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b
= =
𝑛 ∑𝑥𝑦 −(∑𝑥)(∑𝑦) 𝑛 ∑𝑥 2 −(∑𝑥)2 10 (1531756.4) – (26108) (58.67) 10 (78807164)−(26108)2 1614890.3−153756.36
= 788071640−681627664 83133.94
= 106443976 = 0.00078
a
= =
∑𝑦 𝑛
−𝑏
58.67 10
∑𝑥 𝑛
− 0.00078
26108 10
= 5.867 – 2.036 = 3.831
y
= a + bx = 3.831 + 0.00078x
∑
x
y
500 1295 1840 2204 3148 3245 3258 3507 3545 3566 26108
3.95 5.7 4.22 5.76 6.3 6.3 7.65 6.9 5.95 5.94 58.67
xy
x2
1975 250000 7381.5 1677025 7764.8 3385600 12695.04 4857616 19832.4 9909904 20443.5 10530025 24923.7 10614564 24198.3 12299049 21092.75 12567025 21182.04 12716356 1531756.4 681627664
y'
4.221 4.8411 5.2662 5.550 6.286 6.362 6.372 6.566 6.596 6.61 58.6703
9 8 7 6 5 4 3 2
1 0 500
1295
1840
2204
y 3.95
y’
5.7 4.22 5.76 6.3 6.3 7.65 6.9 5.95 5.94
MSE
= =
ln ∑y = =
∑𝑒 2 𝑛
0.456881 ln 58.67 4.071
3148
4.221 4.8411 5.2662 5.55 6.286 6.362 6.372 6.566 6.596 6.61 ∑
3245
3258
3507
e e2 -0.271 0.073441 0.8589 -1.0462 0.21 0.014 -0.062 1.278 0.334 -0.646 -0.67
0.737709 1.094534 0.0441 0.000196 0.003844 1.633284 0.111556 0.417316 0.4489 4.564881
3545
3566
b
= = = =
a
= =
y
𝑛∑x ln 𝑦−(∑x)(∑ln y) 𝑛 ∑𝑥 2 −(∑x)2 10(47294.37) – (26108)( 17.51738) 10 (681627664)− (26108)2 15599.94 106443976
0.000147
∑lny 𝑛
−𝑏
17.51738 10
∑x 𝑛
- 0.000147
26108
=
1.751738 - 0.383788
=
1.36795
=
𝑒 𝑎+𝑏𝑥
=
𝑒 1.36795+(0.000147𝑥)
a
b
10
x
bx
a+bx
y’ (ea+bx)
1.36795
0.000147
500
0.0735
1.44145
4.22682
1.36795
0.000147
1295
0.190365
1.558315
4.750809
1.36795
0.000147
1840
0.27048
1.63843
5.147082
1.36795
0.000147
2204
0.323988
1.691938
5.429994
1.36795
0.000147
3148
0.462756
1.830706
6.238289
1.36795
0.000147
3245
0.477015
1.844965
6.327878
1.36795
0.000147
3258
0.478926
1.846876
6.339982
1.36795
0.000147
3507
0.515529
1.883479
6.576344
1.36795
0.000147
3545
0.521115
1.889065
6.613182
1.36795
0.000147
3566
0.524202
1.892152
6.633629
y’
e
e2
4.22682 4.750809 5.147082 5.429994 6.238289 6.327878 6.339982 6.576344 6.613182 6.633629 58.28401
-0.27682 0.949191 -0.92708 0.330006 0.061711 -0.02788 1.310018 0.323656 -0.66318 -0.69363 0.385991
0.076629 0.900964 0.859481 0.108904 0.003808 0.000777 1.716147 0.104753 0.43981 0.481121 4.692395
