p n | 0,6 | 0,7 | 0,8 | 0,9 | 0,95 | 0,975 | 0,99 | 0,995 | 0,999 |
0,708 | 1,074 | 1,642 | 2,706 | 3,841 | 5,024 | 6,635 | 7,879 | 10,828 | |
1,833 | 2,408 | 3,219 | 4,605 | 5,991 | 7,378 | 9,210 | 10,597 | 13,816 | |
2,946 | 3,665 | 4,642 | 6,251 | 7,815 | 9,348 | 11,345 | 12,838 | 16,266 | |
4,045 | 4,878 | 5,989 | 7,779 | 9,488 | 11,143 | 13,277 | 14,860 | 18,467 | |
5,132 | 6,064 | 7,289 | 9,236 | 11,070 | 12,832 | 15,086 | 16,750 | 20,515 | |
6,211 | 7,231 | 8,558 | 10,645 | 12,592 | 14,449 | 16,812 | 18,548 | 22,458 | |
7,282 | 8,383 | 9,803 | 12,017 | 14,067 | 16,013 | 18,475 | 20,278 | 24,322 | |
8,351 | 9,524 | 11,030 | 13,362 | 15,507 | 17,535 | 20,090 | 21,955 | 26,125 | |
9,414 | 10,656 | 12,242 | 14,684 | 16,919 | 19,023 | 21,666 | 23,589 | 27,877 | |
10,473 | 11,781 | 13,422 | 15,987 | 18,307 | 20,483 | 23,209 | 25,188 | 29,588 | |
11,530 | 12,899 | 14,631 | 17,275 | 19,675 | 21,920 | 24,725 | 26,757 | 31,264 | |
12,584 | 14,011 | 15,812 | 18,549 | 21,026 | 23,336 | 26,217 | 28,300 | 32,909 | |
13,636 | 15,119 | 16,985 | 19,812 | 22,362 | 24,736 | 27,688 | 29,819 | 34,528 | |
14,685 | 16,222 | 18,151 | 21,064 | 23,685 | 26,119 | 29,141 | 31,319 | 36,123 | |
15,733 | 17,322 | 19,311 | 22,307 | 24,996 | 27,488 | 30,578 | 32,801 | 37,697 | |
16,780 | 18,418 | 20,465 | 23,542 | 26,296 | 28,845 | 32,000 | 34,267 | 39,252 | |
17,824 | 19,511 | 21,615 | 24,769 | 27,587 | 30,191 | 33,409 | 35,718 | 40,790 | |
18,868 | 20,601 | 22,760 | 25,989 | 28,869 | 31,526 | 34,805 | 37,156 | 42,312 | |
19,910 | 21,689 | 23,900 | 27,204 | 30,144 | 32,852 | 36,191 | 38,582 | 43,820 | |
20,951 | 22,775 | 25,038 | 28,412 | 31,410 | 34,170 | 37,566 | 39,997 | 45,315 | |
21,991 | 23,858 | 26,171 | 29,615 | 32,671 | 35,479 | 38,932 | 41,401 | 46,797 | |
23,031 | 24,939 | 27,301 | 30,813 | 33,924 | 36,781 | 40,289 | 42,796 | 48,268 | |
24,069 | 26,018 | 28,429 | 32,007 | 35,172 | 38,076 | 41,638 | 44,181 | 49,728 | |
25,106 | 27,096 | 29,553 | 33,196 | 36,415 | 39,364 | 42,980 | 45,558 | 51,179 | |
26,143 | 28,172 | 30,675 | 34,382 | 37,652 | 40,646 | 44,314 | 46,928 | 52,620 | |
