, () , . . = 0, i ≠ j, , .
.
, .
.
.
(4) (5) .
. , (). -.
d = ,
n .
:
) dB < d < 4 -dB, ;
) dH < d < dB 4- dB < d < 4- dH ( );
) 0 < d < dH, ;
) 4- dH < d < 4, .
dH dB d = 0,05 . 1.
1. ?
2. .
3. .
4. .
5. .
6. .
7. .
8. .
1
() 15 - .
1
t | |||||||||||||||
3,38 | 3,53 | 3,7 | 3,8 | 3,78 | 3,84 | 3,76 | 3,9 | 4,15 | 4,28 | 4,4 | 4,54 | 4,78 | 4,84 | 4,88 |
: , . 2, , .
2
t | Yt | Yt | Yt+ 1 | YtYt+ 1 | t² | ||
3,380 | 3,380 | 3,530 | 11,931 | 11,424 | 12,461 | ||
3,530 | 3,530 | 3,700 | 13,061 | 12,461 | 13,690 | ||
3,700 | 3,700 | 3,800 | 14,060 | 13,690 | 14,440 | ||
3,800 | 3,800 | 3,780 | 14,364 | 14,440 | 14,288 | ||
3,780 | 3,780 | 3,840 | 14,515 | 14,288 | 14,746 | ||
3,840 | 3,840 | 3,760 | 14,438 | 14,746 | 14,138 | ||
3,760 | 3,760 | 3,900 | 14,664 | 14,138 | 15,210 | ||
3,900 | 3,900 | 4,150 | 16,185 | 15,210 | 17,223 | ||
4,150 | 4,150 | 4,280 | 17,762 | 17,223 | 18,318 | ||
4,280 | 4,280 | 4,400 | 18,832 | 18,318 | 19,360 | ||
4,400 | 4,400 | 4,540 | 19,976 | 19,360 | 20,612 | ||
4,540 | 4,540 | 4,780 | 21,701 | 20,612 | 22,848 | ||
4,780 | 4,780 | 4,840 | 23,135 | 22,848 | 23,426 | ||
4,840 | 4,840 | 4,880 | 23,619 | 23,426 | 23,814 | ||
4,880 | |||||||
å | 61,560 | 56,680 | 58,180 | 238,245 | 232,183 | 244,573 | |
å /n | 4,104 | 82,667 |
.2
|
|
t | Yt | Yt+ 2 | YtYt+ 2 | tYt | |||
3,380 | 3,700 | 12,506 | 11,424 | 13,690 | 3,380 | 11,424 | |
3,530 | 3,800 | 13,414 | 12,461 | 14,440 | 7,060 | 12,461 | |
3,700 | 3,780 | 13,986 | 13,690 | 14,288 | 11,100 | 13,690 | |
3,800 | 3,840 | 14,592 | 14,440 | 14,746 | 15,200 | 14,440 | |
3,780 | 3,760 | 14,213 | 14,288 | 14,138 | 18,900 | 14,288 | |
3,840 | 3,900 | 14,976 | 14,746 | 15,210 | 23,040 | 14,746 | |
3,760 | 4,150 | 15,604 | 14,138 | 17,223 | 26,320 | 14,138 | |
3,900 | 4,280 | 16,692 | 15,210 | 18,318 | 31,200 | 15,210 | |
4,150 | 4,400 | 18,260 | 17,223 | 19,360 | 37,350 | 17,223 | |
4,280 | 4,540 | 19,431 | 18,318 | 20,612 | 42,800 | 18,318 | |
4,400 | 4,780 | 21,032 | 19,360 | 22,848 | 48,400 | 19,360 | |
4,540 | 4,840 | 21,974 | 20,612 | 23,426 | 54,480 | 20,612 | |
4,780 | 4,880 | 23,326 | 22,848 | 23,814 | 62,140 | 22,848 | |
67,760 | 23,426 | ||||||
73,200 | 23,814 | ||||||
å | 51,840 | 54,650 | 220,006 | 208,758 | 232,113 | 522,330 | 255,998 |