y 3.95 5.7 4.22 5.76 6.3 6.3 7.65 6.9 5.95 5.94 58.67
MSE
=
=
∑𝑒 2 𝑛 4.692395 10
= 0.4692395 𝑦̅
=
= o
∑𝑦 10 58.67 10
= 5.867
Untuk Linear
∑
y
y'
3.95 5.7 4.22 5.76 6.3 6.3 7.65 6.9 5.95 5.94 58.67
4.221 4.8411 5.2662 5.55 6.286 6.362 6.372 6.566 6.596 6.61 58.6703
̅ y'-𝒚
̅)2 (y'-𝒚
-1.646 2.709316 -1.0259 1.052471 -0.6008 0.360961 -0.317 0.100489 0.419 0.175561 0.495 0.245025 0.505 0.255025 0.699 0.488601 0.729 0.531441 0.743 0.552049 0.0003 6.470938
̅ y-𝒚
̅)2 (y-𝒚
-1.917 -0.167 -1.647 -0.107 0.433 0.433 1.783 1.033 0.083 0.073 8.88178E-16
3.674889 0.027889 2.712609 0.011449 0.187489 0.187489 3.179089 1.067089 0.006889 0.005329 11.06021
R2
=
(𝑦 ′ −𝑦̅)2 (𝑦−𝑦̅)2
6.470938
= 11.06021 = 0.585065
k – 1 = 2-1 = 1 n – k = 10-2 = 8 ∑ (y’-𝑦̅)2 = 6.470938 ∑ (y - 𝑦̅)2 = 11.06021 2
Fhitung o
=
̅ ) / (𝑘−1) ∑ (y’−𝑦 2
̅ ) / (𝑛−𝑘) ∑ (y − 𝑦
=
6.470938 1.382526
= 4.680517
Untuk Eksponensial
∑ R2
=
y
y’
̅ y'-𝒚
̅ )2 (y'-𝒚
̅ y-𝒚
̅ )2 (y-𝒚
3.95 5.7 4.22 5.76 6.3 6.3 7.65 6.9 5.95 5.94 58.67
4.22682 4.750809 5.147082 5.429994 6.238289 6.327878 6.339982 6.576344 6.613182 6.633629 58.28401
-1.64018 -1.11619 -0.71992 -0.43701 0.371289 0.460878 0.472982 0.709344 0.746182 0.766629 -0.38599
2.690190432 1.245882348 0.518281927 0.190974244 0.137855522 0.212408531 0.223711972 0.50316891 0.556787577 0.587720024 6.866981487
-1.917 -0.167 -1.647 -0.107 0.433 0.433 1.783 1.033 0.083 0.073 8.88178E-16
3.674889 0.027889 2.712609 0.011449 0.187489 0.187489 3.179089 1.067089 0.006889 0.005329 11.06021
̅) ∑ (y’−𝑦
2
̅) ∑ (y − 𝑦
2
=
6.866981487 11.060873
= 0.620872613
k – 1 = 2-1 = 1 n – k = 10-2 = 8 ∑ (y’-𝑦̅)2 = 6.866981487 ∑ (y - 𝑦̅)2 = 11.06021 2
Fhitung
=
̅ ) / (𝑘−1) ∑ (y’−𝑦 2
̅ ) / (𝑛−𝑘) ∑ (y − 𝑦
= 4.966981
HASIL REKAPITULASI : Linear
MSE R2 Fhitung MSE R2 Fhitung
Eksponen
∑𝑥
𝑥̅
= 10 =
𝑥̅ 2
26108 = 10
2610.8
= 6816277 o
Untuk Linear ̅ ̅ )2 ̅ x-𝒙 (x-𝒙 𝒙 2610.8 -2110.8 4455477 2610.8 -1315.8 1731330 2610.8 -770.8 594132.6 2610.8 -406.8 165486.2 2610.8 537.2 288583.8 2610.8 634.2 402209.6 2610.8 647.2 418867.8 2610.8 896.2 803174.4 2610.8 934.2 872729.6 2610.8 955.2 912407 26108 -1.81899E-12 10644398
x
