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第二章简单线性回归模型
2.1
(1)
①首先分析人均寿命与人均GDP的数量关系,用Eviews分析DependentVariable:YMethod:LeastSquaresDate:12/27/14Time:21:00Sample:122Includedobservations:22VariableCoefficientStd.Errort-StatisticProb.C
56.
647941.
96082028.
889920.0000X
10.
1283600.
0272424.
7118340.0001R-squared
0.526082Meandependentvar
62.50000AdjustedR-squared
0.502386S.D.dependentvar
10.08889S.E.ofregression
7.116881Akaikeinfocriterion
6.849324Sumsquaredresid
1013.000Schwarzcriterion
6.948510Loglikelihood-
73.34257Hannan-Quinncriter.
6.872689F-statistic
22.20138Durbin-Watsonstat
0.629074ProbF-statistic
0.000134有上可知,关系式为y=
56.64794+
0.128360x1
②关于人均寿命与成人识字率的关系,用Eviews分析如下DependentVariable:YMethod:LeastSquaresDate:11/26/14Time:21:10Sample:122Includedobservations:22VariableCoefficientStd.Errort-StatisticProb.C
38.
794243.
53207910.
983400.0000X
20.
3319710.
0466567.
1153080.0000R-squared
0.716825Meandependentvar
62.50000AdjustedR-squared
0.702666S.D.dependentvar
10.08889S.E.ofregression
5.501306Akaikeinfocriterion
6.334356Sumsquaredresid
605.2873Schwarzcriterion
6.433542Loglikelihood-
67.67792Hannan-Quinncriter.
6.357721F-statistic
50.62761Durbin-Watsonstat
1.846406ProbF-statistic
0.000001由上可知,关系式为y=
38.79424+
0.331971x2
③关于人均寿命与一岁儿童疫苗接种率的关系,用Eviews分析如下DependentVariable:YMethod:LeastSquaresDate:11/26/14Time:21:14Sample:122Includedobservations:22VariableCoefficientStd.Errort-StatisticProb.C
31.
799566.
5364344.
8649710.0001X
30.
3872760.
0802604.
8252850.0001R-squared
0.537929Meandependentvar
62.50000AdjustedR-squared
0.514825S.D.dependentvar
10.08889S.E.ofregression
7.027364Akaikeinfocriterion
6.824009Sumsquaredresid
987.6770Schwarzcriterion
6.923194Loglikelihood-
73.06409Hannan-Quinncriter.
6.847374F-statistic
23.28338Durbin-Watsonstat
0.952555ProbF-statistic
0.000103由上可知,关系式为y=
31.79956+
0.387276x3
(2)
①关于人均寿命与人均GDP模型,由上可知,可决系数为
0.526082,说明所建模型整体上对样本数据拟合较好对于回归系数的t检验t(β1)=
4.711834t
0.02520=
2.086,对斜率系数的显著性检验表明,人均GDP对人均寿命有显著影响
②关于人均寿命与成人识字率模型,由上可知,可决系数为
0.716825,说明所建模型整体上对样本数据拟合较好对于回归系数的t检验t(β2)=
7.115308t
0.02520=
2.086,对斜率系数的显著性检验表明,成人识字率对人均寿命有显著影响
③关于人均寿命与一岁儿童疫苗的模型,由上可知,可决系数为
0.537929,说明所建模型整体上对样本数据拟合较好对于回归系数的t检验t(β3)=
4.825285t
0.02520=
2.086,对斜率系数的显著性检验表明,一岁儿童疫苗接种率对人均寿命有显著影响
2.2
(1)
①对于浙江省预算收入与全省生产总值的模型,用Eviews分析结果如下DependentVariable:YMethod:LeastSquaresDate:12/03/14Time:17:00Sampleadjusted:133Includedobservations:33afteradjustmentsVariableCoefficientStd.Errort-StatisticX
0.
1761240.
00407243.25639C-
154.
306339.08196-
3.948274R-squared
0.983702MeandependentvarAdjustedR-squared
0.983177S.D.dependentvarS.E.ofregression
175.2325AkaikeinfocriterionSumsquaredresid
951899.7SchwarzcriterionLoglikelihood-
216.2751Hannan-Quinncriter.F-statistic
1871.115Durbin-WatsonstatProbF-statistic
0.000000Prob.
0.
00000.
0004902.
51481351.
00913.
2288013.
3194913.
259310.100021
②由上可知,模型的参数斜率系数
0.176124,截距为—
154.3063
③关于浙江省财政预算收入与全省生产总值的模型,检验模型的显著性1)可决系数为
0.983702,说明所建模型整体上对样本数据拟合较好2)对于回归系数的t检验t(β2)=
43.25639t
0.02531=
2.0395,对斜率系数的显著性检验表明,全省生产总值对财政预算总收入有显著影响
④用规范形式写出检验结果如下Y=
0.176124X—
154.
30630.
00407239.08196t=
43.25639(-
3.948274)R2=
0.983702F=
1871.115n=33
⑤经济意义是全省生产总值每增加1亿元,财政预算总收入增加
0.176124亿元
(2)当x=32000时,
①进行点预测,由上可知Y=
0.176124X—
154.3063,代入可得Y=Y=
0.176124*32000—
154.3063=
5481.6617
②进行区间预测∑x2=∑(Xi—X)2=δ2xn—1=
7608.0212x33—1=
1852223.473Xf—X2=32000—
6000.4412=
675977068.2当Xf=32000时,将相关数据代入计算得到
5481.6617—
2.0395x
175.2325x√1/33+
1852223.473/
675977068.2≤Yf≤
5481.6617+
2.0395x
175.2325x√1/33+
1852223.473/
675977068.2即Yf的置信区间为(
5481.6617—
64.
96495481.6617+
64.9649)3对于浙江省预算收入对数与全省生产总值对数的模型,由Eviews分析结果如下DependentVariable:LNYMethod:LeastSquaresDate:12/03/14Time:18:00Sampleadjusted:133Includedobservations:33afteradjustmentsVariableCoefficientStd.Errort-StatisticProb.LNX
0.
9802750.
03429628.
582680.0000C-
1.
9182890.268213-
7.
1521210.0000R-squared
0.963442Meandependentvar
5.573120AdjustedR-squared
0.962263S.D.dependentvar
1.684189S.E.ofregression
0.327172Akaikeinfocriterion
0.662028Sumsquaredresid
3.318281Schwarzcriterion
0.752726Loglikelihood-
8.923468Hannan-Quinncriter.
0.692545F-statistic
816.9699Durbin-Watsonstat
0.096208ProbF-statistic
0.000000
①模型方程为lnY=
0.980275lnX-
1.918289
②由上可知,模型的参数斜率系数为
0.980275,截距为-
1.918289
③关于浙江省财政预算收入与全省生产总值的模型,检验其显著性1)可决系数为
0.963442,说明所建模型整体上对样本数据拟合较好2)对于回归系数的t检验t(β2)=
28.58268t
0.02531=
2.0395,对斜率系数的显著性检验表明,全省生产总值对财政预算总收入有显著影响
④经济意义全省生产总值每增长1%,财政预算总收入增长
0.980275%
2.4
(1)对建筑面积与建造单位成本模型,用Eviews分析结果如下DependentVariable:YMethod:LeastSquaresDate:12/01/14Time:12:40Sample:112Includedobservations:12VariableCoefficientStd.Errort-StatisticProb.X-
64.
184004.809828-
13.
344340.0000C
1845.
47519.
2644695.
796880.0000R-squared
0.946829Meandependentvar
1619.333AdjustedR-squared
0.941512S.D.dependentvar
131.2252S.E.ofregression
31.73600Akaikeinfocriterion
9.903792Sumsquaredresid
10071.74Schwarzcriterion
9.984610Loglikelihood-
57.42275Hannan-Quinncriter.
