第三章 多元線性回歸模型案例

第三章多元線性回歸模型案例一、鄒式檢驗(yàn)（突變點(diǎn)檢驗(yàn)、穩(wěn)定性檢驗(yàn)）1.突變點(diǎn)檢驗(yàn)1985—2002年中國(guó)家用汽車擁有量（七,萬(wàn)輛）與城鎮(zhèn)居民家庭人均可支配收入（二,元），數(shù)據(jù)見(jiàn)表3?1。表3.1中國(guó)家用汽車擁有量（七）與城鎮(zhèn)居民家庭人均可支配收入（：）數(shù)據(jù)年份y（萬(wàn)輛）x（元）年份y（萬(wàn)輛）x（元）198528.49739.11994205.423496.2198634.71899.61995249.964283198742.291002.21996289.674838.9198860.421181.41997358.365160.3198973.121375.71998423.655425.1199081.621510.21999533.885854199196.041700.62000625.3362801992118.22026.62001770.786859.61993155.772577.42002968.987702.8下圖是關(guān)于y,和氣的散點(diǎn)圖:100080060040020001000 3000 5000 7000從上圖可以看出，1996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(mǎi)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)。H0：兩個(gè)子樣本（1985—1995年，1996—2002年）相對(duì)應(yīng)的模型回歸參數(shù)相等Hf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1985—2002年樣本范圍內(nèi)做回歸。

nEquation;UNTITLEDdb/t]|FTintnEquation;UNTITLEDdb/t]|FTint11Memi■■11■111■■1111延塘Ift□匚Jlajii-eserLtatiotleEstinationOutputActu:Q.,Fi+tni,Rt：eidu：±l *AFlMAStructuj-H...CradientsarulDerivatives*ItStd.Errort-StatisticProb.936.87504-2.9223600.0100Cuvjdi-ijanecHatrix輸入突變點(diǎn):輸入突變點(diǎn):Stihil￡tyTests?Ch>wEi-h:LkF-LiiritTuwt...LabelCht■青ForecaztTest...E：=uriEe7FLESETTest...51VtEEtlTiitti5(OLEAdjustedR-squaredS.E.ofregressionSumsquaredresid0.096689.5151CiTily)...128209.6Schwarzcriterian12.0300SLoglikelihood-106.3803F-statistic14S.4841Durtiin-Watsoristat0.246365Proti(F-statistic)0.000000LezidualTesti得到如下驗(yàn)證結(jié)果：ChowBreakpointTest:1996F-statistic2720717Prob.F014)0.000000Loglikelihoadratio107.3756Prob.Chi-Square(2)0.000000由相伴概率可以知道，拒絕原假設(shè)，即兩個(gè)樣本（1985—1995年，1996—2002年）的回歸參數(shù)不相等。所以，1996年是突變點(diǎn)。2.穩(wěn)定性檢驗(yàn)以表3.1為例，在用1985—1999年數(shù)據(jù)建立的模型基礎(chǔ)上，檢驗(yàn)當(dāng)把2000—2002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1996年為結(jié)構(gòu)突變點(diǎn)，所以設(shè)定虛擬變量：[0,1985-1995D"11,1996-2002對(duì)1985-2002年的數(shù)據(jù)進(jìn)行回歸分析:EquationEstiMationEquationsjeci￡1catioilDepHrulentv:±t_l8_blefellowelLy11stoEregi~e5EquationEstiMationEquationsjeci￡1catioilDepHrulentv:±t_l8_blefellowelLy11stoEregi~e5esr5andFDLterm5,OFi；ulexplicitenuationlikeEwtimatipns^^ingsOptLonz賢thodLS-LesstSquares(HLSandARMA)e19052002yckAlk:+:dl職消耘匣祖Prcid[c)b|mizt][PrintFileEditDbject[iewProcQuickO^tionsWindowHelpVariableR-=quaiedAdjustedR-squcredS.E.ofrcgrcccionSumsquaredresidLoclikelihoodDurbin-WatsonmtmtChi：i,i?i,BreakfiulntTest...ChowForacastTact...278.4^396.1SS0606.38592118689.76nnnnnnnNameFreeze[E5tim3te][F頃既耘匣祖Prcid[c)b|mizt][PrintFileEditDbject[iewProcQuickO^tionsWindowHelpVariableR-=quaiedAdjustedR-squcredS.E.ofrcgrcccionSumsquaredresidLoclikelihoodDurbin-WatsonmtmtChi：i,i?i,BreakfiulntTest...ChowForacastTact...278.4^396.1SS0606.38592118689.76nnnnnnnNameFreeze[E5tim3te][F頃既20.9997500.9996974.S47BOB329.0174-51.6925417E5734MeandependentvarS.D.dependentva-AkaikcinfocriterionSchwarzcriteiionF-stalisticRamseyE3SETTes-....R^cursivsE5:ima*,e1.0LSonly)DependentVariable:YMethodLeast5qua-esDate:MW8Time:09:19sample:1ytib2UU2InriidpdrihuurvwtinnT1FRe^ressnialicnsEstimaticmOutputActu^jFitted.Kesid.u：ilAHMAStructm-P...Gradi空以七earidD?irivativseCoefficier■16.07490.06362-852.622U.17501Cuv：±rianceMatrixStabilityrestsLabelCoefficientTestEResidu：allasts做鄒模型穩(wěn)定性檢驗(yàn):圈EVievs-[Equation:UITITLEDlorkfile:CASE6A::Case6a\]輸入要檢驗(yàn)的樣本點(diǎn):

