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1、c03-RegressionAnalysisTheoryPage79Thursday,October26,20062:40PMCHAPTER3RegressionAnalysis:TheoryandEstimationavingcoveredthebackgroundinformationinthepreviouschapter,Hwearereadytoturntoourfirstbasictoolineconometrics:regressionanalysis.Inregressionanalysis,weestimate
2、therelationshipbetweenarandomvariableYandoneormorevariablesXi.ThevariablesXicanbeeitherdeterministicvariablesorrandomvariables.ThevariableYissaidtobethedependentvariablebecauseitsvalueisassumedtobedepen-dentonthevalueoftheXi’s.TheXi’sarereferredtoastheindependentvar
3、iables,regressorvariables,orexplanatoryvariables.Ourprimaryfocusinthisbookisonthelinearregressionmodel.Wewillbemorepre-ciseaboutwhatwemeanbya“linear”regressionmodellaterinthischapter.Let’sbeginwithadiscussionoftheconceptofdependence.THECONCEPTOFDEPENDENCERegressions
4、areaboutdependencebetweenvariables.Inthissectionweprovideabriefdiscussionofhowdependenceisrepresentedinbothadeterministicsettingandaprobabilisticsetting.Inadeterministicset-ting,theconceptofdependenceisembodiedinthemathematicalnotionoffunction.Afunctionisacorrespond
5、encebetweentheindividualsofagivendomainAandtheindividualsofagivenrangeB.Inparticular,numericalfunctionsestablishacorrespondencebetweennumbersinadomainAandnumbersinarangeB.Inquantitativescience,weworkwithvariablesobtainedthroughaprocessofobservationormeasurement.Fore
6、xample,priceistheobser-vationofatransaction,timeisthereadingofaclock,positionisdeter-79c03-RegressionAnalysisTheoryPage80Thursday,October26,20062:40PM80FINANCIALECONOMETRICSminedwithmeasurementsofthecoordinates,andsoon.Inquantitativescience,weareinterestedinnumerica
7、lfunctionsy=f(x1,…,xn)thatlinktheresultsofmeasurementssothatbymeasuringtheindependentvari-ables(x1,…,xn)wecanpredictthevalueofthedependentvariabley.Beingtheresultsofmeasurements,variablesarethemselvesfunctionsthatlinkasetΩofunobserved“statesoftheworld”toobservations
8、.Differ-entstatesoftheworldresultindifferentvaluesforthevariablesbutthelinkamongthevariablesremainsconstant.Forexample,acolumnofmercuryina
