.
, B1 B2 , .
:
, B1 B2 , .
.
2 2 . 12, 12. , .
:
21-11. - 2 . 6. .
, 22, 4 : 2 : 21-11 22-11; 2 : 12-11 22-21.
1, 6, 4.
.
1. , 1;
2. , .
, . 1 , 12 21 , 11, , 22 .
(. 2).
3. , .
.
.
4. .
5. . .
6. .
.
.
, , , . , , +1, 1, 0.
, >
Xj +/-1;
- ;
- ;
Ij ;
j .
:
1. , ;
|
|
2. , .
( 10%), ( 30%) (>30%) .
2 .
, , .
22, 4 .
, , - . .
22.
X1 | X2 | y | ||
-1 | -1 | y1 | (1) | |
+ 1 | -1 | y2 | a | |
-1 | +1 | y3 | b | |
+1 | +1 | y4 | ab |
, .
1 . , .
22.
. , =1, .
22 23, , , .
3, , , .
.
, , :
X1 | X2 | X3 | y | |
-1 | -1 | +1 | y1 | |
+1 | -1 | +1 | y2 | |
-1 | +1 | -1 | y3 | |
+1 | +1 | +1 | y4 | |
-1 | -1 | -1 | y5 | |
+1 | -1 | -1 | y6 | |
-1 | +1 | -1 | y7 | |
+1 | +1 | -1 | y8 |
X3, ( 22) , > 1 , .
X1 | X2 | X3 | X4 | |
-1 | -1 | +1 | y1 | |
+1 | -1 | -1 | y2 | |
-1 | +1 | -1 | y3 | |
+1 | +1 | +1 | y4 | |
-1 | -1 | -1 | y5 | |
+1 | -1 | +1 | y6 | |
-1 | +1 | +1 | y7 | |
+1 | +1 | -1 | y8 |
x1*x2 x3. , y .
2k.
, , . , , .
|
|
1. , - =0.
j ;
i ;
N .
2. = .
3. - = 0.
j≠u
4. , , .
.
. y=b0+b1x1+b2x2, b0,b1,b2.
, b0,b1,b2, , . , , , Ѳ=ß0+ ß1x1+ ß 2x2, , Ѳ; ß; ß1;ß 2 .
X1 | X2 | y | |
-1 | -1 | y1 | |
+1 | -1 | y2 | |
-1 | +1 | y3 | |
+1 | +1 | y4 |
b1, X1.
, b0 :
, , .
, . , , , .
22 :
X1 | X2 | X1 X2 | y | |
-1 | -1 | +1 | y1 | |
+1 | -1 | -1 | y2 | |
-1 | +1 | -1 | y3 | |
+1 | +1 | -1 | y4 |
y=b0+b1x1+b2x2+b12x1x2
b12= (+1)y1+(-1)y2+(-1)y3+(-1)y4
.
y1 | y1+ y2 | (y1+ y2)+(y3+ y4) |
y2 | y3+ y4 | (y2- y1)+(y4- y3) |
y3 | y2- y1 | (y3+ y4)-(y1+ y2) |
y4 | y4- y3 | (y4- y3)-(y2- y1) |
- .
1 (2 ) ( ).
2 (3 ) , . , 3 , .
:
:
X1 | X2 | X1 X2 | y | |
-1 | -1 | +1 | ||
+1 | -1 | -1 | ||
-1 | +1 | -1 | ||
+1 | +1 | +1 |
b0= 95+90+85+82 =88
b1= -95+90-85+82 =-2
b2= -95-90+85+82 =-4,5
b12= 95-90-85+82 =0,5
:
Ckm= k!
m!(K-m)!
K
m
24 =
C164= 16! = 16*15*14*13*12! = 43680 =1820
4!(16-4)! 4*3*2*12! 24
.
, .
.
|
|
22:
X1 | X2 | X1 X2 | y | |
-1 | -1 | +1 | y1 | |
+1 | -1 | -1 | y2 | |
-1 | +1 | -1 | y3 | |
+1 | +1 | -1 | y4 |
:
y=b0+b1x1+b2x2+b12x1x2
4 . , , x1*x2 , b0; b1; b2. , b12 ->0();
- (x1x2) x3, b1; b2; b3 :
b1=ß1+ß23;
b2=ß2+ß13;
b3=ß3+ß12.
, , . , , , .
, .
.
- , , . .
.
2 , 23, 8 .
3 , .
, , , .