å /n | 34,822 | 17,067 |
.2
t | Yt | Yt+ 3 | YtYt+ 3 | t | Ŷ | |||
3,380 | 3,800 | 12,844 | 11,424 | 14,440 | 3,355 | 0,025 | ||
3,530 | 3,780 | 13,343 | 12,461 | 14,288 | 3,462 | 0,068 | ||
3,700 | 3,840 | 14,208 | 13,690 | 14,746 | 3,569 | 0,131 | ||
3,800 | 3,760 | 14,288 | 14,440 | 14,138 | 3,676 | 0,124 | ||
3,780 | 3,900 | 14,742 | 14,288 | 15,210 | 3,783 | -0,003 | ||
3,840 | 4,150 | 15,936 | 14,746 | 17,223 | 3,890 | -0,050 | ||
3,760 | 4,280 | 16,093 | 14,138 | 18,318 | 3,997 | -0,237 | ||
3,900 | 4,400 | 17,160 | 15,210 | 19,360 | 4,104 | -0,204 | ||
4,150 | 4,540 | 18,841 | 17,223 | 20,612 | 4,211 | -0,061 | ||
4,280 | 4,780 | 20,458 | 18,318 | 22,848 | 4,318 | -0,038 | ||
4,400 | 4,840 | 21,296 | 19,360 | 23,426 | 4,425 | -0,025 | ||
4,540 | 4,880 | 22,155 | 20,612 | 23,814 | 4,532 | 0,008 | ||
4,639 | 0,141 | |||||||
4,746 | 0,094 | |||||||
4,853 | 0,027 | |||||||
å | 47,060 | 50,950 | 201,365 | 185,909 | 218,423 | 120,000 | 0,000 | |
å /n | 8,000 | 0,000 |
.2
t | ( - )2 | |||
− | − | − | 0,001 | |
0,068 | 0,025 | 0,002 | 0,005 | |
0,131 | 0,068 | 0,004 | 0,017 | |
0,124 | 0,131 | 0,000 | 0,015 | |
-0,003 | 0,124 | 0,016 | 0,000 | |
-0,050 | -0,003 | 0,002 | 0,003 | |
-0,237 | -0,050 | 0,035 | 0,056 | |
-0,204 | -0,237 | 0,001 | 0,042 | |
-0,061 | -0,204 | 0,020 | 0,004 | |
-0,038 | -0,061 | 0,001 | 0,001 | |
-0,025 | -0,038 | 0,000 | 0,001 | |
0,008 | -0,025 | 0,001 | 0,000 | |
0,141 | 0,008 | 0,018 | 0,020 | |
0,094 | 0,141 | 0,002 | 0,009 | |
0,027 | 0,094 | 0,004 | 0,001 | |
å | 0,107 | 0,173 |
|
|
.
, , , (3).
. 2.
r (t = 1) = ;
r (t = 1) = = 0,981;
r (t = 2) = ;
r (t = 2) = = 0,899;
r (t = 3) = ;
r (t = 3) = = 0,923.
.
t = a + bt + ,
b = = = 0,107,
= -b =4,104-0,107 = 3,248,
Tt = 3,248 + 0,107 t +
Yt = 3,248 + 0,107 t +
Ŷt = 3,248 + 0,107 t.
= = = 0,974.
F. = = ×13 = 241,9
F. (α = 0,05; 1 = 1; 2 = 13) = 4,67 (. . 2)
F. > F.
d = = = 0,618.
dH (n = 15, p = 1) = 1,08; dB (n = 15, p = 1) = 1,36 (. . 1).
, ,
0 < d < dH,
- ().
, , .
2
(Yt) W 22 .
3
t | |||||||||||
Yt | 9,71 | 11,66 | 10,44 | 9,07 | 9,57 | 7,27 | 7,52 | 10,19 | 9,72 | 8,15 | 8,23 |
. 3
t | |||||||||||
Yt | 11,12 | 13,86 | 14,28 | 13,64 | 12,41 | 11,45 | 13,51 | 13,25 | 12,26 | 11,89 | 12,13 |
: , . 4, , .
