回归模型的OLS估计及异方差的检验与修正.docx
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回归模型的OLS估计及异方差的检验与修正.docx
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回归模型的OLS估计及异方差的检验与修正
实验1回归模型的OLS估计及异方差的检验与修正
实验内容及要求:
表1列出了2000年中国部分省市城镇居民每个家庭平均全年可支配收入x与消费性支出y的统计数据。
(1)利用OLS法建立人均消费支出与可支配收入的线性模型。
(2)检验模型是否存在异方差。
(3)如果存在异方差,试采用适当的方法加以消除。
表12000年中国部分省市城镇居民人均可支配收入与消费性支岀(单位:
元)
地区
可支配收入X
消费性支出y
北京
10349.69
8493.49
天津
8140.50
6121.04
河北
5661.16
4348.47
山西
4724.11
3941.87
内蒙古
5129.05
3927.75
辽宁
5357.79
4356.06
吉林
4810.00
4020.87
黑龙江
4912.88
3824.44
上海
11718.01
8868.19
江苏
6800.23
5323.18
浙江
9279.16
7020.22
lLi东
6489.97
5022.00
河南
4766.26
3830.71
湖北
5524.54
4644.50
湖南
6218.73
5218.79
广东
9761.57
8016.91
陕西
5124.24
4276.67
甘肃
4916.25
4126.47
青海
5169.96
4185.73
新疆
5644.86
4422.93
实验如下:
1.通过「X的散点图判断,并不存在异方差匚
回归结果分析:
费EViews
FileEditObjectViewProcQuickOptionsWindowHelpdataxy
Isyex
口Equation:
UNTITLEDWorkfile:
UNTITLED-UntitledX
[View||Proc|[object][p「int|[Name||FrEeze|[EstjmNte”ForecBst:
][stats||Resids
DependentVariable:
Y
Method:
LeastSquares
Date:
04/24/15Time:
12:
03
Sample:
120
Includedobservations:
20
Coefficient
Std.Errort-Statistic
Prob.
c
X
272.3635
0.755125
159.67731.705713
0.02331632.38690
0.1053
0.0000
R-squaredAdjustedR-squaredS.E.ofregressionSumsquaredresidLoglikelihoodF-statisticProb(F-statistic)
0.983129
0.982192
216.8900
846743.0
-134.9130
1048.912
0.000000
MeandependentvarS.D.dependentvarAkaikeinfocriterionSchwarzcriterionHannan-Quinncriter.Durbin-Watsonstat
5199.515
1625.275
13.69130
13.79087
13.71073
1.301684
图1人均消费支出与可支配收入的线性模型:
Y=272.3635+0.755125X
t=(1.705713)(32.38690)
R2=0.983129D.W=1.301563F=1048.912
残差分析:
图2
显示回归方程的残差分布有明显的扩大趋势,即表明存在异方差性。
29Goldfeld-Quandt检验
⑴将样本安解释变量排序(SORTX)并分成两部分(分别有1到8共8个样本合13到20共8个样本)
⑵利用样本1建立回归模型1(回归结果如图3),其残差平方和为126528.3
Smpl18
LSYCX
「o]「O|「汨
胡EVievys
FileEditObjectViewProcQuickOptionsWindowHelpsortx
smpl18
Isycx
OEquation;UNTITLEDWorkfile;U\TlTLED;;Untitled\
View]Proc]ObjectPEt]NQniu]|Frc:
uzuEstiniate][F5ecost|[stat5]Resds
Dep©na©n【Variable:
Y
Method:
LeastSquares
Date:
04/22/15Time:
17:
29
Samplo:
18
Includedobservations:
8
Coefficient
Std.Errort-Statistc
Prob.
c
1277.131
1540.6040829000
0.4333
X
0.554125
0.3114321.779287
0.1255
R-squared
0345397
Meandependentyar
4016814
RustedR-squareo
0235295
SD.oepenoent'/ar
166.1712
sEofregression
145.2172
Alcaiiceinfocritenon
1300666
Sumsquaredresid
126528.3
Schwarzenterion
13.02652
Loglikelihood
-50.02663
Hannan-Quinnenter.
12.87271
F-statistic
3.165861
Durbin-Watsonstat
3.004532
Prob(F-statistic)
0.125501
图3
⑶利用样本2建立回归模型2(回归结果如图4),其残差平方和为615472.0。
甬EViews■
FileEditObject_yievrProcQuickOptionsWindov/Help
Isycx
smpl1320
Is/ex
□Equation:
UNTITLEDWorkfilo:
UNTITLED:
:
UntitJed\<=>1「回][S3]
|vfew]Prcc[object]Print[Nane]Freeze]Estn-ate|[ForecdSt]|siats|[Resids]
DependentVariable:
YMethodLeastSquaresDate:
04/22/15Time:
17:
30Sample:
1320
Includedobseniations2
CoefficiontSid.Errort-StatisticProb.
