計量經濟學-龐皓-第三版課后答案(同名20965)第二章簡單線性回歸模型2.1（1）①首先分析人均壽命與人均GDP的數量關系，用Eviews分析：DependentVariable:YMethod:LeastSquaresDate:12/27/14Time:21:00Sample:122Includedobservations:22VariableCoefficientStd.Errort-StatisticProb.

C56.647941.96082028.889920.0000X10.1283600.0272424.7118340.0001Sample:122Includedobservations:22VariableCoefficientStd.Errort-StatisticProb.

C31.799566.5364344.8649710.0001X30.3872760.0802604.8252850.0001R-squared0.537929

Meandependentvar62.50000AdjustedR-squared0.514825

S.D.dependentvar10.08889S.E.ofregression7.027364

Akaikeinfocriterion6.824009Sumsquaredresid987.6770

Schwarzcriterion6.923194Loglikelihood-73.06409

Hannan-Quinncriter.6.847374F-statistic23.28338

Durbin-Watsonstat0.952555Prob(F-statistic)0.000103由上可知，關系式為y=31.79956+0.387276x3（2）①關于人均壽命與人均GDP模型，由上可知，可決系數為0.526082，說明所建模型整體上對樣本數據擬合較好。對于回歸系數的t檢驗：t（β1）=4.711834>t0.025(20)=2.086，對斜率系數的顯著性檢驗表明，人均GDP對人均壽命有顯著影響。②關于人均壽命與成人識字率模型，由上可知，可決系數為0.716825，說明所建模型整體上對樣本數據擬合較好。對于回歸系數的t檢驗：t（β2）=7.115308>t0.025(20)=2.086，對斜率系數的顯著性檢驗表明，成人識字率對人均壽命有顯著影響。③關于人均壽命與一歲兒童疫苗的模型，由上可知，可決系數為0.537929，說明所建模型整體上對樣本數據擬合較好。對于回歸系數的t檢驗：t（β3）=4.825285>t0.025(20)=2.086，對斜率系數的顯著性檢驗表明，一歲兒童疫苗接種率對人均壽命有顯著影響。2.2（1）①對于浙江省預算收入與全省生產總值的模型，用Eviews分析結果如下：DependentVariable:YMethod:LeastSquaresDate:12/03/14Time:17:00Sample(adjusted):133Includedobservations:33afteradjustmentsVariableCoefficientStd.Errort-StatisticProb.

X0.1761240.00407243.256390.0000C-154.306339.08196-3.9482740.0004R-squared0.983702

Meandependentvar902.5148AdjustedR-squared0.983177

S.D.dependentvar1351.009S.E.ofregression175.2325

Akaikeinfocriterion13.22880Sumsquaredresid951899.7

Schwarzcriterion13.31949Loglikelihood-216.2751

Hannan-Quinncriter.13.25931F-statistic1871.115

Durbin-Watsonstat0.100021Prob(F-statistic)0.000000②由上可知，模型的參數：斜率系數0.176124，截距為—154.3063③關于浙江省財政預算收入與全省生產總值的模型，檢驗模型的顯著性：1）可決系數為0.983702，說明所建模型整體上對樣本數據擬合較好。2）對于回歸系數的t檢驗：t（β2）=43.25639>t0.025(31)=2.0395，對斜率系數的顯著性檢驗表明，全省生產總值對財政預算總收入有顯著影響。④用規范形式寫出檢驗結果如下：Y=0.176124X—154.3063(0.004072)(39.08196)t=(43.25639)（-3.948274）R2=0.983702F=1871.115n=33⑤經濟意義是：全省生產總值每增加1億元，財政預算總收入增加0.176124億元。（2）當x=32000時，①進行點預測，由上可知Y=0.176124X—154.3063，代入可得：Y=Y=0.176124*32000—154.3063=5481.6617②進行區間預測：先由Eviews分析：XY

Mean

6000.441

902.5148

Median

2689.280

209.3900

Maximum

27722.31

4895.410

Minimum

123.7200

25.87000

Std.Dev.

7608.021

1351.009

Skewness

1.432519

1.663108

Kurtosis

4.010515

4.590432

Jarque-Bera

12.69068

18.69063

Probability

0.001755

0.000087

Sum

198014.5

29782.99

SumSq.Dev.

1.85E+09

58407195

Observations

33

33由上表可知，∑x2=∑（Xi—X）2=δ2x(n—1)=

7608.0212x(33—1)=1852223.473(Xf—X)2=(32000—

6000.441)2=675977068.2當Xf=32000時，將相關數據代入計算得到：5481.6617—2.0395x175.2325x√1/33+1852223.473/675977068.2≤Yf≤5481.6617+2.0395x175.2325x√1/33+1852223.473/675977068.2即Yf的置信區間為（5481.6617—64.9649,5481.6617+64.9649）(3)對于浙江省預算收入對數與全省生產總值對數的模型，由Eviews分析結果如下：DependentVariable:LNYMethod:LeastSquaresDate:12/03/14Time:18:00Sample(adjusted):133Includedobservations:33afteradjustmentsVariableCoefficientStd.Errort-StatisticProb.

