TransportationPlanningtoexplainthemostfundamentalelementsoftransportationplanningtopresentssomesimpletrafficforecastingMethodstodescribetheconventional4-stagetransportmodelTransportationPlanningOverviewLanduse——transportationinteractionPlanningobjectivesProvideinformationnecessaryformakingdecisionsonwhenandwhereimprovementsshouldbemadeinthetransportationsystem,thuspromotingtravelandlanddevelopmentpatternsthatareinkeepingwithcommunitygoalsandobjectives.TransportationPlanningOverviewPlanningprocedure1.Forecastsforthetargetyearoftheregionalpopulationandeconomicgrowthforthesubjectmetropolitanarea2.Allocationoflandusesandsocioeconomicprojectionstoindividualanalysiszonesaccordingtolandavailability,localzoning,andrelatedpublicpolicies3.Specificationofalternativetransportationplanspartlybasedontheresultsofsteps1and24.CalculationofthecapitalandmaintenancecostsofeachalternativeplanTransportationPlanningOverviewPlanningprocedure5.Applicationofcalibrateddemand-forecastingmodelstopredictthetargetyearequilibriumflowsexpectedtouseeachalternative,giventheland-useandsocioeconomicprojectionsofsteps2andthecharacteristicsofthetransportationalternative(step3)6.Conversionofequilibriumflowstodirectuserbenefits,suchassavingsintraveltimeandtravelcostattributabletotheproposedplan7.Comparativeevaluationandselectionofthe“best”ofthealternativesanalyzedbasedonestimatedcosts(step3)andbenefits(step6)TransportationPlanningOverviewInformationneeds1.Thestudyarea2.Urbanactivities3.Transportationsystem4.TravelTransportationPlanningOverviewThestudyareaTransportationPlanningOverviewDefiningtheBoundaries:includesdeveloped,undevelopedlandthatwillbeencompassedinthenext20,30years.Thedefinedareaisdemarcatedbythecordonline.Factorsofconsiderationinclude:–a)futuregrowth–b)politicaljurisdictions–c)censusareaboundaries–d)naturalboundariesThecordonshouldintersectaminimumnumberofroadstosaveonsubsequentinterviewrequirementsTransportationPlanningOverviewThestudyareaTransportationPlanningOverviewSubdividingtheAreaofForecasting:theareaisdividedintoanalysisunitsorzonestoenabletheplannertolinkinformationaboutactivities,travel,andtransportationtophysicalurbanareaThesizeofazonemayvary.Incentralbusinessdistrict(CBD),zonesmaybesmall–asingleblock.Inundevelopedarea,itmaybelarge–10ormoresquaremiles.Azoneattempttoboundhomogenousurbanactivities:allresidential,commercial,industrial,etc.Itmayalsobedividedbynaturalboundariesandcensusdesignations.TransportationPlanningOverviewSubdividingtheAreaUrbanactivitiesTransportationPlanningOverviewInformationaboutactivitiesisgatheredbyzonesSourcesofinformationincludeactivitiesthatmayinfluencetravelTheresultsofatypicalactivityanalysisprovidetheplannerwithpresentlevelsofactivitiesinzonestohelpinpredictingfuturelevelsthatprovideabasisforforecastingTransportationSystemsTransportationPlanningOverview?Availablemodes(auto,bus,etc.)?Anabstraction–sonoteverylocalroadisincluded?Anetworkisdevelopedtodescribeautoandtruck;aseparatedescriptionfortransit.?Networkgeometryincludes:a)numberingtheintersections(callednodes)b)numberingtheroadsegments(calledlinks)Zonecentroids(centerofactivity)areidentified;connectedtonodesbyimaginarylinks(calledcentroidconnectors).Theyareusedasthepointsatwhichtripsare“l(fā)oaded”.Theyaresometimescalledoriginanddestination.Travel:forecastingtechnologiesTransportationPlanningOverview1.SketchPlanningTool:–Preliminaryscreeningofpossibleconfigurationsorconcepts.Itisusedtocomparealargenumberofproposedpoliciesinsufficientanalyticaldetailtosupportbroadpolicydecisions.