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ISYE 6414 - MIDTERM EXAM 3 QUESTIONS AND 100% CORRECT ANSWERS 2024
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ISYE 6414 - MIDTERM EXAM 3 QUESTIONS AND 100% CORRECT ANSWERS 2024
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ISYE 6414 - MIDTERM EXAM 3QUESTIONS AND 100% CORRECT
ANSWERS 2024
RegressionLAnalysisL-
LANSWERLRegressionLanalysisLisLaLsimpleLwayLtoLinvestigateLtheLrelationshipLbetweenL2LorLmoreLvariablesLi
nLaLnon-deterministicLway.
Response/TargetLVariableL(Y)L-
LANSWERLThisLisLaLvariableLwe'reLinterestedLinLunderstanding,LmodelingLorLtestingL
ThisLisLaLrandomLvariable.LItLvariesLwithLchangesLinLtheLpredictor(s)
2.LPredicting/ExplanatoryL(independent)LVariables(XsL~LX1,LX2)L-
LANSWERLTheseLareLvariablesLweLthinkLmightLbeLusefulLinLpredictingLorLmodelingLtheLresponseLvariableL
ThisLisLaLfixedLvariable.LItLdoesLnotLchangeLwithLtheLresponse
SimpleLLinearLRegressionL-LANSWERLWeLhaveLaLstraightLlineLwhichLdoesn'tLfitLperfectlyLtoLtheLpoints
TheLobjectiveLisLtoLfitLaLnon-deterministicLlinearLmodelLbetweenLtheLpredictingLvariableLandLY.L
InLsimpleLlinearLregression,LweLhaveL3LparametersLtoLestimate.
MultipleLLinearLRegressionL-LANSWERLWeLcanLhaveLaLplaneLifLweLhaveLtwoLpredictions
PolynomialLRegressionL-LANSWERLWeLareLcapturingLaLnonlinearLrelationship
ObjectivesLofLLinearLRegressionL-
LANSWERL1.LPrediction:LWeLwantLtoLseeLhowLtheLresponseLvariableLbehavesLinLdifferentLsettingsL
, 2.LModeling:LWeLareLinterestedLinLmodelingLtheLrelationshipLbetweenLtheLresponseLvariableLandLtheLexpla
natory/predictingLvariables
3.LTesting:LWeLareLalsoLinterestedLinLtestingLtheLhypothesesLofLassociationLrelationships.
SimpleLLinearLRegressionLAssumptionsL-
LANSWERL•LLinearity/MeanLZeroLAssumption:LThisLmeansLthatLtheLexpectedLvalueLofLtheLerrorsLisLzero
•LConstantLVarianceLAssumption:LThisLmeansLthatLtheLvarianceLofLtheLerrorLtermLisLequalLtoLsigma_square
dLisLtheLsameLacrossLallLerrorLterms
•LIndependenceLAssumption:LThisLmeansLthatLtheLerrorLtermsLareLindependentLrandomLvariablesLi.e.Ldevi
ancesL(responseLvariablesLYs)LareLindependentlyLdrawnLfromLtheLdataLgeneratingLprocessL--
LitLcannotLbeLtrueLthatLtheLmodelLunder-
predictsLYLforLoneLparticularLcaseLtellsLyouLanythingLorLallLaboutLwhatLitLdoesLforLanyLotherLcase
•LNormalLAssumption:LTheLerrorsLareLassumedLtoLbeLnormallyLdistributed.
LinearityLAssumptionL-
LANSWERLALviolationLofLthisLassumptionLwillLleadLtoLdifficultiesLinLestimatingL0LandLmeansLthatLyourLmodelL
doesLnotLincludeLaLnecessaryLsystematicLcomponent
ConstantLVarianceLAssumptionL-
LANSWERLThisLmeansLthatLtheLmodelLcannotLbeLmoreLaccurateLinLsomeLpartsLandLlessLaccurateLinLotherLpar
tsLofLtheLmodel.LTheLvarianceLhasLtoLbeLconstant.
LALviolationLofLthisLassumptionLmeansLthatLtheLestimatesLareLnotLasLefficientLasLtheyLcouldLbeLinLestimatingL
theLtrueLparametersLandLbetterLestimatesLcanLbeLcalculatedLalsoLresultsLinLpoorlyLcalibratedLpredictionLinte
rvals
IndependenceLAssumptionL-LANSWERLItLcannotLbeLtrueLthatLtheLmodelLunder-
predictsLY.LOneLparticularLcaseLdoesn'tLtellLyouLanythingLorLallLaboutLwhatLitLdoesLforLanyLotherLcase
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