C212.2118530.88920.3997290.7032
X0.7618930.06034B12625050.0000
R-squared0.963723Meandependentvar6750.477
AdjustedR-squared0Q57676SDdependentvar1556814
S.E.ofregression320.2790AkaiKeinrocriterion1458858
Sumsquaredresid6154720Schwarzcritenon1460344
Loglkelihocd-5635432Hannan-Quinnenter1445463
F-statislic159.3919Durbin-Watsonstat1.722960
Prob(F-statiStic)0.000015
⑷计算F统计量:
RSS2/RSS1=615472.0/126528.3=4.864,RSS2、RSSi分别是模型1和模型2的残差平方和。
取a=0.05时,査F分布表得Fo.os(8-1-1,84-1)=4.28,而实际上F=4.864>Fo.o>=4.28,所以存在异方差。
3,White检验
⑴建立回归模型:
LSYCX,回归结果如图5
FileEditObjectViewProcQuickOptionsWindowHelpdatayy
Isycx
□Equation:
UNTITLEDWorkfile:
LNTITLED:
;Un:
itlcd\
[view]|Prod[Object]pm〔][Name][Feeze|[Estimate]『orecast]^^][Res>Js]
Dependentvariable:
Y
Method:
LeastSquares
cate:
04/22/15Time:
17:
37
Sample:
120
Includedobservations:
20
CoefficientStd.Error^StatisticProb.
C272.3635159.57731.7057130.1053
X0.756125002331632.386900.0000
R-squared
0.983129
Meandependentvar
5199.515
AdjustedR-squared
0.982192
S.D.dependentvar
1625.275
S.E.ofregression
216.8900
AKaiKeinfocriterion
13.69130
Sumsquaredresid
846743.0
Schwarzcriterion
13.79087
Loolikelihood
・1349130
Hannan-Cuinncriter
1371073
F-statistic
1048912
Durbin-Watscnstat
1.301584
Prob(F-statistic)
0.000000
⑵在方程窗口上点击WhiteHeteroskcdastcity,检验结果如图6。
FileEditObjectV/iewProcQuickOptionsWindowHelp
dataxyisycx
□Equation:
UNTITLEDWoHcfile:
UNTinED:
:
Untitled\^]|'Q||丹
Mew/Proc;[Object;iPthl]Name]|j^eexe][Estiniate\;Fcrecast卜饷&(Reid%]
Heteroskedasticrtx-Test:
'^hite
F-St9tl$tiC
14.63596
Prob.F(2.17)
00002
oos'R-squareo
12.65213
Prob.cm-square
(2)
00018
Sc合ladexplainedS3
5568079
Prob.Chi-Square(2>
00618
TestEquation.
DepenoenivariableRESIDEMetnodLeastSquares
Date04^22/15Time:
1729
Sample;120
Indudedobservations:
20
coetnaent
Std.Errort-St3t)3lic
ProD.
C
-180998.9
1033182・1.751858
0.0978
X
49.42846
23.939291.708006
0.1068
沁
-0.002115
0.001847-1.144742
0.2692
R-squared
0632606
Meandependemw
4233715
AdjustedR-squared
0589384
SD.dependentvar
4527967
S.E.dregression
29014.92
Akaikeinfocriterion
23.52649
Sumsquaredresid
1.43E*10
Schwarxciiterion
23.67585
Loglikelihood
•232.2649
Hannan-Quinnalter
23.56665
F-stattstic
14.63595
Durbin-Watsonstat
1008103
Proi>(F-staiislic)
0000201
山图6中的数据,得到
e:
=-180998.9+49.42846X-0.002115X2
(-1.144742)
t=(-1.751858)(1.708006)
R:
=0.632606
White统计量nR1=20x0.632606=12.65212,该值大于5%显著性水平下自山
度为2的才分布的相应临界值加a⑵=5.99,(在估计模型中含有两个解释变量,所以自山度为2)因此拒绝同方差性的原假设。
4、Glejser检验
⑴建立回归模型(结果同图5所示)。
⑵生成新变量序列:
GENRE=ABS(RESID)
⑶分别建立新残差序列(E)对各解释变量(X/XA2/XA(l/2)/XA(-1)/XA(-2)/XA(-1/2))的回归模型:
LSECX,回归结果如图7、8、9、10、11、12所示。
常EViews,
FileEditObjectViewProcQuickOptionsWindowHelp
isycx
GENR£=ABS(RESID)
LSECX
OEquation:
UNTITLEDWorkfile:
UNTITLED:
:
Untitled\「oII回l〔S3
[v^ew[prccjob^ctPnnt][Nam©任应刮|Esn!
nate|[FDrMast]5Eats]|R6gdJ
Dependentvanaoie:
E
Method:
LeastSquares
Date:
04/22/15Time:
1807
Sample:
120
Includedobservations:
20
Coemdenl
SidErrort-Statistlc
Prob.
c
・5793464
53.81476-1262379
02229
X
0.037577
0.0078584.782066
0.0001
R-squarsd
0.559559
M©andepend©ntyar
177.2539
Ad.ustedR-squared
0.535090
SDdependentvar
107.2046
SEoiregression
73.09671
AKaikeinfocriterion
11.51608
Sumsquaredresid
96176.31
Schwarzcriterion
11.61566
Loglikelihood
-113.1608
Hannan-Quinncriter.
