Тихонов Э.Е. - Методы прогнозирования в условиях рынка -...
TRANSCRIPT
-
..
, 2006
-
2
[338.26+004.67](075.8) .. . :
. - , 2006. - 221 . -
. - - - MS Excel, Statistica, Statistica Neural Networks.
. - . , ( - ) -. - Sta-tistica. - Statistica Neural Net-works. .
, : , - , - .
:
- . , . .. - . , . ..
ISBN 5-89571-077-8
- , 2006 .. , 2006
-
3
6
1. -.
8
1.1. 11 1.1.1. . 13 1.1.2. 15 1.1.3. ... 19
1.2. () ... 24 1.3. ... 33 1.4. ..
40
1.4.1. p (AR(p)-) 41 1.4.2. q ((q)-).
43
1.4.3. - (ARMA(p, q)-).
45
1.5. -...
46
1.5.1. - (ARIMA(p, k, q)-)..
46
1.5.2. , .. 48 1.5.3. ARIMA-... 49
1.6. 51 1.7. 55 1.8. . 62 1.9. , ..
63
2.
71
2.1. ...... 71 2.2. . -
72
2.2.1. - (=0)...
73
2.2.2. - (=1).
76
-
4
2.2.3. - (=2)..
80
2.3. ( - )..
83
2.4. -
91
3. - .
97
3.1. . 99 3.2. . 111
4. - Statistica Neural Networks..
122
4.1. Statistica Neural Net-works...
122
4.1.1. .. 122 4.1.2. .. 123 4.1.3. ... 124 4.1.4. ... 124 4.1.5. ... 124 4.1.6. . 126 4.1.7. 126 4.1.8. .. 127 4.1.9. ... 127 4.1.10. .. 129 4.1.11. . 129 4.1.12. 130
4.2. .. 131 4.2.1. . 132 4.2.2. .. 133 4.2.3. ... 134
4.3. . 134 4.3.1.
135
4.4. . 147 4.5. . 149 4.5.1. 149
4.5.2. -.. 155 4.5.3. 159
-
5
-.. 4.6. . 159 4.7. - ..
166
4.7.1. .. 168 4.7.2. , , -.
174
4.8. - .
182
188 . 206
-
6
-
, , -, . - , - , - [19, 27].
, -, , , . , - .
- . , - .
. .
, MS Excel. , - , , .
- . , , - Statistica -.
- . , - .
, ,
-
7
, -.
.
-. , ( - , - ).
. - , , , .
- , , - ( ), , -, ( ) [123, 134]. , - - - , .
, , - , .
-
8
1.
, -
, 100 - . , - , - . , , . -.
. , -. . - , , : , - , -. - 1.1 [19].
, - , -.
- : , , .
. , , , . - , - -.
-
9
1.1.
-
-
- -
-
-
-
-. .
- -
- -
--
- .
. .-
-
-
-
- -
--
-
-
-
- .
- -
. -
-
-
- -
.- .-
-
-
-
- - ..
- - ..
-
-
10
- . , -. . () ()
tt /= ,
t ; xt - .
-, ( 1 ), - .
- , , : .
( ), - - . - , , - .
( -) : , - , . -
-
11
, , ( ).
- , -, - .
, , . - - -- , , -, , . - - - . - -, -.
-. - , - .
- , -.
1.
? 2. ? 3. ?
1.1.
- . - . . - .
-
12
- , - - , .
ty
ttt CSxy +++= (1.1)
tx (); S ; ;
t . () tx
, - t . - , . - tx , , t .
- , . , - , - . .
- -, , .
1. . -
? 2. .
-
13
1.1.1.
, - , . .
( )
==
n
iii yyS
1
2 min (1.2)
iy ; i - ; n .
),,...,,;( 21 taaaxfy ki= , (1.3)
kaaa ,...,, 21 ; t ; xi - -, , , - (1.2), - S ja . - k , - ja .
, - , - , .
1. , - .
2. - , .
3. , - (-).
4. , . . .
5. . -.
6. - .
-
14
- : = ax + b; = 2 + b + ; = an; = ax; = x; =
exbea
+1.
, , . . , - .
, , . , - , . , , , -, , .
- . - - , . - , . . . (1) 1
-
15
, .
1. ? 2. , -
.
3. ?
1.1.2. -
. - , , - . , - , , . . - - , [6,64,72,151].
tpp
t tpa
tataay +++++=!
...2
2210
. (1.5)
, -
, - (1.5), - , - .
[ ]( ) ( ) [ ] ( )
==
n
i
kt
ikt ySyS
011 (1.6)
k- t, .
-
16
- [151]
[ ]( ) [ ]( ) ( ) ( )( )ySySyS ktiktkt 11 1 += . (1.7)
(1.7) -
[ ] [ ] [ ]kSSS 02010 ,...,, . , - -
[ ] ( ) ( )
( ) =
=
+=
n
p j
jpppkt j
jpjkp
aS
0 0 !!1
!1!
1 , (1.8)
= 1, 2, ..., n + 1; pa ; = 1p . - , ,
[ ]
[ ] ;2
;
102
0
101
0
aaS
aaS
=
= (1.9)
[ ] ( )[ ] ( )[ ] ( ) .
2343
;2
232
;22
22103
0
22102
0
22101
0
aaaS
aaaS
aaaS
+=
+=
+= (1.10)
[ ]kS0 ,
[ ]ktS . -
. - ( + 1) ( + 1) , - -. , ,
-
17
[ ] [ ];2 210 tt SSa = (1.11) [ ] [ ]( ); 211 tt SSa =
[ ] [ ]( ) [ ]( ) [ ] ( ) [ ] ( ) [ ][ ]
[ ] [ ] [ ][ ).2;3445256
;3
3212
2
2
32121
3210
ttt
ttt
ttt
SSSa
SSSa
SSSa
+=
+=+=
(1.12)
. -
10 aayt +=+ , 22
10 2 aaayt ++=+ , - .
