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ISYE 6414 - ALL UNITS QUESTIONS AND 100% CORRECT ANSWERS 2024
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ISYE 6414 - ALL UNITS QUESTIONS AND 100% CORRECT ANSWERS 2024
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ISYE 6414 - ALL UNITS QUESTIONS AND100% CORRECT ANSWERS 2024
responseU(dependent)UvariablesU-
UANSWERUoneUparticularUvariableUthatUweUareUinterestedUinUunderstandingUorUmodelingU(y)
predictingUorUexplanatoryU(independent)UvariablesU-
UANSWERUaUsetUofUotherUvariablesUthatUmightUbeUusefulUinUpredictingUorUmodelingUtheUresponseUvariableU
(x1,Ux2)
WhatUkindUofUvariableUisUaUresponseUvariableUandUwhy?U-
UANSWERUrandom,UbecauseUitUvariesUwithUchangesUinUtheUpredictor/sUalongUwithUotherUrandomUchanges.
WhatUkindUofUvariableUisUaUpredictingUvariableUandUwhy?U-
UANSWERUfixed,UbecauseUitUdoesUnotUchangeUwithUtheUresponseUbutUitUisUfixedUbeforeUtheUresponseUisUme
asured.
linearUrelationshipU-UANSWERUaUsimpleUdeterministicUrelationshipUbetweenU2Ufactors,UxUandUy
whatUareUthreeUthingsUthatUaUregressionUanalysisUisUusedUfor?U-
UANSWERU1.UPredictionUofUtheUresponseUvariable,U2.UModelingUtheUrelationshipUbetweenUtheUresponseUa
ndUexplanatoryUvariables,U3.UTestingUhypothesesUofUassociationUrelationships
B0U=U?U-UANSWERUintercept
B1U=U?U-UANSWERUslope
forUourUlinearUmodelUwhere:UYU=UB0U+UB1U+UEPSILONU(E),UwhatUdoesUtheUepsilonUrepresent?U-
UANSWERUdevianceUofUtheUdataUfromUtheUlinearUmodelU(errorUterm)
whatUareUtheU4UassumptionsUofUlinearUregression?U-
UANSWERULinearity/MeanUZero,UConstantUVariance,UIndependence,UNormality
,Linearity/MeanUzeroUassumptionU-
UANSWERUMeansUthatUtheUexpectedUvalueU(deviances)UofUerrorsUisUzero.UThisUleadsUtoUdifficultiesUinUestim
atingUB0UandUmeansUthatUourUmodelUdoesUnotUincludeUaUnecessaryUsystematicUcomponent
ConstantUvarianceUassumptionU-
UANSWERUMeansUthatUitUcannotUbeUtrueUthatUtheUmodelUisUmoreUaccurateUforUsomeUpartsUofUtheUpopulati
on,UandUlessUaccurateUforUotherUpartsUofUtheUpopulations.UThisUcanUresultUinUlessUaccurateUparametersUan
dUpoorly-calibratedUpredictionUintervals.
AssumptionUofUIndependenceU-
UANSWERUMeansUthatUtheUdeviances,UorUinUfactUtheUresponseUvariablesUys,UareUindependentlyUdrawnUfro
mUtheUdata-
generatingUprocess.U(thisUmostUoftenUoccursUinUtimeUseriesUdata)UThisUcanUresultUinUveryUmisleadingUasses
smentsUofUtheUstrengthUofUregression.
NormalityUassumptionU-
UANSWERUThisUisUneededUifUweUwantUtoUdoUanyUconfidenceUorUpredictionUintervals,UorUhypothesisUtest,Uw
hichUweUusuallyUdo.UIfUthisUassumptionUisUviolated,UhypothesisUtestUandUconfidenceUandUpredictionUinterv
alsUandUbeUveryUmisleading.
whatUareUtheU3UparametersUweUestimatedUinUregression?U-
UANSWERUB0,UB1,UsigmaUsquaredU(varianceUofUtheUoneUpop.)
WhatUdoUweUmeanUbyUmodelUparametersUinUstatistics?U-
UANSWERUModelUparametersUareUunknownUquantities,UandUtheyUstayUunknownUregardlessUhowUmuchUda
taUareUobserved.UWeUestimateUthoseUparametersUgivenUtheUmodelUassumptionsUandUtheUdata,UbutUthroug
hUestimation,Uwe'reUnotUidentifyingUtheUtrueUparameters.UWe'reUjustUestimatingUapproximationsUofUthose
Uparameters.