27,179 | 29,246 | 31,795 | 35,563 | 38,885 | 41,923 | 45,642 | 48,290 | 54,052 | |
28,214 | 30,319 | 32,912 | 36,741 | 40,113 | 43,194 | 46,963 | 49,645 | 55,476 | |
29,249 | 31,391 | 34,027 | 37,916 | 41,337 | 44,461 | 48,278 | 50,993 | 56,892 | |
30,283 | 32,461 | 35,139 | 39,087 | 42,557 | 45,722 | 49,588 | 52,336 | 58,301 | |
31,316 | 33,530 | 36,250 | 40,256 | 43,773 | 46,979 | 50,892 | 53,672 | 59,703 | |
33,331 | 35,665 | 38,466 | 42,585 | 46,194 | 49,480 | 53,486 | 56,328 | 62,487 | |
35,444 | 37,795 | 40,676 | 44,903 | 48,602 | 51,966 | 56,061 | 58,964 | 65,247 | |
37,505 | 39,922 | 42,879 | 47,212 | 50,998 | 54,437 | 58,619 | 61,581 | 67,985 | |
39,564 | 42,045 | 45,076 | 49,513 | 53,384 | 56,895 | 61,162 | 64,181 | 70,703 | |
41,622 | 44,165 | 47,269 | 51,805 | 55,758 | 59,342 | 63,691 | 66,766 | 73,402 | |
46,761 | 49,452 | 52,729 | 57,505 | 61,659 | 65,410 | 69,957 | 73,166 | 80,077 | |
51,892 | 54,723 | 58,164 | 63,167 | 67,505 | 71,420 | 76,154 | 79,490 | 86,661 | |
62,135 | 65,226 | 68,972 | 74,397 | 79,082 | 83,298 | 88,298 | 91,952 | 99,607 | |
72,358 | 75,689 | 79,715 | 85,527 | 90,531 | 95,023 | 100,42 | 104,21 | 112,32 | |
82,566 | 86,120 | 90,405 | 96,578 | 101,88 | 106,63 | 112,33 | 116,32 | 124,84 | |
92,761 | 96,524 | 101,05 | 107,56 | 113,14 | 118,14 | 124,12 | 128,30 | 137,21 | |
102,95 | 106,91 | 111,67 | 118,50 | 124,34 | 129,56 | 135,81 | 140,17 | 149,45 |
Таблица 3
Квантили порядка р F -распределения с n 1 и n 2степенями свободы
p = 0,9
n 1 | ¥ | ||||||||||||||||||
n 2 | |||||||||||||||||||
39,86 | 49,50 | 53,59 | 55,83 | 57,24 | 58,20 | 58,91 | 59,44 | 59,86 | 60,19 | 60,71 | 61,22 | 61,74 | 62,00 | 62,26 | 62,53 | 62,79 | 63,06 | 63,33 | |
8,53 | 9,00 | 9,16 | 9,24 | 9,29 | 9,33 | 9,35 | 9,37 | 9,38 | 9,39 | 9,41 | 9,42 | 9,44 | 9,45 | 9,46 | 9,47 | 9,47 | 9,48 | 9,49 | |
5,54 | 5,46 | 5,39 | 5,34 | 5,31 | 5,28 | 5,27 | 5,25 | 5,24 | 5,23 | 5,22 | 5,70 | 5,18 | 5,18 | 5,17 | 5,16 | 5,15 | 5,14 | 5,13 | |
4,54 | 4,32 | 4,19 | 4,11 | 4,05 | 4,01 | 3,98 | 3,95 | 3,94 | 3,92 | 3,90 | 3,87 | 3,84 | 3,83 | 3,82 | 3,80 | 3,79 | 3,78 | 3,76 | |
4,06 | 3,78 | 3,62 | 3,52 | 3,45 | 3,40 | 3,37 | 3,34 | 3,32 | 3,30 | 3,27 | 3,24 | 3,21 | 3,19 | 3,17 | 3,16 | 3,14 | 3,12 | 3,10 | |