LNX0.9802750.03429628.582680.0000C-1.9182890.268213-7.1521210.0000R-squared0.963442

Meandependentvar5.573120AdjustedR-squared0.962263

S.D.dependentvar1.684189S.E.ofregression0.327172

Akaikeinfocriterion0.662028Sumsquaredresid3.318281

Schwarzcriterion0.752726Loglikelihood-8.923468

Hannan-Quinncriter.0.692545F-statistic816.9699

Durbin-Watsonstat0.096208Prob(F-statistic)0.000000①模型方程為：lnY=0.980275lnX-1.918289②由上可知，模型的參數：斜率系數為0.980275，截距為-1.918289③關于浙江省財政預算收入與全省生產總值的模型，檢驗其顯著性：1）可決系數為0.963442，說明所建模型整體上對樣本數據擬合較好。2）對于回歸系數的t檢驗：t（β2）=28.58268>t0.025(31)=2.0395，對斜率系數的顯著性檢驗表明，全省生產總值對財政預算總收入有顯著影響。④經濟意義：全省生產總值每增長1%，財政預算總收入增長0.980275%2.4（1）對建筑面積與建造單位成本模型，用Eviews分析結果如下：DependentVariable:YMethod:LeastSquaresDate:12/01/14Time:12:40Sample:112Includedobservations:12VariableCoefficientStd.Errort-StatisticProb.

X-64.184004.809828-13.344340.0000C1845.47519.2644695.796880.0000R-squared0.946829

Meandependentvar1619.333AdjustedR-squared0.941512

S.D.dependentvar131.2252S.E.ofregression31.73600

Akaikeinfocriterion9.903792Sumsquaredresid10071.74

Schwarzcriterion9.984610Loglikelihood-57.42275

Hannan-Quinncriter.9.873871F-statistic178.0715

Durbin-Watsonstat1.172407Prob(F-statistic)0.000000由上可得：建筑面積與建造成本的回歸方程為：Y=1845.475--64.18400X（2）經濟意義：建筑面積每增加1萬平方米，建筑單位成本每平方米減少64.18400元。（3）①首先進行點預測，由Y=1845.475--64.18400X得，當x=4.5，y=1556.647②再進行區間估計：用Eviews分析：YX

Mean

1619.333

3.523333

Median

1630.000

3.715000

Maximum

1860.000

6.230000

Minimum

1419.000

0.600000

Std.Dev.

131.2252

1.989419

Skewness

0.003403-0.060130

Kurtosis

2.346511

1.664917

Jarque-Bera

0.213547

0.898454

Probability

0.898729

0.638121

Sum

19432.00

42.28000

SumSq.Dev.

189420.7

43.53567

Observations

12

12由上表可知，∑x2=∑（Xi—X）2=δ2x(n—1)=

1.9894192x(12—1)=43.5357(Xf—X)2=(4.5—

3.523333)2=0.95387843當Xf=4.5時，將相關數據代入計算得到：1556.647—2.228x31.73600x√1/12+43.5357/0.95387843≤Yf≤1556.647+2.228x31.73600x√1/12+43.5357/0.95387843即Yf的置信區間為（1556.647—478.1231,1556.647+478.1231）3.1（1）①對百戶擁有家用汽車量計量經濟模型，用Eviews分析結果如下：DependentVariable:YMethod:LeastSquaresDate:11/25/14Time:12:38Sample:131Includedobservations:31VariableCoefficientStd.Errort-StatisticProb.

X25.9968651.4060584.2650200.0002X3-0.5240270.179280-2.9229500.0069X4-2.2656800.518837-4.3668420.0002C246.854051.975004.7494760.0001R-squared0.666062

Meandependentvar16.77355AdjustedR-squared0.628957

S.D.dependentvar8.252535S.E.ofregression5.026889

Akaikeinfocriterion6.187394Sumsquaredresid682.2795

Schwarzcriterion6.372424Loglikelihood-91.90460

Hannan-Quinncriter.6.247709F-statistic17.95108

Durbin-Watsonstat1.147253Prob(F-statistic)0.000001

②得到模型得：Y=246.8540+5.996865X2-0.524027X3-2.265680X4③對模型進行檢驗：可決系數是0.666062，修正的可決系數為0.628957，說明模型對樣本擬合較好F檢驗，F=17.95108>F（3,27）=3.65，回歸方程顯著。3）t檢驗，t統計量分別為4.749476，4.265020，-2.922950，-4.366842，均大于t（27）=2.0518，所以這些系數都是顯著的。④依據：可決系數越大，說明擬合程度越好F的值與臨界值比較，若大于臨界值，則否定原假設，回歸方程是顯著的；若小于臨界值，則接受原假設，回歸方程不顯著。t的值與臨界值比較，若大于臨界值，則否定原假設，系數都是顯著的；若小于臨界值，則接受原假設，系數不顯著。（2）經濟意義：人均ＧＤＰ增加１萬元，百戶擁有家用汽車增加5.996865輛，城鎮人口比重增加１個百分點，百戶擁有家用汽車減少0.524027輛，交通工具消費價格指數每上升１，百戶擁有家用汽車減少2.265680輛。（3）用EViews分析得：DependentVariable:YMethod:LeastSquaresDate:12/08/14Time:17:28Sample:131Includedobservations:31VariableCoefficientStd.Errort-StatisticProb.

