./第二章簡(jiǎn)單線(xiàn)性回歸模型2.1〔1①首先分析人均壽命與人均GDP的數(shù)量關(guān)系,用Eviews分析：DependentVariable:YMethod:LeastSquaresDate:12/27/14Time:21:00Sample:122Includedobservations:22VariableCoefficientStd.Errort-StatisticProb.

C56.647941.96082028.889920.0000X10.1283600.0272424.7118340.0001R-squared0.526082

Meandependentvar62.50000AdjustedR-squared0.502386

S.D.dependentvar10.08889S.E.ofregression7.116881

Akaikeinfocriterion6.849324Sumsquaredresid1013.000

Schwarzcriterion6.948510Loglikelihood-73.34257

Hannan-Quinncriter.6.872689F-statistic22.20138

Durbin-Watsonstat0.629074Prob<F-statistic>0.000134有上可知,關(guān)系式為y=56.64794+0.128360x1②關(guān)于人均壽命與成人識(shí)字率的關(guān)系,用Eviews分析如下：DependentVariable:YMethod:LeastSquaresDate:11/26/14Time:21:10Sample:122Includedobservations:22VariableCoefficientStd.Errort-StatisticProb.

C38.794243.53207910.983400.0000X20.3319710.0466567.1153080.0000R-squared0.716825

Meandependentvar62.50000AdjustedR-squared0.702666

S.D.dependentvar10.08889S.E.ofregression5.501306

Akaikeinfocriterion6.334356Sumsquaredresid605.2873

Schwarzcriterion6.433542Loglikelihood-67.67792

Hannan-Quinncriter.6.357721F-statistic50.62761

Durbin-Watsonstat1.846406Prob<F-statistic>0.000001由上可知,關(guān)系式為y=38.79424+0.331971x2③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:YMethod:LeastSquaresDate:11/26/14Time:21:14Sample: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(guān)系式為y=31.79956+0.387276x3〔2①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(shuō)明所建模型整體上對(duì)樣本數(shù)據(jù)擬合較好。對(duì)于回歸系數(shù)的t檢驗(yàn)：t〔β1=4.711834>t0.025<20>=2.086,對(duì)斜率系數(shù)的顯著性檢驗(yàn)表明,人均GDP對(duì)人均壽命有顯著影響。②關(guān)于人均壽命與成人識(shí)字率模型,由上可知,可決系數(shù)為0.716825,說(shuō)明所建模型整體上對(duì)樣本數(shù)據(jù)擬合較好。對(duì)于回歸系數(shù)的t檢驗(yàn)：t〔β2=7.115308>t0.025<20>=2.086,對(duì)斜率系數(shù)的顯著性檢驗(yàn)表明,成人識(shí)字率對(duì)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(shuō)明所建模型整體上對(duì)樣本數(shù)據(jù)擬合較好。對(duì)于回歸系數(shù)的t檢驗(yàn)：t〔β3=4.825285>t0.025<20>=2.086,對(duì)斜率系數(shù)的顯著性檢驗(yàn)表明,一歲兒童疫苗接種率對(duì)人均壽命有顯著影響。2.2〔1①對(duì)于XX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: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(shù)：斜率系數(shù)0.176124,截距為—154.3063③關(guān)于XX省財(cái)政預(yù)算收入與全省生產(chǎn)總值的模型,檢驗(yàn)?zāi)Ｐ偷娘@著性：1可決系數(shù)為0.983702,說(shuō)明所建模型整體上對(duì)樣本數(shù)據(jù)擬合較好。2對(duì)于回歸系數(shù)的t檢驗(yàn)：t〔β2=43.25639>t0.025<31>=2.0395,對(duì)斜率系數(shù)的顯著性檢驗(yàn)表明,全省生產(chǎn)總值對(duì)財(cái)政預(yù)算總收入有顯著影響。④用規(guī)范形式寫(xiě)出檢驗(yàn)結(jié)果如下：Y=0.176124X—154.3063<0.004072><39.08196>t=<43.25639>〔-3.948274R2=0.983702F=1871.115n=33⑤經(jīng)濟(jì)意義是：全省生產(chǎn)總值每增加1億元,財(cái)政預(yù)算總收入增加0.176124億元。〔2當(dāng)x=32000時(shí),①進(jìn)行點(diǎn)預(yù)測(cè),由上可知Y=0.176124X—154.3063,代入可得：Y=Y=0.176124*32000—154.3063=5481.6617②進(jìn)行區(qū)間預(yù)測(cè)：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—X2=δ2x<n—1>=

