計(jì)量經(jīng)濟(jì)學(xué)實(shí)驗(yàn)報(bào)告csust

實(shí)驗(yàn)報(bào)告課程名稱(chēng)：計(jì)量經(jīng)濟(jì)學(xué)實(shí)驗(yàn)項(xiàng)目：計(jì)量經(jīng)濟(jì)學(xué)Eviews應(yīng)用與操作學(xué)生姓名：學(xué)號(hào)：班級(jí)：專(zhuān)業(yè)：指導(dǎo)教師：2015年12月指導(dǎo)老師評(píng)語(yǔ)：簽字：年月日成績(jī)等級(jí)：備注：實(shí)驗(yàn)任務(wù)一根據(jù)數(shù)據(jù)1構(gòu)建截面數(shù)據(jù)一元線性模型。假設(shè)擬建立如下一元回歸模型：Y=下圖為用Eviews軟件對(duì)數(shù)據(jù)進(jìn)行回歸分析的計(jì)算結(jié)果：DependentVariable:YMethod:LeastSquaresDate:01/07/03Time:23:44Sample:131Includedobservations:31CoefficientStd.Errort-StatisticProb.

X1.3594770.04330231.395250.0000C-57.90655377.7595-0.1532890.8792R-squared0.971419

Meandependentvar11363.69AdjustedR-squared0.970433

S.D.dependentvar3294.469S.E.ofregression566.4812

Akaikeinfocriterion15.57911Sumsquaredresid9306127.

Schwarzcriterion15.67162Loglikelihood-239.4761

Hannan-Quinncriter.15.60926F-statistic985.6616

Durbin-Watsonstat1.294974Prob(F-statistic)0.000000

由此可得：（377.76）（0.043）（-0.15）（31.40）R2=0.97對(duì)模型進(jìn)行檢驗(yàn)。從回歸估計(jì)的結(jié)果看，模型擬合較好?？蓻Q系數(shù)R2=0.97，擬合優(yōu)度較高，表明該地區(qū)消費(fèi)支出變化的97%可以由該地區(qū)可支配收入的變化來(lái)解釋。從斜率項(xiàng)的t檢驗(yàn)值來(lái)看，在1%的水平上通過(guò)了顯著性檢驗(yàn)，它表明，人均可支配收入每增加1元，人均消費(fèi)支出增加1.36元。但是斜率值1.36＞1，不符合經(jīng)濟(jì)規(guī)律。若2006年某地區(qū)人均可支配收入為4100元，那么該地區(qū)消費(fèi)支出是多少？（元）實(shí)驗(yàn)任務(wù)二根據(jù)數(shù)據(jù)2構(gòu)建時(shí)間數(shù)據(jù)一元線性模型。假設(shè)擬建立如下一元回歸模型：Y=下圖為用Eviews軟件對(duì)數(shù)據(jù)進(jìn)行回歸分析的計(jì)算結(jié)果：DependentVariable:YMethod:LeastSquaresDate:01/31/02Time:15:25Sample:19782006Includedobservations:29CoefficientStd.Errort-StatisticProb.

