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i = 1, 2, ..., k). .
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1. :
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2.5.
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21
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L (L 2) [2].
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2.2.
1) 4 4,15 4 4,03 9 0,001
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3) 5 4,83 5 4,93 10 0,080
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5) 5 4,86 5 4,55 3 0,500
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7)}.
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= 4,15. = 0,87
(4,83 4,15 = 0,68 4,15 3,28 = 0,87).
= (3,285 + 4,159 + 4,8310)/(5 + 9 + 10) = 4.25.
V = {(2,88; 5) (3,09; 8) (4,03; 9) (4,55; 3)
(4,83; 7) (4,93; 10)}; N = 42; = 4,03. = 0,94
(4,55 4,03 = 0,52 4,03 3,09 = 0,94).
= (3,098 + 4,039 + 4,553)/(8 + 9 + 3) = 74,64/20 = 3,73.
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< i + k < m.
3.6. = '' m = || = 6; ''
3; '' 4.
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32
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a b.
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[14, . 260].
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1. = '12m' m
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2. V Y
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, (3.1).
V1 [17] (. 3.1.)
d() = 0, d() = 0 d() = 1,
,
.
-
33
, Y
(|| = |Y|) , .
(3.1) [7,
17, 19], d() = 1
V2 (. . 3.1.).
3.1. Vi .
d() [7, 17]
, V1 0 0 1
, V2 1 1 1
, V3 1 1 2
V3 (. . 3.1.) d() = 1,
d() = 1 d() = 2.
3.7. (3.1), 2 (. 3.2.),
= 'keiner' Y = 'meister' : V1 = 2; V2 = 3;
V3 = 5; = 'keiner' Z = 'klein': V1 = 0; V2 = 3; V3 = 3.
3.2. Vi*
k e i n e r k e i n e r
- -
- - - - - -
m e i s t e r
k l e i n
: C d() Vi C d() Vi V1 1 0 0 1 0 0 0 2 0 0 0 0 0 0 0 0 V2 1 0 0
1 1 0 0 3 0 1 0 0 0 1 1 3 V3 2 0 0 2 1 0 0 5 0 1 0 0 0 1 1 3
* : Vi , : (), () ().
-
34
3.2.2.
- ,
. .
Y (|| > 0; |Y| > 0) .
,
.
,
(. 3.3.),
Y ,
.
.
3.8. = 'keiner' Y = 'klein' (. .
3.3.) : 'k', 'e', 'i', 'n'; 'ke',
'ki', 'kn', 'ei', 'en', 'in'; 'kei', 'kin', 'ein' : 'kein'
[: L = L(, Y) = 'kein' |L| = 4].
,
: 'k', 'e', 'i', 'n'; 'ei', 'in'
: 'ein' [: L = L(, Y) = 'ein' |L| = 3].
3.8.1. Y = '' (|Y| = 5) = ''
(|| = 15) (. 3.1.).
: '', '', '';
'', '', '', '';
''. , :
'' 10 ; '' 4 , ''
; '' 6 .
3.2.3.
,
. ,
.
3.3. () = 'keiner'
Y = 'klein'.
k e i n e r
k l e i n
k e i n
-
35
, , ,
, .
, ,
( ) .
.
3.2.3.1.
- , . .
Y (|| > 0, |Y| > 0
|| > |Y|). V4
V2 (. (3.1) . 3.1.)
Y ,
() |Y| .
Y
(|| = |Y|) V2.
V4
Y
|Y| [20].
Y
|Y|, V2 Y
, |Y|.
Y
V2, . . ,
V2.
V4 .
3.9. Y 3.8.1.
( 11- ) V4 = V2('', '') = 2.
3.2.3.2.
, . .
Y (|| > 0, |Y| > 0
|| > |Y|).
, ()
-
36
,
.
3.9.1. 3.8.1. ''
10 ,
Y = '' = '' '' = 1.
:
() .
3.9.2. Y = '' = '' (.
3.1.) : '' '';
''. '', '' '' 3 ,
''. ''
= 2. . .
'': (), ().
, ,
Y : V5 = ||| |Y||.
3.10. Y = '' (|Y| = 5)
= '' (|| = 15; . 3.8.1.) V5 = ||5| |15|| = 10.
3.2.4.
, , .
,
.
ti i- xi
ti,j xi xj ti
ti,j, (, , , , , , . .),
, : 'x1t1t12x2t2t2,3...xm-1tm-1tm-1,mxmtm'. ti
m xi;
ti,j xi xj
m xi , . . = m2.
3.11. ,
{s, a}, , , :
'a5|30s10|10a40|7a20', , .
3.5. ,
. ,
-
37
(, ),
( ) .
3.2.4.1.
:
, .
, ,
[17 20]
(SPSS, STATISTICA, SAS [76] .).
) zi,j = m2 , -
xi xj. , ,
'x1t1t1,2x2t2t2,3 ...xmti,m'
'x1t1z1,2t1,2x2t2z2,3t2,3...xmtm'.
3.12. {s, a, b},
ti,j s, a b = 32 = 9.
9 c, d, e, f, g, h, l, p q,
sa, as, sb, bs, ab, ba, ss, aa bb.
'a5|30s10|10a40|7a20' 3.11. 'a5d30s10c10a40p7a20'.
) k,
.
3.2.4.2.
( ).
t ,
k + 1 :
t = {u0, u1, , uk}, u0 < u1 < < uk, (3.3)
ui (ui R1, i = 0, k ) .
( )
(k, t) k t
t, (ui-1, ui] (i = 1,k ) t
i, i = 0, k .
-
38
(ui-1, ui] (i = 1,k ) t
; t ,
(ui-1, ui] ,
(i 1) .
t :
(1);
(2); (3).
3.2.4.3.
. .
t
. {ui} ,
, . (3.3)
t = {ui}, i = 0, k , ui = Qi, (3.4)
ui , Q .
{ui} , (3.3) :
t = u0, {ui}, i = 1,k ; u0 = 0; ui = u1q(i-1)
; u1 > 0; q > 1, (3.5)
ui , q .
: (3.4) (3.5)
Q u1 q.
k (
(ui-1, ui]) t (3.4)
k = (t/Q), (3.6)
t x, t (3.5)
k = 0 0 t < u1 k = [lg(t/u1)/(lgq) + 1] t u1, (3.7)
[] .
3.13. .
, t ,
= 6 , .
.
(3.4) t = {0, 6, 12, 18 }
(. . u0 = 0 , u1 = 6 , u2 = 12 . .).
-
39
3.14. , x
t = 2 . t = 2 {0,
6} t, k = 0
.
3.15. , t = 7 .
{6, 12} t, k = 1
.
ki ki,j xi zi,j
: x iki
z ijkij
.
'x1k
1 z12k
12 x2k
2 z23k
23 x3k
3 xmk
m '. (3.8)
xi ( zi,j) ki = 0 ( ki,j = 0)
xi ( zi,j) .
, . 3.1.
ti ti,j ( )
ki ki,j ( ).
3.16. i xi
3.12. 10 , () xi
(3.4) ti = {0, 10, 20, 30 }.
'a5d30s10c10a40p7a20'
: 'a0d3s1c1a4p0a2', 'd3sca6', 'dddscaaaaa'.
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3.2.4.4.
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,
.
-
40
, . ,
[2, 8, 12, 13].
3.17. (. 3.13.).
. 20
. .
20 ,
.
N = 300 .
t 3 , = 1 .
3.2.4.5.
,
.
3.17. ,
(. . 2.1),
, t
( ).
t /. t / 2,
, ~ N(, ) (
). t / < 2,
( ), L = Lg; L ~ N(L, L) [2].
N ti { } 1N
i it
=
( i )
. ()
1
1
N
iit N t
==
(3.9)
( )0,5
2
1( /( 1))Nsi it t N
== , (3.10)
-
41
t s .
N ( N > 20) , s.
t / 2, (. ); t / < 2, ti
tLi = Lgti, L L
L (3.9) (3.10) ti
tLi, t t L s sL L .
u0
. u1 100(1 )
[100(1 )%
], = [2].