–Itusesminimumdatayieldingaggregateestimatesofcapitalandoperatingcosts,patronage,corridortrafficflows,servicelevels,energyconsumptionandairpollution–ThefinalproductmaybeastrategicplanTravel:forecastingtechnologiesTransportationPlanningOverview2.TraditionalTools:–Theyprovideananalysisinmuchgreaterdetailthansketchplanning.Examplesincludelocationofprincipalhighwayfacilitiesanddelineatedtransitroutes–Theoutputsaredetailedestimatesoftransitfleetsize,refinedcostandpatronageforecasts,andlevel-of-servicemeasuresforspecificgeographicalareas.–Thecostofexamininganalternativeisabout10to20timesitscostatthesketchplanninglevel.Travel:forecastingtechnologiesTransportationPlanningOverview3.Micro-analysistools–Theyarethemostdetailedofallplanningtools.–Examples:detailedevaluationoftheextension,rescheduling,orpricingofexistingbusservice;toanalyzepassengerandvehicleflowsthroughatransportationterminaloractivitycenter.–Itismosteffectiveinnear-termplanning,whenagreatmanyoutsidevariablescanbeaccuratelyobservedorestimated.TransportationPlanningOverviewTravel:surveysTransportationPlanningOverviewOrigin-destination(OD)surveyRoadsideinterviewCordon/screenlinesurveyTraveldiarysurveyOrigin-destinationsurveyTransportationPlanningOverviewExpensiveanddifficult,however,offersthepossibilityofobtainingmoreusefuldataCouldgatheralotofinformation,mosttypicalonesincludeO-D,modechoiceandassignment(routechoice)inshort-termstudiesencompassingtraveldistance,time,andcostsOrigin-destinationsurveyTransportationPlanningOverviewGeneralconsiderations–Theproceduretocollectdatawillaffectresultssignificantly.–Surveydate:Besttimesoftheyeararespringandautumn.Duringatypicalworkday–DaysandTimes:NoMondaysandFridays.Noweekends.Bestistoensureagoodrecollectionofeventsinthepreviousday.SothesurveyshouldbeconductedduringWednesday,Thursday.Household-based:6pm-9pm.Workplacebased:workinghours.–SurveyPeriod:Ideallyalltheselectedsampleshouldbeinterrogatedononedayinordertoobtainasnapshotofwhathappenedonthepreviousday.However,thisrequiresalargenumberofinterviewers.Practically,theperiodnormallylastforseveraldays.Origin-destinationsurveyTransportationPlanningOverviewContainthreedistinctsections:–Personalcharacteristicsandidentification:age,sex,possessionofadrivinglicense,educationallevel,andactivity.Acompletesetofactivitiesshouldbefirstdefined–Tripdata:detectingandcharacterizingalltripsmadebyallthehouseholdmembers.Atripisnormallydefinedasanymovementgreaterthan300metersfromanorigintoadestinationwithagivenpurpose.Tripsarecharacterizedby:originanddestination(expressedbynearestcross-junction),trippurpose,tripstartandendtimes,modeused,walkingdistance(includingtransfers),public-transportlineandtransferstationsorbusstop–Householdcharacteristics:socioeconomicinfoaboutthehousehold,suchascharacteristicsofthehouse,identificationofhouseholdvehicles,houseownership,andincome.Origin-destinationsurveyTransportationPlanningOverviewSamplesize:thefollowingtableistherecommendedfiguresfortraditionalsurveys,typicallyhugeanduneconomical.RoadsideinterviewsTransportationPlanningOverviewTheseprovideusefulinformationabouttripsnotregisteredinhouseholdsurvey(i.e.external-externaltripsinacordonsurvey)Oftenabettermethodforestimatingtripmatricesthanhomeinterviewsaslargersamplesarepossible.Resultscouldbeusedtovalidateandextendhouse-holdbasedinformationInvolveaskingasampleofdriversandpassengersofvehiclescrossingaroadsidestationInformationcollectedinclude:–origin,destination,trippurposeduetotimelimitation,thesearequestionsaskedonlyiftimeallows:sex,age,incomeCordonsurveyTransportationPlanningOverviewTheseprovideexternal-externalandexternal-internaltrips.Theirobjectiveistodeterminethenumberoftripsthatenter,leave,and/orcrossthecordonedarea,thushelpingtocompletetheinformationcomingfromhouseholdO-Dsurvey.Themainoneistakenattheexternalcordon,althoughsurveysmaybeconductedatinternalcordons.Toreducedelay,theyinvolvestoppingasampleofthevehiclespassingacontrolstation,towhichashortquestionnaireisgiven.Sometimes,asampleoflicenseplatesisregisteredandthequestionnairesaresenttothecorrespondingaddresses.CordonsurveyTransportationPlanningOverviewAnimportantproblemisthatreturn-mailsurveysareknowntoproducebiasedresults.Lessthan50%questionnairesareusuallyreturnedandithasbeenshownthatthetypeofpersonwhoreturnsthemisdifferentfromthosewhodonot.Therefore,roadsidesurveysoftenaskaratherlimitednumberofquestions(e.g.,occupation,purpose,origin,destinationandmodesavailable)toencouragebetterresponserates.ScreenlinesurveyTransportationPlanningOverviewScreenlinesdividetheareaintolargenaturalzones(e.g.atbothsidesofariverormotorway),withfewcrossingpointsbetweenthem.Theprocedureisanalogoustothatofcordonsurveysandthedataalsoservetofillgapsinandvalidatetheinformationcomingfromthehouseholdandcordonsurveys.TraveldiarysurveyTransportationPlanningOverviewThesearesurveysconductedwithagreatlevelofdetail.Theyareappliedseparatelytoeachmemberofthehouseholdtravelingatthetimeofthestudy.TheyarecarriedoutandcompletedbythesubjectsduringthedayTraveldiarysurveyTransportationPlanningOverviewCriteria:–Easeoftransport:asmallformattobestoredorcarried–Easeofunderstandingtotheuser:–EaseofcompletionProcedures:–Afirstvisittoeachhouseholdinthesample.Intervieweesaretrainedtousetheinstrumentandaskedtofillitwithcompletedetailsoftheirtraveldataforthefollowingday–Asecondvisitthedayfollowingthelastsurveyedday(24hourslaterinthecaseofone-daydiaries).4-stepprocedureTransportationPlanningOverview1.Tripgenerationforecaststhenumberoftripsthatwillbemade:thedecisiontotravel2.Tripdistributiondetermineswherethetripswillgo:thechoiceofdestination3.Modeusage(modalchoice)predictshowthetripswillbedividedamongtheavailablemodesoftravel:thechoiceoftravelmode4.Tripassignmentpredictstheroutesthatthetripswilltake,resultingintrafficforecastsforthehighwaysystemandridershipforecastforthetransitsystem:thechoiceofrouteofpath?Outputsofeachstepbecomesinputstothefollowingstep.ThissimplifiestheactualdecisionprocesstremendouslyTransportationPlanningOverview4-stepprocedure(travelers)TypesandCharacteristicsofFreightMajortypesoffreightBulk

