AppliedEconometricsILecture2TheSimpleRegressionModelJi_MianzhouSCUTSpring2012SimpleRegressionModelSimpleregressionmodel:“explainonefactor(y)intermsofanotherfactor(x)”,y=f(x).Morespecifically,wehavefunction:y=β0+β1x+uCallsimplelinearregressionmodel,ortwo-variablelinearregressionmodel,orbivariatelinearregressionmodel.AppliedEconometricsIlecture22SomeTerminologyInthesimplelinearregressionmodelofyonx,wetypicallyrefertoyastheDependentVariable,orExplainedVariable,orResponseVariableInthesimplelinearregressionofyonx,wetypicallyrefertoxastheIndependentVariable,orExplanatoryVariable,orControlVariables3AppliedEconometricsIlecture2SomeTerminology,cont.Inthesimplelinearregressionofyonx,wetypicallyrefertouastheerrortermordisturbance.errortermrepresentsallfactorsaffectingyotherthanxasbeingunobserved.β0isinterceptparameter;β1isslopeparameter.4AppliedEconometricsIlecture2E2.1SoybeanyieldandfertilizerTheagriculturalresearcherisinterestedintheeffectoffertilizeronyield,sowesupposethatsoybeanyieldisdeterminedbythemodelyield=β0+β1fertilizer+uyieldisdependentvariable,fertilizerisindependentvariable.errortermucontainsfactorsuchaslandquality,rainfall,andsoon.β1measurestheeffectoffertilizeronyield,holdingotherfactorfixed.AppliedEconometricsIlecture25E2.2AsimplewageequationAmodelrelatingaperson’swagetoobservededucationandotherunobservedfactorsiswage=β0+β1educ+uerrortermuincludelaborforceexperience,innateability,tenurewithcurrentemployer,andotherthingsβ1measuresthechangeinhourlywagegivenanotheryearofeducation,holdingallotherfactorsfixed.AppliedEconometricsIlecture26ASimpleAssumptionTheaveragevalueofu,theerrorterm,inthepopulationis0.Thatis,E(u)=0Thisisnotarestrictiveassumption,sincewecanalwaysuseβ0tonormalizeE(u)to0.Todrawceterisparibusconclusionsabouthowxaffectsy,Weneedtomakeacrucialassumptionabouthowuandxarerelated.7AppliedEconometricsIlecture2ZeroConditionalMeanWewantittobetheca