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第五章异方差性参考答案
1.简述题略
2.单选题1-5BB AAB6-10DDCBB
3.多选题
1.BCD
2.ACD
3.BCD
4.AB
5.BD
6.AB
7.ABCD
8.BCD
9.ABD
10.ACD
11.AC
12.BCD
13.ABCD
14.AC
15.BD
4.判断题错对错错对对错错错对对错对对错1-56-1011-
155.填空题异方差
1.截面数据；横截面数据
2.递增；单调递增
3.存在
4.绝对值
5.大于
6.；自回归条件异方差
7.ARCH加权最小二乘法
8.；
9.lsw=wl yc xLSw=wl YC X最小
10.；
11.sort XSORTX
12.F解释变量
13.较大
14.
15.F
6.计算操作题作回归，得回归方程:
1.1OLSY=-
383.5407+
0.0246*X t=-
0.
838514.0683R2=
0.8722F=
197.9163作检验，得:2White回Equation:UNTITLED Workfile:UNTITLED::Untitled\回View ProcObject PrintName FreezeEstimate Forecast Stats ResidsHeteroskedasticity Test:WhiteF-statistic
1.763010Prob.F2,
280.1900Obs*R-squared Scaled
3.467187Prob.Chi-Square
20.1766explained SS
10.11295Prob.Chi-Square
20.0064Null hypothesis:HomoskedasticityTest Equation:Dependent Variable:RESIDA2Method:Least SquaresDate:03/29/23Time:16:20Sample:131Included observations:31VariableC-
1705587.
2294921.-
0.
7432010.4636XA2-
4.63E-
053.04E-05-
1.
5235070.1388X33,
5587818.
567391.
8074050.0815R-squared
0.111845Mean dependent var
2165147.Adjusted R-squared
0.048405S.D.dependent var
5682464.S.E.of regressionSum
5543228.Akaike infocriterion
33.98582squared residLog
8.60E+14Schwarz criterion
34.12459likelihood F-statistic-
523.7802Hannan-Quinn criter.
34.
031052.247124ProbF-statistic
1.763010Durbin-Watson stat
0.190040Coefficient Std.Error t-Statistic Prob.取显著性水平=由于的伴随概率〉因此判断模型不存在异方
0.05,nR2p
0.05,差性根据检验结果，无需进行修正但如果检验方法选择的是检验3white G-Q法，则会判断模型存在异方差性，需进一步修正模型作相关图得:
2.1|View ProcObject PrintName FreezeOptions UpdateAddText Line/Shade RemoveTemplate Zoom10,0008,0006,0004,0002,000-2,00002,0004,0006,0008,00012,000由图可知变量和接近线性相关，因此建立回归模型匕=+与,Y Xa+作回归，得回归方程OLSY=
494.9099+L0412*Xt=
1.
890410.2356R2=
0.7287n=41作检验2G-Q对解释变量排序后，剔除中间个观测值，可得检验的统计量值X11G-Q F41961053_________=69,89取显著性水平查分布表得由于2=
0.05,F F.05Q3,13=
2.58,F0取，因此判断模型存在异方差性51313,作检验WhiteView ProcObject PrintName FreezeEstimate ForecastStats ResidsHeteroskedasticityTest:WhiteNull hypothesis:HomoskedasticityF-statistic
3.392943Prob.F2,
380.0441Obs*R-squared
6.212255Prob.Chi-Square
20.0448Scaled explainedSS
15.58097Prob.Chi-Square
20.0004Test Equation:Dependent Variable:RESIDA2Method:Least SquaresDate:03/29/23Time:16:38Sample:141Included observations:41Variable Coefficient Std.Error t-Statistic Prob.C-
308349.
0889514.8-
0.
3466490.7308XA2-
0.
1232760.080441-
1.
5325090.1337X
1545.
213688.
39712.
2446540.0307R-squared
0.151518Mean dependent var
1504476.Adjusted R-squared
0.106861S.D.dependent var
3586362.S.E.of regression
3389328.Akaike infocriterion
32.98052Sum squared resid
4.37E+14Schwarz criterion
33.10590Log likelihood-
673.1006Hannan-Quinn criter.