9.873871F-statistic
178.0715Durbin-Watsonstat
1.172407ProbF-statistic
0.000000由上可得建筑面积与建造成本的回归方程为Y=
1845.475--
64.18400X
(2)经济意义建筑面积每增加1万平方米,建筑单位成本每平方米减少
64.18400元
(3)
①首先进行点预测,由Y=
1845.475--
64.18400X得,当x=
4.5,y=
1556.647
②再进行区间估计由上表可知,∑x2=∑(Xi—X)2=δ2xn—1=
1.9894192x12—1=
43.5357Xf—X2=
4.5—
3.5233332=
0.95387843当Xf=
4.5时,将相关数据代入计算得到
1556.647—
2.228x
31.73600x√1/12+
43.5357/
0.95387843≤Yf≤
1556.647+
2.228x
31.73600x√1/12+
43.5357/
0.95387843即Yf的置信区间为(
1556.647—
478.
12311556.647+
478.1231)
3.1
(1)
①对百户拥有家用汽车量计量经济模型,用Eviews分析结果如下DependentVariable:YMethod:LeastSquaresDate:11/25/14Time:12:38Sample:131Includedobservations:31VariableCoefficientStd.Errort-StatisticProb.X
25.
9968651.
4060584.
2650200.0002X3-
0.
5240270.179280-
2.
9229500.0069X4-
2.
2656800.518837-
4.
3668420.0002C
246.
854051.
975004.
7494760.0001R-squared
0.666062Meandependentvar
16.77355AdjustedR-squared
0.628957S.D.dependentvar
8.252535S.E.ofregression
5.026889Akaikeinfocriterion
6.187394Sumsquaredresid
682.2795Schwarzcriterion
6.372424Loglikelihood-
91.90460Hannan-Quinncriter.
6.247709F-statistic
17.95108Durbin-Watsonstat
1.147253ProbF-statistic
0.000001
②得到模型得Y=
246.8540+
5.996865X2-
0.524027X3-
2.265680X4
③对模型进行检验1)可决系数是
0.666062,修正的可决系数为
0.628957,说明模型对样本拟合较好2)F检验,F=
17.95108F
(327)=
3.65,回归方程显著3)t检验,t统计量分别为
4.749476,
4.265020,-
2.922950,-
4.366842,均大于t
(27)=
2.0518,所以这些系数都是显著的
④依据1)可决系数越大,说明拟合程度越好2)F的值与临界值比较,若大于临界值,则否定原假设,回归方程是显著的;若小于临界值,则接受原假设,回归方程不显著3)t的值与临界值比较,若大于临界值,则否定原假设,系数都是显著的;若小于临界值,则接受原假设,系数不显著
(2)经济意义人均GDP增加1万元,百户拥有家用汽车增加
5.996865辆,城镇人口比重增加1个百分点,百户拥有家用汽车减少
0.524027辆,交通工具消费价格指数每上升1,百户拥有家用汽车减少
2.265680辆
(3)用EViews分析得DependentVariable:YMethod:LeastSquaresDate:12/08/14Time:17:28Sample:131Includedobservations:31VariableCoefficientStd.Errort-StatisticProb.X
25.
1356701.
0102705.
0834650.0000LNX3-
22.
810056.771820-
3.
3683780.0023LNX4-
230.
848149.46791-
4.
6666240.0001C
1148.
758228.
29175.
0319740.0000R-squared
0.691952Meandependentvar
16.77355AdjustedR-squared
0.657725S.D.dependentvar
8.252535S.E.ofregression
4.828088Akaikeinfocriterion
6.106692Sumsquaredresid
629.3818Schwarzcriterion
6.291723Loglikelihood-
90.65373Hannan-Quinncriter.
6.167008F-statistic
20.21624Durbin-Watsonstat
1.150090ProbF-statistic
0.000000模型方程为Y=
5.135670X2-
22.81005LNX3-
230.8481LNX4+
1148.758此分析得出的可决系数为
0.
6919520.666062,拟合程度得到了提高,可这样改进
3.2(1)对出口货物总额计量经济模型,用Eviews分析结果如下DependentVariable:YMethod:LeastSquaresDate:12/01/14Time:20:25Sample:19942011Includedobservations:18VariableCoefficientStd.Errort-StatisticProb.X
20.
1354740.
01279910.
584540.0000X
318.
853489.
7761811.
9285120.0729C-
18231.
588638.216-
2.
1105730.0520R-squared
0.985838Meandependentvar
6619.191AdjustedR-squared
0.983950S.D.dependentvar
5767.152S.E.ofregression
730.6306Akaikeinfocriterion
16.17670Sumsquaredresid
8007316.Schwarzcriterion
16.32510Loglikelihood-
142.5903Hannan-Quinncriter.
16.19717F-statistic
522.0976Durbin-Watsonstat
1.173432ProbF-statistic
0.000000
①由上可知,模型为Y=
0.135474X2+
18.85348X3-
18231.58
②对模型进行检验1)可决系数是
0.985838,修正的可决系数为
0.983950,说明模型对样本拟合较好2)F检验,F=
522.0976F
(215)=
4.77,回归方程显著3)t检验,t统计量分别为X2的系数对应t值为
10.58454,大于t
(15)=
2.131,系数是显著的,X3的系数对应t值为
1.928512,小于t
(15)=
2.131,说明此系数是不显著的
(2)对于对数模型,用Eviews分析结果如下DependentVariable:LNYMethod:LeastSquaresDate:12/01/14Time:20:25Sample:19942011Includedobservations:18VariableCoefficientStd.Errort-StatisticProb.LNX
21.
5642210.
08898817.
577890.0000LNX
31.
7606950.
6821152.
5812290.0209C-
20.
520485.432487-
3.
7773630.0018R-squared
0.986295Meandependentvar
8.400112AdjustedR-squared
0.984467S.D.dependentvar
0.941530S.E.ofregression
0.117343Akaikeinfocriterion-
1.296424Sumsquaredresid
0.206540Schwarzcriterion-
1.148029Loglikelihood
14.66782Hannan-Quinncriter.-
1.275962F-statistic
539.7364Durbin-Watsonstat
0.686656ProbF-statistic
0.000000
①由上可知,模型为LNY=-
20.52048+
1.564221LNX2+
1.760695LNX3
②对模型进行检验1)可决系数是
0.986295,修正的可决系数为
0.984467,说明模型对样本拟合较好2)F检验,F=
539.7364F
(215)=
4.77,回归方程显著3)t检验,t统计量分别为-
3.777363,
17.57789,
2.581229,均大于t
(15)=
2.131,所以这些系数都是显著的
(3)
①
(1)式中的经济意义工业增加1亿元,出口货物总额增加
0.135474亿元,人民币汇率增加1,出口货物总额增加
18.85348亿元
②
(2)式中的经济意义工业增加额每增加1%,出口货物总额增加
1.564221%,人民币汇率每增加1%,出口货物总额增加
1.760695%
3.3
(1)对家庭书刊消费对家庭月平均收入和户主受教育年数计量模型,由Eviews分析结果如下DependentVariable:YMethod:LeastSquaresDate:12/01/14Time:20:30Sample:118Includedobservations:18VariableCoefficientStd.Errort-StatisticProb.X
0.
0864500.
0293632.
9441860.0101T
52.
370315.
20216710.
067020.0000C-
50.
0163849.46026-
1.
0112440.3279R-squared
0.951235Meandependentvar
755.1222AdjustedR-squared
0.944732S.D.dependentvar
258.7206S.E.ofregression
60.82273Akaikeinfocriterion
11.20482Sumsquaredresid
55491.07SchwarzcriterionLoglikelihood-
97.84334Hannan-Quinncriter.F-statistic
146.2974Durbin-WatsonstatProbF-statistic
0.000000
①模型为Y=
0.086450X+
52.37031T-
50.
