7. soal 6 perhitungan model regresi
DESCRIPTION
tubes hidrologi teknik dasarTRANSCRIPT
1
Perhitungan Model Regresi Linier (Debit 1)
Tabel 6.1. Perhitungan Model Regresi LinierHubungan Duga Air (h) dengan Debit (Q)
No Yi (Q) Xi (h)1 0.00 0.00 -11.20 -0.80 125.55 0.64 8.962 0.49 0.10 -10.71 -0.70 114.80 0.49 7.503 0.98 0.20 -10.22 -0.60 104.54 0.36 6.134 1.76 0.30 -9.44 -0.50 89.20 0.25 4.725 2.55 0.40 -8.65 -0.40 74.90 0.16 3.466 3.72 0.50 -7.48 -0.30 56.02 0.09 2.257 5.29 0.60 -5.91 -0.20 34.98 0.04 1.188 6.66 0.70 -4.54 -0.10 20.65 0.01 0.459 8.52 0.80 -2.68 0.00 7.21 0.00 0.0010 10.39 0.90 -0.81 0.10 0.66 0.01 -0.0811 12.84 1.00 1.64 0.20 2.67 0.04 0.3312 15.38 1.10 4.18 0.30 17.43 0.09 1.2513 18.32 1.20 7.12 0.40 50.63 0.16 2.8514 21.07 1.30 9.87 0.50 97.32 0.25 4.9315 24.20 1.40 13.00 0.60 168.88 0.36 7.8016 27.54 1.50 16.34 0.70 266.84 0.49 11.4317 30.77 1.60 19.57 0.80 382.80 0.64 15.65
Jumlah 190.48 13.60 0.00 0.00 1615.11 4.08 78.83Rata-Rata 11.20 0.80 0.00 0.00 95.01 0.24 4.64
Yi-Yrerata Xi-Xrerata (Yi-Yrerata)2 (Xi-Xrerata)2 (Yi-Y rerata) (Xi-Xrerata)
0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60 1.800.00
5.00
10.00
15.00
20.00
25.00
30.00
35.00
f(x) = 19.3203431372549 x − 4.25156862745098R² = 0.942947601417135
Perhitungan Lengkung Debit Metode Linear
Lengkung Debit Linear (Lengkung Debit)
2
R
8.96 R27.506.13 DX4.72 DY3.462.251.18 DY/DX0.45 DX/DY0.00-0.080.33 a11.25 a22.854.937.80
(Yi-Y rerata) (Xi-Xrerata)
Perhitungan Model Regresi Linier (Debit 2)
Tabel 6.2. Perhitungan Model Regresi LinierHubungan Duga Air (h) dengan Debit (Q)
Perhitungan Lengkung Debit Metode Linear Debit 2
No Yi (Q) Xi (h)1 0.00 0.00 -11.13 -0.80 123.81 0.64 8.902 0.40 0.10 -10.73 -0.70 115.07 0.49 7.513 0.94 0.20 -10.19 -0.60 103.78 0.36 6.114 1.62 0.30 -9.51 -0.50 90.38 0.25 4.755 2.46 0.40 -8.67 -0.40 75.12 0.16 3.47
Yi-Yrerata Xi-Xrerata (Yi-Yrerata)2 (Xi-Xrerata)2 (Yi-Y rerata) (Xi-Xrerata)
0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60 1.800.00
5.00
10.00
15.00
20.00
25.00
30.00
35.00
f(x) = 19.3203431372549 x − 4.25156862745098R² = 0.942947601417135
Perhitungan Lengkung Debit Metode Linear
Lengkung Debit
Linear (Lengkung Debit)
3
0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60 1.800.00
5.00
10.00
15.00
20.00
25.00
30.00
35.00
f(x) = 19.2872549019608 x − 4.30274509803922R² = 0.9430398761617
Perhitungan Lengkung Debit Metode Linear
Lengkung Debit
Linear (Lengkung Debit)
R
8.90 R27.516.11 DX4.75 DY3.472.231.20 DY/DX0.46 DX/DY0.00-0.060.33 a11.24 a22.794.93
(Yi-Y rerata) (Xi-Xrerata)
4
data NO H (m) Q1 (m3/dt) Q2 (m3/dt)1 0.00 0.00 0.002 0.10 0.49 0.403 0.20 0.98 0.944 0.30 1.76 1.625 0.40 2.55 2.466 0.50 3.72 3.687 0.60 5.29 5.158 0.70 6.66 6.579 0.80 8.52 8.4810 0.90 10.39 10.5411 1.00 12.84 12.8012 1.10 15.38 15.2513 1.20 18.32 18.0914 1.30 21.07 20.9815 1.40 24.20 24.0716 1.50 27.54 27.40
