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4.
1
1 1.
1.1. Y ( ).
. .1. . 3.
3
xi | |||||||
yi |
. 1 . , . Y .
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. 1
1.2. Y :
=b0+ b1x. | (1) |
. :
(2)
. 3 , (2).
4
xi | yi | x2 | xiyi | (xi- )2 | xi | ei2=( xi-yi)2 |
5,90 | 1,97 | 0,00 | ||||
5,90 | 1,97 | 1,06 | ||||
2,04 | 3,51 | 0,22 | ||||
0,18 | 5,05 | 0,00 | ||||
0,32 | 6,59 | 2,53 | ||||
2,46 | 8,13 | 1,28 | ||||
20,88 | 12,75 | 1,56 | ||||
37,68 | 6,65 |
(3) |
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:
b1= (27,86-3,43×5,71)/(17,14-3,432) =8,27/5,38=1,54 b0=5,71-1,54×3,43=0,43 =0,43+1,54x. |
1.3. XY.
. (. . 1), (0; 0,43) (8,00; 12,75).
1.4. , (, ).
. .1 , ( =3,43; =5,71). : =0,43+1,54×3,43 = 5,71, .
1.5. 1.
. 1 (100 2) b1= 1,54 (.. 15400 ./).
1.6. .
. b0=0,43 , .. .
1.7. X Y.
. :
(4)
,
( ) .
1.8. "" =11 (, 1100 2).
. .1 :
=0,43+1,54×11=17,37 (173700 ./)
1.9, ) 95%- .
. =11(Y) 17,37. =11, .
(. . 4, 4-6):
k = n 2 = 7 2 = 5. . 2 t0,95;5=2,57 . 95%- "":
: 17,37-2,57×1,48=13,57.
: 17,37+2,57×1,48=21,37.
:
13,57 £ Mx(Y) £ 17,37.
1.9, ). 95%- xo=11.
. o=11, :
: 17,37-2,57×1,88=12,54.
: 17,37+2,57×1,88=22,20.
:
12,54 £ £ 22,20.
, . :
=(R/ )100%= ((22,2-12,54)/17,37)100%=55,6%.
1.10, ) 0,95 b1.
. :
b1-D £ b1 £ b1+D,
: 1,54-0,48=1,06.
: 1,54+0,48=2,02.
:
1,06 £ b1 £ 2,02.
1.10, ) 0,95 s2.
. .3 ( ) -:
:
|
|
1.11, ) a=0,05 Y .
. .
:
Q=å(yi- )2=13,77+7,35+2,93+0,51+0,51+1,67+68,73= 95,47.
:
QR=å( i- )2=13,99+13,99+4,84+0,44+0,78+8,56+49,56=92,16.
: Qe=å( i-)2=6,65 (. . 4).
:
, F > Fa,k1,k2, k1=m-1=2-1=1, k2=n-m=7-2=5. . 4 F0,05;1;5=6,61. 69,66 > 6,61, : b1 =1,54 .
1.11, ) a=0,05 Y .
. , t>t. :
. 2 t.=t0,95;7-2=5=2,57. 8,22 > 2,57, ( : β1=0) 1: .
1.12. R2 : .
. : R2= QR/Q = 92,16 / 95,47 = 0,97. R2 , . : 97%.
2
2 . 1 2.
2.1) 2 ( ).
. . 1 2. . 2 , 2. .
15 | |||||||
2 | |||||||
. 2
2.2. ( ).
. . . 2.4.
2.3. .
. . . 2.4.
2.4. .
.
2.5. ()-1.
. : = . -1. :
- ,
, .
=7×120×79+24×96×21+21×96×24-21×120×21-96×96×7-79×24×24=192.
:
11 = 120 × 79 96 × 96 =264; | 12 = -(24 × 79 96 × 21) = 120; |
13 = 24 × 96 120 × 21 = -216; | 21 = -(24 × 79 21 × 96) = 120; |
22 = 7 × 79 - 21 × 21 = 112; | 23 = -(7 × 96 24 × 21)= -168; |
31 = 24 × 96 21 × 120 = -216; | 32 = -(7 × 96 21 × 24) = -168; |
33 = 7 × 120 24 × 24 = 264. |
:
. , :
-1 = .
1/192 .
, , .
2.6. .
.
2.7. Y 1 2 =b0+ b1 1 + + b22 (.)-1 , .. b=()-1 .
.