3,78 | 3,46 | 3,29 | 3,18 | 3,11 | 3,05 | 3,01 | 2,98 | 2,96 | 2,94 | 2,90 | 2,87 | 2,84 | 2,82 | 2,80 | 2,78 | 2,76 | 2,74 | 2,72 | |
3,59 | 3,26 | 3,07 | 2,96 | 2,88 | 2,83 | 2,78 | 2,75 | 2,72 | 2,70 | 2,67 | 2,63 | 2,59 | 2,58 | 2,56 | 2,54 | 2,51 | 2,49 | 2,47 | |
3,46 | 3,11 | 2,92 | 2,81 | 2,73 | 2,67 | 2,62 | 2,59 | 2,56 | 2,54 | 2,50 | 2,46 | 2,42 | 2,40 | 2,38 | 2,36 | 2,34 | 2,32 | 2,29 | |
3,36 | 3,01 | 2,81 | 2,69 | 2,61 | 2,55 | 2,51 | 2,47 | 2,44 | 2,42 | 2,38 | 2,34 | 2,30 | 2,28 | 2,25 | 2,23 | 2,21 | 2,18 | 2,16 | |
3,29 | 2,92 | 2,73 | 2,61 | 2,52 | 2,46 | 2,41 | 2,38 | 2,35 | 2,32 | 2,28 | 2,24 | 2,20 | 2,18 | 2,16 | 2,13 | 2,11 | 2,08 | 2,06 | |
3,23 | 2,86 | 2,66 | 2,54 | 2,45 | 2,39 | 2,34 | 2,30 | 2,27 | 2,25 | 2,21 | 2,17 | 2,12 | 2,10 | 2,08 | 2,05 | 2,03 | 2,00 | 1,97 | |
2,04 | 2,01 | 1,99 | 1,96 | 1,93 | |||||||||||||||
1,98 | 1,96 | ||||||||||||||||||
1,96 | |||||||||||||||||||
1,97 | |||||||||||||||||||
1,99 | |||||||||||||||||||
1,98 | |||||||||||||||||||
2,99 | 1,98 | 1,96 | |||||||||||||||||
2,97 | 1,96 | 1,94 | |||||||||||||||||
2,96 | 2,57 | 2,36 | 2,23 | 2,14 | 2,08 | 2,02 | 1,98 | 1,95 | 1,92 | 1,87 | 1,83 | 1,78 | 1,75 | 1,72 | 1,69 | 1,66 | 1,62 | 1,59 | |
2,01 | |||||||||||||||||||
1,99 | |||||||||||||||||||
1,99 | |||||||||||||||||||
1,98 | |||||||||||||||||||
2,84 | 2,44 | 2,23 | 2,09 | 2,00 | 1,93 | 1,87 | 1,83 | 1,79 | 1,76 | 1,71 | 1,66 | 1,61 | 1,57 | 1,54 | 1,51 | 1,47 | 1,42 | 1,38 | |
2,39 | 2,18 | 2,04 | 1,95 | 1,87 | 1,82 | 1,77 | 1,74 | 1,71 | 1,66 | 1,60 | 1,54 | 1,51 | 1,48 | 1,44 | 1,40 | 1,35 | 1,29 | ||
2,35 | 2,13 | 1,99 | 1,90 | 1,82 | 1,77 | 1,72 | 1,68 | 1,65 | 1,60 | 1,55 | 1,48 | 1,45 | 1,41 | 1,37 | 1,32 | 1,26 | 1,19 | ||
¥ | 2,71 | 2,30 | 2,08 | 1,94 | 1,85 | 1,77 | 1,72 | 1,67 | 1,63 | 1,60 | 1,55 | 1,49 | 1,42 | 1,38 | 1,34 | 1,30 | 1,24 | 1,17 | 1,00 |
Продолжение таблицы 3
p = 0,95
n 1 | ¥ | ||||||||||||||||||
n 2 | |||||||||||||||||||
161,4 | 199,5 | 215,7 | 224,6 | 230,2 | 234,0 | 236,8 | 238,9 | 240,5 | 241,9 | 243,9 | 245,9 | 248,0 | 249,1 | 250,1 | 251,1 | 252,2 | 253,3 | 254,3 | |