得到如下檢驗(yàn)結(jié)果：ChowForecastTest:Forecastfrom2000to2002F-statistic 0.433432 日比，F(xiàn)（3』1） [J,733333Loglikelihoodratio 2.011105 Prob.Chi-Squ恥⑶ 0.570105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2000、2001和2002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：DEBT=P+PGDP+PDEF+PREPAY+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tt t年還本付息額（億元）。1980—2001年數(shù)據(jù)見(jiàn)表3.2。表3.2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)tt t t據(jù)年份DEBTGDPDEFREPAY年份DEBTGDPDEFREPAY198043.0145.17868.928.581991461.4216.178237.14246.81981121.7448.624-37.3862.891992669.68266.381258.83438.57198283.8652.94717.6555.521993739.22346.344293.35336.22198379.4159.34542.5742.4719941175.25467.594574.52499.36198477.3471.7158.1628.919951549.76584.781581.52882.96198589.8589.644-0.5739.5619961967.28678.846529.561355.031986138.25102.02282.950.1719972476.82744.626582.421918.371987223.55119.62562.8379.8319983310.93783.452922.232352.921988270.78149.283133.9776.7619993715.03820.67461743.591910.531989407.97169.092158.8872.3720004180.1894.4222491.271579.821990375.45185.479146.49190.0720014604959.3332516.542007.73對(duì)以上數(shù)據(jù)進(jìn)行回歸分析:得到如下輸出結(jié)果：DependentVariable:DEBTMethod:LeastSquaresDate:07/01/03Time:10:22Sample:19802001Includedobservations:22VariableCoefficientStd.Errort-StatisticProb.C4.31400821.667250.1991030.8444GDP0.3452020.1544702.2347560.0384DEF0.9954030.03161331.466990.0000REPAY0.8797600.04950817770220.0000R-squared0.998966Meandependentvar1216.396AdjustedR-squared0.998781S.D.dependentvar1485.993S.E.ofregression51.88706Akaikeinfocriterion10.89898Sumsquaredresid4846078Schwarzcriterion11.09736Loglikelihood-115.B888F-statistic5735.346Durbiri-Watsonstat2.116834Proti(F-statistic)0.000000對(duì)應(yīng)的回歸表達(dá)式為:DEBTt4.310.3宙DPt1.00DEF0.88REPAYt(0.2)(2.2)(31.5)(17.8)R20.999,DW2.1F5735.3現(xiàn)在用似然比（LR）統(tǒng)計(jì)量檢驗(yàn)約束GDPt對(duì)應(yīng)的回歸系數(shù)1等于零是否成立。過(guò)程如下：

