計量經(jīng)濟(jì)學(xué)龐皓第三版課后答案資料

第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(shù)量關(guān)系，用Eviews分析:

DependentVariable:Y

Method:LeastSquares

Date:12/27/14Time:21:00

Sample:122

Includedobservations:22

VariableCoefficientStd.Errort-StatisticProb.

c56.647941.96082028.889920.0000

X10.1283600.0272424.7118340.0001

R-squared0.526082Meandependentvar62.50000

AdjustedR-squared0.502386S.D.dependentvar10.08889

S.E.ofregression7.116881Akaikeinfocriterion6.849324

Sumsquaredresid1013.000Schwarzcriterion6.948510

Loglikelihood-73.34257Hannan-Quinncriter.6.872689

F-statistic22.20138Durbin-Watsonstat0.629074

Prob(F-statistic)0.000134

有上可知,關(guān)系式為y=56.64794+0.128360x(

②關(guān)于人均壽命與成人識字率的關(guān)系，用Eviews分析如下:

DependentVariable:Y

Method:LeastSquares

Date:11/26/14Time:21:10

Sample:122

Includedobservations:22

VariableCoefficientStd.Errort-StatisticProb.

C38.794243.53207910.983400.0000

X20.3319710.0466567.1153080.0000

R-squared0.716825Meandependentvar62.50000

AdjustedR-squared0.702666S.D.dependentvar10.08889

S.E.ofregression5.501306Akaikeinfocriterion6.334356

Sumsquaredresid605.2873Schwarzcriterion6.433542

Loglikelihood-67.67792Hannan-Quinncriter.6.357721

F-statistic50.62761Durbin-Watsonstat1.846406

Prob(F-statistic)0.000001

由上可知,關(guān)系式為尸38.79424+0.331971X2

③關(guān)于人均壽命與一歲兒童疫苗接種率的關(guān)系，用Eviews分析如下:

DependentVariable:Y

Method:LeastSquares

Date:11/26/14Time:21:14

Sample:122

Includedobservations:22

VariableCoefficientStd.Errort-StatisticProb.

c31.799566.5364344.8649710.0001

X30.3872760.0802604.8252850.0001

R-squared0.537929Meandependentvar62.50000

AdjustedR-squared0.514825S.D.dependentvar10.08889

S.E.ofregression7.027364Akaikeinfocriterion6.824009

Sumsquaredresid987.6770Schwarzcriterion6.923194

Loglikelihood-73.06409Hannan-Quinncriter.6.847374

F-statistic23.28338Durbin-Watsonstat0.952555

Prob(F-statistic)0.000103

由上可知,關(guān)系式為y=31.79956+0.387276x3

(2)①關(guān)于人均壽命與人均GDP模型，由上可知，可決系數(shù)為0.526082,說明

所建模型整體上對樣本數(shù)據(jù)擬合較好。

對于回歸系數(shù)的t檢驗：t(0.)=4.711834>to.o25(2O)=2.O86,對斜率系數(shù)的顯

著性檢驗表明，人均GDP對人均壽命有顯著影響。

②關(guān)于人均壽命與成人識字率模型，由上可知，可決系數(shù)為0.716825,說明所

建模型整體上對樣本數(shù)據(jù)擬合較好。

對于回歸系數(shù)的t檢驗：t(82)=7.1153O8>to.o25(2O)=2.O86,對斜率系數(shù)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(guān)于人均壽命與一歲兒童疫苗的模型，由上可知，可決系數(shù)為0.537929,說

明所建模型整體上對樣本數(shù)據(jù)擬合較好。

對于回歸系數(shù)的t檢驗：t(03)=4.825285>to.o25(2O)=2.O86,對斜率系數(shù)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(yù)算收入與全省生產(chǎn)總值的模型，用Eviews分析結(jié)果如下：

DependentVariable:Y

Method:LeastSquares

Date:12/03/14Time:17:00

Sample(adjusted):133

Includedobservations:33afteradjustments

VariableCoefficientStd.Errort-StatisticProb.