. (0):
t , . . 0: = 0.
(H1): t , . .
H1: > 0. ( )
0: = 0 z-:
z = (t t )/. (3.11)
z -
z, = , . . z < z,
0: = 0 : z > z 0: = 0
H1: > 0.
[2],
z.
( z ) :
( = 0,16 z = 1), ( = 0,023 z = 2) ( = 0,0014 z = 3).
, ( = 0,023
z = 2) u1
t > u1 = t + 2, (3.12)
u1 100(1 )
, 100 (1 )% = 99,86%.
u2 , 100 (1 )
2.
-
42
2 , 2 ~ N(2, 20,5)
u2 = 2 t + 220,5. , i-
ui = i t + 2i0,5. (3.13)
k
t, (3.13) i ,
i = (((2 + t t)0,5 )/ t )2 :
k = ((((2 + t t)0,5 )/ t )2). (3.14)
, , = 0 (
) (3.14) (3.6).
, t / < 2, (3.14) , t
tL , t t L L.
3.18. 3.15. (t = 7 ) 3.17. ( t = 3 , = 1 )
k .
(3.14) k = ((((12 +37)0,5 1)/3)2) = (1,51) = 1.
3.19. (. 3.13.).
, , ;
N = 1000 ti.
t = 1 ,
= 1 . t / < 2, ti
lgti, L L
1 (3.9), (3.10) (3.14) ti
tLi = Lgti, t t L L. tL= 0,12 L = 0,013
().
3.2.5.
, . .
(3.8)
Vi (. 3.2.1. 3.2.3.) V1,
V2, V3, V4
V5. ,
Vi , ,
, .
5 Vi
-
43
.
.
,
X Y (|X|, |Y| > 0 |X| |Y|)
X Y, , min((|X|, |Y|). :
V6 = min(|X|, |Y|) (3.15)
: V6 ,
.
3.20. 3.9.1.
Y = '' = '' '' = 1.
(3.15) Y V6 = min(15; 5) 1 = 4.
3.20.1. (3.15) Y
3.9.2. V6 = min(6; 2) 2 = 0.
V
Vi, (i = 1, 2, , 5)
V6 :
V = V ii i =6
1 , (3.16) V ; i
, :
=6
1i i = 1; 0 i 1; (i = 1, 2, , 6). (3.17)
(3.17) i,
.
i
.
i (,
.) Vi
(3.16).
i i % (. 2),
- = 0 % Vi;
+ = 100 %. j = j/ =6
1i ie ; j = 1, 2, , 6.
-
44
i 4-.
2- 5-
i,
,
(3.16).
V (3.16)
,
i (i = 1),
;
( 6-) V = Vi.
i
(. 3.3.).
(n 1) ,
-
n [51, . 269]. 1, 2, ,
n ,
(, n = 6)
(3.17).
(n = 2)
, 1,
, 1 = 1, 2 = 0
, 1 = 0,
2 = 1 (.3.3..);
(n = 3)
, 1,
, , . 3.3..; (n = 4)
,
1 (. 3.3. .).
) ;
1 = 2 = 0,5.
) ;
1 = 2 = 3 = 0,333.
) ;
1 = 2 = 3 = 4 = 0,25.
. 3.3.
i
(3.17) .
-
45
i
(3.16) .
3.3
.
,
.
.
,
(, ).
: (
), , - . [14, 25, 26].
||V(,Y)||, V(,Y) (3.16)
Y;
(3.17).
> 0 ,
, .
.
,
. , ,
. .
.
( ),
,
, . , ,
(
), .
. .
. (
, , )
. . : ,
, , ;
-
46
,
,
, , ,
,
) .
,
, , , .
-.
, , ,
. ,
. ,
- .
( - -,
, , .),
, .
ti (3.4) (3.5),
Qi u1i qi ( )
||V(,Y)||.
.
3.3.1.
, , , .
.
.
i (3.16)
.
.
,
.
-
47
,
, ,
. ,
,
.
, .
, ,
,
.
,
.
3.3.2.
, , ,
. .
.
.
: ti (3.4) (3.5);
di u1i qi, ; i
. ( = 1, 2,
3, ), .
,
. , ,
ti (3.4) (3.4) .
3.21. = 3.
,
12% (. 3.4..).
, 28 % (. 3.4..). -
-
48
. 3.4.. 12-
.
. 3.4.. 28-
.
( = 1, 2, 3, )
.
3.3.3.
, ,
. . .
( )
|Vi,j|, (i, j (1, 2, , L); i < j)
(3.16) .
,
. .
,
.
(, ) .
Wm,
mV i (i = 1, 2, , Nm)
m ,
Wm = arg(m
min (mV )); mV = iMVi,m/Nm, m(, b,); M (A, B,), (3.18)
m , b, ; Nm
xi m; Nm = L; M i -
A, B,
-
49
3.6. (3.16)
i j.
Vi,j = Vj,i, i, j j, i .
3.7. Wm
,
.
m ( )
xim, ,
.
sm
m:
sm = (iM (Vi,m)2/(Nm 1))
0,5; m ( , b, ); M (A, B, ); (3.19)
m Vi,j
:
m = m (Vi,j); (i, j ; i < j); m( , b, ); M (A, B, ).
(3.20)
(3.16)
() ,
. . [2, 8, 14].
3.3.4.
,
. .
- .
;
Wm ,
xim ,
. Wm xim
.
,
, ,
,
. .
-
50
.
, 3.4.
,
. , ,
, ,
, , ,
, ,
.
3.3.5.
-:
: !
,
, :
, ,
, .
, ,
,
.
,
,
(
). ,
,
.
V1,
V2, V3 V5.
V4 () V6 (3.17)
V (
-
51
4 () 6 1, i
0).
(.) = f(.)/|| (. 3.26.1.).
.
(3.5) (
[2]: -
, ,
).
3.21.1.
. ('',
'' . .)
.
,
.
(3.8): '23' '3112'.
.
q (3.5), q = 3 u1 = 1 .
(3.3) = (0; 1; 3; 9; 27; 81; ); (, ).
k , : k = (0, 1, 2, 3,
4, ). k :
(k) = [0(0)1(1)3(2)9(3)27(4)81 ],
. : '12' '43'.
3.4.
,
. .
( , . .)
(, .)
.
-
52
3.4.1.
,
. . .
(. . 3.2.). ,
( )
,
.
.
3.22.
( )
.
(. 3.1.)
(. . 3.2.)
.
,
(. 3.5.).
.
,
.
. 3.5. 279-
: 1, 2 154 125
; , . 3.2.
-
53
3.4.2. -
, . .
- [ (1, 2, 3)]. ,
,
( = 1), ( = 2),
( = 3) . .
- . ,
,
,
. .
( = 3) ( = 2).
,
(, ,
. .). 5 (. 5.4. 5.5.).
3.4.3.
, .
, ,
.
.
,
.
.
(
) .
[25, . 3, . 336]
. ,
. ,
(,
-
54
StatSoft Statistica v.6.0,
, 9090 ). .
1) (, )
(, ).
( ).
; ; .
.
2) .
.
; ;
. .
3) ( > 3)
, . 2),
,
.
1
, , . .
3.8. , . 3),
[25, 26] (
).
. , ,
,
. ,
( > 3)
, , .
, i
[i (1, 2, , L), L ],
|Vi,j|, (i, j (1, 2, , L); i < j) (3.21)
(3.16) .
-
55
RK-1, K
K (2, 3, ).
A B
( = 2). Si (. 3.6.)
i, i (1, 2, , L)
R1 ( S)
:
1) (3.18)
Wa Wb A B
;
2) (3.16)
Va,b Wa Wb A B;
3) S Sa = 0, Sb = Va,b;
4) R2 (. . 3.6.),
Va,b, Va,i Vi,b [Va,i Vi,b
(i (1, 2, , L)] Wa Wb );
5) Si S
Si = [(Va,b )2
+ (Va,i)2 (Vi,b)
2]/(2Va,b); (3.22)
6) S Si i, i (1, 2, , L) (. . 3.6.).