500 1295 1840 2204 3148 3245 3258 3507 3545 3566 26108
∑
ʈe
∑(𝑦−𝑦′)2 𝑛−2
=√
4.564881 = 0.7553873179 8
=√
Sea
0.456881 0.585065 4.680517 0.4692395 0.620872613 4.966981
1
= ʈe √𝑛 +
𝑥̅ 2 ∑(x−𝑥̅ )2
1
6816277
= 0.7553873179 √10 + 10644398 = 0.7553873179 √0.740363
y
y'
y-y' 3.95 4.221 -0.271 5.7 4.8411 0.8589 4.22 5.2662 -1.0462 5.76 5.55 0.21 6.3 6.286 0.014 6.3 6.362 -0.062 7.65 6.372 1.278 6.9 6.566 0.334 5.95 6.596 -0.646 5.94 6.61 -0.67 58.67 58.6703 -0.0003
(y-y')2 0.073441 0.737709 1.094534 0.0441 0.000196 0.003844 1.633284 0.111556 0.417316 0.4489 4.564881
= 0.6499681003 1
Seb
= ʈe √∑(𝑥−𝑥̅ )2 1
= 0.7553873179 √10644398 = 0.0002314741
thitung (untuk perpotongan) t
= =
𝑎−𝛼 𝑠𝑒𝑎
3.831−0 0.6499681003
= 5.8941354172
thitung (untuk kemiringan) t
=
𝑏−𝛽 𝑠𝑒𝑏
0.00078 − 0
= 0.0002314741 = 3.3697074532 o
Untuk Eksponensial
∑
ʈe
x 500 1295 1840 2204 3148 3245 3258 3507 3545 3566 26108
̅ 𝒙 2610.8 2610.8 2610.8 2610.8 2610.8 2610.8 2610.8 2610.8 2610.8 2610.8 26108
=√
∑(𝑦−𝑦′)2 𝑛−2
=√
4.692395 8
= 0.765865
̅ ̅ )2 x-𝒙 (x-𝒙 -2110.8 4455477 -1315.8 1731330 -770.8 594132.6 -406.8 165486.2 537.2 288583.8 634.2 402209.6 647.2 418867.8 896.2 803174.4 934.2 872729.6 955.2 912407 -1.13687E-12 10644398
y 3.95 5.7 4.22 5.76 6.3 6.3 7.65 6.9 5.95 5.94 58.67
y' 4.22682 4.750809 5.147082 5.429994 6.238289 6.327878 6.339982 6.576344 6.613182 6.633629 58.28401
y-y' -0.27682 0.949191 -0.92708 0.330006 0.061711 -0.02788 1.310018 0.323656 -0.66318 -0.69363 0.385991
(y-y')2 0.076629 0.900964 0.859481 0.108904 0.003808 0.000777 1.716147 0.104753 0.43981 0.481121 4.692395
𝑥̅ 2
1
= ʈe √𝑛 +
Sea
∑(x−𝑥̅ )2
1 10
= 0.765865 √
+
6816277 10644398
= 0.658984 1
Seb
= ʈe √∑(𝑥−𝑥̅ )2 1
= 0.765865 √10644398 = 0.000306506
thitung (untuk perpotongan) t
= =
𝑎−𝛼 𝑠𝑒𝑎
1.36795−0 0.658984
= 2.075848
thitung (untuk kemiringan) t
=
𝑏−𝛽 𝑠𝑒𝑏
0.000147−0
=0.000306506 = 0.479599 Korelasi Rxy =
𝑛∑𝑥𝑦−(∑𝑥)(∑𝑦) √𝑛∑𝑥 2 −(∑𝑥)2 √𝑛∑𝑦 2 −∑(𝑦)2
= =
10 (1531756.4)−(26108)(58.67) √10(681627664)−(26108)2 √10(355.271)−(58.67)2
10(161489) − (26108)(58,67) √10(681627664) − (26108)2 √10(355,2771) − (58,67)2
=
1614890−1531756 823714.1856
=
83133,94 823714.1856
= 0.100926
