NAMA : MOHAMMAD FATIH AHDA
NPM : 0953010030 Buatlah analisa ketepatan untuk model Y = ax + b Y = ax2 + bx Y = ax2 + bx + c Tentukan yang mana yang paling teliti ? Jawab :
x | y | x² | xy |
1 | 120 | 1 | 120 |
3 | 250 | 9 | 750 |
5 | 370 | 25 | 1850 |
7 | 550 | 49 | 3850 |
9 | 760 | 81 | 6840 |
11 | 980 | 121 | 10780 |
13 | 1260 | 169 | 16380 |
15 | 1840 | 225 | 27600 |
64 | 6130 | 680 | 68170 |
Y = ax + b Pers. Nominal ![]() 2 + b ![]() ![]() + b N
68170 | 680 | 64b | *8 |
6130 | 64 | 8b | *64 |
545360 | 5440 | 512 |
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392320 | 4096 | 512 |
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153040 | 1344 | 0 |
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A | 113.869 |
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6130 | 64a | 8b |
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6130 | 7287.619 | 8b |
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8b | -1157.62 |
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B | -144.702 |
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Pers. Least quare Y = 4.859x2 – 42.171
X | Y | Ŷ | X-Ŷ | (Y-Ŷ)^2 |
1 | 120 | -37.312 | 38.312 | 24747.065 |
3 | 250 | 1.560 | 1.440 | 61722.434 |
5 | 370 | 79.304 | -74.304 | 84504.164 |
7 | 550 | 195.920 | -188.920 | 125372.646 |
9 | 760 | 351.408 | -342.408 | 166947.422 |
11 | 980 | 545.768 | -534.768 | 188557.430 |
13 | 1260 | 779.000 | -766.000 | 231361.000 |
15 | 1480 | 1051.104 | -1036.104 | 183951.779 |
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| 1067163.941 |
SD =![]() = ![]() = 390.451 Y = ax2 + bx
X | y | x² | x³ | x⁴ | xy | x²y |
1 | 120 | 1 | 1 | 1 | 120 | 120 |
3 | 250 | 9 | 27 | 81 | 750 | 2250 |
5 | 370 | 25 | 125 | 625 | 1850 | 9250 |
7 | 550 | 49 | 343 | 2401 | 3850 | 26950 |
9 | 760 | 81 | 729 | 6561 | 6840 | 61560 |
11 | 980 | 121 | 1331 | 14641 | 10780 | 118580 |
13 | 1260 | 169 | 2197 | 28561 | 16380 | 212940 |
15 | 1840 | 225 | 3375 | 50625 | 27600 | 414000 |
64 | 6130 | 680 | 8128 | 103496 | 68170 | 845650 |
Pers. Least quare Y = 4.859x2 – 42.171x
x | y | Ŷ | X-Ŷ | (Y-Ŷ)^2 |
1 | 120 | -37.312 | 38.312 | 24747.07 |
3 | 250 | 1.56 | 1.44 | 61722.43 |
5 | 370 | 79.304 | -74.304 | 84504.16 |
7 | 550 | 195.92 | -188.92 | 125372.6 |
9 | 760 | 351.408 | -342.408 | 166947.4 |
11 | 980 | 545.768 | -534.768 | 188557.4 |
13 | 1260 | 779 | -766 | 231361 |
15 | 1840 | 1051.104 | -1036.1 | 622356.9 |
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| 1505569 |
SD =![]() = ![]() = 463.77 Y = ax2 + bx + c
x | y | x² | x³ | x⁴ | xy | x²y |
1 | 120 | 1 | 1 | 1 | 120 | 120 |
3 | 250 | 9 | 27 | 81 | 750 | 2250 |
5 | 370 | 25 | 125 | 625 | 1850 | 9250 |
7 | 550 | 49 | 343 | 2401 | 3850 | 26950 |
9 | 760 | 81 | 729 | 6561 | 6840 | 61560 |
11 | 980 | 121 | 1331 | 14641 | 10780 | 118580 |
13 | 1260 | 169 | 2197 | 28561 | 16380 | 212940 |
15 | 1840 | 225 | 3375 | 50625 | 27600 | 414000 |
64 | 6130 | 680 | 8128 | 103496 | 68170 | 845650 |
Pers. Least quare Y = 6x2 .89+ 3.631x + 151.526
X | Y | Ŷ | X-Ŷ | (Y-Ŷ)^2 |
1 | 120 | 162.047 | -161.047 | 1767.95 |
3 | 250 | 224.429 | -221.429 | 653.876 |
5 | 370 | 341.931 | -336.931 | 787.8688 |
7 | 550 | 514.553 | -507.553 | 1256.49 |
9 | 760 | 742.295 | -733.295 | 313.467 |
11 | 980 | 1025.157 | -1014.16 | 2039.155 |
13 | 1260 | 1363.139 | -1350.14 | 10637.65 |
15 | 1840 | 1756.241 | -1741.24 | 7015.57 |
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| 24472.03 |
SD =![]() = ![]() = 59.127 Jadi yang lebih teliti adalah mempergunakan Pers. Least quare Y = 6x2 .89+ 3.631x + 151.526 dengan nilai SD=59.127
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