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9.260.556.804.253.7030
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………………
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g
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110
xy
-0.2 0 0.2 0.4 0.6
7
7.5
8
8.5
9
9.5
10
x
1
y
εββββ ++++=
2
2322110
xxxy
εβββ +++=
2
22210
xxy
5 5.5 6 6.5 7 7.5
7
7.5
8
8.5
9
9.5
10
x
2
y
x
1
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2
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dM
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)
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0
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1
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2
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3
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M
MATLAB d9y Q
? p3
[b,bint,r,rint,stats]=regress(y,x,alpha)
{ ?
εββββ ++++=
2
2322110
xxxy
b~β￥9′
?
y,x
1
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2
9 β
bint~b￥?? uW
y~n?
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x= ~n×4
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2
221
xxx
r ~?μ_
y-xb
rint~r￥?? uW
alpha(??
￡
ü,0.05)
?
?
9′ ?? uW
17.3244 [5.7282 28.9206]
1.3070 [0.6829 1.9311 ]
-3.6956 [-7.4989 0.1077 ]
0.3486 [0.0379 0.6594 ]
R
2
=0.9054 F=82.9409 p=0.0000
β
0
β
1
β
2
β
3
Stats~
_d9
R
2
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2Ts
y￥ 90.54% V?
? ??
?
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17.3244 [5.7282 28.9206]
1.3070 [0.6829 1.9311 ]
-3.6956 [-7.4989 0.1077 ]
0.3486 [0.0379 0.6594 ]
R
2
=0.9054 F=82.9409 p=0.0000
β
0
β
1
β
2
β
3
εββββ ++++=
2
2322110
xxxy
Fù?V F_￥
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pùl? α=0.05
β
2
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2
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(?￡| )
g
r
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??95%
K¨T oi5 ?￥
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3
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r- 7.8320×3.7≈ 29
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x
1
x
2
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εββββ ++++=
2
2322110
xxxy
εβββββ +++++=
214
2
2322110
xxxxxy
?
?
9′ ?? uW
17.3244 [5.7282 28.9206]
1.3070 [0.6829 1.9311 ]
-3.6956 [-7.4989 0.1077 ]
0.3486 [0.0379 0.6594 ]
R
2
=0.9054 F=82.9409 p=0.0000
β
0
β
1
β
2
β
3
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29.1133 [13.7013 44.5252]
11.1342 [1.9778 20.2906 ]
-7.6080 [-12.6932 -2.5228 ]
0.6712 [0.2538 1.0887 ]
-1.4777 [-2.8518 -0.1037 ]
R
2
=0.9209 F=72.7771 p=0.0000
β
3
β
0
β
1
β
2
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1
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2
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xxxy ββββ +++=
uW [7.8230 8.7636]
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uW [7.8953 8.7592]
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x
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1
y
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8.5
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221.0
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1.03.0
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MATLAB?μ
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443322110
xaxaxaxaay
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M?
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?
?
9′ ?? uW
a
0
11032 [ 10258 11807 ]
a
1
546 [ 484 608 ]
a
2
6883 [ 6248 7517 ]
a
3
-2994 [ -3826 -2162 ]
a
4
148 [ -636 931 ]
R
2
=0.957 F=226 p=0.000
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6883
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=
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1 2 3 4 5 6
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1
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0 5 10 15 20
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0
1000
2000
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1000
2000
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426325443322110
xxaxxaxaxaxaxaay
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2
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3
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4
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0 5 10 15 20
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1 2 3 4 5 6
-1000
-500
0
500
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a
0
11204 [11044 11363]
a
1
497 [486 508]
a
2
7048 [6841 7255]
a
3
-1727 [-1939 -1514]
a
4
-348 [-545 –152]
a
5
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a
6
1836 [1571 2101]
R
2
=0.999 F=554 p=0.000
R
2
Fμ?é
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-100
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a
0
11200 [11139 11261]
a
1
498 [494 503]
a
2
7041 [6962 7120]
a
3
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a
4
-356 [-431 –281]
a
5
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a
6
1997 [1894 2100]
R
2
= 0.9998 F=36701 p=0.0000
1 2 3 4 5 6
-200
-100
0
100
200
e ~F
R
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0.957 → 0.999 → 0.9998
F 226 → 554 → 36701