33.02617F-statistic
3.392943Durbin-Watson stat
2.469386ProbF-statistic
0.044076取显著性水平由于的伴随概率因此判断模型存在异方差性a=
0.05,nR2p
0.05,作检验Park建立回归模型并生成新序列:LSYCX,GENR LNE2=LOGRESIDA2GENR LNX=LOGX建立对的回归模型可得:LNE2LNX LSLNE2cLNX,回Equation:UNTITLED Workfile:UNTITLED::Untitled\View ProcObject PrintName FreezeEstimate ForecastStats ResidsDependent Variable:LNE2Method:Least SquaresDate:03/29/23Time:16:39Sample:141Included observations:41Variable Coefficient Std.Error t-Statistic Prob.C
8.
9287251.
6810025.
3115480.0000LNX
0.
5225730.
2424982.
1549630.0374R-squared
0.106404Mean dependent var
12.47057Adjusted R-squared
0.083491S.D.dependent var
2.359203S.E.of regression
2.258571Akaike infocriterion
4.514892Sum squared resid
198.9446Schwarz criterion
4.598481Log likelihood-
90.55529Hannan-Quinn criter.
4.545331F-statistic
4.643863Durbin-Watson stat
1.748494ProbF-statistic
0.037398由上图回归结果可以看出的系数估计值显著不为因此推断回归模型存在LNX0,异方差性取权重用加权最小二乘法修正模型，得:3W1=1/SQRX,国Equation:UNTITLED Workfile:UNTITLED::Untitled\,回View ProcObject PrintName FreezeEstimate ForecastStats ResidsDependentVariable:YMethod:Least SquaresDate:03/29/23Time:16:40Sample:141Included observations:41Weighting series:W1Weight type:Inverse standarddeviation EViewsdefault scalingVariableCoefficientStd.Error t-Statistic Prob.
1.
82468830.
471040.
0598830.
95261.
3310270.
10087713.
194560.0000Mean dependentvar
903.5188S.D.dependentvar
630.7742S.E.of regressionSum
474.8126Akaike infocriterion
15.21127squaredresidLog
8792433.Schwarz criterion
15.29486likelihood-
309.8310Hannan-Quinn criter.
15.24171Durbin-Watson stat
2.382522Weighted meandep.-
1841.822Weighted StatisticsR-squared
0.672286Mean dependentvar
2266.659Adjusted R-squared
0.663883S.D.dependentvar
2384.252S.E.of regression
1382.285Sum squaredresid74517740Durbin-Watson stat
2.108451Unweighted Statistics对修正后的模型再进行检验，可知已不存在异方差性WhiteView ProcObject PrintName FreezeEstimate|ForecastStatsResidsHeteroskedasticityTest:WhiteNull hypothesis:HomoskedasticityF-statistic
1.310406Prob.F2,
380.2816Obs*R-squared
2.645276Prob.Chi-Square
20.2664Scaled explainedSS
5.903360Prob.Chi-Square
20.0523Test Equation:DependentVariable:WGT_RESIDA2Method:Least SquaresDate:03/29/23Time:16:41Sample:141Included observations:41Collinear testregressors droppedfrom specificationVariableCoefficientStd.Error t-Statistic Prob.C
114437.
3102218.
51.
1195360.2699XA2*WGTA
20.
1848330.
1193571.
5485760.1298WGTA2-
508.
98562140.996-
0.
2377330.8134R-squared
0.064519Mean dependentvar
214449.6Adjusted R-squared
0.015283S.D.dependentvar
482209.
2478510.2Akaike infocriterion
29.06510S.E.of regressionSumsquaredresid
8.70E+12Schwarz criterion
29.19048Log likelihood-
592.8345Hannan-Quinn criter.
29.11076F-statistic
1.310406Durbin-Watson stat
2.197084ProbF-statistic
0.281621。
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