3.23. : Va,b = 52; Va,i = 36; Vi,b = 48. (3.22) Si = 16.
A, ( = 3). Si i, i
[i (1, 2, , L)] :
1) (3.18) Wa, Wb W A, B
.
2) (3.16) Va,b Wa Wb A
B, Va, Wa W A , V,b W Wb B.
3) S Sa = 0, Sb = Va,b. ,
Va, Va,b, Va, V,b (. 3.7.).
( ) S .
a = 0 = Va,.
. 3.6. i
S: S ; ;
b- b S;
Si i, S.
-
56
4)
R3 c
S, Q,
Va,b, Va, V,b
Vi,a, Vi,b Vi, (Vi,a, Vi,b Vi,
,
i (1, 2, , L) Wa, Wb W
).
S
Va,b Va,
. (Si i),
S
(3.22)
i = [(Va, )2
+ (Va,i)2 (Vi,)
2]/(2Va,). (3.23)
5) S
Si i i,
i (1, 2, , L), S0
(. .
3.7.).
0S (. 3.8.)
0
0 0S
S0. Si i
i, i (1, 2, , L)
0S
Si = Si + i[(Va,b)2
+ (Va,)2
(Vb,)2]/(2Va,bVa,); (3.24)
i = 2i [ab(ab Va,b)(ab Va,)(ab
Vb,)]0,5
/(Va,bVa,), (3.25)
ab = (Va,b + Va, + Vb,)/2
. 3.7. xi, S0 ( ):
S ; Q ; , b, , b, S0; (Si i)
xi, S0.
. 3.8. xi, S0 (
): S ; ; , b,
, b, S0; (Si i) xi, S0; Si i i S0; .
-
57
b.
3.24. : Va,b = 52; Va, = 76; Vb, = 66; Va,i = 53; Vi, = 67; Vi,b
= 62.
(3.22) (3.23): Si = (522 + 53
2 62
2)/252 = 16;
i = 27: (3.24) (3.25):
SI = 16 + 27[522
+ 762
66
2]/(25276) = 30;
ab = (52 + 76 + 66)/2 = 97; i = 227[97452131]0,5
/(5276) = 23.
A, , , D, ... ( > 3).
,
, = 3 ,
,
, R2.
, , = 4 A, ,
D. 4
, A,
; A, D; , D; A, D.
3.25. . 3.9.
,
(1- 2-)
. 3.5.
(, . 3.2.
!).
3.5.
, . .
-
(. 3.10.) ( ),
, ,
(SPSS, STATISTICA, SAS [76] .)
( ), . A
xi
ti xi ti,j
. 3.9.
(.
3.24): 1, 2, 3 .
-
58
xi xj; ( )
: it t Li
i Li; (3.16)
; ; ti
(3.4) (3.5), Qi u1i qi, ,
||V(,Y)|| .
. 3.10. -
:
+ ; - ;
;
, [
ti (3.4) (3.5), Qi u1i qi ,
||V(,Y)|| ;
];
W ?;
X ?;
Y (3.8);
Z ;
:
,
( )
, ;
( , ,
, );
.
, ( )
Z
-
59
( + 1) .
- (. . 3.10.)
; . ,
;
,
. .
Z
.
i (i = 1, 2, , 6)
(3.16) , 1,
6 i.
i, , , 0,05, m
. m i: i =
(m i). i
(, = 3% ),
i- i = 1 ( ).
i, m,
.
.
3.26.
Keiner zu klein, ein Meister zu sein ( :
).
V3 (.
3.7.).
( SPSS [76], . 3.4.). C
(. 3.11.) .
. 3.4.
1 2 3 4 5 6
1 3 4 7 9 >9
V3 0 1 3 4 7 9
V3 1 2 1 3 2 -
6 5 4 3 2 1
-
60
(. 3.12): 1) meister;
2) zu, zu; 3) sein, ein, klein, keiner.
3 ||V3(i,j)||
V3 (. 3.5) (2.18) (2.19)
Wm = ein; = 1 (2.20) m = 3.
3.6.
; , .
,
, ,
.
,
.
.
.
. 3.5. ||V3 (i,j)|| 3- .
keiner klein ein sein *
keiner 0 3 3 4 10 3,33
klein 3 0 2 3 8 2,67
ein 3 2 0 1 6 2 1 3
sein 4 3 1 0 8 2,67
* .
. 3.12.
.
-
61
3.26.1. Wi (i = 1, 2, ...,
I), I . = 'keiner'
:
,
: W1 = 5 ;
|| : W2 = || = 6;
,
f(.) (.) = f(.)/|| : 'k':
W3 = fk = 1; W4 = k = fk/|| = 1/6 0,17; 'e': W5 = fe = 2; W6 = e
= fe/|| = 2/6 0,33 .
. W7 W12; 'ke': W13 = fke = 1;
W14 = ke = fke/|| = 1/6 0,17 . . . 3.31.
3.26.2. () (.
3.1.); Y = ''
:
,
Y: W1 = 2 ;
|Y| Y: W2 = |Y| = 4 ;
Y:
'': W3 = f = 2; W4 = = f/|Y| = 2/4 = 0,5;
'': W5 = f = 2; W6 = = f/|Y| = 0,5;
'': W7 = f = 1; W8 = = f/|Y| = 0,25; '':
W9 = f = 1; W10 = = f/|Y| = 0,25; '': W11 = f = 1; W12 =
= f/|Y| = 0,25;
'': W13 = f = 1; W14 = = f/|Y| = 0,25;
'': W15 = f = 1; W16 = = f/|Y| = 0,25.
Wi
.
3.26.3. () ;
= ''
:
,
: W1 = 2 ;
|| : W2 = || = 36;
:
'': W3 = f = 29; W4 = = f/|| = 29/36 0,81; '': W5 = f = 7;
-
62
W6 = = f/|| = 7/36 0,19; '': W(.) = f = 7;
W(.) = = f/|| = 7/36 0,19; '': W(.) = f = 6;
W(.) = = f/|| = 6/36 0,17 . .
3.26.2. 3.26.3. Y : |Y| = 4 || =
36; : V5 = ||| |Y|| = 32.
'' = 1. Y [.
(3.15)] V6 = min(|X|, |Y|) = min(36; 4) 1 = 3.
V4 = V2('', '') = 1.
,
. ,
f(.) (.)
-, - .
3.6.1.
! .
N- N
x1, x2, ..., xN. xaxb ...xs
[a, b, , s (1, , N)] : fi xi
[i (1, , N)], fij 2 xixj [i, j (1, , N)],
fijk - 3 xixjxk [i, j, k (1, , N)], fijk
- xixjxk [i, j, k, (1, , N)] . .,
[ (1, 2, )].
:
= 1v
i= Ni, m, (3.26)
m .
3.27. {a}, N = 1;
= 3. = 3, : fa, faa faaa.
3.28. {a; }, N = 2; = 3.
= N1 + N2 + N3 = 2 + 4 + 8 = 14, ( f): (, ),
[(, ), (, )], [(, ), (, )], [(, ), (, )].
.
3.29. {a, , }, N = 3; = 3.
= N1 + N2 + N3 = 3 + 9 + 27 = 39, ( f): (, , ), [(, , ),
-
63
(, , ), (, , )], [(, , ), (, , ), (, , )], [(, , ), (,
, ), (, , )], [(, , ), (, , ), (, , )].
3.30. aas,
{s,a}, N = 2, = 3.
= 14- : fa = 2; fs = 1; fas = 1; fsa = 0; faa = 1; fss = 0; fasa
= 0; fsaa = 0; faaa = 0;
fssa = 0; fass = 0; fsas = 0; faas = 1; fsss = 0.
, f .
fi fij (1, 2) fijk = 3,
> 3. -
N :
,
.
.
3.6.2.
. .
f -
,
. ,
, 3.31.
3.6.3.
? , . .