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)0.038350Loglikelihoodratio5.387082Prob.Chi-Square(1)□.心英日E1eatbquation:DependentVariable:DEBTMethod:LeastSquaresDate:07/01/08Time:10:35Sample:19802001Includedobsen/ations:22VariableCoefficientStd.Errort-StaiisticProb.C40.5021715.83705 2.5574320.0193DEF1.0406280.026718 38.94864□.□□DOREPAY0.9777640.025272 38.689060.0000R-squared□.99B&55MeandependentvarI216.395AdjustedR-squared0.998524S.D.dependentvar1485.993S.E.ofregression57.08088Akaikeinfocriterion11.05294Sumsquaredresid61906.32Schwarzcriterion11.20172Loglikelihood-118.5823F-statistic7106.592Durbin-Watsonstat1.814741Prob(F-statistic)0.000000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)。由于兩種檢驗(yàn)的相應(yīng)概率均小于0.05，即拒接原假設(shè)，GDP系數(shù)1不為零，模型中應(yīng)該保留解釋變量GDP。輸出結(jié)果下部是去掉了GDP變量的約束模型估計(jì)結(jié)果。三、Wald檢驗(yàn)（以表3.2為例進(jìn)行Wald檢驗(yàn)，對(duì)輸出結(jié)果進(jìn)行檢驗(yàn)。）檢驗(yàn)過(guò)程如下：榆EVievs-[Eiiualion:UHTITLEDVorkfile:C1SE6B::Case6b\]IIFileEditCl'aiaetViewFreeQuizkCptionsVii.dcwH-ilpRiE詢〔Pro匚Print.ManneFi-*b]區(qū)5日川口1:』版口1-口匚dzsElvtatsHNcnicI』Ecfcndcnl\-arablc:L'E3TMelhLiJ.LtiailSquarbsDate:D7/O1/UBTime10:4BSanple:198J2001lrrlir|prn□n'fltinnd■7?VariableCoefficieiRe￡rs5entationsEstitii>3tlEcfcndcnl\-arablc:L'E3TMelhLiJ.LtiailSquarbsDate:D7/O1/UBTime10:4BSanple:198J2001lrrlir|prn□n'fltinnd■7?VariableCoefficieiRe￡rs5entationsEstitii>3tlOutputActual,Fitted.Residual.AFlJASiructui-e..五白nt.]-srid.Il^ravitivoECuv：i￡-i：uli：eMatrixCGDPDEFREPAYCoefficientTestsReEidu：ilTestsSt-ibi1:tyTests?Lobe!4.3140Jn34520D.3茹們0.B7976CcmfideneeEllipse..Wald一CoefficientRestric+ions...Unit+tdVoriibles— Ra.t3 .Redimd：=iTLtYariablez_L]kelihuodRati0...R-squared0.998955Meandependentvar1216.395AdjustedR-sqiaredn998781S「dependentvar1405993E.E.ofregrassion51.88705.AkaiksinfocritBrion10.S9B9SBurnsquaredresid4C4C07CSchwarzcriteriun11.爐艾Loglikeihooj-I15.8888F-statistic5735.346Lurjin-Watsjnslat2.116834Frob(l--stctistic)U.UUUJUJ輸入約束表達(dá)式:

