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ISYE 6414 - ALL UNITS COMPLETELY SOLVED GRADED A 2024
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ISYE 6414 - ALL UNITS COMPLETELY SOLVED GRADED A 2024
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ISYE 6414 - ALL UNITS COMPLETELY
SOLVED GRADED A 2024
responsev(dependent)vvariablesv-
vans✔✔onevparticularvvariablevthatvwevarevinterestedvinvunderstandingvorvmodelingv(y)
predictingvorvexplanatoryv(independent)vvariablesv-
vans✔✔avsetvofvothervvariablesvthatvmightvbevusefulvinvpredictingvorvmodelingvthevrespons
evvariablev(x1,vx2)
Whatvkindvofvvariablevisvavresponsevvariablevandvwhy?v-
vans✔✔random,vbecausevitvvariesvwithvchangesvinvthevpredictor/svalongvwithvothervrando
mvchanges.
Whatvkindvofvvariablevisvavpredictingvvariablevandvwhy?v-
vans✔✔fixed,vbecausevitvdoesvnotvchangevwithvthevresponsevbutvitvisvfixedvbeforevthevresp
onsevisvmeasured.
linearvrelationshipv-vans✔✔avsimplevdeterministicvrelationshipvbetweenv2vfactors,vxvandvy
whatvarevthreevthingsvthatvavregressionvanalysisvisvusedvfor?v-
vans✔✔1.vPredictionvofvthevresponsevvariable,v2.vModelingvthevrelationshipvbetweenvthevr
esponsevandvexplanatoryvvariables,v3.vTestingvhypothesesvofvassociationvrelationships
B0v=v?v-vans✔✔intercept
B1v=v?v-vans✔✔slope
forvourvlinearvmodelvwhere:vYv=vB0v+vB1v+vEPSILONv(E),vwhatvdoesvthevepsilonvrepresent
?v-vans✔✔deviancevofvthevdatavfromvthevlinearvmodelv(errorvterm)
,whatvarevthev4vassumptionsvofvlinearvregression?v-
vans✔✔Linearity/MeanvZero,vConstantvVariance,vIndependence,vNormality
Linearity/Meanvzerovassumptionv-
vans✔✔Meansvthatvthevexpectedvvaluev(deviances)vofverrorsvisvzero.vThisvleadsvtovdifficul
tiesvinvestimatingvB0vandvmeansvthatvourvmodelvdoesvnotvincludevavnecessaryvsystematicv
component
Constantvvariancevassumptionv-
vans✔✔Meansvthatvitvcannotvbevtruevthatvthevmodelvisvmorevaccuratevforvsomevpartsvofvth
evpopulation,vandvlessvaccuratevforvothervpartsvofvthevpopulations.vThisvcanvresultvinvlessv
accuratevparametersvandvpoorly-calibratedvpredictionvintervals.
AssumptionvofvIndependencev-
vans✔✔Meansvthatvthevdeviances,vorvinvfactvthevresponsevvariablesvys,varevindependentl
yvdrawnvfromvthevdata-
generatingvprocess.v(thisvmostvoftenvoccursvinvtimevseriesvdata)vThisvcanvresultvinvveryvmi
sleadingvassessmentsvofvthevstrengthvofvregression.
Normalityvassumptionv-
vans✔✔Thisvisvneededvifvwevwantvtovdovanyvconfidencevorvpredictionvintervals,vorvhypothe
sisvtest,vwhichvwevusuallyvdo.vIfvthisvassumptionvisvviolated,vhypothesisvtestvandvconfidenc
evandvpredictionvintervalsvandvbevveryvmisleading.
whatvarevthev3vparametersvwevestimatedvinvregression?v-
vans✔✔B0,vB1,vsigmavsquaredv(variancevofvthevonevpop.)
Whatvdovwevmeanvbyvmodelvparametersvinvstatistics?v-
vans✔✔Modelvparametersvarevunknownvquantities,vandvtheyvstayvunknownvregardlessvho
wvmuchvdatavarevobserved.vWevestimatevthosevparametersvgivenvthevmodelvassumptions
vandvthevdata,vbutvthroughvestimation,vwe'revnotvidentifyingvthevtruevparameters.vWe'revjus
tvestimatingvapproximationsvofvthosevparameters.
Whatvisvthevestimatedvsamplingvdistributionvofvs^2?v-vans✔✔chi-squarevwithvn-1vDF
Whyvdovwevlosev1vDFvforvs^2?v-vans✔✔wevreplacevmuvwithvzbar
whatvisvthevrelationshipvbetweenvs^2vandvsigma^2?v-vans✔✔S^2vestimatesvsigma^2
Whatvisvthevestimatedvsamplingvdistributionvofvsigma^2?v-vans✔✔chi-squarevwithvn-
2vDFv(~vequivalentvtovMSE)
Whyvdovwevlosev2vDFvforvsigma^2?v-vans✔✔wevreplacedvtwovparameters,vB0vandvB1
,InvSLR,vwevarevinterestedvinvthevbehaviorvofvwhichvparameter?v-vans✔✔B1
IfvwevhavevavpositivevvaluevforvB1,....v-
vans✔✔thenvthat'svconsistentvwithvavdirectvrelationshipvbetweenvthevpredictingvvariablevxv
andvthevresponsevvariablevy.
