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ISYE 6414 MIDTERM, SUMMER 2024 QUESTIONS AND 100% CORRECT ANSWERS 2024
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ISYE 6414 MIDTERM, SUMMER 2024 QUESTIONS AND 100% CORRECT ANSWERS 2024
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ISYE 6414 MIDTERM, SUMMER 2024QUESTIONS AND 100% CORRECT
ANSWERS 2024
TheOpredictionOintervalOofOoneOmemberOofOtheOpopulationOwillOalwaysObeOlargerOthanOtheOconfidenceOint
ervalOofOtheOmeanOresponseOforOallOmembersOofOtheOpopulationOwhenOusingOtheOsameOpredictingOvalues.
O-OANSWEROtrue
SeeO1.7ORegressionOLine:OEstimationO&OPredictionOExamples
"JustOtoOwrapOupOtheOcomparison,OtheOconfidenceOintervalsOunderOestimationOareOnarrowerOthanOtheOpre
dictionOintervalsObecauseOtheOpredictionOintervalsOhaveOadditionalOvarianceOfromOtheOvariationOofOaOnewO
measurement."
InOANOVA,OtheOlinearityOassumptionOisOassessedOusingOaOplotOofOtheOresponseOagainstOtheOpredictingOvari
able.O-OANSWEROfalse
SeeO2.2.OEstimationOMethod
LinearityOisOnotOanOassumptionOofOANOVA.
IfOtheOmodelOassumptionsOhold,OthenOtheOestimatorOforOtheOvariance,OσO^O2,OisOaOrandomOvariable.O-
OANSWEROtrue
SeeO1.8OStatisticalOInference
WeOassumeOthatOtheOerrorOtermsOareOindependentOrandomOvariables.OTherefore,OtheOresidualsOareOindep
endentOrandomOvariables.OSinceOσO^O2OisOaOcombinationOofOtheOresiduals,OitOisOalsoOaOrandomOvariable.
TheOmeanOsumOofOsquaredOerrorsOinOANOVAOmeasuresOvariabilityOwithinOgroups.O-OANSWEROtrue
SeeO2.4OTestOforOEqualOMeans
MSEO=Owithin-groupOvariability
,TheOsimpleOlinearOregressionOcoefficient,OβO^O0,OisOusedOtoOmeasureOtheOlinearOrelationshipObetweenOtheO
predictingOandOresponseOvariables.O-OANSWEROfalse
SeeO1.2OEstimationOMethod
βO^O0OisOtheOinterceptOandOdoesOnotOtellOusOaboutOtheOrelationshipObetweenOtheOpredictingOandOresponse
Ovariables.
TheOsamplingOdistributionOforOtheOvarianceOestimatorOinOsimpleOlinearOregressionOisOχO2O(chi-
squared)OregardlessOofOtheOassumptionsOofOtheOdata.O-OANSWEROfalse
SeeO1.2OEstimationOMethod
"TheOsamplingOdistributionOofOtheOestimatorOofOtheOvarianceOisOchi-squared,OwithOnO-
O2OdegreesOofOfreedomO(moreOonOthisOinOaOmoment).OThisOisOunderOtheOassumptionOofOnormalityOofOtheOe
rrorOterms."
βO^O1OisOanOunbiasedOestimatorOforOβO0.O-OANSWEROFalse
SeeO1.4OStatisticalOInference
"WhatOthatOmeansOisOthatOβO^O1OisOanOunbiasedOestimatorOforOβO1."OItOisOnotOanOunbiasedOestimatorOforOβ
O0.
IfOtheOpairwiseOcomparisonOintervalObetweenOgroupsOinOanOANOVAOmodelOincludesOzero,OweOconcludeOth
atOtheOtwoOmeansOareOplausiblyOequal.O-OANSWEROtrue
SeeO2.8ODataOExample
IfOtheOcomparisonOintervalOincludesOzero,OthenOtheOtwoOmeansOareOnotOstatisticallyOsignificantlyOdifferent,
OandOareOthus,OplausiblyOequal.
UnderOtheOnormalityOassumption,OtheOestimatorOforOβO1OisOaOlinearOcombinationOofOnormallyOdistributedO
randomOvariables.O-OANSWEROtrue
SeeO1.4OStatisticalOInference
, "UnderOtheOnormalityOassumption,OβO1OisOthusOaOlinearOcombinationOofOnormallyOdistributedOrandomOvar
iables...OβO^O0OisOalsoOlinearOcombinationOofOrandomOvariables"
AnOANOVAOmodelOwithOaOsingleOqualitativeOpredictingOvariableOcontainingOkOgroupsOwillOhaveOkO+O1Opara
metersOtoOestimate.O-OANSWEROtrue
SeeO2.2OEstimationOMethod
WeOhaveOtoOestimateOtheOmeansOofOtheOkOgroupsOandOtheOpooledOvarianceOestimator,OsOpOoOoOlOeOdO2.
InOsimpleOlinearOregressionOmodels,OweOloseOthreeOdegreesOofOfreedomOwhenOestimatingOtheOvarianceOb
ecauseOofOtheOestimationOofOtheOthreeOmodelOparametersOβO0O,OβO1O,OσO2.O-OANSWEROfalse
SeeO1.2OEstimationOMethod
"TheOestimatorOforOσO2OisOσO^O2,OandOisOtheOsumOofOtheOsquaredOresiduals,OdividedObyOnO-O2."
TheOpooledOvarianceOestimator,OsOpOoOoOlOeOdO2,OinOANOVAOisOsynonymousOwithOtheOvarianceOestimator,Oσ
O^O2,OinOsimpleOlinearOregressionObecauseOtheyObothOuseOmeanOsquaredOerrorO(MSE)OforOtheirOcalculation
s.O-OANSWEROtrue
SeeO1.2OEstimationOMethodOforOsimpleOlinearOregression
SeeO2.2OEstimationOMethodOforOANOVA
TheOpooledOvarianceOestimatorOis,OinOfact,OtheOvarianceOestimator.
TheOnormalityOassumptionOstatesOthatOtheOresponseOvariableOisOnormallyOdistributed.O-OANSWEROfalse
SeeO1.8ODiagnostics
"NormalityOassumption:OtheOerrorOtermsOareOnormallyOdistributed."
TheOresponseOmayOorOmayOnotObeOnormallyOdistributed,ObutOtheOerrorOtermsOareOassumedOtoObeOnormall
yOdistributed.
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