-Coal-Oil,Gas-MineralsandSand-AgriculturalGeneralMerchandise

-SupermarketgrocerySpecializedFreight

-Automobile-ChemicalsSmallPackageTransportationPlanningOverviewBulkCommodityCharacteristics-Cheap-Vastquantities-TransportationcostisamajorconcernRelevanttransportationtools-Railunittrain-Heavytruck-Bargeandspecializedships-PipelineTypesandCharacteristicsofFreightTransportationPlanningOverviewGeneralMerchandisesCommodityCharacteristics-Highervalue-Greaterdiversity-Manymoreshippersandreceivers-LogisticscostsareasimportantastransportcostsRelevanttransportationtools-Railroadfreightcar-Intermodal-Truckload(fulltruckload)-LTL(Less-Than-Truckload)TypesandCharacteristicsofFreightTransportationPlanningOverviewSpecializedFreightCommodityCharacteristics-Largervolumes,relativelyfewcustomers-Specializedrequirementstoreduceriskoflossanddamage-Highvalue(canaffordspecialtreatment)Relevanttransportationtools-Specializedrail(multi-levels,tankcars)-Specializedtrucks(tanktrucks,movingvans)-AirfreightTypesandCharacteristicsofFreightTransportationPlanningOverviewSmallPackageCommodityCharacteristics-Veryhighvalue-Logisticscostsaremoreimportantthantransportcosts-DeliveriestothesmallbusinessesandcustomersRelevanttransportationtools-LTL-Smallpackageservices-Expressservices-AirfreightTypesandCharacteristicsofFreightTransportationPlanningOverviewAustralianTransportFreightCommoditiesClassificationbyproductandmodeTransportationPlanningOverview4-stepprocedure(freight)TransportationPlanningOverview4-stepprocedure(freight)GenerationDistributionModalchoiceNetworkassignmentTotaltonsTonsbyODODtonsbymodeODtonsbymodeandrouteTheFour-StepModelGeneration(production&attraction):thequantitiesofgoodstobetransportedfromthevariousoriginzones,andthequantitiestobetransportedtothevariousdestinationzonesaredetermined(tonsofgoods,ormonetaryunits)Distribution:theflowsingoodstransportbetweenoriginsanddestinations(cellsoftheODmatrix(tons)ModalChoice:theallocationofthecommodityflowstomodes(road,train,combinedtransportation,inlandwaterway)NetworkAssignment:convertingtheflowsintonstovehicleunits,andthenassigningtonetwork(truckand/orpassengercarsflowstoroadnetwork)4-stepprocedure(freight)TransportationPlanningOverview123456789ZoneIDproductionattraction………1xxxxxxxxxx2xxxxxxxxxx3xxxxxxxxxx………Generation4-stepprocedureTransportationPlanningOverview123456789DistributionO/D12341xxxxxxxxxxxx2xxxxxxxxxxxx3xxxxxxxxxxxx4xxxxxxxxxxxx4-stepprocedureTransportationPlanningOverview123456789ModalchoiceO/D12341xxxxxxxxxxxx2xxxxxxxxxxxx3xxxxxxxxxxxx4xxxxxxxxxxxxtrainO/D12341xxxxxxxxxxxx2xxxxxxxxxxxx3xxxxxxxxxxxx4xxxxxxxxxxxxwaterO/D12341xxxxxxxxxxxx2xxxxxxxxxxxx3xxxxxxxxxxxx4xxxxxxxxxxxxtruck4-stepprocedureTransportationPlanningOverview123456789Networkassignment(4,1)xxxxxxxxxxxx(1,2)xxxxxxxxxxxx(2,3)xxxxxxxxxxxx…xxxxxxxxxxxxtrucklink4-stepprocedureTransportationPlanningOverviewTransportationPlanning4-stepprocedure(travelers)4-stepprocedure(travelers)TransportationPlanningOverviewTripgenerationforecaststhenumberoftripsthatwillbemade:thedecisiontotravelTripdistributiondetermineswherethetripswillgo:thechoiceofdestinationModeusage(modalchoice)predictshowthetripswillbedividedamongtheavailablemodesoftravel:thechoiceoftravelmodeTripassignmentpredictstheroutesthatthetripswilltake,resultingintrafficforecastsforthehighwaysystemandridershipforecastforthetransitsystem:thechoiceofrouteofpathTransportationPlanning4-stepprocedure(freight)GenerationDistributionModalchoiceNetworkassignmentTotaltonsTonsbyODODtonsbymodeODtonsbymodeandrouteTheFour-StepModelGeneration(production&attraction):thequantitiesofgoodstobetransportedfromthevariousoriginzones,andthequantitiestobetransportedtothevariousdestinationzonesaredetermined(tonsofgoods,ormonetaryunits)Distribution:theflowsingoodstransportbetweenoriginsanddestinations(cellsoftheODmatrix(tons)ModalChoice:theallocationofthecommodityflowstomodes(road,train,combinedtransportation,inlandwaterway)NetworkAssignment:convertingtheflowsintonstovehicleunits,andthenassigningtonetwork(truckand/orpassengercarsflowstoroadnetwork)TransportationPlanning4-stepprocedure(freight)123456789ZoneIDproductionattraction………1xxxxxxxxxx2xxxxxxxxxx3xxxxxxxxxx………GenerationTransportationPlanning4-stepprocedure(freight)123456789DistributionO/D12341xxxxxxxxxxxx2xxxxxxxxxxxx3xxxxxxxxxxxx4xxxxxxxxxxxxTransportationPlanning4-stepprocedure(freight)123456789ModalchoiceO/D12341xxxxxxxxxxxx2xxxxxxxxxxxx3xxxxxxxxxxxx4xxxxxxxxxxxxtrainO/D12341xxxxxxxxxxxx2xxxxxxxxxxxx3xxxxxxxxxxxx4xxxxxxxxxxxxwaterO/D12341xxxxxxxxxxxx2xxxxxxxxxxxx3xxxxxxxxxxxx4xxxxxxxxxxxxtruckTransportationPlanning4-stepprocedure(freight)123456789Networkassignment(4,1)xxxxxxxxxxxx(1,2)xxxxxxxxxxxx(2,3)xxxxxxxxxxxx…xxxxxxxxxxxxtrucklinkTransportationPlanning4-stepprocedure(freight)TransportationPlanning4-stepprocedureGeneration(travelers)Generation(freight)123456789ZoneIDproductionattraction………1xxxxxxxxxx2xxxxxxxxxx3xxxxxxxxxx………TransportationPlanningGeneration(travelers)Generation(travelers)TransportationPlanning?Journey:Thisisaone-waymovementfromapointoforigintoapointofdestination.?Home-based(HB)trip:Homeiseithertheoriginorthedestinationofthejourney?Non-home-based(NHB)trip:neitherendofthetripisthehomeofthetravelerOrigin&duction&attractionTransportationPlanningEachtriphastwotripends(oneorigin&onedestination)Originsanddestinationsaredefinedintermsofthedirectionofagiventrip.Thetermsproductionandattractionaredefinedintermsofthelanduseassociatedwitheachtripend(notintermsofthedirectionsoftrips).Namely,whenweconsiderthetermsoftripproductionandtripattraction,weshouldconsiderimplicationsofthelanduse.HBtripvs.NHBtripTransportationPlanningIntheHBtripsproductionsarealwaysconnectedwithresidentialarea,andtripattractionsarealwaysconnectedwithnonresidentialarea.HOMEWORKproductionproductionattractionattraction(a)Home-basedtripInthiscase:Productionisnotnecessaryorigin