X0.1761240.00407243.256390.0000

C-154.306339.08196-3.9482740.0004

R-squared0.983702Meandependentvar902.5148

AdjustedR-squared0.983177S.D.dependentvar1351.009

S.E.ofregression175.2325Akaikeinfocriterion13.22880

Sumsquaredresid951899.7Schwarzcriterion13.31949

Loglikelihood-216.2751Hannan-Quinncriter.13.25931

F-statistic1871.115Durbin-Watsonstat0.100021

Prob(F-statistic)0.000000

②由上可知，模型的參數(shù)：斜率系數(shù)0.176124,截距為一154.3063

③關(guān)于浙江省財政預(yù)算收入與全省生產(chǎn)總值的模型，檢驗?zāi)Ｐ偷娘@著性：

1)可決系數(shù)為0.983702,說明所建模型整體上對樣本數(shù)據(jù)擬合較好。

2)對于回歸系數(shù)的t檢驗：t(B2)=43.25639>to.o25(31)=2.0395,對斜率系

數(shù)的顯著性檢驗表明，全省生產(chǎn)總值對財政預(yù)算總收入有顯著影響。

④用規(guī)范形式寫出檢驗結(jié)果如下：

Y=0.176124X—154.3063

(0.004072)(39.08196)

t=(43.25639)(-3.948274)

R2=0.983702F=1871.115n=33

⑤經(jīng)濟(jì)意義是：全省生產(chǎn)總值每增加1億元，財政預(yù)算總收入增加0.176124億

JLo

(2)當(dāng)x=32000時,

①進(jìn)行點(diǎn)預(yù)測，由上可知丫=0.176124X—154.3063,代入可得：

Y=Y=0.176124*32000—154.3063=5481.6617

②進(jìn)行區(qū)間預(yù)測：

先由Eviews分析：

XY

Mean6000.441902.5148

Median2689.280209.3900

Maximum27722.314895.410

Minimum123.720025.87000

Std.Dev.7608.0211351.009

Skewness1.4325191.663108

Kurtosis4.0105154.590432

Jarque-Bera12.6906818.69063

Probability0.0017550.000087

Sum198014.529782.99

SumSq.Dev.1.85E+09

Observations3333

由上表可知，

2222

Ex=E(Xi—X)=8x(n—1)=7608.021x(33—1)=1852223.473

(X—X)2=(32000—6000.441)2

當(dāng)Xf=32000時，將相關(guān)數(shù)據(jù)代入計算得到：

即Yf的置信區(qū)間為(5481.6617—64.9649,5481.6617+64.9649)

(3)對于浙江省預(yù)算收入對數(shù)與全省生產(chǎn)總值對數(shù)的模型，由Eviews分析結(jié)果

如下：

DependentVariable:LNY

Method:LeastSquares

Date:12/03/14Time:18:00

Sample(adjusted):133

Includedobservations:33afteradjustments

VariableCoefficientStd.Errort-StatisticProb.

LNX0.9802750.03429628.582680.0000

C-1.9182890.268213-7.1521210.0000

R-squared0.963442Meandependentvar5.573120

AdjustedR-squared0.962263S.D.dependentvar1.684189

S.E.ofregression0.327172Akaikeinfocriterion0.662028

Sumsquaredresid3.318281Schwarzcriterion0.752726

Loglikelihood-8.923468Hannan-Quinncriter.0.692545

F-statistic816.9699Durbin-Watsonstat0.096208

Prob(F-statistic)0.000000

①模型方程為：lnY=0.980275lnX-1.918289

②由上可知，模型的參數(shù)：斜率系數(shù)為0.980275,截距為-1.918289

③關(guān)于浙江省財政預(yù)算收入與全省生產(chǎn)總值的模型，檢驗其顯著性：

1)可決系數(shù)為0.963442,說明所建模型整體上對樣本數(shù)據(jù)擬合較好。

2)對于回歸系數(shù)的t檢驗：t(82)=28.58268>to.o25(31)=2.0395,對斜率系數(shù)

的顯著性檢驗表明，全省生產(chǎn)總值對財政預(yù)算總收入有顯著影響。

④經(jīng)濟(jì)意義：全省生產(chǎn)總值每增長1%,財政預(yù)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(jié)果如下：

DependentVariable:Y

Method:LeastSquares

Date:12/01/14Time:12:40

Sample:112

Includedobservations:12

VariableCoefficientStd.Errort-StatisticProb.