, , , , - [72, 103, 215].
- : , - , . - , -.
, - . ,
12+= N , N , -
( ). -
n , n -
; - . ,
-
18
n .
-, - , - , [103, 129].
( ) ( )[ ] 232222 23122411 ++++++=x . (1.13) [ ] 2232 332 ++x . (1.14)
( ) ( )=
+=n
itii tfaty
1 . (1.15)
( ) ( ) ( ) ( )= =
==n
j
n
k
Tkkjix Vfffaaf
1 1
22 ,cov
r, (1.6)
; fi(t) ; V - .
, 0= . , ,
, t , , . - .
, , , , , . - [103].
-
19
, (1.13)-(1.16) : - , , .
, (1.13)-(1.16) - , -: . , . - (1.13)-(1.16).
, , - .
- , . -, [40, 53].
. , - [129, 138].
1.
? 2. ?
1.1.3. -
. - , .
, -
-
20
. -, .
n -. , (n + 1) : x1, x2, , xn. , x(t), , , . . - k, , ( ) kk xtxx
-
21
( )kkk pp rr = 122 , (1.18)
( )10 , - .
. - , pk ( 1), ( 0). . , -, .
-, . , , . .
- . - , . , . , . -, , - . - , . , - ( ) , ; - [54, 72].
- . ( )tpr , , . - (t), nxxx 0 x0 n .
-
22
- xp, - ( ) pxtxx 0 , (100 ) - ( ) np xtxx . , - , -
{ } =
==k
iikkr PPxxp
1
. (1.19)
, 0 = 0 k = 1, 0. ,
. = k k, - [54]
( ) ( ) ( ) ( ) = =
=
-
23
2x - . , . .
m - . 21n , .
-.
( )
> d2, ; d1 d d2, - . , . . Yt=Yt+1-Yt; Xt=Xt+1-Xt. , - , - j j- -.
-
38
j
jj Rr
Rr
11
11
11
+= , (1.58)
r1 - ; R1j - j- - .
, , . , - [ XX T ] , , -, .
. - =f(x1, , xn). -
[ ]XXnN T ~~lg)52(6112
+= (1.59)
XX T~ - [ ]XX T~ ), - )1(
21 nn .
(16) N , n , -,
NSxxX
i
iikik
=~ , (1.60)
ii xS , - i- . ( )
XXXX
dT
iiT
ii ~~~~
= , (1.61)
, , i,
-
39
( )1
1 =
nnNdw iii , c
nNv =1 12 = nv . , , .
- . , , - . - , - . , - , - , . -, -
=
=m
iii xy
111 , -
=
=m
iii xy
122 , 21 ii , , , -
, . -
- . - -, -, . , , , . , : - . . - - , ,
-
40
- , , , - . , , - .
1. ? 2.
F- t- ? 3. ? 4. -
?
1.4.
-
. , t, () xt (). , - , , - , - .
. - , t, , t , .. Et 0. , - , t.
- , ,
,0
=
=k
ktkt (1.62)
-
41
0 = 1
-
42
. ,
t = t1 + t, (1.65)
, (|| < 1), t , . t t , . , (1.65) t t1 - . , t (-).
, (1.65), .
2- AR(2) ( ). , AR(1), - , j (1.63) , . ,
t = 1t1 + 2t2 + t, (1.66)
1, 2, .
(1.66) ( -)
1; - , - ;
- ,,...,1, kTtxkt = xt k- , ARMA(p, q).
, ARIMA(p, k, p)- - xt,
,...... 112211 qtqt
kptp
kt
kt
kt xxxx ++++= (1.78)
-
47
( ) .1...2211 ktktktkttkkt xxCxCxxx ++== , ARIMA -
- ( ). - (1.63), = 1,
t = t1 + t. (1.79)
t -
, .. ARMA(0, 0). ARIMA ARIMA(0, 1, 0).
ARIMA-. , k . ( )k2 k: k k0, ( )k2 ( )k2 . - k ARIMA- - xt, 2xt,. - xt , 2, . , l < k lxt -, . , k , t
kkt xx = .
k xt, k- . ARMA(p, q).
-
48
1.5.2. ,
, , , - / .
- : , ( , ) ; - , , . . -, - ( ) , . -, - - , , .. - .
ARIMA- . - , ARIMA-, - T = 1 FT_, - ( ., , [15]:
- xt T - ;
- ( ) ( )tx TKk , ARMA- -
( ) ARMA-; - ( ) ( )tx TKk ,
( ) ; (
xt ) - ,
-
49
, -.
1.5.3. ARIMA-
ARIMA- - , . , ARIMA-. ARIMA-, , AR-, MA- ARMA-. , , , . , -.
xt+l, l 1 , xt - , . ltx .
, ltx 11
+
ltx
xt+l, -, .. .
x, ARIMA(p, k, q)-, - ( > k)
( ) ( ) ,...1...1 110
1 qq
k
jj
jk
kpp xCLL
= = (1.80)
L .
(1.80) x = t q,, t 1, t, t + 1,, t + + l.
( ) .1111011
+
+
=
==
==
q
j
jj
k
ii
ik
ip
j
jj
p
j
jj LxCLxLx
(1.81)
-
50
p + k ( ) x, q . , - , , .. - .
(1.81) l . , - ( ) t l xt+l, - , x t. - (. [237, 198, 235]).
E(xt+l | x1,, xt) (10) = t + l :
E(xtj | x1,, xt) = xtj j = 0, 1, 2,, t 1 (1.82) E(xt+j | x1,, xt) = jtx j = 1, 2,; (1.83) E(xt+j | x1,, xt) = 0 j = 1, 2,; (1.84) E(xtj | x1,, xt) = 1 1 jtjt xx j = 0, 1, 2,, t 1. (1.85)
,
: (1.81) 1 1 qtx ,
1 qtx ,, 1
1 tx ; 1 + mqtx xtq+m (m = 0, 1,) (1.81) E(tq+mj | x1,, xtq+m), (1.85), , ; > t (1.82)(1.85) - - .