7608.0212x<33—1>=1852223.473<Xf—X>2=<32000—

6000.441>2=675977068.2當(dāng)Xf=32000時(shí),將相關(guān)數(shù)據(jù)代入計(jì)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(qū)間為〔5481.6617—64.9649,5481.6617+64.9649<3>對(duì)于XX省預(yù)算收入對(duì)數(shù)與全省生產(chǎn)總值對(duì)數(shù)的模型,由Eviews分析結(jié)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=②由上可知,模型的參數(shù)：斜率系數(shù)為0.980275,截距為-1.918289③關(guān)于XX省財(cái)政預(yù)算收入與全省生產(chǎn)總值的模型,檢驗(yàn)其顯著性：1可決系數(shù)為0.963442,說(shuō)明所建模型整體上對(duì)樣本數(shù)據(jù)擬合較好。2對(duì)于回歸系數(shù)的t檢驗(yàn)：t〔β2=28.58268>t0.025<31>=2.0395,對(duì)斜率系數(shù)的顯著性檢驗(yàn)表明,全省生產(chǎn)總值對(duì)財(cái)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(zhǎng)1%,財(cái)政預(yù)算總收入增長(zhǎng)0.980275%2.4〔1對(duì)建筑面積與建造單位成本模型,用Eviews分析結(jié)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=〔2經(jīng)濟(jì)意義：建筑面積每增加1萬(wàn)平方米,建筑單位成本每平方米減少64.18400元。〔3①首先進(jìn)行點(diǎn)預(yù)測(cè),由Y=得,當(dāng)x=4.5,y=1556.647②再進(jìn)行區(qū)間估計(jì)：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—X2=δ2x<n—1>=

1.9894192x<12—1>=43.5357<Xf—X>2=<4.5—

3.523333>2=0.95387843當(dāng)Xf=4.5時(shí),將相關(guān)數(shù)據(jù)代入計(jì)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(qū)間為〔1556.647—478.1231,1556.647+478.12313.1〔1①對(duì)百戶(hù)擁有家用汽車(chē)量計(jì)量經(jīng)濟(jì)模型,用Eviews分析結(jié)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>0.000001②得到模型得：Y=246.8540+5.996865X2-0.524027X3-2.265680X4③對(duì)模型進(jìn)行檢驗(yàn)：可決系數(shù)是0.666062,修正的可決系數(shù)為0.628957,說(shuō)明模型對(duì)樣本擬合較好F檢驗(yàn),F=17.95108>F〔3,27=3.65,回歸方程顯著。3t檢驗(yàn),t統(tǒng)計(jì)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(shù)都是顯著的。④依據(jù)：可決系數(shù)越大,說(shuō)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(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。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?！?經(jīng)濟(jì)意義：人均ＧＤＰ增加１萬(wàn)元,百戶(hù)擁有家用汽車(chē)增加5.996865輛,城鎮(zhèn)人口比重增加１個(gè)百分點(diǎn),百戶(hù)擁有家用汽車(chē)減少0.524027輛,交通工具消費(fèi)價(jià)格指數(shù)每上升１,百戶(hù)擁有家用汽車(chē)減少2.265680輛?！?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(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(duì)出口貨物總額計(jì)量經(jīng)濟(jì)模型,用Eviews分析結(jié)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(duì)模型進(jìn)行檢驗(yàn)：1可決系數(shù)是0.985838,修正的可決系數(shù)為0.983950,說(shuō)明模型對(duì)樣本擬合較好2F檢驗(yàn),F=522.0976>F〔2,15=4.77,回歸方程顯著3t檢驗(yàn),t統(tǒng)計(jì)量分別為X2的系數(shù)對(duì)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(duì)應(yīng)t值為1.928512,小于t〔15=2.131,說(shuō)明此系數(shù)是不顯著的。〔2對(duì)于對(duì)數(shù)模型,用Eviews分析結(jié)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(duì)模型進(jìn)行檢驗(yàn)：1可決系數(shù)是0.986295,修正的可決系數(shù)為0.984467,說(shuō)明模型對(duì)樣本擬合較好。2F檢驗(yàn),F=539.7364>F〔2,15=4.77,回歸方程顯著。3t檢驗(yàn),t統(tǒng)計(jì)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?！?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(duì)家庭書(shū)刊消費(fèi)對(duì)家庭月平均收入和戶(hù)主受教育年數(shù)計(jì)量模型,由Eviews分析結(jié)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(duì)模型進(jìn)行檢驗(yàn)：1可決系數(shù)是0.951235,修正的可決系數(shù)為0.944732,說(shuō)明模型對(duì)樣本擬合較好。2F檢驗(yàn),F=539.7364>F〔2,15=4.77,回歸方程顯著。3t檢驗(yàn),t統(tǒng)計(jì)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(shū)刊年消費(fèi)支出增加0.086450元,戶(hù)主受教育年數(shù)增加1年,家庭書(shū)刊年消費(fèi)支出增加52.37031元?！?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(duì)殘差進(jìn)行模型分析,用Eviews分析結(jié)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(shù)：斜率系數(shù)α為0.086450,截距為3.96e-14〔3由上可知,β2與α2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(hào)是X1,X2,X3,X4,X5的符號(hào)為正,X6的符號(hào)為負(fù)〔2根據(jù)Eviews分析得到數(shù)據(jù)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(yù)期不相符。②評(píng)價(jià)：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。F檢驗(yàn),F=465.3617>F〔5.12=3,89,回歸方程顯著T檢驗(yàn),X1,X2,X3,X4,X5,X6系數(shù)對(duì)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?！?根據(jù)Eviews分析得到數(shù)據(jù)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(píng)價(jià)：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。F檢驗(yàn),F=1164.567>F〔5.12=3,89,回歸方程顯著T檢驗(yàn),X5系數(shù)對(duì)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(duì)年底存款余額有顯著影響。X6系數(shù)對(duì)應(yīng)的t值為-1.762581,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: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(shù)為0.988051,可決系數(shù)很高,F檢驗(yàn)值為992.2582,明顯顯著。但當(dāng)α=0.05時(shí),t〔24=2.064,LNCPI的系數(shù)不顯著,可能存在多重共線(xiàn)性。②得到相關(guān)系數(shù)矩陣如下：LNYLNGDPLNCPILNY