0163811.
3532111.
225282.605783
②对模型进行检验1)可决系数是
0.951235,修正的可决系数为
0.944732,说明模型对样本拟合较好2)F检验,F=
539.7364F
(215)=
4.77,回归方程显著3)t检验,t统计量分别为
2.944186,
10.06702,均大于t
(15)=
2.131,所以这些系数都是显著的
③经济意义家庭月平均收入增加1元,家庭书刊年消费支出增加
0.086450元,户主受教育年数增加1年,家庭书刊年消费支出增加
52.37031元
(2)用Eviews分析
①DependentVariable:YMethod:LeastSquaresDate:12/01/14Time:22:30Sample:118Includedobservations:18VariableCoefficientStd.Errort-StatisticProb.T
63.
016764.
54858113.
854160.0000C-
11.
5817158.02290-
0.
1996060.8443R-squared
0.923054Meandependentvar
755.1222AdjustedR-squared
0.918245S.D.dependentvar
258.7206S.E.ofregression
73.97565Akaikeinfocriterion
11.54979Sumsquaredresid
87558.36Schwarzcriterion
11.64872Loglikelihood-
101.9481Hannan-Quinncriter.
11.56343F-statistic
191.9377Durbin-Watsonstat
2.134043ProbF-statistic
0.000000
②DependentVariable:XMethod:LeastSquaresDate:12/01/14Time:22:34Sample:118Includedobservations:18VariableCoefficientStd.Errort-StatisticProb.T
123.
151631.
841503.
8676440.0014C
444.
5888406.
17861.
0945650.2899R-squared
0.483182Meandependentvar
1942.933AdjustedR-squared
0.450881S.D.dependentvar
698.8325S.E.ofregression
517.8529Akaikeinfocriterion
15.44170Sumsquaredresid
4290746.Schwarzcriterion
15.54063Loglikelihood-
136.9753Hannan-Quinncriter.
15.45534F-statistic
14.95867Durbin-Watsonstat
1.052251ProbF-statistic
0.001364以上分别是y与T,X与T的一元回归模型分别是Y=
63.01676T-
11.58171X=
123.1516T+
444.5888
(3)对残差进行模型分析,用Eviews分析结果如下DependentVariable:E1Method:LeastSquaresDate:12/03/14Time:20:39Sample:118Includedobservations:18VariableCoefficientStd.Errort-StatisticProb.E
20.
0864500.
0284313.
0407420.0078C
3.96E-
1413.
880832.85E-
151.0000R-squared
0.366239Meandependentvar
2.30E-14AdjustedR-squared
0.326629S.D.dependentvar
71.76693S.E.ofregression
58.89136Akaikeinfocriterion
11.09370Sumsquaredresid
55491.07Schwarzcriterion
11.19264Loglikelihood-
97.84334Hannan-Quinncriter.
11.10735F-statistic
9.246111Durbin-Watsonstat
2.605783ProbF-statistic
0.007788模型为E1=
0.086450E2+
3.96e-14参数斜率系数α为
0.086450,截距为
3.96e-14
(3)由上可知,β2与α2的系数是一样的回归系数与被解释变量的残差系数是一样的,它们的变化规律是一致的
3.6
(1)预期的符号是X1,X2X3X4X5的符号为正,X6的符号为负
(2)根据Eviews分析得到数据如下DependentVariable:YMethod:LeastSquaresDate:12/04/14Time:13:24Sample:19942011Includedobservations:18VariableCoefficientStd.Errort-StatisticProb.X
20.
0013820.
0011021.
2543300.2336X
30.
0019420.
0039600.
4905010.6326X4-
3.
5790903.559949-
1.
0053770.3346X
50.
0047910.
0050340.
9516710.3600X
60.
0455420.
0955520.
4766210.6422C-
13.
7773215.73366-
0.
8756590.3984R-squared
0.994869Meandependentvar
12.76667AdjustedR-squared
0.992731S.D.dependentvar
9.746631S.E.ofregression
0.830963Akaikeinfocriterion
2.728738Sumsquaredresid
8.285993Schwarzcriterion
3.025529Loglikelihood-
18.55865Hannan-Quinncriter.
2.769662F-statistic
465.3617Durbin-Watsonstat
1.553294ProbF-statistic
0.000000
①与预期不相符
②评价1)可决系数为
0.994869,数据相当大,可以认为拟合程度很好2)F检验,F=
465.3617F(
5.12)=389,回归方程显著3)T检验,X1,X2X3X4X5,X6系数对应的t值分别为
1.254330,
0.490501,-
1.005377,
0.951671,
0.476621,均小于t
(12)=
2.179,所以所得系数都是不显著的
(3)根据Eviews分析得到数据如下DependentVariable:YMethod:LeastSquaresDate:12/03/14Time:11:12Sample:19942011Includedobservations:18VariableCoefficientStd.Errort-StatisticX
50.
0010322.20E-
0546.79946X6-
0.
0549650.031184-
1.762581C
4.
2054813.
3356021.260786Prob.
0.
00000.
09830.2266R-squared
0.993601Meandependentvar
12.76667AdjustedR-squared
0.992748S.D.dependentvar
9.746631S.E.ofregression
0.830018Akaikeinfocriterion
2.616274Sumsquaredresid
10.33396Schwarzcriterion
2.764669Loglikelihood-
20.54646Hannan-Quinncriter.
2.636736F-statistic
1164.567Durbin-Watsonstat
1.341880ProbF-statistic
0.000000
①得到模型的方程为Y=
0.001032X5-
0.054965X6+
4.205481
②评价1)可决系数为
0.993601,数据相当大,可以认为拟合程度很好2)F检验,F=
1164.567F(
5.12)=389,回归方程显著3)T检验,X5系数对应的t值为
46.79946,大于t
(12)=
2.179,所以系数是显著的,即人均GDP对年底存款余额有显著影响X6系数对应的t值为-
1.762581,小于t
(12)=
2.179,所以系数是不显著的
4.3
(1)根据Eviews分析得到数据如下DependentVariable:LNYMethod:LeastSquaresDate:12/05/14Time:11:39Sample:19852011Includedobservations:27VariableCoefficientStd.Errort-StatisticProb.LNGDP
1.
3385330.
08861015.
105820.0000LNCPI-
0.
4217910.233295-
1.
8079750.0832C-
3.
1114860.463010-
6.
7201260.0000R-squared
0.988051Meandependentvar
9.484710AdjustedR-squared
0.987055S.D.dependentvar
1.425517S.E.ofregression
0.162189Akaikeinfocriterion-
0.695670Sumsquaredresid
0.631326Schwarzcriterion-
0.551689Loglikelihood
12.39155Hannan-Quinncriter.-
0.652857F-statistic
992.2582Durbin-Watsonstat
0.522613ProbF-statistic
0.000000得到的模型方程为LNY=
1.338533LNGDPt-
0.421791LNCPIt-
3.111486
(2)
①该模型的可决系数为
0.988051,可决系数很高,F检验值为
992.2582,明显显著但当α=
0.05时,t
(24)=
2.064,LNCPI的系数不显著,可能存在多重共线性
②得到相关系数矩阵如下LNGDP,LNCPI之间的相关系数很高,证实确实存在多重共线性
(3)由Eviews得a)DependentVariable:LNYMethod:LeastSquaresDate:12/03/14Time:14:41Sample:19852011Includedobservations:27VariableCoefficientStd.Errort-StatisticProb.LNGDP
1.
1857390.
02782242.
619330.0000C-
3.
7506700.312255-
12.
