03slides.pdf - The Simple Linear Regression Model Tyler...

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TheSimpleLinearRegressionModel TylerRansom UnivofOklahoma Jantwo.osftwo.osf,two.osfzero.osfone.osfnine.osf one.osf/two.osfthree.osf
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Today’splan one.osf. Reviewreadingtopics one.osf.one.osf DefinitionoftheSimpleRegressionModel one.osf.two.osf DerivingtheOrdinaryLeastSquaresEstimates one.osf.three.osf PropertiesofOLSonanySampleofData two.osf. In-classactivity:HypothesistestingandbasicregressionsinR two.osf/two.osfthree.osf
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TheSimpleRegressionModel three.osf/two.osfthree.osf
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Background - Supposetherearetwovariables, x and y ,andwewouldliketo“studyhow y varieswithchangesin x .” - Threeissues: one.osf. Howdoweallow factorsotherthan x toaffect y ?Thereisneveranexact relationshipbetweentwovariables(ininterestingcases). two.osf. Whatisthe functionalrelationship between y and x ? three.osf. Howcanwebesurewearecapturinga ceterisparibus relationship between y and x (asissooftenthegoal)? four.osf/two.osfthree.osf
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TheSimpleRegressionModel(SLR) - Considerthefollowingequationrelating y to x : y = β zero.osf + β one.osf x + u , whichisassumedtoholdinthepopulationofinterest. - Thisequationdefinesthe simplelinearregressionmodel (orbivariate regressionmodel). - “regression”comesfromthe“regression-to-the-mean”phenomenon. - Wewanttoexplain y intermsof x . - Fromacausalitystandpoint,itmakesnosenseto“explain”pasteducational attainmentintermsoffuturelaborearnings. five.osf/two.osfthree.osf
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Terminology y x DependentVariable IndependentVar. ExplainedVar. ExplanatoryVar. ResponseVar. ControlVar. PredictedVar. PredictorVar. Regressand Regressor OutcomeVar. Covariate six.osf/two.osfthree.osf
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Backtoourthreeissues RecalltheSLRmodelfrombefore: y = β zero.osf + β one.osf x + u , one.osf. u encompassesthe“ otherfactors ”discussedpreviously two.osf. y isassumedtobe linearly relatedto x .Wecall β zero.osf the interceptparameter and β one.osf the
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