計量經(jīng)濟學(英文)重點知識點考試必備

1、第一章Econometrics（計量經(jīng)濟學）：thesocialscienceinwhichthetoolsofeconomictheory,mathematics,andstatisticalinferenceareappliedtotheanalysisofeconomicphenomena.theresultofacertainoutlookontheroleofeconomics,consistsoftheapplicationofmathematicalstatisticstoeconomicdatatolendempiricalsupporttothemodelsconstruct

2、edbymathematicaleconomicsandtoobtainnumericalresults.Econometricanalysisproceedsalongthefollowinglines計量經(jīng)濟學分析步驟Creatingastatementoftheoryorhypothesis.建立一個理論假說2）Collectingdata.收集數(shù)據(jù)3）Specifyingthemathematicalmodeloftheory.設(shè)定數(shù)學模型4）Specifyingthestatistical,oreconometric,modeloftheory.設(shè)立統(tǒng)計或經(jīng)濟計量模型5）Estima

3、tingtheparametersofthechoseneconometricmodel.估計經(jīng)濟計量模型參數(shù)6）Checkingformodeladequacy:Modelspecificationtesting.核查模型的適用性：模型設(shè)定檢驗7）Testingthehypothesisderivedfromthemodel.檢驗自模型的假設(shè)8）Usingthemodelforpredictionorforecasting.利用模型進行預測Step2：收集數(shù)據(jù)Threetypesofdata三類可用于分析的數(shù)據(jù)1）Timeseries（時間序列數(shù)據(jù)Collectedoveraperiodof

4、time,arecollectedatregularintervals.按時間跨度收集得到2）Cross-sectional截面數(shù)據(jù):Collectedoveraperiodoftime,arecollectedatregularintervals.按時間跨度收集得到3）Pooleddata合并數(shù)據(jù)（上兩種的結(jié)合）Step3：設(shè)定數(shù)學模型plotscatterdiagramorscattergramwritethemathematicalmodelStep4:設(shè)立統(tǒng)計或經(jīng)濟計量模型CLFPRisdependentvariable應(yīng)變量CUNRisindependentorexplanatory

5、variable獨立或解釋變量（自變量）WegiveacatchallvariableUtostandforalltheseneglectedfactorsInlinearregressionanalysisourprimaryobjectiveistoexplainthebehaviorofthedependentvariableinrelationtothebehaviorofoneormoreothervariables,allowingforthedatathattherelationshipbetweenthemisinexact.線性回歸分析的主要目標就是解釋一個變量（應(yīng)變量）與其

6、他一個或多個變量（自變量）只見的行為關(guān)系，當然這種關(guān)系并非完全正確Step5：估計經(jīng)濟計量模型參數(shù)Inshort,theestimatedregressionlinegivestherelationshipbetweenaverageCLFPRandCUNR簡言之，估計的回歸直線給出了平均應(yīng)變量和自變量之間的關(guān)系Thatis,onaverage,howthedependentvariablerespondstoaunitchangeintheindependentvariable.單位因變量的變化引起的自變量平均變化量的多少。Step6:核查模型的適用性：模型設(shè)定檢驗Thepurposeofd

7、evelopinganeconometricmodelisnottocapturetotalreality,butjustitssalientfeatures.Step7:檢驗自模型的假設(shè)Whydoweperformhypothesistesting?Wewanttofindourwhethertheestimatedmodelmakeseconomicsenseandwhethertheresultsobtainsconformwiththeunderlyingeconomictheory.AA*第二章Themeaningofregression(回歸)Regressionanalysisi

8、sconcernedwiththestudyoftherelationshipbetweenonevariablecalledthedependentorexplainedvariable,andoneormoreothervariablescalledindependentorexplanatoryvariables.ObjectivesofregressionEstimatethemean,oraverage,andthedependentvaluesgiventheindependentvaluesTesthypothesesaboutthenatureofthedependencehy

9、pothesessuggestedbytheunderlyingeconomictheoryPredictorforecastthemeanvalueofthedependentvariablegiventhevaluesoftheindependentsOneormoreoftheprecedingobjectivescombinedPopulationRegressionLine(PRL)Inshort,thePRLtellsushowthemean,oraverage,valueofYisrelatedtoeachvalueofXinthewholepopulationThedepend