011560.0000R-squared
0.986423Meandependentvar
9.484710AdjustedR-squared
0.985880S.D.dependentvar
1.425517S.E.ofregression
0.169389Akaikeinfocriterion-
0.642056Sumsquaredresid
0.717312Schwarzcriterion-
0.546068Loglikelihood
10.66776Hannan-Quinncriter.-
0.613514F-statistic
1816.407Durbin-Watsonstat
0.471111ProbF-statistic
0.000000bDependentVariable:LNYMethod:LeastSquaresDate:12/03/14Time:14:41Sample:19852011Includedobservations:27VariableCoefficientStd.Errort-StatisticProb.LNCPI
2.
9392950.
22275613.
195110.0000C-
6.
8545351.242243-
5.
5178710.0000R-squared
0.874442Meandependentvar
9.484710AdjustedR-squared
0.869419S.D.dependentvar
1.425517S.E.ofregression
0.515124Akaikeinfocriterion
1.582368Sumsquaredresid
6.633810Schwarzcriterion
1.678356Loglikelihood-
19.36196Hannan-Quinncriter.
1.610910F-statistic
174.1108Durbin-Watsonstat
0.137042ProbF-statistic
0.000000cDependentVariable:LNGDPMethod:LeastSquaresDate:12/05/14Time:11:11Sample:19852011Includedobservations:27VariableCoefficientStd.Errort-StatisticProb.LNCPI
2.
5110220.
15830215.
862270.0000C-
2.
7963810.882798-
3.
1676340.0040R-squared
0.909621Meandependentvar
11.16214AdjustedR-squared
0.906005S.D.dependentvar
1.194029S.E.ofregression
0.366072Akaikeinfocriterion
0.899213Sumsquaredresid
3.350216Schwarzcriterion
0.995201Loglikelihood-
10.13938Hannan-Quinncriter.
0.927755F-statistic
251.6117Durbin-Watsonstat
0.099623ProbF-statistic
0.000000
①得到的回归方程分别为1)LNY=
1.185739LNGDPt-
3.7506702)LNY=
2.939295LNCPIt-
6.8545353)LNGDPt=
2.511022LNCPIt-
2.796381
②对多重共线性的认识单方程拟合效果都很好,回归系数显著,判定系数较高,GDP和CPI对进口的显著的单一影响,在这两个变量同时引入模型时影响方向发生了改变,这只有通过相关系数的分析才能发现
(4)建议如果仅仅是作预测,可以不在意这种多重共线性,但如果是进行结构分析,还是应该引起注意的
4.4
(1)按照设计的理论模型,由Eviews分析得DependentVariable:CZSRMethod:LeastSquaresDate:12/03/14Time:11:40Sample:19852011Includedobservations:27VariableCoefficientStd.Errort-StatisticCZZC
0.
0901140.
0443672.031129GDP-
0.
0253340.005069-
4.998036SSZE
1.
1768940.
06216218.93271C-
221.
8540130.6532-
1.698038R-squared
0.999857MeandependentvarAdjustedR-squared
0.999838S.D.dependentvarS.E.ofregression
353.0540AkaikeinfocriterionSumsquaredresid
2866884.SchwarzcriterionLoglikelihood-
194.5455Hannan-Quinncriter.F-statistic
53493.93Durbin-WatsonstatProbF-statistic
0.000000Prob.
0.
05400.
00000.
00000.
103022572.
5627739.
4914.
7070714.
8990514.
764161.458128从回归结果可见,可决系数为
0.999857,校正的可决系数为
0.999838,模型拟合的很好F的统计量为
53493.93,说明在α=
0.05水平下,回归方程回归方程整体上是显著的但是t检验结果表明,国内生产总值对财政收入的影响显著,但回归系数的符号为负,与实际不符合由此可得知,该方程可能存在多重共线性
(2)得到相关系数矩阵如下由上表可知,CZZC与GDP,CZZC与SSZE,GDP与SSZE之间的相关系数都非常高,说明确实存在多重共线性方差扩大因子均大于10,存在严重多重共线性并且通过以上分析,两两被解释变量之间相关性都很高
(4)解决方式分别作出财政收入与财政支出、国内生产总值、税收总额之间的一元回归
5.2
(1)
①用图形法检验绘制e2的散点图,用Eviews分析如下由上图可知,模型可能存在异方差,
②Goldfeld-Quanadt检验1)定义区间为1-7时,由软件分析得DependentVariable:YMethod:LeastSquaresDate:12/10/14Time:14:52Sample:17Includedobservations:7VariableCoefficientStd.Errort-StatisticT
35.
206644.
9014927.182843X
0.
1099490.
0619651.774380C
77.
1258882.
328440.936807R-squared
0.943099MeandependentvarAdjustedR-squared
0.914649S.D.dependentvarS.E.ofregression
31.63265AkaikeinfocriterionSumsquaredresid
4002.499SchwarzcriterionLoglikelihood-
32.15324Hannan-Quinncriter.F-statistic
33.14880Durbin-WatsonstatProbF-statistic
0.0032382得∑e1i=
4002.4992)定义区间为12-18时,由软件分析得Prob.
0.
00200.
15070.
4019565.
6857108.
275510.
0437810.
020609.
7572671.426262DependentVariable:YMethod:LeastSquaresDate:12/10/14Time:13:50Sample:1218Includedobservations:7VariableCoefficientStd.Errort-StatisticProb.T
52.
405886.
9233787.
5694090.0016X
0.
0686890.
0537631.
2776350.2705C-
8.
78926579.92542-
0.
1099680.9177R-squared
0.984688Meandependentvar
887.6143AdjustedR-squared
0.977032S.D.dependentvar
274.4148S.E.ofregression
41.58810Akaikeinfocriterion
10.59103Sumsquaredresid
6918.280Schwarzcriterion
10.56785Loglikelihood-
34.06861Hannan-Quinncriter.
10.30451F-statistic
128.6166Durbin-Watsonstat
2.390329ProbF-statistic
0.0002342得∑e2i=
6918.2803)根据Goldfeld-Quanadt检验,F统计量为F=∑e2i2/∑e1i2=
6918.280/
4002.499=
1.7285在α=
0.05水平下,分子分母的自由度均为4,查分布表得临界值F
0.05
(44)=
6.39,因为F=
1.7285F
0.05
(44)=
6.39,所以接受原假设,此检验表明模型不存在异方差
(2)存在异方差,估计参数的方法
①可以对模型进行变换
②使用加权最小二乘法进行计算,得出模型方程,并对其进行相关检验
③对模型进行对数变换,进行分析
(3)评价
3.3所得结论是可以相信的,随机扰动项之间不存在异方差回归方程是显著的
5.31由Eviews软件分析得DependentVariable:YMethod:LeastSquaresDate:12/10/14Time:16:00Sample:131Includedobservations:31VariableCoefficientStd.Errort-StatisticProb.X
1.
2442810.
07903215.
744110.0000C
242.
4488291.
19400.
8326020.4119R-squared
0.895260Meandependentvar
4443.526AdjustedR-squared
0.891649S.D.dependentvar
1972.072S.E.ofregression
649.1426Akaikeinfocriterion
15.85152Sumsquaredresid12220196Schwarzcriterion
15.94404Loglikelihood-
243.6986Hannan-Quinncriter.
15.88168F-statistic
247.8769Durbin-Watsonstat
1.078581ProbF-statistic
0.000000由上表可知,2007年我国农村居民家庭人均消费支出(x)对人均纯收入(y)的模型为Y=
1.244281X+
242.4488
(2)
①由图形法检验由上图可知,模型可能存在异方差
②Goldfeld-Quanadt检验1)定义区间为1-12时,由软件分析得DependentVariable:Y1Method:LeastSquaresDate:12/10/14Time:11:34Sample:112Includedobservations:12VariableCoefficientStd.Errort-StatisticProb.X
11.
4852960.
5003862.
9682970.0141C-
550.
