1.表1列出了某地區(qū)家庭人均雞肉年消費(fèi)量Y與家庭月平均收入X,雞肉價(jià)格Py豬肉價(jià)格P2與牛肉價(jià)格P3的相關(guān)數(shù)據(jù)。年份Y/千X/PJ(元/P2/(7U/P3/(7U/年份Y/千PJ(元/P2/(7U/P3/(7U/克元千克）千克）千克）克X/元千克）千克）千克）19802.783974.225.077.8319924.189113.977.9111.4019812.994133.815.207.9219934.049315.219.5412.4119822.984394.035.407.9219944.0710214.899.4212.7619833.084593.955.537.9219954.0111655.8312.3514.2919843.124923.735.477.7419964.2713495.7912.9914.3619853.335283.816.378.0219974.4114495.6711.7613.9219863.565603.936.988.0419984.6715756.3713.0916.5519873.646243.786.598.3919995.0617596.1612.9820.3319883.676663.846.458.5520005.0119945.8912.8021.9619893.847174.017.009.3720015.1722586.6414.1022.1619904.047683.867.3210.6120025.2924787.0416.8223.2619914.038433.986.7810.48（1）求出該地區(qū)關(guān)于家庭雞肉消費(fèi)需求的如下模型:(2)lnY=P+PInX+PInP+PInP+PInP+u(2)請(qǐng)分析，雞肉的家庭消費(fèi)需求是否受豬肉及牛肉價(jià)格的影響。先做回歸分析，過(guò)程如下:EquationEst1七EquationEst1七1on輸出結(jié)果如下:VariableCoefficientStd.Errort-StatisticProb.C-07315200.296947■2.4634670.0241LOG(X)0.3452570.0825654.1816490.0006L0G(P1)-0.5021220.109891-4.5692940.0002L0G(P2)0.146S680.0990061.4834200.1553L0G(P3)口國(guó)儂0.099B520.8731370.3941R-squared0.9B2474Meandependentvar1.361301AdjustedR-squared0.978579S.D.dependentvar0.187659S.E.ofregression0.027465Akaikeinfocriterion-4.162123Sumsquaredresid0.013578Schwarzcriterion-3.915276Laglikelihood52.B6441F-statistic252.2633Durbin-Watsonstat1.B24S20Prob(F-statistic)0.000000所以，回歸方程為：InY=—0.7315+0.3463山X—0.50211nP+0.14691nP+0.08721nP1 2 3(-2.463) (4.182) (-4.569) (1.483) (0.873)由上述回歸結(jié)果可以知道，雞肉消費(fèi)需求受家庭收入水平和雞肉價(jià)格的影響，而牛肉價(jià)格和豬肉價(jià)格對(duì)雞肉消費(fèi)需求的影響并不顯著。驗(yàn)證豬肉價(jià)格和雞肉價(jià)格是否有影響，可以通過(guò)赤池準(zhǔn)則(AIC)和施瓦茨準(zhǔn)則(SC)。若AIC值或SC值增加了，就應(yīng)該去掉該解釋變量。去掉豬肉價(jià)格P2與牛肉價(jià)格P3重新進(jìn)行回歸分析，結(jié)果如下：VariableCoefficientStd.Errort-StatisticProb.C-1.1257970.088420-12.732370.0000LOG(X)0.4515470.02455418.389660.0000LOG(P1)-0.3727350.063104-5.9066680.0000R-squared0.980287Meandependentvar1.361301AdjustedR-squared0.978316S.D.dependentvar0.187659S.E.ofregression0.027634Akaikeinfocriterion-4.218445Sumsquaredresid0.015273Schwarzcriterion-4.070337Loglikelihood51.51212F-statistic497.2843Durbin-Watsonstat1.877706Prob(F-statistic)0.000000通過(guò)比較可以看出，AIC值和SC值都變小了，所以應(yīng)該去掉豬肉價(jià)格P2與牛肉價(jià)格P3這兩個(gè)解釋變量。所以該地區(qū)豬肉與牛肉價(jià)格確實(shí)對(duì)家庭的雞肉消費(fèi)不產(chǎn)生顯著影響。2.表2列出了中國(guó)2012年按行業(yè)分的全部制造業(yè)國(guó)有企業(yè)及規(guī)模以上制造業(yè)非國(guó)有企業(yè)的工業(yè)總產(chǎn)值Y，資產(chǎn)合計(jì)K及職工人數(shù)L。工業(yè)總產(chǎn)資產(chǎn)合計(jì)職工人數(shù) 工業(yè)總產(chǎn)資產(chǎn)合計(jì)職工人數(shù)

