计量经济学回归模型实验报告.docx
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计量经济学回归模型实验报告
回归模型分析报告
背景意义:
教育是立国之本,强国之基。
随着改革开放的进行、经济的快速发展和人们生活水平的逐步提高,“教育”越来越受到人们的重视。
一方面,人均国内生产总值的增加与教育经费收入的增加有着某种联系,而人口的增长也必定会对教育经费收入产生影响。
本报告将从这两个方
面进行分析。
我国1991年~2013年的教育经费收入、人均国内生产总值指数、年末城镇人口数的统计资
料如下表所示。
试建立教育经费收入Y关于人均国内生产总值指数Xi和年末城镇人口数X2的回归模型,并进行回归分析。
年份
教育经费收入
Y(亿元)
人均国内生产总值指数
X1(1978年=100)
年末城镇人口数
X2(万人)
1991
731.50282
256.67
31203
1992
867.04905
289.72
32175
1993
1059.93744
326.32
33173
1994
1488.78126
364.91
34169
1995
1877.95011
400.6
35174
1996
2262.33935
435.76
37304
1997
2531.73257
471.13
39449
1998
2949.05918
503.25
41608
1999
3349.04164
536.94
43748
2000
3849.08058
577.64
45906
2001
4637.66262
621.09
48064
2002
5480.02776
672.99
50212
2003
6208.2653
735.84
52376
2004
7242.59892
805.2
54283
2005
8418.83905
891.31
56212
2006
9815.30865
998.79
58288
2007
12148.0663
1134.67
60633
2008
14500.73742
1237.48
62403
2009
16502.7065
1345.07
64512
2010
19561.84707
1480.87
66978
2011
23869.29356
1613.61
69079
2012
28655.30519
1730.18
71182
2013
30364.71815
1853.97
73111
资料来源:
中经网统计数据库
根据经济理论和对实际情况的分析可以知道,教育经费收入Y依赖于人均国内生产总值指
数Xi和年末城镇人口数X的变化,因此我们设定回归模型为
应用EViews的最小二乘法程序,输出结果如下表
DcpencieniVana&ie:
YMethod:
LeastSquares
Date:
12C21/15Time:
09:
30
Sample:
19912013
Includedobservations:
23
Variable
Coefficient
StdErmrt-StaUstic
Fran
C
5053.355
lSeSJ772.6S1774
0.0143
对
28.74900
1.81170115,36356
0.0000
X2
-0.398176
0.065569-63&1639
0.0000
R-squared
0999147
Meandependent^ar
9D59.S46
AdjustedR-squarea
O90SD62
SOdependentvar
5050.681
SEofreoression
9005
infocntenon
15.75217
Sumsquaredresid
19558484
Schwarzcriterior
16.90028
Losjiifceiihaod
-189.6500
Hanran-Quinncriter
1578942
F-statistic
911.4038
Durbin-Wabanstat
0.549B16
Prob(F-stalistic)
0.000000
(2.68)(15.9)(-6.1)
R2=0.992=0.99F=911.4
异方差的检验
1.Goldfeld-Quandt检验
Xi和X2的样本观测值均已按照升序排列,去掉中间Xi和X2各5个观测值,
用第一个子样本回归:
DependentVariable:
¥
Method:
LeastSquares
Date:
12/21/15Time:
0933
Sample:
19911999
lreludedobseevations:
9
Variable
Cosffldent
Std.Errort-Statishc
Pron.
C
-3510.568
&73,0425-5.216116
0.0020
5909540
1.58Z5343.734103
0.0097
X2
0.083020
00350552.393285
00538
R-squared
0.993516
Meand«pe
1901.933
AdjustedR-squared
0.991355
S.D.dependent\ar
937J6S9
S.E.ofregression
8721013
Akaikeinfocriterion
1203572
Sumsquaredresid
45633.64
Schwarzcriterion
121Q146
Loglikelihood
-5116074
Harnan-Quinncriter.
1189385
Fatalistic
4597017
Durbin-Watsonstal
1554407
Prob(F-statistic)
&.OOOODO
SSE1=45633.64
用第二个子样本回归:
DependentVariable:
Y
Method:
LeastSquares
Date12/21/15Time:
09:
34
Sample20052C13
Includedobs«r¥atjon»;9
Variable
Coeffideni
StdErrcrt-Statisbc
Prob.
C
170035.6
11006421622022
01557
X1
107£361
47.715122254T&9
00550
X2
-4.748797
2.706982-1754277
Q1299
R^squared
0.987065
Meandependentvar
1820409
AdjustedR-squared
0982753
SDdependentvar
7937917
S.E.ofregression
1049.035
toikeInfocriterion
17.0103+
Sumsquaredresid
6602S9S.
