tugas pemodelan - model regresi polinomial
TRANSCRIPT
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7/25/2019 Tugas Pemodelan - Model Regresi Polinomial
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Afham Ramadhan Kuliah Pemodelan dan Rekayasa Sistem
S2 Teknik Elektro
Tugas pemodelan
Membuat model regresi polinomial dari data berikut
No. Solids reduction x (%) Chemical oxygen demand, y (%)
1 3 5
2 7 11
3 11 21
4 15 16
5 18 16
6 27 28
7 29 27
8 30 25
9 30 35
10 31 30
11 31 40
12 32 32
13 33 34
14 33 32
15 34 34
16 36 37
17 36 38
18 36 34
19 37 36
20 38 38
21 39 37
22 39 36
23 39 45
24 40 39
25 41 41
26 42 40
27 42 44
28 43 37
29 44 44
30 45 46
31 46 4632 47 49
33 50 51
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7/25/2019 Tugas Pemodelan - Model Regresi Polinomial
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Afham Ramadhan Kuliah Pemodelan dan Rekayasa Sistem
S2 Teknik Elektro
Membuat model dari persamaan polinomial dengan metode Least Square
Input : x
[
]
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7/25/2019 Tugas Pemodelan - Model Regresi Polinomial
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Afham Ramadhan Kuliah Pemodelan dan Rekayasa Sistem
S2 Teknik Elektro
Polinomial orde satu
H =
[ 1 3 ]
1 7
1 111 15
1 18
1 27
1 29
1 30
1 30
1 31
1 31
1 32
1 33
1 33
1 34
1 36
1 36
1 36
1 37
1 38
1 39
1 39
1 39
1 40
1 41
1 421 42
1 43
1 44
1 45
1 46
1 47
1 50
....
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Afham Ramadhan Kuliah Pemodelan dan Rekayasa Sistem
S2 Teknik Elektro [ 6.5406 ]
10.1551
13.7697
17.3843
20.0952
28.2280
30.0353
30.9389
30.9389
31.8426
31.8426
32.7462
33.6499
33.6499
34.5535
36.3608
36.360836.3608
37.2644
38.1681
39.0717
39.0717
39.0717
39.9754
40.8790
41.7826
41.7826
42.686343.5899
44.4936
45.3972
46.3009
49.0118
Akumulasi kuadrat error : .
Persamaan Polinomial orde empat :
y = -7E-06x4+ 0.0009x
3- 0.0407x
2+ 1.5074x + 2.0835
persamaan polinomial orde dua :
=
[1.5406]
-0.8449
-7.2303
1.3843
4.0952
0.2280
3.0353
5.9389
-4.0611
1.8426
-8.1574
0.7462
-0.3501
1.6499
0.5535-0.6392
-1.6392
2.3608
1.2644
0.1681
2.0717
3.0717
-5.9283
0.9754
-0.1210
1.7826
-2.2174
5.6863
-0.4101
-1.5064
-0.6028
-2.6991
-1.9882
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Afham Ramadhan Kuliah Pemodelan dan Rekayasa Sistem
S2 Teknik Elektro H =[ 1 3 9 ]
1 7 49
1 11 121
1 15 2251 18 324
1 27 729
1 29 841
1 30 900
1 30 900
1 31 961
1 31 961
1 32 1024
1 33 1089
1 33 1089
1 34 11561 36 1296
1 36 1296
1 36 1296
1 37 1369
1 38 1444
1 39 1521
1 39 1521
1 39 1521
1 40 1600
1 41 1681
1 42 1764
1 42 1764
1 43 1849
1 44 1936
1 45 2025
1 46 2116
1 47 2209
1 50 2500
...
.. .Persamaan polinomial orde dua :
y = 0.0028x2+ 0.7504x + 5.4281
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Afham Ramadhan Kuliah Pemodelan dan Rekayasa Sistem
S2 Teknik Elektro
[ 7.7047]
10.8196
14.0252
17.321519.8532
27.7546
29.5728
30.4904
30.4904
31.4137
31.4137
32.3426
33.2772
33.2772
34.217536.1151
36.1151
36.1151
37.0724
38.0354
39.0040
39.0040
39.0040
39.9783
40.9583
41.9439
41.9439
42.9352
43.9322
44.9349
45.9432
46.9572
50.0332
=
[ 2.7047 ]
-0.1804
-6.9748
1.3215
3.8532
-0.2454
2.5728
5.4904
-4.5096
1.4137
-8.5863
0.3426-0.7228
1.2772
0.2175
-0.8849
-1.8849
2.1151
1.0724
0.0354
2.0040
3.0040
-5.99600.9783
-0.0417
1.9439
-2.0561
5.9352
-0.0678
-1.0651
-0.0568
-2.0428
-0.9668
.
Akumulasi kuadrat error :
Error rata-rata :
9.6117
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Afham Ramadhan Kuliah Pemodelan dan Rekayasa Sistem
S2 Teknik Elektro
Persamaan Polinom orde tiga : H = [ 1 3 9 27 ]
1 7 49 343
1 11 121 1331
1 15 225 3375
1 18 324 5832
1 27 729 19683
1 29 841 24389
1 30 900 27000
1 30 900 27000
1 31 961 29791
1 31 961 29791
1 32 1024 32768
1 33 1089 35937
1 33 1089 359371 34 1156 39304
1 36 1296 46656
1 36 1296 46656
1 36 1296 46656
1 37 1369 50653
1 38 1444 54872
1 39 1521 59319
1 39 1521 59319
1 39 1521 59319
1 40 1600 64000
1 41 1681 68921
1 42 1764 74088
1 42 1764 74088
1 43 1849 79507
1 44 1936 85184
1 45 2025 91125
1 46 2116 97336
1 47 2209 103823
1 50 2500 125000
.... .. . .
