第五章异方差性.docx
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第五章异方差性.docx
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第五章异方差性
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.Errort-Statistic
Prob.
C
-673.0863
15354.24-0.043837
0.9654
X
4.061131
0.20167720.13684
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:
A
Y673.08634.0611Xi
t(0.0438)(20.1368)
R20.9463,n25
(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:
RESIDE
Method:
LeastSquares
Date:
04/18/20Time:
17:
45
Sample:
19912015
Includedobservations:
25
Variable
Coefficient
Std.Errort-Statistic
Prob.
C
-1.00E+09
1.43E+09-0.700378
0.4910
XA2
-0.455420
0.420966-1.081847
0.2910
X
102226.2
60664.191.685117
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:
RESIDA2
Method:
LeastSquares
Date:
04/18/20Time:
19:
55
Sample(adjusted):
19922015
Includedobservations:
24afteradjustments
Variable
Coefficient
Std.Errort-Statistic
Prob.
C
8.66E+08
6.92E+081.251684
0.2238
RESIDA2(-1)
0.817146
0.1889444.324802
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
却WFWoricflil-riUTLECiidtle^cJ\
i«Tt"lt-| H L日芦£臼电*电引OdiJ10*左(■203>5 r^lucilifl-MI^ITGR1Z7QISw=—T,皿”= eBa^-oa山口fE=-UHap-oe=-口曰3.21且-口9IB之与尸-口口ti.3-Z2E-DO出q,峙尸・C旦(4.3-1E-O^ 303IE09N.HMUO-QI立o右匚 >-nO 4TDE--WZ.&15^=-DC 1hi-tiE-"IIIJi.umrciQsj^F-iiii旦日二-①口 DependentVariable: Y Method: LeastSquares Date: 04/18/20Time: 20: 46 Sample: 19912015 Includedobservations: 25 Weightingseries: W2 Weighttype: Inversevariance(averagescaling) Variable Coefficient Std.Errort-Statistic Prob. C 10781.17 2188.7064.925821 0.0001 X 3.931606 0.19200420.47667 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_RESIDA2 Method: LeastSquares Date: 04/18/20Time: 20: 41 Sample: 19912015 Includedobservations: 25 Collineartestregressorsdroppedfromspecification Variable Coefficient Std.Errort-Statistic Prob. C 71441488 220462123.240534 0.0038 X*WGTA2 -2711.961 5055.773-0.536409 0.5971 WGTA2 13536351 207148710.653461 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 A Y10781.173.931606Xi t(4.925821)(20.47667) R20.9480,n25 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 Variablei Coefficient Std.Errort-Statistic Prob. C 2.368138 9.0493710.261691 0.7954 X 0.034980 0.00175419.94530 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 40.83473Prob.Chi-Square (2) 0.0000 TestEquation: DependentVariable: RESIDA2 Method: LeastSquares Date: 04/18/20Time: 21: 19 Sample: 131 Includedobservations: 31 Variable Coefficient Std.Errort-Statistic Prob. C 498.3340 559.41850.890807 0.3806 XA2 4.51E-05 1.45E-053.110610 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) VariableCoefficientStd.Errort-StatisticProb. C0.0207341.3518420.0153380.9879 X0.0345050.00244514.110490.0000 WeightedStatistics R-squared0.872866Meandependentvar19.08548 AdjustedR-squared 0.868482 S.D.dependentvar 6.416052 S.E.ofregression 6.525709 Akaikeinfocriterion 6.651717 Sumsquaredresid 1234.962 Schwarzcriterion 6.744233 Loglikelihood -101.1016 Hannan-Quinncriter. 6.681875 F-statistic 199.1059 Durbin-Watsonstat 2.201198 Prob(F-statistic) 0.000000 Weightedmeandep. 9.525906 UnweightedStatistics R-squared 0.930826 Meandependentvar 134.4574 AdjustedR-squared 0.928441 S.D.dependentvar 129.5145 S.E.ofregression 34.64582 Sumsquaredresid 34809.66 Durbin-Watsonstat 2.531761 加权后进行white检验: HeteroskedasticityTest: White F-statistic 0.224402 Prob.F(2,28) 0.8004 Obs*R-squared 0.489051 Prob.Chi-Square (2) 0.7831 ScaledexplainedSS 1.141138 Prob.Chi-Square (2) 0.5652 TestEquation: DependentVariable: WGT_RESIDA2 Method: LeastSquares Date: 04/18/20Time: 21: 25 Sample: 131 Includedobservations: 31 Collineartestregressorsdroppedfromspecification Variable Coefficient Std.Errort-Statistic Prob. C 28.90647 24.350741.187088 0.2452 X*WGTA2 0.074634 0.1114710.669539 0.5086 WGTA2 -9.628706 15.02003-0.641058 0.5267 R-squared 0.015776 Meandependentvar 39.83747 AdjustedR-squared -0.054526 S.D.depen
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