X0.4375270.00929747.059500.0000C2091.295334.98696.2429140.0000R-squared0.987955

Meandependentvar14855.72AdjustedR-squared0.987509

S.D.dependentvar9472.076S.E.ofregression1058.633

Akaikeinfocriterion16.83382Sumsquaredresid30259014

Schwarzcriterion16.92811Loglikelihood-242.0903

Hannan-Quinncriter.16.86335F-statistic2214.596

Durbin-Watsonstat0.277155Prob(F-statistic)0.000000由此可得：（334.99）（0.009）（6.24）（47.06）R2=0.99對(duì)模型進(jìn)行檢驗(yàn)。從回歸估計(jì)的結(jié)果看，可決系數(shù)R2=0.99，擬合優(yōu)度較高，模型擬合較好，表明實(shí)際消費(fèi)支出的變化的99%可以由實(shí)際可支配收入的變化來(lái)解釋。從斜率項(xiàng)的t檢驗(yàn)值來(lái)看，在1%的水平上通過(guò)了顯著性檢驗(yàn)，且斜率項(xiàng)0<0.44<1,符合經(jīng)濟(jì)規(guī)律，表明人均可支配收入每增加1億元，消費(fèi)支出增加0.44億元。若2007年我國(guó)可支配總收入為54180億元，那么該相應(yīng)的總消費(fèi)是多少？（億元）實(shí)驗(yàn)任務(wù)三根據(jù)數(shù)據(jù)3構(gòu)建截面數(shù)據(jù)多元線性模型。假設(shè)擬建立如下多元截面數(shù)據(jù)模型：Y=下圖為用Eviews軟件對(duì)數(shù)據(jù)進(jìn)行回歸分析的計(jì)算結(jié)果：DependentVariable:YMethod:LeastSquaresDate:06/09/15Time:22:08Sample:131Includedobservations:31CoefficientStd.Errort-StatisticProb.

X10.5556440.0753087.3783200.0000X20.2500850.1136342.2007910.0362C143.3265260.40320.5504020.5864R-squared0.975634

Meandependentvar8401.468AdjustedR-squared0.973893

S.D.dependentvar2388.459S.E.ofregression385.9169

Akaikeinfocriterion14.84089Sumsquaredresid4170093.

Schwarzcriterion14.97966Loglikelihood-227.0337

Hannan-Quinncriter.14.88612F-statistic560.5650

Durbin-Watsonstat1.843488Prob(F-statistic)0.000000散點(diǎn)圖：表明2006年可支配收入X1與Y存在線性正相關(guān)關(guān)系，并且，2005年消費(fèi)支出X2與Y存在線性正相關(guān)關(guān)系，這表明居民消費(fèi)支出不僅受本年可支配收入的影響，也受上一年消費(fèi)支出的影響，即存在棘輪效應(yīng)。

估計(jì)方程：（0.55）（7.38）（2.20）對(duì)模型進(jìn)行檢驗(yàn)。①?gòu)幕貧w估計(jì)結(jié)果看出，R2=0.98，，這說(shuō)明擬合優(yōu)度高，模型擬合較好，表明2006年消費(fèi)支出變化的98%可以由2006年可支配收入X1和2005年消費(fèi)支出X2來(lái)解釋。②從回歸模型的t檢驗(yàn)值來(lái)看，X1在1%的水平上通過(guò)了顯著性檢驗(yàn)，X2在5%的水平上通過(guò)了顯著性檢驗(yàn)，可判斷X1和X2對(duì)Y均有顯著影響。從回歸模型的F檢驗(yàn)值來(lái)看，F(xiàn)=560.57，其伴隨概率為零，在1%的水平上通過(guò)顯著性檢驗(yàn)，說(shuō)明回歸方程顯著。③斜率項(xiàng)0<0.56<1,0<0.25<1，符合經(jīng)濟(jì)規(guī)律。這表明了在2006年可支配收入X1保持不變的情況下,每增加1元2005年消費(fèi)支出X2,2006年消費(fèi)支出Y變動(dòng)0.25元;在2005年消費(fèi)支出X2保持不變的情況下,每增加1元2006年可支配收入X1,2006年消費(fèi)支出Y變動(dòng)0.56元。實(shí)驗(yàn)任務(wù)四根據(jù)數(shù)據(jù)4構(gòu)建時(shí)間序列數(shù)據(jù)多元線性模型。根據(jù)需求理論，P0為食品價(jià)格，P1為通貨膨脹率，X為食品消費(fèi)支出總額。Q=f(X,P0,P1),用Eviews軟件對(duì)數(shù)據(jù)進(jìn)行回歸分析，結(jié)果如下：DependentVariable:QMethod:LeastSquaresDate:06/10/15Time:02:02Sample:19852006Includedobservations:22CoefficientStd.Errort-StatisticProb.