4
t | Yt | Yt- 1 | YtYt- 1 | YtYt- 1 | t² | Yt | ||
9,7100 | | | | | − | − | − | |
11,6600 | 9,7100 | 113,2186 | 94,2841 | 135,9556 | 113,2186 | 11,6600 | ||
10,4400 | 11,6600 | 121,7304 | 135,9556 | 108,9936 | 121,7304 | 10,4400 | ||
9,0700 | 10,4400 | 94,6908 | 108,9936 | 82,2649 | 94,6908 | 9,0700 | ||
9,5700 | 9,0700 | 86,7999 | 82,2649 | 91,5849 | 86,7999 | 9,5700 | ||
7,2700 | 9,5700 | 69,5739 | 91,5849 | 52,8529 | 69,5739 | 7,2700 | ||
7,5200 | 7,2700 | 54,6704 | 52,8529 | 56,5504 | 54,6704 | 7,5200 | ||
10,1900 | 7,5200 | 76,6288 | 56,5504 | 103,8361 | 76,6288 | 10,1900 | ||
9,7200 | 10,1900 | 99,0468 | 103,8361 | 94,4784 | 99,0468 | 9,7200 | ||
8,1500 | 9,7200 | 79,2180 | 94,4784 | 66,4225 | 79,2180 | 8,1500 | ||
8,2300 | 8,1500 | 67,0745 | 66,4225 | 67,7329 | 67,0745 | 8,2300 | ||
11,1200 | 8,2300 | 91,5176 | 67,7329 | 123,6544 | 91,5176 | 11,1200 | ||
13,8600 | 11,1200 | 154,1232 | 123,6544 | 192,0996 | 154,1232 | 13,8600 | ||
14,2800 | 13,8600 | 197,9208 | 192,0996 | 203,9184 | 197,9208 | 14,2800 |
. 4
t | Yt | Yt- 1 | YtYt- 1 | YtYt- 1 | t² | Yt | ||
13,6400 | 14,2800 | 194,7792 | 203,9184 | 186,0496 | 194,7792 | 13,6400 | ||
12,4100 | 13,6400 | 169,2724 | 186,0496 | 154,0081 | 169,2724 | 12,4100 | ||
11,4500 | 12,4100 | 142,0945 | 154,0081 | 131,1025 | 142,0945 | 11,4500 | ||
13,5100 | 11,4500 | 154,6895 | 131,1025 | 182,5201 | 154,6895 | 13,5100 | ||
13,2500 | 13,5100 | 179,0075 | 182,5201 | 175,5625 | 179,0075 | 13,2500 | ||
12,2600 | 13,2500 | 162,4450 | 175,5625 | 150,3076 | 162,4450 | 12,2600 | ||
11,8900 | 12,2600 | 145,7714 | 150,3076 | 141,3721 | 145,7714 | 11,8900 | ||
12,1300 | 11,8900 | 144,2257 | 141,3721 | 147,1369 | 144,2257 | 12,1300 | ||
å | 231,6200 | 229,2000 | 2598,4989 | 2595,5512 | 2648,4040 | 2598,4989 | 231,6200 | |
å /n | 10,5282 | 10,9143 | 123,7380 | 123,5977 | 126,1145 | 123,7380 | 172,4545 | 11,0295 |
|
|
.4
t | Ŷ | Y - Ŷ | ( - )2 | ||||
− | − | − | − | − | − | ||
10,1262 | 1,5338 | 2,3526 | − | − | − | ||
11,5895 | -1,1495 | 1,3213 | 1,5338 | -1,1495 | 7,2000 | ||
10,6740 | -1,6040 | 2,5727 | -1,1495 | -1,6040 | 0,2066 | ||
9,6459 | -0,0759 | 0,0058 | -1,6040 | -0,0759 | 2,3349 | ||
10,0211 | -2,7511 | 7,5687 | -0,0759 | -2,7511 | 7,1567 | ||
8,2952 | -0,7752 | 0,6009 | -2,7511 | -0,7752 | 3,9043 | ||
8,4828 | 1,7072 | 2,9145 | -0,7752 | 1,7072 | 6,1623 | ||
10,4864 | -0,7664 | 0,5873 | 1,7072 | -0,7664 | 6,1185 | ||
10,1337 | -1,9837 | 3,9350 | -0,7664 | -1,9837 | 1,4818 | ||
8,9556 | -0,7256 | 0,5264 | -1,9837 | -0,7256 | 1,5829 | ||
9,0156 | 2,1044 | 4,4285 | -0,7256 | 2,1044 | 8,0087 | ||
11,1842 | 2,6758 | 7,1596 | 2,1044 | 2,6758 | 0,3264 | ||
13,2403 | 1,0397 | 1,0809 | 2,6758 | 1,0397 | 2,6768 | ||
13,5555 | 0,0845 | 0,0071 | 1,0397 | 0,0845 | 0,9123 | ||
13,0753 | -0,6653 | 0,4426 | 0,0845 | -0,6653 | 0,5621 | ||
12,1523 | -0,7023 | 0,4932 | -0,6653 | -0,7023 | 0,0014 | ||
11,4319 | 2,0781 | 4,3186 | -0,7023 | 2,0781 | 7,7305 | ||
12,9777 | 0,2723 | 0,0741 | 2,0781 | 0,2723 | 3,2610 | ||
12,7826 | -0,5226 | 0,2731 | 0,2723 | -0,5226 | 0,6319 | ||
12,0397 | -0,1497 | 0,0224 | -0,5226 | -0,1497 | 0,1391 | ||
11,7621 | 0,3679 | 0,1354 | -0,1497 | 0,3679 | 0,2680 | ||
å | -0,0075 | 40,8209 | 60,6662 | ||||
å /n | 11,5000 | -0,0004 |