-
51
. p, q k .
1.
? 2. ARIMA? 3.
, ? 4. ()
ARIMA?
1.6.
, - - , - , , , -, . - . - , .. , , - . , -, , - - . -, , - .
( - [151]) - . .
x, = 1, 2,, t -
x = a0 + , (1.86)
-
52
a0 , , - , , . , x t ( )tx (- ) (0 < < 1)
( ) ,11 1
0
=
=t
jjt
jtt xx
(1.87)
: ( ) ( ) .minarg 10
2=
=t
jjt
j
ataxx
, - .
(1.87)
( ) ( ) .10
=
=j
jtj
t xx (1.88) -
1tx xt+1 - t xt - ( ),1 tt xx = (1.89)
( )tx (1.87) (1.88), - .
(1.89) , , , - (t + 1)- xt+1 - ( )11 1 ++ = tt xx ( ) ( ) ( ) .1 11 ++ += ttt xxx
- , .. , (1.86) -
-
53
xt+ = a0 + a1 ++ akk + , (1.90)
k 1. (1.90) t, . , 1tx xt+1 (1.90) = 1 (4)
( )( ) ( )( ) ( )( ),,...,, 1011 tatataxx kkkktt +++== + (1.91)
( ) kjta j ,...,1,0,, = -
( ) .min...
,...,,0
210
10 kaaaj
kkjt
j jajaax =
(1.92) (1.92) -
. ,
, .
. [195] -, , - 1 2 (0 < 1, 2 < 1). ltx l t -
( ) ( ),,,,, 211210 taltaxlt += (1.93)
( ) ( ) ( ) ( )( ),,,,,1,,1 21121011210 tataxta t ++=+ (1.94) ( ) ( ) ( )( )( ) ( ).,,1
,,,,1,,1
2112
2112102211
tatatata
+++=+
-
54
, , 1 2, ( )210 ,,0 a ( )211 ,,0 a .
. [236] , . , - t l ,
( ) ( )[ ] , 10 Nltlt taltax ++= (1.95)
, N , . - . - 1, 2, 3 (0 < j < 1, j = 1, 2, 3), -
( ) ( ) ( ) ( )[ ]
( ) ( )( ) ( ) ( )[ ] ( ) ( ).111
,11
,11
130031
120
121
1011
110
tatatatata
x
tataxta
Ntt
t
Nt
t
++=+++=
++=+
++
+
++
(1.96)
,
, - 1, 2 3, ( ) ( )0,0 10 aa 0.
. - . - - , - , . - . ( , -) ( )
( ) ( ) ( ),1,
100
0
aaa
ax+=
++= (1.97)
-
55
a0() -, a1() , t - , t .
, t l ,
( ) ( ) , 10 lNtlt taltax +++= (1.98)
10 , aa
( ) ( ) ( ) [ ]( ) ( ) [ ]
( ) [ ].1 ;1
;11
1131
112111
111100
+=+=
++=
xxxxaa
xxaaa
Nt
(1.99)
, , N -
, , 1, 2 3 - .
1.
? 2. ? 3.
-?
1.7.
- (), - . , , [52,51].
, ( ). , - , , -
-
56
. [51]
)...,,,( 21 mxxxfy = , (1.100)
f , , - :
1- - )(...,),,(),,( 1312211 mmS xxfyxxfyxxfy === ;
2- - )(...,),,(),,( 1312211 nnk yyfzyyfzyyfz === .
. . -
, , . . - - ( - ). - . , , . . . -, , - .
[51]. -
.0,210 miyaxaay iik
-
57
25
243210 jijijik xaxaxxaxaxaay +++++= .
-
, .
- -, : )(...,),(),( 21 mxfxfxf . -
)(...)()( 22110 mm xfaxfaxfaay ++++= . (1.103)
, -
( ) . - . . - .
- , - [51].
- , - , , . , ,
)()()()()( 443322111 xfxfxfxftf ++++=+ . (1.104)
-
[51]
-
58
).,,,()();,()()()();,()()()();,()()()();,()()()();,()()()();,()()()(
);,,()()();,,()()();,,()()();,,()()(
);()()()()(
432111
21342311
21342211
41332211
32342111
42332111
43322111
4322411
4322311
4322211
4322111
443322111
xxxxftfxxfxfxftfxxfxfxftfxxfxfxftfxxfxfxftfxxfxfxftfxxfxfxftf
xxxfxftfxxxfxftfxxxfxftfxxxfxftf
xfxfxfxftf
+=+++=+++=+++=+++=+++=+++=
++=++=++=++=
++++=
+
+
+
+
+
+
+
+
+
+
+
+
(1.105)
, -
. , -
, - ( -). - , . - - .
, . , , rfyr = . -
njnjjn PPPf +++=+ ...1101 , (1.106)
-
59
rjrP I jx - : ml 0 ; ijP - { }miiij xxxL ...,,, 10= ,
ljSmj ,1,)1(1 =+ . ijP , . , 1+nf - , .
- - .
- , [52, 51].
1. , ( ), , - - .
2. - . , - , - .
3. - , .
4. , - , - .
5. - , .
-
60
() [51]: ( ) min22 ( ) min1 , ( )1 ( - ); ( )22 - - ( ). , ( ) min1 [51]:
1. 1=yT 2=nT - x(t).
2. [*(t)-(t)] - (N), *(t) - , (t) .
3.
( ) [ ] ( ) ( )[ ]
.
)(1
%10011;)()(11
1
21
2
==
==np
np
N
jj
np
N
jjj
nptx
N
txtxN
(1.107)
)2(2 [51]. 1. 1=yT , 2=nT -
, -: ( )21210 ,,, = xxxxfx . )(tx .
2. [ ])()( txtx - .