10、enceofYonX,technicallycalledtheregressionofYonX.Howdoweexplainit?AstudentsS.A.T.score,say,theithindividual,correspondingtoaspecificfamilyincomecanbeexpressedasthesumoftwocomponentsThecomponentcanbecalledthesystematic,ordeterministic,component.MaybecalledthenonsystematicorrandomcomponentWhatisthenatu

11、reofU(stochasticerror)term？Theerrortermmayrepresenttheinfluenceofthosevariablesthatarenotexplicitlyincludedinthemodel.誤差項代表了未納入模型變量的影響Someintrinsicrandomnessinthemathscoreisboundtooccurthatcannotbeexplainedevenweincludeallrelevantvariables.即使模型包括了決定性數(shù)學分數(shù)的所有變量，內(nèi)在隨機性也不可避免，這是做任何努力都無法解釋的。Umayalsoreprese

12、nterrorsofmeasurement.U還代表了度量誤差TheprincipleofOckhamsrazor-thedescriptionbekeptassimpleaspossibleuntilprovedinadequate-wouldsuggestthatwekeepourregressionmodelassimpleaspossible.“奧卡姆剃刀原則”描述應(yīng)該盡可能簡單，只要不遺漏重要信息。這表明回歸模型應(yīng)盡可能簡單。HowdoweestimatethePRF(populationregressionfunction)?Unfortunately,inpractice,Wer

13、arelyhavetheentirepopulationinourdisposal,oftenwehaveonlyasamplefromthispopulation.GrantedthattheSRFisonlyanapproximationofPRF.Canwefindamethodoraprocedurethatwillmakethisapproximationascloseaspossible?SRF僅僅是PRF的近似，那么能不能找到一種方法使這種近似盡可能接近真實呢？Specialmeaningof“l(fā)inearLinearityinthevariables變量線性Theconditi

14、onalmeanvalueofthedependentvariableisalinearfunctionoftheindependentvariablesLinearityintheParameters參數(shù)線性Theconditionalmeanofthedependentvariableisalinearfunctionoftheparameters,theBs;itmayormaynotbelinearinthevariables.第三章UnlesswearewillingtoassumehowthestochasticUtermsaregenerated,wewillnotbeablet

15、otellhowgoodanSRFisasanestimateofthetruePRF.只有假定了隨機誤差的生成過程，才能判定SRF對PRF擬合的是好是壞。ClassicalLinearRegressionModelAssumption1:Theregressionmodelislinearintheparameters.Itmayormaynotbelinearinthevariables.回歸模型是參數(shù)線性的，但不一定是變量線性的。Assumption2:TheexplanatoryvariablesXisuncorrelatedwiththedisturbancetermU.Xsaren

16、onstochastic,Uisstochastic.解釋變量X與擾動誤差項u不相關(guān).X是非隨機的，U是隨機的。Assumption3:GiventhevalueofXi,theexpected,ormeanvalueofthedisturbancetermUiszero.給定Xi,擾動項的期望或均值為零。DisturbanceUrepresentallthosefactorsthatarenotspecificallyintroducedinthemodel干擾項U代表了所有未納入模型的影響因素。Assumption4:ThevarianceofeachUiisconstant,orhomo

17、scedastic.U的方差為常數(shù)，或同方差。Homoscedasticity(同方差)：ThisassumptionsimplymeansthattheconditionaldistributionofeachYpopulationcorrespondingtothegivenvalueofXhasthesamevariance.該假定表明，與給定的X相對應(yīng)的每個Y的條件分布具有同方差。TheindividualYvaluesarespreadaroundtheirmeanvalueswiththesamevariance.即每個Y值以相同的方差分布在其均值周圍。Assumption5:Th

18、ereisnocorrelationbetweentwoerrorterms,thisistheassumptionofno-autocorrelation.無自相關(guān)假定，即兩個誤差項之間不相關(guān)。Assumption6:Theregressionmodeliscorrectlyspecified.回歸模型是正確假定的。Thereisnospecificationbiasorspecificationerrorinthemodel.實證分析的模型不存在設(shè)定偏差或設(shè)定誤差。Thisassumptioncanbeexplainedinformallyasfollows.Aneconometricin