序號(hào)值Y/億元K/億元L/萬(wàn)人序號(hào)值Y/億元K/億元L/萬(wàn)人13722.7003078.220113.000017812.70001118.81043.0000021442.5201684.43067.00000181899.7002052.16061.0000031752.3702742.77084.00000193692.8506113.110240.000041451.2901973.82027.00000204732.9009228.250222.000055149.3005917.010327.0000212180.2302866.65080.0000062291.1601758.770120.0000222539.7602545.63096.0000071345.170939.100058.00000233046.9504787.900222.00008656.7700694.940031.00000242192.6303255.290163.00009370.1800363.480016.00000255364.8308129.680244.0000101590.3602511.99066.00000264834.6805260.200145.000011616.7100973.730058.00000277549.5807518.790138.000012617.9400516.010028.0000028867.9100984.520046.00000134429.1903785.91061.00000294611.39018626.94218.0000145749.0208688.030254.000030170.3000610.910019.00000151781.3702798.90083.0000031325.53001523.19045.00000161243.0701808.44033.00000設(shè)定模型為：Y=AKaL3e^利用上述資料，進(jìn)行回歸分析；回答：中國(guó)2000年的制造業(yè)總體呈現(xiàn)規(guī)模報(bào)酬不變狀態(tài)嗎?將模型進(jìn)行雙對(duì)數(shù)變換如下：InK=lnA+ocln^+PlnL+|Li1)進(jìn)行回歸分析:EquationEstiBationSpeci11cationj-ptiQHL二Equationspecific：i+￡onIieiiemlentv：±riablefoilowedbylistotregi-essors：xtl>1PELtermSjORulgfjlicitequati'jnL口gj%)二L「gJ：k；iLog：CL)IEetimationsettirL^sHethod：]_S.-tMqmir白工(HLS皿&WJA)S：iniple131取消確定

取消得到如下回歸結(jié)果:VariableCoefficientStd.Errort-StatisticProb.cLOG的LOG(L)1.1539940.6092360.3607960.727611 1.6060040.176378 3.4641490.201691 17897410.12400.0018O.OS43R-squared0.809925Meandependentvar7.493997AdjustedR-squared0.796348S.D.dependentvar0.942960S.E.ofregression0.42553SAkaikeinfocriterion1.220839Sumsquaredresid5.070303Schwarzcriterion1.359612Laglikelihood-15.92300F-statistic59,65501Durbin-Watsonstat0.793209Prab(F-statistic)0.000000于是，樣本回歸方程為：八Inr=1.154+0.6091nK+0.3611nL(1.59)(3.45) (1.79)R2:0.8099,R=0.7963,F=59.66從回歸結(jié)果可以看出，模型的擬合度較好，在顯著性水平0.1的條件下，各項(xiàng)系數(shù)均通過(guò)了t檢驗(yàn)。從F檢驗(yàn)可以看出，方程對(duì)Y的解釋程度較少。R=0.7963表明，工業(yè)總產(chǎn)值對(duì)數(shù)值的79.6%的變化可以由資產(chǎn)合計(jì)對(duì)數(shù)與職工的對(duì)數(shù)值的變化來(lái)解釋，但仍有20.4%的變化是由其他因素的變化影響的。從上述回歸結(jié)果看，&+8=0.97“1,即資產(chǎn)與勞動(dòng)的產(chǎn)出彈性之和近似為1,表明中國(guó)制造業(yè)在2000年基本呈現(xiàn)規(guī)模報(bào)酬不變的狀態(tài)。下面進(jìn)行Wald檢驗(yàn)對(duì)約束關(guān)系進(jìn)行檢驗(yàn)。過(guò)程如下:?EVievs-[Equation:UNTITLEDlorkfile:UNTITLED::UntilleiFileEditObjectViewFreeQuickO^tionsTfindowMeLp過(guò)后圓Pr口匚][口團(tuán)日匚H[Prinl:][rJmnn日][Fr日曰w1][Enimatn 日匚aiHGtmwRREsidE]RsEi-esentationsEztinitiunOutputActualFitted.Residual.MlMAStruetm-&...gradient與wdDerivatives”ii!