FJ (J -
) m
, . . F mJ , ,
: F 1J F2
J F3
J
F 1MJ F MJ .
3.31. Keiner
zu klein, ein Meister zu sein.
. : 1 keiner, 2 zu, 3 klein, 4
ein, 5 meister, 6 zu, 7 sein.
-
64
1. fj .
, N = 11 ; = {k, e, i, n, r, z, u, l, m, s, t}; ;
j , j (1, 2, , n); n
(n = 7).
1.1. keiner k
fj [ = k; j (1, , 7)] k
: fk1 = 1; fk2 = 0; fk3 = 1; f k4 = 0; fk5 = 0; fk6 = 0; fk7
=
0, , fkj = (1, 0, 1, 0, 0, 0, 0).
1.2. e
fj [ = e; j (1, , 7)] e: fej = (2, 0, 1, 1, 2, 0, 1).
1.3. fij = (1, 0, 1, 1, 1, 0, 1).
1.4. fnj = (1, 0, 1, 1, 0, 0, 1).
1.5. keiner
e, ,
(. . 1.2).
1.6. frj = (1, 0, 0, 0, 1, 0, 0).
1.7. zu z
fj [ = z; j (1, , 7)] z: fzj = (0, 1, 0, 0, 0, 1, 0).
1.8. fuj = (0, 1, 0, 0, 0, 1, 0).
fj ,
.
2. fgj
( ) g; , g .
2.1. keiner
ke fgj [ = k; g = e; j
(1, , 7)] ke : fkej = (1, 0, 0, 0, 0, 0, 0).
2.2.
ei fgj [ = e; g = i; j (1, , 7)]
ei : feij = (1, 0, 1, 1, 1, 0, 1).
2.3. finj = (1, 0, 1, 1, 0, 0, 1).
. klein
ei (. . 2.2), ,
( . 2.2).
-
65
fgj
, .
3. fgpj
( ) gp; , g, p .
3.1. keiner kei
fgpj kei
[0 = k; g = e; p = i; j (1, , 7)]: fkeij = (1, 0, 0, 0, 0, 0,
0).
fgpj
, .
4. F ( ): F = 1n
j= fj.
4.1. F = 1n
j= fj, ( = k) k
: Fk = 7
1
n
j
== fkj = 1 + 0 + 1 + 0 + 0 + 0 + 0 = 2.
Fe = 7; Fi = 5 . .
4.2. Fg fgj 2
g (, g ): Fg = 7
1
n
j
== fgj: Fke =
7
1
n
j
== fkej = 1; Fei = 5; Fin = 4 . .
.
4.3. Fgp fgpj 3
gp (, g, p ): Fgp = 7
1
n
j
== fgpj: Fkei =
7
1
n
j
== fkeij = 1 . . .
. keiner zu klein,
ein meister zu sein : 11 ; 7;
: 7, 2; 2-
7- ; 29.
: e 7; i 5; n 4; s 2; k 2; r 2; u 2; t 1; l 1; z 2; m 1.
:
2:
1. ei 5; 2. in 4; 3. er 2; 4. ke 1; 5. ne 1; 6. zu 2; 7. kl 1;
8. le 1; 9. me
1; 10. is 1; 11. st 1; 12. te 1; 13. se 1;
3:
1. ein 4; 2. kei 1; 3. ine 1; 4. ner 1; 5. kle 1; 6. lei 1; 7.
mei 1; 8. eis 1;
9. ist 1; 10. ste 1; 11. ter 1; 12. sei 1;
-
66
4:
1. kein 1; 2. eine 1; 3. iner 1; 4. klei 1; 5. lein 1; 6. meis
1; 7. eist 1; 8.
iste 1; 9. ster 1; 10. sein 1;
5:
1. keine 1; 2. einer 1; 3. klein 1; 4. meist 1; 5. eiste 1; 6.
ister 1;
6:
1. keiner 1; 2. meiste 1; 3. eister 1;
7:
1. meister 1;
- 8 : .
3.7.
,
, .
,
, ,
.
.
[25, . 2],
.
.
,
.
,
,
, .
,
,
, .
.
,
[25, . 2].
-
67
4.
, ,
. . .
, . [4],
() (. 4.1.).
[2], -
,
,
,
. Xi (i
= 1, 2, , n) Zi (i = 1, 2, , m), Xi (i = 1, 2, , k)
, Xi (i = k + 1, k + 2, , n) .
Zi (i = 1, 2, , m) .
. 4.1.
(): Xi (i = 1, 2, , n) ;
Xi (i = 1, 2, , k) ; Xi (i = k + 1, k + 2, , n)
; Zi (i = 1, 2, , m) ; W
(); Y ( ).
Y, . Y
, W (,
, ).
Xi, Zi, W Y , ,
, (, , , . .)
(, , . .).
-
68
4.1.
10 : ,
, .
:
Y = 1(1, 2, , n, Z1, , Zm) + W, (4.1)
1() ( ) .
.
. ,
1(, 1, 2, , n, Z1, , Zm) = (, 1, 2, , n) + 2(Z1, , Zm),
(4.2)
() (
), 2(Z1, , Zm) () ,
2(Z1, , Zm) + W = ,
{} = 0 Y = (D{})0,5
( {}
D{} ).
.
() , Zi
Y. , ()
: .
, 2()
[5, 6].
:
Y = (, 1, 2, , n) + (4.3)
(), () ,
~ N(0, Y) , Y .
Xi (i = 1,n )
Y .
()
, ,
, , , ,
, [2, 3, 6, 7, 31].
-
69
.
N <
().
{XijYj}, N XijYj, (i = 1,n ; j = N 1, )
, ,
.
().
: N
( ) [5]. N
, . N
, ,
.
.
(, , ,
.). N
.
XijYj .
XijYj
Y, .
.
() (4.3)
{k}n
k = 1 () = 0 + n
k = 1 kk,
Y = 0 + n
k = 1 kk + , (4.4)
{k}n
k = 1 , , ().
, , ,
( - ,
), . .
{k}n
k = 1
,
.
-
70
.
, ,
,
.
[8, . 23].
.
,
,
.
4.1. ,
,
,
.
,
. , -,
,
, -, .
, , -,
[14, 69] , -,
. ,
, .
4.1. , ,
99 , ,
, , 100 .
(199 + 1001)/100 = 1,99 , , .
, ,
. (100
) .
.
()
, .
-
71
, ,
, .
[8].
1953 . . .
,
,
[76]. . . [91, . 206]:
,
.
,
.
. ,
(,
[87]). ,
, ,
. .
0. [47,
. 223], , ,
. , -, .
, -1 +2
0,05 0,04 0,07. -,
,
, . , -
, N
, .
,
, [. (4.13), (4.14)].
()
[2, 10].
, ,
.
-
72
, ,
, .
, ,
, .
, ,
, ,
[8].
4.2.
100:1.
[32, . 173; 33, . 64],
, ,
.
, , , , . .
, :
,
.
. , ,
,
. ,
, .
k (4.3) .
.
-
73
4.3.
, .
{ij} ( )1, ; 1,i N j M= = ,
i (N ) j (M ).
,
i, ib (a b; a, b 1, 2, , ),
[25].
:
[2], ,
() .
, ,
25 (. 4.2.). 13, 68 1113
,
4, 5, 9, 10, 14, 1518, 2123 19, 20, 24 25
, ,
. (
) i ib
( , .),
[2, . 592].
( . 4.2. = 4).
. ij
,
.
4.2. 3
, = t: (15 < t < 25) ,
= (25 15)/0,1 = 100.
(, ),
(. 4.2.) [2].
-
74
. 4.2. 25-
: X-, Y-.
4.3.
: ( :
0 1), ( ),
( , :
1, 2, 3 . .), ( ),
( -100% +100%
).
. 4.2. . . 5.5. 5.6.
-
75
4.4.
, , . .
k Y (4.4)
[2, 3, 6, 8, 9].
, () = n
k = 1 kk
Xk (
), .
, , .
,
Xk ,
Zi (. 4.1.).