Sctiwancriterion
17.076QS
Loglikelihood
-73.54652
Hannari-Quinncriter.
16.86347
F-statistic
220.9229
Dufbin-Watsonslat
1.923931
Prob(Fatalistic)
Q.OOOOC2
SSE2=6602898
Ho=ut具有同方差,
Hi=ut具有递增型异方差
构造F统计量。
——=114.7>F0.05(9,9)=3.18
所以拒绝原假设,计量模型的随机误差项存在异方差
2.White检验
因为模型中含有两个解释变量,辅助回归式一般形式如下
辅助回归式估计结果如下
HeteraskedastidtyTest:
Whits
F-statistic
2.942706
ProbF(5117)
0.0430
□bs^R-squared
10.&7089
FnsChi'Square(5;
00583
ScaledexplainedSS
6726204
ProD.ChhSquare(S)
0241S
TestEquaiion:
DependentVariable-RESIDA2
Method:
LeastSquares
Date:
12/21/15Time:
09:
38
Sample19512013
Includedobsedations.23
Variable
Coefficient
Sbd.Error
t-Statistic
Prob.
C
-124S2775
30348W
■0.41032S
06S67
X1
-40476.22
72466.12
-0.558681
0.5937
X1A2
-18.91957
2891602
-0.6&4254
0.5217
XFX2
1363340
2.237312
0,609365
0.5503
X2
1057.432
2249.S10
0.474454
0.6412
X2A2
-0020235
0038467
■0.525770
0.6053
Ft-squarea
0.453951
Meatdepenaent^ar
8503689
AdjustedR-s0.305250
S.D.dependentvar
1122691.
S.Eolregression
935081.3
AkaikeinfocdteriQil
30.55411
Sumsquaredresit!
Schwarzcriterion
3085033
Loglikelihood
-345.3723
Hanran-Quinncriter.
30&2061
F-statistic
294270&
Durnin-Watsonstat
2.844510
Prob[F-&tatisticj
0.043027
该回归模型中存在异方差
3.克服异方差
以1/Xi做加权最小二乘估计,
DependentV/ariable:
Y
Method:
LeastSquares
Date:
12121/15Time:
10:
09
Sample:
19912013
Includedobservations:
23
Welghiingseries:
1/K1
TVeighttypeInversevananee(averagescaling)
Variable
Coefficient
&td.Errort-Statisti匚
Prob
C
387B.201
1412.4052745813
0.0125
X1
27.02457
1.6fi2C4216.C6653
0.0000
X2
-f>,345154
0.054423-6.M0397
o.oo&o
WeightedSU1isties
R^squared
0.937992
Meandependentwar
6585.276
AdjustedR-eqiuared
0.99B791
S.D.dependentvar
4981.347
SE.ofregression
7519206
Akaikeinfocriterion
16.20956
Sumsquaredresid
11367925
Schwarzcriterion
16.35767
LogliKelihood
-1834099
Hannan-Quinnenter.
16.24681
F-statistic
8227495
Durbin-Watsofistat
0472689
Prob(Fstatistic)
O.DOOODO
'Aeigtitedm«andep
5093.234
UnweightedStatistics
R-squared
0.9&34^3
Meandependentvar
9059.64&
AdjustedR-squared
□987331
SOdependentvar
9O5O6B1
SEofregression
1010.697
Sumsquaredresid
20754674
Durbin-Watsonstat
0521574
估计的结果还原变量,得
HeteroskedasticityTest讥tin®
F^statistic
2069422
Prob.F(5,17)
0.1197
Obs^'squared
3702330
Prob.CtihSquare⑸
01215
ScaledexplainedSS
3985003
Prob.Chi-Square(S)
Q.5516
TestEquation.
DependentVariable:
WGT
_RESIDJl2
MethodLeastSquares
Date:
12/21/15Time:
1C:
12
Sample:
19912013
indudedobservations:
23
Collineartestregressorsdroppedfromspedficalicn
Variable
GoEfficient
StdlError
l-Stafistic
Frob
C
1113169.
21479597
0.051624
0.9595
WGT*2
157496Z
15S10501
0.529010
0.9210
X忖少WGT也
3.652&92
17.85124
0.205179
03299
X1fiX2*WGTft2
-0137455
1.253073
-0,109702
d.913'3
X2A2*WGTA2
0D03178
0.021253
0.149431
0.3830
X2*WGTn2
-190.9551
1171936
4.162940
08725
R-squared
0.378362
Meandependent*白r
494257.6
adjustedR-squared
0.195527
S.D.dependentsar
556180.0
S.E.ofregression
+98S511
Akaikeinfocriteriun
2S.29746
Sumsqusr^dresid
4,2^12
Schwarzcriterion
29.59368
Loglikelihood
-330.9208
Hannan-Quinncriter.