1.000000

0.993189

0.935116LNGDP

0.993189

1.000000

0.953740LNCPI

0.935116

0.953740

1.000000LNGDP,LNCPI之間的相關(guān)系數(shù)很高,證實(shí)確實(shí)存在多重共線(xiàn)性?！?由Eviews得：aDependentVariable: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1LNY=1.185739LNGDPt-3.7506702LNY=2.939295LNCPIt-6.8545353LNGDPt=2.511022LNCPIt-2.796381②對(duì)多重共線(xiàn)性的認(rèn)識(shí)：?jiǎn)畏匠虜M合效果都很好,回歸系數(shù)顯著,判定系數(shù)較高,GDP和CPI對(duì)進(jìn)口的顯著的單一影響,在這兩個(gè)變量同時(shí)引入模型時(shí)影響方向發(fā)生了改變,這只有通過(guò)相關(guān)系數(shù)的分析才能發(fā)現(xiàn)?！?建議：如果僅僅是作預(yù)測(cè),可以不在意這種多重共線(xiàn)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(jì)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(jié)果可見(jiàn),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(jì)量為53493.93,說(shuō)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(yàn)結(jié)果表明,國(guó)內(nèi)生產(chǎn)總值對(duì)財(cái)政收入的影響顯著,但回歸系數(shù)的符號(hào)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(xiàn)性。〔2得到相關(guān)系數(shù)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(guān)系數(shù)都非常高,說(shuō)明確實(shí)存在多重共線(xiàn)性?！?做輔助回歸被解釋變量可決系數(shù)方差擴(kuò)大因子CZZC0.997168353GDP0.98883390SSZE0.997862468方差擴(kuò)大因子均大于10,存在嚴(yán)重多重共線(xiàn)性。并且通過(guò)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(cái)政收入與財(cái)政支出、國(guó)內(nèi)生產(chǎn)總值、稅收總額之間的一元回歸。5.2〔1①用圖形法檢驗(yàn)繪制e2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,Goldfeld-Quanadt檢驗(yàn)1定義區(qū)間為1-7時(shí),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(qū)間為12-18時(shí),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(jù)Goldfeld-Quanadt檢驗(yàn),F統(tǒng)計(jì)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?yàn)镕=1.7285<F0.05〔4,4=6.39,所以接受原假設(shè),此檢驗(yàn)表明模型不存在異方差?！?存在異方差,估計(jì)參數(shù)的方法：①可以對(duì)模型進(jìn)行變換②使用加權(quán)最小二乘法進(jìn)行計(jì)算,得出模型方程,并對(duì)其進(jìn)行相關(guān)檢驗(yàn)③對(duì)模型進(jìn)行對(duì)數(shù)變換,進(jìn)行分析〔3評(píng)價(jià)：3.3所得結(jié)論是可以相信的,隨機(jī)擾動(dòng)項(xiàng)之間不存在異方差?；貧w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,20XX我國(guó)農(nóng)村居民家庭人均消費(fèi)支出〔x對(duì)人均純收入〔y的模型為：Y=1.244281X+242.4488〔2①由圖形法檢驗(yàn)由上圖可知,模型可能存在異方差。②Goldfeld-Quanadt檢驗(yàn)1定義區(qū)間為1-12時(shí),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(qū)間為20-31時(shí),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(jù)Goldfeld-Quanadt檢驗(yàn),F統(tǒng)計(jì)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?yàn)镕=4.4631>F0.05〔10,10=2.98,所以拒絕原假設(shè),此檢驗(yàn)表明模型存在異方差?！?1采用WLS法估計(jì)過(guò)程中,①用權(quán)數(shù)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(duì)此模型進(jìn)行White檢驗(yàn)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(jì)算的統(tǒng)計(jì)量的臨界值,因?yàn)閚R2=0.649065<0.05〔2=5.9915,所以接受原假設(shè),該模型消除了異方差。估計(jì)結(jié)果為：t=〔11.97157〔-0.972298R2=0.875855F=143.3184DW=1.369081②用權(quán)數(shù)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(duì)此模型進(jìn)行White檢驗(yàn)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(jì)算的統(tǒng)計(jì)量的臨界值,因?yàn)閚R2=0.999322<0.05〔2=5.9915,所以接受原假設(shè),該模型消除了異方差。估計(jì)結(jié)果為：t=〔10.70922〔-1.841272R2=0.798173F=114.6875DW=1.562975③用權(quán)數(shù)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(duì)此模型進(jìn)行White檢驗(yàn)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:131Inclu