= =
𝑛 ∑𝑥𝑦 −(∑𝑥)(∑𝑦) 𝑛 ∑𝑥 2 −(∑𝑥)2 10 (1531756.4) – (26108) (58.67) 10 (78807164)−(26108)2 1614890.3−153756.36
= 788071640−681627664 83133.94
= 106443976 = 0.00078
a
= =
∑𝑦 𝑛
−𝑏
58.67 10
∑𝑥 𝑛
− 0.00078
26108 10
= 5.867 – 2.036 = 3.831
y
= a + bx = 3.831 + 0.00078x
∑
x
y
500 1295 1840 2204 3148 3245 3258 3507 3545 3566 26108
3.95 5.7 4.22 5.76 6.3 6.3 7.65 6.9 5.95 5.94 58.67
xy
x2
1975 250000 7381.5 1677025 7764.8 3385600 12695.04 4857616 19832.4 9909904 20443.5 10530025 24923.7 10614564 24198.3 12299049 21092.75 12567025 21182.04 12716356 1531756.4 681627664
y'
4.221 4.8411 5.2662 5.550 6.286 6.362 6.372 6.566 6.596 6.61 58.6703
9 8 7 6 5 4 3 2
1 0 500
1295
1840
2204
y 3.95
y’
5.7 4.22 5.76 6.3 6.3 7.65 6.9 5.95 5.94
MSE
= =
ln ∑y = =
∑𝑒 2 𝑛
0.456881 ln 58.67 4.071
3148
4.221 4.8411 5.2662 5.55 6.286 6.362 6.372 6.566 6.596 6.61 ∑
3245
3258
3507
e e2 -0.271 0.073441 0.8589 -1.0462 0.21 0.014 -0.062 1.278 0.334 -0.646 -0.67
0.737709 1.094534 0.0441 0.000196 0.003844 1.633284 0.111556 0.417316 0.4489 4.564881
3545
3566
b
= = = =
a
= =
y
𝑛∑x ln 𝑦−(∑x)(∑ln y) 𝑛 ∑𝑥 2 −(∑x)2 10(47294.37) – (26108)( 17.51738) 10 (681627664)− (26108)2 15599.94 106443976
0.000147
∑lny 𝑛
−𝑏
17.51738 10
∑x 𝑛
- 0.000147
26108
=
1.751738 - 0.383788
=
1.36795
=
𝑒 𝑎+𝑏𝑥
=
𝑒 1.36795+(0.000147𝑥)
a
b
10
x
bx
a+bx
y’ (ea+bx)
1.36795
0.000147
500
0.0735
1.44145
4.22682
1.36795
0.000147
1295
0.190365
1.558315
4.750809
1.36795
0.000147
1840
0.27048
1.63843
5.147082
1.36795
0.000147
2204
0.323988
1.691938
5.429994
1.36795
0.000147
3148
0.462756
1.830706
6.238289
1.36795
0.000147
3245
0.477015
1.844965
6.327878
1.36795
0.000147
3258
0.478926
1.846876
6.339982
1.36795
0.000147
3507
0.515529
1.883479
6.576344
1.36795
0.000147
3545
0.521115
1.889065
6.613182
1.36795
0.000147
3566
0.524202
1.892152
6.633629
y’
e
e2
4.22682 4.750809 5.147082 5.429994 6.238289 6.327878 6.339982 6.576344 6.613182 6.633629 58.28401
-0.27682 0.949191 -0.92708 0.330006 0.061711 -0.02788 1.310018 0.323656 -0.66318 -0.69363 0.385991
0.076629 0.900964 0.859481 0.108904 0.003808 0.000777 1.716147 0.104753 0.43981 0.481121 4.692395
y 3.95 5.7 4.22 5.76 6.3 6.3 7.65 6.9 5.95 5.94 58.67