3.
( ) [ ]=
=yTN
jjj
y
txtxTN 1
22 )()(12 (1.108)
( ) ( ) [ ] .)(1%10022 1
1
2
22
=
= Nj
jy
txTN
(1.109)
-
61
)2(2 , , - . - - . , , , .
- [52, 51]:
1. , .
2. - f. fMm .
3. . 4. -
. , -
. - , . - ( - ).
-, .
. - ( ) , - .
. [53] - . , - , , . .
-
62
, -, , . . - - . - , .
1. ? 2. ? 3. -
.
1.8.
-
. , [4, 24, 25, 67, 75, 105, 126].
- . , , - - , -, . , - -. , . [126].
- - , .
, - , - , . , -
-
63
, ( ) - . , .
, , . , . - , . - , - . - , . . - , -.
- , , .
1. -
. 2.
? 3.
?
1.9. ,
-, , .. , , , , ,
-
64
, , ( + -+) [14 ,20, 21].
- [29, 36, 104, 109] , -, , - , [114].
- , . , - . 1943 . .- .. , - [36]. 1949 . , [29]. 1957-1962 . . - , [104]. 1959 . . . ADALINE. " " [36]. 1969 . . . "", - , , - . 80- - . . 1982 . - - . . . , [29, 36, 104]. , : -, , , . [1, 4, 28, 47, 51, 52].
. -
-
65
,
),(1
WXFxwFyn
iii
= =
(1.110)
TnxxxX ),...,,( 21= - -; ),...,,( 21 nwwwW = ; F - .
- [9, 11, 22, 42, 70, 139]. -, - . , [85, 127]. . . , , - , , [94]. (t). 4 . , - [29, 36].
, - - . - , - [0,1] [-1,1]. - , - . - -, , .
, - , , -
-
66
[70].
- - :
1. - ;
2. ;
3. . - , - -;
4. , ;
5. .
- [114]. - [14, 110]. , , . , , . , . - [94, 127].
-. (machine learning) 1970- [241, 245, 244, 246]. 1980- - . ( - -), , , - , - , ( -
-
67
) . - -, , - [10, 28, 100].
, "" ( ) [28].
- . - , . , - , .
[28, 88, 100] . - , - .
- . . , , - .
- , - "-", , , [241, 244, 245].
1. -
? 2.
? 3. -
? 4. -
?
-
68
, - . , , , , , , - , , . [31, 32, 35, 41, 46, 49, 56, 96]. - - , - . , - [12, 33, 50, 58, 59, 78, 82, 101, 140].
, - , . (). -
, -, , - : 1. -, ; 2. , - ; 3. - , (); 4. , . . - ; 5. -. ; 6. - .
. - , , , - .
. . ,
-
69
. -, . . -.
. - . - : 1. ; 2. ; 3. ; 4. ; 5. Z- ; 6. F- ; 7. - ( ).
, . - , , .., , - , , .
-. - , -. , - .
. , .
. , - . . -, - , -
-
70
. , , 20 30 .
( - ). , - , - .
, - . - , - , , . -. , .
, - . , - , - . -
, .
-
71
2.
2.1.
-
-. . - - . - - 12 4 . () . , . - [6, 62, 79].
, - . - - , , - . , . - . - -, , - [15, 34].
- -, , . - -, -, .
. , -
-
72
. - , -. - , . , , - , -, . . - () -. :
- ; - ; - .
, - . -, , , .
, - , - () , . . - , .
, - . , .
( ) .
2.2. .
t -
(, 25 ), n = 25 . = 0,5 =1,
-
73
-:
1. (=0); 2. (=1); 3. (=2); 4. ; 5. .
2.2.1. (=0)
=+= 1,1ttt SxS (2.1) : , 0,10 aS = 0,1a -
, , .
51151
5
10,1 ==
=ttxa . (2.2)
() -
511 == tt Sx . (2.3)
2.4.
txxtxE
2)( = . (2.4) 1
. 2.1 = 0,5, . t = 1
-
74
( ) 5,5155115,05205,01 01 =+=+= SxS i . 511 01 == Sx
t =2 25,5065,5155,04975,02 =+=S
5,515 12 == Sx t = 3
125,50525,5065,05045,03 =+=S 25,506 23 == Sx
A B C D E F G 1 p=0
2 t xt
St *x 2)( xtx
3 1 0 511 4 1 1 520 515,5 511 81,00 0,16 5 1 2 497 506,25 515,5 342,25 0,69 6 1 3 504 505,125 506,25 5,06 0,01 7 1 4 525 515,063 505,125 395,02 0,75 . . . 27 1 24 560 541,884 523,769 1312,69 2,34 28 1 25 529 535,442 541,884 166,01 0,31 29 1 26 535,442 0,5 0,5
2.1. xt ( ( = 0) )
, -
. - , .
0,1 0,9 0,1. - . -
-
75
, - .
- 2.2.
2.2.
2.3.
8,50 9,00 9,50
10,00 10,50 11,00 11,50 12,00
0 0,2 0,4 0,6 0,8 1
(=0)
480 490 500 510 520 530 540 550 560 570
0 5 10 15 20 25 =0,4
-
76
2.2 , - = 0,4, - = 8,85.
2.3. 2.4.
A B C D E F G 1 p=0
2 t xt
St *x 2)( xtx
3 1 0 511 4 1 1 520 514,6 511 511 81,00 5 1 2 497 507,56 514,6 515,5 309,76 6 1 3 504 506,136 507,56 506,25 12,67 7 1 4 525 513,682 506,136 505,125 355,85 . . . 27 1 24 560 537,895 523,159 523,769 1357,27 28 1 25 529 534,337 537,895 541,884 79,13 29 1 26 534,337 535,442 0,4 0,6
2.4. = 0,4 2.4 ,
26 534,3. .
