回归模型的OLS估计及异方差的检验与修正Word文档下载推荐.docx
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回归模型的OLS估计及异方差的检验与修正Word文档下载推荐.docx
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4185.73
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实验如下:
1、通过Y-X的散点图判断,并不存在异方差。
回归结果分析:
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UNTTTLED;
:
Untitled\
|View][Proc11Object|Print]NameFreeze底tirn曰teForecastIjStafcsResds
DependentVariableY
Hethoa.LeastSquares
Date.04/24/15Time:
12:
03
Sample.120
Includedobservations:
20
Coefficient
Std.Errort-Statistic
Prob.
c
272.3635
15967721.705713
01055
X
0755125
0.02331e323B5SQ
00000
R-squared
0.983129
Meandependent^ar
5199.515
AdjustedR-squared
0.9&
2192
S.D,dependentwar
1625.275
S.E.ofregression
216.8900
Akaikeinfocriterion
13.69130
Sumsquaredresid
846743.0
Schwarzcriterion
1379037
Loglikelihood
-134.9130
Hanna□'
Quinncriter.
1371Q73
F-statisflc
10^3912
Durbin-Watsonstat
1.301694
Prob(F-statistic)
0.000000
人均消费支出与可支配收入的线性模型:
Y=272.3635+0.755125Xt=(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。
2,Goldfeld-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
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uependent拒tig。
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D=to:
O4/22dETima:
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8
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0.55412ft
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0.1255
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4016814iMinz13D065S
U.Q2662
12.87271
3JMJ4532
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。
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0c^7676
323,2790
615472.0
-tj&
36432
159.3919
0000015
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155&
.S14
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1445463
1.7229(0
⑷计算F统计量:
RSS2/RSSi=615472.0/126528.3=4.864,RSS2、RSS1分别是模型1
和模型2的残差平方和。
取a=0.05时,查F分布表得Fo』5(8-1-1,8-1-1)=4.28,而实际上F=4.864>
Fo』5=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
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DependentVariable:
Y
Method.LeastSquares
Liate:
04^2/1!
)1ime:
1/:
3/
Samplei120
Indudsd23
Coeffident
Std.Error:
-Statistic
Prcb.
■HiW
272.3035
0.75E12E
159.D7731.705713
00233163239690
01353
00300
R'
SquaredAdjustedRsqjaredS.E.orrsgriSSlonEum3quaredrcaidLoaNkelihoMlFstatislcProb(F-statstic)
0.383129
0.982192
2ia.B90Q
846743.0-134.0130
1048912
O.JOOOOO
MeandependentvaiSD.dependent^arAKdKeinrocrlerionSchwvzcriterion
Hannan-QuinncritsrDurbin-Watsonstat
5199.515162&
27513.69130
1379207
1371^73
1.301684
图5
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由图6中的数据,得到
22
e=-180998.9+49.42846X-0.002115X
t=(-1.751858)(1.708006)(-1.144742)
R2=0.632606
White统计量nR2=200.632606=12.65212,该值大于5%显著性水平下自由
度为2的/2分布的相应临界值鴛.05
(2)=5.99,(在估计模型中含有两个解释变量,所以自由度为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(1/2)/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。
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- 回归 模型 OLS 估计 方差 检验 修正
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