. , , , , , . () .
() , (), () , .
2 : (), .
x y , x y, x y . . , , (S = a2). (), . . , [38] (y) (x), , 5%, y = 0,05. , 8.
, , () . , , , , , ( ) , . , .. ( ) , , , , ( ) ( , , ; .), .
, , , , , . [39]. [40].
|
|
[41] , , . .
, -. , () ( ). , y - x, , 2 (x1, x2, , xm) [42].
x y . , .. () x () y. .
:
1) () ;
2) ( ) ( );
3) , ( ).
- (.. ).
- . 2006 33.
33.
, .. | , .. | |
27,068 | 172,17 | |
29,889 | 200,90 | |
34,444 | 231,83 | |
33,158 | 232,10 | |
37,755 | 233,40 | |
37,554 | 236,99 | |
37,299 | 246,53 | |
40,370 | 253,62 | |
37,909 | 256,43 | |
38,348 | 261,89 | |
39,137 | 259,36 | |
46,298 | 278,87 |
x . . , y . .
x | y |
27,068 | 172,17 |
29,889 | 200,90 |
33,158 | 232,10 |
34,444 | 231,83 |
37,299 | 246,53 |
37,554 | 236,99 |
37,755 | 233,40 |
37,909 | 256,43 |
38,348 | 261,89 |
39,137 | 259,36 |
40,370 | 253,62 |
46,298 | 278,87 |
.
1. ( x y n ). ( ) () .
|
|
6 x y, 5 , .
2. . , n x y , x y. (. 21), , , (. 22).
. 21. . 22.
, x y. (.22) , .
3. () , (x y) . () (), (+ ). , () (). , .. :
. (106)
, , = 1, . , = 1( ). å=å, = 0. , , 0 1. , = 1, .
(10):
; .
34 . 10, 2, () (106):
=
34.
/ | x | y | x | y |
27,068 | 172,17 | |||
29,889 | 200,90 | |||
33,158 | 232,10 | |||
34,444 | 231,83 | |||
37,299 | 246,53 | + | + | |
37,554 | 236,99 | + | ||
37,755 | 233,40 | + | ||
37,909 | 256,43 | + | + | |
38,348 | 261,89 | + | + | |
39,137 | 259,36 | + | + | |
40,370 | 253,62 | + | + | |
46,298 | 278,87 | + | + | |
439,229 | 2864,09 |
x y, , , , , .
4. x y. , [43] x () (). x y.
|
|
, , t:
.
r x :
, (107) . (108)
(108), n, , x y :
(109)
, , . , :
. (110)
[44] , :
, (111) , (112)
, (113) . (114)
1 +1, . , , r (111) , , (r< 0) . , r= 0, , r= 1 . , r 0 1 . ( ) , 35.
35.
| r | | |
0,1 | |
0,1 ÷ 0,3 | |
0,3 ÷ 0,5 | |
0,5 ÷ 0,7 | |
0,7 | () |
, , , . r 0 , , .
r 36.
36.
/ | x | y | tx | ty | tx ty | xy | |||
27,068 | 172,17 | 90,905 | 4422,804 | -1,993 | -2,408 | 4,799 | 634,078 | 4660,298 | |
29,889 | 200,90 | 45,070 | 1426,888 | -1,403 | -1,368 | 1,919 | 253,594 | 6004,700 | |
33,158 | 232,10 | 11,864 | 43,220 | -0,720 | -0,238 | 0,171 | 22,644 | 7695,972 | |
34,444 | 231,83 | 4,659 | 46,843 | -0,451 | -0,248 | 0,112 | 14,773 | 7985,153 | |
37,299 | 246,53 | 0,485 | 61,714 | 0,146 | 0,284 | 0,041 | 5,472 | 9195,322 | |
37,554 | 236,99 | 0,906 | 2,836 | 0,199 | -0,061 | -0,012 | -1,603 | 8899,922 | |
37,755 | 233,40 | 1,328 | 27,817 | 0,241 | -0,191 | -0,046 | -6,079 | 8812,017 | |
37,909 | 256,43 | 1,707 | 315,270 | 0,273 | 0,643 | 0,176 | 23,199 | 9721,005 | |
38,348 | 261,89 | 3,047 | 538,975 | 0,365 | 0,841 | 0,307 | 40,525 | 10042,958 | |
39,137 | 259,36 | 6,424 | 427,904 | 0,530 | 0,749 | 0,397 | 52,430 | 10150,572 | |
40,37 | 253,62 | 14,195 | 223,378 | 0,788 | 0,541 | 0,426 | 56,310 | 10238,639 | |
46,298 | 278,87 | 94,004 | 1615,705 | 2,027 | 1,455 | 2,950 | 389,722 | 12911,123 | |
439,229 | 2864,09 | 274,594 | 9153,353 | 11,241 | 1485,066 | 106317,681 |
: = = 4,784; = = 27,618.
|
|
(107): r = 11,241/12 = 0,937.
(108):
r = 1485,066/(12*4,784*27,618) = 0,937
(111):
r = (106317,681/12 36,602*238,674) / (4,784*27,618) = 0,937,
, ( ).
(). , , , x y, . , , . , () r , , , σr. () r r : .
σr ( ) n.
1. (n >30), σr (115):
. (115)
, >3, r (), . , () r = (), t , (. 17).
2. (n <30), σr (116):
, (116)
r t- , (117) c t.
. (117)
t t - (. 9) α=1-β ν=n2. t> t , r , . (t< t) , , r, , .
, , () (116) (117):
= 0,349/3,162 = 0,110;
= 0,937/0,110 = 8,482.
9 , ν = 12 2 = 10 ( 10- ) β = 95% ( α =1 β = 0,05) t= 2,2281, 99% (α =0,01) t= 3,169, , t > t, r = 0,937 .
