.


:




:

































 

 

 

 


7.




. , , , , , . () .

() , (), () , .

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)                    




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