X25.1356701.0102705.0834650.0000LNX3-22.810056.771820-3.3683780.0023LNX4-230.848149.46791-4.6666240.0001C1148.758228.29175.0319740.0000R-squared0.691952

Meandependentvar16.77355AdjustedR-squared0.657725

S.D.dependentvar8.252535S.E.ofregression4.828088

Akaikeinfocriterion6.106692Sumsquaredresid629.3818

Schwarzcriterion6.291723Loglikelihood-90.65373

Hannan-Quinncriter.6.167008F-statistic20.21624

Durbin-Watsonstat1.150090Prob(F-statistic)0.000000模型方程為：Y=5.135670X2-22.81005LNX3-230.8481LNX4+1148.758此分析得出的可決系數為0.691952>0.666062，擬合程度得到了提高，可這樣改進。3.2（１）對出口貨物總額計量經濟模型，用Eviews分析結果如下：：DependentVariable:YMethod:LeastSquaresDate:12/01/14Time:20:25Sample:19942011Includedobservations:18VariableCoefficientStd.Errort-StatisticProb.

X20.1354740.01279910.584540.0000X318.853489.7761811.9285120.0729C-18231.588638.216-2.1105730.0520R-squared0.985838

Meandependentvar6619.191AdjustedR-squared0.983950

S.D.dependentvar5767.152S.E.ofregression730.6306

Akaikeinfocriterion16.17670Sumsquaredresid8007316.

Schwarzcriterion16.32510Loglikelihood-142.5903

Hannan-Quinncriter.16.19717F-statistic522.0976

Durbin-Watsonstat1.173432Prob(F-statistic)0.000000①由上可知，模型為：Y=0.135474X2+18.85348X3-18231.58②對模型進行檢驗： 1）可決系數是0.985838，修正的可決系數為0.983950，說明模型對樣本擬合較好2）F檢驗，F=522.0976>F（2,15）=4.77，回歸方程顯著3）t檢驗，t統計量分別為X2的系數對應t值為10.58454，大于t（15）=2.131，系數是顯著的，X3的系數對應t值為1.928512，小于t（15）=2.131，說明此系數是不顯著的。（2）對于對數模型，用Eviews分析結果如下：DependentVariable:LNYMethod:LeastSquaresDate:12/01/14Time:20:25Sample:19942011Includedobservations:18VariableCoefficientStd.Errort-StatisticProb.

LNX21.5642210.08898817.577890.0000LNX31.7606950.6821152.5812290.0209C-20.520485.432487-3.7773630.0018R-squared0.986295

Meandependentvar8.400112AdjustedR-squared0.984467

S.D.dependentvar0.941530S.E.ofregression0.117343

Akaikeinfocriterion-1.296424Sumsquaredresid0.206540

Schwarzcriterion-1.148029Loglikelihood14.66782

Hannan-Quinncriter.-1.275962F-statistic539.7364

Durbin-Watsonstat0.686656Prob(F-statistic)0.000000①由上可知，模型為：LNY=-20.52048+1.564221LNX2+1.760695LNX3②對模型進行檢驗：1）可決系數是0.986295，修正的可決系數為0.984467，說明模型對樣本擬合較好。2）F檢驗，F=539.7364>F（2,15）=4.77，回歸方程顯著。3）t檢驗，t統計量分別為-3.777363，17.57789，2.581229，均大于t（15）=2.131，所以這些系數都是顯著的。（3）①（1）式中的經濟意義：工業增加1億元，出口貨物總額增加0.135474億元，人民幣匯率增加1，出口貨物總額增加18.85348億元。②（2）式中的經濟意義：工業增加額每增加1%，出口貨物總額增加1.564221%，人民幣匯率每增加1%，出口貨物總額增加1.760695%3.3（1）對家庭書刊消費對家庭月平均收入和戶主受教育年數計量模型，由Eviews分析結果如下：DependentVariable:YMethod:LeastSquaresDate:12/01/14Time:20:30Sample:118Includedobservations:18VariableCoefficientStd.Errort-StatisticProb.