5. [45] () . , , , , , .. . , .
. . (: , ) , .. = f(x).
, , . ; . , .
, 28 ( t x). , , ( ), .
( 28), . , .
|
|
. (). : , , ..
.
, , a0, a1 .. . 6 Ļ, , (95) , t x:
(118)
(118) a0, [46]:
. (119)
(119) (118), n, :
. (120)
3 , :
. (121)
a1 , a1:
. (122)
a1 , y x .
37.
37.
/ | x | y | x 2 | xy | |||
27,068 | 172,17 | 732,677 | 4660,298 | 187,124 | 223,612 | 2657,453 | |
29,889 | 200,90 | 893,352 | 6004,700 | 202,377 | 2,181 | 1317,497 | |
33,158 | 232,10 | 1099,453 | 7695,972 | 220,052 | 145,147 | 346,774 | |
34,444 | 231,83 | 1186,389 | 7985,153 | 227,006 | 23,274 | 136,153 | |
37,299 | 246,53 | 1391,215 | 9195,322 | 242,443 | 16,706 | 14,202 | |
37,554 | 236,99 | 1410,303 | 8899,922 | 243,821 | 46,669 | 26,495 | |
37,755 | 233,40 | 1425,440 | 8812,017 | 244,908 | 132,441 | 38,864 | |
37,909 | 256,43 | 1437,092 | 9721,005 | 245,741 | 114,256 | 49,940 | |
38,348 | 261,89 | 1470,569 | 10042,958 | 248,115 | 189,761 | 89,122 | |
39,137 | 259,36 | 1531,705 | 10150,572 | 252,381 | 48,710 | 187,871 | |
40,370 | 253,62 | 1629,737 | 10238,639 | 259,048 | 29,459 | 415,076 | |
46,298 | 278,87 | 2143,505 | 12911,123 | 291,100 | 149,580 | 2748,498 | |
439,229 | 2864,09 | 16351,437 | 106317,681 | 2864,115 | 1121,795 | 8027,945 |
(122): = 5,407.
(119): a0 = 238,674 5,407*36,602 = 40,767.
: =40,767+5,407x, x (2- 37), (6- 37)[47]. ( 6).
.6.
6 , , , .
, () . () a1 a2 (123) (124) :
, (123) , (124) . (125)
. t:
, (126)
(n >30) ai , >3.
(n <30), ai t - ν = n -2 α ( 9). (126) , .
(125): = 9,669.
a0 (123): = 3,06.
a1 (124): =0,639.
(126) a0: =13,3.
a1: =8,46.
, α=0,05 10- 9 tα =2,23, 13,3 8,46, .
, , 8. , (97) [48]:
F = 71,56 F = 4,96, 8 ν1 = k 1 = 2 1 = 1 ν2 = n k = 12 2 = 10 (.. 1- 10- ) α=0,05, , .
6. , y x 1%. :
, (127)
y x.
, .. x. , :
. (128)
, ( = 40,767 + 5,407x), (128): .
x, . , , x = 40 = 0,84, x = 50 = 0,87 .. , x 40 40,4 .. (.. 1%), 0,84% ; x 50 50,5 .. (.. 1%) y 0,87% ..
. , .. . , , , . .
: x y , .. x = f(t) y = f(t), x y , , .
, , () , x y. , x, y. , .. () . , , .
, () t, yt, () yt-1. , (111) yt yt-1, :
, (129)
, [49] :
, (130) . (131)
() , y1 = yn ( ).
(130) (131)[50] . .
, n α : (130) (131) , . , . , 10.
(130), 38.
38.
xt | xt-1 | xt xt-1 | xt 2 | yt | yt-1 | yt yt-1 | yt 2 | |
27,068 | 46,298 | 1253,194 | 732,677 | 172,170 | 278,870 | 48013,048 | 29642,509 | |
29,889 | 27,068 | 809,035 | 893,352 | 200,900 | 172,170 | 34588,953 | 40360,810 | |
34,444 | 29,889 | 1029,497 | 1186,389 | 231,830 | 200,900 | 46574,647 | 53745,149 | |
33,158 | 34,444 | 1142,094 | 1099,453 | 232,100 | 231,830 | 53807,743 | 53870,410 | |
37,755 | 33,158 | 1251,880 | 1425,440 | 233,400 | 232,100 | 54172,140 | 54475,560 | |
37,554 | 37,755 | 1417,851 | 1410,303 | 236,990 | 233,400 | 55313,466 | 56164,260 | |
37,299 | 37,554 | 1400,727 | 1391,215 | 246,530 | 236,990 | 58425,145 | 60777,041 | |
40,370 | 37,299 | 1505,761 | 1629,737 | 253,620 | 246,530 | 62524,939 | 64323,104 | |
37,909 | 40,370 | 1530,386 | 1437,092 | 256,430 | 253,620 | 65035,777 | 65756,345 | |
38,348 | 37,909 | 1453,734 | 1470,569 | 261,890 | 256,430 | 67156,453 | 68586,372 | |
39,137 | 38,348 | 1500,826 | 1531,705 | 259,360 | 261,890 | 67923,790 | 67267,610 | |
46,298 | 39,137 | 1811,965 | 2143,505 | 278,870 | 259,360 | 72327,723 | 77768,477 | |
439,229 | 439,229 | 16106,951 | 16351,437 | 2864,090 | 2864,090 | 685863,823 | 692737,647 |
(130) x: ra = = 0,111.
(130) y: ra = = 0,249.
10 () n = 12 α = 0,05. 0,348. , , , x y.
. ( ) , . . . (.. )[51], (.. [52], : ). (, ), , . dx dy. :
. (132)
6 39 x y 6- .
39.
x ( 6) | ||||||||||
y ( 6) |