2.2.2. (=1)
t, -
taaxt 21 += (2.5)
-
77
10,1 aa = . 20,2 aa = 0,1a 0,2a -
t, ( 2.5).
txt 2,1498 += ,
498 10,1 == aa .2,1 20,2 == aa
2.5.
1- 2-
1+= ttt SxS (2.6) [ ] [ ]2
12
+= ttt SSS (2.7)
=1-.
0,20,10 aaS = (2.8)
y = 1,2031x + 498
480 490 500 510 520 530 540 550 560 570
0 5 10 15 20 25
( )
-
78
[ ]0,20,1
20
2 aaS = (2.9)
() -
[ ]212
+
+= ttt SSx (2.10)
[ ] 6,4952,124982
8,4962,15,0/5,0498
0,20,12
0
0,20,10
===
===
aaS
aaS
(2.10)
[ ] 2,4996,49515,05,018,4961
5,05,0212 2 =
+
+=
+
+=
ttt SSx
A B C D E F G H 1 p=1
2 t xt
St St[2] *x 2)( xtx
3 1 0 496,80 495,60 4 1 1 520 508,40 502,00 499,20 432,64 0,83 5 1 2 497 502,70 502,35 521,20 585,64 1,18 6 1 3 504 503,35 502,85 503,40 0,36 0,00 7 1 4 525 514,18 508,51 504,35 426,42 0,81 . . . 27 1 24 560 541,88 532,37 525,61 1182,83 2,11 28 1 25 529 535,44 533,90 560,92 1018,85 1,93 29 1 26 538,52 0,5 0,5
2.6. = 0,5
-
79
t = 1
[ ] [ ] 00,5026,4955,04,5085,04,5088,4965,05205,0
201
21
011
=+=+==+=+=
SSSSxS
(2.10)
[ ] 2,5210,50215,05,014,5081
5,05,0212 2 =
+
+=
+
+=
ttt SSx
tx 2.6.
= 0,5 = 1. , . , , , .
2.7 .
2.7.
, -
8,50
13,50 18,50
23,50 28,50
33,50
0,00 0,20 0,40 0,60 0,80
-
80
= 0,1 ( = 9,06). -
2.8.
2.8.
2.2.3. (=2)
t - -
2321 tataaxt ++= (2.11)
(. 2.9):
215,079,296,515 ttxt +=
;79,2;96,515 20,210,1 ==== aaaa 15,0 30,3 == aa
( =1)
480 490 500 510 520 530 540 550 560 570
0 5 10 15 20 25 30 = 0,1
-
81
y = 0,1535x2 - 2,7873x + 515,96
480490500510520530540550560570
0 5 10 15 20 25
( )
2.9. -
xt 1-, 2- 3-
;1+= ttt SxS [ ] [ ] ;212 += ttt SSS [ ] [ ] [ ]3
123
+= ttt SSS (2.12)
0,00
50,00
100,00
150,00
200,00
0,00 0,20 0,40 0,60 0,80 1,00
2.10.
-
82
: ( ) ;
22 0,320,20,10 aaaS
+= (2.13)
[ ] ( ) ;232 0,320,20,120 aaaS
+= (2.14)
[ ] ( )0,320,20,1
30 2
3433 aaaS
+= (2.15)
() -
( )[ ] ( ) [ ]
( )[ ] [ ] .2
342
224526
2566
2
3222
2
2
22
2
2222
+++
+
++++=
t
ttt
S
SSx (2.16)
,
(. 2.10). = 0,1 ( = 9,06) (. 2.11).
( =2)
440
460
480
500
520
540
560
580
0 5 10 15 20 25
2.11. ( = 2)
-
83
. 1. , -
(=0), (=1), (=2) .
2. . 3. , -
, .
2.3. (
) -
. , - (. .) (n = 8). - 2.1.
2.1. xt - (2003-2005 .).
t kt
( )
t xt tx
t
t
xx
*tx (*tt xx )
1 1 499 483,91 1,031 508,28 1,9% 9,28 2 2 475 475,36 0,999 486,55 2,4% 4,55 3 3 452 466,82 0,968 452,32 0,1% 0,32 4
2003 1
4 415 458,27 0,906 422,58 1,8% 7,58 5 1 481 449,72 1,070 457,84 4,8% 23,16 6 2 467 441,17 1,059 443,15 5,1% 23,85 7 3 431 432,63 0,996 422,95 1,9% 8,05 8
2004 2
4 412 424,08 0,972 397,88 3,4% 14,12 9 2005 3 448,16 : 56,04
: 7,49
( t = 9) , -
-
84
- ( ) = 1 - 1 = 0,2; 2 = 0,3 3 = 0,4.
,,1 tktt ttfax += (2.17)
xt t = l,2,...,n; a1,t -
, .. - xt t;
fvtkt vt kt- ; vt =1,2,,l vt=t-l(kt-1); l ( l
=12, l =4 ..); t . , ( ),,0 2 nn IN ( )Tnt ,...,,...,1= In (). -
t,
( )( )( )
( ) ( )( )
+=+=
+=
++=
1,,2,1
1,231,1,13,2
,2,1
2.
1,21,1,
1,1
1
1
1
1
1
tt
tttt
tt
kvttt
tttt
kvt
tkv
ttkv
tt
faaxaaaa
faxf
aaf
xa
(2.18)
a2,t t - 1 t; ( )txxt = , t , .. - (t -); 1, 2, 3 , (0< 1, 2 3
-
85
, j . -, .
. , , . - : ,;; 0,0,20,1 tvfaa lvt ,...,2,1= .
, tx xt, 1, 2 3 . j , - t. 0,20,1 ; aa ,
ttv aaf t ,2,10, , ,
tt kvf ,
. . n = 8 xt
- taaxt 10 += .
txt = 5476,846,492
5476,8;46,492 10,200,1 ==== aaaa .
0,
tvf -
tt xx / vt-
;029,12
059,1999,0;050,12
070,1031,10,20,1 =+==+= ff
939,02
972,0906,0;982,02
996,0968,00,40,3 =+==+= ff .
