ISYE 6414 - MIDTERM 1 PREP
QUESTIONS AND 100% CORRECT
ANSWERS 2024
IfPλ=1P-PANSWERPwePdoPnotPtransform
non-deterministicP-
PANSWERPRegressionPanalysisPisPonePofPthePsimplestPwaysPwePhavePinPstatisticsPtoPinvestigatePthePrelations
hipPbetweenPtwoPorPmorePvariablesPinPaP___Pway
randomP-
PANSWERPThePresponsePvariablePisPaP___Pvariable,PbecausePitPvariesPwithPchangesPinPthePpredictingPvariabl
e,PorPwithPotherPchangesPinPthePenvironment
fixedP-PANSWERPThePpredictingPvariablePisPaP___Pvariable.PItPisPsetPfixed,PbeforePthePresponsePisPmeasured.
simplePlinearPregressionP-
PANSWERPregressionPanalysisPinvolvingPonePindependentPvariablePandPonePdependentPvariablePinPwhichPt
hePrelationshipPbetweenPthePvariablesPisPapproximatedPbyPaPstraightPline
MultiplePLinearPRegressionP-
PANSWERPAPstatisticalPmethodPusedPtoPmodelPthePrelationshipPbetweenPonePdependentP(orPresponse)Pvari
ablePandPtwoPorPmorePindependentP(orPexplanatory)PvariablesPbyPfittingPaPlinearPequationPtoPobservedPdat
a
polynomialPregressionP-
PANSWERPaPregressionPmodelPwhichPdoesPnotPassumePaPlinearPrelationship;PaPcurvilinearPcorrelationPcoeffi
cientPisPcomputedP(wePcanPthinkPofPXPandPX-squaredPasPtwoPdifferentPpredictingPvariables)
threePobjectivesPinPregressionP-PANSWERP1)PPrediction
2)PModeling
3)PTestingPhypothesis
,PredictionP-
PANSWERPWePwantPtoPseePhowPthePresponsePvariablePbehavesPinPdifferentPsettings.PForPexample,PforPaPdiff
erentPlocation,PifPwePthinkPaboutPaPgeographicPprediction,PorPinPtime,PifPwePthinkPaboutPtemporalPpredictio
n
ModelingP-
PANSWERPmodelingPthePrelationshipPbetweenPthePresponsePvariablePandPthePexplanatoryPvariables,PorPpre
dictingPvariables
TestingPhypothesesP-PANSWERPofPassociationPrelationships
usefulPrepresentationPofPrealityP-
PANSWERPWePdoPnotPbelievePthatPthePlinearPmodelPrepresentsPaPtruePrepresentationPofPreality.PRather,Pwe
PthinkPthat,Pperhaps,PitPprovidesPaP___
β0P-PANSWERPinterceptPparameterP(thePvaluePatPwhichPthePlinePintersectsPthePy-axis)
β1P-PANSWERPslopePparameterP(slopePofPthePlinePweParePtryingPtoPfit)
epsilonP(ε)P-PANSWERPisPthePdeviancePofPthePdataPfromPthePlinearPmodel
toPfindPβ0PandPβ1P-
PANSWERPtoPfindPthePlinePthatPdescribesPaPlinearPrelationship,PsuchPthatPwePfitPthisPmodel.
simplePlinearPregressionPdataPstructureP-
PANSWERPpairsPofPdataPconsistingPofPaPvaluePforPthePresponsePvariable,andPaPvaluePforPthePpredictingPvaria
ble.PAndPwePhavePnPsuchPpairs
modelingPframeworkPforPthePsimplePlinearPregression:P-PANSWERP1)PidentifyingPdataPstructure
2)PclearlyPstatingPthePmodelPassumptions
linearPregressionPassumptionsP-PANSWERP1)Plinearity
, 2)PconstantPvariancePassumption
3)PindependencePassumption
linearityPassumptionP-
PANSWERPmeanPzeroPassumption,PmeansPthatPthePexpectedPvaluePofPthePerrorsPisPzero.