11.53552
F-statistic
22.86815
Durbin-V/atsonstat
1.513422
ProtXF-statistic)
0000149
船EViews
FileEditObjectViewProcQuickOptionsWindowHelpGENRE=ABS(RESID)
LSECX
LSECXZ*2
□Equation:
UNTITLEDWorkfile:
UNTITLED:
:
Untitled\|o||回丨S3|
[viQw[Proc][a^ectPrnt[Nam石[Freez©EfhtnatQ[Farmcast$tats]Rg胡
Dependentvariable.E
MethodLeastSquares
Date04J22/15Time:
18:
08
Sample:
120
Includedobservations:
20
Coefficient
Sid.Errort-Stalistic
Prob.
c
68.36615
29.774782296109
0.0339
*2
2.32E-06
521E-074.453042
0.0003
R-squared
0.524182
Meandependentm
177.2539
AQjusiedR-squared
0497748
SDdependentvar
1072046
SE01regression
75.97567
Akaikemrocmenon
1159334
Sumsquaredresid
103901.4
Schwarzcritenon
11.69292
Loglikelihood
・113.9334
HannanQuinncriter.
11.61278
F-statistic
19.82958
Durbin-Watsonstat
1.513828
ProtXF-statistic)
0.000307
需EViews
FileEditObjectViewProcQuickOptionsWindowHelpLSECX^
LSECK'2
LSECXAG/2)
□Equation:
UNTITLED
Workfib:
UNHTLED:
:
Unt«cd\
1口II回丨哭
[veA)Pra:
[ooject][pnnt][hcn)e]Freeze
Estfnate][F0fecast]5tats]Resids]
Dependentvadawe:
E
MethodLoastSquares
Date:
04/22/15Time:
18:
09
Sample:
120
Indudedobservations:
20
Coenicierit
SWErrorbStaiisiic
ProD
C
-3472134
108.4444-3.201763
0.0049
K'(”2)
6565885
13425144890739
00001
R-squared
0.570604
Meandependentvar
177.2539
AdjustedR-squared
0.546748
SDdependentvar
107.2046
S.E.ofregression
72.17439
AKaikeinfocntericn
11.49069
Sumsquaredresid
93764.58
Schwarzcriterion
11.59026
Loglikelihood
-1129069
Hannan-Quinncriter.
11.51012
F-stansac
2391933
Duroin-v/atsonstat
1.506289
Prob(F-statstc)
0.000118
FileEditObjectViewProcQuickOptionsWindowHelpLSECXA2
LSECXx(l/2)
LSECXA(-1)
口Equation:
UNTRIEDWorkfile:
UNTlTLEI>:
Untitled\
[viiewjproc^fobject]Print(Name][Free7e[Estnate[Forecast|[stats][Re5Xte]
DependentVariable:
E
Method:
LeastSquares
Date:
04/22J15Time:
18:
10
Sample:
120
includedooservaiions:
20
Coefficient
StdErrort-Statistic
Prob.
c
XA(-1)
5007513・1949783.
67.459037.423043
394911.5-4.937266
0.0000
0.0001
R-$quared
AdjustedR-squaredS.E.ofrecressionSumsquaredresid
Loglikelihood
F-statistic
Pfot>(F-$tatlstjc)
0.5752370551639
71.78394
92752.81-112.7984
24.37559
0.000106
Meandepend^ntvarSDdependentyarAkaikeinfocriterionSchwarzcriterionHannan-Quinncmer.Durumwatsonstai
177.2539
1072046
11.47984
11.57941
11.49928
1.490315
图10
豁EViews
FileEditOtjectWewProcQ«i:
LSECX^-1) LSECXz(-2) □Equation: UNHTLEDWorkfile: UNTnLED: : Untitled\|o||回"! |23| I'/cv/[Pfoc]ObjectPrintj[Nanc[Freeze]lEstrnatejlForccastHstats]Rcsids DependentVariable: EMethod: LeastsquaresDate: 04/22/15Time18: 11Sampie120 Inductedot>3ervations: 20 CoetfiaGnt Std.Error t-StatStic Prob. C 361.1702 41.92131 8.615433 00000 XA(-2) ・6.30E39 1.32E-09 -4.755848 00002
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