IfvwevhavevavnegativevvaluevforvB1,....v-
vans✔✔isvconsistentvwithvanvinversevrelationshipvbetweenvxvandvy
WhenvB1visvclosevtovzero...v-
vans✔✔wevinterpretvthatvtherevisvnotvavsignificantvassociationvbetweenvpredictingvvariable
s,vbetweenvthevpredictingvvariablevx,vandvthevresponsevvariablevy.
HowvdovwevinterpretvB1?v-
vans✔✔Itvisvthevestimatedvexpectedvchangevinvthevresponsevvariablevassociatedvwithvone
vunitvofvchangevinvthevpredictingvvariable.
Howvwevinterpretv^B0?v-
vans✔✔Itvisvthevestimatedvexpectedvvaluevofvthevresponsevvariable,vwhenvthevpredictingvv
ariablevequalsvzero.
Whatvisvthevsamplingvdistributionvofv^B1?v-vans✔✔tvdistributionvwithvN-2vDF
Whatvcanvwevusevtovtestvforvstatisticalvsignificance?v-vans✔✔t-test
WhatvwouldvwevdovifvthevTvvaluevisvlarge?v-
vans✔✔Rejectvthevnullvhypothesisvthatvβ1visvequalvtovzero.vIfvthevnullvhypothesisvisvrejecte
d,vwevinterpretvthisvthatvβ1visvstatisticallyvsignificant.
whatvdoesv'statisticalvsignificance'vmean?v-vans✔✔B1visvstatisticallyvdifferentvfromvzero.
whatvisvthevdistributionvofvB1?v-vans✔✔Normal
Thevestimatorsvforvthevregressionvcoefficientsvare:
A)vBiasedvbutvwithvsmallvvariance
B)vUnbiasedvundervnormalityvassumptionsvbutvbiasedvotherwise.
C)vUnbiasedvregardlessvofvthevdistributionvofvthevdata.v-vans✔✔C
Thevassumptionvofvnormality:
A)vItvisvneededvforvderivingvthevestimatorsvofvthevregressionvcoefficients.
B)vItvisvnotvneededvforvlinearvregressionvmodelingvandvinference.
C)vItvisvneededvforvthevsamplingvdistributionvofvthevestimatorsvofvthevregressionvcoefficient
svandvhencevforvinference.
, D)vItvisvneededvforvderivingvthevexpectationvandvvariancevofvthevestimatorsvofvthevregressi
onvcoefficients.v-vans✔✔C
Whatvisv'X*'?v-vans✔✔predictor
Wherevdoesvuncertaintyvfromvestimationvcomevfrom?v-vans✔✔fromvestimationvalone
Wherevdoesvuncertaintyvfromvpredictionvcomevfrom?v-
vans✔✔fromvthevestimationvofvregressionvparametersvandvfromvthevnewnessvofvthevobser
vationvitself
whatvisvthevpredictionvintervalvusedvfor?v-
vans✔✔usedvtovprovidevanvintervalvestimatevforvavpredictionvofvyvforvonevmembervofvthevp
opulationvwithvavparticularvvaluevofvx*
whatvisvthevconfidencevintervalvusedvfor?v-
vans✔✔tovprovidevanvintervalvestimatevforvthevtruevaveragevvaluevofvyvforvallvmembersvofvt
hevpopulationvwithvavparticularvvaluevofvx*
Thevestimatedvversusvpredictedvregressionvlinevforvavgivenvx*:
A)vHavevthevsamevvariance
B)vHavevthevsamevexpectation
C)vHavevthevsamevvariancevandvexpectation
D)vNonevofvthevabovev-vans✔✔B
Thevvariabilityvinvthevpredictionvcomesvfrom:
A)vThevvariabilityvduevtovavnewvmeasurement.
B)vThevvariabilityvduevtovestimation.
C)vThevvariabilityvduevtovavnewvmeasurementvandvduevtovestimation.
D)vNonevofvthevabove.v-vans✔✔C
residualsv-
vans✔✔thevdifferencevbetweenvthevobservedvresponsevandvthevfittedvresponses
whatvdoesvresidualvanalysisvNOTvcheckvfor?v(forvSLRvassumptions)v-
vans✔✔independence
whatvcanvwevusevtovcheckvforvnormality?v-vans✔✔QQvplotvandvhistogram
whatvarevtwovwaysvtovtransformvdata?v-vans✔✔powervandvlogvtransformation
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