19、vestigationbeginswiththespecificationoftheeconometricmodelunderlyingthephenomenonofinterest.VariancesandStandarderrorsofOLSestimators普通最小二乘估計量的方差與標準誤:OneimmediateresultoftheassumptionsintroducedisthattheyenableustoestimatethevariancesandstandarderrorsoftheOLSestimatorsgiveninEq.(2.16)and(2.17).Wesho

20、uldknow:VariancesoftheestimatorsStandarderrorsoftheestimatorsWhatisthevalueofoThehomoscedasticoisestimatedfromformula6.StandardErroroftheRegression(SER)回歸標準誤IssimplythestandarddeviationoftheYvaluesabouttheestimatedregressionline.Y值偏離估計回歸的標準差。7.SummaryofmathS.A.T.scorefunction1)InterpretationThestand

21、arddeviation,orstandarderror,is0.000245,isameasureofvariabilityofb2fromsampletosample.Ifwecansaythatourcomputedb2lieswithinacertainnumberofstandarddeviationunitsfromthetrueB2,wecanstatewithsomeconfidencehowgoodthecomputedSRFisasanestimatorofthetruePRF.2)SamplingDistribution抽樣分布Oncewedeterminethesamp

22、lingdistributionofourtwoestimators,thetaskofhypothesistestingbecomesstraightforward.一旦確定了兩個估計量的抽樣分布，那么假設(shè)檢驗就是舉手之勞的事情。WhydoweuseOLS?ThepropertiesofOLSestimatorsThemethodofOLSisusedpopularlynotonlybecauseitiseasytousebutalsobecauseithassomestrongtheoreticalproperties.OLS法得到廣泛使用，不僅是因為它簡單易行，還因為它具有很強的理論性質(zhì)

23、。Gauss-Markovtheorem高斯-馬爾科夫定理Giventheassumptionsoftheclassicallinearregressionmodel(CLRM),theOLSestimatorshaveminimumvarianceintheclassoflinearestimators.TheOLSestimatorsareBLUE(bestlinearunbiasedestimators)滿足古典線性模型的基本假定，則在所有線性據(jù)計量中，OLS估計兩具有最小方差性，即OLS是最優(yōu)線性無偏估計量(BLUE)BLUEproperty最優(yōu)線性無偏估計量的性質(zhì)B1andB2are

24、linearestimators.B1和B2是線性估計量Theyareunbiased,thatisE(b1)=B1,E(b2)=B2.B1和B2是無偏估計兩TheOLSestimatoroftheerrorvarianceisunbiased.誤差方差的OLS估計量是無偏的b1andb2areefficientestimators.B1和B2是有效估計量Var(b1)islessthanthevarianceofanyotherlinearunbiasedestimatorofB1Var(b2)islessthanthevarianceofanyotherlinearunbiasedesti

25、matorofB2MonteCarlosimulation蒙特卡洛模擬DotheexperimentatlabDoitbyExcell.=NORMINV(RAND(),0,2)Doitbymatlab.=NORMINV(uniform(),MU,SIGMA)DoitbyStata.=invnorm(uniform()CentralLimitTheorem中心極限定理Ifthereisalargenumberofindependentandidenticallydistributed(iid)randomvariables,then,withafewexceptions,thedistribut

26、ionoftheirsumtendstobeanormaldistributionasthenumberofsuchvariablesincreasesindefinitely.隨著變量個數(shù)的無限增加，獨立同分布隨機變量近似服從正態(tài)分布RecallU,theerrortermrepresentstheinfluenceofallthoseforcesthataffectYbutarenotspecificallyincludedintheregressionmodelbecausetherearesomanyofthemandtheindividualeffectofanyonesuchfor

27、ceonYmaybetoominor.誤差項代表了未納入回歸模型的其他所有因素的影響。因為在這些影響中，每種因素對Y的影響都很微弱Ifalltheseforcesarerandom,ifweletUrepresentthesumofalltheseforces,thenbyinvokingtheCLT,wecanassumethattheerrortermUfollowsthenormaldistribution.如果所有這些影響因素都是隨機的，用U代表所有這些影響因素之和，那么根據(jù)中心極限定理，可以假定誤差項服從正態(tài)分布。Anotherpropertyofnormaldistribution