APviolationPofPthisPassumptionPwillPleadPtoPdifficultiesPinPestimatingPβ0,PandPmeansPthatPyourPmodelPdoesP
notPincludePaPnecessaryPsystematicPcomponent.
constantPvariancePassumptionP-
PANSWERPwhichPmeansPthatPthePvarianceP(σ^2)PofPthePerrorPtermsPorPdeviancesPisPconstantPforPthePgivenP
population.PAPviolationPofPthisPassumptionPmeansPthatPthePestimatesParePnotPasPefficientPasPtheyPcouldPbeP
inPestimatingPthePtruePparameters
IndependencePAssumptionP-
PANSWERPwhichPmeansPthatPthePdeviancesParePindependentPrandomPvariables.
ViolationPofPthisPassumptionPcanPleadPtoPmisleadingPassessmentsPofPthePstrengthPofPthePregression.
normalityPassumptionP-
PANSWERPerrorsP(ε)ParePnormallyPdistributed.PThisPisPneededPforPstatisticalPinference,PforPexample,Pconfide
ncePorPpredictionPintervals,PandPhypothesisPtesting.PIfPthisPassumptionPisPviolated,PhypothesisPtestsPandPco
nfidencePandPpredictionPintervalsPcanPbePmisleading.v
thirdPparameterP-PANSWERPthePvariancePofPthePerrorPtermsP(σ^2)
OnePapproachPisPtoPminimizePthePsumPofPsquaredPresidualsPorPerrorsPwithPrespectPtoPβ0PandPβ1.PThisPtrans
latedPintoPfindingPthePlinePsuchPthatPthePtotalPsquaredPdeviancesPfromPthePlinePisPminimum.P-
PANSWERPHowPcanPwePgetPestimatesPofPthePregressionPcoefficientsPorPparametersPinPlinear
regressionPanalysis?
fittedPvaluesP-PANSWERPtoPbePthePregressionPlinePwherePthePparametersParePreplaced
byPthePestimatedPvaluesPofPthePparameters.
ResidualsP-PANSWERParePsimplyPthePdifference
QUESTIONS AND 100% CORRECT
ANSWERS 2024
IfPλ=1P-PANSWERPwePdoPnotPtransform
non-deterministicP-
PANSWERPRegressionPanalysisPisPonePofPthePsimplestPwaysPwePhavePinPstatisticsPtoPinvestigatePthePrelations
hipPbetweenPtwoPorPmorePvariablesPinPaP___Pway
randomP-
PANSWERPThePresponsePvariablePisPaP___Pvariable,PbecausePitPvariesPwithPchangesPinPthePpredictingPvariabl
e,PorPwithPotherPchangesPinPthePenvironment
fixedP-PANSWERPThePpredictingPvariablePisPaP___Pvariable.PItPisPsetPfixed,PbeforePthePresponsePisPmeasured.
simplePlinearPregressionP-
PANSWERPregressionPanalysisPinvolvingPonePindependentPvariablePandPonePdependentPvariablePinPwhichPt
hePrelationshipPbetweenPthePvariablesPisPapproximatedPbyPaPstraightPline
MultiplePLinearPRegressionP-
PANSWERPAPstatisticalPmethodPusedPtoPmodelPthePrelationshipPbetweenPonePdependentP(orPresponse)Pvari
ablePandPtwoPorPmorePindependentP(orPexplanatory)PvariablesPbyPfittingPaPlinearPequationPtoPobservedPdat
a
polynomialPregressionP-
PANSWERPaPregressionPmodelPwhichPdoesPnotPassumePaPlinearPrelationship;PaPcurvilinearPcorrelationPcoeffi
cientPisPcomputedP(wePcanPthinkPofPXPandPX-squaredPasPtwoPdifferentPpredictingPvariables)
threePobjectivesPinPregressionP-PANSWERP1)PPrediction
2)PModeling
3)PTestingPhypothesis
,PredictionP-
PANSWERPWePwantPtoPseePhowPthePresponsePvariablePbehavesPinPdifferentPsettings.PForPexample,PforPaPdiff