得到如下結(jié)果：WaldTest:Equation:UntitledTestStatisticValuedfProbabilityF-statistic0.006892(1,18)0.9348Chi-square0.0068921D.9338NullHypothesisSummary;NormalizedRestriction(=Q)ValueStd.Err.3*C(2)-C(3)0.0402030.484255Restrictionsarelinearincoefficienls.從輸出結(jié)果上部可以看出，相應(yīng)概率非常大，遠(yuǎn)遠(yuǎn)大于0?05，表明原假設(shè)成立，即約束條件3*c(2)=c(3)成立，P2是P1的3倍。輸出結(jié)果的下部給出了約束條件3*c(2)-c(3)=0的樣本值和樣本標(biāo)準(zhǔn)差，分別為0?04和0?48。四、表3.3中列出了中國(guó)2000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。表3.3中國(guó)2000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序號(hào)工業(yè)總產(chǎn)值Y/億元資產(chǎn)合計(jì)K/億元職工人數(shù)L/萬(wàn)人序號(hào)工業(yè)總產(chǎn)值Y/億元資產(chǎn)合計(jì)K/億元職工人數(shù)L/萬(wàn)人13722.7003078.220113.000017812.70001118.81043.0000021442.5201684.43067.00000181899.7002052.16061.0000031752.3702742.77084.00000193692.8506113.110240.000041451.2901973.82027.00000204732.9009228.250222.000055149.3005917.010327.0000212180.2302866.65080.0000062291.1601758.770120.0000222539.7602545.63096.0000071345.170939.100058.00000233046.9504787.900222.00008656.7700694.940031.00000242192.6303255.290163.00009370.1800363.480016.00000255364.8308129.680244.0000101590.3602511.99066.00000264834.6805260.200145.0000

11616.7100973.730058.00000277549.5807518.790138.000012617.9400516.010028.0000028867.9100984.520046.00000134429.1903785.91061.00000294611.39018626.94218.0000145749.0208688.030254.000030170.3000610.910019.00000151781.3702798.90083.0000031325.53001523.19045.0000016|1243.070 1808.440 33.00000設(shè)定模型為：Y=AKa￡pe四（1） 利用上述資料，進(jìn)行回歸分析；（2） 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：lnY=lnA+aInK+PInL+p1）進(jìn)行回歸分析：得到如下回歸結(jié)果:DependentVariable:LOG(Y)Meihod:LeastSquaresDate:07/03/08Time:14:19Sample:131Includedobservations:31VariableCoefficientStd.Errort-StatisticProb.C1.1539940.7276111.5860040.1240LOGCK]0.6092360.1763783.4541490.0010LOG(L)0.3607960.2015911.7S97410.0S43R-squared0.SO9925Meandependentvmr7.493997AdjustedR-squared0.796348S.D.dependentvar0.942960S.E.ofregression0.425538Akaikeinfocriterion1.220839Sumsquaredresid6.070303Schwarzcriterion1.369612Loglikelihood-15.92300F-statistic59.65501Durbin-Watsonstat0.793209Prob(F-statistic)0.000000于是，樣本回歸方程為：一八..一一_ 一….一lnY=1.154+0.609lnK+0.361lnL(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，a+0=0.97牝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：^lEVievs-[Equation:UNTITLEDlorkfile:UNTITLED::UntilleirIIFileEditObjectVi Free日口ickOjitiotlejVindowHelpyiejw|[Proc][obiect][PrintNsnneFr&ese][Estimate][Foreca5t][stat5][Re5id5]ReiireierLtitiori-Ee11natiotlUutputActual,F111eil,Residual *MJilAStructure...Grhh+eatHDeriv：±tivge?CoefficieRtTastE ?Residu.alTests ，StatilityTests *11 dFrrnrt-St：=itic：tir- PrnhCuntideneeEllipse...一Coe￡￡icientRes+rictions...Omitted 一Lih^LihcxjdEati'；'...ReduiLii：mt i：ibl口二一LikelihoodRatlo._.rl fa4

結(jié)果如下:WaldTest:Equation:UntitledTestStatisticValuedfProbabilityF-statisticChi-square0.10111B0.101118(1,2日)1I07529I|口75島|NullHypothesisSummary:NormalizedRestriction(=0)ValueSid.Err.-1十G(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)。五、已知數(shù)據(jù)如表:YX1X211103298351541285-61、先根據(jù)表中數(shù)據(jù)估計(jì)以下回歸模型的方程:Y=a+aX+uTOC\o"1-5"\h\zi0 11i 1iY=X+人X+ui0 2 2i2iY=P+PX+PX+ui011i22ii（1）回答下列問(wèn)題：a=0嗎？為什么？X=P嗎？為什么？11 22對(duì)上述3個(gè)方程進(jìn)行回歸分析，結(jié)果分別如下：