--!tnFrrnr =十i匚:h「 Pii!--!tnFrrnr =十i匚:h「 PrnhC_urLtideneeEllipse...jVald-Coe±ticientRestricticms...OmittedTariabl已三一Lihelihoc?dEatio...ReduiLilsmtVari：iblqe_Likelihoo■!Ratlo...Coe±ticierbtTestsReeidn：dlTestsStati.1ityLih^LtaI I Ii -r-L?L?LiLi-T

結(jié)果如下:WaldTest:Equation:UntitledTestStatistic ValuedfProbabilityF-statistic 0.10111B(1,冽I07529)Chi-square 0.10111B1|口75口5|NullHypothesisSummary:NormalizedRestriction(=□)ValueSid.Err.-1+0(2)十C(3)-0.0299680.094242Restrictionsarelinearincoefficients.由對(duì)應(yīng)概率可以知道，不能拒絕原假設(shè)，即資產(chǎn)與勞動(dòng)的產(chǎn)出彈性之和為1,表明中國(guó)制造業(yè)在2000年呈現(xiàn)規(guī)模報(bào)酬不變的狀態(tài)。一、鄒式檢驗(yàn)（突變點(diǎn)檢驗(yàn)、穩(wěn)定性檢驗(yàn)）.突變點(diǎn)檢驗(yàn)1995-2012年中國(guó)家用汽車擁有量（y，萬(wàn)輛）與城鎮(zhèn)居民家庭人均可支配收入t（X，元），數(shù)據(jù)見(jiàn)表3。t表3中國(guó)家用汽車擁有量（y）與城鎮(zhèn)居民家庭人均可支配收入（1）數(shù)據(jù)t t年份y（萬(wàn)輛）tX(元)t年份y（萬(wàn)輛）tX(元)t199528.49739.12004205.423496.2199634.71899.62005249.964283199742.291002.22006289.674838.9199860.421181.42007358.365160.3199973.121375.72008423.655425.1

200081.621510.22009533.885854200196.041700.62010625.3362802002118.22026.62011770.786859.62003155.772577.42012968.987702.8下圖是關(guān)于y和x的散點(diǎn)圖:t t1000800-6DD-4001000800-6DD-4002000-□1QQQ30005QQQ?□□□X從上圖可以看出，2006年是一個(gè)突變點(diǎn)，當(dāng)城鎮(zhèn)居民家庭人均可支配收入突破4838.9元之后，城鎮(zhèn)居民家庭購(gòu)買家用汽車的能力大大提高?，F(xiàn)在用鄒突變點(diǎn)檢驗(yàn)法檢驗(yàn)1996年是不是一個(gè)突變點(diǎn)。Ho：兩個(gè)字樣本（1995—2005年，2006—2012年）相對(duì)應(yīng)的模型回歸參數(shù)相等H1：備擇假設(shè)是兩個(gè)子樣本對(duì)應(yīng)的回歸參數(shù)不等。在1995—2012年樣本范圍內(nèi)做回歸。0.245355ProL(F-statistic)在回歸結(jié)果中作如下步驟：0.245355ProL(F-statistic)Jlajii-eserLtatiotleTstini：±tiunUutputActual,Fittei,Re5idu；1l ,AEMAStructure...Gr：id1 e：=lTlJD&r1vat1vee?C至Matfi器itStd.Errort-StatisticProb.CueffinientTests ，Eeziilu：=J_Teste .—9 38.87504 -2.9223S0 0.0100StaLilityTests lChowBre：=Jq：iointTest...LabelChij'iii'ForecastT也=t...MSETT口與t.一Rguur-iv.EstimatesI.IJLS口工LLy」...AdjustedR-squared 0,B966-S.E.ofregression 89.515l12日2口9石-105.380312,03000140.48410.000000SchwarzcritericinF-statisticSumsquaredresidLoglikelihoodDurtiin-Watsonstat□Equation:UNTITLEDTorkfile:HASEBa，:Cas.??匚〕回國(guó)Objc匚[Prinl:][Narne