erentPlocation,PifPwePthinkPaboutPaPgeographicPprediction,PorPinPtime,PifPwePthinkPaboutPtemporalPpredictio
n
ModelingP-
PANSWERPmodelingPthePrelationshipPbetweenPthePresponsePvariablePandPthePexplanatoryPvariables,PorPpre
dictingPvariables
TestingPhypothesesP-PANSWERPofPassociationPrelationships
usefulPrepresentationPofPrealityP-
PANSWERPWePdoPnotPbelievePthatPthePlinearPmodelPrepresentsPaPtruePrepresentationPofPreality.PRather,Pwe
PthinkPthat,Pperhaps,PitPprovidesPaP___
β0P-PANSWERPinterceptPparameterP(thePvaluePatPwhichPthePlinePintersectsPthePy-axis)
β1P-PANSWERPslopePparameterP(slopePofPthePlinePweParePtryingPtoPfit)
epsilonP(ε)P-PANSWERPisPthePdeviancePofPthePdataPfromPthePlinearPmodel
toPfindPβ0PandPβ1P-
PANSWERPtoPfindPthePlinePthatPdescribesPaPlinearPrelationship,PsuchPthatPwePfitPthisPmodel.
simplePlinearPregressionPdataPstructureP-
PANSWERPpairsPofPdataPconsistingPofPaPvaluePforPthePresponsePvariable,andPaPvaluePforPthePpredictingPvaria
ble.PAndPwePhavePnPsuchPpairs
modelingPframeworkPforPthePsimplePlinearPregression:P-PANSWERP1)PidentifyingPdataPstructure
2)PclearlyPstatingPthePmodelPassumptions
linearPregressionPassumptionsP-PANSWERP1)Plinearity
, 2)PconstantPvariancePassumption
3)PindependencePassumption
linearityPassumptionP-
PANSWERPmeanPzeroPassumption,PmeansPthatPthePexpectedPvaluePofPthePerrorsPisPzero.
APviolationPofPthisPassumptionPwillPleadPtoPdifficultiesPinPestimatingPβ0,PandPmeansPthatPyourPmodelPdoesP
notPincludePaPnecessaryPsystematicPcomponent.
constantPvariancePassumptionP-
PANSWERPwhichPmeansPthatPthePvarianceP(σ^2)PofPthePerrorPtermsPorPdeviancesPisPconstantPforPthePgivenP
population.PAPviolationPofPthisPassumptionPmeansPthatPthePestimatesParePnotPasPefficientPasPtheyPcouldPbeP
inPestimatingPthePtruePparameters
IndependencePAssumptionP-
PANSWERPwhichPmeansPthatPthePdeviancesParePindependentPrandomPvariables.
ViolationPofPthisPassumptionPcanPleadPtoPmisleadingPassessmentsPofPthePstrengthPofPthePregression.
normalityPassumptionP-
PANSWERPerrorsP(ε)ParePnormallyPdistributed.PThisPisPneededPforPstatisticalPinference,PforPexample,Pconfide
ncePorPpredictionPintervals,PandPhypothesisPtesting.PIfPthisPassumptionPisPviolated,PhypothesisPtestsPandPco
nfidencePandPpredictionPintervalsPcanPbePmisleading.v
thirdPparameterP-PANSWERPthePvariancePofPthePerrorPtermsP(σ^2)
OnePapproachPisPtoPminimizePthePsumPofPsquaredPresidualsPorPerrorsPwithPrespectPtoPβ0PandPβ1.PThisPtrans
latedPintoPfindingPthePlinePsuchPthatPthePtotalPsquaredPdeviancesPfromPthePlinePisPminimum.P-
PANSWERPHowPcanPwePgetPestimatesPofPthePregressionPcoefficientsPorPparametersPinPlinear
regressionPanalysis?
fittedPvaluesP-PANSWERPtoPbePthePregressionPlinePwherePthePparametersParePreplaced
byPthePestimatedPvaluesPofPthePparameters.
ResidualsP-PANSWERParePsimplyPthePdifference