Perhitungan Model Regresi eksponensial (Debit 1)
Tabel 6.3. Perhitungan Model Regresi EksponensialHubungan Duga Air (h) dengan Debit (Q)
No Yi (Q) Xi (h) P = ln Y1 0.00 0.00 0.00 -1.84 -0.80 3.39 0.64 1.472 0.49 0.10 -0.71 -2.55 -0.70 6.52 0.49 1.793 0.98 0.20 -0.02 -1.86 -0.60 3.46 0.36 1.124 1.76 0.30 0.57 -1.28 -0.50 1.63 0.25 0.645 2.55 0.40 0.94 -0.90 -0.40 0.82 0.16 0.366 3.72 0.50 1.31 -0.53 -0.30 0.28 0.09 0.167 5.29 0.60 1.67 -0.18 -0.20 0.03 0.04 0.048 6.66 0.70 1.90 0.06 -0.10 0.00 0.01 -0.019 8.52 0.80 2.14 0.30 0.00 0.09 0.00 0.0010 10.39 0.90 2.34 0.50 0.10 0.25 0.01 0.0511 12.84 1.00 2.55 0.71 0.20 0.51 0.04 0.1412 15.38 1.10 2.73 0.89 0.30 0.80 0.09 0.2713 18.32 1.20 2.91 1.07 0.40 1.14 0.16 0.4314 21.07 1.30 3.05 1.21 0.50 1.46 0.25 0.6015 24.20 1.40 3.19 1.35 0.60 1.81 0.36 0.8116 27.54 1.50 3.32 1.47 0.70 2.17 0.49 1.0317 30.77 1.60 3.43 1.59 0.80 2.51 0.64 1.27
Jumlah 190.48 13.60 31.30 0.00 0.00 26.87 4.08 10.16
P-Prerata Xi-Xrerata (P-Prerata)2 (Xi-Xrerata)2 (P-Prerata) (Xi-Xrerata)
5
0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60 1.800.00
2.00
4.00
6.00
8.00
10.00
12.00
f(x) = NaN exp( NaN x )R² = NaN Perhitungan Lengkung Debit Metode Eksponensial
Lengkung Debit
Exponential (Lengkung Debit)
h Q dataQ
modelKesalahan Relatif
(%)
0,00 0,59 1,16 96,120,10 1,08 1,48 36,950,20 1,86 1,89 1,640,30 2,65 2,42 8,810,40 3,82 3,09 19,140,50 5,39 3,95 26,750,60 6,76 5,05 25,350,70 8,62 6,45 25,170,80 10,49 8,25 21,400,90 12,94 10,54 18,561,00 15,48 13,47 12,981,10 18,42 17,22 6,521,20 21,17 22,01 3,961,30 24,30 28,13 15,771,40 27,64 35,96 30,101,50 30,87 45,96 48,89
Kesalahan Relatif Maksimum 96,12
6
Perhitungan Model Regresi eksponensial (Debit 2)
Tabel 6.4. Perhitungan Model Regresi EksponensialHubungan Duga Air (h) dengan Debit (Q
Perhitungan Lengkung Debit Metode Eksponensial Debit 2
No Yi (Q) Xi (h) P = ln Y1 0.00 0.00 0.00 -1.81 -0.80 3.29 0.64 1.452 0.40 0.10 -0.92 -2.73 -0.70 7.46 0.49 1.913 0.94 0.20 -0.06 -1.88 -0.60 3.52 0.36 1.134 1.62 0.30 0.48 -1.33 -0.50 1.78 0.25 0.675 2.46 0.40 0.90 -0.91 -0.40 0.84 0.16 0.376 3.68 0.50 1.30 -0.51 -0.30 0.26 0.09 0.157 5.15 0.60 1.64 -0.18 -0.20 0.03 0.04 0.048 6.57 0.70 1.88 0.07 -0.10 0.00 0.01 -0.01
P-Prerata Xi-Xrerata (P-Prerata)2 (Xi-Xrerata)2 (P-Prerata) (Xi-Xrerata)
0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.600.00
5.00
10.00
15.00
20.00
25.00
30.00
35.00f(x) = 0.979181059676664 exp( 2.59900451954483 x )R² = 0.925221420606696
Perhitungan Lengkung Debit Metode Eksponensial
Lengkung Debit
Exponential (Lengkung Debit)
7