Persamaan Polinomial orde tiga :
y = 0.0002x3- 0.0153x
2+ 1.1741x + 3.2189
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Afham Ramadhan Kuliah Pemodelan dan Rekayasa Sistem
S2 Teknik Elektro
[ 6.6097 ]
10.7640
14.5763
18.1303
20.6768
28.0817
29.7467
30.5897
30.5897
31.4414
31.4414
32.3033
33.1765
33.176534.0624
35.8775
35.8775
35.8775
36.8094
37.7592
38.7282
38.7282
38.7282
39.7178
40.729241.7638
41.7638
42.8229
43.9078
45.0198
46.1602
47.3304
51.0322
=
[ 1.6097 ]
-0.2360
-6.4237
2.1303
4.6768
0.0817
2.7467
5.5897
-4.4103
1.4414
-8.5586
0.3033
-0.8235
1.17650.0624
-1.1225
-2.1225
1.8775
0.8094
-0.2408
1.7282
2.7282
-6.2718
0.7178
-0.27081.7638
-2.2362
5.8229
-0.0922
-0.9802
0.1602
-1.6696
0.0322
.Akumulasi kuadrat error :Error rata-rata :
9.4609
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Afham Ramadhan Kuliah Pemodelan dan Rekayasa Sistem
S2 Teknik Elektro
Dengan cara yang sama maka untuk mencari nilai error terkecil polinomial berikut adalah :
Orde empat :
Orde lima :
[4]
[.....]
.
.. . . .4y = -7E-06x
4+ 0.0009x
3- 0.0407x
2+ 1.5074x + 2.0835
Akumulasi kuadrat error :
Error rata-rata :
9.4354
[
45] [
...... ]
... . . .4 .5y = 4E-06x
5- 0.0005x
4+ 0.0249x
3- 0.5597x
2+ 6.0305x - 8.9618
Akumulasi kuadrat error :
Error rata-rata :
8.6126
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Afham Ramadhan Kuliah Pemodelan dan Rekayasa Sistem
S2 Teknik Elektro
orde enam :
GRAFIK
0 5 10 15 20 25 30 35 40 45 505
10
15
20
25
30
35
40
45
50
55
y = 0.9*x + 3.8
data1
linear
[
456]
[....... ]
.
.. . . .4 .5 .6y = -1E-07x
6+ 2E-05x
5- 0.0018x
4+ 0.0656x
3- 1.1678x
2+ 10.017x - 16.964
Akumulasi kuadrat error :
Error rata-rata :
8.405
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Afham Ramadhan Kuliah Pemodelan dan Rekayasa Sistem
S2 Teknik Elektro
0 5 10 15 20 25 30 35 40 45 505
10
15
20
25
30
35
40
45
50
55
y = 0.0028*x2+ 0.75*x + 5.4
data1
quadratic
0 5 10 15 20 25 30 35 40 45 505
10
15
20
25
30
35
40
45
50
55
y = 0.00022*x3- 0.015*x2+ 1.2*x + 3.2
data1
cubic
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Afham Ramadhan Kuliah Pemodelan dan Rekayasa Sistem
S2 Teknik Elektro
0 5 10 15 20 25 30 35 40 45 505
10
15
20
25
30
35
40
45
50
55
y = - 6.6e-06*x4+ 0.00093*x3- 0.041*x2+ 1.5*x + 2.1
data1
4th degree
0 5 10 15 20 25 30 35 40 45 505
10
15
20
25
30
35
40
45
50
55
y = 3.5e-06*x
5
- 0.00049*x
4
+ 0.025*x
3
- 0.56*x
2
+ 6*x - 9
data1
5th degree
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Afham Ramadhan Kuliah Pemodelan dan Rekayasa Sistem
S2 Teknik Elektro
0 5 10 15 20 25 30 35 40 45 505
10
15
20
25
30
35
40
45
50
55
y = - 1.3e-07*x
6
+ 2.5e-05*x
5
- 0.0018*x
4
+ 0.066*x
3
- 1.2*x
2
+ 10*x - 17
data1
6th degree
0 5 10 15 20 25 30 35 40 45 505
10
15
20
25
30
35
40
45
50
55
y = - 2.6e-08*x7
+ 4.7e-06*x6
- 0.00035*x5
+ 0.013*x4
- 0.24*x3
+ 2.2*x2- 7.1*x + 12
data1
7th degree
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7/25/2019 Tugas Pemodelan - Model Regresi Polinomial
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Afham Ramadhan Kuliah Pemodelan dan Rekayasa Sistem
S2 Teknik Elektro
0 5 10 15 20 25 30 35 40 45 505
10
15
20
25
30
35
40
45
50
55
y = 1.5e-09*x8- 3.6e-07*x7+ 3.5e-05*x6- 0.0018*x5+ 0.054*x4-
0.91*x3+ 8.2*x2- 33*x + 51
data1
8th degree
0 5 10 15 20 25 30 35 40 45 505
10
15
20
25
30
35
40
45
50
55
y = - 1.8e-10*x
9
+ 4.6e-08*x
8
- 5e-06*x
7
+ 0.0003*x
6
- 0.011*x
5
+ 0.25*x4- 3.4*x3+ 26*x2- 1e+02*x + 1.4e+02
data1
9th degree