28、另一個正態(tài)分布的性質(zhì)Anylinearfunctionofanormallydistributedvariableisitselfnormallydistributed.正態(tài)變量的性質(zhì)函數(shù)仍服從正態(tài)分布。Hypothesistesting假設(shè)檢驗HavingknownthedistributionofOLSestimatorsblandb2,wecanproceedthetopicofhypothesistesting.Nullhypothesis零假設(shè)“zero”nullhypothesisisdeliberatelychosentofindoutwhetherYisrelatedtoXal

29、all,whichisalsocalledstrawmanhypothesis.之所以選擇這樣一個假設(shè)是為了確定Y是否與X有關(guān)，也稱為稻草人假設(shè)。Weneedsomeformaltestingproceduretorejectorreceivethenullhypothesisandmaketheskepticalguysshutup.需要正規(guī)的檢驗過程拒絕或接受零假設(shè)IfournullhypothesisisB2=0andthecomputedb2=0.0013,wecanfindouttheprobabilityofobtainingsuchavaluefromtheZ,thestanda

30、rdnormaldistribution.女口果零假設(shè)為B2=0，計算得到b2=0.0013，那么根據(jù)標準正態(tài)分布乙能夠求得獲此b2值的概率Iftheprobabilityisverysmall,wecanrejectthenullhypothesis.如果這個概率非常小，則拒絕零假設(shè)。Iftheprobabilityislarger,say,greaterthan10percent,wemaynotrejectthenullhypothesis.如果這概率比較大，比如大于10%，就不拒絕零假設(shè)。Wedontknowtheo2Wemustknowthetrueo2,butwecanestima

31、teitbyusing2Whatwillhappen訐wereplaceobyitsestimatoro-hatbBitn2or,moregenerallybB-2tse(b)n22Letusassumethata,thelevelofsignificanceortheprobabilityofcommittingatypeIerror,isfixedat5percent.假定a,顯著水平成犯第一類錯誤的概率為5%。redarea=rejectionregionfor2-sidedtestf(t)LoopandballThisisa95%confidenceintervalforB2給出了B2

32、的一個95%的置信區(qū)間。inrepeatedapplications95outof100suchintervalswillincludethetrueB2重復上述過程，100個這樣的區(qū)間中將有95個包括真實的B2。Suchaconfidenceintervalisknownastheregionofacceptance（ofH0）andtheareaoutsidetheconfidenceintervalisknownastherejectionregion（ofH0）用假設(shè)檢驗的語言把這樣的置信區(qū)間稱為（H0的）接受區(qū)域，把置信區(qū)間以外的區(qū)間成為（H0的）拒絕區(qū)域24回歸系數(shù)的假設(shè)檢驗?zāi)康模?/p>

33、簡單線性回歸中，檢驗X對Y是否真有顯著影響基本概念回顧：臨界值與概率、大概率事件與小概率事件相對于顯著性水平的臨界值為：。（單側(cè)）或匕（雙側(cè)）量tConclusionsSincethisintervaldoesnotincludethenull-hypothesizedvalueof0.因為這個區(qū)間沒有包括零假設(shè)值0。WecanrejectthenullhypothesisthatannualfamilyincomeisnotrelatedtomathS.A.T.Scores.所以拒絕假設(shè)：家庭年收入對數(shù)學SAT沒有影響。Putpositively,incomedoeshavearelatio

34、nshiptomathS.A.T.scores.換言之，收入確實與數(shù)學SAT有關(guān)系。AcautionarynoteAlthoughthestatementgivenistrue,wecannotsaythattheprobabilityis95percentthattheparticularintervalincludesB2,forthisintervalisnotarandominterval,itisfixed,therefore,theprobabilityiseither1ore0thattheintervalincludesB2雖然式子3.26為真，但不能說某個特定區(qū)間式3.27包

35、括真實B2的概率為95%，因為與式子3.26不同，式3.27是固定的，而不是一根隨機區(qū)間，所以區(qū)間3.27包括B2的概率為1或0.Wecanonlysaythatifweconstruct100intervalslikethisinterval,95outof100suchintervalswillincludethetrueB2我們只能說,如果建立100個像式3.27這樣的區(qū)間，則有95個區(qū)間包括真實的B2.WecannotguaranteethatthisparticularintervalwillnecessarilyincludesB2.并不能保證某個區(qū)間一定有B2.Thetestof

