1、習(xí)題各地區(qū)建筑業(yè)總產(chǎn)值和建筑業(yè)企業(yè)利潤總額案例分析13應(yīng)用統(tǒng)計(jì)班1姬紫朝習(xí)題各地區(qū)建筑業(yè)總產(chǎn)值和建筑業(yè)企業(yè)利潤總額案例分析一、模型設(shè)定：為分析比較各地區(qū)建筑業(yè)總產(chǎn)值和建筑業(yè)企業(yè)利潤總額的關(guān)系，建立各地區(qū)建筑業(yè)總產(chǎn)值和建筑業(yè)企業(yè)利潤總額的回歸模型。假設(shè)各地區(qū)建筑業(yè)總產(chǎn)值和建筑業(yè)企業(yè)利潤總額之間滿足線性約束，則理論模型設(shè)定為：Yi=B1+B2X+Ni式中，Y表示建筑業(yè)企業(yè)利潤總額；X建筑業(yè)總產(chǎn)值。由國家統(tǒng)計(jì)網(wǎng)站得到表所示的數(shù)據(jù)。地區(qū)建筑業(yè)總產(chǎn)除建筑業(yè)企業(yè)利潤總題f地K建筑業(yè)總產(chǎn)府建筑業(yè)企業(yè)利潤總領(lǐng)Y北京0046.22216.78湖北5S98.4523L4B天津MH.4579.51湖南M15.021

2、24.77河北39卑,65127r東5TT4,012sLM山E23249149.22r西1553.0706.24向款古13M.63g37萍南255.47644遼寧BEFL5222431重慶332S.e3155.34吉林160&.&589.03四川5256.65ITT19股EiL0029.16弭92貫卅024,7214,39上海4556.2S:云南:LS6S.461.B8江蘇151紇85海37西藏U4.4T5.75浙江1490711157陜西3216,6310438安敬3E972B127J2甘肅925.84M.33福S36ftz.52126.47青海:319.4J635江西ZC95.4T62.3

3、T寧豆42T.0Z1L25山東6482SMl.H新建120.3TE7.6河南52TS35300.的表各地區(qū)建筑業(yè)總產(chǎn)值（X）和建筑業(yè)企業(yè)利潤總額（Y）參數(shù)估計(jì):利用EViews軟件，生成Y、X的數(shù)據(jù)，采用OLS方法估計(jì)參數(shù)，得到回歸結(jié)果如吧?PnolObjectPrint呼舊日曰回EstimateForecast5目仁住竺史|DepndentVariabk;YMWhod;LeastSquaresDate:OE/11f15Time:19.57Sample1131IncludedobseRations:31回歸結(jié)果估計(jì)結(jié)果為VanableCoeHcienlStd.Errort-StatisticP

4、rob.C2368139904937102&16910.7954X0034980000175419.945300.0000R-squared0.932055Meandependentvar134,4574Adjusted&-squwgdC.929712SDdependentvar12g.5145SE.ofregression3433673Akaikeinfocriterion9972649Sumsquaredresid3419133Sctiwarzcriterion100S518Loslikelihood-1526761Hannan-Quinnalter.10.00261F-statistic

5、3978152Durbin-Watsonstat2.5T2WProfF-statiStic)O.WOOOOY?i=+R2=F=三、檢驗(yàn)?zāi)Ｐ彤惙讲睿河捎诘貐^(qū)建筑業(yè)總產(chǎn)值不同，對建筑業(yè)企業(yè)利潤總額有不同的影響,這種差異使得模型很容易產(chǎn)生異方差，從而影響模型的估計(jì)和運(yùn)用。為此,需對模型是否存在異方差進(jìn)行檢驗(yàn)。（一）White檢驗(yàn)利用EViews軟件進(jìn)行White檢驗(yàn)，構(gòu)造輔助函數(shù)為：a0+aiXt+22X2t+ut(T2檢驗(yàn)結(jié)果如圖所示此時(shí)ProdObjectPrint|Name|rreEEieEstimateForecastSlatsResideHetqromkedagticitvTest:Whi

6、teF-statisticO&sR-squaredScaledexplainedSS5238907199541540435S3Prob.F(1,29)ProsChi-Square(l)Pros.Chi-Square(1)0.0oco0.0ocoC.0000TstEtjualion:DependentVariable:RESIDA2LIemod：LeastSquaresDate:C5/11/15Time:19:59Sample：151Includedobservations:31VariableCoeffldentStd.Errort-StatisticProb.C160.03613.54E-0

7、5292.63490.545110489E-O07.237960O.69S9OOOCORsqu31rgeIAdjustedR*squaredS.E.ofregressionSumsquaredeiciLoglikelihoodF-statisticProt(F-siatistic)06435820.631396140487362229718-263.9285S2.388070.000000MeandependentvarS.D.dependentvarAkaikeinfocriterionSchwarzenterienHannan-Quinnerrter.Durbin-Watson3t譏110