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MATLAB d9y Q
[beta,R,J] = nlinfit (x,y,’model’,beta0)
x
x
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x= ; y= ;
beta0=[195.8027 0.04841];
[beta,R,J]=nlinfit(x,y,’f1’,beta0);
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beta,betaci
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β
1
212.6819 [197.2029
228.1609]
β
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0.0641 [0.0457
0.0826 ]
P/Z￥ Export
{
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50
100
150
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0
50
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150
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β
1
160.2802 [145.8466
174.7137]
β
2
0.0477 [0.0304
0.0650 ]
γ
1
52.4035 [32.4130
72.3941 ]
γ
2
0.0164 [-0.0075
0.0403]
2
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2
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166.6025 [154.4886 178.7164]
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0.0580 [0.0456 0.0703 ]
γ
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42.0252 [28.9419 55.1085]
e￥
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67 47.3443 9.2078 42.7358 5.4446
51 47.3443 9.2078 42.7358 5.4446
84 89.2856 9.5710 84.7356 7.0478
…… … … …
191 190.8329 9.1484 189.0574 8.8438
201 190.8329 9.1484 189.0574 8.8438
207 200.9688 11.0447 198.1837 10.1812
200 200.9688 11.0447 198.1837 10.1812
e
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3á9′ ( GNP ) #tN·
(PI) ￥1"
2.06883073.0424.5201.00001185.9195.010
1.95142954.7474.9190.96011077.6166.49
1.78422631.7401.9180.9145992.7144.28
1.63422417.8423.0170.8679944.0149.37
1.50422163.9386.6160.8254873.4133.36
1.40051918.3324.1150.7906799.0122.85
1.32341718.0257.9140.7676756.0125.74
1.25791549.2206.1130.7436691.1113.53
1.15081434.2228.7120.7277637.797.42
1.05751326.4229.8110.7167596.790.91
tN
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1.32341718.0257.9140.7676756.0125.74
1.25791549.2206.1130.7436691.1113.53
1.15081434.2228.7120.7277637.797.42
1.05751326.4229.8110.7167596.790.91
tN
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0
322.7250 [224.3386 421.1114]
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0.6185 [0.4773 0.7596]
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R
2
= 0.9908 F= 919.8529 p=0.0000
ttt
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21
479.8596185.0725.322
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163.4905 [1265.4592 2005.2178]
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0.6990 [0.5751 0.8247]
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2
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033.1009699.04905.163
ttt
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1,2,2
1,1,11
3794.5670333.1009
3930.0699.05623.04905.163
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++=
tt
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xx
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479.8596185.0725.322
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3794.5670333.1009
3930.0699.05623.04905.163
+?
++=
tt
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xx
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B¨1íB
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t
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0 5 10 15 20
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100
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300
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2.06883073.0424.520
1.95142954.7474.919
1.78422631.7401.918
0.7436691.1113.53
0.7277637.797.42
0.7167596.790.91
tN
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3
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t
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t
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2
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xxxy
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2
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xxy
5 5.5 6 6.5 7 7.5
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7.5
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8.5
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MATLAB d9y Q
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2
2322110
xxxy
b~β￥9′
?
y,x
1
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2
9 β
bint~b￥?? uW
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17.3244 [5.7282 28.9206]
1.3070 [0.6829 1.9311 ]
-3.6956 [-7.4989 0.1077 ]
0.3486 [0.0379 0.6594 ]
R
2
=0.9054 F=82.9409 p=0.0000
β
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β
1
β
2
β
3
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R
2
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17.3244 [5.7282 28.9206]
1.3070 [0.6829 1.9311 ]
-3.6956 [-7.4989 0.1077 ]
0.3486 [0.0379 0.6594 ]
R
2
=0.9054 F=82.9409 p=0.0000
β
0
β
1
β
2
β
3
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2
2322110
xxxy
Fù?V F_￥
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2
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xxxy
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214
2
2322110
xxxxxy
?