,
, ,
.
, , ,
, , .
[2, 6, 9, 34].
4.4.1.
, .
.
.
i pi = 2 {i, i}.
i ,
, i (0, 1).
() (4.4) i
ii.
i
{i, i, i, }, ji {1, 2, , pi} pi > 2.
. i pi
-
76
i1, i2, , ij , iip
X , 0 1
: ij = 1, i = j ij = 0, i j.
() (4.4) ij
ip
j=1 ijij, ij .
ij ip
j=1ij = 1, , , pi
(4.4) (
).
. ? [34, . 2] ij,
.
[2, 10, 22],
.
(4.4) ip
j=1 ijij ,
:
pi 1, ij !
n i
i ij, ,
. , n + pi, , pi
ij .
.
4.4.2.
, .
fJ (. 3.6).
fi, fij, fijk . ., , fi, fij, fijk . .
.
. ,
( ), ,
.
,
.
-
77
. fJ
, h ; h 1. .
, h, . h
5 20. , ,
.
.
fJ YJ
rYJ YJ Y fJ ,
.
H1YJ: YJ 0 (
YJ ),
fJ .
( 0, 1, , 100)% [2], , = 30%
[2] k = (1 0,01)4,3
= 0,2. fJ ,
, YJ < k ( ,
YJ rYJ k),
fJ.
. fJ
.
fJ fJ,
.
4.5.
, . . .
. : ,
, , .
.
4.4. [29]
:
(Y1), (Y2),
(Y3), (Y4), (Y5), (Y6),
(Y7), (Y8) (Y9).
-
78
Yi [i (1, 2, , 9)]
[2] 100% +100%,
( Y- = 100%) ( Y+ = 100%) .
Y :
Y = 9 9
i i ii=1 i=1Yq / q ; Yi, Y (Y-, Y+); qi ( q-, q+), (4.5)
qi , i- Yi; q- = 0%
, q+ = 100% .
qi
[2]. (, ,
, .).
qi, , . , (%): q1 = 80,
q2 = 30, q3 = 40, q4 = 30, q5 = 20, q6 = 20, q7 = 30, q8 = 50,
q9 = 70.
Y
.
, , ,
( ), .
4.5.1.
, . .
,
, , ,
. ,
Yi iY
.
, ,
. ,
.
( 95 99%)
( , , 95%).
( 1 5%)
. ( )
, Yi
().
-
79
Yi - [37, . 101]
().
. [2] .
(q = 1) ( R2
Y ) ;
0; N -
Yi. , Yi
i
Y , , :
q = 2, ( q )
:
( ) 1/0 01 (1 ) , 1q q
k kq = (4.6)
. , , q = 3
. ., (0 < N f, f ).
, . ,
, , .
4.5.2.
. ! .
[50] ,
. . , ,
,
. ,
, . ,
,
.
(, ) .
, - . ,
, ,
[25, 35] , ,
.
,
() [35 . 192; 36, . 37].
( ) W,
-
80
(
).
W,
.
,
,
.
4.5.3.
, .
Y .
Y [2].
(), .
,
. , (4.5)
20% Yi, Y
. Yi
. ( ),
. ,
Y (4.5) 8 Yi,
Yi iY
, .
4.6.
.
, .
. , n = 2,
X1 X2, ,
E
-
81
E = {X 1 X1 X 1
+ }{X 2 X2 X 2
+ }, (4.7)
X i X i
+ i- ,
. , - Xk (4.4)
E .
,
, , ().
, n = 2 X1 X2,
, E ,
. E
(4.7), , , E.
, ,
E
[9, 25]. .
E [2, 15].
iX , Si ( 1,i k= ) rij,
1 i < j k. X i X i
+ i-
,
:
X i = { } { }min maxij i ij
j jX X X< < = X i
+ , 1, , 1,j N i k = (4.8)
(1 )
( ) ( )/ 2 / 2; ; 1, ,i i i i i ik kX X Z S X X Z S i k += = + =
(4.9)
X i X i
+
i R; Z/(2k) /(2k)
[2, 9, 25].
, (1 ) = 0,94 k = 3 Z/ = Z0,01 = 2,6.
E
i j [2, 15]:
( ) ( ) sign / , 1ij i ij i j j jX X r S X X S i j k = + < ,
(4.10)
-
82
( ( )sign /ij i jr S S )
i j j i;
sign(rij) : sign(rij) = -1 rij < 0; sign(rij) = 1 rij >
0.
, sign(rij) = 0 rij , . .
|rij| < r/2, r/2
[2, 15].
,
(4.10). ,
, ,
(4.10):
( ) max ;ij ij ij inn
X X X X = % ( ) max ; 1,ij ij in ij
nX X X X n N
+ = + =% . (4.11)
(1 ).
, :
( ) ( ) ( ) ( )
2 2
/ 2 / 2 1 ; X 1ij ij i ij ij ij i ijk kX X Z S r X Z S r
+= = + . (4.12)
(4.11) (4.12) ijX% , ijX
ijX+% , ijX
+ (1 i < j k),
i,
i j. . 5.
4.7.
, : .
,
[25, . 2, . 251].
.
, , (4.3) (n = 2)
Xi Xj. H0ij: ij = 0
rij
H1ij: |ij| > 0.
ij .
[2], H0ij
ij ,
-
83
(. . 4.5.). ,
% (
. 7.2. . 7.1.), - < < +; - = 0%
; + = 100% .
H1ij,
( )3,4
01,01 ek = [ = 100(1 0,233
k )]; (4.13)
H0ij,
( )3,4
01,0 ek = ( = 1000,233
k ). (4.14)
,
ij < , (4.15)
H0ij H1ij, ij ,
H0ij .
, = 50%,
(
[2]) = (0,0150)4,3 0,05.
.
H0ij
, , 10% 20%, , . 7.1.,
(4.14), = 0,14,3 510-5
= 0,24,3
0,001.
rij
Xi Xj N
. , rij = 0,2 N = 500, = 20%
= 10-5
[2].
n Xi, , ,
rij = n(n 1)/2 ,
[2, 9], ij H0ij: ij = 0
rij
:
1ij = 1 (1 ij); = n(n 1)/2, (4.16)
1ij .
H0ij
rij
-
84
1
m , max(rij)
:
1mij = 1 [1 min ( ij)] (4.17)
. 1mij ,
0ij, 1mij < , 0ij
,
(4.16) 1ij.
4.5. n = 4 min ij = 10-4. = n(n 1)/2 = 6 1
m = 1 (1
10-4
)6 = 610-4 [. .
1
m = 6 , min( ij)].
4.8.
, .
()
0
2OY 2
BY [2, 12, 13, 25, 34, 35, 3941],
:
0: 2
OY = 2
BY 1: 2
OY > 2
BY , (4.18)
1 .
, ,
, , ,
. 2BY
.
.
, ,
R2
Y
J = S 2 /S2
OY , S2
, S 2OY , [31].
-
85
4.8.1.
. .
[2, 21, 28] S 2BY
2BY .
(4.18) .
2BY .
[16] :
Y = f(b, ), (4.19)
Y ; b ; n-
. S 2OY 2
OY .
S 21
2BY . S2
OY S2
1
.
(4.19) ,
,
. ,
, .
S 21 . i j
, :
( ) 1 x , xn
i j ijr ir jr KrD x x L
== , (4.20)
[ ]
( ) rxx
ijr xfDji
= /xb,max;
;
i, xj ; xr r- ; ,
( 2B = Const).
LK , (4.20)
i xj:
H0: f(, xi) = f(, xj) H1: f(, xi) f(, xj). (4.21)
[9] (4.19) f(b, )
f(, )
-
86
( ) ( )2 TYf x f xC , 2
Y ; ;
f(x) , f(, x) = Tf(x). H0 (4.21)
:
z = [f(b, i) f(b, j)]/[fT(i)Cf(j) + f
T(j)f(j)]
0,5SOY. (4.22)
2Y
S 2OY , (); 0 (4.21)
. (4.22). -,
(4.22) fT(xr)Cf(xr) , N-1
(N
); -, , z ~ N(0; 1) ,
= 0,05, (/2)-: z = l,96.
