第五章异方差性作业任务.docx
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第五章异方差性作业任务
5.3为了研究中国出口商品总额EXPORT对国内生产总值GDP的影响,搜集了1990~2015年相关的指标数据,如表5.3所示。
表3中国出口商品总额与国内生产总值(单位:
亿元)
时间
出口商品总额
EXPORT
国内生产总值
GDP
时间
出口商品总额
EXPORT
国内生产总值
GDP
1991
3827.1
22005.6
2004
49103.3
161840.2
1992
4676.3
27194.5
2005
62648.1
187318.9
1993
5284.8
35673.2
2006
77597.2
219438.5
1994
10421.8
48637.5
2007
93627.1
270232.3
1995
12451.8
61339.9
2008
100394.9
319515.5
1996
12576.4
71813.6
2009
82029.7
349081.4
1997
15160.7
79715.0
2010
107022.8
413030.3
1998
15223.6
85195.5
2011
123240.6
489300.6
1999
16159.8
90564.4
2012
129359.3
540367.4
2000
20634.4
100280.1
2013
137131.4
595244.4
2001
22024.4
110863.1
2014
143883.7
643974.0
2002
26947.9
121717.4
2015
141166.8
685505.8
2003
36287.9
137422.0
资料来源:
《国家统计局网站》
(1)根据以上数据,建立适当线性回归模型。
(2)试分别用White检验法与ARCH检验法检验模型是否存在异方差?
(3)如果存在异方差,用适当方法加以修正。
解:
(1)
DependentVariable:
Y
Method:
LeastSquares
Date:
04/18/20Time:
15:
38
Sample:
19912015
Includedobservations:
25
Variable
Coefficient
Std.Error
t-Statistic
Prob.
C
-673.0863
15354.24
-0.043837
0.9654
X
4.061131
0.201677
20.13684
0.0000
R-squared
0.946323
Meandependentvar
234690.8
AdjustedR-squared
0.943990
S.D.dependentvar
210356.7
S.E.ofregression
49784.06
Akaikeinfocriterion
24.54540
Sumsquaredresid
5.70E+10
Schwarzcriterion
24.64291
Loglikelihood
-304.8174
Hannan-Quinncriter.
24.57244
F-statistic
405.4924
Durbin-Watsonstat
0.366228
Prob(F-statistic)
0.000000
模型回归的结果:
(2)white:
该模型存在异方差
HeteroskedasticityTest:
White
F-statistic
4.493068
Prob.F(2,22)
0.0231
Obs*R-squared
7.250127
Prob.Chi-Square
(2)
0.0266
ScaledexplainedSS
8.361541
Prob.Chi-Square
(2)
0.0153
TestEquation:
DependentVariable:
RESID^2
Method:
LeastSquares
Date:
04/18/20Time:
17:
45
Sample:
19912015
Includedobservations:
25
Variable
Coefficient
Std.Error
t-Statistic
Prob.
C
-1.00E+09
1.43E+09
-0.700378
0.4910
X^2
-0.455420
0.420966
-1.081847
0.2910
X
102226.2
60664.19
1.685117
0.1061
R-squared
0.290005
Meandependentvar
2.28E+09
AdjustedR-squared
0.225460
S.D.dependentvar
3.84E+09
S.E.ofregression
3.38E+09
Akaikeinfocriterion
46.83295
Sumsquaredresid
2.51E+20
Schwarzcriterion
46.97922
Loglikelihood
-582.4119
Hannan-Quinncriter.
46.87352
F-statistic
4.493068
Durbin-Watsonstat
0.749886
Prob(F-statistic)
0.023110
ARCH检验:
该模型存在异方差
HeteroskedasticityTest:
ARCH
F-statistic
18.70391
Prob.F(1,22)
0.0003
Obs*R-squared
11.02827
Prob.Chi-Square
(1)
0.0009
TestEquation:
DependentVariable:
RESID^2
Method:
LeastSquares
Date:
04/18/20Time:
19:
55
Sample(adjusted):
19922015
Includedobservations:
24afteradjustments
Variable
Coefficient
Std.Error
t-Statistic
Prob.
C
8.66E+08
6.92E+08
1.251684
0.2238
RESID^2(-1)
0.817146
0.188944
4.324802
0.0003
R-squared
0.459511
Meandependentvar
2.37E+09
AdjustedR-squared
0.434944
S.D.dependentvar
3.90E+09
S.E.ofregression
2.93E+09
Akaikeinfocriterion
46.51293
Sumsquaredresid
1.89E+20
Schwarzcriterion
46.61110
Loglikelihood
-556.1552
Hannan-Quinncriter.
46.53898
F-statistic
18.70391
Durbin-Watsonstat
0.888067
Prob(F-statistic)
0.000273
(3)修正:
加权最小二乘法修正
DependentVariable:
Y
Method:
LeastSquares
Date:
04/18/20Time:
20:
46
Sample:
19912015
Includedobservations:
25
Weightingseries:
W2
Weighttype:
Inversevariance(averagescaling)
Variable
Coefficient
Std.Error
t-Statistic
Prob.
C
10781.17
2188.706
4.925821
0.0001
X
3.931606
0.192004
20.47667
0.0000
WeightedStatistics
R-squared
0.947998
Meandependentvar
51703.40
AdjustedR-squared
0.945737
S.D.dependentvar
11816.72
S.E.ofregression
8420.515
Akaikeinfocriterion
20.99135
Sumsquaredresid
1.63E+09
Schwarzcriterion
21.08886
Loglikelihood
-260.3919
Hannan-Quinncriter.
21.01839
F-statistic
419.2938
Durbin-Watsonstat
0.539863
Prob(F-statistic)
0.000000
Weightedmeandep.