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17.3244 [5.7282 28.9206]
1.3070 [0.6829 1.9311 ]
-3.6956 [-7.4989 0.1077 ]
0.3486 [0.0379 0.6594 ]
R
2
=0.9054 F=82.9409 p=0.0000
β
0
β
1
β
2
β
3
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29.1133 [13.7013 44.5252]
11.1342 [1.9778 20.2906 ]
-7.6080 [-12.6932 -2.5228 ]
0.6712 [0.2538 1.0887 ]
-1.4777 [-2.8518 -0.1037 ]
R
2
=0.9209 F=72.7771 p=0.0000
β
3
β
0
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1
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a
0
11032 [ 10258 11807 ]
a
1
546 [ 484 608 ]
a
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6883 [ 6248 7517 ]
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a
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1
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0 5 10 15 20
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xxaxxaxaxaxaxaay
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3
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4
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0
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a
0
11204 [11044 11363]
a
1
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a
2
7048 [6841 7255]
a
3
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a
4
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a
5
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a
6
1836 [1571 2101]
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2
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0
100
200
e ~ x
1
?
?
9′ ?? uW
a
0
11200 [11139 11261]
a
1
498 [494 503]
a
2
7041 [6962 7120]
a
3
-1737 [-1818 -1656]
a
4
-356 [-431 –281]
a
5
-3056 [-3171 –2942]
a
6
1997 [1894 2100]
R
2
= 0.9998 F=36701 p=0.0000
1 2 3 4 5 6
-200
-100
0
100
200
e ~F
R
2
0.957 → 0.999 → 0.9998
F 226 → 554 → 36701
?? uWé÷
?μm
Es?è
K?
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??¨
426325443322110
xxaxxaxaxaxaxaay ++++++=
?è 6?5 ? —?aF |?￥,$,?á ' ?1 0
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3
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x
x
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+
=
2
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111
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2
1
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θ
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5.107 [3.539 6.676]
θ
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0.247 [0.176 0.319]
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/
122
== θθβ
8027.195
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11
== θβ
L?
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0 10 20 30 40 50
0
0.005
0.01
0.015
0.02
0.025
1/y
1/x
xy
11
21
θθ +=
0 0.5 1 1.5
0
50
100
150
200
250
x
x
y
+
=
2
1
β
β
x
y
1/x?l
Hμz￥
L? t
] 1/x?v
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9
MATLAB d9y Q
[beta,R,J] = nlinfit (x,y,’model’,beta0)
x
x
y
+
=
2
1
β
β
{ ? x~1M
?
y ~yM
_
beta0~L?
?92T
x= ; y= ;
beta0=[195.8027 0.04841];
[beta,R,J]=nlinfit(x,y,’f1’,beta0);
betaci=nlparci(beta,R,J);
beta,betaci
model ~
?￥f
Móq
beta0 ~ó?￥?
′
beta ~?
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R ~?μ J ~9?
?μ￥ Jacobi ?
{
function y=f1(beta,x)
y=beta(1)*x./(beta(2)+x);
beta￥?? uW
betaci =nlparci(beta,R,J)
dL?
?2Ts
?
?
9′ ?? uW
β
1
212.6819 [197.2029
228.1609]
β
2
0.0641 [0.0457
0.0826 ]
P/Z￥ Export
{
d92T b
??
￥
E3L¤
y￥??′?? uW
:?Sμ s= 10.9337
x
x
y
+
=
2
1
β
β
K?Q?
1
?
? (r?K?
B?
H￥ x′ )1
6831.212
1
=β
0641.0
2
=β
{
7 nlintool ó?o
0 0.5 1 1.5
0
50
100
150
200
250
o ~e
S
+ ~
E2T
0 0.2 0.4 0.6 0.8 1
-50
0
50
100
150
200
250
Q?
?
]B
?? I
nw
í) ?￥?Y
1222
1211
)( xx
xx
y
++
+
=
γβ
γβ
x
x
y
+
=
2
1
β
β
x
1
1?t
i x
2
1B
U?M
x
2
=1V
UüV) ? x
2
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1
^?ü) ?￥K?Q?
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1
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^?ü) ?￥Q?￥?
?
'
2
^ü) ?aQ?￥?
?￥9é′
1222
1211
)( xx
xx
y
++
+
=
γβ
γβ
? p3
¨ nlinfit nlintool
7
,170
0
1
=β,60
0
1
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0
2
=β 01.0
0
2
=γ
?
′
(?
￥s )
o ~e
S
+ ~
E2T
92T??
:?Sμ s= 10.4000
?
?
9′ ?? uW
β
1
160.2802 [145.8466
174.7137]
β
2
0.0477 [0.0304
0.0650 ]
γ
1
52.4035 [32.4130
72.3941 ]
γ
2
0.0164 [-0.0075
0.0403]
2
?? uWc
,? V
ü γ
2
yM
y￥?Y?A÷
üw
í) ?￥T¨??Y?