X0.0864500.0293632.9441860.0101T52.370315.20216710.067020.0000C-50.0163849.46026-1.0112440.3279R-squared0.951235

Meandependentvar755.1222AdjustedR-squared0.944732

S.D.dependentvar258.7206S.E.ofregression60.82273

Akaikeinfocriterion11.20482Sumsquaredresid55491.07

Schwarzcriterion11.35321Loglikelihood-97.84334

Hannan-Quinncriter.11.22528F-statistic146.2974

Durbin-Watsonstat2.605783Prob(F-statistic)0.000000①模型為：Y=0.086450X+52.37031T-50.01638②對模型進行檢驗：1）可決系數是0.951235，修正的可決系數為0.944732，說明模型對樣本擬合較好。2）F檢驗，F=539.7364>F（2,15）=4.77，回歸方程顯著。3）t檢驗，t統計量分別為2.944186，10.06702，均大于t（15）=2.131，所以這些系數都是顯著的。③經濟意義：家庭月平均收入增加1元，家庭書刊年消費支出增加0.086450元，戶主受教育年數增加1年，家庭書刊年消費支出增加52.37031元。（2）用Eviews分析：①DependentVariable:YMethod:LeastSquaresDate:12/01/14Time:22:30Sample:118Includedobservations:18VariableCoefficientStd.Errort-StatisticProb.

T63.016764.54858113.854160.0000C-11.5817158.02290-0.1996060.8443R-squared0.923054

Meandependentvar755.1222AdjustedR-squared0.918245

S.D.dependentvar258.7206S.E.ofregression73.97565

Akaikeinfocriterion11.54979Sumsquaredresid87558.36

Schwarzcriterion11.64872Loglikelihood-101.9481

Hannan-Quinncriter.11.56343F-statistic191.9377

Durbin-Watsonstat2.134043Prob(F-statistic)0.000000②DependentVariable:XMethod:LeastSquaresDate:12/01/14Time:22:34Sample:118Includedobservations:18VariableCoefficientStd.Errort-StatisticProb.

T123.151631.841503.8676440.0014C444.5888406.17861.0945650.2899R-squared0.483182

Meandependentvar1942.933AdjustedR-squared0.450881

S.D.dependentvar698.8325S.E.ofregression517.8529

Akaikeinfocriterion15.44170Sumsquaredresid4290746.

Schwarzcriterion15.54063Loglikelihood-136.9753

Hannan-Quinncriter.15.45534F-statistic14.95867

Durbin-Watsonstat1.052251Prob(F-statistic)0.001364以上分別是y與T，X與T的一元回歸模型分別是：Y=63.01676T-11.58171X=123.1516T+444.5888（3）對殘差進行模型分析，用Eviews分析結果如下：DependentVariable:E1Method:LeastSquaresDate:12/03/14Time:20:39Sample:118Includedobservations:18VariableCoefficientStd.Errort-StatisticProb.

E20.0864500.0284313.0407420.0078C3.96E-1413.880832.85E-151.0000R-squared0.366239

Meandependentvar2.30E-14AdjustedR-squared0.326629

S.D.dependentvar71.76693S.E.ofregression58.89136

Akaikeinfocriterion11.09370Sumsquaredresid55491.07

Schwarzcriterion11.19264Loglikelihood-97.84334

Hannan-Quinncriter.11.10735F-statistic9.246111

Durbin-Watsonstat2.605783Prob(F-statistic)0.007788模型為：E1=0.086450E2+3.96e-14參數：斜率系數α為0.086450，截距為3.96e-14（3）由上可知，β2與α2的系數是一樣的。回歸系數與被解釋變量的殘差系數是一樣的，它們的變化規律是一致的。3.6（1）預期的符號是X1，X2,X3,X4,X5的符號為正，X6的符號為負（2）根據Eviews分析得到數據如下：DependentVariable:YMethod:LeastSquaresDate:12/04/14Time:13:24Sample:19942011Includedobservations:18VariableCoefficientStd.Errort-StatisticProb.

X20.0013820.0011021.2543300.2336X30.0019420.0039600.4905010.6326X4-3.5790903.559949-1.0053770.3346X50.0047910.0050340.9516710.3600X60.0455420.0955520.4766210.6422C-13.7773215.73366-0.8756590.3984R-squared0.994869

Meandependentvar12.76667AdjustedR-squared0.992731

S.D.dependentvar9.746631S.E.ofregression0.830963

Akaikeinfocriterion2.728738Sumsquaredresid8.285993

Schwarzcriterion3.025529Loglikelihood-18.55865

Hannan-Quinncriter.2.769662F-statistic465.3617

Durbin-Watsonstat1.553294Prob(F-statistic)0.000000①與預期不相符。②評價：可決系數為0.994869，數據相當大，可以認為擬合程度很好。F檢驗，F=465.3617>F（5.12）=3,89，回歸方程顯著T檢驗，X1，X2,X3,X4,X5，X6系數對應的t值分別為：1.254330，0.490501，-1.005377，0.951671，0.476621，均小于t（12）=2.179，所以所得系數都是不顯著的。（3）根據Eviews分析得到數據如下：DependentVariable:YMethod:LeastSquaresDate:12/03/14Time:11:12Sample:19942011Includedobservations:18VariableCoefficientStd.Errort-StatisticProb.