X-64.184004.809828-13.344340.0000

C1845.47519.2644695.796880.0000

R-squared0.946829Meandependentvar1619.333

AdjustedR-squared0.941512S.D.dependentvar131.2252

S.E.ofregression31.73600Akaikeinfocriterion9.903792

Sumsquaredresid10071.74Schwarzcriterion9.984610

Loglikelihood-57.42275Hannan-Quinncriter.9.873871

F-statistic178.0715Durbin-Watsonstat1.172407

Prob(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(jīng)濟(jì)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(jìn)行點(diǎn)預(yù)測，由Y=1845.475—64.18400X得，當(dāng)x=4.5,y=1556.647

②再進(jìn)行區(qū)間估計：

用Eviews分析：

YX

Mean1619.3333.523333

Median1630.0003.715000

Maximum1860.0006.230000

Minimum1419.0000.600000

Std.Dev.131.22521.989419

Skewness0.003403-0.060130

Kurtosis2.3465111.664917

Jarque-Bera0.2135470.898454

Probability0.8987290.638121

Sum19432.0042.28000

SumSq.Dev.189420.743.53567

Observations1212

由上表可知，

222

Ex=S(X—X)=8x(n—1)=1.989419?x(12—1)=43.5357

(X—X)2=(4.5—3.523333)2

當(dāng)Xf=4.5時，將相關(guān)數(shù)據(jù)代入計算得到：

1556.647—2.228x31.73600

Yf<1556.647+2.228x31.73600

即Yf的置信區(qū)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(jīng)濟(jì)模型，用Eviews分析結(jié)果如下:

DependentVariable:Y

Method:LeastSquares

Date:11/25/14Time:12:38

Sample:131

Includedobservations:31

VariableCoefficientStd.Errort-StatisticProb.

X25.9968651.4060584.2650200.0002

X3-0.5240270.179280-2.9229500.0069

X4-2.2656800.518837-4.3668420.0002

c246.854051.975004.7494760.0001

R-squared0.666062Meandependentvar16.77355

AdjustedR-squared0.628957S.D.dependentvar8.252535

S.E.ofregression5.026889Akaikeinfocriterion6.187394

Sumsquaredresid682.2795Schwarzcriterion6.372424

Loglikelihood-91.90460Hannan-Quinncriter.6.247709

F-statistic17.95108Durbin-Watsonstat1.147253

Prob(F-statistic)0.000001

②得到模型得：

丫=246.8540+5.996865X2-0.524027X3-2.265680X4

③對模型進(jìn)行檢驗：

1)可決系數(shù)是0.666062,修正的可決系數(shù)為0.628957,說明模型對樣本擬合

較好

2)F檢驗，F(xiàn)=17.95108>F(3,27)=3.65,回歸方程顯著。

3)t檢驗，t統(tǒng)計量分另U為4.749476,4.265020,-2.922950,-4.366842,均

大于

t(27)=2.0518,所以這些系數(shù)都是顯著的。

④依據(jù)：

1)可決系數(shù)越大，說明擬合程度越好

2)F的值與臨界值比較，若大于臨界值，則否定原假設(shè)，回歸方程是顯著的；

若小于臨界值，則接受原假設(shè)，回歸方程不顯著。

3)t的值與臨界值比較，若大于臨界值，則否定原假設(shè)，系數(shù)都是顯著的；若

小于臨界值，則接受原假設(shè)，系數(shù)不顯著。

(2)經(jīng)濟(jì)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(zhèn)人口比重增加1個百分點(diǎn)，百戶擁有家用汽車減少0.524027輛，交通工具

消費(fèi)價格指數(shù)每上升1,百戶擁有家用汽車減少2.265680輛。

(3)用EViews分析得:

DependentVariable:Y

Method:LeastSquares

Date:12/08/14Time:17:28

Sample:131

Includedobservations:31

VariableCoefficientStd.Errort-StatisticProb.

X25.1356701.0102705.0834650.0000

LNX3-22.810056.771820-3.3683780.0023

LNX4-230.848149.46791-4.6666240.0001

c1148.758228.29175.0319740.0000

R-squared0.691952Meandependentvar16.77355

AdjustedR-squared0.657725S.D.dependentvar8.252535

S.E.ofregression4.828088Akaikeinfocriterion6.106692

Sumsquaredresid629.3818Schwarzcriterion6.291723

Loglikelihood-90.65373Hannan-Quinncriter.6.167008

F-statistic20.21624Durbin-Watsonstat1.150090

Prob(F-statistic)0.000000

模型方程為：

Y=5.135670X2-22.81005LNXs-230.8481LNX4+1148.758

此分析得出的可決系數(shù)為0.691952>0.666062,擬合程度得到了提高，可這樣

改進(jìn)。

3.2

(1)對出口貨物總額計量經(jīng)濟(jì)模型，用Eviews分析結(jié)果如下：：

DependentVariable:Y

Method:LeastSquares

Date:12/01/14Time:20:25

Sample:19942011

Includedobservations:18

VariableCoefficientStd.Errort-StatisticProb.