54921220.063-
0.
4512470.6614R-squared
0.468390Meandependentvar
3052.950AdjustedR-squared
0.415229S.D.dependentvar
550.5148S.E.ofregression
420.9803Akaikeinfocriterion
15.07406Sumsquaredresid
1772245.Schwarzcriterion
15.15488Loglikelihood-
88.44437Hannan-Quinncriter.
15.04414F-statistic
8.810789Durbin-Watsonstat
2.354167ProbF-statistic
0.0140872得∑e1i=
1772245.2)定义区间为20-31时,由软件分析得DependentVariable:Y1Method:LeastSquaresDate:12/10/14Time:16:36Sample:2031Includedobservations:12VariableCoefficientStd.Errort-StatisticProb.X
11.
0869400.
1488637.
3016230.0000C
1173.
307733.
25201.
6001410.1407R-squared
0.842056Meandependentvar
6188.329AdjustedR-squared
0.826262S.D.dependentvar
2133.692S.E.ofregression
889.3633Akaikeinfocriterion
16.56990Sumsquaredresid
7909670.Schwarzcriterion
16.65072Loglikelihood-
97.41940Hannan-Quinncriter.
16.53998F-statistic
53.31370Durbin-Watsonstat
2.339767ProbF-statistic
0.0000262得∑e2i=
7909670.3)根据Goldfeld-Quanadt检验,F统计量为F=∑e2i2/∑e1i2=
7909670./1772245=
4.4631在α=
0.05水平下,分子分母的自由度均为10,查分布表得临界值F
0.05
(1010)=
2.98,因为F=
4.4631F
0.05
(1010)=
2.98,所以拒绝原假设,此检验表明模型存在异方差
(3)1)采用WLS法估计过程中,
①用权数w1=1/X建立回归得DependentVariable:YMethod:LeastSquaresDate:12/09/14Time:11:13Sample:131Includedobservations:31Weightingseries:W1VariableCoefficientStd.Errort-StatisticProb.X
1.
4258590.
11910411.
971570.0000C-
334.
8131344.3523-
0.
9722980.3389WeightedStatisticsR-squared
0.831707Meandependentvar
3946.082AdjustedR-squared
0.825904S.D.dependentvar
536.1907S.E.ofregression
536.6796Akaikeinfocriterion
15.47102Sumsquaredresid
8352726.Schwarzcriterion
15.56354Loglikelihood-
237.8008Hannan-Quinncriter.
15.50118F-statistic
143.3184Durbin-Watsonstat
1.369081ProbF-statistic
0.000000UnweightedStatisticsR-squared
0.875855Meandependentvar
4443.526AdjustedR-squared
0.871574S.D.dependentvar
1972.072S.E.ofregression
706.7236Sumsquaredresid14484289Durbin-Watsonstat
1.532908对此模型进行White检验得HeteroskedasticityTest:WhiteF-statistic
0.299395Prob.F
2280.7436Obs*R-squared
0.649065Prob.Chi-Square
20.7229ScaledexplainedSS
1.798067Prob.Chi-Square
20.4070TestEquation:DependentVariable:WGT_RESID^2Method:LeastSquaresDate:12/10/14Time:21:13Sample:131Includedobservations:31CollineartestregressorsdroppedfromspecificationVariableCoefficientStd.Errort-StatisticProb.C
61927.
891045682.
0.
0592220.9532WGT^2-
593927.
91173622.-
0.
5060640.6168X*WGT^
2282.
4407747.
97800.
3776060.7086R-squared
0.020938Meandependentvar
269442.8AdjustedR-squared-
0.048995S.D.dependentvar
689166.5S.E.ofregression
705847.6Akaikeinfocriterion
29.86395Sumsquaredresid
1.40E+13Schwarzcriterion
30.00273Loglikelihood-
459.8913Hannan-Quinncriter.
29.90919F-statistic
0.299395Durbin-Watsonstat
1.922336ProbF-statistic
0.743610从上可知,nR2=
0.649065,比较计算的统计量的临界值,因为nR2=
0.649065
(2)=
5.9915,所以接受原假设,该模型消除了异方差估计结果为Y=
1.425859X-
334.8131t=(
11.97157)(-
0.972298)R2=
0.875855F=
143.3184DW=
1.369081
②用权数w2=1/x2用回归分析得DependentVariable:YMethod:LeastSquaresDate:12/09/14Time:21:08Sample:131Includedobservations:31Weightingseries:W2VariableCoefficientStd.Errort-StatisticX
1.
5570400.
14539210.70922C-
693.
1946376.4760-
1.841272WeightedStatisticsR-squared
0.798173MeandependentvarAdjustedR-squared
0.791214S.D.dependentvarS.E.ofregression
466.8513AkaikeinfocriterionSumsquaredresid
6320554.SchwarzcriterionLoglikelihood-
233.4797Hannan-Quinncriter.F-statistic
114.6875Durbin-Watsonstat
0.05Prob.
0.
00000.
07583635.
0281029.
83015.
1922415.
2847515.
222401.562975ProbF-statistic
0.000000UnweightedStatisticsR-squared
0.834850Meandependentvar
4443.526AdjustedR-squared
0.829156S.D.dependentvar
1972.072S.E.ofregression
815.1229Sumsquaredresid19268334Durbin-Watsonstat
1.678365对此模型进行White检验得HeteroskedasticityTest:WhiteF-statistic
0.299790Prob.F
3270.8252Obs*R-squared
0.999322Prob.Chi-Square
30.8014ScaledexplainedSS
1.789507Prob.Chi-Square
30.6172TestEquation:DependentVariable:WGT_RESID^2Method:LeastSquaresDate:12/10/14Time:21:29Sample:131Includedobservations:31VariableCoefficientStd.Errort-StatisticProb.C-
111661.
8549855.7-
0.
2030750.8406WGT^
2426220.
22240181.
0.
1902620.8505X^2*WGT^
20.
1948880.
5163950.
3774020.7088X*WGT^2-
583.
21512082.820-
0.
2800120.7816R-squared
0.032236Meandependentvar
203888.8AdjustedR-squared-
0.075293S.D.dependentvar
419282.0S.E.ofregression
434780.1Akaikeinfocriterion
28.92298Sumsquaredresid
5.10E+12Schwarzcriterion
29.10801Loglikelihood-
444.3062Hannan-Quinncriter.
28.98330F-statistic
0.299790Durbin-Watsonstat
1.835854ProbF-statistic
0.825233从上可知,nR2=
0.999322,比较计算的统计量的临界值,因为nR2=
0.999322
(2)=
5.9915,所以接受原假设,该模型消除了异方差估计结果为Y=
1.557040X-
693.1946t=(
10.70922)(-
1.841272)R2=
0.798173F=
114.6875DW=
1.
5629750.05
③用权数w3=1/sqr(x)用回归分析得DependentVariable:YMethod:LeastSquaresDate:12/09/14Time:21:35Sample:131Includedobservations:31Weightingseries:W3VariableCoefficientStd.Errort-StatisticProb.X
1.
3301300.
09834513.
525070.0000C-
47.
40242313.1154-
0.
1513900.8807WeightedStatisticsR-squared
0.863161Meandependentvar
4164.118AdjustedR-squared
0.858442S.D.dependentvar
991.2079S.E.ofregression
586.9555Akaikeinfocriterion
15.65012Sumsquaredresid
9990985.Schwarzcriterion
15.74263Loglikelihood-
240.5768Hannan-Quinncriter.