8、2945241279117.4792717,5717817,509422746747L圖White檢驗(yàn)結(jié)果從圖可以看出，nR2=,由White檢驗(yàn)知，在a=下，查2分布表，得臨界值x(2)=，同時(shí)X和X2的t檢驗(yàn)值也顯著。比較計(jì)算的x2統(tǒng)計(jì)量與臨界值，因?yàn)閚R2=x(2)=，所以拒接原假設(shè)，不拒絕備擇假設(shè)，表明存在異方差。四、異方差性的修正(一)加權(quán)最小二乘法1利用EViews軟件進(jìn)行加權(quán)最小二乘法選用權(quán)數(shù)=1消除模型中的異方差性，得到圖的加權(quán)最小二乘結(jié)果Dependent/ariable:YMethodLeaslSquaresDate:05J11/15rime:20:01Sample:131

9、Indudedobservations：31Weightingseries：VariableCoefficient用dErrort-StafisticProbC0.020734135184200153360.9879X0034505000244514110190.0000UVehhtedStatisticsR-squared0972866Meandependertvar38.30107AdjustedR-squ-arad0.&6SWS.D.dep&ndentvar12.97594SEofregression13.09591Akaikeinfocriterion3044817Sumsquared

10、resid4973.581Schwarzcriterion3.137333Loglikelihood-122.6947Hannan-Quirnenter3.074975F-statistic1199.1059Durbin-Watsonstat2.201196Proti(F-statistic)Q.OQDCOOVieA1Pnx|Cbjcct|Estirnm*|ForecaMt|弓tats|川PnitName|Freeze圖用權(quán)數(shù)W的估計(jì)結(jié)果在對次結(jié)果進(jìn)行White檢驗(yàn)得到結(jié)果如圖所示Equation：UNTTTLEDWorkfile：UNJTTLED:Urtitled怔科|所聰1pEt|Mame

11、|Freeze|EftiiTi曰teForecat|Stats|3sid|H2t白rGskedsEticrtTefitVihitaF-statistic0.000631ProbF(1f29)9818Obs*R-squaredO.OOOS67Prob.Chi-Square：1；:09610ScaledexplainedSS0.001324Prob.Chi-Square：1;9710TestEquation:Dpendent7ariat)le:AGT_RESIDA2Methoct-LeastSquaresDate-05/11-15Time-20:03Sample：131Includedobserv

12、ations:31Collineartestregrassors日oppMfromspecificationVariableGoeflicientStdErrort-StafisticProbC160.883671.4S48522512270.0321WGTA2-01106254.902426-002303509S18R-squared0.000016Meandependentar1604301AdjustedR-sqtiaredg034454SD.dependent37&6158S.E.ofregression383.0506Akaikeinfocriterion1479655Sumsqua

13、redresid42551OSSchwarzenterion148&S07Loglikelihood*227.3456HannanOuirncriter.1432671F-statistic0.000531Durbin-Watsonstat2.071335ProbCF-slaMStic)0.081730圖加權(quán)最小二乘法所得結(jié)果White檢驗(yàn)結(jié)果由圖和圖看出，運(yùn)用加權(quán)最小二乘法無法消除異方差性。（二）對數(shù)變換法利用EViews軟件進(jìn)行對數(shù)變換消除模型中的異方差性，所得結(jié)果的最小二乘估計(jì)如圖所示EquationsUNTITLEDWorldife;UNTTTLED-Urtitied巨11aeezeE

14、stimateForecastStatsflesidsDependantVarianie.LNYMethod:LeastSquaresDate:0511/15Time:20:05Sample：131includedobservations:31VariableCoefficientStd.Errort-StatisticProb.C-3894B3704034B2-GC530600,0000LNX1.061G58Q.0514Q420.5&3220,0000Rsquared0.936341Meandependentva4.35&311AdjustedR-squared0.934145S口depen

15、dentvar1.229215S.E.ofegrgssiun0.315441Akaikeinfocriterion0.5&2648Sumsquaredresid2885581SchwarzcriterionC.68516JLoglikelihood-7.186051Hannan-Quinricriler.0622906F-slatistic426.5557Durbin-Watsonstat2260966ProtHF-statistic)0.000000圖對數(shù)變換法后估計(jì)結(jié)果再對此結(jié)果進(jìn)行White檢驗(yàn)得到結(jié)果如圖所示VieAPfdcObjec|Pint|Name|Freeze|EMtimate

16、由口鵬曰川ItaisResids|Heleroskedas-ticit/Test:WhiteF-stetisti卜Obs*F?-squaredScaledexplainedS3008770.0025004543.123712Prob,可協(xié)3.014442Prob.Chi-Squaref14.004260Prob.Ctii-Square(1)TestEquation:DependentVariable:RESIDEMethod:LeastSquaresDale:C5/11；15Time:20:06Sample131Includedobser/alions31VariableCoefficientStdErrort-StatistlcProb.C02851920.1123992637S180.0168LNXA2-00-0311S0.C017S4-1.7674020.0877R-squaredC097240Meandependentvar0093083AdjustedR-squsred0.056110S口dependentvar0154365S.E.ofregression0.159322Akaikeinfocriterion-0773137Sumsquaredreid0.736122Schwarzcrite