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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
responsed(dependent)dvariablesd-
dans✔✔onedparticulardvariabledthatdwedaredinteresteddindunderstandingdordmodelingd(y)
predictingdordexplanatoryd(independent)dvariablesd-
dans✔✔adsetdofdotherdvariablesdthatdmightdbedusefuldindpredictingdordmodelingdthedrespon
sedvariabled(x1,dx2)
Whatdkinddofdvariabledisdadresponsedvariabledanddwhy?d-
dans✔✔random,dbecauseditdvariesdwithdchangesdindthedpredictor/
sdalongdwithdotherdrandomdchanges.
Whatdkinddofdvariabledisdadpredictingdvariabledanddwhy?d-
dans✔✔fixed,dbecauseditddoesdnotdchangedwithdthedresponsedbutditdisdfixeddbeforedthedres
ponsedisdmeasured.
lineardrelationshipd-
dans✔✔adsimpleddeterministicdrelationshipdbetweend2dfactors,dxdanddy
whatdaredthreedthingsdthatdadregressiondanalysisdisduseddfor?d-
dans✔✔1.dPredictiondofdthedresponsedvariable,d2.dModelingdthedrelationshipdbetweendthed
responsedanddexplanatorydvariables,d3.dTestingdhypothesesdofdassociationdrelationships
B0d=d?d-dans✔✔intercept
B1d=d?d-dans✔✔slope
fordourdlineardmodeldwhere:dYd=dB0d+dB1d+dEPSILONd(E),dwhatddoesdthedepsilondreprese
nt?d-dans✔✔deviancedofdtheddatadfromdthedlineardmodeld(errordterm)
,whatdaredthed4dassumptionsdofdlineardregression?d-dans✔✔Linearity/
MeandZero,dConstantdVariance,dIndependence,dNormality
Linearity/Meandzerodassumptiond-
dans✔✔Meansdthatdthedexpecteddvalued(deviances)dofderrorsdisdzero.dThisdleadsdtoddifficu
ltiesdindestimatingdB0danddmeansdthatdourdmodelddoesdnotdincludedadnecessarydsystemati
cdcomponent
Constantdvariancedassumptiond-
dans✔✔Meansdthatditdcannotdbedtruedthatdthedmodeldisdmoredaccuratedfordsomedpartsdofdt
hedpopulation,danddlessdaccuratedfordotherdpartsdofdthedpopulations.dThisdcandresultdindles
sdaccuratedparametersdanddpoorly-calibrateddpredictiondintervals.
AssumptiondofdIndependenced-
dans✔✔Meansdthatdtheddeviances,dordindfactdthedresponsedvariablesdys,daredindependent
lyddrawndfromdtheddata-
generatingdprocess.d(thisdmostdoftendoccursdindtimedseriesddata)dThisdcandresultdindverydm
isleadingdassessmentsdofdthedstrengthdofdregression.
Normalitydassumptiond-
dans✔✔Thisdisdneededdifdwedwantdtoddodanydconfidencedordpredictiondintervals,dordhypoth
esisdtest,dwhichdwedusuallyddo.dIfdthisdassumptiondisdviolated,dhypothesisdtestdanddconfide
ncedanddpredictiondintervalsdanddbedverydmisleading.
whatdaredthed3dparametersdwedestimateddindregression?d-
dans✔✔B0,dB1,dsigmadsquaredd(variancedofdthedonedpop.)
Whatddodwedmeandbydmodeldparametersdindstatistics?d-
dans✔✔Modeldparametersdaredunknowndquantities,danddtheydstaydunknowndregardlessdh
owdmuchddatadaredobserved.dWedestimatedthosedparametersdgivendthedmodeldassumptio
nsdanddtheddata,dbutdthroughdestimation,dwe'rednotdidentifyingdthedtruedparameters.dWe're
djustdestimatingdapproximationsdofdthosedparameters.
Whatdisdthedestimateddsamplingddistributiondofds^2?d-dans✔✔chi-squaredwithdn-1dDF
Whyddodwedlosed1dDFdfords^2?d-dans✔✔wedreplacedmudwithdzbar
whatdisdthedrelationshipdbetweends^2danddsigma^2?d-dans✔✔S^2destimatesdsigma^2
Whatdisdthedestimateddsamplingddistributiondofdsigma^2?d-dans✔✔chi-squaredwithdn-
2dDFd(~dequivalentdtodMSE)
Whyddodwedlosed2dDFdfordsigma^2?d-dans✔✔wedreplaceddtwodparameters,dB0danddB1
IndSLR,dwedaredinteresteddindthedbehaviordofdwhichdparameter?d-dans✔✔B1
,IfdwedhavedadpositivedvaluedfordB1,....d-
dans✔✔thendthat'sdconsistentdwithdaddirectdrelationshipdbetweendthedpredictingdvariabledx
danddthedresponsedvariabledy.