X0.2102060.01175117.888570.0000P06.6803343.3066302.0202850.0585P1-5.8547232.929604-1.9984690.0610C877.204137.0912423.649900.0000R-squared0.982629

Meandependentvar1830.000AdjustedR-squared0.979734

S.D.dependentvar365.1392S.E.ofregression51.98063

Akaikeinfocriterion10.90258Sumsquaredresid48635.74

Schwarzcriterion11.10096Loglikelihood-115.9284

Hannan-Quinncriter.10.94932F-statistic339.4076

Durbin-Watsonstat0.737832Prob(F-statistic)0.000000對(duì)模型進(jìn)行檢驗(yàn)?？蓻Q系數(shù)R2=0.9826，,擬合優(yōu)度較高,模型擬合好。從t檢驗(yàn)值看，解釋變量X、P0、P1分別在1%、10%、10%的水平上通過(guò)了顯著性檢驗(yàn)。F值=339.41，所對(duì)應(yīng)的伴隨概率為0，小于1%，表明整體模型在1%的水平上通過(guò)了顯著性檢驗(yàn)。P1的斜率項(xiàng)為-5.85，與理論相悖，是因?yàn)殡S著通貨膨脹率的增加，實(shí)際收入水平會(huì)下降，食品消費(fèi)支出減少，食品需求減少。P0斜率項(xiàng)為正，說(shuō)明隨著食品價(jià)格的增加，消費(fèi)支出也會(huì)增加，此商品為吉芬商品，符合經(jīng)濟(jì)規(guī)律。實(shí)驗(yàn)任務(wù)五估計(jì)中國(guó)農(nóng)村居民人均消費(fèi)函數(shù)。假設(shè)擬建立如下回歸模型：=+X1+X2+下圖為用Eviews軟件對(duì)數(shù)據(jù)進(jìn)行回歸分析的計(jì)算結(jié)果：DependentVariable:YMethod:LeastSquaresDate:05/25/15Time:03:06Sample:131Includedobservations:31CoefficientStd.Errort-StatisticProb.

X10.4020970.1648942.4385140.0213X20.7090300.04171016.999110.0000C728.1402328.15582.2188860.0348R-squared0.922173

Meandependentvar2981.623AdjustedR-squared0.916614

S.D.dependentvar1368.763S.E.ofregression395.2538

Akaikeinfocriterion14.88870Sumsquaredresid4374316.

Schwarzcriterion15.02747Loglikelihood-227.7748

Hannan-Quinncriter.14.93394F-statistic165.8853

Durbin-Watsonstat1.428986Prob(F-statistic)0.000000用普通最小二乘法的估計(jì)結(jié)果如下：=728.14+0.40X1+0.71X2（2.22）（2.44）（17.00）=0.92D.W.=1.43F=165.89對(duì)模型進(jìn)行異方差檢驗(yàn)。2.1圖示法不同地區(qū)農(nóng)村人均消費(fèi)支出的差別主要來(lái)源于非農(nóng)經(jīng)營(yíng)收入及工資收入、財(cái)政收入等其他收入的差別上，因此，如果存在異方差性，則可能是X2引起的。上圖我們得到了殘差平方項(xiàng)與X2的散點(diǎn)圖，殘差平方項(xiàng)在不斷變化，存在明顯的散點(diǎn)擴(kuò)大趨勢(shì)，且隨著X2的增大，殘差平方項(xiàng)也在不斷增大，因此存在遞增型異方差性。2.2G-Q檢驗(yàn)HeteroskedasticityTest:Breusch-Pagan-GodfreyF-statistic8.048853

Prob.F(2,28)0.0017Obs*R-squared11.31644

Prob.Chi-Square(2)0.0035ScaledexplainedSS23.78437

Prob.Chi-Square(2)0.0000TestEquation:DependentVariable:RESID^2Method:LeastSquaresDate:06/10/15Time:13:57Sample:131Includedobservations:31CoefficientStd.Errort-StatisticProb.

C-246960.3222964.1-1.1076230.2774X188.52762112.03690.7901650.4361X2108.509628.339553.8289090.0007R-squared0.365046

Meandependentvar141107.0AdjustedR-squared0.319692

S.D.dependentvar325595.5S.E.ofregression268553.6

Akaikeinfocriterion27.93125Sumsquaredresid2.02E+12

Schwarzcriterion28.07003Loglikelihood-429.9344

Hannan-Quinncriter.27.97649F-statistic8.048853

Durbin-Watsonstat2.178345Prob(F-statistic)0.001731由此可得，在1%的顯著性水平下拒絕同方差的原假設(shè)，該模型存在異方差。2.3懷特檢驗(yàn)HeteroskedasticityTest:WhiteF-statistic3.898573

Prob.F(5,25)0.0095Obs*R-squared13.58148

Prob.Chi-Square(5)0.0185ScaledexplainedSS28.54493

Prob.Chi-Square(5)0.0000TestEquation:DependentVariable:RESID^2Method:LeastSquaresDate:05/25/15Time:03:11Sample:131Includedobservations:31CoefficientStd.Errort-StatisticProb.