輸入突變點(diǎn):得到如下驗(yàn)證結(jié)果：ChowBreakpointTest:200&NullHypothesis:NobreaksatspecifiedbreakpointsVaryingregressors:AllequationvariablesEquationSample:19952011F-statistic1416.403Prob.F(2.13J0.0000Loglikelihoodratio91.G0709Prob-.Chi-Square(2)0.0000WaldStatistic2832.806Prob-.Ghi-Square(2)0.0000由相伴概率可以知道，拒絕原假設(shè)，即兩個(gè)樣本（1995—2005年，2006—2012年）的回歸參數(shù)不相等。所以，2006年是突變點(diǎn)。.穩(wěn)定性檢驗(yàn)以表3為例，在用1995—2009年數(shù)據(jù)建立的模型基礎(chǔ)上，檢驗(yàn)當(dāng)把2010—2012年數(shù)據(jù)加入樣本后，模型的回歸參數(shù)時(shí)候出現(xiàn)顯著性變化。因?yàn)橐呀?jīng)知道2006年為結(jié)構(gòu)突變點(diǎn)，所以設(shè)定虛擬變量：101995—2005D1\|12006—2012對(duì)1995—2012年的數(shù)據(jù)進(jìn)行回歸分析:

EquationE￡timstian.確定耳乂消做鄒氏穩(wěn)定性檢驗(yàn):ViewProcObjectPrintN^meFreezeEstimateForecastStatsResids□ependentVariable:YMethod二LeastSquares□ate:10/25/1STime:21:05Sample:19%2012Includedobservations:18VariableCoefficientStd.Errort-StatisticProb.C-16.074912.945554 -5.4571620.0001X0.0535240.001353 47.02409O.QOOOD1-852.6.22512.29131 -69.36791O.ftOOOtm0.1750130.002381 73.49329o.aoooR-squared0.999750Meandependentvar234.260GAdjustedR-squared0.999697S.D.dependentvar27S.4439S.E.ofregression4.047800Akaikeinfocriterion6.108060Sumsquaredresid3290174Schwarzcriterion6.385921Loglikelihood-51692MHannan-Quinncriter6.215343F-statistic1868976Durbin-Watsonstat1.766734ProbfF-statistic)0.000000輸入要檢驗(yàn)的樣本點(diǎn):得到如下檢驗(yàn)結(jié)果:ChowForecastTestEquation:UNTITLEDSpecification:YCXD1DI^XTestpredi-ctionsforobservationsfrom2010to2012Value出ProIbabiIityF-statistic0.433432PJ1)0.7333Likelihooti「atio2.01110430.5701由上述結(jié)果可以知道，F(xiàn)值對(duì)應(yīng)的概率為0.73,所以接受原假設(shè)，模型加入2010、2011和2012年的樣本值后，回歸參數(shù)沒(méi)有發(fā)生顯著性變化。二、似然比（LR）檢驗(yàn)有中國(guó)國(guó)債發(fā)行總量（DEBT，億元）模型如下：tDEBT=P+PGDP+PDEF+0REPAY+ut0 1t2t3 tt其中GDP表示國(guó)內(nèi)生產(chǎn)總值（百億元），DEF表示年財(cái)政赤字額（億元），REPAY表示t t t年還本付息額（億元）。1990—2011年數(shù)據(jù)見(jiàn)表4。表4國(guó)債發(fā)行總量DEBT、GDP、財(cái)政赤字額DEF、年還本付息額（REPAY）數(shù)據(jù)t t t t199043.0145.17868.928.582001461.4216.178237.14246.81991121.7448.624-37.3862.892002669.68266.381258.83438.57199283.8652.94717.6555.522003739.22346.344293.35336.22199379.4159.34542.5742.4720041175.25467.594574.52499.36199477.3471.7158.1628.920051549.76584.781581.52882.96199589.8589.644-0.5739.5620061967.28678.846529.561355.031996138.25102.02282.950.1720072476.82744.626582.421918.371997223.55119.62562.8379.8320083310.93783.452922.232352.921998270.78149.283133.9776.7620093715.03820.67461743.591910.531999407.97169.092158.8872.3720104180.1894.4222491.271579.822000375.45185.479146.49190.0720114604959.3332516.542007.73對(duì)以上數(shù)據(jù)進(jìn)行回歸分析:EquationEstimation