18,51 | 19,00 | 19,16 | 19,25 | 19,30 | 19,33 | 19,35 | 19,37 | 19,38 | 19,40 | 19,41 | 19,43 | 19,45 | 19,45 | 19,46 | 19,47 | 19,48 | 19,49 | 19,56 | |
10,13 | 9,55 | 9,28 | 9,12 | 9,01 | 8,94 | 8,89 | 8,85 | 8,91 | 8,79 | 8,74 | 8,70 | 8,66 | 8,64 | 8,62 | 8,59 | 8,57 | 8,55 | 8,53 | |
7,71 | 6,94 | 6,59 | 6,39 | 6,26 | 6,16 | 6,09 | 6,04 | 6,00 | 5,96 | 5,91 | 5,86 | 5,80 | 5,77 | 5,75 | 5,72 | 5,69 | 5,66 | 5,63 | |
6,61 | 5,79 | 5,41 | 5,19 | 5,05 | 4,95 | 4,88 | 4,82 | 4,77 | 4,74 | 4,68 | 4,62 | 4,56 | 4,53 | 4,50 | 4,46 | 4,43 | 4,40 | 4,36 | |
5,99 | 5,14 | 4,76 | 4,53 | 4,39 | 4,28 | 4,21 | 4,15 | 4,10 | 4,06 | 4,00 | 3,94 | 3,87 | 3,84 | 3,81 | 3,77 | 3,74 | 3,70 | 3,67 | |
5,59 | 4,74 | 4,35 | 4,12 | 3,97 | 3,87 | 3,79 | 3,73 | 3,68 | 3,64 | 3,57 | 3,51 | 3,44 | 3,41 | 3,38 | 3,34 | 3,30 | 3,27 | 3,23 | |
5,32 | 4,46 | 4,07 | 3,84 | 3,69 | 3,58 | 3,50 | 3,44 | 3,39 | 3,35 | 3,28 | 3,22 | 3,15 | 3,12 | 3,08 | 3,04 | 3,01 | 2,97 | 2,93 | |
5,12 | 4,26 | 3,86 | 3,63 | 3,48 | 3,37 | 3,29 | 3,23 | 3,18 | 3,14 | 3,07 | 3,01 | 2,94 | 2,90 | 2,86 | 2,83 | 2,79 | 2,75 | 2,71 | |
4,96 | 4,10 | 3,71 | 3,48 | 3,33 | 3,22 | 3,14 | 3,07 | 3,02 | 2,98 | 2,91 | 2,85 | 2,77 | 2,74 | 2,70 | 2,66 | 2,62 | 2,58 | 2,54 | |
4,84 | 3,98 | 3,59 | 3,36 | 3,20 | 3,09 | 3,01 | 2,95 | 2,90 | 2,85 | 2,79 | 2,72 | 2,65 | 2,61 | 2,57 | 2,53 | 2,49 | 2,45 | 2,40 | |
3,00 | 2,91 | ||||||||||||||||||
2,92 | |||||||||||||||||||
2,96 | |||||||||||||||||||
2,96 | 1,96 | ||||||||||||||||||
1,97 | |||||||||||||||||||
1,98 | |||||||||||||||||||
1,99 | 1,95 | ||||||||||||||||||
4,32 | 3,47 | 3,07 | 2,84 | 2,68 | 2,57 | 2,49 | 2,42 | 2,37 | 2,32 | 2,25 | 2,18 | 2,10 | 2,05 | 2,01 | 1,96 | 1,92 | 1,87 | 1,81 | |
1,98 | |||||||||||||||||||
1,98 | |||||||||||||||||||
2,99 | |||||||||||||||||||
1,99 | |||||||||||||||||||
4,08 | 3,23 | 2,84 | 2,61 | 2,45 | 2,34 | 2,25 | 2,18 | 2,12 | 2,08 | 2,00 | 1,92 | 1,84 | 1,79 | 1,74 | 1,69 | 1,64 | 1,58 | 1,51 | |
4,00 | 3,15 | 2,76 | 2,53 | 2,37 | 2,25 | 2,17 | 2,10 | 2,04 | 1,99 | 1,92 | 1,84 | 1,75 | 1,70 | 1,65 | 1,59 | 1,53 | 1,47 | 1,39 | |