X50.0010322.20E-0546.799460.0000X6-0.0549650.031184-1.7625810.0983C4.2054813.3356021.2607860.2266R-squared0.993601

Meandependentvar12.76667AdjustedR-squared0.992748

S.D.dependentvar9.746631S.E.ofregression0.830018

Akaikeinfocriterion2.616274Sumsquaredresid10.33396

Schwarzcriterion2.764669Loglikelihood-20.54646

Hannan-Quinncriter.2.636736F-statistic1164.567

Durbin-Watsonstat1.341880Prob(F-statistic)0.000000①得到模型的方程為：Y=0.001032X5-0.054965X6+4.205481②評價：可決系數為0.993601，數據相當大，可以認為擬合程度很好。F檢驗，F=1164.567>F（5.12）=3,89，回歸方程顯著T檢驗，X5系數對應的t值為46.79946，大于t（12）=2.179，所以系數是顯著的，即人均GDP對年底存款余額有顯著影響。X6系數對應的t值為-1.762581，小于t（12）=2.179，所以系數是不顯著的。4.3（1）根據Eviews分析得到數據如下：DependentVariable:LNYMethod:LeastSquaresDate:12/05/14Time:11:39Sample:19852011Includedobservations:27VariableCoefficientStd.Errort-StatisticProb.

LNGDP1.3385330.08861015.105820.0000LNCPI-0.4217910.233295-1.8079750.0832C-3.1114860.463010-6.7201260.0000R-squared0.988051

Meandependentvar9.484710AdjustedR-squared0.987055

S.D.dependentvar1.425517S.E.ofregression0.162189

Akaikeinfocriterion-0.695670Sumsquaredresid0.631326

Schwarzcriterion-0.551689Loglikelihood12.39155

Hannan-Quinncriter.-0.652857F-statistic992.2582

Durbin-Watsonstat0.522613Prob(F-statistic)0.000000得到的模型方程為：LNY=1.338533LNGDPt-0.421791LNCPIt-3.111486（2）該模型的可決系數為0.988051，可決系數很高，F檢驗值為992.2582，明顯顯著。但當α=0.05時，t（24）=2.064，LNCPI的系數不顯著，可能存在多重共線性。②得到相關系數矩陣如下：LNYLNGDPLNCPILNY

1.000000

0.993189

0.935116LNGDP

0.993189

1.000000

0.953740LNCPI

0.935116

0.953740

1.000000

LNGDP，LNCPI之間的相關系數很高，證實確實存在多重共線性。（3）由Eviews得：a）DependentVariable:LNYMethod:LeastSquaresDate:12/03/14Time:14:41Sample:19852011Includedobservations:27VariableCoefficientStd.Errort-StatisticProb.

LNGDP1.1857390.02782242.619330.0000C-3.7506700.312255-12.011560.0000R-squared0.986423

Meandependentvar9.484710AdjustedR-squared0.985880

S.D.dependentvar1.425517S.E.ofregression0.169389

Akaikeinfocriterion-0.642056Sumsquaredresid0.717312

Schwarzcriterion-0.546068Loglikelihood10.66776

Hannan-Quinncriter.-0.613514F-statistic1816.407

Durbin-Watsonstat0.471111Prob(F-statistic)0.000000b)DependentVariable:LNYMethod:LeastSquaresDate:12/03/14Time:14:41Sample:19852011Includedobservations:27VariableCoefficientStd.Errort-StatisticProb.

LNCPI2.9392950.22275613.195110.0000C-6.8545351.242243-5.5178710.0000R-squared0.874442

Meandependentvar9.484710AdjustedR-squared0.869419

S.D.dependentvar1.425517S.E.ofregression0.515124

Akaikeinfocriterion1.582368Sumsquaredresid6.633810

Schwarzcriterion1.678356Loglikelihood-19.36196

Hannan-Quinncriter.1.610910F-statistic174.1108

Durbin-Watsonstat0.137042Prob(F-statistic)0.000000c)DependentVariable:LNGDPMethod:LeastSquaresDate:12/05/14Time:11:11Sample:19852011Includedobservations:27VariableCoefficientStd.Errort-StatisticProb.

LNCPI2.5110220.15830215.862270.0000C-2.7963810.882798-3.1676340.0040R-squared0.909621

Meandependentvar11.16214AdjustedR-squared0.906005

S.D.dependentvar1.194029S.E.ofregression0.366072

Akaikeinfocriterion0.899213Sumsquaredresid3.350216

Schwarzcriterion0.995201Loglikelihood-10.13938

Hannan-Quinncriter.0.927755F-statistic251.6117

Durbin-Watsonstat0.099623Prob(F-statistic)0.000000①得到的回歸方程分別為1）LNY=1.185739LNGDPt-3.7506702）LNY=2.939295LNCPIt-6.8545353）LNGDPt=2.511022LNCPIt-2.796381②對多重共線性的認識：單方程擬合效果都很好，回歸系數顯著，判定系數較高，GDP和CPI對進口的顯著的單一影響，在這兩個變量同時引入模型時影響方向發生了改變，這只有通過相關系數的分析才能發現。（4）建議：如果僅僅是作預測，可以不在意這種多重共線性，但如果是進行結構分析，還是應該引起注意的。4.4（1）按照設計的理論模型，由Eviews分析得：DependentVariable:CZSRMethod:LeastSquaresDate:12/03/14Time:11:40Sample:19852011Includedobservations:27VariableCoefficientStd.Errort-StatisticProb.