WhatUisUtheUestimatedUsamplingUdistributionUofUs^2?U-UANSWERUchi-squareUwithUn-1UDF
WhyUdoUweUloseU1UDFUforUs^2?U-UANSWERUweUreplaceUmuUwithUzbar
whatUisUtheUrelationshipUbetweenUs^2UandUsigma^2?U-UANSWERUS^2UestimatesUsigma^2
,WhatUisUtheUestimatedUsamplingUdistributionUofUsigma^2?U-UANSWERUchi-squareUwithUn-
2UDFU(~UequivalentUtoUMSE)
WhyUdoUweUloseU2UDFUforUsigma^2?U-UANSWERUweUreplacedUtwoUparameters,UB0UandUB1
InUSLR,UweUareUinterestedUinUtheUbehaviorUofUwhichUparameter?U-UANSWERUB1
IfUweUhaveUaUpositiveUvalueUforUB1,....U-
UANSWERUthenUthat'sUconsistentUwithUaUdirectUrelationshipUbetweenUtheUpredictingUvariableUxUandUtheUre
sponseUvariableUy.
IfUweUhaveUaUnegativeUvalueUforUB1,....U-
UANSWERUisUconsistentUwithUanUinverseUrelationshipUbetweenUxUandUy
WhenUB1UisUcloseUtoUzero...U-
UANSWERUweUinterpretUthatUthereUisUnotUaUsignificantUassociationUbetweenUpredictingUvariables,Ubetwee
nUtheUpredictingUvariableUx,UandUtheUresponseUvariableUy.
HowUdoUweUinterpretUB1?U-
UANSWERUItUisUtheUestimatedUexpectedUchangeUinUtheUresponseUvariableUassociatedUwithUoneUunitUofUcha
ngeUinUtheUpredictingUvariable.
HowUweUinterpretU^B0?U-
UANSWERUItUisUtheUestimatedUexpectedUvalueUofUtheUresponseUvariable,UwhenUtheUpredictingUvariableUeq
ualsUzero.
WhatUisUtheUsamplingUdistributionUofU^B1?U-UANSWERUtUdistributionUwithUN-2UDF
WhatUcanUweUuseUtoUtestUforUstatisticalUsignificance?U-UANSWERUt-test
WhatUwouldUweUdoUifUtheUTUvalueUisUlarge?U-
UANSWERURejectUtheUnullUhypothesisUthatUβ1UisUequalUtoUzero.UIfUtheUnullUhypothesisUisUrejected,UweUinter
pretUthisUthatUβ1UisUstatisticallyUsignificant.
, whatUdoesU'statisticalUsignificance'Umean?U-UANSWERUB1UisUstatisticallyUdifferentUfromUzero.
whatUisUtheUdistributionUofUB1?U-UANSWERUNormal
TheUestimatorsUforUtheUregressionUcoefficientsUare:
A)UBiasedUbutUwithUsmallUvariance
B)UUnbiasedUunderUnormalityUassumptionsUbutUbiasedUotherwise.
C)UUnbiasedUregardlessUofUtheUdistributionUofUtheUdata.U-UANSWERUC
TheUassumptionUofUnormality:
A)UItUisUneededUforUderivingUtheUestimatorsUofUtheUregressionUcoefficients.
B)UItUisUnotUneededUforUlinearUregressionUmodelingUandUinference.
C)UItUisUneededUforUtheUsamplingUdistributionUofUtheUestimatorsUofUtheUregressionUcoefficientsUandUhenceU
forUinference.
D)UItUisUneededUforUderivingUtheUexpectationUandUvarianceUofUtheUestimatorsUofUtheUregressionUcoefficient
s.U-UANSWERUC
WhatUisU'X*'?U-UANSWERUpredictor
WhereUdoesUuncertaintyUfromUestimationUcomeUfrom?U-UANSWERUfromUestimationUalone
WhereUdoesUuncertaintyUfromUpredictionUcomeUfrom?U-
UANSWERUfromUtheUestimationUofUregressionUparametersUandUfromUtheUnewnessUofUtheUobservationUitsel
f
whatUisUtheUpredictionUintervalUusedUfor?U-
UANSWERUusedUtoUprovideUanUintervalUestimateUforUaUpredictionUofUyUforUoneUmemberUofUtheUpopulationU
withUaUparticularUvalueUofUx*
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