23.37196
Fatalistit
2D69422
Durbin-Watsonstat
2507731
Prob(F-statistic}
0119712
由上表可知TR2=8.7<⑸=9.236,说明以及克服了异方差性
自相关的检验
1.DW检验
DependentVariable:
Y
Methcd-LeastSquares
Datat12/21/15Time-10:
08
Samiple:
19912013
Indudedobservations:
23
Weightingseries:
1W11
Weigtiltype:
Inversevariance(averagescaling)
Variable
Cqefficient
StlErrort-Statistic
Froth
c
3876.201
14124052.745813
0.012&
X1
27.02457
1.&82C4216.C&653
0.0000
X2
-0.345154
0.0S4423-6.3C0397
a.oooo
WeightedStatistics
R'Squared
0987992
Meandependent^ar
5535.276
MustedR-squared
0.98&791
S.D.4901.347
S.E.ofregression
753.5206
Akaikeinfccriterion
16.20956
Sumsquaredresid
11367&25
Schwarzcriterion
1635767
Loglikelihood
-1B34Q99
Hannan-Quinrienter.
16.24681
F-statistic
8227495
Durbin-Watsonstat
0472639
Prob(F^tatistic)
0.000000
'.Vsightedmeandep
5093.234
UnweightedStatistics
R-squared
0.983483
Meandependentvar
905664&
AdjustedR^squared
0.987331
S.D.dependsntvar
9050.681
S.E.ofregression
1019.697
Sumsquaredresid
20764874
Durbh-Wats-on封取
0521574
已知DW=0.47,若给定=0.05,查表得DW检验的临界值dL=1.17,du=1.54。
因为
DW=0.47<1.17,根据判别规则,认为误差项ut存在严重的正自相关。
2.LM检验
F-statistic
3.459721
Prot>FCZ17)
U.0&49
Obs*R^squared
6364134
ProbChi-Square{2)
00415
lestEquation.
DependentVariattle:
RESIO
MethodLeastSquares
Date:
12/21/15Time:
12:
31
Sample:
19922013
Includedobsarvattnns:
22
Presample'missingvaluelaggedresidualssettozero.
Variable
Coeffidert
Std.Errort-Statisti匚
Prob
C
-706.2706
1164736-036378
0552^
X1-0765*X1(-1)
*4602240
331B005-1.205407
0.2446
X2-0765NX2(-1)
0.132050
01515570.871356
0.3557
RESlDi-1)
0.957807
0364S095.62910S
0.0176
RESID(-2)
-1.261570
0576139-2J89697
0.0428
R^squar&d
□208281
Meandependentw
^2.48E-13
AdjustedR-squared
0122053
S.Ddependentvar
6528291
S.E.cfregression
6111.0932
Akaikeinfocrlierlon
15.B6706
Sumsquaredresid
636085C
ScnwarzGritenon
10.11502
Loglikelihood
-16*5376
Hannan-QuinnGriter.
15,92547
F-statistic
172985Q
Dwrtjin-Watsanstat
1709&70
Prob(F^stati-stic}
0JQ9832
LM=6.36>
所以误差项存在二阶自相关
3.克服自相关
首先估计自相关系数
对原变量做广义差分变换。
令
GDYt=Yt-0.765Yt-1
GDXit=Xit-0.765Xit-i
GDX2t=X2t-0.765X2t-i
以GDYt,GDXit,GDX2t(1992~2013年)为样本再次回归
DependentJariaDimY-0.765"'¥{-1)
MethodLeastSquares
Date:
12/21/15Time:
12:
19
Sample(adjustedy19922013
Includedobservations:
22aft&radjusiments
Variable
Coefficient
Std.Error
1-Statistic
Prob.
C
241.1220
1257X25
0J91856
0,8499
X1-0.766*X1r-1}
2742970
3.&46518
7.522163
a.ocoo
X2^.765*X2G1)
-030243&
0.156989
-1.926490
0.0691
R-squared
0954230
Meandependent\/ar
3249404
AfljusteelR-squamd
0.949412
SD.depenaentvar
3051.462
SEofregression
&S63290
Afcaifcemfocriterion
1602672
Sumsquaredresid
8949904.
2匚hwarzcriterion
16.17549
Loglivelihood
-1732939
Hannan-Quinnenter.
10.06176
F-statistic
193B535
Durbin-Watsanstat
1363592
ProbtF-statistic)
0.009000
得到GDYt=241.322+27.