15.68027F-statistic
182.9276Durbin-Watsonstat
1.237664ProbF-statistic
0.000000UnweightedStatisticsR-squared
0.890999Meandependentvar
4443.526AdjustedR-squared
0.887240S.D.dependentvar
1972.072S.E.ofregression
662.2171Sumsquaredresid12717412Durbin-Watsonstat
1.314859对此模型进行White检验得HeteroskedasticityTest:WhiteF-statistic
0.423886Prob.F
2280.6586Obs*R-squared
0.911022Prob.Chi-Square
20.6341ScaledexplainedSS
2.768332Prob.Chi-Square
20.2505TestEquation:DependentVariable:WGT_RESID^2Method:LeastSquaresDate:12/09/14Time:20:36Sample:131Includedobservations:31CollineartestregressorsdroppedfromspecificationVariableCoefficientStd.Errort-StatisticC
1212308.
2141958.
0.565981WGT^2-
715673.
01301839.-
0.549740X^2*WGT^2-
0.
0151940.082276-
0.184677R-squared
0.029388MeandependentvarAdjustedR-squared-
0.039942S.D.dependentvarS.E.ofregression
880429.8AkaikeinfocriterionSumsquaredresid
2.17E+13SchwarzcriterionLoglikelihood-
466.7426Hannan-Quinncriter.F-statistic
0.423886Durbin-WatsonstatProbF-statistic
0.658628Prob.
0.
57590.
58690.
8548322289.
8863356.
730.
3059730.
4447530.
351211.887426估计结果为Y=
1.330130X-
47.40242t=(
13.52507)(-
0.151390)R2=
0.863161F=
182.9276DW=
1.237664经过检验发现,用权数w1的效果最好,所以综上可知,即修改后的结果为Y=
1.425859X-
334.8131t=(
11.97157)(-
0.972298)R2=
0.875855F=
143.3184DW=
1.
3690815.61a用Eviews模型分析得DependentVariable:YMethod:LeastSquaresDate:12/10/14Time:20:16Sample:19782011Includedobservations:34VariableCoefficientStd.Errort-StatisticX
0.
7462410.
01912039.03027C
92.
5542242.
805292.162215R-squared
0.979426MeandependentvarAdjustedR-squared
0.978783S.D.dependentvarS.E.ofregression
173.1597AkaikeinfocriterionSumsquaredresid
959497.2SchwarzcriterionLoglikelihood-
222.4566Hannan-Quinncriter.F-statistic
1523.362Durbin-WatsonstatProbF-statistic
0.000000得回归模型为Y=
0.746241X+
92.55422b检验是否存在异方差
①用Goldfeld-Quanadt检验如下1)当定义区间为1-13时,由软件分析得DependentVariable:YMethod:LeastSquaresDate:12/11/14Time:11:47Sample:113Includedobservations:13VariableCoefficientStd.Errort-StatisticX
0.
9678390.
02687936.00771C-
18.
868618.963780-
2.104984R-squared
0.991587MeandependentvarAdjustedR-squared
0.990823S.D.dependentvarS.E.ofregression
12.17039AkaikeinfocriterionSumsquaredresid
1629.301SchwarzcriterionLoglikelihood-
49.84742Hannan-Quinncriter.F-statistic
1296.555Durbin-WatsonstatProbF-statistic
0.000000Prob.
0.
00000.
03821295.
8021188.
79113.
2033313.
2931113.
233951.534491Prob.
0.
00000.
0591280.
1377127.
04097.
9765278.
0634427.
9586621.071505得∑e1i2=
1629.3012)当定义区间为1-13时,由软件分析得DependentVariable:YMethod:LeastSquaresDate:12/11/14Time:12:21Sample:2234Includedobservations:13VariableCoefficientStd.Errort-StatisticProb.X
0.
7195670.
05831212.
339980.0000C
179.
3950202.
87640.
8842580.3955R-squared
0.932629Meandependentvar
2496.127AdjustedR-squared
0.926504S.D.dependentvar
1022.591S.E.ofregression
277.2250Akaikeinfocriterion
14.22817Sumsquaredresid
845390.4Schwarzcriterion
14.31509Loglikelihood-
90.48313Hannan-Quinncriter.
14.21031F-statistic
152.2752Durbin-Watsonstat
1.658418ProbF-statistic
0.0000002得∑e2i=
845390.43)根据Goldfeld-Quanadt检验,F统计量为F=∑e2i2/∑e1i2=
845390.4/
1629.301=
518.8669在α=
0.05水平下,分子分母的自由度均为11,查分布表得临界值F
0.05
(1111)=
4.47,因为F=
518.8669F
0.05
(1111)=
4.47,所以拒绝原假设,此检验表明模型存在异方差
②White检验用EViews软件分析得HeteroskedasticityTest:WhiteF-statistic
10.36759Prob.F
2310.0004Obs*R-squared
13.62701Prob.Chi-Square
20.0011ScaledexplainedSS
76.13635Prob.Chi-Square
20.0000TestEquation:DependentVariable:RESID^2Method:LeastSquaresDate:12/11/14Time:12:56Sample:134Includedobservations:34VariableCoefficientStd.Errort-StatisticC
11581.
1126117.
110.443430X-
27.
6990127.86540-
0.994029X^
20.
0122300.
0051562.371861R-squared
0.400795MeandependentvarAdjustedR-squared
0.362136S.D.dependentvarS.E.ofregression
81255.15AkaikeinfocriterionSumsquaredresid
2.05E+11SchwarzcriterionLoglikelihood-
431.0554Hannan-Quinncriter.F-statistic
10.36759Durbin-WatsonstatProbF-statistic
0.000357从上图中可以看出,nR2=
13.62701,比较计算的nR2=
13.62701异方差用以上两种方法,可以检验模型是存在异方差的c修正模型1)用加权二乘法修正异方差现象步骤如下
①当权数w1=1/x时,用软件分析得DependentVariable:YMethod:LeastSquaresDate:12/11/14Time:13:22Sample:134Includedobservations:34Weightingseries:W1VariableCoefficientStd.Errort-StatisticX
0.
8210130.
01686648.67993C
17.
693186.
2832562.815926WeightedStatisticsR-squared
0.986676MeandependentvarAdjustedR-squared
0.986260S.D.dependentvarS.E.ofregression
37.91285AkaikeinfocriterionSumsquaredresid
45996.29SchwarzcriterionLoglikelihood-
170.8132Hannan-Quinncriter.Prob.
0.
66050.
32790.
024128220.
51101738.
925.
5326725.
6673525.
578603.021651统计量的临界值,因为
0.05
(2)=
5.9915,所以拒绝原假设,不拒绝备择假设,表明模型存在Prob.
0.
00000.
0083457.
850541.
7038410.
1654810.
2552710.19610F-statistic
2369.735Durbin-Watsonstat
0.605852ProbF-statistic
0.000000UnweightedStatisticsR-squared
0.968070Meandependentvar
1295.802AdjustedR-squared
0.967072S.D.dependentvar
1188.791S.E.ofregression
215.7175Sumsquaredresid
1489089.Durbin-Watsonstat
1.079107得方程模型为Y=
0.821013X-
17.69318t=(
48.67993)(
2.815926)R2=
0.986676F=
2369.735DW=
0.605852对此模型进行White检验如下HeteroskedasticityTest:WhiteF-statistic
1.348072Prob.F
2310.2745Obs*R-squared
2.720457Prob.Chi-Square
20.2566ScaledexplainedSS
1.221901Prob.Chi-Square
20.5428TestEquation:DependentVariable:WGT_RESID^2Method:LeastSquaresDate:12/11/14Time:11:20Sample:134Includedobservations:34CollineartestregressorsdroppedfromspecificationVariableCoefficientStd.Errort-StatisticProb.C
1678.
870416.
54174.
0304980.0003WGT^2-
32.
13071187.6175-
0.
1712570.8651X*WGT^2-
0.
4840401.279449-
0.