C1062731.993615.41.0695590.2950X1-902.44931056.763-0.8539750.4012X1^20.1852650.2692490.6880790.4977X1*X20.2467970.1389101.7766650.0878X2-522.6261363.4949-1.4377810.1629X2^20.0455460.0293261.5531150.1330R-squared0.438112

Meandependentvar141107.0AdjustedR-squared0.325735

S.D.dependentvar325595.5S.E.ofregression267358.4

Akaikeinfocriterion28.00255Sumsquaredresid1.79E+12

Schwarzcriterion28.28010Loglikelihood-428.0396

Hannan-Quinncriter.28.09303F-statistic3.898573

Durbin-Watsonstat2.151382Prob(F-statistic)0.009480

由此可得，模型在1%的顯著性水平下拒絕同方差的原假設(shè)，該模型存在異方差。采用加權(quán)最小二乘法估計(jì)方程DependentVariable:YMethod:LeastSquaresDate:05/25/15Time:03:27Sample:131Includedobservations:31Weightingseries:1/ABS(RESID)CoefficientStd.Errort-StatisticProb.

X10.4710240.03557013.242210.0000X20.6912980.01162859.451730.0000C642.164056.7915711.307380.0000WeightedStatisticsR-squared0.992927

Meandependentvar2595.506AdjustedR-squared0.992422

S.D.dependentvar3551.699S.E.ofregression67.05808

Akaikeinfocriterion11.34076Sumsquaredresid125910.0

Schwarzcriterion11.47953Loglikelihood-172.7818

Hannan-Quinncriter.11.38600F-statistic1965.400

Durbin-Watsonstat1.604499Prob(F-statistic)0.000000UnweightedStatisticsR-squared0.920129

Meandependentvar2981.623AdjustedR-squared0.914424

S.D.dependentvar1368.763S.E.ofregression400.4084

Sumsquaredresid4489153.Durbin-Watsonstat1.580905由此可得：（11.31）（13.24）（59.45）R2=0.99經(jīng)過(guò)比較，可以發(fā)現(xiàn)在加權(quán)后，R2值增加了，模型的擬合優(yōu)度提高，消除了異方差。同時(shí)X1，X2的t統(tǒng)計(jì)量有了顯著改進(jìn)，都在1%的程度上通過(guò)了顯著性檢驗(yàn)，更好擬合了原模型。實(shí)驗(yàn)任務(wù)六對(duì)實(shí)驗(yàn)數(shù)據(jù)3各變量取對(duì)數(shù)，并估計(jì)方程，判斷其是否存在序列相關(guān)性。下圖為用Eviews軟件對(duì)數(shù)據(jù)進(jìn)行回歸分析的計(jì)算結(jié)果：DependentVariable:LNYMethod:LeastSquaresDate:06/10/15Time:15:28Sample:19802007Includedobservations:28CoefficientStd.Errort-StatisticProb.

LNX0.8544150.01421960.090580.0000C1.5884780.13422011.834920.0000R-squared0.992851

Meandependentvar9.552256AdjustedR-squared0.992576

S.D.dependentvar1.303948S.E.ofregression0.112351

Akaikeinfocriterion-1.465625Sumsquaredresid0.328192

Schwarzcriterion-1.370468Loglikelihood22.51875

Hannan-Quinncriter.-1.436535F-statistic3610.878

Durbin-Watsonstat0.379323Prob(F-statistic)0.000000

由此可得： （11.83）（60.09）R2=0.99D.W=0.3793F=3610.882.對(duì)模型進(jìn)行序列相關(guān)性檢驗(yàn)。2.1 圖示法由圖：這期的殘差e隨著上一期的殘差e1的增加而增加，存在正序列相關(guān)性。2.2 D.W.檢驗(yàn)法由于D.W=0.3793,n=28,k=2,查D.W分布表可得，dL=1.33,du=1.48,0<D.W<1.33,所以存在一階正自相關(guān)。2.3 拉格朗日乘數(shù)(LM)檢驗(yàn)法（1）1階自相關(guān)檢驗(yàn)：如下圖，只看rob.Chi-Square(1)=0.0001，因此在1%的水平上拒絕不存在自相關(guān)的原假設(shè)，表明存在一階自相關(guān)。Breusch-GodfreySerialCorrelationLMTest:F-statistic32.78471

