06slides.pdf - Multiple Regression Properties Tyler Ransom...

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MultipleRegressionProperties TylerRansom UnivofOklahoma Janthree.osfone.osf,two.osfzero.osfone.osfnine.osf one.osf/two.osfsix.osf
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Today’splan one.osf. Reviewreadingtopics one.osf.one.osf ExpectedValueofOLSEstimators - Omittedvariablebias one.osf.two.osf VarianceofOLSEstimators - Multicollinearity two.osf. In-classactivity:Practicewithregressionproperties two.osf/two.osfsix.osf
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ExpectedValueofOLSEstimators three.osf/two.osfsix.osf
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Assumptions - Aswithsimpleregression,haveassumptionsunderwhichOLSisunbiased - Similartosimpleregression,butsomeslightdifferences: one.osf. LinearinParameters two.osf. RandomSampling three.osf. NoPerfectCollinearity four.osf. E ( u | x one.osf , . . . , x k )= zero.osf four.osf/two.osfsix.osf
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one.osf.LinearinParameters;two.osf.RandomSampling - Weassumethatthemodelinthepopulationcanbewrittenas y = β zero.osf + β one.osf x one.osf + β two.osf x two.osf + ... + β k x k + u wherethe β j ’sarethepopulationparametersand u istheunobservederror - Recallthatwecanapplynonlinearfunctionstoanyofthevariables - Linear-in-parametersassumptionisnotsolimiting - Randomsamplingisanassumptionmadeaboutthedatacollectionprocess five.osf/two.osfsix.osf
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three.osf.NoPerfectCollinearity - Whatiscollinearity? - Inthesample(andpopulation), noneofthe x ’scanbeconstant - Noneofthe x ’scanbeexact linear relationshipsofanyother x ’s - Thisisthemulti-dimensionalanalogof“ var ( x ) > zero.osf” - e.g.if x one.osf isanexactlinearfunctionof x two.osf and x three.osf inthesample: - wesaythemodelsuffersfrom perfectcollinearity six.osf/two.osfsix.osf
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Whatcausesperfectcollinearity? - numbersign.osfone.osfcause:usererror(specifymodelthathasperfectlycollinearvariables) - Othercause:badluckindrawingthesample - Also:need N K + one.osf( N issamplesize, K isnumbersign.osfofslope β ’s) - Howtofixperfectcollinearityproblem? - Excludeoneoftheoffendingvariables - e.g.if x one.osf and x two.osf areperfectlycollinear,droponeofthem - Rwillusuallydothisforyou seven.osf/two.osfsix.osf
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Correlationamongthe x ’s - “NoPerfectCollinearity”does not meanthe x ’shavetobeuncorrelated - inthepopulationorthesample - Nordoesitsaytheycannotbe“highly”correlated - Itsimplyrulesout corr ( x one.osf , x two.osf )= ± one.osf -
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