AttractionisnotnecessarilydestinationHBtripvs.NHBtripTransportationPlanningIntheNHBtrips,originofatripcorrespondstoitsproductionend,destinationofatripcorrespondstoitsattractionendWORKSHOPproductionattractionattractionproduction(b)Non-home-basedtripInthiscase:Productionisorigin

AttractionisdestinationTransportationPlanninghomeofficeShoppingcenterFriend’shomeTripgeneration=4Tripproduction=3?Tripattraction=1?Trip1Trip2Trip3Trip4Generation(travelers)TransportationPlanningGeneration(travelers)TransportationPlanning?Tripproduction:eitherthehomeendofaHBtriportheoriginofaNHBtrip(notbasedonthedirectionofatrip)?TripAttraction:thenon-homeendofaHBtriporthedestinationofaNHBtrip(notbasedonthedirectionofatrip)?TripGenerations:thetotalnumberoftripsgeneratedbyhouseholdsinazoneGeneration(travelers)TransportationPlanning?ClassificationofTrips–ByTrippurpose:TriptoworkTriptoschoolorcollegeShoppingtripssocialandrecreationaltripsothers–Bytimeofday:Peaktripsoff-peakperiodtripsGeneration(travelers)TransportationPlanningGeneration(travelers)TransportationPlanning?Developtripgenerationexpressionsfromsurveydatatoconvertestimatesofhorizonyeardevelopmentpatternsintozonalproductionsandattractionsforeachtrippurpose?Criteria:–providegoodexplanatorypowerofobservedbaseyeartravelbehavior–parametersofthesetripgenerationexpressionsshouldbestableovertime(assumption)–theindependentorpredictorvariableshouldbeeasilypredictablewithsomeprecisionforthehorizonyear(thenumberofhouseholds)TransportationPlanningHorizonorTargetYear:Theyearforwhichtrafficdemandisforecasted(e.g.,year2020)Baseyear:Theyearwhenthesurveywasconducted(orthestudywasconducted)(e.g.,year2005)TransportationPlanningregressionanalysiscross-classificationtablesTwoanalyticaltechnologiesfortripgenerationTransportationPlanningLinearRegressionModelsTransportationPlanningResidentiallanduseisanimportanttripgeneratorNon-residentiallanduseisagoodattractoroftrips–Y=trips/household–X1=carownership–X2=familyincome–X3=familysize–A,Bi=parametersdeterminedthroughacalibrationprocessfromsurveydataAtypicalequation:DependentvariableindependentvariablesTransportationPlanningModelparametersandvariablesvaryfromonestudyareatoanotherandareestablishedbyusingbase-yearinformationOncetheequationsarecalibrated,theyareusedtoestimatefuturetravelforatargetyear.LinearRegressionModelsConstantA:Captureeffectsthatarenotexplicitlyincludedinthemodel(limitednumberofvariables)ParameterBi:MeasuresensitivityofYtoXi,changeofYforoneunitchangeofXiequalsBiTransportationPlanningAssumptions:Alltheindependentvariablesareindependentofeachother.Theindependentvariablesarecontinuous.Alltheindependentvariablesmustbelinearlyrelatedtothedependentvariable.Alltheindependentvariablesmustbehighlycorrelatedwiththedependentvariable.LinearRegressionModelsExample1TransportationPlanningY=trips/householdX1=familysizeX2=residentialdensityX3=totalfamilyincomeX4=cars/household?ToderiveYforafutureyear,appropriateestimatesofX1,X2,X3,X4aresubstituted.?Qualityoffitofaregressionlinedeterminedbymultiplelinearregressionanalysisisindicatedbythemultipleregressioncoefficient(goodnessoffit)representedbyR,between-1and1.ThecloserRisto1or-1,thebetteristhelinearrelationshipbetweenthevariables.Example1TransportationPlanning

IndependentvariableAllhome-basedtripsX1familysize0.61X2residentialdensity-0.76 X3totalfamilyincome0.73X4carsperhousehold0.86 X5traveltimetoCBD0.32X6proportionofschool-goingchildren0.27 ?Inpreliminaryinvestigation,itisusefultocomputeRbetweentripmakingandseparateindependentvariables.?Intheaboveexample,YishighlycorrelatedwithX1throughX4andweaklywithX5andX6.?MultipleregressionisappearingbecauseitiseasytodeterminethedegreeofrelationshipbetweenthedependentandindependentvariablesTransportationPlanning?Onecanalsoderive:–thestandarderrorofestimate(MSE):ameasureofthedeviationbetweenobservedtripsfrompredictedvalues–partialcorrelationcoefficientofeachoftheindependentvariables–t-testtodeterminewhetheranestimatedregressioncoefficientissignificantLinearRegressionModelsTransportationPlanningHowtouselinearregressionmodels?LinearRegressionModelsSamplingInputObservingEstimatingFittinginordertominimizetotalsumofthesquarederrorsTransportationPlanningLinearRegressionLinearRegressionModelsExample2