Prob.F(1,25)0.0000Obs*R-squared15.88607

Prob.Chi-Square(1)0.0001TestEquation:DependentVariable:RESIDMethod:LeastSquaresDate:06/10/15Time:16:28Sample:19802007Includedobservations:28Presamplemissingvaluelaggedresidualssettozero.CoefficientStd.Errort-StatisticProb.

INX-0.0028360.009551-0.2969270.7690C0.0233450.0901240.2590330.7977RESID(-1)0.7697160.1344305.7257930.0000R-squared0.567360

Meandependentvar7.33E-16AdjustedR-squared0.532748

S.D.dependentvar0.110251S.E.ofregression0.075363

Akaikeinfocriterion-2.232045Sumsquaredresid0.141989

Schwarzcriterion-2.089309Loglikelihood34.24863

Hannan-Quinncriter.-2.188409F-statistic16.39235

Durbin-Watsonstat1.042286Prob(F-statistic)0.000028(2)一直檢驗(yàn)到15階，伴隨概率11.14%才大于10%，沒(méi)有通過(guò)檢驗(yàn)，這表明模型存在直到15階的自相關(guān)。下圖為15階自相關(guān)檢驗(yàn)。Breusch-GodfreySerialCorrelationLMTest:F-statistic2.612572

Prob.F(15,11)0.0568Obs*R-squared21.86315

Prob.Chi-Square(15)0.1114TestEquation:DependentVariable:RESIDMethod:LeastSquaresDate:06/10/15Time:16:48Sample:19802007Includedobservations:28Presamplemissingvaluelaggedresidualssettozero.CoefficientStd.Errort-StatisticProb.

INX-0.0021080.011190-0.1883620.8540C0.0135300.1037070.1304660.8986RESID(-1)1.0446830.2987283.4971020.0050RESID(-2)-0.6892050.434177-1.5873820.1407RESID(-3)0.3008100.4825390.6233890.5457RESID(-4)-0.4679020.484487-0.9657670.3549RESID(-5)0.4257730.5048990.8432830.4170RESID(-6)-0.3247090.519778-0.6247060.5449RESID(-7)-0.0283210.530359-0.0534000.9584RESID(-8)-0.1106780.531208-0.2083520.8388RESID(-9)0.0829660.5409900.1533600.8809RESID(-10)-0.2237300.553029-0.4045530.6936RESID(-11)0.0322670.5699230.0566170.9559RESID(-12)-0.3127620.549093-0.5695970.5804RESID(-13)-0.0303290.555608-0.0545860.9574RESID(-14)0.0273480.4941170.0553470.9569RESID(-15)-0.1786250.354512-0.5038630.6243R-squared0.780827

Meandependentvar7.33E-16AdjustedR-squared0.462029

S.D.dependentvar0.110251S.E.ofregression0.080865

Akaikeinfocriterion-1.912089Sumsquaredresid0.071931

Schwarzcriterion-1.103251Loglikelihood43.76925

Hannan-Quinncriter.-1.664819F-statistic2.449286

Durbin-Watsonstat1.536255Prob(F-statistic)0.0683063.采用廣義差分法估計(jì)方程（1）一階廣義差分：如下圖，D.W=0.83,n=27,k=3,查表，得到臨界值dL=1.02和du=1.32,0<D.W<1.02，存在正自相關(guān)。DependentVariable:INYMethod:LeastSquaresDate:06/10/15Time:17:07Sample(adjusted):19812007Includedobservations:27afteradjustmentsConvergenceachievedafter200iterationsCoefficientStd.Errort-StatisticProb.