Perhitungan Lengkung Debit Metode Eksponensial Debit 2
Yi (Q) Xi (h) P = ln Y0.00 0.00 0.00 -1.810.40 0.10 -0.92 -2.730.94 0.20 -0.06 -1.881.62 0.30 0.48 -1.332.46 0.40 0.90 -0.913.68 0.50 1.30 -0.515.15 0.60 1.64 -0.186.57 0.70 1.88 0.078.48 0.80 2.14 0.3210.54 0.90 2.36 0.5412.80 1.00 2.55 0.7315.25 1.10 2.72 0.9118.09 1.20 2.90 1.0820.98 1.30 3.04 1.2324.07 1.40 3.18 1.3727.40 1.50 3.31 1.50
P-Prerata
Perhitungan Model Regresi Berpangkat(Debit 1)
Tabel 6.5. Perhitungan Model Regresi BerpangkatHubungan Duga Air (h) dengan Debit (Q)
Perhitungan Lengkung Debit Metode Berpangkat Debit 1
No Yi (Q) Xi (h) P = log Y q = log X1 0.49 0.10 -0.31 -1.00 -1.16 -0.83 1.34 0.69 0.972 0.98 0.20 -0.01 -0.70 -0.86 -0.53 0.74 0.28 0.463 1.76 0.30 0.25 -0.52 -0.60 -0.36 0.36 0.13 0.214 2.55 0.40 0.41 -0.40 -0.44 -0.23 0.20 0.05 0.105 3.72 0.50 0.57 -0.30 -0.28 -0.13 0.08 0.02 0.046 5.29 0.60 0.72 -0.22 -0.13 -0.05 0.02 0.00 0.017 6.66 0.70 0.82 -0.15 -0.03 0.01 0.00 0.00 0.008 8.52 0.80 0.93 -0.10 0.08 0.07 0.01 0.00 0.019 10.39 0.90 1.02 -0.05 0.17 0.12 0.03 0.01 0.0210 12.84 1.00 1.11 0.00 0.26 0.17 0.07 0.03 0.0411 15.38 1.10 1.19 0.04 0.34 0.21 0.11 0.04 0.0712 18.32 1.20 1.26 0.08 0.41 0.25 0.17 0.06 0.1013 21.07 1.30 1.32 0.11 0.47 0.28 0.22 0.08 0.1314 24.20 1.40 1.38 0.15 0.53 0.31 0.29 0.10 0.17
P-Prerata q-qrerata (P-Prerata)2 (q-qrerata)2 (P-Prerata) (q-qrerata)
8
0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60 1.800.00
5.00
10.00
15.00
20.00
25.00
30.00
35.00
f(x) = 12.9506151336739 x^1.56925280033722R² = 0.988524866333575
Perhitungan Lengkung Debit Metode Berpangkat
Lengkung Debit
Power (Lengkung Debit)
a1 1.57a2 0.63
9
Perhitungan Model Regresi Berpangkat(Debit 2)
Tabel 6.6. Perhitungan Model Regresi BerpangkatHubungan Duga Air (h) dengan Debit (Q)
Perhitungan Lengkung Debit Metode Berpangkat Debit 2
No Yi (Q) Xi (h) P = log Y q = log X1 0.40 0.10 -0.40 -1.00 -1.24 -0.83 1.53 0.69 1.032 0.94 0.20 -0.03 -0.70 -0.86 -0.53 0.75 0.28 0.463 1.62 0.30 0.21 -0.52 -0.63 -0.36 0.39 0.13 0.224 2.46 0.40 0.39 -0.40 -0.45 -0.23 0.20 0.05 0.105 3.68 0.50 0.57 -0.30 -0.27 -0.13 0.07 0.02 0.046 5.15 0.60 0.71 -0.22 -0.13 -0.05 0.02 0.00 0.017 6.57 0.70 0.82 -0.15 -0.02 0.01 0.00 0.00 0.008 8.48 0.80 0.93 -0.10 0.09 0.07 0.01 0.00 0.01
P-Prerata q-qrerata (P-Prerata)2 (q-qrerata)2 (P-Prerata) (q-qrerata)
0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60 1.800.00
5.00
10.00
15.00
20.00
25.00
30.00
35.00
f(x) = 12.864242945485 x^1.62408435843792R² = 0.992637662012426
Perhitungan Lengkung Debit Metode Berpangkat
Lengkung Debit
Power (Lengkung Debit)
10
Perhitungan Model logaritmik(Debit 1)
Tabel 6.7. Perhitungan Model logaritmikHubungan Duga Air (h) dengan Debit (Q)