(LinearRegression)TransportationPlanningy=a+bxYearTripsYearsfrom1993x-x_bary-y_bar

LinearRegression19931044370-7.125-997171044.2750.76563104739.980819941119551-6.125-245315025.3937.51563106096.913319951018072-5.125-1260164580.7726.26563107453.845819971096594-3.125-474914841.029.765625110167.71092003117896102.8753487.910027.648.265625118309.3062004120266113.8755857.922699.2715.01563119666.23852005121445124.8757036.934304.7723.76563121023.17112010127800179.87513392132244.897.51563127807.83372015

22

134592.49632020

27

141377.1589

114408.17.125

232523.1171.3594

b=1356.933

a=104740

DeterminingMeanSquaredErrorWhyMSE

?ToexaminehowwellthemodelfitsthedatawellTransportationPlanningLinearRegressionModelsDeterminingcorrelationcoefficientTransportationPlanningLinearRegressionModelsameasureofhowwellthepredictedvaluesfromaforecastmodel"fit"withthereal-lifedata;indicatesthestrengthanddirectionofalinearrelationshipbetweentworandomvariables;anumberbetween-1and1.

WhyR2?TransportationPlanningLinearRegressionModelsConductT-test(one-tail)Nullhypothesis:thestandarderroroftheestimates(residualvariable)thestandarddeviationoftheindependentvariableAlternativehypothesis:TransportationPlanningLinearRegressionModelsThedegreeoffreedom:N-(n+1)Upper-tailarea:meaningthatbissignificantat(1?)levelofsignificancet-value:TransportationPlanningT-test(two-tail)

If:wehaveaminimumconfidenceleveltobelievethat

If:wecannotbelievethat(significantlevelisloverthan)Nullhypothesis:Alternativehypothesis:T-test(one-tail)t-value:TransportationPlanningLinearRegressionModelsYXToosmallsamplesizeandunluckyYXPropersamplesizeTrueregressionlineTrueregressionlineEstimatedregressionlineEstimatedregressionlineTheestimatedlineseldommeetsthetrueline,unlesswehave100%samplingrateorweareverylucky,thoughweneverknow.Whyt-test?Wehaveaminimumconfidencelevel(aprobabilityrelativetothefreedomofthemodel)tobelievethatthemodelissignificant.TransportationPlanningLinearRegressionModelsTransportationPlanningExample3Solution:

WeselectanappropriatemodelfromtheperspectivesofMSE,R2,t–testandthequalityoftheexplanatoryvariables.t–testSinceitisanticipatedtoobtainthecalibratedsign(i.e.positive)coefficients,weuseone-tailtest.ForM1andM2,thedegreeoffreedomisandsot0.05

=

1.746.SoM1passesthenullhypothesisandisacceptedwhileM2failsinthenullhypothesisandisstatisticallyunacceptable.ForM3,thedegreeoffreedomisandsot0.05=1.753.SoM3passesthenullhypothesisandisaccepted.TransportationPlanningExample3Solution(cond’t)MSE,R2BothM1andM3havesimilarR2andsoneithergivesacompetitiveedge.However,M3isbetterthanM1intermsoftheMSE.ExplanatoryVariablesSinceρX1,X2=0.11,X1andX2arealmostindependent,sotheinclusionofbothvariablesenrichestheexplanatorypowerofthemodel.SoM3issuperior.Finally,asacompromise,wechooseM3follo