-
86
y = -8,5476x + 492,46
390
410
430
450
470
490
510
0 2 4 6 8 10
( )
2.12. - 1 = 0,2; 2
= 0,3; 3 = 0,4 = 1. 1- (kt = l,vt = t). (18) t = 1 ( ) ( )
( )( ) ( )( )
( ) ( )( ) ( ) ( )
( ) ;255,95476,86.046,49214,4824.01
046,1050,13,0114,482
4993.01
14,4825476,846,492
2,01050,1
4992.01
28,508050.15476,846,492
0,230,11,131,2
0,121,1
121,1
0,20,110,1
111,1
0,10,20,11
=+=+=
=+=+==
+=++===+=
aaaa
faxf
aafxa
faax
-
87
t = 2 ( ) ( )
( )( )( )
( )( ) ( ) ( )
( ) 153,10255,96,014,48264,4704,01
023,1029,17,064,470
4753,01
64,470255,914,482
8.0029,1
4752,01
55,486029,1255,914,482
1,231,12,132,2
0,222,1
221,2
1,21,110,2
212,1
0,21,21,12
=+=+=
=+=+==
+=++===+=
aaaa
faxf
aafxa
faax
t = 3 ( ) ( )
( )( )( )
( )( ) ( ) ( )
( ) 179,10153,106,064,47043,4604,01
982,0982.07.043,460
4523,01
43,460153,1064,470
8.0982.0
4522,01
32,452982,0153,1064,470
2,232,13,133,2
0,323,1
321,3
2,22,110,3
313,1
0,32,22,13
=+=+=
=+=+==
+=++===+=
aaaa
faxf
aafxa
faax
t = 4 ( ) ( )
( )
( ) ( ) 825,10179,106,043,46063,4484,0934,0939,07,0
63,4484153,0
63,448179,1043,4608,0939,0
4152,0
58,422939,0179,1043,460
4,2
1,4
4,1
0,43,23,14
=+==+=
=+===+=
a
f
a
faax
-
88
2- (kt = 2,vt = t-4). -
, 1-
934,0982,0;023,1;046,1 1,41,31,21,1 ==== ffff t = 5 ( ) ( ) 84,457046,1825,1063,448 1,14,24,15 ==+= faax .. 5x 2- (kt = 2), 1, tt kvf -
, vt = 5-4 = 1
( )( )( )
( )( ) ( ) ( )
( ) 053,9825,106,063,44824,4424,01
058,1046,17,024,442
4813,01
24,442825,1063,448
8,0046,14812,01
4,234,15,135,2
1,125,1
522,1
4,24,111,1
515,1
=+=+=
=+=+==
+=++=
aaaa
faxf
aafxa
t = 6 ( ) ( )
( )( )( )
( )( ) ( ) 187,7053,96,024,44285,4374,0
036,1023,17,085,437
4673,01
85,437053,924,442
8,0023,1
4672,01
15,443023,1053,924,442
2,2
1,226,1
622,2
5,25,111,2
616,1
1,25,25,16
=+==+=+=
=+=++=
==+=
a
faxf
aafxa
faax
-
89
t = 7 ( )
( )
( ) ( ) 531,6187,76,085,30437,4324,0987,0982,07,0
30,4324313,0
30,432187,785,4378,0982,0
4312,0
95,422982,0187,785,437
7,2
2,3
7,1
7
=+==+=
=+===
a
f
a
x
t = 8 ( )
( )
( ) ( ) 323,5531,66,030,43279,4284,0942,0934,07,0
79,4284123,0
79,428531,630,4328,0934,0
4122,0
88,397934,0531,630,432
8,2
2,4
8,1
8
=+==+=
=+===
a
f
a
x
t = 9 () ( ) ( ) 16,448058,1323,579,428 2,18,28,19 ==+= faax tx ,
xt, 2.1 2.13. - , - - , .
, .
-
90
390
410
430
450
470
490
510
530
0 2 4 6 8 10
2.13.
. 1. , -
( ).
2. . 3. , -
, .
-
91
2.4. -
2.2 (xt)
2003 2005 . (. . ).
2.2.
t kt
( )
vt
xt tx tt xxt = *tx ( *tt xx )
1 1 7,2 6,82 0,38 6,93 3,7% 0,27 2 2 6,5 6,63 -0,13 6,52 0,2% -0,02 3 3 6,1 6,44 -0,34 6,47 6,1% -0,33 4
2003 1
4 6,3 6,25 0,05 6,28 0,3% 0,07 5 1 5,9 6,05 -0,15 6,26 6,2% -0,31 6 2 5,7 5,86 -0,16 5,66 0,7% 0,08 7 3 6 5,67 0,33 5,47 8,8% 0,56 8
2004 2
4 5,5 5,48 0,02 5,52 0,4% 0,02
9 2005 3 1 - 5,37 : 0,07
0,27
- ( -) - tx t = 9, = 1, 1 = 0,1; 2 = 0,4; 3 = 0,3.
- ( . . ).
, - , , - . - , - - .
-
92
xt vt- kt- , vt = t - l(kt - l), l - ( l = 4, l = 12).
ttt
tkvtt
aaa
gaxtt
,21,1,1
,1
+=++=
(2.19)
i t ;
a2,t t-1 t;
ttkvg vt- kt-
; t .