3783190.7078R-squared
0.080013Meandependentvar
1352.832AdjustedR-squared
0.020659S.D.dependentvar
1382.825S.E.ofregression
1368.467Akaikeinfocriterion
17.36487Sumsquaredresid58053732Schwarzcriterion
17.49955Loglikelihood-
292.2027Hannan-Quinncriter.
17.41080F-statistic
1.348072Durbin-Watsonstat
1.199640ProbF-statistic
0.2745452从上图中可以看出,nR=
2.720457,比较计算的统计量的临界值,因为nR2=
2.720457响
0.05
(2)=
5.9915,所以接受原假设,即该模型消除了异方差的影
②当权数w2=1/x2时,用软件分析得DependentVariable:YMethod:LeastSquaresDate:12/11/14Time:13:27Sample:134Includedobservations:34Weightingseries:W2VariableCoefficientStd.Errort-StatisticX
0.
8521930.
02015042.29335C
8.
8908863.
6043012.466744WeightedStatisticsR-squared
0.982425MeandependentvarAdjustedR-squared
0.981875S.D.dependentvarS.E.ofregression
16.20273AkaikeinfocriterionSumsquaredresid
8400.912SchwarzcriterionLoglikelihood-
141.9094Hannan-Quinncriter.F-statistic
1788.728Durbin-WatsonstatProbF-statistic
0.000000UnweightedStatisticsR-squared
0.954142MeandependentvarAdjustedR-squared
0.952709S.D.dependentvarS.E.ofregression
258.5207SumsquaredresidDurbin-Watsonstat
0.781788得方程模型为Y=
0.852193X+
8.890886t=(
42.29335)(
2.466744)R2=
0.982425F=
1788.728DW=
0.604647用White检验模型得HeteroskedasticityTest:WhiteF-statistic
7.462185Prob.F330Obs*R-squared
14.52935Prob.Chi-Square3ScaledexplainedSS
19.40139Prob.Chi-Square3Prob.
0.
00000.
0192230.
2433247.
17188.
4652598.
5550458.
4958790.
6046471295.
8021188.
7912138654.
0.
00070.
00230.0002TestEquation:DependentVariable:WGT_RESID^2Method:LeastSquaresDate:12/11/14Time:11:19Sample:134Includedobservations:34VariableCoefficientStd.Errort-StatisticC-
7.
68470085.76169-
0.089605WGT^
264.
2001696.
111600.667975X^2*WGT^
20.
0063060.
0034311.838317X*WGT^2-
1.
2472221.163558-
1.071903R-squared
0.427334MeandependentvarAdjustedR-squared
0.370067S.D.dependentvarS.E.ofregression
345.6323AkaikeinfocriterionSumsquaredresid
3583851.SchwarzcriterionLoglikelihood-
244.8589Hannan-Quinncriter.F-statistic
7.462185Durbin-WatsonstatProbF-statistic
0.000712从上图中可以看出,nR2=
14.52935,比较计算的nR2=
14.52935Prob.
0.
92920.
50930.
07590.
2923247.
0857435.
479114.
6387614.
8183314.
700001.586012统计量的临界值,因为
0.05
(2)=
5.9915,所以拒绝原假设,不拒绝备择假设,表明模型存在异方差此模型并未消除异方差
③当权数w3=1/sqrx时,用软件分析得DependentVariable:YMethod:LeastSquaresDate:12/11/14Time:13:21Sample:134Includedobservations:34Weightingseries:W3VariableCoefficientStd.Errort-StatisticProb.X
0.
7785510.
01567749.
663470.0000C
40.
4577014.
575282.
7757750.0091WeightedStatisticsR-squared
0.987192Meandependentvar
776.3266AdjustedR-squared
0.986792S.D.dependentvarS.E.ofregression
79.19828AkaikeinfocriterionSumsquaredresid
200715.8SchwarzcriterionLoglikelihood-
195.8597Hannan-Quinncriter.F-statistic
2466.460Durbin-WatsonstatProbF-statistic
0.000000UnweightedStatisticsR-squared
0.977590MeandependentvarAdjustedR-squared
0.976890S.D.dependentvarS.E.ofregression
180.7210SumsquaredresidDurbin-Watsonstat
1.460832得方程模型为Y=
0.778551X+
40.45770t=(
49.66347)(
2.775775)R2=
0.986792F=
2466.460DW=
1.178340对所得模型进行White检验HeteroskedasticityTest:WhiteF-statistic
8.158958Prob.F231Obs*R-squared
11.72514Prob.Chi-Square2ScaledexplainedSS
28.08353Prob.Chi-Square2TestEquation:DependentVariable:WGT_RESID^2Method:LeastSquaresDate:12/10/14Time:13:23Sample:134Includedobservations:34CollineartestregressorsdroppedfromspecificationVariableCoefficientStd.Errort-StatisticC-
7585.
1865311.263-
1.428132WGT^
22468.
3691996.
0411.236632X^2*WGT^
20.
0091390.
0024813.684177R-squared
0.344857MeandependentvarAdjustedR-squared
0.302590S.D.dependentvarS.E.ofregression
11636.97AkaikeinfocriterionSumsquaredresid
4.20E+09SchwarzcriterionLoglikelihood-
364.9796Hannan-Quinncriter.
367.
315211.
6388111.
7285911.
669431.
1783401295.
8021188.
7911045123.
0.
00140.
00280.0000Prob.
0.
16330.
22550.
00095903.
40513934.
6421.
6458621.
7805421.69179F-statistic
8.158958Durbin-WatsonstatProbF-statistic
0.001423从上图中可以看出,nR2=
11.72514,比较计算的nR2=
11.
725142.344068统计量的临界值,因为
0.05
(2)=
5.9915,所以拒绝原假设,不拒绝备择假设,表明模型存在异方差此模型并未消除异方差综上所述,用加权二乘法w1的效果最好,所以模型为得方程模型为Y=
0.821013X-
17.69318t=(
48.67993)(
2.815926)R2=
0.986676F=
2369.735DW=
0.6058522)用对数模型法用软件分析得DependentVariable:LNYMethod:LeastSquaresDate:12/11/14Time:09:54Sample:134Includedobservations:34VariableCoefficientStd.Errort-StatisticProb.LNX
0.
9468870.
01122884.
335490.0000C
0.
2018610.
0779052.
5911000.0143R-squared
0.995521Meandependentvar
6.687779AdjustedR-squared
0.995381S.D.dependentvar
1.067124S.E.ofregression
0.072525Akaikeinfocriterion-
2.352753Sumsquaredresid
0.168315Schwarzcriterion-
2.262967Loglikelihood
41.99680Hannan-Quinncriter.-
2.322134F-statistic
7112.475Durbin-Watsonstat
0.812150ProbF-statistic
0.000000得到模型为LnY=
0.946887LNX+
0.201861对此模型进行White检验得HeteroskedasticityTest:WhiteF-statistic
1.003964Prob.F
2310.3780Obs*R-squared
2.068278Prob.Chi-Square
20.3555ScaledexplainedSS
1.469638Prob.Chi-Square
20.4796TestEquation:DependentVariable:RESID^2Method:LeastSquaresDate:12/11/14Time:09:55Sample:134Includedobservations:34VariableCoefficientStd.Errort-StatisticProb.C
0.
0395470.
0467590.
8457530.4042LNX-
0.
0116010.014012-
0.
8279690.4140LNX^
20.
0009320.
0010280.
9067740.3715R-squared
0.060832Meandependentvar
0.004950AdjustedR-squared
0.000240S.D.dependentvar
0.006365S.E.ofregression
0.006364Akaikeinfocriterion-
7.192271Sumsquaredresid
0.001255Schwarzcriterion-
7.057592Loglikelihood
125.2686Hannan-Quinncriter.-
7.146342F-statistic
1.003964Durbin-Watsonstat
2.022904ProbF-statistic
0.378027从上图中可以看出,nR2=
2.068278,比较计算的统计量的临界值,nR2=
2.