CZZC0.0901140.0443672.0311290.0540GDP-0.0253340.005069-4.9980360.0000SSZE1.1768940.06216218.932710.0000C-221.8540130.6532-1.6980380.1030R-squared0.999857

Meandependentvar22572.56AdjustedR-squared0.999838

S.D.dependentvar27739.49S.E.ofregression353.0540

Akaikeinfocriterion14.70707Sumsquaredresid2866884.

Schwarzcriterion14.89905Loglikelihood-194.5455

Hannan-Quinncriter.14.76416F-statistic53493.93

Durbin-Watsonstat1.458128Prob(F-statistic)0.000000從回歸結果可見，可決系數為0.999857，校正的可決系數為0.999838，模型擬合的很好。F的統計量為53493.93，說明在α=0.05,水平下，回歸方程回歸方程整體上是顯著的。但是t檢驗結果表明，國內生產總值對財政收入的影響顯著，但回歸系數的符號為負，與實際不符合。由此可得知，該方程可能存在多重共線性。（2）得到相關系數矩陣如下：CZSRCZZCGDPSSZECZSR

1.000000

0.998729

0.992838

0.999832CZZC

0.998729

1.000000

0.992536

0.998575GDP

0.992838

0.992536

1.000000

0.994370SSZE

0.999832

0.998575

0.994370

1.000000由上表可知，CZZC與GDP，CZZC與SSZE，GDP與SSZE之間的相關系數都非常高，說明確實存在多重共線性。（3）做輔助回歸被解釋變量可決系數方差擴大因子CZZC0.997168353GDP0.98883390SSZE0.997862468方差擴大因子均大于10，存在嚴重多重共線性。并且通過以上分析，兩兩被解釋變量之間相關性都很高。（4）解決方式：分別作出財政收入與財政支出、國內生產總值、稅收總額之間的一元回歸。5.2（1）①用圖形法檢驗繪制e2的散點圖，用Eviews分析如下：由上圖可知，模型可能存在異方差，Goldfeld-Quanadt檢驗1）定義區間為1-7時，由軟件分析得：DependentVariable:YMethod:LeastSquaresDate:12/10/14Time:14:52Sample:17Includedobservations:7VariableCoefficientStd.Errort-StatisticProb.

T35.206644.9014927.1828430.0020X0.1099490.0619651.7743800.1507C77.1258882.328440.9368070.4019R-squared0.943099

Meandependentvar565.6857AdjustedR-squared0.914649

S.D.dependentvar108.2755S.E.ofregression31.63265

Akaikeinfocriterion10.04378Sumsquaredresid4002.499

Schwarzcriterion10.02060Loglikelihood-32.15324

Hannan-Quinncriter.9.757267F-statistic33.14880

Durbin-Watsonstat1.426262Prob(F-statistic)0.003238得∑e1i2=4002.4992）定義區間為12-18時，由軟件分析得：DependentVariable:YMethod:LeastSquaresDate:12/10/14Time:13:50Sample:1218Includedobservations:7VariableCoefficientStd.Errort-StatisticProb.

T52.405886.9233787.5694090.0016X0.0686890.0537631.2776350.2705C-8.78926579.92542-0.1099680.9177R-squared0.984688

Meandependentvar887.6143AdjustedR-squared0.977032

S.D.dependentvar274.4148S.E.ofregression41.58810

Akaikeinfocriterion10.59103Sumsquaredresid6918.280

Schwarzcriterion10.56785Loglikelihood-34.06861

Hannan-Quinncriter.10.30451F-statistic128.6166

Durbin-Watsonstat2.390329Prob(F-statistic)0.000234得∑e2i2=6918.2803）根據Goldfeld-Quanadt檢驗，F統計量為：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為4，查分布表得臨界值F0.05（4,4）=6.39，因為F=1.7285<F0.05（4,4）=6.39，所以接受原假設，此檢驗表明模型不存在異方差。（2）存在異方差，估計參數的方法：①可以對模型進行變換②使用加權最小二乘法進行計算，得出模型方程，并對其進行相關檢驗③對模型進行對數變換，進行分析（3）評價：3.3所得結論是可以相信的，隨機擾動項之間不存在異方差。回歸方程是顯著的。5.3(1)由Eviews軟件分析得：DependentVariable:YMethod:LeastSquaresDate:12/10/14Time:16:00Sample:131Includedobservations:31VariableCoefficientStd.Errort-StatisticProb.