??
?ü
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ü) ?
12
1211
x
xx
y
+
+
=
β
γβ
1222
1211
)( xx
xx
y
++
+
=
γβ
γβ
e￥
?
92T??
o ~e
S
+ ~
E2T
?ü
) ?
ü) ?
?
?
9′
?? uW
β
1
166.6025 [154.4886 178.7164]
β
2
0.0580 [0.0456 0.0703 ]
γ
1
42.0252 [28.9419 55.1085]
e￥
??
Te??
?? uW?c
,?
:?Sμ s = 10.58511B?
?
{v
B?
?De
???1?
1222
1211
)( xx
xx
y
++
+
=
γβ
γβ
12
1211
x
xx
y
+
+
=
β
γβ
?? uW1
??′ ±
L=′ B?
???′
(B?
?
e
???′
(e
?
67 47.3443 9.2078 42.7358 5.4446
51 47.3443 9.2078 42.7358 5.4446
84 89.2856 9.5710 84.7356 7.0478
…… … … …
191 190.8329 9.1484 189.0574 8.8438
201 190.8329 9.1484 189.0574 8.8438
207 200.9688 11.0447 198.1837 10.1812
200 200.9688 11.0447 198.1837 10.1812
e
?￥?? uW?
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L¨ aμr
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Q?
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3á9′tN·
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5
y ?g'-
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L=g'-DS
3á9′ ( GNP ) #tN·
(PI) ￥1"
2.06883073.0424.5201.00001185.9195.010
1.95142954.7474.9190.96011077.6166.49
1.78422631.7401.9180.9145992.7144.28
1.63422417.8423.0170.8679944.0149.37
1.50422163.9386.6160.8254873.4133.36
1.40051918.3324.1150.7906799.0122.85
1.32341718.0257.9140.7676756.0125.74
1.25791549.2206.1130.7436691.1113.53
1.15081434.2228.7120.7277637.797.42
1.05751326.4229.8110.7167596.790.91
tN
·
S
3
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g'-
Mz
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tN
·
S
3á
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3á9′tN·
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[
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￥
¨?4?′-Wi 1M1
??¨
YíB
?°¤) ?|C?
aT
31?ih"
￥1M1?y ??￥
?
……………………
1.32341718.0257.9140.7676756.0125.74
1.25791549.2206.1130.7436691.1113.53
1.15081434.2228.7120.7277637.797.42
1.05751326.4229.8110.7167596.790.91
tN
·
S
3
á9′
g'-
Mz
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tN
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S
3á
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Mz
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t ~
Mz y
t
~ g'- x
1t
~ GNP,x
2t
~ tN·
x
1t
y
t
x
2t
y
t
g'-D GNP#tN·
W (μ <￥L?1"
tttt
xxy εβββ +++=
22110
β
0
,β
1
,β
2
~íB"
ε
t
~ tMo? ?￥
, (′?
M
'íB
?￥2TDs
?
?
9′ ?? uW
β
0
322.7250 [224.3386 421.1114]
β
1
0.6185 [0.4773 0.7596]
β
2
-859.4790 [-1121.4757 -597.4823 ]
R
2
= 0.9908 F= 919.8529 p=0.0000
ttt
xxy
21
479.8596185.0725.322
+=
:?Sμ
s=12.7164
?a?
R
2
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Eú
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àμ I
n
HW?
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V
-
j
μi 1M1 ?T
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?μ?
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1M1?￥??? ?μ?E
ttt
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=
??μ
T?μ e
t
~e
t-1
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MATLAByT u?
{
e
t
1
μ ε
t
￥9′
-30 -20 -10 0 10 20
-30
-20
-10
0
10
20
e
t-1
e
t
v?s?
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t
i ?￥1M1
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t
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t
i ?￥1M1
1M1?°4
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1íB
?
ttttttt
uxxy +=+++=
122110
,ρεεεβββ
5 ~1M1"
1|| ≤ρ
β
0
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1
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2
~íB"
u
t
~ tMo? ?￥
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M
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i ?1M1?
5 > 0
i μ1M1?
