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2633.7
1478.9
-31.2
1980
4545.624
3007.9
1599.7
-27.6
1981
4891.561
3361.5
1630.2
-0.1
1982
5323.351
3714.8
1784.2
56.3
1983
5962.652
4126.4
2039
16.5
1984
7208.052
4846.3
2515.1
-40
1985
9016.037
5986.3
3457.5
-448.9
1986
10275.18
6821.8
3941.9
-416.2
1987
12058.62
7804.6
4462
-144.2
1988
15042.82
9839.5
5700.2
-288.4
1989
16992.32
11164.2
6332.7
-243.9
1990
18667.82
12090.5
6747
411.5
1991
21781.5
14091.9
7868
428.4
1992
26923.48
17203.3
10086.3
233
1993
35333.92
21899.9
15717.7
-701.4
1994
48197.86
29242.2
20341.1
461.7
1995
60793.73
36748.2
25470.1
1403.7
1996
71176.59
43919.5
28784.9
1019
1997
78973.03
48140.6
29968
3354.2
1998
84402.28
51588.2
31314.2
3597.5
1999
89677.05
55636.9
32951.5
2423.4
2000
99214.55
61516
34842.8
1995.6
2001
109655.2
66933.9
39769.4
1865.2
2002
120332.7
71816.5
45565
2517.6
2003
135822.8
77685.5
55963
2092.3
2004
159878.3
87552.6
69168.4
2667.5
2005
184937.4
99051.3
77856.9
8374.4
2006
216314.4
112631.9
92954.1
14217.7
2007
265810.3
131510.2
110943.2
20171.1
2008
314045.4
152346.6
138325.3
20868.4
2009
340506.9
165526.8
164463.5
13411.3
注:
Y为国内生产总值;
X2为消费;
X3为投资;
X4为净出口额;
单位均为亿元。
五、模型的估计与调整
1、对整个模型进行估计
DependentVariable:
Y
Method:
LeastSquares
Date:
05/29/11Time:
10:
36
Sample:
19782009
Includedobservations:
32
Variable
Coefficient
Std.Error
t-Statistic
Prob.
C
-478.2347
414.0969
-1.154886
0.2579
1.017517
0.031113
32.70416
0.0000
0.956819
0.037723
25.36414
1.211299
0.103751
11.67511
R-squared
0.999794
Meandependentvar
80670.91
AdjustedR-squared
0.999772
S.D.dependentvar
94125.31
S.E.ofregression
1422.649
Akaikeinfocriterion
17.47490
Sumsquaredresid
56670053
Schwarzcriterion
17.65811
Loglikelihood
-275.5984
F-statistic
45223.91
Durbin-Watsonstat
1.268534
Prob(F-statistic)
0.000000
Y=-478.2347+1.017517X2+0.956819X3+1.211299X4
(414.0969)(0.031113)(0.037723)(0.103751)
T=(-1.154886)(32.70416)(25.36414)(11.67511)
R²
=0.999772
可知:
A、解释变量与被解释变量同向变动,且均为正值,符合经济含义
B、被解释变量有99.9772%由解释变量解释,具有很高的拟合优度。
C、若显著性水平α=0.05,由t分布表可查出自由度为n-4=28的临界值t0.025(28)=2.048。
由于解释变量参数的T值均大于t0.025,拒绝原假设接受备择假设,认为解释变量对被解释变量有显著性影响。
2.多重共线性检测:
06/01/11Time:
15:
26
-8229.111
2259.757
-3.641591
0.0010
1.999609
0.035278
56.68218
0.990749
0.990441
9202.854
21.15288
2.54E+09
21.24449
-336.4460
3212.869
0.111303
11:
24
6099.144
2031.480
3.002316
0.0054
2.218944
0.038004
58.38696
0.991277
0.990986
8936.528
21.09414
2.40E+09
21.18575
-335.5063
3409.037
0.614109
25
34868.18
7893.575
4.417286
0.0001
14.77141
1.213264
12.17494
0.831677
0.826067
39255.27
24.05402
4.62E+10
24.14563
-382.8643
148.2291
0.680675
经比较可知:
X3的拟合优度为0.990986大于X2和X4且X2>
因此,检验多重共线性:
在X3的基础上,先加入一个解释变量X2得:
30
-1584.425
959.5243
-1.651261
0.1095
0.990680
0.073855
13.41383
1.136999
0.081934
13.87694
0.998789
0.998706
3386.323
19.18194
3.33E+08
19.31935
-303.9110
11960.84
1.272850
可知拟合优度为0.998706>
0.990986,且T值通过检验,选择保留X2
于是,再加入一个解释变量X4得
可知拟合优度为0.999772>
0.998706且经济含义和T值均通过检验,所以不存在多重共线性
3.异方差的检验
WhiteHeteroskedasticityTest:
F-statistic
5.614322
Probability
0.000839
Obs*R-squared
18.36811
0.005375
TestEquation:
RESID^2
37
-283090.3
852367.5
-0.332122
0.7426
-40.16258
137.0357
-0.293081
0.7719
X2^2
-0.002043
0.001322
-1.545750
0.1347
234.7806
192.4579
1.219906
0.2339
X3^2
0.000454
0.001026
0.442391
0.6620
1401.119
496.7498
2.820573
0.0093
X4^2
-0.030934
0.020452
-1.512495
0.1429
0.574004
1770939.
0.471764
3004554.
2183704.
32.22158
1.19E+14
32.54221
-508.5453
3.118247
NR²
=18.36811>
x^2(0.05)(9)(卡方分布)=16.9190,表明模型中存在异方差。
4.异方差的修正
当权重为W1=1/X2、W2=1/x2^2、W3=1/sqr(X2)、W4=1/X3、W5=1/x3^2、W6=1/sqr(X3)、W7=1/X4、W8=1/x4^2、W9=1/sqr(X4)时得:
12:
01
Weightingseries:
1/X2
66.95187
51.48904
1.300313
0.2041
0.917538
0.038649
23.74023
1.082311
0.058950
18.35993
1.026917
0.137304
7.479146
WeightedStatistics
0.975377
15870.67
0.972739
1677.557
276.9823
14.20225
2148137.
14.38547
-223.2360
22681.38
0.666622
UnweightedStatistics
0.999684
0.999650
1761.841
Sumsquaredresid
86914309
1.239213
03
1/X2^2
117.3531
19.09308
6.146368
0.791676
0.021034
37.63723
1.279119
0.042975
29.76450
0.557112
0.106078
5.251922
0.999937
6177.428
0.999931
7390.519
61.54214
11.19379
106048.2
11.37701
-175.1006
21820.14
1.931551
0.999104
0.999008
2964.737
2.46E+08
1.