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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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  • September 7, 2024
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  • 2024/2025
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  • ISYE 6414
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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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