, .
1) ?
2) ?
3) ?
4) ?
5) , .
6) ?
7) ?
8) ?
9) , .
2
.
: .
: , , .
- () :
1. ;
2. ;
3. ;
4. ( );
5. .
, (x 01, x 02, , x 0 ). (. 2.1). :
i = (x i - x oi) / ∆ x i (2.1)
i = 1, 2, , n; ∆xi i. i .
. 2.1.
:
y = b0 + b1 x 1 + b2 x 2 + + b x + b12 x 1 x 2 + b13 x 1 x 3+ +b 1, x 1 x + b11 x 21 +
+b22 x 22 + +b x 2 +
b0 = (0,, 0)
bi = / i; bij = 2 / i j; bij = ½ 2 / i 2 ..
. , . , . , , , , b b, , . , :
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y = b 0 + b 1 x 1 + b 2 x 2 + + b x + b 12 x 1 x 2 + b 13 x 1 x 3+ + b 1, x 1 x
, b .
, . , i (1) (+1). (-1) , (+1) . , () , .
2k, 2 , ; k , ; (.. ) N =2 k.
1 2 (. 2.1). (. 2.2) (. 2.1) . , . 0 =1 ( ) .
.
, , , .
(2-5 ) .
. 2.2. | 2.1.
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:
. . ,
. , - x 0, , ,
. , i - .
N ; i - ; j n .
. .
, . ( m=3) . 2.2.
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, .
2.2.
ỹ | Sy2 | G | |||||
y 11 | y 12 | Y1m | ỹ1 | S12 | |||
Y 21 | Y 22 | Y2m | ỹ2 | S22 | |||
Y 31 | Y 32 | Y3m | ỹ3 | S32 | |||
j | yj1 | yj2 | yjm | ỹj | sj2 | ||
N | yN1 | yN2 | yNm | ỹN | sN2 |
:
1. , , .
2. , .
3. , , ().
:
(2.2)
m- ; ỹ .
:
(2.3)
.
S , .. S (yij) .
S (ỹ) .
:
(2.4)
ij , , f:
f=m 1. (2.5)
, , .. . f=m.
yim , . - , . , 2.3.
, : , , . , , , , . , . , , t
(2.6)
t t - . , t . .
∆yij>y, .
y , , .
, , , f →∞ =σ2 (σ2 - ). 2- :
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, , =0,95 ( q=0,05).
0,95 =0,68, =0,997, =2(t) 1
(t) t , :
(2.7)
() , , .
rmax(P, m), 2.3. rmax r, :
(2.8)
(2.9)
2.3. r max (r min) 0,01 0,05
0,01 | 0,05 | 0,01 | 0,05 | 0,01 | 0,05 | |||
1,414 1,723 1,955 2,130 2,265 2,374 2,464 2,540 | 1,412 1,689 1,869 1,996 2,093 2,172 2,237 2,294 | 2,606 2,663 2,714 2,759 2,800 2,837 2,871 2,903 | 2,343 2,387 2,426 2,461 2,493 2,523 2,551 2,557 | 2,932 2,959 2,984 3,008 3,030 3,051 3,071 3,092 | 2,600 2,623 2,644 2,664 3,683 2,701 2,717 2,738 |
r>rmax, , ỹ , ∆ ij S2(yij) S2y. ỹ S2y, r <= rmax.
(2.9) , , .
, . :
1) yij , (y1), (ym);
2) , , ym, (2.10):
(2.10)
y1 (2.11):
; (2.11)
3) α m r.;
4) r>r, .
r , r r.
, 2 (2 ) , , r r :
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(2.12)
(2.13)
(2.14):
(2.14)
G , .4 ( 4) α =0,05 : f1=(m 1) - ; f2 = N - .
, Gp , G > Gp, , sy2 - .
, , .
, , (B-)
(2.15):
(2.15)
- ,
- =V/C
(2.16)
(2.17)
r 1 - , r . 2 k .
≤ χ2, χ2- , . χ2 (r 1) α=0,01; 0,025; 0,05; 0,1.
, F -. , .
(2.18)
, , , . . . Fp F, α =0,05 f (1)=(m-1) f(2) = N(m-1) ( 4). Fp< F, , sy2 - .
, .. , . , ij , .
( , ).
, . , .
1. 1 , (-1) (+1), .
2. 1, . 2.4.
3. ij, 3 .
4. .
5. .
6. .
. , . : 1 - , ; 2 - , /. : - , .
, , , , (. 2.4), . . (. 2.4).
2.4.
N | i | m | . . . ỹj | S2 | G | ||||||
X0 | X1, | X2, | X1X2 | ỹ1j | ỹ2j | ỹ3j | |||||
j | +1 | -1 | -1 | +1 | 0,511 | ||||||
j | +1 | +1 | -1 | -1 | |||||||
j | +1 | -1 | +1 | -1 | |||||||
j | +1 | +1 | +1 | +1 |
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ỹj 2.2 (m = 3)
Y11 = (43+35+48)/3 = 42,
Y12 = (90+86+94)/3 = 90
Y13 = (42+51+45)/3 = 46,
Y14 = (56+54+58)/3 = 56.
(2.4)
S2{y11}= [(4342)2 +(3542)2 + (4842)2]/2 = 43
S2{y12}= [(9090)2 +(8690)2 + (9490)2]/2 = 16
S2{y13}= [(4246)2 +(5146)2 + (4546)2]/2 = 21
S2{y14}= [(5656)2 +(5456)2 + (5856)2]/2 = 4
2.14.
Gp = 43/(43+16+21+4) = 0,511.
G , a f1 f2
f1= m 1; f2 = N.
f1 ( 1) ( ), f2 ( ) G.
a = 0,05; f1 =31=2; f2 =4, G =0,77; G>Gp, .. . , , s2 - .
(. . 5)