36、significanceapproachtohypothesistesting假設(shè)檢驗的顯著性檢驗方法Hypothesistestingisthatofateststatisticandthesamplingdistributionoftheteststatisticunderthenullhypothesis,H0.假設(shè)檢驗方法涉及兩個重要的概念檢驗統(tǒng)計量和零假設(shè)下檢驗統(tǒng)計量的扌由樣分布。ThedecisiontoacceptorrejectH0ismadeonthebasisofthevalueoftheteststatisticobtainedfromthesampledata.根據(jù)從樣

37、本數(shù)據(jù)求得的檢驗統(tǒng)計量的值決定接受或拒絕零假設(shè)。TtestWecanusethetvaluecomputedhereadtheteststatistic,whichfollowsthetdistributionwith(n-2)d.f.可以計算出t值作為檢驗統(tǒng)計量，它服從自由度為(n-2)的t分布。29.Insteadofarbitrarilychoosingtheavalue,wecanfindthepvalue(theexactlevelofsignificance)andrejectthenullhypothesisifthecomputedPvalueissufficientlylow

38、為了避免選擇顯著水平的隨意性，通常求出p值(精確的顯著水平)，如果計算的p值充分小，則拒絕零假設(shè)。ConclusionsInthecaseoftwo-sidedttest雙邊檢驗情況中IfthecomputedItl,theabsolutevalueoft,exceedsthecriticaltvalueatthechosenlevelofsignificance,wecanrejectthenullhypothesis.如果計算得到的Itl值超過臨界t值，則拒絕零假設(shè)。PvalueThePvalueofthattstatisticof5.4354isabout0.0006.t統(tǒng)計量(5.43

39、54)的p值(概率值)約為0.0006。Thesmallerthepvalue,themoreconfidentwearewhenrejectthenullhypothesis.p值越小，在拒絕零假設(shè)的時候就越有自信。ThusifweweretorejectthenullhypothesisthatthetrueslopecoefficientiszeroatthisPvalue,wewouldbewronginsixoutoftenthousandoccasions如果在這個p值水平之上拒絕零假設(shè)：真實的斜率系數(shù)為0,則犯錯誤的機會有萬分之六。HowcanwecomputedtWefirst

40、computethetvalueasifthenullhypothesiswerethatB2=0,westillgetthett=.13-=5.4354、0.000245首先計算在零假設(shè)B2=0下的t值Sincethisvalueexceedsanyofthecriticalvaluesshownintheprecedingtable,followingtheruleslaiddown.t值大與上表給出的任何臨界值，附錄D表D-2列出的規(guī)則，WecanrejectthehypothesisthatannualfamilyincomehasnorelationshiptomathS.A.T.S

41、cores拒絕零假設(shè)：家庭年收入對數(shù)學SAT沒有影響。Howgoodisthefittedregressionline:thecoefficientofdeterminationr2Onthebasisofttestboththeestimatedinterceptandslopecoefficientsarestatisticallysignificant(i.e.significantlydifferentfromzero)suggeststhattheSRFseemsto“fitthedata“reasonablywell.根據(jù)t檢驗，估計的斜率和結(jié)局都是統(tǒng)計顯著的，這說明樣本回歸函數(shù)式

42、3.16很好地擬合了樣本數(shù)據(jù)。CoefficientofdeterminationCanwedevelopanoverallmeasureof“goodnessoffit”thatwilltellushowwelltheestimatedregressionlinefitstheactualYvalues?能否建立一個“擬合優(yōu)度”的判定規(guī)則，從而辨別估計的回歸線擬合真實Y值的優(yōu)劣程度呢？Suchameasurehasbeendevelopedandisknownasthecoefficientofdetermination.稱之為判定系數(shù)。Recally=y+eTOC o 1-5 h ziii

43、Rearrangeit=Y+enYY=eiiiiiiY=YY+ei_i_i(YY)=(YY)+(YY)iiii(YY):variationinYiiexplainedby.X(=Y)aroundiitsmeanvalu¬e:Y=Y)Decomposition(YY):variation-inY HYPERLINK l bookmark8 o Current Document iifromitsmeanvalue1、23、(YY):unexplainedorresidualvariation38.Indeviationforms1、2、(YY)=(YY)+(YY)TOC o 1-5 h z