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D-Wd9
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<lμsE
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D D-W_
∑
∑
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=
=
n
t
t
n
t
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2
2
2
1
)(
∑
∑
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=
n
t
t
n
t
tt
e
ee
2
2
2
1
12
ρ
12?=
n?v
≈
∑∑
==
=
n
t
t
n
t
tt
eee
2
2
2
1
/
ρ
401
1 ≤≤→≤≤? DWρ
01
=→= DWρ 41
=→?= DWρ
20
=→= DWρ
DW
4-d
U
44-d
L
d
U
d
L
20
?
1
M
1
μ
1
M
1
?
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í
1
M
1
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￡
ü
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"
D-Ws?V
? DW′￥vl ??1M1?
_
"?′ d
L
d
U
<lμsMD
e
?
ttttttt
uxxy +=+++=
122110
,ρεεεβββ
ρ
12?=DW
2
1
DW
=ρ
,
1
*
=
ttt
yyy ρ 2,1,
1,
*
=?=
ixxx
tiitit
ρ
MD
)1(
0
*
0
ρββ?=
[ β
*
0
,β
1
,β
2
1íB"
￥
YíB
?
?
?
tttt
uxxy +++=
*
22
*
11
*
0
*
βββ
??
D-W
_
í1M1
μ1M1
<l
μs
??N
V?
e
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ê¨
ZE
e
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DW′
g'-?
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∑
∑
=
=
=
n
t
t
n
t
tt
e
ee
DW
2
2
2
2
1
)(
DW
old
=
0.8754
e
?
?μ e
t
"' ?
n=20íB
M
" k=3 α=0.05
e
?μ
?1M1
DW
old
< d
L
°V
5623.02/1
=?= DWρ
"?′ d
L
=1.10,d
U
=1.54
TMD
DW
4-d
U
44-d
L
d
U
d
L
20
?
1
M
1
μ
1
M
1
?
?
?
?
?
?
í
1
M
1
1
*
5623.0
=
ttt
yyy
2,1,5623.0
1,
*
=?=
ixxx
tiitit
g'-?
?￥y ?
1
*
5623.0
=
ttt
yyy 2,1,5623.0
1,
*
=?=
ixxx
tiitit
tttt
uxxy +++=
*
22
*
11
*
0
*
βββ
21
*
0
*
2
*
1
*
,,βββ 9"
?
ttt
xxy
?
?
9′ ?? uW
β
*
0
163.4905 [1265.4592 2005.2178]
β
1
0.6990 [0.5751 0.8247]
β
2
-1009.0333 [-1235.9392 -782.1274]
R
2
= 0.9772 F=342.8988 p=0.0000
98rT
z
:?Sμ
s
new
= 9.8277 < s
old
=12.7164
?
?￥1M1?_
d
U
< DW
new
<4-d
U
?
?
?μ e
t
"' ?
n=19íB
M
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°V
"?′ d
L
=1.08,d
U
=1.53
DW
new
=
1.5751
?
?í1M1?
DW
4-d
U
44-d
L
d
U
d
L
20
?
1
M
1
μ
1
M
1
?
?
?
?
?
?
í
1
M
1
*
2
*
1
*
033.1009699.04905.163
ttt
xxy?+=
?
?
1,2,2
1,1,11
3794.5670333.1009
3930.0699.05623.04905.163
+?
++=
tt
tttt
xx
xxyy
e1
e
SM
B¨1íB
?
?2T1?
ttt
xxy
21
479.8596185.0725.322
+=
'íB
?
B¨1íB
?
1,2,2
1,1,11
3794.5670333.1009
3930.0699.05623.04905.163
+?
++=
tt
tttt
xx
xxyy
B¨1íB
??μ e
t
1'íB
?1l
0 5 10 15 20
-30
-20
-10
0
10
20
?
? e
t
~ * e
? e
t
~ +
?μm1?
0 5 10 15 20
0
100
200
300
400
500
?
t
~ * ?
t
~ +
Em1?
g'-??
? ?g'- y
t
T??359? ?￥S
3á9′ x
1t
tN·
x
2t
7638.469
=
t
y
B¨1íB
?
2.06883073.0424.520
1.95142954.7474.919
1.78422631.7401.918
0.7436691.1113.53
0.7277637.797.42
0.7167596.790.91
tN
·
S
3
á9′
g'-
Mz
?|
tN
·
S
3á
9′
g'-
Mz
?|
!X? t=21
H x
1t
=3312 x
2t
=2.1938
'íB
?
6720.485
=
t
y
B¨1íB
?
7638.469
=
t
y
t
?l
^?? y
t-1
=424.5Vl
á
Discussions
