultan Model Regresi Spline Truncated Linier Terbaik dengan
Menggunakan SPSS 16.0
Input data variabel dari knot optimal
Variabel
,
diberi label X
Variabel
diberi label XK
Variabel
diberi label XK2
Variabel
dan
diberi label Y
Kemudian klik Analyze > Regression > Linear sehingga muncul kotak
kerja Linear Regression
Kemudian masukkan variabel X, XK, XK2 ke dalam kotak Independent,
variabel Y ke dalam kotak Dependent
Klik Statistic sehingga muncul kotak kerja Linear Regression: Statistics
Klik Estimates, Model Fit
Lalu klik Continue > OK
Ouputnya,
Lampiran 5. Uji Normalitas dengan Uji Kolmogorov-Smirnov
Input data dari knot optimal
dan
,
Kemudian klik Analyze > Nonparametric Test > 1-Sample K-S
sehingga muncul kotak kerja One-Sample Kolmogorov-Smirnov Test
Kemudian masukkan variabel e dan masukkan ke kotak kerja Test
Variable List
Klik Normal pada kotak kerja Test Distribution
Klik OK
Outputnya,