44、iiiiY=Y(YY)=(YY)+(YY)iiiiy=y+eiiiy=y+eiii=(YY)+eii=(b+bX)(b+bX)+e12丄12i=b(XX)+e2iiny=bx+ei2ii39.Squarebothsidesandsum工y2=工y2+工e2Ey=bx+ei2iii1y2=b2x2+乙e2i2iiy2=thetotalvariationoftheactualYvaluesabouttheirsamplingmeanYbar,whichmaybecalledthetotalsumofsquares(TSS)總平方和，真實Y值圍繞其均值的總變異工y2yi=Thetotalvariat

45、ionoftheestimatedYvaluesabouttheirmeanvalue,Yhatbar,whichmaybecalledappropriatelythesumofsquaresduetoregression(i.e.,duetotheexplanatoryvariables),orsimplycalledtheexplainedsumofsquares(ESS)解釋平方和，估計的Y值圍繞氣均值的變異，也稱回歸平方和(由解釋變量解釋的部分)PutsimplyTSS=ESS+rssSThetotalvariationintheobservedYvaluesabouttheirmea

46、nvaluecanbepartitionedintotwoparts,oneattributabletotheregressionlineandtheothertorandomforces,becausenotallactualYobservationslieonthefittedline.Y值與其均值的總離差可以分解為兩部分：一部分歸于回歸線，另一部分歸于隨機因素，因為不是所有的真實觀察值Y都落在你和直線上。ESSvsRSSIfthechosenSRFfitsthedataquitewell,ESSshouldbemuchlargerthanRSS.如果選擇的SRF很好的擬合了樣本數(shù)據(jù)，則S

47、EE遠大于RSS。IftheSRFfitsthedatapoorlyRSSwillbemuchlargerthanESS.如果SRF擬合的不好，則RSS遠大于ESSoLetusdefine定義2ESSr2=TSSR2樣本判定系數(shù)R2measurestheproportionorpercentageofthetotalvariationinYexplainedbytheregressionmodel樣本判定系數(shù)度量了回歸模型對Y變異的解釋比例(或百分比)R2isthecoefficientofdeterminationandisthemostcommonlyusedmeasureofthegoo

48、dnessoffitofaregressionline.樣本判定系數(shù)通常用來度量回歸線的擬合優(yōu)度。PropertiesofR2itisanon-negativequantity.非負性itslimitsareOWR2W1sinceapart(ESS)cannotbegreaterthanthewhole(TSS).OWR2W1,因為部分(ESS)不可能大于整體(TSS)。AnR2of1meansa“perfectfitfortheentirevariationinYisexplainedbytheregression.若R2=1，貝V表示完全擬合，即線性模型完全解釋Y的變異。AnR2ofzer

49、omeansnorelationshipbetweenYandXwhatsoever.若R2=0，則表示Y與X之間無任何關(guān)系。ReportingtheresultsY=432.413*0.001Xiise=(16.9O61)(O.OOO245)t=(25.5774)(5.4354)n=0.7849p-value=(5.851,RA2barWRA2,thatis,asthenumberofexplanatoryvariablesincreasesinamodel,theadjustedRA2babecomeincreasinglysmallerthantheunadjustedRA2.There

50、seemtobea“penalty”involvedinaddingmoreexplanatoryvariablestoaregressionmodel.隨著模型中解釋變量個數(shù)的增加，校正判定系數(shù)RA2bar越來越小于未校正判定系數(shù)R9,這似乎是增加解釋變量的“懲罰”2、althoughtheunadjustedR2isalwayspositive,theadjustedR2canonoccasionturnouttobenegative.Thisisduetoitsspecialformulaform.雖然未校正判定系數(shù)RA2總為正，但校正判定系數(shù)RA2bar可能為負27、Whendoesa

51、djustedR2increase?什么時候增加新的解釋變量R2barwillincreaseifthe|t|(absolutet)valueofthecoefficientoftheaddedvariableislargerthan1,wherethetvalueiscomputedunderthenullhypothesisthatthepopulationvalueofthesaidcoefficientiszero.如果增加變量系數(shù)的Itl值大于1，RA2bar就會增加，這里的t值是在零假設(shè)“真實系數(shù)為零”下計算得到的28、SomeinterestingfactsIfyousquare

52、thetvalueof5.8457,weget(5.8457)人2=34.1722,whichisaboutthesameastheFvalueof34.1723shownbefore.如果將t值平方，與F值幾乎相等Itisnotsurprisingbecausetk2F1,k29、Thenullhypothesishereisthattherestrictionsimposedbytherestrictedmodelarevalid.檢驗的零假設(shè)為：受限模型的約束是有效的30、IftheFvalueestimatedfromitsstatisticexceedsthecriticalFval