3,92 | 3,07 | 2,68 | 2,45 | 2,29 | 2,17 | 2,09 | 2,02 | 1,96 | 1,91 | 1,83 | 1,75 | 1,66 | 1,61 | 1,55 | 1,50 | 1,43 | 1,35 | 1,25 | |
¥ | 3,84 | 3,00 | 2,60 | 2,37 | 2,21 | 2,10 | 2,01 | 1,94 | 1,88 | 1,83 | 1,75 | 1,67 | 1,57 | 1,52 | 1,46 | 1,39 | 1,32 | 1,22 | 1,00 |
Продолжение таблицы 3
p = 0,99
n 1 | ¥ | ||||||||||||||||||
n 2 | |||||||||||||||||||
98,50 | 99,00 | 99,17 | 99,25 | 99,30 | 99,33 | 99,36 | 99,37 | 99,39 | 99,40 | 99,42 | 99,43 | 99,45 | 99,46 | 99,47 | 99,47 | 99,48 | 99,48 | 99,50 | |
34,12 | 30,82 | 29,46 | 28,71 | 28,24 | 27,91 | 27,67 | 27,49 | 27,35 | 27,23 | 27,05 | 26,87 | 26,69 | 26,60 | 26,50 | 26,41 | 26,32 | 26,22 | 26,13 | |
21,20 | 18,00 | 16,69 | 15,98 | 15,52 | 15,21 | 14,98 | 14,80 | 14,66 | 14,55 | 14,37 | 14,20 | 14,02 | 13,93 | 13,84 | 13,75 | 13,65 | 13,56 | 13,46 | |
16,26 | 13,27 | 12,06 | 11,39 | 10,97 | 10,67 | 10,46 | 10,29 | 10,16 | 10,05 | 9,89 | 9,72 | 9,55 | 9,47 | 9,38 | 9,29 | 9,20 | 9,11 | 9,02 | |
13,75 | 10,92 | 9,78 | 9,15 | 8,75 | 8,47 | 8,26 | 8,10 | 7,98 | 7,87 | 7,72 | 7,56 | 7,40 | 7,31 | 7,23 | 7,14 | 7,06 | 6,97 | 6,88 | |
12,25 | 9,55 | 8,45 | 7,85 | 7,46 | 7,19 | 6,99 | 6,84 | 6,72 | 6,62 | 6,47 | 6,31 | 6,16 | 6,07 | 5,99 | 5,81 | 5,82 | 5,74 | 5,65 | |
11,26 | 8,65 | 7,59 | 7,01 | 6,63 | 6,37 | 6,18 | 6,03 | 5,91 | 5,81 | 5,67 | 5,52 | 5,36 | 5,28 | 5,20 | 5,12 | 5,03 | 4,95 | 4,86 | |
10,56 | 8,02 | 6,99 | 6,42 | 6,06 | 5,80 | 5,61 | 5,47 | 5,35 | 5,26 | 5,11 | 4,96 | 4,81 | 4,73 | 4,65 | 4,57 | 4,48 | 4,40 | 4,31 | |
10,04 | 7,56 | 6,55 | 5,99 | 5,64 | 5,39 | 5,20 | 5,06 | 4,94 | 4,85 | 4,71 | 4,56 | 4,41 | 4,33 | 4,25 | 4,17 | 4,08 | 4,00 | 3,91 | |
9,65 | 7,21 | 6,22 | 5,67 | 5,32 | 5,07 | 4,89 | 4,74 | 4,63 | 4,54 | 4,40 | 4,25 | 4,10 | 4,02 | 3,94 | 3,86 | 3,78 | 3,69 | 3,60 | |
9,33 | 6,93 | 5,95 | 5,41 | 5,06 | 4,82 | 4,64 | 4,16 | 4,01 | 3,86 | 3,78 | |||||||||
9,07 | 5,21 | 4,86 | 3,96 | 3,82 | |||||||||||||||
8,86 | 5,04 | 3,94 | |||||||||||||||||
4,89 | 3,89 | 2,96 | 2,87 | ||||||||||||||||
3,89 | 2,93 | ||||||||||||||||||
3,93 | 2,92 | ||||||||||||||||||
2,92 | |||||||||||||||||||
5,93 | 3,94 | 2,92 | |||||||||||||||||
5,85 | 4,94 | 3,87 | 2,94 | 2,86 | |||||||||||||||