X1 | X2 | X1 X2 | y | |
-1 | -1 | +1 | y1 | |
+1 | -1 | +1 | y2 | |
-1 | +1 | +1 | y3 | |
+1 | +1 | +1 | y4 | |
-1 | -1 | -1 | y5 | |
+1 | -1 | -1 | y6 | |
-1 | +1 | -1 | y7 | |
+1 | +1 | -1 | y7 |
X3, 22 . 1 , , :
b1=ß1+ß23;
b2=ß2+ß13;
b3=ß3+ß12.
, , .
, , , , :
b1͌ ß1;
b2 ͌ ß2;
b3͌ß3.
.
.
4 3 23, , X3=-X1*x2, 23.
:
b1=ß1-ß23;
b2=ß2-ß13;
b3=ß3-ß12.
, 23, 2 23.
8 4 , . 24, 5 25.
m , , :
2k-m,
k- ;
m .
½ 23 | 23-1 | |||
½ 24 | 24-1 | |||
½ 25 | 25-2 | |||
½ 26 | 26-3 |
.
|
|
, .
, 23-1, 2 :
X3 +X12
X3 = +X1X2
X3 -X12
X3 = -X1 X2
.
I X3=X1X2 | I X3=-X1X2 | ||||||||
X1 | X2 | X3 | X1 X2 X3 | X1 | X2 | X3 | X1 X2 X3 | ||
+ | + | + | + | + | + | - | + | ||
- | - | + | + | - | - | - | - | ||
+ | - | - | + | + | - | + | - | ||
- | + | - | + | + | + | + | + |
X3, :
X32=X3X1X2 => 1=X3X1X2
X32=-X3X1X2 => 1=-X3X1X2
X3 , .
, , .
1=X1X2X3
X1
X1=X12X2X3 (X12=1); X1=X2X3
X2=X1X22X3; X2=X1X3
X3=X1X2X32; X3=X1X2
, :
b1=ß1-ß23;
b2=ß2-ß13;
b3=ß3-ß12.
b1, b2, b3 .
1 X1X2X3:
1=- X1X2X3
X1=-X12X2X3; X1=-X2X3
X2=-X1X22X3; X2=-X1X3
X3=-X1X2X32; X3=-X1X2
b1=ß1-ß23;
b2=ß2-ß13;
b3=ß3-ß12.
.
, , , , , , , . :
1.
a) ;
b) ;
c) ;
d) ;
e) ;
f) .
2.
a) , ;
b) , ;
c) ;
d) , .
3.
a) ;
b) ;
c) ;
d) || .
4. .
yi.
, , .
, 2 t .
.
t= | y 1 - y 2 |.
S√(1/n1+1/n2)
y1;y2 1 2 ;
S ( 1 2 );
n1;n2 1 2 .
2 .
, , ().
:
y1=40%; y2=42,1%; S=1; n1=n2=2; t=2,1.
:
υ=n1+n2-2
n1;n2 ;
- 2, 2 .
t2, υ=n1+n2-2
( )
=t0,05,2=2,92
t υ=2 5% =2,92.
, , t, , 2,95 =0,05, t , .
=1-L=0,95 , 2 .
.
|y- y | ≥t
S
, |t| .
: , 400,2 4 39,9; 39,8; 39,82; 39,84.
|
|
1 , 1 :
y= 39,82+39,84+39,8 =39,82
S2=1/(n-1)∑(yi-y)2
.
|39,9-39,82| =4
0,02
T 2,92
t >t , 1 .
.
.
:
S2{y}= ∑N1∑n1(yiq-yi)2
N(n-1)
N ( );
q 1,2,,n
, .
, , ∑ , .
.
.
F
, , , , , .
:
S12=4,8; Ϡ1=6
S22=0,8; Ϡ2=5
F=4,8/0,8=6
q=0,05 , F0,05;5;6=4,4
F>F=>
.
, >2 .
, .
.
G= Smax2.
∑i=1N Si
, .
.
, .
y=f(x)
().
, , , ., .
n , y Xi.
8 :
X | 1,5 | 4,0 | 5,0 | 8,5 | 12,5 | |||
y | 5,0 | 4,5 | 6,5 | 9,5 |
, , oy . ( ) :
y=b0+b1x
y=b0+b1z2
z2*x 2 1.
, , b0 b1 , :
U = ∑Ni=1=[yi-(b0+b1xi)]min (1)
, () , X=1,5 X=12,5 y X.
(1) b0 b1 0.
U , :
.
(2) , Ѳ - :
x | y | x 2 | xy | |
1,5 | 2,25 | 7,5 | ||
4,5 | ||||
6,5 | 45,5 | |||
8,5 | 9,5 | 72,25 | 80,75 | |
12,5 | 156,25 | 112,5 | ||
∑ | 59,5 | 61,5 | 541,75 | 510,25 |
:
y=3,7+0,5x.
() .
b0 , .
b1 .