X20.1354740.01279910.584540.0000

X318.853489.7761811.9285120.0729

C-18231.588638.216-2,1105730.0520

R-squared0.985838Meandependentvar6619.191

AdjustedR-squared0.983950S.D.dependentvar5767.152

S.E.ofregression730.6306Akaikeinfocriterion16.17670

Sumsquaredresid8007316.Schwarzcriterion16.32510

Loglikelihood-142.5903Hannan-Quinncriter.16.19717

F-statistic522.0976Durbin-Watsonstat1.173432

Prob(F-statistic)0.000000

①由上可知，模型為：

Y=0.135474X2+18.85348X3-18231.58

②對模型進(jìn)行檢驗：

1)可決系數(shù)是0.985838,修正的可決系數(shù)為0.983950,說明模型對樣本擬合

較好

2)F檢驗，F(xiàn)=522.0976>F(2,15)=4.77,回歸方程顯著

3)t檢驗，t統(tǒng)計量分別為X2的系數(shù)對應(yīng)t值為10.58454,大于t(15)=2.131,

系數(shù)是顯著的，X3的系數(shù)對應(yīng)t值為1.928512,小于t(15)=2.131,說明此

系數(shù)是不顯著的。

(2)對于對數(shù)模型，用Eviews分析結(jié)果如下：

DependentVariable:LNY

Method:LeastSquares

Date:12/01/14Time:20:25

Sample:19942011

Includedobservations:18

VariableCoefficientStd.Errort-StatisticProb.

LNX21.5642210.08898817.577890.0000

LNX31.7606950.6821152.5812290.0209

C-20.520485.432487-3.7773630.0018

R-squared0.986295Meandependentvar8.400112

AdjustedR-squared0.984467S.D.dependentvar0.941530

S.E.ofregression0.117343Akaikeinfocriterion-1.296424

Sumsquaredresid0.206540Schwarzcriterion-1.148029

Loglikelihood14.66782Hannan-Quinncriter.-1.275962

F-statistic539.7364Durbin-Watsonstat0.686656

Prob(F-statistic)0.000000

①由上可知，模型為：

LNY=-20.52048+1.564221LNX2+1.760695LNX3

②對模型進(jìn)行檢驗：

1)可決系數(shù)是0.986295,修正的可決系數(shù)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(tǒng)計量分別為-3.777363,17.57789,2.581229,均大于t(15)

=2.131,所以這些系數(shù)都是顯著的。

(3)

①(1)式中的經(jīng)濟(jì)意義：工業(yè)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(jīng)濟(jì)意義：工業(yè)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(fèi)對家庭月平均收入和戶主受教育年數(shù)計量模型，由Eviews

分析結(jié)果如下：

DependentVariable:Y

Method:LeastSquares

Date:12/01/14Time:20:30

Sample:118

Includedobservations:18

VariableCoefficientStd.Errort-StatisticProb.

X0.0864500.0293632.9441860.0101

T52.370315.20216710.067020.0000

C-50.0163849.46026-1.0112440.3279

R-squared0.951235Meandependentvar755.1222

AdjustedR-squared0.944732S.D.dependentvar258.7206

S.E.ofregression60.82273Akaikeinfocriterion11.20482

Sumsquaredresid55491.07Schwarzcriterion11.35321

Loglikelihood-97.84334Hannan-Quinncriter.11.22528

F-statistic146.2974Durbin-Watsonstat2.605783

Prob(F-statistic)0.000000

①模型為：Y=0.086450X+52.37031T-50.01638

②對模型進(jìn)行檢驗：

1)可決系數(shù)是0.951235,修正的可決系數(shù)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(tǒng)計量分別為2.944186,10.06702,均大于t(15)=2.131,所

以這些系數(shù)都是顯著的。

③經(jīng)濟(jì)意義：家庭月平均收入增加1元，家庭書刊年消費(fèi)支出增加0.086450元,

戶主受教育年數(shù)增加1年，家庭書刊年消費(fèi)支出增加52.37031元。

(2)用Eviews分析:

①

DependentVariable:Y

Method:LeastSquares

Date:12/01/14Time:22:30

Sample:118

Includedobservations:18

VariableCoefficientStd.Errort-StatisticProb.