X1.2442810.07903215.744110.0000C242.4488291.19400.8326020.4119R-squared0.895260

Meandependentvar4443.526AdjustedR-squared0.891649

S.D.dependentvar1972.072S.E.ofregression649.1426

Akaikeinfocriterion15.85152Sumsquaredresid12220196

Schwarzcriterion15.94404Loglikelihood-243.6986

Hannan-Quinncriter.15.88168F-statistic247.8769

Durbin-Watsonstat1.078581Prob(F-statistic)0.000000由上表可知，2007年我國農村居民家庭人均消費支出（x）對人均純收入（y）的模型為：Y=1.244281X+242.4488（2）①由圖形法檢驗由上圖可知，模型可能存在異方差。②Goldfeld-Quanadt檢驗1）定義區間為1-12時，由軟件分析得：DependentVariable:Y1Method:LeastSquaresDate:12/10/14Time:11:34Sample:112Includedobservations:12VariableCoefficientStd.Errort-StatisticProb.

X11.4852960.5003862.9682970.0141C-550.54921220.063-0.4512470.6614R-squared0.468390

Meandependentvar3052.950AdjustedR-squared0.415229

S.D.dependentvar550.5148S.E.ofregression420.9803

Akaikeinfocriterion15.07406Sumsquaredresid1772245.

Schwarzcriterion15.15488Loglikelihood-88.44437

Hannan-Quinncriter.15.04414F-statistic8.810789

Durbin-Watsonstat2.354167Prob(F-statistic)0.014087得∑e1i2=1772245.2）定義區間為20-31時，由軟件分析得：DependentVariable:Y1Method:LeastSquaresDate:12/10/14Time:16:36Sample:2031Includedobservations:12VariableCoefficientStd.Errort-StatisticProb.

X11.0869400.1488637.3016230.0000C1173.307733.25201.6001410.1407R-squared0.842056

Meandependentvar6188.329AdjustedR-squared0.826262

S.D.dependentvar2133.692S.E.ofregression889.3633

Akaikeinfocriterion16.56990Sumsquaredresid7909670.

Schwarzcriterion16.65072Loglikelihood-97.41940

Hannan-Quinncriter.16.53998F-statistic53.31370

Durbin-Watsonstat2.339767Prob(F-statistic)0.000026得∑e2i2=7909670.3）根據Goldfeld-Quanadt檢驗，F統計量為：F=∑e2i2/∑e1i2=7909670./1772245=4.4631在α=0.05水平下，分子分母的自由度均為10，查分布表得臨界值F0.05（10,10）=2.98，因為F=4.4631>F0.05（10,10）=2.98，所以拒絕原假設，此檢驗表明模型存在異方差。（3）1）采用WLS法估計過程中，①用權數w1=1/X,建立回歸得：DependentVariable:YMethod:LeastSquaresDate:12/09/14Time:11:13Sample:131Includedobservations:31Weightingseries:W1VariableCoefficientStd.Errort-StatisticProb.

X1.4258590.11910411.971570.0000C-334.8131344.3523-0.9722980.3389WeightedStatisticsR-squared0.831707

Meandependentvar3946.082AdjustedR-squared0.825904

S.D.dependentvar536.1907S.E.ofregression536.6796

Akaikeinfocriterion15.47102Sumsquaredresid8352726.

Schwarzcriterion15.56354Loglikelihood-237.8008

Hannan-Quinncriter.15.50118F-statistic143.3184

Durbin-Watsonstat1.369081Prob(F-statistic)0.000000UnweightedStatisticsR-squared0.875855

Meandependentvar4443.526AdjustedR-squared0.871574

S.D.dependentvar1972.072S.E.ofregression706.7236

Sumsquaredresid14484289Durbin-Watsonstat1.532908

對此模型進行White檢驗得：HeteroskedasticityTest:WhiteF-statistic0.299395

Prob.F(2,28)0.7436Obs*R-squared0.649065

Prob.Chi-Square(2)0.7229ScaledexplainedSS1.798067

Prob.Chi-Square(2)0.4070TestEquation:DependentVariable:WGT_RESID^2Method:LeastSquaresDate:12/10/14Time:21:13Sample:131Includedobservations:31CollineartestregressorsdroppedfromspecificationVariableCoefficientStd.Errort-StatisticProb.

C61927.891045682.0.0592220.9532WGT^2-593927.91173622.-0.5060640.6168X*WGT^2282.4407747.97800.3776060.7086R-squared0.020938

Meandependentvar269442.8AdjustedR-squared-0.048995

S.D.dependentvar689166.5S.E.ofregression705847.6

Akaikeinfocriterion29.86395Sumsquaredresid1.40E+13

Schwarzcriterion30.00273Loglikelihood-459.8913

Hannan-Quinncriter.29.90919F-statistic0.299395

Durbin-Watsonstat1.922336Prob(F-statistic)0.743610從上可知，nR2=0.649065，比較計算的統計量的臨界值，因為nR2=0.649065<0.05（2）=5.9915，所以接受原假設，該模型消除了異方差。估計結果為：Y=1.425859X-334.8131t=（11.97157）（-0.972298）R2=0.875855F=143.3184DW=1.369081②用權數w2=1/x2,用回歸分析得：DependentVariable:YMethod:LeastSquaresDate:12/09/14Time:21:08Sample:131Includedobservations:31Weightingseries:W2VariableCoefficientStd.Errort-StatisticProb.