INX0.4963880.1005394.9372500.0000C333.655840410.850.0082570.9935AR(1)0.9998320.02077048.138720.0000R-squared0.998115

Meandependentvar9.624593AdjustedR-squared0.997958

S.D.dependentvar1.270246S.E.ofregression0.057404

Akaikeinfocriterion-2.772959Sumsquaredresid0.079086

Schwarzcriterion-2.628977Loglikelihood40.43494

Hannan-Quinncriter.-2.730145F-statistic6353.483

Durbin-Watsonstat0.834489Prob(F-statistic)0.000000InvertedARRoots

1.00(2)二階廣義差分：如下圖，D.W=1.8197,n=26,k=4,查表，可得，dL=1.14,du=1.65,1.65<D.W<4-1.65,無(wú)自相關(guān)，消除自相關(guān)。

DependentVariable:INYMethod:LeastSquaresDate:06/10/15Time:17:19Sample(adjusted):19822007Includedobservations:26afteradjustmentsConvergenceachievedafter8iterationsCoefficientStd.Errort-StatisticProb.

INX0.8657250.02274138.068500.0000C1.4624130.2203116.6379390.0000AR(1)1.1531000.1794896.4243650.0000AR(2)-0.5166720.168869-3.0596100.0057R-squared0.998087

Meandependentvar9.701508AdjustedR-squared0.997826

S.D.dependentvar1.229613S.E.ofregression0.057334

Akaikeinfocriterion-2.739210Sumsquaredresid0.072318

Schwarzcriterion-2.545657Loglikelihood39.60973

Hannan-Quinncriter.-2.683474F-statistic3825.609

Durbin-Watsonstat1.819703Prob(F-statistic)0.000000InvertedARRoots

.58-.43i

.58+.43i4.采用拉格朗日乘數(shù)(LM)檢驗(yàn)法檢驗(yàn)廣義差分法的估計(jì)結(jié)果Breusch-GodfreySerialCorrelationLMTest:F-statistic0.136597

Prob.F(2,20)0.8731Obs*R-squared0.350367

Prob.Chi-Square(2)0.8393TestEquation:DependentVariable:RESIDMethod:LeastSquaresDate:06/10/15Time:17:30Sample:19822007Includedobservations:26Presamplemissingvaluelaggedresidualssettozero.CoefficientStd.Errort-StatisticProb.

INX-0.0043030.025183-0.1708830.8660C0.0377260.2418980.1559570.8776AR(1)-0.2159270.455541-0.4740020.6406AR(2)0.1349880.3216240.4197090.6792RESID(-1)0.2569300.5145450.4993340.6230RESID(-2)0.1545100.3586550.4308030.6712R-squared0.013476

Meandependentvar-8.53E-13AdjustedR-squared-0.233155

S.D.dependentvar0.053784S.E.ofregression0.059726

Akaikeinfocriterion-2.598931Sumsquaredresid0.071343

Schwarzcriterion-2.308601Loglikelihood39.78610

Hannan-Quinncriter.-2.515327F-statistic0.054639

Durbin-Watsonstat1.880462Prob(F-statistic)0.997807lnx,AR(1),AR(2),RESID(-1),RESID(-2)的伴隨概率都沒(méi)有通過(guò)檢驗(yàn)，說(shuō)明接受原假設(shè)，接受不存在自相關(guān)，說(shuō)明自相關(guān)已經(jīng)消除。實(shí)驗(yàn)任務(wù)七1.對(duì)實(shí)驗(yàn)數(shù)據(jù)4各變量取對(duì)數(shù)，并采用普通最小二乘法估計(jì)模型。假設(shè)擬建立如下一元回歸模型：DependentVariable:LNYMethod:LeastSquaresDate:06/10/15Time:17:45Sample:19832007Includedobservations:25CoefficientStd.Errort-StatisticProb.

LNX10.3811450.0502427.5861820.0000LNX21.2222890.1351799.0420300.0000LNX3-0.0811100.015304-5.3000240.0000LNX4-0.0472290.044767-1.0549800.3047LNX5-0.1011740.057687-1.7538530.0956C-4.1731741.923624-2.1694340.0429R-squared0.981597

