ISYE 6414 MIDTERM 1 STUDY NOTES
QUESTIONS AND ANSWERS WITH
SOLUTIONS 2024
responseEvariableE-EANSWERE-dependentEvariableErepresentedEbyEY
-theEvariableEweEareEinterestedEinEmodeling
-randomEvariable
predicting/explanatoryEvariableE-EANSWERE-independentEvariableErepresentedEbyEx1,Ex1,Eetc.
-usefulEinEpredictingEtheEresponseEvariable
-fixedEvariable
randomEvariableE-EANSWEREvariesEwithEchangeEinEpredictorsEalongEwithEotherErandomEchanges
fixedEvariableE-EANSWEREdoesEnotEchangeEwithEtheEresponse,EbutEisEsetEbeforeEtheEresponseEisEmeasured
simpleElinearEregressionE-EANSWERE-relationshipEbetweenEtwoEfactorsEinEaEnon-deterministicEway
-estimateEtheErelationshipEbetweenEresponseEandEpredictingEvariableEwithEoneEstraightEline
yE=Eβ0E+Eβ1(x)E+Eε
multipleElinearEregressionE-EANSWERE-moreEthanEoneEpredictingEvariable
-estimateEtheErelationshipEwithEaEplane
y=Eβ0E+Eβ1(x1)E+Eβ2(x2)E+Eε
polynomialEregressionE-EANSWERE-canEincludeEmoreEcomplexErelationships,ElikeEquadratics...
-nonlinearErelationship,EbutEcanEstillEbeEtranslatedEintoEaElinearEregression,EthinkingEofExEandEx-
squaredEasEtwoEdifferentEpredictingEvariables
, yE=Eβ0E+Eβ1(x)E+Eβ2(x-squared)E+Eε
objectivesEofEregressionE-EANSWERE-predictingEresponseEvariableEbehaviorEinEdifferentEsettings
-modelingErelationshipEbetweenEresponseEvariableEandEpredictingEvariables
-testingEhypothesesEofEassociationErelationships
WhyEuseElinearEmodels?E-
EANSWEREtheyEareEeasyEtoEunderstand,EmathematicallyEsimple,EandEworkEwellEforEaEwideErangeEofEcircums
tances
"AllEmodelsEareEwrong,E_________________"E-EANSWEREbutEsomeEareEuseful
AreElinearEmodelsEaEtrueErepresentationEofEreality?E-EANSWEREno
objectiveEofEsimpleElinearEregressionE-EANSWEREfitEaEnon-
deterministicElinearEmodelEbetweenEtheEpredictingEvariableEXEandEtheEresponseEvariableEY
parametersEtoEestimateE(neverEtrulyEknown)EinEsimpleElinearEregressionE-EANSWEREβ0,Eβ1,Eε
simpleElinearEregressionEequationE-EANSWEREyE=Eβ0E+Eβ1xE+Eε
β0E-EANSWEREintercept
εE-EANSWEREdevianceEofEtheEdataEfromEtheElinearEmodel
varianceEofEtheEerrorEterms
β1E-EANSWEREslope
QUESTIONS AND ANSWERS WITH
SOLUTIONS 2024
responseEvariableE-EANSWERE-dependentEvariableErepresentedEbyEY
-theEvariableEweEareEinterestedEinEmodeling
-randomEvariable
predicting/explanatoryEvariableE-EANSWERE-independentEvariableErepresentedEbyEx1,Ex1,Eetc.
-usefulEinEpredictingEtheEresponseEvariable
-fixedEvariable
randomEvariableE-EANSWEREvariesEwithEchangeEinEpredictorsEalongEwithEotherErandomEchanges
fixedEvariableE-EANSWEREdoesEnotEchangeEwithEtheEresponse,EbutEisEsetEbeforeEtheEresponseEisEmeasured
simpleElinearEregressionE-EANSWERE-relationshipEbetweenEtwoEfactorsEinEaEnon-deterministicEway
-estimateEtheErelationshipEbetweenEresponseEandEpredictingEvariableEwithEoneEstraightEline
yE=Eβ0E+Eβ1(x)E+Eε
multipleElinearEregressionE-EANSWERE-moreEthanEoneEpredictingEvariable
-estimateEtheErelationshipEwithEaEplane
y=Eβ0E+Eβ1(x1)E+Eβ2(x2)E+Eε
polynomialEregressionE-EANSWERE-canEincludeEmoreEcomplexErelationships,ElikeEquadratics...
-nonlinearErelationship,EbutEcanEstillEbeEtranslatedEintoEaElinearEregression,EthinkingEofExEandEx-
squaredEasEtwoEdifferentEpredictingEvariables
, yE=Eβ0E+Eβ1(x)E+Eβ2(x-squared)E+Eε
objectivesEofEregressionE-EANSWERE-predictingEresponseEvariableEbehaviorEinEdifferentEsettings
-modelingErelationshipEbetweenEresponseEvariableEandEpredictingEvariables
-testingEhypothesesEofEassociationErelationships
WhyEuseElinearEmodels?E-
EANSWEREtheyEareEeasyEtoEunderstand,EmathematicallyEsimple,EandEworkEwellEforEaEwideErangeEofEcircums
tances
"AllEmodelsEareEwrong,E_________________"E-EANSWEREbutEsomeEareEuseful
AreElinearEmodelsEaEtrueErepresentationEofEreality?E-EANSWEREno
objectiveEofEsimpleElinearEregressionE-EANSWEREfitEaEnon-
deterministicElinearEmodelEbetweenEtheEpredictingEvariableEXEandEtheEresponseEvariableEY
parametersEtoEestimateE(neverEtrulyEknown)EinEsimpleElinearEregressionE-EANSWEREβ0,Eβ1,Eε
simpleElinearEregressionEequationE-EANSWEREyE=Eβ0E+Eβ1xE+Eε
β0E-EANSWEREintercept
εE-EANSWEREdevianceEofEtheEdataEfromEtheElinearEmodel
varianceEofEtheEerrorEterms
β1E-EANSWEREslope