T63.016764.54858113.854160.0000

c-11.5817158.02290-0.1996060.8443

R-squared0.923054Meandependentvar755.1222

AdjustedR-squared0.918245S.D.dependentvar258.7206

S.E.ofregression73.97565Akaikeinfocriterion11.54979

Sumsquaredresid87558.36Schwarzcriterion11.64872

Loglikelihood-101.9481Hannan-Quinncriter.11.56343

F-statistic191.9377Durbin-Watsonstat2.134043

Prob(F-statistic)0.000000

②

DependentVariable:X

Method:LeastSquares

Date:12/01/14Time:22:34

Sample:118

Includedobservations:18

VariableCoefficientStd.Errort-StatisticProb.

T123.151631.841503.8676440.0014

c444.5888406.17861.0945650.2899

R-squared0.483182Meandependentvar1942.933

AdjustedR-squared0.450881S.D.dependentvar698.8325

S.E.ofregression517.8529Akaikeinfocriterion15.44170

Sumsquaredresid4290746.Schwarzcriterion15.54063

Loglikelihood-136.9753Hannan-Quinncriter.15.45534

F-statistic14.95867Durbin-Watsonstat1.052251

Prob(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-11.58171

X=123.1516T+444.5888

(3)對殘差進(jìn)行模型分析，用Eviews分析結(jié)果如下:

DependentVariable:E1

Method:LeastSquares

Date:12/03/14Time:20:39

Sample:118

Includedobservations:18

VariableCoefficientStd.Errort-StatisticProb.

E20.0864500.0284313.0407420.0078

c3.96E-1413.880832.85E-151.0000

R-squared0.366239Meandependentvar2.30E-14

AdjustedR-squared0.326629S.D.dependentvar71.76693

S.E.ofregression58.89136Akaikeinfocriterion11.09370

Sumsquaredresid55491.07Schwarzcriterion11.19264

Loglikelihood-97.84334Hannan-Quinncriter.11.10735

F-statistic9.246111Durbin-Watsonstat2.605783

Prob(F-statistic)0.007788

模型為：

Ei=0.086450E2+3.96e-14

參數(shù)：斜率系數(shù)a為0.086450,截距為3.96e-14

(3)由上可知，62與a2的系數(shù)是一樣的?；貧w系數(shù)與被解釋變量的殘差系

數(shù)是一樣的，它們的變化規(guī)律是一致的。

3.6

(1)預(yù)期的符號是X”X2,X3,X.i,X5的符號為正，Xe的符號為負(fù)

(2)根據(jù)Eviews分析得到數(shù)據(jù)如下：

DependentVariable:Y

Method:LeastSquares

Date:12/04/14Time:13:24

Sample:19942011

Includedobservations:18

VariableCoefficientStd.Errort-StatisticProb.

X20.0013820.0011021.2543300.2336

X30.0019420.0039600.4905010.6326

X4-3.5790903.559949-1.0053770.3346

X50.0047910.0050340.9516710.3600

X60.0455420.0955520.4766210.6422

C-13.7773215.73366-0.8756590.3984

R-squared0.994869Meandependentvar12.76667

AdjustedR-squared0.992731S.D.dependentvar9.746631

S.E.ofregression0.830963Akaikeinfocriterion2.728738

Sumsquaredresid8.285993Schwarzcriterion3.025529

Loglikelihood-18.55865Hannan-Quinncriter.2.769662

F-statistic465.3617Durbin-Watsonstat1.553294

Prob(F-statistic)0.000000

①與預(yù)期不相符。

②評價：

1)可決系數(shù)為0.994869,數(shù)據(jù)相當(dāng)大，可以認(rèn)為擬合程度很好。

2)F檢驗,F=465.3617>F(5.12)=3,89,回歸方程顯著

3)T檢驗,X”X2,X3,X“X5.XG系數(shù)對應(yīng)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(shù)

都是不顯著的。

(3)根據(jù)Eviews分析得到數(shù)據(jù)如下：

DependentVariable:Y

Method:LeastSquares

Date:12/03/14Time:11:12

Sample:19942011

Includedobservations:18

VariableCoefficientStd.Errort-StatisticProb.