Perhitungan Lengkung Debit Metode Logaritmik Debit 1
No Yi (Q) Xi (h) q = log Xi1 0.49 0.10 -1.00 -11.42 -0.83 130.30 0.692 0.98 0.20 -0.70 -10.92 -0.53 119.36 0.283 1.76 0.30 -0.52 -10.15 -0.36 102.92 0.134 2.55 0.40 -0.40 -9.36 -0.23 87.52 0.055 3.72 0.50 -0.30 -8.18 -0.13 66.99 0.026 5.29 0.60 -0.22 -6.61 -0.05 43.76 0.007 6.66 0.70 -0.15 -5.24 0.01 27.51 0.008 8.52 0.80 -0.10 -3.39 0.07 11.46 0.009 10.39 0.90 -0.05 -1.51 0.12 2.30 0.0110 12.84 1.00 0.00 0.94 0.17 0.87 0.0311 15.38 1.10 0.04 3.48 0.21 12.08 0.0412 18.32 1.20 0.08 6.42 0.25 41.15 0.0613 21.07 1.30 0.11 9.17 0.28 84.00 0.0814 24.20 1.40 0.15 12.30 0.31 151.17 0.10
Yi-Yrerata q-qrerata (Yi-Yrerata)2 (q-qrerata)2
0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60 1.800.00
5.00
10.00
15.00
20.00
25.00
30.00
35.00
f(x) = 10.6769726654914 ln(x) + 16.0219748508404R² = 0.718706244409984
Perhitungan Lengkung Debit Metode Logaritmik
Lengkung Debit
Logarithmic (Lengkung Debit)
11
Xi (h) q = log Xi0.10 -1.00 -11.42 -0.830.20 -0.70 -10.92 -0.530.30 -0.52 -10.15 -0.360.40 -0.40 -9.36 -0.230.50 -0.30 -8.18 -0.130.60 -0.22 -6.61 -0.050.70 -0.15 -5.24 0.010.80 -0.10 -3.39 0.070.90 -0.05 -1.51 0.121.00 0.00 0.94 0.171.10 0.04 3.48 0.211.20 0.08 6.42 0.251.30 0.11 9.17 0.281.40 0.15 12.30 0.311.50 0.18 15.64 0.341.60 0.20 18.87 0.37
Yi-Yrerata q-qrerata
Perhitungan Model logaritmik(Debit 2)
Tabel 6.8. Perhitungan Model logaritmikHubungan Duga Air (h) dengan Debit (Q)
Perhitungan Lengkung Debit Metode Logaritmik Debit 2
No Yi (Q) Xi (h) q = log Xi1 0.40 0.10 -1.00 -11.42 -0.83 130.47 0.692 0.94 0.20 -0.70 -10.88 -0.53 118.43 0.283 1.62 0.30 -0.52 -10.20 -0.36 104.09 0.134 2.46 0.40 -0.40 -9.36 -0.23 87.66 0.055 3.68 0.50 -0.30 -8.14 -0.13 66.30 0.02
Yi-Yrerata q-qrerata (Yi-Yrerata)2 (q-qrerata)2
0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60 1.800.00
5.00
10.00
15.00
20.00
25.00
30.00
35.00
f(x) = 10.6769726654914 ln(x) + 16.0219748508404R² = 0.718706244409984
Perhitungan Lengkung Debit Metode Logar-itmik
Lengkung Debit
Logarithmic (Lengkung Debit)
12
0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60 1.800.00
5.00
10.00
15.00
20.00
25.00
30.00
35.00
f(x) = 10.6706427847171 ln(x) + 15.937034087829R² = 0.71972075396224
Perhitungan Lengkung Debit Metode Logar-itmik
Lengkung Debit
Logarithmic (Lengkung Debit)
h Q dataQ
model
Kesalahan Relatif
(%)0,10 0,40 -8,56 2240,670,20 0,94 -1,16 223,610,30 1,62 3,17 95,510,40 2,46 6,24 153,610,50 3,68 8,62 134,270,60 5,15 10,57 105,200,70 6,57 12,21 85,900,80 8,48 13,64 60,840,90 10,54 14,90 41,341,00 12,80 16,02 25,171,10 15,25 17,04 11,741,20 18,09 17,97 0,671,30 20,98 18,82 10,281,40 24,07 19,61 18,511,50 27,40 20,35 25,731,60 30,73 21,04 31,53
Kesalahan Relatif Maksimum 2240,67