TUGAS KE-3 MATEMATIKA REKAYASA II
Fransiskus X E Lie / 0953210064
x | Y |
1 | 124 |
3 | 254 |
5 | 374 |
7 | 554 |
9 | 764 |
11 | 984 |
13 | 1264 |
15 | 1484 |
64 | 5802 |
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 | X*Y |
1 | 124 | 1 | 124 |
3 | 254 | 9 | 762 |
5 | 374 | 25 | 1870 |
7 | 554 | 49 | 3878 |
9 | 764 | 81 | 6876 |
11 | 984 | 121 | 10824 |
13 | 1264 | 169 | 16432 |
15 | 1484 | 225 | 22260 |
64 | 5802 | 680 | 63026 |
A). Y = ax + b
Pers. Nominal
64 (98.869) + 8 b = 5802
b = -65.702
Pers. Least quare Y = 98.869x – 65.702
X | Y | Ŷ | X-Ŷ | (Y-Ŷ)^2 |
1 | 124 | 33.167 | -32.167 | 8250.634 |
3 | 254 | 230.905 | -227.905 | 533.379 |
5 | 374 | 428.643 | -423.643 | 2985.857 |
7 | 554 | 626.381 | -619.381 | 5239.009 |
9 | 764 | 824.119 | -815.119 | 3614.294 |
11 | 984 | 1021.857 | -1010.857 | 1433.152 |
13 | 1264 | 1219.595 | -1206.595 | 1971.804 |
15 | 1484 | 1417.333 | -1402.333 | 4444.489 |
28472.619 |
B). Y = ax2 + bx
Pers. Least quare Y = 98.869x2 – 65.702x
X | Y | Ŷ | X-Ŷ | (Y-Ŷ)^2 |
1 | 124 | 33.17 | -32.17 | 8250.63 |
3 | 254 | 692.72 | -689.72 | 192470.85 |
5 | 374 | 2143.22 | -2138.22 | 3130121.72 |
7 | 554 | 4384.67 | -4377.67 | 14674009.66 |
9 | 764 | 7417.07 | -7408.07 | 44263353.73 |
11 | 984 | 11240.43 | -11229.43 | 105194294.81 |
13 | 1264 | 15854.74 | -15841.74 | 212889547.84 |
15 | 1484 | 21260.00 | -21245.00 | 391089978.24 |
771442027.48 |
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