DependentVariable:YMethod:LeastSquaresDate:07/C3/08Time:14:56Sample:15Includedobsen/atiors:5VariableCoefficientStd.Errort-StatisticProb.C-8.8000003.942926 -2.2318450.1118X16.6000001.188837 5.5516440.0115R-squared0.911297Meandependentvar11.00000AdjustedR-squared0.881729S.D.dependentvar10.93161S.E.ofregression3.759433Akaikeinfocriterion5.775588Sumsquaredresid42.40000Schwarzcriterion5.619363Loglikelihood-12.43897F-statistic30.82075Durbin-Watsonstat1.529245Prob(F-statistic)0.011526即：Y=—8.8+6.6XiDependentVariable:YMethod:LeastSquaresDate:07/U3>0STime:14:69Sample:15即：Y=即：Y=17.34—1.66XVariableCoefficientStd.Errort-StatisticPrab.C17.340750.48144436.010200.0000X2-1.6686100.069060-24.161300.0002R-squared0.994867Meandependentvar11.00000AdjustedR-squared0.993163S.D.dependent傾10.93161S.E.ofregression0.902661Akaikeinfocriterion2.921991Sumsquaredresid2.443794Schwarzcriterion2766766Loglikelihood-5.304977F-statistic5837926Durbin-Watsoristat1.948272Prob(F-statistic)0.0001552從上述回歸結(jié)果可知：&。8,尤。&。二元回歸與分別對(duì)X與X所作的一元回歸，112 2 1 2其對(duì)應(yīng)的參數(shù)估計(jì)不相等，主要原因在于X］與X2有很強(qiáng)的相關(guān)性。其相關(guān)分析結(jié)果如下:X1X2X11.000000-0.967868X2-0.9678681.000000可見(jiàn)，兩者的相關(guān)系數(shù)為0.9679。

DependentVariable:YMethod:LeastSquaresDate:07/03AJ8Time:15:01Sample:16Includedobsen/ations:5VariableCaefficientStd.Errort-StatisticProb.C21.922224.3552505.0335070.0373X1-1.1777781.113026-1.0581760.4009X2-1.9444440.269316-7.2199490.0186R-squared0.996722Meandependentvar11.00000AdjustedR-squared0.993445S.D.dependentvar10.93161S.E.ofregression0.885061Akaikeinfocriterion2.877389Sumsquaredresid1.666667Schwarzcriterion2.643062Loglikelihood4.193473F-statistic304.1064Durbiri-Watsonstat2.912057Proti(F-statistic)0.00327B即：Y=21.92-1.18X]-1.94X2六、表3.4中列出了某地區(qū)家庭人均雞肉年消費(fèi)量Y與家庭月平均收入乂，雞肉價(jià)格P1,豬肉價(jià)格P2與牛肉價(jià)格P3的相關(guān)數(shù)據(jù)。表3.4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P]，豬肉價(jià)格P2與牛肉價(jià)格P3年份Y/千克X/元P1/（元/千克）P2/（元/千克）P3/（元/千克）年份Y/千克X/元P1/（元/千克）P2/（元/千克）P3/（元/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:lnY=P+PlnX+PlnP+PInP+PInP+u0 1 2 1 3 2 4 3（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：