(4.21) ,
|f(b,xi) f(b,xj)| 1,96SOY(2/N)0,5
= 2,8 SOYN-0,5
= LK (4.23)
, , |f(b,i) f(b,j)| (i,j).
, :
( ) ( )( )
( )( )
1 1 1
b,x b,xb,x b,x
n n nij ij
i j ir jr ir jr ijr ir jr
r r rr r
f ff f x x x x D x x
x x= = =
= =
( ) x ,xi j , xij
[i; j]. nN(N 1)/2 Dijr
, LK .
(, ) L(a, ):
( ) 11
a,cn
K r r rrL L D a c
== ; ( ) r
xr xfD =
/xb,max ; a, c . (4.24)
(i, j) L(i, j)LK, , Dijr Dr,
(4.20) . ,
i j,
L(i, j) 1. (4.25)
( )( )2
2
1 ,2i ji j IS Y Y l= , (4.26)
I ,
; l 21S ,
I; Yi, Yj i j.
-
87
( ) ( )( )2
2 2
OY, b,x b,x / 2 3,9i ji j I f f l S N
= . (4.27) ,
N ,
R2
Y .
4.8.2.
- . .
[2]
2BY (4.18)
.
L (4.24) , 21S
2BY , - [2, 9, 27, 44]
( 01 ) , -
R2
Y , ( 12 ) -
( 03 )
S 2OY 2
1S ( ,
(4.18) ) . i ij
: i = 0 ( ), i = 1 (
); j .
0: 2
OY = 2
BY (4.18)
.
( 0, 1, , 100%)
[2] 03k = (0,01)4,3
. ,
= 50%. 03k = (0,0150)4,3
= 0,05.
( = 30%), 03k = 0,006; ( =
70%), 03k = 0,2 . . (
) [46, . 264]
( ). 03
. , , S 2OY 2
1S .
-
88
.
1 03, ,OYf f
F = S2
OY /2
1S , fOY f1 S2
OY
2
1S . 03 = ( 1 03, ,OYf fF , fOY, f1)
[9, 34, 35, 36].
21S
, l, r l :
( )( ) ( ) ( )01 01 12 12 x , x 1; ; ,i j K KL r r r < (4.28)
01, 12
.
0 (4.18) , r Q,
Q N; Q = N(N-1)/2, ( )03 03, Kr ,
( ) { }03 03,min , 1, 2, ...,Kr r Q . (4.29)
4.8.3.
( ).
[2] 2BY
, [9, 34, 35,
36]. i j
L(i, j) (4.24).
. (4.26) ,
[2], ( )
. l
M (M l)
Km (Km > 2), 1,m M= .
,
-
89
, , .
Lm,max m (Lm,max =
max(Lm(i, j)) (4.25), (
), (4.26), :
( ) ( )22
n 1/ 1
mK
mmn mmY Y KS == , m = 1, , M, (4.30)
S 2m , m-
, Km 1 = fm; Ynm
n m; mY m- ; mY = n 1
/mK
mn mY K= .
21eS
S 2m . ,
S 2m [2],
, [46]. - , S 2m
( 1 ),
, .
.
. , 01 = 0,01.
S 2max = max(S2
m ) S2
min = min(S2
m ) (
)
[46, . 264] ( ).
,
S2
max S2
min . [9, .
123] 01 = ( )1 1 2
u
,
( )2 1 2Mu c M M= = S2
m 2. 01 < 01,
S 2m , 01 > 01,
:
( ) ( )22
1 1 11 / 1
l l
e m mmm mS K KS= == (4.31)
, ( )1 1 1 1 .l l
e m mm mf f K
= == =
-
90
4.2.
Y, .
(4.26), (4.30) (4.31),
S 2m (4.30) .
S 2Y1 ( ),
.
Yi Yj , . . Yi = Yj = L10V
,
Y , L V
. S 2Y1
, ,
[2, . 49] S 2Y1 = 102V
/12, S 2i jY Y
i jY Y ( ,
S 2i jY Y+
i jY Y+ ) ,
Yi Yj; S2
i jY Y= 10
2V/6. ,
Yi = Yj = 2 = 2100 .
S 2Y1 = 100V
/12 = 1/12 0,292, S2
i jY Y = 1/6,
(4.26), l = 1, Yi Yj = 0 102V
/3 = 1/3;
21S = 1/6 0,412.
4.3.
- S 2Y
2Y fY [2, . 477; 12, . 181; 41],
.
N ( )
( )
S 2Y ( ) fY.
, 21S S2
OY ,
: fOY >> f1.
[2] S 2Y
S 2OY .
0 (4.18) ,
[47, . 226].
-
91
S 2OY fOY. S2
Y
fY .
4.9.
,
. .
(4.4) .
(,
, . .).
(Y)
Xk [12, .
191]. - ,
. ,
[13],
.
( )
,
. ,
(, 1, 2, , n) ,
, (4.4).
[12, 13], b n + 1
(4.4)
.
( ),
.
(. 4.6) .
,
, .
, , ,
-
92
( ,
).
, , N
, ,
.
(4.4), ,
. ( )
bk Xk (k = 1, 2, , n) ,
bk,
Xk
. (, , .)
Xk , ,
.
Xk
(. 5).
4.9.1.
: .
(Yi, Xi), i = 1, N ,
i- Yi , Xi n- (n
), N ( ).
,
Yi = (Yi - Y )/SY ; Xki = (Xki - X k)/SXk, k (1, , n), i (1, ,
N), (4.32)
Yi Xik (
); Y X k ; SY SXk .
[9],
.
(4.4)
Y = n
k = 1 kk + . (4.33)
-
93
(. . ,
, ) Nn, Y
N. ,
[9], (n + 1) b (4.4)
'Xb = XY. 2
Y ,
b ('X)-12
Y .
.
C ,
xi = (xi ix )/||xi ix ||, i i- X; ix
, xi;
. XXbc = XY bc (
bc n c). bi
bi = bci/||xi ix ||, i = 1, , n. (4.34)
, XX
; (XX)-1
bc. bi bci
, bc b .
, (4.4) (4.33) , k k
. (4.4) ,
Y k, (4.33)
.
(4.4) (4.33) .
k k
. y
. k k
Y
Y k k. k SXk.
Y
k
k:
-
94
1) k SXk
Y k SY
2) k
k.
k. 3
, k ,
. , , , Y,
, k ,
, , .
.
k, k , ,
(4.33)
, . k
k.
4.9.2.
( ).
XkiXpi [k < p, k, p (1, , n)], i (1, ,
N) (4.4)
(4.33) kpkp, kpkp,
. kp kp
,
Xk Xp [12]. (4.4) (4.33),
,
.
, k p
, 0,
1;
;
.
k p (kk + pp) (4.33)
, kp (kpkp)
-
95
, ,
Xk Xp
. -
. kp
,
.
. kp ,
Xk,
Xp 1 .
, kp, k p
,
. , :
kk + pp + kpkp = kk + p; = (p + kpk) (4.35)
k p [2].
[2].
0 1, ,
( ).
, (2.4),
,
, .
4.9.3.
,
( ).
. : ,
. ,
, ,
. ,
.
[12]:
-
96
, ,
( )
.
, , ,
, , ,
.
,
.
.
XX
(XX)-1 (. 4.7). (4.33)
n = 2,
bci.
Y = b11 + b22 1
SX1 Y b1
SY, 2
1. , ( )
bci
. , bci
i.
,
( ), .
4.6. [48, . 55]
Y : xl , 2
, , 4
.
(. 4.1.) ,
Y 4.
4 (0,993)2 = 98,6%
-
97
4.1. .
1 2 4 Y
1 1 12 13 13 15
2 0.97 1 23 24 25
0.95 0.997 1 34 35
4 0.96 0.993 0.996 1 45
Y 0.92 0.981 0.990 0.993 1
: ,
,
ij < 10-7
.