X50.0010322.20E-0546.799460.0000

X6-0.0549650.031184-1.7625810.0983

c4.2054813.3356021.2607860.2266

R-squared0.993601Meandependentvar12.76667

AdjustedR-squared0.992748S.D.dependentvar9.746631

S.E.ofregression0.830018Akaikeinfocriterion2.616274

Sumsquaredresid10.33396Schwarzcriterion2.764669

Loglikelihood-20.54646Hannan-Quinncriter.2.636736

F-statistic1164.567Durbin-Watsonstat1.341880

Prob(F-statistic)0.000000

①得到模型的方程為：

Y=0.001032X5-0.054965X6+4.205481

②評價：

1)可決系數(shù)為0.993601,數(shù)據(jù)相當(dāng)大，可以認(rèn)為擬合程度很好。

2)F檢驗，F(xiàn)=1164.567>F(5.12)=3,89,回歸方程顯著

3)T檢驗，X5系數(shù)對應(yīng)的t值為46.79946,大于t(12)=2.179,所以系

數(shù)是顯著的，即人均GDP對年底存款余額有顯著影響。X6系數(shù)對應(yīng)的t

值為1762581,小于t(12)=2.179,所以系數(shù)是不顯著的。

4.3

(1)根據(jù)Eviews分析得到數(shù)據(jù)如下：

DependentVariable:LNY

Method:LeastSquares

Date:12/05/14Time:11:39

Sample:19852011

Includedobservations:27

VariableCoefficientStd.Errort-StatisticProb.

LNGDP1.3385330.08861015.105820.0000

LNCPI-0.4217910.233295-1.8079750.0832

C-3.1114860.463010-6.7201260.0000

R-squared0.988051Meandependentvar9.484710

AdjustedR-squared0.987055S.D.dependentvar1.425517

S.E.ofregression0.162189Akaikeinfocriterion-0.695670

Sumsquaredresid0.631326Schwarzcriterion-0.551689

Loglikelihood12.39155Hannan-Quinncriter.-0.652857

F-statistic992.2582Durbin-Watsonstat0.522613

Prob(F-statistic)0.000000

得到的模型方程為：

LNY=1.338533LNGDPt-0.421791LNCPIt-3.111486

(2)

①該模型的可決系數(shù)為0.988051,可決系數(shù)很高，F(xiàn)檢驗值為992.2582,

明顯顯著。但當(dāng)a=0.05時、t(24)=2.064,LNCPI的系數(shù)不顯著，可能存在

多重共線性。

②得到相關(guān)系數(shù)矩陣如下：

LNYLNGDPLNCPI

LNY1.0000000.9931890.935116

LNGDP0.9931891.0000000.953740

LNCPI0.9351160.9537401.000000

LNGDP,LNCPI之間的相關(guān)系數(shù)很高，證實(shí)確實(shí)存在多重共線性。

(3)由Eviews得:

a)

DependentVariable:LNY

Method:LeastSquares

Date:12/03/14Time:14:41

Sample:19852011

Includedobservations:27

VariableCoefficientStd.Errort-StatisticProb.

LNGDP1.1857390.02782242.619330.0000

c-3.7506700.312255-12.011560.0000

R-squared0.986423Meandependentvar9.484710

AdjustedR-squared0.985880S.D.dependentvar1.425517

S.E.ofregression0.169389Akaikeinfocriterion-0.642056

Sumsquaredresid0.717312Schwarzcriterion-0.546068

Loglikelihood10.66776Hannan-Quinncriter.-0.613514

F-statistic1816.407Durbin-Watsonstat0.471111

Prob(F-statistic)0.000000

b)

DependentVariable:LNY

Method:LeastSquares

Date:12/03/14Time:14:41

Sample:19852011

Includedobservations:27

VariableCoefficientStd.Errort-StatisticProb.

LNCPI2.9392950.22275613.195110.0000

C-6.8545351.242243-5.5178710.0000

R-squared0.874442Meandependentvar9.484710

AdjustedR-squared0.869419S.D.dependentvar1.425517

S.E.ofregression0.515124Akaikeinfocriterion1.582368

Sumsquaredresid6.633810Schwarzcriterion1.678356

Loglikelihood-19.36196Hannan-Quinncriter.1.610910

F-statistic174.1108Durbin-Watsonstat0.137042

Prob(F-statistic)0.000000

c)

DependentVariable:LNGDP

Method:LeastSquares

Date:12/05/14Time:11:11

Sample:19852011

Includedobservations:27

VariableCoefficientStd.Errort-StatisticProb.