Meandependentvar10.70905AdjustedR-squared0.976753

S.D.dependentvar0.093396S.E.ofregression0.014240

Akaikeinfocriterion-5.459968Sumsquaredresid0.003853

Schwarzcriterion-5.167438Loglikelihood74.24960

Hannan-Quinncriter.-5.378833F-statistic202.6826

Durbin-Watsonstat1.791427Prob(F-statistic)0.000000由此可得：（-2,17）（7.59）（9.04）（-5.30）（-1.05）（-1.75）R2=0.98F=202.68D.W.=1.79由此可得：R2=98%，擬合優(yōu)度較好，lnX1,lnX2,lnX3都在1%的水平上通過(guò)檢驗(yàn)，說(shuō)明農(nóng)業(yè)化肥施用量X1，糧食播種面積X2，成災(zāi)面積X3對(duì)糧食產(chǎn)量Y的影響較為顯著，但由于X4，X5前參數(shù)估計(jì)值未能通過(guò)檢驗(yàn)，而且符號(hào)的經(jīng)濟(jì)意義不合理，故認(rèn)為解釋變量之間存在多重共線性。測(cè)算模型中各變量的相關(guān)系數(shù)。CovarianceAnalysis:OrdinaryDate:11/03/14Time:08:25Sample:19832007Includedobservations:25Correlationt-StatisticProbabilityLNY

LNX1

LNX2

LNX3

LNX4

LNX5

LNY

1.000000-----

-----

LNX1

0.8775961.0000008.779293-----

0.0000-----

LNX2

-0.154974-0.5687441.000000-0.752321-3.316174-----

0.45950.0030-----

LNX3

0.2554880.451700-0.2140971.0000001.2673352.428101-1.051148-----

0.21770.02340.3041-----

LNX4

0.7762760.964357-0.6976250.3987801.0000005.90567017.47840-4.6697342.085480-----

0.00000.00000.00010.0483-----

LNX5

0.3984130.440205-0.0732700.4112790.2795281.0000002.0831992.351216-0.3523392.1639121.396228-----

0.04850.02770.72780.04110.1760-----

由上圖可得，X4與X5不顯著，相關(guān)系數(shù)是0.28，而X4與X1顯著，相關(guān)系數(shù)為0.96，X4與X1，X2，X3高度相關(guān)，存在多重共線性。分別作被解釋變量與各解釋變量的回歸，找出最簡(jiǎn)單的回歸形式。分別做lnY與lnx1,lnx2,lnx3,lnx4,lnx5的回歸，如圖：（1）DependentVariable:LNYMethod:LeastSquaresDate:06/10/15Time:18:29Sample:19832007Includedobservations:25CoefficientStd.Errort-StatisticProb.

LNX10.2240050.0255158.7792930.0000C8.9020080.20603443.206570.0000R-squared0.770175

Meandependentvar10.70905AdjustedR-squared0.760182

S.D.dependentvar0.093396S.E.ofregression0.045737

Akaikeinfocriterion-3.255189Sumsquaredresid0.048114

Schwarzcriterion-3.157679Loglikelihood42.68986

Hannan-Quinncriter.-3.228144F-statistic77.07599

Durbin-Watsonstat0.939435Prob(F-statistic)0.000000

（2）DependentVariable:LNYMethod:LeastSquaresDate:06/10/15Time:18:30Sample:19832007Includedobservations:25CoefficientStd.Errort-StatisticProb.

LNX2-0.3834340.509669-0.7523210.4595C15.157485.9129712.5634290.0174R-squared0.024017

Meandependentvar10.70905AdjustedR-squared-0.018417

S.D.dependentvar0.093396S.E.ofregression0.094252

Akaikeinfocriterion-1.809063Sumsquaredresid0.204321

Schwarzcriterion-1.711553Loglikelihood24.61329

Hannan-Quinncriter.-1.782018F-statistic0.565986

Durbin-Watsonstat0.335219Prob(F-statistic)0.459489(3)

DependentVariable:LNYMethod:LeastSquaresDate:06/10/15Time:18:31Sample:19832007Includedobservations:25CoefficientStd.Errort-StatisticProb.

LNX30.1080670.0852711.2673350.2177C9.6197220.85974411.189050.0000R-squared0.065274

Meandependentvar10.70905AdjustedR-squared0.024634

S.D.dependentvar0.093396S.E.ofregression0.092239

Akaikeinfocriterion-1.852255Sumsquaredresid0.195684

Schwarzcriterion-1.754745Loglikelihood25.15319

Hannan-Quinncriter.-1.825210F-statistic1.606139

Durbin-Watsonstat0.597749Prob(F-statistic)0.217717

（4）DependentVariable:LNYMethod:LeastSquaresDate:06/10/15Time:18:31Sample:19832007Includedobservations:25CoefficientStd.Errort-StatisticProb.