Y.
Y = 223 0,591 0,942 + 1,24 + 1,234. (4.36)
R2
Y = 99,7% Y.
: xl 2
Y !
: 4
.
, ,
.
4.10.
( ).
, (4.3)
[2, 5, 9, 12, 13, 15].
,
.
[12].
Xi (i = 1, 2, , n)
. ,
.
-
98
Xi (i = 1, 2, , k),
[2, 5, 9, 1214]
. Xi
(i = 1, 2, , n), , Xi (i =
1, 2, , k) Xi (i = k + 1, k + 2, , n) .
Xi,
.
. ,
, , ,
. . , ,
,
. ,
,
, , . .,
.
.
, , 34
,
,
,
. ,
[2, . 271]
N.
[16]
.
,
rij .
. 4.3.
( ),
Y X
[2, 3.6.2]: 1, 2
; 3 4,
n = 32- .
-
99
,
. ,
, .
,
.
.
: (
) , ,
, .
|rij| 1.
1, N
(. 4.3.),
.
2, 3 . . ,
rij
r. [2, 3.6.2]
,
,
.
(. 4.3.).
k = 0,1
.
(
)
,
.
,
, rij
1, .
(-) [48, . 55; 49, . 232; 25, . 2, . 259],
-
100
XX (
) (-) k.
k
,
(). ,
, .
4.7. 4.6.
k = 0,02 XX
xl ( ) [48, . 59]
Y = 400 + 0,1932 + 0,811 + 0,6334; R2
Y = 98,4%. (4.37)
:
(2), () (4)
Y .
4.10.1.
,
, . .
.
( ) ,
- .
.
,
.
.
,
[12],
() ()
. , ,
.
.
-
101
,
,
.
,
.
4.10.2.
( )
[16] INTER ,
.
(SPSS, STATISTICA, SAS [76] .)
INTER. ,
,
,
.
(,
),
r (. 4.11).
Xi Xj,
(|rij|) .
|rij| , ,
.
, .
.
,
. . ,
|rij|
r.
-
102
4.10.3.
( ).
.
:
Xi.
[2, 5, 9, 1214] -
,
N [2, . 271].
,
. 4.4.1
0 1.
( 0 1).
ui (0 < ui < 1) [9, 34].
, , [2, 9, 34].
, (
) (
[2]).
[25, 34, 47 49].
, ( , )
|rij|
R2(i|j) .
.
.
; (. 4.10.1)
.
-
103
4.11.
, . , II .
.
k
k(k),
. kp,
k p ,
,
.
, N
rij Xi Xj
. , rij = 0,2 N = 500
= 10-5
[2].
: , , , ,
. ,
, .
, Xi Y.
,
rij Xi Xj (j = 1, 2, , i -1, i + 1)
, , |rij| < 0,4; 0,4 |rij| < 0,7;
0,7 |rij| < 0,95 , 0,95 |rij| < 1
.
rij ,
(4.4), .
, i (i 1, , n)
j (j 1, , i -1, i + 1, ..., n).
R2(i|j) (i 1, , n) ( i , j ).
rij ,
-
104
R2(i|j) [
R(i|j)].
rij, R2(i|j).
, Xi Y
,
R2(i|j) , , R
2(i|j) < 16%;
16% R2(i|j) < 49%; 49% R2(i|j) < 90%
, 90% R2(i|j) < 100% .
4.12.
, , , . .
, ,
.
,
,
.
, ,
. . ,
, , , . .
, Xk
Y .
.
, :
,
.
4.13.
, .
, ,
,
-
105
, , , ,
-.
(. 5).
1) , .
2) .
,
.
( ): , ,
.
3) .
m
(m = 1, 2, , n) (
m , )
m
( m ,
).
,
,
0,0001 0,00001.
.
4) .
, ,
.
5) .
, ,
,
, , .
-
106
4.14.
, ,
, . . .
, ,
[21].
() ()
.
, ,
(. [2, 6.3.2]
5.6.). - , i,
(4.1), (4.19) Zi.
,
[2].
.
(
) (4.3).
, , ,
0
2
Y
2
Y [9]. ,
2
Y -
, [2, 21, 28]
(; . 4.8.1.), .
( !)
R2
Y ( R2
Y ,
, ). ,
R2
Y !
-
107
,
. , [9], Xi
( )1,i n= ( ), , . ,
, (
ip
j=1ij = 1 . 4.4.1). , R2
Y
ti (3.4)
(3.5), Qi u1i qi , i,
. , [9], ,
- (4.3) (4.4),
.
.
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-
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.
( R2
Y ) .
(.
3.6.).
4.15.
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. . .
(SPSS, STATISTICA, SAS
[76] .) ,
.
[2, 31].
(4.19) ,
Xi Y
-
108
Y Xi
,
.
,
(). Y Y
(4.19) [2, 9, 25, 34, 41,
4749]
Y, = [fT(b,)Cf(b,)]0,5SOYtf;/2, (4.38)
tf;/2 /2 f- .
,
[2].
4.8. 134-
(. 5.2.) Y5 = 0,61 +
1,04X17.3 0,271X8X74, Y5
; Y5 (-3; 3) { Y5
, (-3)
(+3) }; X17.3 (X17.3 = 1
; X17.3 = 0 ); X8
? (X8 = 0 ; X8 = 1 ).
(. 4.4.) , ,
,
, (X74) .
X74 = {, , , },
( )
{Y, Y, Y, } (
).
, (, X = 4 =
5 . 4.4.), Y X74 ; , , X, Y
Xi . . 4.4. , { }
X74 () .
, X74
( 5%): { }
. ,
-
109
X74 (
5%).
X ,
,
. ,
X74
(4 ) = 3
, 1,2
,
X74
( 4) = 5
,
1,9 .
4.16.
!
( ,
. .), ( ) - [8, 12, 13].
.
() ;
(
, )
. 4.4.
(X74): Y5
, ; 1
; 2, 3
95%- ; ,
; Y, Y Y
; X
, .
-
110
; ( ) (4.4)
,
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, (SPSS, STATISTICA,
SAS [76] .) ( ),
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-
111
. 4.5. -
() ():
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;
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;
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J
;
K
;
L
;
M
;
N ;
;
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
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. 4.5.
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112
O ?
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;
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);
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3.6.).
.
- [2, 27],
.
,
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,
, .
(. . 3.10.), (. . 4.5.).
R2
Y c V .
( )
, ( G, ).
-
113
[9, 62,
63].
, ,
. ,
, ,
(n)
: (2n 2),
, .
4.9. n = 5 ( n = 10);
52 = 45/2 = 10 ( 10
2 = 910/2 = 45);
5 + 10 = 15 ( 10 + 45 = 55); (215 2) =
32765 ( 245 1 3,61016).
,
. :
1) ;
2)
[62, (2.65)];
3) - ( 20-) , .
[63]: Forward Selection ( ), Backward Elimination (
), Stepwise ( ) Best Subsets ( ).
,
[23], [2].
. m - ,
n (n > 1) ,
.
m + 1 n. n = 1
.
( J).
( , ),
( N) [2, 28]
( R).
( Q) ,
-
114
(
), , , ,
[2, 15].
( S),
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,
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, .
( ).
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.
( V) .
,
(. . 3).
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(, 0,3),
( N ).
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.
-
115
5.
pp , p pp. .
.
,
.
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(
,
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""),
.
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(
, 134 , ,
, )
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.
(. 5.1)
: ()
, ,
(), ,
.
X7, X8, X10, X17.1,
X17.2, X17.3, X23.1, X23.2 X23.3
( 134) . ,
-
116
10X = 0,75 ,
75% 98 ; 25%, 34
(. 5.2.), 17.2X = 0,67 , 67% (90 )
(X17 ; X17.2
).
5.1.
,
, . .
Yi {i (1, 2, , 6)}
-3- +3- , ( -3)
( +3) .
5.1. [29]
( = 0 ) (
= 7 ).
Yi = 6/7 3. -100% +100%
, . . .