LNCPI2.5110220.15830215.862270.0000

C-2.7963810.882798-3.1676340.0040

R-squared0.909621Meandependentvar11,16214

AdjustedR-squared0.906005S.D.dependentvar1.194029

S.E.ofregression0.366072Akaikeinfocriterion0.899213

Sumsquaredresid3.350216Schwarzcriterion0.995201

Loglikelihood-10.13938Hannan-Quinncriter.0.927755

F-statistic251.6117Durbin-Watsonstat0.099623

Prob(F-statistic)0.000000

①得到的回歸方程分別為

1)LNY=1.185739LNGDPt-3.750670

2)LNY=2.939295LNCPIt-6.854535

3)LNGDPt=2.511022LNCPIt-2.796381

②對多重共線性的認(rèn)識：

單方程擬合效果都很好，回歸系數(shù)顯著，判定系數(shù)較高，GDP和CPI對進(jìn)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(fā)生了改變，這只有通

過相關(guān)系數(shù)的分析才能發(fā)現(xiàn)。

(4)建議：如果僅僅是作預(yù)測，可以不在意這種多重共線性，但如果是進(jìn)行結(jié)

構(gòu)分析，還是應(yīng)該引起注意的。

4.4

(1)按照設(shè)計的理論模型，由Eviews分析得：

DependentVariable:CZSR

Method:LeastSquares

Date:12/03/14Time:11:40

Sample:19852011

Includedobservations:27

VariableCoefficientStd.Errort-StatisticProb.

CZZC0.0901140.0443672.0311290.0540

GDP-0.0253340.005069-4.9980360.0000

SSZE1.1768940.06216218.932710.0000

c-221.8540130.6532-1.6980380.1030

R-squared0.999857Meandependentvar22572.56

AdjustedR-squared0.999838S.D.dependentvar27739.49

S.E.ofregression353.0540Akaikeinfocriterion14.70707

Sumsquaredresid2866884.Schwarzcriterion14.89905

Loglikelihood-194.5455Hannan-Quinncriter.14.76416

F-statistic53493.93Durbin-Watsonstat1.458128

Prob(F-statistic)0.000000

從回歸結(jié)果可見，可決系數(shù)為0.999857,校正的可決系數(shù)為0.999838,模型擬

合的很好。F的統(tǒng)計量為53493.93,說明在a=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(jié)果表明，國內(nèi)生產(chǎn)總值對財政收入的影響顯著,

但回歸系數(shù)的符號為負(fù)，與實(shí)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(guān)系數(shù)矩陣如下：

CZSRCZZCGDPSSZE

CZSR1.0000000.9987290.9928380.999832

CZZC0.9987291.0000000.9925360.998575

GDP0.9928380.9925361.0000000.994370

SSZE0.9998320.9985750.9943701.000000

由上表可知，CZZC與GDP,CZZC與SSZE,GDP與SSZE之間的相關(guān)系數(shù)

都非常高，說明確實(shí)存在多重共線性。

(3)做輔助回歸

被解釋變量可決系數(shù)方差擴(kuò)大因子

czzc0.997168353

GDP0.98883390

SSZE0.997862468

方差擴(kuò)大因子均大于10,存在嚴(yán)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(guān)性都很高。

(4)解決方式：分別作出財政收入與財政支出、國內(nèi)生產(chǎn)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e?的散點(diǎn)圖，用Eviews分析如下:

由上圖可知，模型可能存在異方差，

②Go1dfe1d-Quanadt檢驗

1)定義區(qū)間為17時，由軟件分析得：

DependentVariable:Y

Method:LeastSquares

Date:12/10/14Time:14:52

Sample:17

Includedobservations:7

VariableCoefficientStd.Errort-StatisticProb.

T35.206644.9014927.1828430.0020

X0.1099490.0619651.7743800.1507

c77.1258882.328440.9368070.4019

R-squared0.943099Meandependentvar565.6857

AdjustedR-squared0.914649S.D.dependentvar108.2755

S.E.ofregression31.63265Akaikeinfocriterion10.04378

S