MSE
=
=
∑𝑒 2 𝑛 4.692395 10
= 0.4692395 𝑦̅
=
= o
∑𝑦 10 58.67 10
= 5.867
Untuk Linear
∑
y
y'
3.95 5.7 4.22 5.76 6.3 6.3 7.65 6.9 5.95 5.94 58.67
4.221 4.8411 5.2662 5.55 6.286 6.362 6.372 6.566 6.596 6.61 58.6703
̅ y'-𝒚
̅)2 (y'-𝒚
-1.646 2.709316 -1.0259 1.052471 -0.6008 0.360961 -0.317 0.100489 0.419 0.175561 0.495 0.245025 0.505 0.255025 0.699 0.488601 0.729 0.531441 0.743 0.552049 0.0003 6.470938
̅ y-𝒚
̅)2 (y-𝒚
-1.917 -0.167 -1.647 -0.107 0.433 0.433 1.783 1.033 0.083 0.073 8.88178E-16
3.674889 0.027889 2.712609 0.011449 0.187489 0.187489 3.179089 1.067089 0.006889 0.005329 11.06021
R2
=
(𝑦 ′ −𝑦̅)2 (𝑦−𝑦̅)2
6.470938
= 11.06021 = 0.585065
k – 1 = 2-1 = 1 n – k = 10-2 = 8 ∑ (y’-𝑦̅)2 = 6.470938 ∑ (y - 𝑦̅)2 = 11.06021 2
Fhitung o
=
̅ ) / (𝑘−1) ∑ (y’−𝑦 2
̅ ) / (𝑛−𝑘) ∑ (y − 𝑦
=
6.470938 1.382526
= 4.680517
Untuk Eksponensial
∑ R2
=
y
y’
̅ y'-𝒚
̅ )2 (y'-𝒚
̅ y-𝒚
̅ )2 (y-𝒚
3.95 5.7 4.22 5.76 6.3 6.3 7.65 6.9 5.95 5.94 58.67
4.22682 4.750809 5.147082 5.429994 6.238289 6.327878 6.339982 6.576344 6.613182 6.633629 58.28401
-1.64018 -1.11619 -0.71992 -0.43701 0.371289 0.460878 0.472982 0.709344 0.746182 0.766629 -0.38599
2.690190432 1.245882348 0.518281927 0.190974244 0.137855522 0.212408531 0.223711972 0.50316891 0.556787577 0.587720024 6.866981487
-1.917 -0.167 -1.647 -0.107 0.433 0.433 1.783 1.033 0.083 0.073 8.88178E-16
3.674889 0.027889 2.712609 0.011449 0.187489 0.187489 3.179089 1.067089 0.006889 0.005329 11.06021
̅) ∑ (y’−𝑦
2
̅) ∑ (y − 𝑦
2
=
6.866981487 11.060873
= 0.620872613
k – 1 = 2-1 = 1 n – k = 10-2 = 8 ∑ (y’-𝑦̅)2 = 6.866981487 ∑ (y - 𝑦̅)2 = 11.06021 2
Fhitung
=
̅ ) / (𝑘−1) ∑ (y’−𝑦 2
̅ ) / (𝑛−𝑘) ∑ (y − 𝑦
= 4.966981
HASIL REKAPITULASI : Linear
MSE R2 Fhitung MSE R2 Fhitung
Eksponen
∑𝑥
𝑥̅
= 10 =
𝑥̅ 2
26108 = 10
2610.8
= 6816277 o
Untuk Linear ̅ ̅ )2 ̅ x-𝒙 (x-𝒙 𝒙 2610.8 -2110.8 4455477 2610.8 -1315.8 1731330 2610.8 -770.8 594132.6 2610.8 -406.8 165486.2 2610.8 537.2 288583.8 2610.8 634.2 402209.6 2610.8 647.2 418867.8 2610.8 896.2 803174.4 2610.8 934.2 872729.6 2610.8 955.2 912407 26108 -1.81899E-12 10644398
x
500 1295 1840 2204 3148 3245 3258 3507 3545 3566 26108