Y
:
Y = ==6
1
6
1/
i iii iqqY ; Yi, Y (-3, 3); qi (q
-, q
+)%, (5.1)
qi , i- Yi; q- = 0%
, q+ = 100% .
qi (%): q1 = 70,
q2 = 40, q3 = 40, q4 = 90, q5 = 50 q6 = 30.
5.1.
Yi. Y (5.1)
. .
Yi.
Yi.
-
117
5.1. [29]
-
. 1
-
2 3
- - 1 2 134
() Y1 YZg 2 0 ... 1 -3 3 Y2 YZp 2 -1 ... 1 -3 3 Y3 YZs -1 -1 ...
1 -3 3 Y4 YZw 1 -3 ... -1 -3 3 Y5 YWm . . - 3 -2 ... 3 -3 3 Y6 YWJ
- . . 3 2 ... 3 -3 3 Y YZs 1,6 -1,2 ... 0,9 -2,14 2,59 ()4
X7 XGr 5 - 0 1 ... 1 0 1
X8 XKf ?6 - 1 0 ... 0 0 1
X10 XSex 7 - 1 0 ... 0 0 1
X12 XStm 3 2 ... 3 -3 3 X14 XStm -1 0 ... 0 -2 2 X15 XAlt 21 28
... 27 13 62 X16 XVrs - 1 1 ... 1 1 4 X17j XHf
8 - 3 2 ... 2 1 3
X23j XVrf 9 - 2 2 ... 3 1 3
X24 XAnK - 1 0 ... 0 0 4 X25 XUng - 0 0 ... 0 0 2 X30 XKnn 3 2
... 2 -3 3 X31 XEinf .- -3 1 ... 0 -3 3 X32 XKnt - 1 0 ... 0 0 2
X33 XEnt , - 2 5 ... 1 0 11 X46 XKgn - 25 19 ... 9 4 40 X72 XLfZ .
257 107 ... 224 42 1594X73 XFlK - 16 27 ... 12 3 37 X74 XKf - 2 9
... 2 0 12 X76 XAbK - 14 18 ... 10 1 26
: 1 - 1 134. 2 - . 3 - . 4 - . 5, 6 - 0 , 1 . 7 - 0 , 1 . 8 - 1
, 2 , 3 . 9 - 1 , 2 , , 3 .
5.2. (X15) (X10).
, 1, (X10 = 0) 34 24 10 (X10 = 1) 98 29 12
1322 28 11
: 1 . 2 .
-
118
(Yi Y) ,
(i):
Y = 0 + i=1n
i i(i) + 1 i j nn
< ijij(i, Xj) + , (5.2)
() ; .
(i) (Yi) .
() (. 5.1.).
i(i) i,
( ) i (12, 15, 16, 24, 25, 3033, 46, 72, 73),
i(i) = i; 72 (XLfZ
), ( ),
72(72) = lg72 ( ,
lg72 72
). ij(i, Xj)
ij(i, Xj) = XiXj. XiXj .
Y
Xk, ( = 0,2)
Xk XiXj.
i i (7, 8, 10), {i (0; 1)},
(5.1) : i(i) = i. ,
,
. 5.1. ( 0.i
), , . 4.2.1.
, Xij (j = i1,p , pi > 2) ip
j=1ij = 1. ,
1 (. 5.1.) X23j = 2 pi = 3. ,
, X23.1 = 0 X23.2 = 1 X23.3 = 0.
Xi (. 5.1.) (5.2).
,
(. 5.3).
-
119
5.3.
, .
1 2 3 95
(dd:mm:yy) 15:22:48 15:22:52 15:23:00
(hh:mm:ss) 00:00:00 0:00:04 0:00:12
3
(X73, . 5.1.) 2 200
Handy
1
(. . 5.6.) IZ ZF AS
(dd:mm:yy) 15:48:52 15:48:57 15:49:01 16:06:37
(hh:mm:ss) 00:00:00 0:00:05 0:00:09 0:17:45
9
(X73, . 5.1.) 1 4 99
2
(. . 5.6.) IZ V
(dd:mm:yy) 11:46:25 11:46:32 11:46:38
(hh:mm:ss) 0:00:00 0:00:07 0:00:13
(X73, . 5.1.) 1 4 99
134
(. . 5.6.) V ZF
(. 5.1. 5.2.)
, ,
( 5.4. 5.5).
5.1.
Yi. Y (5.1)
. .
Yi.
Yi.
-
120
. 5.1. : ; ; ; ; ; -
; .
. 5.2. : ; ; ; .
-
121
5.4.
100 01 500 1 05
200 02 700 2 07
300 03 800 08
400 04 900 09
99 1000 10
5.5.
99
2000 - 20 2900 HiFi-Studio 29
2100 - 21 3000 DVD-Player 30
2200 1 22 3100 31
2300 2 23 3200 HiFi-. 32
2400 24 3300 HiFi- . 33
2500 25 3400 (DVD) 34
2600 26 3500 (CD) 35
2700 -Studio 27 3600 36
2800 , , DVD 28 3700 37
: 1
; 2 ( ); 3
( ); 5
; 7 ; 9 .
11- (. 5.6.).
, ,
-
122
5.6.
1 . ? O
2 , , . 2 IZ
3
:
.
AS
4
,
.
,
!
AB
5
.
AA
6
(
, ).
,
ZF
7
.
,
, !
ZE
8
3
V
9
.
?
U
10
, .
X
11
.
P
:
.
, ,
.
, , .
: ,
, .
{}, ()
. {01}, ,
-
123
.
{11} {1100}, .
1. {01} {02} IZ {200} ZF {200} (3) AS {200} (9) AB {200} (1)
{200} (9) {02} IZ {04} ZF {99} AS {99} ZF {21} AS (l) ZF {26}
{2600} {2600}
(1) AS {2600} (9) {2600} X {2600} AS {2600} (5) {2600} AB {2600}
AA {2600}
(9) AB {2600} (9) (l) {21} AS {99} {04} {07} {09} AS {11} AS
{11} IZ {11}
X {11}
(. . 5.1. 5.2.)
2. {01} IZ {04} {99} V {99} U {21} (l) OR {26} {3000} {3000}
(2)
AB {3000} AB {3000} ZF {3000} (9) V {3000} (2) {3000} (9) {30}
{31} {32} {34}
IZ {3400} ZF {3400} (3) AS {3400} (9) AB {3400} (3) AB {3400}
(9) {3400} (3)
AS {3400} AB {3400} (9) AB {3400} (3) AS {3400} AS {3400} (9)
{3400} (1)
AS {3400} AS {3400} (9) {3400} (3) X {3400} AB {3400} (9) {3400}
(1) {3400} (9)
{3400} (3) {3400} (9) {3400} (1) {3400} (9) {3400} (3) {3400}
(9) {3400} (1) {3400} (9)
{3400} (3) {3400} (9) {3500} {3500} (1) {3500} (9) {3500} (3)
{3500} (9) {3500} (1) {3500}
(9) {3500} (3) {3500} (9) {3300} {3300} (2) {3300} (9) {29}
{2800} {2700} {2700} (2)
{2700} (9) {2700} (2) {2700} (9) {2700} (2) {2700} (9) {2700}
(2) {2700} (9) {2700} (3)
{2700} (9) {26} (l) {23} {21} {99} {04} {400} {400} (3) {400}
(9) {07} {700} {700} (1)
{700} (9) {700} (3) {700} (9) {700} (3) {700} (9) {700} (3)
{700} (9) {1100} {1100} (1)
{1100} (9) {1100} ...
134. {01} {04} V {99} ZF {21} IZ {23} X {3400} {3500} {3500}
(2)
V {3500} IZ {3500} AS {3500} (9) {3500} (3) AS {3500} {3500} AB
{3500} (9)
{23} IZ {22} {99} {04} {01}
5.1. ( )
: 134 {01}, {04},
V, {99}, ZF, {23}, X,
{3400}, {3500} . . , {99}
{04} {01} (, ).