1, 2, 3, (0< 1, 2, 3
-
93
2.2 tx - ttt xx = . -
.0359,02
02,005,0
;0046,02
33,034,0
;1451,02
16,013,0
;1144,02
15,038,0
0,4
0,3
0,2
0,1
=+=
=+=
==
==
g
g
g
g
3,0;4,0;1,0 321 === = 1. 2003 . ( : vt = t; kt =
1; = 1)
.0359,0;0046,0;1451,0
;1144,0
0,4
0,3
0,2
0,1
===
=
gggg
(20) t = 1
( ) ( ) ( )( )( ) ( ) 182,01905,07,00071,7844,63,0
211,01144,06,0844,62,74,0844,61905,00071,71,011144,02,71,0
93,61144,01905,00071,7
1,2
1,1
1,1
0,10,20,11
=+==+=
=+==+=++=
aga
gaax
t = 2
-
94
( ) ( )( ) ( )( ) ( ) 183,0182,07,0844,66595,63,0
1508,01451,06,06595,65,64,06595,6182,0844,69,01451,05,61,0
52,61451,0182,0844,6
2,2
1,2
2,1
2
=+==+=
=++===
agax
t = 3
( ) ( )( ) ( )( ) ( ) 194,0183,07,06595,64394,63,0
1385,00046,06,04394,61,64,04394,6183,06595,69,00046,01,61,0
472,60046,0183,06595,6
3,2
1,3
3,1
3
=+==+=
=++===
agax
t = 4
( ) ( )( )( ) ( ) 194,0194,07,04394,62472,63,0
0427,00359,06,02472,63,64,02472,6194,04394,69,00359,03,61,0
281,60359,0194,04394,6
4,2
1,4
4,1
4
=+==+=
=+==+=
agax
2004 . ( : vt = t-4; kt = 2).
0427,0;1385,0;1508,0;211,0 1,41,31,21,1 ==== gggg 5x , 5- 2-
(k5 = 2), v5 = t l (k5 - 1) = 5-4(2-1) = 1 211,0 1,1155 == gg k .
( ) ( )( )( ) ( ) 204,0194,07,02472,60172,63,0
0799,0211,06,00172,69,54,00172,6194,02472,69,0211,09,51,0
265,6211,0194,02472,6
5,2
2,1
5,1
5
=+==+=
=+==+=
agax
-
95
t = 6
( ) ( )( ) ( )( ) ( ) 203,0204,07,00172,68165,53,0
1371,01508,06,08165,57,54,08165,5204,00172,69,01508,07,51,0
662,51508,0204,00172,6
6,2
2,2
6,1
6
=+==+=
=++===
agax
t = 7
( ) ( )( ) ( )( ) ( ) 188,0203,07,08165,56658,53,0
0506,01385,06,06658,564,06658,5203,08165,59,01385,061,0
475,51385,0203,08165,5
7,2
2,3
7,1
7
=+==+=
=++===
agax
t = 8
( ) ( )( )( ) ( ) 188,0188,07,06658,54761,53,0
0352,00427,06,04761,55,54,04761,5188,06658,59,00427,05,51,0
521,50427,0188,06658,5
8,2
2,4
8,1
8
=+==+=
=++==+=
agax
9x ,
t = 9 3- , k9-1 = 2 v9 = 9-42 = 1,
2,1, 199 gg kv = =0,0799.
368,50799,0188,04761,5 2,18,28,19 =+=++= gaax 0, tvg -
ttt xx = , vt- , vt = 1, 2,, l.
- tx 2.2 2.14, - xt.
-
96
-
5,00
5,50
6,00
6,50
7,00
7,50
0 2 4 6 8 10
2.14.
-
. . 1. ,
-. 2. . 3. , -
, .
-
97
3.
-
, . , , , - , . . , - , , -.
- Statistica. , - - .
- - . , , .. , -, .
: -
, .
, .
30 - . , , .
-
98
: 1 ( ); 2 1 , , ( ); 3 ( ); 4 () ( ); 5 ( ); -
.
3.1. 7 Y X1 X2 X3 X4 X5 1 50000 90,3 2600 0,77 0.689 0,58 2 58000 86.4 3000 0,873 0,699 0,58 3 65000 73,2 3900 0,898 0,71 0,58 4 66000 72,1 3900 0,89 0,7 0,58 5 67000 71,3 3900 0,89 0,71 0,59 6 68000 70,9 3900 0,89 0,72 0,6 7 69000 68,7 4000 0,9 0,73 0,6 8 70000 67 4100 0,9 0,74 0,6 9 71000 66 4150 0,9 0,75 0,6 10 72000 65 4160 0,9 0,76 0,6 11 73000 64 4170 0,89 0,77 0,61 12 75000 50,4 4180 0,89 0,78 0,62 13 80000 51,2 4200 0,9 0,79 0,77 14 79000 53,8 4300 0,89 0,8 0,78 15 83000 50,3 4400 0,88 0,81 0,79 16 85000 50 4500 0,9 0,82 0,8 17 79000 55,6 4600 0,88 0,83 0,8 18 83000 53,1 4700 0,88 0,84 0,81 19 86000 50,1 4800 0,89 0,85 0,81 20 89000 49,9 4900 1 0,86 0,83 21 90000 50,8 4900 1 0,87 0,84 22 91000 50,6 4900 1 0,88 0,86
23 90000 51,4 4900 1 0,89 0,9
24 91000 52,3 5000 1 0,9 1
25 93000 50 5000 1 0,9 1,1
26 100000 50 5100 1 0,9 1,1
27 100000 51,3 5200 1 0,9 1,1
28 100000 50 5300 1 0,9 1,1
29 110000 50 5400 1 0,9 1,1
30 110000 50 5500 1 0,9 1,1
-
99
3.1.
, 3.1.
3.1. .
STATISTICA Multiple Regression
Switch To. : : - ; - ; Switch to .
, 10 30. Add:
-
100
3.2.
(
6) Delete. , - .
Analysis Resume Analysis Multiple Regression ( 3.3).
3.3. Multiple Regression ( ) Variables . Independent:X1-X5 . Dependent :Y . Input file: . Mode- Standard.
-
101
Variables (-), , , - . - , - 3.4.
3.4.
(dependent) Y (
), (independent) , Y ( ). .
, - - , 3.5.
, , , . , -. , .
. - .
Dep. var. ( ) Y. No of Cases ( , -
). 30.
