15.1 Построение уравнения тренда
Построение уравнения тренда
|
t |
y |
t2 |
yt |
|
1 |
45 |
1 |
45 |
|
2 |
32 |
4 |
64 |
|
3 |
36 |
9 |
108 |
|
4 |
43 |
16 |
172 |
|
5 |
39 |
25 |
195 |
|
6 |
52 |
36 |
312 |
|
7 |
57 |
49 |
399 |
|
8 |
54 |
64 |
432 |
|
9 |
61 |
81 |
549 |
|
10 |
64 |
100 |
640 |
|
11 |
67 |
121 |
737 |
|
12 |
61 |
144 |
732 |
|
13 |
52 |
169 |
676 |
|
14 |
59 |
196 |
826 |
|
15 |
50 |
225 |
750 |
|
17 |
50 |
289 |
850 |
|
17 |
57 |
289 |
969 |
|
18 |
57 |
324 |
1026 |
|
19 |
62 |
361 |
1178 |
|
20 |
70 |
400 |
1400 |
|
21 |
74 |
441 |
1554 |
|
22 |
76 |
484 |
1672 |
|
23 |
74 |
529 |
1702 |
|
24 |
69 |
576 |
1656 |
|
25 |
66 |
625 |
1650 |
|
26 |
63 |
676 |
1638 |
|
27 |
68 |
729 |
1836 |
|
28 |
62 |
784 |
1736 |
|
29 |
65 |
841 |
1885 |
|
30 |
69 |
900 |
2070 |
|
31 |
79 |
961 |
2449 |
|
32 |
88 |
1024 |
2816 |
|
33 |
87 |
1089 |
2871 |
|
34 |
91 |
1156 |
3094 |
|
596 |
2099 |
13718 |
40689 |
Линейный тренд описывается с помощью линейного уравнения относительно времени:
y=a+bt;
Составим систему нормальных уравнений:
|
|
34a + b596 = 2099 | |||
|
596a + b13718 = 40689 | ||||
|
|
|
| ||
|
a = 40,8597 | ||||
|
b = 1,1909 | ||||
|
|
|
| ||
|
= 40,8597 + 1,1909t | ||||
Нанесем линию тренда на график
15.2 Определение величины остаточной дисперсии
Определение величины остаточной дисперсии
|
Yt |
Y(t) |
(y(t)-yt) |
(y(t)-yt)2 |
|
45 |
42,0506 |
-2,9494 |
8,699 |
|
32 |
43,2415 |
11,2415 |
126,3713 |
|
36 |
44,4324 |
8,4324 |
71,1054 |
|
43 |
45,6233 |
2,6233 |
6,8817 |
|
39 |
46,8142 |
7,8142 |
61,0617 |
|
52 |
48,0051 |
-3,9949 |
15,9592 |
|
57 |
49,196 |
-7,804 |
60,9024 |
|
54 |
50,3869 |
-3,6131 |
13,0545 |
|
61 |
51,5778 |
-9,4222 |
88,7779 |
|
64 |
52,7687 |
-11,2313 |
126,1421 |
|
67 |
53,9596 |
-13,0404 |
170,052 |
|
61 |
55,1505 |
-5,8495 |
34,2167 |
|
52 |
56,3414 |
4,3414 |
18,8478 |
|
59 |
57,5323 |
-1,4677 |
2,1541 |
|
50 |
58,7232 |
8,7232 |
76,0942 |
|
50 |
61,105 |
11,105 |
123,321 |
|
57 |
61,105 |
4,105 |
16,851 |
|
57 |
62,2959 |
5,2959 |
28,0466 |
|
62 |
63,4868 |
1,4868 |
2,2106 |
|
70 |
64,6777 |
-5,3223 |
28,3269 |
|
74 |
65,8686 |
-8,1314 |
66,1197 |
|
76 |
67,0595 |
-8,9405 |
79,9325 |
|
74 |
68,2504 |
-5,7496 |
33,0579 |
|
69 |
69,4413 |
0,4413 |
0,1947 |
|
66 |
70,6322 |
4,6322 |
21,4573 |
|
63 |
71,8231 |
8,8231 |
77,8471 |
|
68 |
73,014 |
5,014 |
25,1402 |
|
62 |
74,2049 |
12,2049 |
148,9596 |
|
65 |
75,3958 |
10,3958 |
108,0727 |
|
69 |
76,5867 |
7,5867 |
57,558 |
|
79 |
77,7776 |
-1,2224 |
1,4943 |
|
88 |
78,9685 |
-9,0315 |
81,568 |
|
87 |
80,1594 |
-6,8406 |
46,7938 |
|
91 |
81,3503 |
-9,6497 |
93,1167 |
|
|
|
|
1920,3886 |
Dост=