LNX40.1669760.0282745.9056700.0000C8.9490900.29825530.004790.0000R-squared0.602605

Meandependentvar10.70905AdjustedR-squared0.585327

S.D.dependentvar0.093396S.E.ofregression0.060143

Akaikeinfocriterion-2.707578Sumsquaredresid0.083194

Schwarzcriterion-2.610068Loglikelihood35.84472

Hannan-Quinncriter.-2.680533F-statistic34.87693

Durbin-Watsonstat0.625528Prob(F-statistic)0.000005

（5）DependentVariable:LNYMethod:LeastSquaresDate:06/10/15Time:18:32Sample:19832007Includedobservations:25CoefficientStd.Errort-StatisticProb.

LNX50.4887310.2346062.0831990.0485C5.6007492.4522072.2839620.0319R-squared0.158733

Meandependentvar10.70905AdjustedR-squared0.122156

S.D.dependentvar0.093396S.E.ofregression0.087506

Akaikeinfocriterion-1.957599Sumsquaredresid0.176118

Schwarzcriterion-1.860089Loglikelihood26.46999

Hannan-Quinncriter.-1.930554F-statistic4.339718

Durbin-Watsonstat0.327932Prob(F-statistic)0.048538通過(guò)分析比較，模型與InX1的回歸結(jié)果最好，R2為0.7702，在五組數(shù)據(jù)中是最大的，同時(shí)，解釋變量在1%的水平上通過(guò)檢驗(yàn)，因此最擬合原方程，選（1）為初始的回歸模型。（43.2）（8.78）=0.7702采用逐步回歸法估計(jì)方程，完成下表。y模型1模型2模型3模型4模型5lnX10.2240.2980.3230.3300.322（8.78）(19.24)(29.78)(28.66)(8.22)lnX21.261.291.321.29(8.39)(13.42)(13.67)(9.56)lnX3-0.087-0.081-0.087(-5.72)(-5.30)(-5.51)lnX40.001(0.035)lnX5-0.064(-1.40)R20.770.950.980.980.98D.W.0.941.601.411.641.42模型一：即初始回歸模型，X1化肥的作用對(duì)農(nóng)業(yè)生產(chǎn)明顯。DependentVariable:LNYMethod:LeastSquaresDate:06/10/15Time:18:29Sample:19832007Includedobservations:25CoefficientStd.Errort-StatisticProb.

LNX10.2240050.0255158.7792930.0000C8.9020080.20603443.206570.0000R-squared0.770175

Meandependentvar10.70905AdjustedR-squared0.760182

S.D.dependentvar0.093396S.E.ofregression0.045737

Akaikeinfocriterion-3.255189Sumsquaredresid0.048114

Schwarzcriterion-3.157679Loglikelihood42.68986

Hannan-Quinncriter.-3.228144F-statistic77.07599

Durbin-Watsonstat0.939435Prob(F-statistic)0.000000

模型二：在初始模型中引入X2，R2值上升，模型擬合優(yōu)度提高，且參數(shù)符號(hào)合理，變量lnX1，lnX2都在1%的水平上通過(guò)檢驗(yàn)。X2播種面積越大，規(guī)模經(jīng)濟(jì)效應(yīng)越強(qiáng)。DependentVariable:LNYMethod:LeastSquaresDate:06/10/15Time:18:59Sample:19832007Includedobservations:25CoefficientStd.Errort-StatisticProb.

LNX10.2978540.01548219.239290.0000LNX21.2586220.1500668.3871270.0000C-6.2956821.814941-3.4688090.0022R-squared0.945246

Meandependentvar10.70905AdjustedR-squared0.940269

S.D.dependentvar0.093396S.E.ofregression0.022826

Akaikeinfocriterion-4.609666Sumsquaredresid0.011463

Schwarzcriterion-4.463401Loglikelihood60.62083

Hannan-Quinncriter.-4.569098F-statistic189.9002

Durbin-Watsonstat1.595748Prob(F-s