39406.30
UnweightedStatistics
R-squared
0.944994
Meandependentvar
234690.8
AdjustedR-squared
0.942602
S.D.dependentvar
210356.7
S.E.ofregression
50396.82
Sumsquaredresid
5.84E+10
修正后进行white检验:
HeteroskedasticityTest:
White
F-statistic
0.261901
Prob.F(2,22)
0.7720
Obs*R-squared
0.581387
Prob.Chi-Square
(2)
0.7477
ScaledexplainedSS
0.211737
Prob.Chi-Square
(2)
0.8995
TestEquation:
DependentVariable:
WGT_RESID^2
Method:
LeastSquares
Date:
04/18/20Time:
20:
41
Sample:
19912015
Includedobservations:
25
Collineartestregressorsdroppedfromspecification
Variable
Coefficient
Std.Error
t-Statistic
Prob.
C
71441488
22046212
3.240534
0.0038
X*WGT^2
-2711.961
5055.773
-0.536409
0.5971
WGT^2
13536351
20714871
0.653461
0.5202
R-squared
0.023255
Meandependentvar
65232673
AdjustedR-squared
-0.065539
S.D.dependentvar
61762160
S.E.ofregression
63753972
Akaikeinfocriterion
38.89113
Sumsquaredresid
8.94E+16
Schwarzcriterion
39.03739
Loglikelihood
-483.1391
Hannan-Quinncriter.
38.93170
F-statistic
0.261901
Durbin-Watsonstat
0.898907
Prob(F-statistic)
0.771953
修正后的模型为
5.4表5.4的数据是2011年各地区建筑业总产值(X)和建筑业企业利润总额(Y)。
表5.4各地区建筑业总产值(X)和建筑业企业利润总额(Y)(单位:
亿元)
地区
建筑业总产值X
建筑业企业利润总额Y
地区
建筑业总产值X
建筑业企业利润总额Y
北京
6046.22
216.78
湖北
5586.45
231.46
天津
2986.45
79.54
湖南
3915.02
124.77
河北
3972.66
127.00
广东
5774.01
251.69
山西
2324.91
49.22
广西
1553.07
26.24
内蒙古
1394.68
105.37
海南
255.47
6.44
辽宁
6217.52
224.31
重庆
3328.83
155.34
吉林
1626.65
89.03
四川
5256.65
177.19
黑龙江
2029.16
58.92
贵州
824.72
14.39
上海
4586.28
166.69
云南
1868.40
61.88
江苏
15122.85
595.87
西藏
124.47
5.75
浙江
14907.42
411.57
陕西
3216.63
104.38
安徽
3597.26
127.12
甘肃
925.84
29.33
福建
3692.62
126.47
青海
319.42
8.35
江西
2095.47
62.37
宁夏
427.92
11.25
山东
6482.90
291.77
新疆
1320.37
27.60
河南
5279.36
200.09
数据来源:
国家统计局网站
根据样本资料建立回归模型,分析建筑业企业利润总额与建筑业总产值的关系,并判断模型是否存在异方差,如果有异方差,选用最简单的方法加以修正。
解:
散点图:
建立线性回归模型:
DependentVariable:
Y
Method:
LeastSquares
Date:
04/18/20Time:
21:
16
Sample:
131
Includedobservations:
31
Variable
Coefficient
Std.Error
t-Statistic
Prob.
C
2.368138
9.049371
0.261691
0.7954
X
0.034980
0.001754
19.94530
0.0000
R-squared
0.932055
Meandependentvar
134.4574
AdjustedR-squared
0.929712
S.D.dependentvar
129.5145
S.E.ofregression
34.33673
Akaikeinfocriterion
9.972649
Sumsquaredresid
34191.33
Schwarzcriterion
10.06516
Loglikelihood
-152.5761
Hannan-Quinncriter.
10.00281
F-statistic
397.8152
Durbin-Watsonstat
2.572841
Prob(F-statistic)
0.000000
white检验:
HeteroskedasticityTest:
White
F-statistic
26.00369
Prob.F(2,28)
0.0000
Obs*R-squared
20.15100
Prob.Chi-Square
(2)
0.0000
ScaledexplainedSS
40.83473
Prob.Chi-Square
(2)
0.0000
TestEquation:
DependentVariable:
RESID^2
Method:
LeastSquares
Date:
04/18/20Time:
21:
19
Sample:
131
Includedobservations:
31
Variable
Coefficient
Std.Error
t-Statistic
Prob.
C
498.3340
559.4185
0.890807
0.3806
X^2
4.51E-05
1.45E-05
3.110610
0.0043
X
-0.158176
0.221918
-0.712768
0.4819
R-squared
0.650032
Meandependentvar
1102.946
AdjustedR-squared
0.625035
S.D.dependentvar
2412.791
S.E.ofregression
1477.458
Akaikeinfocriterion
17.52580
Sumsquaredresid
61120730
Schwarzcriterion
17.66457
Loglikelihood
-268.6499
Hannan-Quinncriter.
17.57104
F-statistic
26.00369
Durbin-Watsonstat
2.732318
Prob(F-statistic)
0.000000
模型存在异方差
模型修正:
加权最小二乘法
DependentVariable:
Y
Method:
LeastSquares
Date:
04/18/20Time:
21:
24
Sample:
131
Includedobservations:
31
Weightingseries:
W2
Weighttype:
Inversevariance(averagescaling)
Variable
Coefficient
Std.Error
t-Statistic
Prob.
C
0.020734
1.351842
0.015338
0.9879
X
0.034505
0.002445
14.11049
0.0000
WeightedStatistics
R-squared
0.872866
Meandependentvar
19.08548
AdjustedR-squared
0.868482
S.D.dependentvar
6.416052
S.E.ofregression
6.525709
Akaikeinfocriterion
6.651717
Sumsquaredresid
1234.962