輸出結(jié)果如下：DeperidentVariable:LOG(Y)Method:LeastSquaresDate:07/03AJ8Time:15:32Sample:19002002Includedobsen'ations:23VariableCoeffic舊ntStd.Errort-StatisticProb.C-07315200.296947-2.4634670.0241LOGW0.3452570.0825654.1016490.0006LOG(P1)-0.5021220.109891-4.5692940.0002LOG(P2)0.1468660.0990061.4834200.1553LOG(P3)0.0871850.0998520.8731370.3941R-squared0.982474Meandependentvar1.361301AdjustedR-squared0.978579S.D.dependentvar0.187659S.E.ofregression0.027465Akaikeinfocriterion-4.162123Sumsquaredresid0.013578Schwarzcriterion-3.915276Loglikelihood52.86441F-statistic252.2633Durbiri-Watsonstat1.B2402OProb(F-statistic)0.000000所以，回歸方程為：InY=—0.7315+0.3463lnX-0.5021lnP1+0.1469lnP2+0.0872lnP3(-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^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)0.4515470.024554 18.389660.0000LOG(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。七、某硫酸廠生產(chǎn)的硫酸的透明度指標(biāo)一直達(dá)不到優(yōu)質(zhì)要求，經(jīng)分析透明度低與硫酸中金屬雜質(zhì)的含量太高有關(guān)。影響透明度的主要金屬雜質(zhì)是鐵、鈣、鉛、鎂等。通過(guò)正交試驗(yàn)的方法發(fā)現(xiàn)鐵是影響硫酸透明度的最主要原因。測(cè)量了47組樣本值，數(shù)據(jù)見(jiàn)表3.5。表3.5硫酸透明度y與鐵雜質(zhì)含量x數(shù)據(jù)序數(shù)XY序數(shù)XY1311902560502321902660413341802761524351402863345361502964406371203065257391103169308408132742094210033744010428034762511431103579301243803685251348683787161449803889161550503999201652704076201752504110020185360421002019544443110152054544411015

215648451222722565046154202358564721020245852硫酸透明度y與鐵雜質(zhì)含量的散點(diǎn)圖如下所以應(yīng)該建立非線性回歸模型。1.通過(guò)線性化的方式估計(jì)非線性模型。（1） 建立倒數(shù)模型，在EquationSpecification（方程設(shè)定）框中輸入得到輸出結(jié)果為

?EVievs-[Equation:UHTITLEDTorkfile:CASE2::Case2a\][object]PrintNameFreeseEstimateForecastResideView][ProcFileEditObjectViewProcRuitk?？趖ionwWindowHelpDependentVariable;1/YMethod;LeastSquaresDate;06/29A38Time;19;13Sample;147Includedobservations;47VariableCoeificientStd.Errort-StatisticPrcb.C0.0692770.003730 13.570950.0000依-2.3721320.198508-11.949790.0000R-squared0.7603BOMeandependentvar0.027578AdjustedR-squared0755055S.D.dependentvar0.01B266S.E.ofregression0.009040Akaikeinfocriterion-6.532609Sumsquaredresid0.00367BSchwaricriterion-6.453879Loglikelihood155.5163F-statistic1427975Durbin-Watsonstat1.095271Prob(F-statistic)0.000000所以倒數(shù)表達(dá)式為:1/y=0.069-2.37(1/x)(18.57)(-11.95)R2=0.76,F=143,DW=1.095（2）建立指數(shù)函數(shù)方程設(shè)定為：

得到輸出結(jié)果為：DeperidentVariable:LOG(Y)Method:LeastSquaresDate:OG/29AJ8Time:19:21Sample:147Includedobservations:47VariableCoefficientStd.Errort-StatisticProb.C1.9937330.090755 21.9胡270.00001/X104.51954.829431 21.642190.0000R-squared0.912346Meandependentvar3.031065AdjustedR-squared0.910399S.D.dependentvar0.734762S.E.ofregression0.219940Akaikeinfacriterion-0.149302Sumsquaredresid2.176813Schwarzcriterion-0.070573Loglikelihood5.608606F-statistic460.3045Durbin-Watsonstat1.711647Prob(F-statistic)0.000000所以指數(shù)表達(dá)式為：Iny=1.99+104.5(1/x)(22) (21.6)R2=0.91,F=468.38,DW=1.71把表達(dá)式還原為指數(shù)形式：lny=ln(7.33)+104.5(1/x) 即 y=7.33e104-5(t)可決系數(shù)也由0.76提高到0.91,可見(jiàn)擬合為指數(shù)函數(shù)比倒數(shù)函數(shù)更好。2.直接估計(jì)非線性回歸模型直接估計(jì)的方程設(shè)定如下圖所示：

得到輸出結(jié)果為：Dependent