0682780.05
(2)=
5.9915,所以接受原假设,此模型消除了异方差综合两种方法,改进后的模型最好为LnY=
0.946887LNX+
0.20186121)考虑价格因素,首先用软件三者关系进行分析如下DependentVariable:YMethod:LeastSquaresDate:12/12/14Time:19:26Sample:134Includedobservations:34VariableCoefficientStd.Errort-StatisticProb.X
0.
7416840.
01990537.
260950.0000P
0.
2350250.
2717010.
8650120.3937C
43.
4171571.
229460.
6095390.5466R-squared
0.979911Meandependentvar
1295.802为因AdjustedR-squared
0.978615S.D.dependentvarS.E.ofregression
173.8449AkaikeinfocriterionSumsquaredresid
936883.7SchwarzcriterionLoglikelihood-
222.0511Hannan-Quinncriter.F-statistic
756.0627Durbin-WatsonstatProbF-statistic
0.0000001)用Goldfeld-Quanadt检验如下
①当样本为1-13时,进行回归分析DependentVariable:PMethod:LeastSquaresDate:12/14/14Time:19:26Sample:113Includedobservations:13VariableCoefficientStd.Errort-StatisticX-
0.
1704840.203868-
0.836247Y
0.
4586600.
2097552.186646C
59.
504967.
3858418.056627R-squared
0.956255MeandependentvarAdjustedR-squared
0.947506S.D.dependentvarS.E.ofregression
8.466678AkaikeinfocriterionSumsquaredresid
716.8464SchwarzcriterionLoglikelihood-
44.51063Hannan-Quinncriter.F-statistic
109.2993Durbin-WatsonstatProbF-statistic
0.0000002得∑e1i=
716.8464
②当样本为22-34时,做回归分析得DependentVariable:YMethod:LeastSquaresDate:12/14/14Time:20:39Sample:2234Includedobservations:13VariableCoefficientStd.Errort-StatisticX
0.
6411970.
0926786.918569P-
1.
2062221.114278-
1.082514C
795.
6887603.
86051.
3176701188.
79113.
2383013.
3729813.
284231.681521Prob.
0.
42250.
05360.
0000135.
323136.
953807.
3093287.
4397017.
2825300.637181Prob.
0.
00000.
30440.2170R-squared
0.939696Meandependentvar
2496.127AdjustedR-squared
0.927635S.D.dependentvar
1022.591S.E.ofregression
275.0847Akaikeinfocriterion
14.27121Sumsquaredresid
756715.7Schwarzcriterion
14.40158Loglikelihood-
89.76286Hannan-Quinncriter.
14.24441F-statistic
77.91291Durbin-Watsonstat
1.128778ProbF-statistic
0.0000012得∑e2i=
756715.7
③根据Goldfeld-Quanadt检验,F统计量为F=∑e2i2/∑e1i2=
756715.7/
716.8464=
1055.6176在α=
0.05水平下,分子分母的自由度均为11,查分布表得临界值F
0.05
(1010)=
2.98,因为F=
1055.6176F
0.05
(1010)=
2.98,所以拒绝原假设,此检验表明模型存在异方差2)用White检验,软件分析结果为HeteroskedasticityTest:WhiteF-statistic
7.312529Prob.F528Obs*R-squared
19.25463Prob.Chi-Square5ScaledexplainedSS
119.3072Prob.Chi-Square5TestEquation:DependentVariable:RESID^2Method:LeastSquaresDate:12/12/14Time:19:31Sample:134Includedobservations:34VariableCoefficientStd.Errort-StatisticC
79541.
08112647.
30.706107X
209.
496463.
904003.278298X^2-
0.
0241330.010712-
2.252841X*P-
0.
2351370.106647-
2.204822P-
1175.
3261156.253-
1.016495P^
21.
6373662.
6000200.629751R-squared
0.566313MeandependentvarAdjustedR-squared
0.488869S.D.dependentvarS.E.ofregression
77206.44AkaikeinfocriterionSumsquaredresid
1.67E+11SchwarzcriterionLoglikelihood-
427.5874Hannan-Quinncriter.F-statistic
7.312529Durbin-WatsonstatProbF-statistic
0.
0001710.
00020.
00170.0000Prob.
0.
48600.
00280.
03230.
03580.
31810.
534027555.
40107990.
925.
5051425.
7745025.
597002.787044从上图中可以看出,nR2=
19.25463,比较计算的nR2=
19.25463统计量的临界值,因为
0.05
(5)=
11.0705,所以拒绝原假设,不拒绝备择假设,表明模型存在异方差2)修正
①建立对数模型,用软件分析如下DependentVariable:LNYMethod:LeastSquaresDate:12/12/14Time:19:24Sample:134Includedobservations:34VariableCoefficientStd.Errort-StatisticProb.LNX
0.
9396050.
01364568.
860880.0000LNP
0.
0268210.
0284540.
9426090.3532C
0.
1082300.
1263220.
8567840.3981R-squared
0.995646Meandependentvar
6.687779AdjustedR-squared
0.995365S.D.dependentvar
1.067124S.E.ofregression
0.072652Akaikeinfocriterion-
2.322188Sumsquaredresid
0.163625Schwarzcriterion-
2.187509Loglikelihood
42.47720Hannan-Quinncriter.-
2.276259F-statistic
3544.292Durbin-Watsonstat
0.930109ProbF-statistic
0.000000对此模型进行White检验HeteroskedasticityTest:WhiteF-statistic
3.523832Prob.F
5280.0135Obs*R-squared
13.13158Prob.Chi-Square
50.0222ScaledexplainedSS
12.14373Prob.Chi-Square
50.0329TestEquation:DependentVariable:RESID^2Method:LeastSquaresDate:12/12/14Time:19:24Sample:134Includedobservations:34VariableCoefficientStd.Errort-StatisticProb.C
0.
4228720.
2737461.
5447590.1336LNX
0.
0807120.
0318332.
5355020.0171LNX^2-
0.
0039170.003037-
1.
2895640.2078LNX*LNP-
0.
0049550.005136-
0.
9647650.3429LNP-
0.
2549920.129858-
1.
9636310.0596LNP^
20.
0264700.
0126752.
0883900.0460R-squared
0.386223Meandependentvar
0.004813AdjustedR-squared
0.276620S.D.dependentvar
0.007286S.E.ofregression
0.006197Akaikeinfocriterion-
7.170690Sumsquaredresid
0.001075Schwarzcriterion-
6.901332Loglikelihood
127.9017Hannan-Quinncriter.-
7.078831F-statistic
3.523832Durbin-Watsonstat
2.264261ProbF-statistic
0.0135022从上图中可以看出,nR=
13.13158,比较计算的统计量的临界值,因为nR2=
13.
131580.05
(5)=
11.0705,所以拒绝原假设,不拒绝备择假设,表明模型存在异方差,所以此模型没有消除异方差
②当w1=1/x时,用软件分析如下DependentVariable:YMethod:LeastSquaresDate:12/13/14Time:18:49Sample:134Includedobservations:34Weightingseries:W1VariableCoefficientStd.Errort-StatisticX
0.
7232180.
02296531.49212P
0.
7195060.
1410855.099795C-
44.
7208413.11268-
3.410502WeightedStatisticsR-squared
0.992755MeandependentvarAdjustedR-squared
0.992287S.D.dependentvarS.E.ofregression
28.40494AkaikeinfocriterionSumsquaredresid
25012.05SchwarzcriterionLoglikelihood-
160.4567Hannan-Quinncriter.F-statistic
2123.843Durbin-WatsonstatProbF-statistic
0.000000UnweightedStatisticsProb.
0.
00000.
00000.
0018457.
850541.
703849.
6151009.
7497799.
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