. R .
, 4 , (ryx4 = 0,58).
. , (x1) x3 (rx1x3) = 0,98.
rx1x2 = 0,85 rx3x2 = 0,88.
, , :
= 3,515 0,006 x1 + 15,542 x2 + 110 x3 + 4,475 4 - 2,932 x5. (53.22)
(-0,01) (0,72) (0,13) (2,90) (-0,95)
t (β j) = tj t - 0: β j = 0, j = 1, 2, 3, 4, 5. t = 1,76 t - α = 0,1 v = 14. , 4, | t4 | = 2,90 > t = 1,76. 1 x5, , (1) (x5) . , .
, (x1, 2 x3),
= 7,342 + 0,345 x1 + 3,294 x4. (53.23)
(11,12) (2,09) (3,02)
α = 0,05, F = 266 > F = 3,20, F - α = 0,05, v 1 = 3 v 2 = 17. β1 β4, |tj| > t = 2,11 ( α = 0,05, v = 17). β1 (β1 ≠ 0) ; t1 = 2,09 t = 2,11. α = 0, 1, t = 1,74 β1 .
, 100 0,345 / (b1 = 0,345).
1 = 0,068 4 = 0,161 ( j = ) , x1 4 1% 0,068% 0,161%.
r = 0,469 , 46,9% (x1 x4), .. . (2, x3, 5, .). = 10,5% , s2 = 1,97.
|
|
k k ( ). , , , k- . , , , , .
. ( << k).
.
k, ij. j - i - (i = 1, 2,..., n; j = 1, 2,.... k), s1,..., sk
:
(53.24)
(53.25)
j, l= 1, 2, .... k.
R, .. j = l,
(53.26)
aiv , .. v - j - ;
f iv v - i - (), v = 1, 2, ...,k.
(53.26)
(53.27)
f iv v - i - ();
aiv v - j - .
F k . F , .. fv = , a . ,
(53.28)
(53.28)
(53.29)
zj , , f1 - . z f1 , (53.26):
(53.29),
,
(53.30)
j = 1, 2,.,., k v = 1, 2,.... k.
, ajv zj fv, .. 1 ≤ ajv ≤ +1.
zj. (53.26)
v, v' = 1, 2,..., k.
(53.29),
|
|
(53.31)
, zj s = 1. , zj, (53.31), , k .
v - k
(53.32)
R . (53.27) (53.24),
(53.28),
(53.33)
R.
, R U,
(53.34)
R , .. , λ v > 0 v =1, 2,..., k.
Λ : λ 1 ≥ λ 2 ≥ ... ≥λ v... ≥ λ k ≥ 0. , λ v v - .
, , , k- , .
U v - , λ v - .
λ 1 ≥... ≥ λ v.... ≥λ k
(53.35)
Vv, λ v R, , (53.34):
(53.36)
Uv
U , U-1 = UT, , , R Λ , , (53.34),
,
, R k,
,
(53.37)
(53.38)
v -
Uv R, λ v.
v:
(53.39)
, Uv U Uv = 1. ,
(53.32), , λ v v - . (53.38) ,
(53.40)
(53.37), k. v - .
.
, 6070%.
, . f v j, |a jv | > 0,5.
i - (i = 1, 2,.... n) F.
, , . , . .
|
|
.
53.2 Y .
. 53.2 . (x1 x4). , .
, x1, 2, 3, 4, 5 (. 53.2).
53.2