53、ueatthechosenlevelofsignificance,werejecttherestrictedregression.Thatis,inthissituation,therestrictionsimposedbytherestrictedmodelarenotvalid.如果從估計的F值大于所選顯著水平下的臨界F值，則拒絕受限回歸。這種情況下，受限模型的約束是無效的AAZT?第五章1、Inthistextbook,ourconcerniswithmodelsthatarelinearinparameters(LIP滲數(shù)線性模型，2、WithintheconfinesofLIPlog

54、-linearorconstantelasticitymodels雙對數(shù)模型或不變彈性模型semilogmodels半對數(shù)模型reciprocalmodels倒數(shù)模型Polynomialregressionmodels多項式回歸模型regression-through-the-origin,orzerointercept,model過原點的回歸模型，或零截距模型3、Howtomeasureelasticity:theLog-linearmodel如何度量彈性：雙對數(shù)模型Toeasethealgebra,wewillintroducetheerrortermuilater為了使代數(shù)形式更簡潔，引

55、入隨機誤差項第六章1、Artificialvariablevs.dummyvariable定性變量和虛擬變量Onemethodof“qualifying”theseattributesisbyconstructingartificialvariablesthattakeonvaluesof0or1indicatingthepresence(orpossession)ofthatattribute.把定性因素“定量化”的一個方法是獨立人工變量，并賦值0和1,0表示變量不具有某種性質(zhì)，1表示變量具有某種性質(zhì)Forexample,1mayindicatethatapersonisafemaleand

56、0maydesignateamale,or1mayindicatethatapersonisacollegegraduateandthat0heorsheisnot,or1mayindicatethatmembershipintheDemocraticpartyand0membershipintheRepublicanparty.第七章Theattributesofagoodmodel模型判斷的一些標準。Parsimony簡約性Amodelcannevercompletelycapturethereality;someamountofabstractionorsimplificationisi

57、nevitableinanymodelbuilding.TheOccamsrazor,ortheprincipleofparsimonysuggestingthatamodelbekeptassimpleaspossible.模型永遠無法完全把握現(xiàn)實，在建模過程中，一定程度的抽象或簡化是不可避免的。簡單優(yōu)于復雜或者簡約原則表明模型應(yīng)盡可能簡單。Identifiability可識別性Thismeansthat,foragivensetofdata,theestimatedparametersmusthaveuniquevaluesor,whatamountstothesamething,ther

58、eisonlyoneestimateperparameter.對于給定的一組數(shù)據(jù)，估計的參數(shù)值必須是唯一的，或者說，每個參數(shù)只有一個估計值。Goodnessoffit擬合優(yōu)度Sincethebasicthrust(活動、思想的)要點，主要內(nèi)容，要旨ofregressionanalysisistoexplainasmuchofthevariationinthedependentvariableaspossiblebyexplanatoryvariablesincludedinthemodel,amodelisjudgedtobegoodifthisexplanatory,asmeasured,s

59、aybytheadjustedR2isashighaspossible.回歸分析的基本思想是用模型中所包含的解釋變量來盡可能地解釋應(yīng)變量的變化，如可用校正的RA2度量擬合優(yōu)度，RA2越高，模型越好Theoreticalconsistency理論一致性Nomatterhowhighthegoodnessoffitmeasures,amodelmaynotbejudgedtobegoodifoneormorecoefficientshavethewrongsigns.Inshort,inconsideringamodelweshouldhavesometheoreticalunderpinning

60、toit;“measurementwithouttheory”oftenleadstoverydisappointingresults.無論擬合優(yōu)度有多高，一單模型中的一個或多個系數(shù)的符號有誤，就不能說是一個好的模型。簡而言之，在構(gòu)建模型時，必須有一定的理論基礎(chǔ)，“沒有理論基礎(chǔ)的度量”經(jīng)常是導致令人失望的結(jié)果。Predicativepower預測能力theonlyrelevanttestofthevalidityofahypothesis(model)iscomparisonofitspredictionwithexperience.對假設(shè)(模型)有效性的唯一檢驗就是將預測值與經(jīng)驗值相比較。I