IfdwedhavedadnegativedvaluedfordB1,....d-
dans✔✔isdconsistentdwithdandinversedrelationshipdbetweendxdanddy
WhendB1disdclosedtodzero...d-
dans✔✔wedinterpretdthatdtheredisdnotdadsignificantdassociationdbetweendpredictingdvariabl
es,dbetweendthedpredictingdvariabledx,danddthedresponsedvariabledy.
HowddodwedinterpretdB1?d-
dans✔✔Itdisdthedestimateddexpecteddchangedindthedresponsedvariabledassociateddwithdon
edunitdofdchangedindthedpredictingdvariable.
Howdwedinterpretd^B0?d-
dans✔✔Itdisdthedestimateddexpecteddvaluedofdthedresponsedvariable,dwhendthedpredictingd
variabledequalsdzero.
Whatdisdthedsamplingddistributiondofd^B1?d-dans✔✔tddistributiondwithdN-2dDF
Whatdcandwedusedtodtestdfordstatisticaldsignificance?d-dans✔✔t-test
WhatdwoulddweddodifdthedTdvaluedisdlarge?d-
dans✔✔Rejectdthednulldhypothesisdthatdβ1disdequaldtodzero.dIfdthednulldhypothesisdisdreject
ed,dwedinterpretdthisdthatdβ1disdstatisticallydsignificant.
whatddoesd'statisticaldsignificance'dmean?d-dans✔✔B1disdstatisticallyddifferentdfromdzero.
whatdisdtheddistributiondofdB1?d-dans✔✔Normal
Thedestimatorsdfordthedregressiondcoefficientsdare:
A)dBiaseddbutdwithdsmalldvariance
B)dUnbiaseddunderdnormalitydassumptionsdbutdbiaseddotherwise.
C)dUnbiaseddregardlessdofdtheddistributiondofdtheddata.d-dans✔✔C
Thedassumptiondofdnormality:
A)dItdisdneededdfordderivingdthedestimatorsdofdthedregressiondcoefficients.
B)dItdisdnotdneededdfordlineardregressiondmodelingdanddinference.
C)dItdisdneededdfordthedsamplingddistributiondofdthedestimatorsdofdthedregressiondcoefficien
tsdanddhencedfordinference.
D)dItdisdneededdfordderivingdthedexpectationdanddvariancedofdthedestimatorsdofdthedregress
iondcoefficients.d-dans✔✔C
Whatdisd'X*'?d-dans✔✔predictor
, Whereddoesduncertaintydfromdestimationdcomedfrom?d-dans✔✔fromdestimationdalone
Whereddoesduncertaintydfromdpredictiondcomedfrom?d-
dans✔✔fromdthedestimationdofdregressiondparametersdanddfromdthednewnessdofdthedobse
rvationditself
whatdisdthedpredictiondintervalduseddfor?d-
dans✔✔useddtodprovidedandintervaldestimatedfordadpredictiondofdydfordonedmemberdofdthed
populationdwithdadparticulardvaluedofdx*
whatdisdthedconfidencedintervalduseddfor?d-
dans✔✔todprovidedandintervaldestimatedfordthedtruedaveragedvaluedofdydfordalldmembersdof
dthedpopulationdwithdadparticulardvaluedofdx*
Thedestimateddversusdpredicteddregressiondlinedfordadgivendx*:
A)dHavedthedsamedvariance
B)dHavedthedsamedexpectation
C)dHavedthedsamedvariancedanddexpectation
D)dNonedofdthedaboved-dans✔✔B
Thedvariabilitydindthedpredictiondcomesdfrom:
A)dThedvariabilitydduedtodadnewdmeasurement.
B)dThedvariabilitydduedtodestimation.
C)dThedvariabilitydduedtodadnewdmeasurementdanddduedtodestimation.
D)dNonedofdthedabove.d-dans✔✔C
residualsd-
dans✔✔theddifferencedbetweendthedobserveddresponsedanddthedfitteddresponses
whatddoesdresidualdanalysisdNOTdcheckdfor?d(fordSLRdassumptions)d-
dans✔✔independence
whatdcandwedusedtodcheckdfordnormality?d-dans✔✔QQdplotdanddhistogram
whatdaredtwodwaysdtodtransformddata?d-dans✔✔powerdanddlogdtransformation
outliersd-
dans✔✔whichdareddatadpointsdfardfromdthedmajoritydofdtheddatadindbothdxdanddydordjustdx
leveragedpointsd-dans✔✔Datadpointsdthatdaredfardfromdthedmeandofdthedx's
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