-
102
Multiple R ( ). R2
( ).
3.5.
, -
.
= (1-R2)*100%. = 15%. , MS Excel
-. . .
-
103
(. 3.5) - Correlations and desc.stats Correla-tions. , - 3.6.
3.6.
,
, : 2,3,4. y ( 0,96; -0,8; 0,95), - - 1.
(. 3.7), 3 , , , .
- . . 0,7, -, , - , .
, - , , 3.5, Regression Summary, , , , 3.8.
-
104
3.8.
3.8
, - 3.5. RI . - F(5,24) = 117,36 - ( 5 24 v1 = 5 v2 = 24). (), :
- ; - (BETA) -; - (St.Err of BETA) -; - (B) , -
; - (St. Err of B)
; - (t(24) ) ,
-.
, , - -43201.
3.8, -
54321 23764952911264843201 x,xx,x,x,y +++= (3.1)
-
105
- ().
1 ( 1) =-48,6 2 ( 2) =12,1 3 ( 3) =-29,5 4 ( 4) =649 5 ( 5) =37,2 ,
, -, , , , - .
, , , , -, . , - , - , , , , .
, - ( , ) ( , ) ( , , -, ).
, , R2 = 0,96 ( 1, ). -.
, 4%.
-. - (F), 3.8. F(5,24) = 117,36. FP , 5 v1=5 v2 = 24 FT = 2,62.
FP > FT.
-
106
(117,36 > 2,62). - .
1. F-
- , - ..
2. F- , - . , .
3. F- , - . .
, , , - , .
-
, . , ? -
, 3.8, 6 (t(24)) - . ( 1,2 5 ).
, 5, , - .
, - .
(. 3.9) - 1,2,3,4 ( y).
3.10, - 3, -, 1 .
-
107
3.9.
. -
3.10.
-
108
Regression Summary, -
-, , 3.11.
3.11.
( - )
4321 63932741295438995 xx,x,x,y ++= . (3.2)
, ,
, -, -, .
. , - , RI (R2) 0,96. , - - 4%. 5 ( , , - , - 1 ).
, , v1 = 4 v2 = 25 FP > FT (143,75 > 2,76). 3, .
-
109
3.12.
3 .
3.13. , -
: - 1 ; - 2 1 () ; - 4 .
3.13.
-
110
.
3.14.
421 807112756958261 xx,x,,y ++= (3.3) , , -
-, , - . , - , - . - , 1 .
, , - RI =0,96, . , - , 4%. - , , FP > FT, ( v1=3 v2 = 26 143,75 > 2,98). .
, -
421 807112756958261 xx,x,,y ++= (3.4)
-
111
3.2. .
Mode Fixed non linear ( ). .
3.15.
, , -
, . - ().
3.16.
-
112
- 1,2,4, , , . . , , . - , .
3.17.
. -
; (Method) Standart Variables.
3.18.
-
113
Variables. .
3.19.
, 3.19,
(Dependent) , V2**2,V3**2,V5**2, , - 12,22,42. ,
- V2**2 - 12; - V3**2 - 22; - V5**2 - 42. ,
, (. 3.20).
, - .
3.20.
-
114
Regression summary Y
3.21.
Y , -
, - RI = 0,97, , , . , 3%. , , FP > FT ( v1 = 3 v2 = 26 256,34 > 2,98), , 12.
24
22
21 11200202309217831 x,x,x,,y ++= (3.5)
, , -
, , : , , , -.
, , - 12.
-
115
24
22 6110020418480 x,x,,y ++= (3.6)
3.22.
3.23
Y
(RI = 0,96), 4%. , FP > FT ( v1=2 v2 = 27 - 351,18 > 3,35), , 42. , - (. 3.24).
22003,017,29612 xy += (3.7)
-
116
3.24
3.25 Y , -
. , - , - (. 3.26 3.27).
3.24, . RI = 0,96, 4% -. , , - . , 2 (- ).
-
117
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4.
STATISTICA NEURAL NETWORKS
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4.1. Statistica Neural Networks
4.1.1.
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1. - Create Data Set - Data Set... - - File-New.
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123
4.1.
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124
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4.1.6.
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127
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128
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-
129
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4.1.10.
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4.1.11.
-
130
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4.1.12. - Trainig Graph
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4.6.
ST Neural Networks -
- Case Errors, - - Case Errors - Statistics
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-
131
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ST Neural Networks -:
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-
132
4.2.1.
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ST Neural Networks ( - - Outputs Shown). Variables.
-
133
4.2.2.
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-
134
4.2.3. -
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4.3.
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TISTICA Neural Networks Open Data Set - SERIES_G.
-
135
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4.3.1.
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4.11.
Intelligent Problem Solver-Basic or Advanced
( 4.12) Advanced ( , -) Next.
-
136
. - .
4.12. - -
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141
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142
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143
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-
144
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( Next) Intelligent Problem Solver Results Shown, - 4.22, :
- ; - ; - () ; - . . Finish.
-
145
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: 4.23 - 4.26.
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146
4.24 , , 10 .
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4.26 Network Illustration, -
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STATISTICA Neural Networks STA-TISTICA Neural Networks Open Data Set - SERIES_G.FileNewNetwork.
4.27 - Create Network.
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-
148
4.27.
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4.28.
4.28.
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-
150
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4.29.
4.30.
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-
151
2.2. : TrainMultilayer PerceptronBack Propagation ( 4.30).
2.3. : Statistics Case Errors ( 4.31).
4.31.
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152
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ST Neural Networks - , - .
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153
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7.1. : Run Run Single Case Case No ( , ) Run Output -.
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-
155
4.34.
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4.36.
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-
157
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4.37.
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-
158
4.39.
4.40.
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Case Errors. - Regression Statistics. , .
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-
159
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4.5.3.
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160
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161
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162
- Data Set Editor.
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4.41.
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163
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164
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165
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166
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