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ISYE 6414 - ALL UNITS COMPLETELY SOLVED GRADED A 2024 $11.99   Add to cart

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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
  • Exam (elaborations)
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  • ISYE 6414
  • ISYE 6414
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ISYE 6414 - MIDTERM 1 PREP
QUESTIONS AND VERIFIED ANSWERS
2024




Ifvλ=1v-vans✔✔wevdovnotvtransform

non-deterministicv-
vans✔✔Regressionvanalysisvisvonevofvthevsimplestvwaysvwevhavevinvstatisticsvtovinvestiga

tevthevrelationshipvbetweenvtwovorvmorevvariablesvinvav___vway

randomv-
vans✔✔Thevresponsevvariablevisvav___vvariable,vbecausevitvvariesvwithvchangesvinvthevpr

edictingvvariable,vorvwithvothervchangesvinvthevenvironment

fixedv-
vans✔✔Thevpredictingvvariablevisvav___vvariable.vItvisvsetvfixed,vbeforevthevresponsevisvme

asured.

simplevlinearvregressionv-
vans✔✔regressionvanalysisvinvolvingvonevindependentvvariablevandvonevdependentvvaria

blevinvwhichvthevrelationshipvbetweenvthevvariablesvisvapproximatedvbyvavstraightvline

MultiplevLinearvRegressionv-
vans✔✔Avstatisticalvmethodvusedvtovmodelvthevrelationshipvbetweenvonevdependentv(orvr

esponse)vvariablevandvtwovorvmorevindependentv(orvexplanatory)vvariablesvbyvfittingvavlin
earvequationvtovobservedvdata

,polynomialvregressionv-
vans✔✔avregressionvmodelvwhichvdoesvnotvassumevavlinearvrelationship;vavcurvilinearvcor

relationvcoefficientvisvcomputedv(wevcanvthinkvofvXvandvX-
squaredvasvtwovdifferentvpredictingvvariables)

threevobjectivesvinvregressionv-vans✔✔1)vPrediction
2)vModeling
3)vTestingvhypothesis

Predictionv-
vans✔✔Wevwantvtovseevhowvthevresponsevvariablevbehavesvinvdifferentvsettings.vForvexa

mple,vforvavdifferentvlocation,vifvwevthinkvaboutvavgeographicvprediction,vorvinvtime,vifvwevthi
nkvaboutvtemporalvprediction

Modelingv-
vans✔✔modelingvthevrelationshipvbetweenvthevresponsevvariablevandvthevexplanatoryvvar

iables,vorvpredictingvvariables

Testingvhypothesesv-vans✔✔ofvassociationvrelationships

usefulvrepresentationvofvrealityv-
vans✔✔Wevdovnotvbelievevthatvthevlinearvmodelvrepresentsvavtruevrepresentationvofvrealit

y.vRather,vwevthinkvthat,vperhaps,vitvprovidesvav___

β0v-vans✔✔interceptvparameterv(thevvaluevatvwhichvthevlinevintersectsvthevy-axis)

β1v-vans✔✔slopevparameterv(slopevofvthevlinevwevarevtryingvtovfit)

epsilonv(ε)v-vans✔✔isvthevdeviancevofvthevdatavfromvthevlinearvmodel

tovfindvβ0vandvβ1v-
vans✔✔tovfindvthevlinevthatvdescribesvavlinearvrelationship,vsuchvthatvwevfitvthisvmodel.



simplevlinearvregressionvdatavstructurev-
vans✔✔pairsvofvdatavconsistingvofvavvaluevforvthevresponsevvariable,andvavvaluevforvthevpr

edictingvvariable.vAndvwevhavevnvsuchvpairs

modelingvframeworkvforvthevsimplevlinearvregression:v-
vans✔✔1)videntifyingvdatavstructure

2)vclearlyvstatingvthevmodelvassumptions

linearvregressionvassumptionsv-vans✔✔1)vlinearity
2)vconstantvvariancevassumption
3)vindependencevassumption

, linearityvassumptionv-
vans✔✔meanvzerovassumption,vmeansvthatvthevexpectedvvaluevofvtheverrorsvisvzero.

Avviolationvofvthisvassumptionvwillvleadvtovdifficultiesvinvestimatingvβ0,vandvmeansvthatvyou
rvmodelvdoesvnotvincludevavnecessaryvsystematicvcomponent.

constantvvariancevassumptionv-
vans✔✔whichvmeansvthatvthevvariancev(σ^2)vofvtheverrorvtermsvorvdeviancesvisvconstantvf

orvthevgivenvpopulation.vAvviolationvofvthisvassumptionvmeansvthatvthevestimatesvarevnotva
svefficientvasvtheyvcouldvbevinvestimatingvthevtruevparameters

IndependencevAssumptionv-
vans✔✔whichvmeansvthatvthevdeviancesvarevindependentvrandomvvariables.

Violationvofvthisvassumptionvcanvleadvtovmisleadingvassessmentsvofvthevstrengthvofvthevre
gression.

normalityvassumptionv-
vans✔✔errorsv(ε)varevnormallyvdistributed.vThisvisvneededvforvstatisticalvinference,vforvexa

mple,vconfidencevorvpredictionvintervals,vandvhypothesisvtesting.vIfvthisvassumptionvisvviol
ated,vhypothesisvtestsvandvconfidencevandvpredictionvintervalsvcanvbevmisleading.v

thirdvparameterv-vans✔✔thevvariancevofvtheverrorvtermsv(σ^2)

Onevapproachvisvtovminimizevthevsumvofvsquaredvresidualsvorverrorsvwithvrespectvtovβ0van
dvβ1.vThisvtranslatedvintovfindingvthevlinevsuchvthatvthevtotalvsquaredvdeviancesvfromvthevli
nevisvminimum.v-
vans✔✔Howvcanvwevgetvestimatesvofvthevregressionvcoefficientsvorvparametersvinvlinear

regressionvanalysis?

fittedvvaluesv-vans✔✔tovbevthevregressionvlinevwherevthevparametersvarevreplaced
byvthevestimatedvvaluesvofvthevparameters.

Residualsv-vans✔✔arevsimplyvthevdifference
betweenvobservedvresponsevandvfittedvvalues,vandvtheyvarevproxiesvofvtheverrorvtermsvin
thevregressionvmodel

MSEv-vans✔✔Thevestimatorvforvsigmavsquarevisvsigmavsquarevhat,vandvisvthe
sumvofvthevsquaredvresiduals,vdividedvbyvnv-v2.

σ^2v(samplevdistributionvofvthevvariancevestimator)v-vans✔✔isvchi-
squaredvdistributionvwithvnv-v2vdegreesvofvfreedomv(We
losevtwovdegreesvofvfreedomvbecausevwevreplacedvthevtwovparametersvß0vandvß1vwith
theirvestimatorsvtovobtainvthevresiduals.)

epsilonvivhatv-vans✔✔proxiesvforvthevdeviancesvorvtheverrorvterms

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