, : b0 = -0,88; b1 = 0,50; b2 = 1,63. : = -0,88 + 0,50x1 + 1,63x2.
2.8. b1.
|
|
. 1 b1=1,54, b1=0,50. , .
2.9. .
. , :
1 1% 0,30%. 2 1% 0,86%.
2.10. "" 1=11 (1100 2) 2 = 8 (80 ).
. :
= -0,88 + 0,50 × 11 + 1,63 × 8 = 17,66.
2.11, ) 95%- "".
. (Y), . O (Y) (11, 8) = 17,66. (Y) s2:
. 5.
5
i | xi1 | xi2 | yi | ei | ||
1,25 | 0,75 | 0,56 | ||||
2,88 | 0,12 | 0,02 | ||||
3.38 | 0,62 | 0,39 | ||||
5.51 | -0,51 | 0,26 | ||||
6,01 | -1,01 | 1,02 | ||||
8,14 | -1,14 | 1,30 | ||||
12,90 | 1,10 | 1,21 | ||||
∑ | 40,07 | -0,07 | 4,76 |
:
. 2 t0,95; 7-2-1=5 = 2,78. D = t0,95; 5∙ = 2,78 × 1,46 = 4,05.
: min = Xo - D = 17,66 - 4,05 = 13,61.
: m = Xo + D = 17,66 + 4,05 = 21,71. Xo: 13,61 £ o(Y) £ 21,71. , .
2.11, ) 95%- "" .
. :
D = 2,78 × 1,82 = 5,06. : min = 17,66 - 5,06 = 12,60 max = 17,66 + 5,06 = 22,72. : 12,60 £ £ 22,72. , .
2.12. .
. :
-1.
: sb1 = 1,09 = 1,28; sb2 =1,09 = 0,83.
t = çb1ç/ sb1 = 0,50/1,28 = 0,39 < t0,95;4 = 2,78, b1 ( ).
t = çb2ç/ sb2 = 1,63/0,83 = 1,96 < t0,95;4 = 2,78, b2 5%- .
2.13. 0,95 b1 b2 s2.
. : bj + t1-a,n-p-1sbj £ bj £ bj + t1-a,n-p-1sbj.
, .
2.14. a=0,05.
. :
;
, ( ):
F = R2 (n-p-1)/(1- R2) p > Fa;k1;k2.
F = 0,96(7-2-1)/(1-0,962)2 = 24,62 > F0,05;2;4.
: .
2.15. , .
. : R2 = 0,97 R2 = 0,96. . .
3
3 . 1 2.
3.1. . 1 t (. . 6 . 3).
6
t1 | |||||||
yi |
3.2. st, (. 3, . 6).
st = 3,69 | ||||||||
st = 3,69 | ||||||||
T | ||||||||
. 3
3.3. τ = 1;2.
.
τ = 1 :
. . 7. :
r(2), . . 8:
7
τ = 1
t | y(t) | y(t+τ) | y(t)- ( =5,72) | y(t+τ)- | (y(t)- ) (y(t+τ)- ) | (y(t)- )2 |
-3,72 | -2,72 | 10,12 | 13,84 | |||
-2,72 | -1,72 | 4,68 | 7,40 | |||
-1,72 | -0,72 | 1,24 | 2,96 | |||
-0,72 | -0,72 | 0,52 | 0,52 | |||
-0,72 | 1,28 | -0,92 | 0,52 | |||
1,28 | 8,28 | 10,60 | 1,64 | |||
- | - | - | - | - | 68,56 | |
- | - | 26,23 | 95,43 |
8
τ = 2
t | y(t) | y(t+τ) | y(t)- ( =5,72) | y(t+τ)- | (y(t)- ) (y(t+τ)- ) | (y(t)- )2 |
-3,72 | -1,72 | 6,40 | 13,84 | |||
-2,72 | -0,72 | 1,96 | 7,40 | |||
-1,72 | -0,72 | 1,24 | 2,96 | |||
-0,72 | 1,28 | -0,92 | 0,52 | |||
-0,72 | 8,28 | -5,96 | 0,52 | |||
- | - | - | - | - | 1,64 | |
- | - | - | - | - | 68,56 | |
- | - | 2,71 | 95,43 |
3.4. (0,00; 1,00), (1,00; 0,32), (2,00; 0,10) .
. . . 4.
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. 4.
5. ""
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