∑
ʈe
∑(𝑦−𝑦′)2 𝑛−2
=√
4.564881 = 0.7553873179 8
=√
Sea
0.456881 0.585065 4.680517 0.4692395 0.620872613 4.966981
1
= ʈe √𝑛 +
𝑥̅ 2 ∑(x−𝑥̅ )2
1
6816277
= 0.7553873179 √10 + 10644398 = 0.7553873179 √0.740363
y
y'
y-y' 3.95 4.221 -0.271 5.7 4.8411 0.8589 4.22 5.2662 -1.0462 5.76 5.55 0.21 6.3 6.286 0.014 6.3 6.362 -0.062 7.65 6.372 1.278 6.9 6.566 0.334 5.95 6.596 -0.646 5.94 6.61 -0.67 58.67 58.6703 -0.0003
(y-y')2 0.073441 0.737709 1.094534 0.0441 0.000196 0.003844 1.633284 0.111556 0.417316 0.4489 4.564881
= 0.6499681003 1
Seb
= ʈe √∑(𝑥−𝑥̅ )2 1
= 0.7553873179 √10644398 = 0.0002314741
thitung (untuk perpotongan) t
= =
𝑎−𝛼 𝑠𝑒𝑎
3.831−0 0.6499681003
= 5.8941354172
thitung (untuk kemiringan) t
=
𝑏−𝛽 𝑠𝑒𝑏
0.00078 − 0
= 0.0002314741 = 3.3697074532 o
Untuk Eksponensial
∑
ʈe
x 500 1295 1840 2204 3148 3245 3258 3507 3545 3566 26108
̅ 𝒙 2610.8 2610.8 2610.8 2610.8 2610.8 2610.8 2610.8 2610.8 2610.8 2610.8 26108
=√
∑(𝑦−𝑦′)2 𝑛−2
=√
4.692395 8
= 0.765865
̅ ̅ )2 x-𝒙 (x-𝒙 -2110.8 4455477 -1315.8 1731330 -770.8 594132.6 -406.8 165486.2 537.2 288583.8 634.2 402209.6 647.2 418867.8 896.2 803174.4 934.2 872729.6 955.2 912407 -1.13687E-12 10644398
y 3.95 5.7 4.22 5.76 6.3 6.3 7.65 6.9 5.95 5.94 58.67
y' 4.22682 4.750809 5.147082 5.429994 6.238289 6.327878 6.339982 6.576344 6.613182 6.633629 58.28401
y-y' -0.27682 0.949191 -0.92708 0.330006 0.061711 -0.02788 1.310018 0.323656 -0.66318 -0.69363 0.385991
(y-y')2 0.076629 0.900964 0.859481 0.108904 0.003808 0.000777 1.716147 0.104753 0.43981 0.481121 4.692395
𝑥̅ 2
1
= ʈe √𝑛 +
Sea
∑(x−𝑥̅ )2
1 10
= 0.765865 √
+
6816277 10644398
= 0.658984 1
Seb
= ʈe √∑(𝑥−𝑥̅ )2 1
= 0.765865 √10644398 = 0.000306506
thitung (untuk perpotongan) t
= =
𝑎−𝛼 𝑠𝑒𝑎
1.36795−0 0.658984
= 2.075848
thitung (untuk kemiringan) t
=
𝑏−𝛽 𝑠𝑒𝑏
0.000147−0
=0.000306506 = 0.479599 Korelasi Rxy =
𝑛∑𝑥𝑦−(∑𝑥)(∑𝑦) √𝑛∑𝑥 2 −(∑𝑥)2 √𝑛∑𝑦 2 −∑(𝑦)2
= =
10 (1531756.4)−(26108)(58.67) √10(681627664)−(26108)2 √10(355.271)−(58.67)2
10(161489) − (26108)(58,67) √10(681627664) − (26108)2 √10(355,2771) − (58,67)2
=
1614890−1531756 823714.1856
=
83133,94 823714.1856
= 0.100926
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