ISYE 6414 REGRESSION MODULES 1-2
QUESTIONS AND VERIFIED ANSWERS
2024
Assumingdthatdtheddatadarednormallyddistributed,dunderdthedsimpledlineardmodel,dthedesti
mateddvariancedhasdthedfollowingdsamplingddistribution:d-dans✔✔Chi-squareddwithdn-
2ddegreesdofdfreedom.
Thedfitteddvaluesdareddefineddas?d-
dans✔✔Thedregressiondlinedwithdparametersdreplaceddwithdthedestimateddregressiondcoe
fficients.
Thedestimatorsdfodthedlineardregressiondmodeldaredderiveddby?d-
dans✔✔Minimizingdthedsumdofdsquaredddifferencesdbetweendthedobserveddanddexpected
dvaluesdofdthedresponsedvariable.
Thedestimatorsdfordthedregressiondcoefficientsdare:d-
dans✔✔Unbiaseddregardlessdofdtheddistributiondofdtheddata.
Thedassumptiondofdnormality:d-
dans✔✔Isdneededdfordthedsamplingddistributiondofdthedestimatorsdofdthedregressiondcoeffi
cientsdanddhencedfordinference.
Thedestimateddversusdpredicteddregressiondlinedfordadgivendx*d-
dans✔✔havedthedsamedexpectation.
Thedvariabilitydindthedpredictiondcomesdfromd-
dans✔✔thedvariabilitydduedtodadnewdmeasurementdanddduedtodestimation.
Residualdanalysisdcandonlydbeduseddtodassessduncorrelatedderrors.d-dans✔✔False
, Independencedassumptiondcandbedassessdusingdthednormaldprobabilitydplot.d-
dans✔✔False
Independencedassumptiondcandbedassesseddusingdthedresidualsdvsdfitteddvalues.d-
dans✔✔False
Weddetectddeparturedfromdthedassumptiondofdconstantdvarianced-
dans✔✔whendthedresidualsdvsdfitteddvaluesdaredlargerdindthedendsdbutdsmallerdindthedmidd
le.
Ifdaddeparturedfromdnormalitydisddetected,dwedtransformdthedpredictingdvariabledtodimprov
edupondthednormalitydassumption.d-dans✔✔False
Ifdaddeparturedfromdthedindependencedassumptiondisddetected,dwedtransformdthedrespons
edvariabledtodimprovedupondthedindependencedassumption.d-dans✔✔False
ThedBox-
Coxdtransformationdisdcommonlyduseddtodimprovedupondthedlinearitydassumption.d-
dans✔✔False
Indevaluatingdadsimpledlineardmodeld-
dans✔✔theredisdaddirectdrelationshipdbetweendthedcoefficientdofddeterminationdanddthedco
rrelationdbetweendthedpredictingdanddresponsedvariables.
Goodnessdofdfitdassessmentdisddonedbyd-dans✔✔residualdanalysis
R-squaredd(thedcoefficientdofdvariation)disdinterpreteddasd-
dans✔✔thedpercentagedofdvariabilitydindthedresponsedvariabledexplaineddbydthedmodel.
ThedparametersdofdANOVAdared-
dans✔✔thedkdsampledmeansdanddthedpopulationdvariance.
Thedpooleddvariancedestimatordisd-
dans✔✔thedsampledvariancedestimatordassumingdequaldvariances.
IndANOVA,dthedmeandsumdofdsquaresddivideddbydN-1disd-
dans✔✔thedsampledvariancedestimatordassumingdequaldmeansdanddequaldvariances.
MSEdmeasuresd-dans✔✔thedwithin-treatmentdvariability.
MSSTrdmeasuresd-dans✔✔thedbetweendtreatmentdvariability.
Ifdwedrejectdthedtestdofdequaldmeans,dwedconcludedthatdatdleastdonedpairdofdmeansdareddiff
erent.d-dans✔✔True
QUESTIONS AND VERIFIED ANSWERS
2024
Assumingdthatdtheddatadarednormallyddistributed,dunderdthedsimpledlineardmodel,dthedesti
mateddvariancedhasdthedfollowingdsamplingddistribution:d-dans✔✔Chi-squareddwithdn-
2ddegreesdofdfreedom.
Thedfitteddvaluesdareddefineddas?d-
dans✔✔Thedregressiondlinedwithdparametersdreplaceddwithdthedestimateddregressiondcoe
fficients.
Thedestimatorsdfodthedlineardregressiondmodeldaredderiveddby?d-
dans✔✔Minimizingdthedsumdofdsquaredddifferencesdbetweendthedobserveddanddexpected
dvaluesdofdthedresponsedvariable.
Thedestimatorsdfordthedregressiondcoefficientsdare:d-
dans✔✔Unbiaseddregardlessdofdtheddistributiondofdtheddata.
Thedassumptiondofdnormality:d-
dans✔✔Isdneededdfordthedsamplingddistributiondofdthedestimatorsdofdthedregressiondcoeffi
cientsdanddhencedfordinference.
Thedestimateddversusdpredicteddregressiondlinedfordadgivendx*d-
dans✔✔havedthedsamedexpectation.
Thedvariabilitydindthedpredictiondcomesdfromd-
dans✔✔thedvariabilitydduedtodadnewdmeasurementdanddduedtodestimation.
Residualdanalysisdcandonlydbeduseddtodassessduncorrelatedderrors.d-dans✔✔False
, Independencedassumptiondcandbedassessdusingdthednormaldprobabilitydplot.d-
dans✔✔False
Independencedassumptiondcandbedassesseddusingdthedresidualsdvsdfitteddvalues.d-
dans✔✔False
Weddetectddeparturedfromdthedassumptiondofdconstantdvarianced-
dans✔✔whendthedresidualsdvsdfitteddvaluesdaredlargerdindthedendsdbutdsmallerdindthedmidd
le.
Ifdaddeparturedfromdnormalitydisddetected,dwedtransformdthedpredictingdvariabledtodimprov
edupondthednormalitydassumption.d-dans✔✔False
Ifdaddeparturedfromdthedindependencedassumptiondisddetected,dwedtransformdthedrespons
edvariabledtodimprovedupondthedindependencedassumption.d-dans✔✔False
ThedBox-
Coxdtransformationdisdcommonlyduseddtodimprovedupondthedlinearitydassumption.d-
dans✔✔False
Indevaluatingdadsimpledlineardmodeld-
dans✔✔theredisdaddirectdrelationshipdbetweendthedcoefficientdofddeterminationdanddthedco
rrelationdbetweendthedpredictingdanddresponsedvariables.
Goodnessdofdfitdassessmentdisddonedbyd-dans✔✔residualdanalysis
R-squaredd(thedcoefficientdofdvariation)disdinterpreteddasd-
dans✔✔thedpercentagedofdvariabilitydindthedresponsedvariabledexplaineddbydthedmodel.
ThedparametersdofdANOVAdared-
dans✔✔thedkdsampledmeansdanddthedpopulationdvariance.
Thedpooleddvariancedestimatordisd-
dans✔✔thedsampledvariancedestimatordassumingdequaldvariances.
IndANOVA,dthedmeandsumdofdsquaresddivideddbydN-1disd-
dans✔✔thedsampledvariancedestimatordassumingdequaldmeansdanddequaldvariances.
MSEdmeasuresd-dans✔✔thedwithin-treatmentdvariability.
MSSTrdmeasuresd-dans✔✔thedbetweendtreatmentdvariability.
Ifdwedrejectdthedtestdofdequaldmeans,dwedconcludedthatdatdleastdonedpairdofdmeansdareddiff
erent.d-dans✔✔True