8,02 | 5,78 | 4,87 | 4,37 | 4,04 | 3,81 | 3,64 | 3,51 | 3,40 | 3,31 | 3,17 | 3,03 | 2,88 | 2,80 | 2,72 | 2, 64 | 2,55 | 2,46 | 2,36 | |
7,93 | 3,99 | 2,98 | |||||||||||||||||
2,99 | |||||||||||||||||||
2,98 | |||||||||||||||||||
7,31 | 5,18 | 4,31 | 3,83 | 3,51 | 3.29 | 3,12 | 2,99 | 2,89 | 2,80 | 2,66 | 2,52 | 2,37 | 2,29 | 2,20 | 2,11 | 2,02 | 1,92 | 1,80 | |
7,08 | 4,98 | 4,13 | 3,65 | 3,34 | 3,12 | 2,95 | 2,82 | 2,72 | 2,63 | 2,50 | 2,35 | 2,20 | 2,12 | 2,03 | 1,94 | 1,84 | 1,73 | 1,60 | |
6,85 | 4,79 | 3,95 | 3,48 | 3,17 | 2,96 | 2,79 | 2,66 | 2,56 | 2,47 | 2,34 | 2,19 | 2,03 | 1,95 | 1,86 | 1,76 | 1,66 | 1,53 | 1,38 | |
¥ | 6,63 | 4,61 | 3,78 | 3,32 | 3,02 | 2,80 | 2,64 | 2,51 | 2,41 | 2,32 | 2,18 | 2,04 | 1,88 | 1,79 | 1,70 | 1,59 | 1,47 | 1,32 | 1,00 |
Таблица 4
Критические точки dн и dв
Распределения Дарбина – Уотсона
( n – объем выборки, m – число объясняющих переменных модели)
Уровень значимости a = 0, 05
n | m = 1 | m = 2 | m = 3 | m = 4 | ||||
dн | dв | dн | dв | dн | dв | dн | dв | |
0,610 | 1,400 | |||||||
0,467 | 1,896 | |||||||
0,368 | 2,287 | |||||||
0,296 | 2,388 | |||||||
0,376 | 2,414 | |||||||
0,927 | 1,324 | 0,658 | 1,604 | 0,595 | 1,928 | 0,444 | 2,283 | |
0,971 | ||||||||
1,010 | ||||||||
1,977 | ||||||||
1,015 | ||||||||
1,221 | 1,420 | 1,125 | 1,538 | 1,026 | 1,669 | 0,927 | 1,812 | |
1,363 | 1,496 | 1,297 | 1,570 | 1,229 | 1,650 | 1,160 | 1,735 | |
1,475 | 1,566 | 1,430 | 1,615 | 1,383 | 1,666 | 1,336 | 1,720 | |
Продолжение таблицы 4
Уровень значимости a = 0, 01
n | m = 1 | m = 2 | m = 3 | m = 4 | ||||
dн | dв | dн | dв | dн | dв | dн | dв | |
0,390 | 1,142 | |||||||
1,036 | 0,294 | 1,676 | ||||||
1,003 | 0,229 | 2,102 | ||||||
0,998 | 1,873 | 0,183 | 2,433 | |||||
1,001 | 1,733 | 0,230 | 2,193 | |||||
0,633 | 1,010 | 0,319 | 1,297 | 0,396 | 1,640 | 0,286 | 2,030 | |
1,913 | ||||||||
0,973 | 1,161 | 0,890 | 1,277 | 0,803 | 0,803 | 0,718 | 1,334 | |
0,997 | ||||||||
1,018 | ||||||||
1,001 | ||||||||
1,006 | 1,006 | |||||||
1,147 | 1,273 | 1,083 | 1,343 | 1,023 | 1,023 | 0,960 | 1,310 | |
1,012 | ||||||||
1,288 | 1,376 | 1,243 | 1,423 | 1,201 | 1,201 | 1,136 | 1,328 | |