EquationEstimation 次得到如下輸出結(jié)果：DependentVariable:DEBTMethod:LeastSquaresDate;10/25/15Time;21;13Sample:19902011Includedobservations:22VariableCoefficientStd.Errort-StatisticProb.C4.3MOOB21一667250.1991030.8444GDP0.3462020.1644702.2347560.0384DEF0.9954030.031E1331.486990.0000REPAY0.3797600.04950817770220.0000R-squa.red099S955Meandependentvar1216.355AdjustedR-squared0.998781S.D.dependentvar1405.993S.E.ofregression51.88705Akaikeinfiocriterion10.09398Sumsquaredresid484E0.7SSchwarzcriterio-n11.09735Loglikelihood-115.8888Hannan-Quinncriter10.94571F-statistic5735.346Durbin-Watsonstat2.116834Prob(F-statistic)0000000對(duì)應(yīng)的回歸表達(dá)式為：DEBT=4.31+0.35GDP+1.00DEF+0.88REPAYt t t t(0.2)(2.2) (31.5) (17.8)R2=0.999,DW=2.1,F=5735.3現(xiàn)在用似然比（LR）統(tǒng)計(jì)量檢驗(yàn)約束GDP對(duì)應(yīng)的回歸系數(shù)P等于零是否成立。t 1過(guò)程如下：S'ETievs-[Eauation:UKTITLEDTorkflie:CASEGB::CaseGb\]FileEditObJactViawProcQuiukQ^tiansWind-owHalpM縣以介「□匚gblE匚H[p門nHIrJamc][Freeze][Estimate]/口叱匚至川5H5][艮6與出]ReuresentaticmsE5tirria+1oilUixtpij.t.Actual,Fitted..Eesidual ?ATlfilAS,tmctur..Gra.d.1ant.eand.Darivativac，匚口文ari：mi2eM：itrix1+ !二：+「』匚rrnv t-!=：ti==+ir- Pfti1--■ConfiiienceZEllipEe_..-ild-CoohhiaisritBLqetrlct￡ofle...QmitiedV：±t-iablee-LikelihoodRati'ii...CoefficientTests .Ra=idualTqe-Le +StabilityTests 卜LatiplRediiriilaxLt.VariabLes一Lik^lihood.Rati□...1—■,—,■,*+--1*,—,,?*--*■*■1—■二二1-1—11R-squared 0.990955 Meandependentvar 1216,395AdjustedR-squared D998731 S□.dependentvar 1435993S.E.ofregression 51.B8705 Akaikeinfocriterion 10.89S9BSumsquaredresid 40460.70 SchwarzciiLeiion 11.09735Loglikslihood -11G.aasaF-statietic 5735.34BDurbin-Watscnstat 2.11BB34 Prob(F-statiGtic) 0.000000輸入要檢驗(yàn)的變量名:得到如下輸出結(jié)果：RedundantVariables:GDPF-statistic4.994134Prob.F(1.18)0.033350Loglikelihoodratio5.387082Prob.Chi-Square(l)口.口2口2加R.estrictedTestEquation:□■ependentVariatjle.DEBTMethod:LeastSquaresMe-10/25/15Time12+17Sample:19902011Includedobservations:22VariableCoefficientStd.Errort-StatisticPr&b.c40.5021715.83705 2.557432U..0193□EF1040S280026718 38948G400000REPAY0.9777S4□025272 3S.6.890G□,0000R.-sqjared0998665Meandependentvar1216.396AdjustedR-squar@d099S524S.D.dependentvar1485.993S.E.ofriegression57.oaoaaAkiaikeinfocriterion11.05294Sumsquaredresi-dB1906.32Schwarzcriterion11.20172L&glik且lih口ad-11BS823Hannan-Quinncriter1100799F-3tatistic710G.5^2Durbin-Wat3onstat1.014741ProbfF-statistic)0000000

輸出結(jié)果上部是關(guān)于約束GDP系數(shù)為零的F檢驗(yàn)和LR檢驗(yàn)。由于兩