X1.5570400.14539210.709220.0000C-693.1946376.4760-1.8412720.0758WeightedStatisticsR-squared0.798173

Meandependentvar3635.028AdjustedR-squared0.791214

S.D.dependentvar1029.830S.E.ofregression466.8513

Akaikeinfocriterion15.19224Sumsquaredresid6320554.

Schwarzcriterion15.28475Loglikelihood-233.4797

Hannan-Quinncriter.15.22240F-statistic114.6875

Durbin-Watsonstat1.562975Prob(F-statistic)0.000000UnweightedStatisticsR-squared0.834850

Meandependentvar4443.526AdjustedR-squared0.829156

S.D.dependentvar1972.072S.E.ofregression815.1229

Sumsquaredresid19268334Durbin-Watsonstat1.678365

對此模型進行White檢驗得：HeteroskedasticityTest:WhiteF-statistic0.299790

Prob.F(3,27)0.8252Obs*R-squared0.999322

Prob.Chi-Square(3)0.8014ScaledexplainedSS1.789507

Prob.Chi-Square(3)0.6172TestEquation: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-squared0.032236

Meandependentvar203888.8AdjustedR-squared-0.075293

S.D.dependentvar419282.0S.E.ofregression434780.1

Akaikeinfocriterion28.92298Sumsquaredresid5.10E+12

Schwarzcriterion29.10801Loglikelihood-444.3062

Hannan-Quinncriter.28.98330F-statistic0.299790

Durbin-Watsonstat1.835854Prob(F-statistic)0.825233從上可知，nR2=0.999322，比較計算的統計量的臨界值，因為nR2=0.999322<0.05（2）=5.9915，所以接受原假設，該模型消除了異方差。估計結果為：Y=1.557040X-693.1946t=（10.70922）（-1.841272）R2=0.798173F=114.6875DW=1.562975③用權數w3=1/sqr（x）,用回歸分析得：DependentVariable:YMethod:LeastSquaresDate:12/09/14Time:21:35Sample:131Includedobservations:31Weightingseries:W3VariableCoefficientStd.Errort-StatisticProb.

X1.3301300.09834513.525070.0000C-47.40242313.1154-0.1513900.8807WeightedStatisticsR-squared0.863161

Meandependentvar4164.118AdjustedR-squared0.858442

S.D.dependentvar991.2079S.E.ofregression586.9555

Akaikeinfocriterion15.65012Sumsquaredresid9990985.

Schwarzcriterion15.74263Loglikelihood-240.5768

Hannan-Quinncriter.15.68027F-statistic182.9276

Durbin-Watsonstat1.237664Prob(F-statistic)0.000000UnweightedStatisticsR-squared0.890999

Meandependentvar4443.526AdjustedR-squared0.887240

S.D.dependentvar1972.072S.E.ofregression662.2171

Sumsquaredresid12717412Durbin-Watsonstat1.314859

對此模型進行White檢驗得：HeteroskedasticityTest:WhiteF-statistic0.423886

Prob.F(2,28)0.6586Obs*R-squared0.911022

Prob.Chi-Square(2)0.6341ScaledexplainedSS2.768332

Prob.Chi-Square(2)0.2505TestEquation:DependentVariable:WGT_RESID^2Method:LeastSquaresDate:12/09/14Time:20:36Sample:131Includedobservations:31CollineartestregressorsdroppedfromspecificationVariableCoefficientStd.Errort-StatisticProb.

C1212308.2141958.0.5659810.5759WGT^2-715673.01301839.-0.5497400.5869X^2*WGT^2-0.0151940.082276-0.1846770.8548R-squared0.029388

Meandependentvar322289.8AdjustedR-squared-0.039942

S.D.dependentvar863356.7S.E.ofregression880429.8

Akaikeinfocriterion30.30597Sumsquaredresid2.17E+13

Schwarzcriterion30.44475Loglikelihood-466.7426

Hannan-Quinncriter.30.35121F-statistic0.423886

Durbin-Watsonstat1.887426Prob(F-statistic)0.658628從上可知，nR2=0.911022，比較計算的統計量的臨界值，因為nR2=0.911022<0.05（2）=5.9915，所以接受原假設，該模型消除了異方差。估計結果為：Y=1.330130X-47.40242t=（13.52507）（-0.151390）R2=0.863161F=182.9276DW=1.237664經過檢驗發現，用權數w1的效果最好，所以綜上可知，即修改后的結果為：Y=1.425859X-334.8131t=（11.97157）（-0.972298）R2=0.875855F=143.3184DW=1.369