管理经济学托马斯版Chap004ppt课件.ppt

Chapter4 BasicEstimationTechniques McGraw Hill Irwin Copyright 2011bytheMcGraw HillCompanies Inc Allrightsreserved BasicEstimation ParametersThecoefficientsinanequationthatdeterminetheexactmathematicalrelationamongthevariablesParameterestimationTheprocessoffindingestimatesofthenumericalvaluesoftheparametersofanequation RegressionAnalysis RegressionanalysisAstatisticaltechniqueforestimatingtheparametersofanequationandtestingforstatisticalsignificance Interceptparameter a givesvalueofYwhereregressionlinecrossesY axis valueofYwhenXiszero Slopeparameter b givesthechangeinYassociatedwithaone unitchangeinX SimpleLinearRegression SimplelinearregressionmodelrelatesdependentvariableYtooneindependent orexplanatory variableX SimpleLinearRegression Parameterestimatesareobtainedbychoosingvaluesofa bthatminimizethesumofsquaredresidualsTheresidualisthedifferencebetweentheactualandfittedvaluesofY Yi iThesampleregressionlineisanestimateofthetrueregressionline SampleRegressionLine Figure4 2 A 0 8 000 2 000 10 000 4 000 6 000 10 000 20 000 30 000 40 000 50 000 60 000 70 000 Advertisingexpenditures dollars Sales dollars S Sampleregressionline i 11 573 4 9719A UnbiasedEstimators Thedistributionofvaluestheestimatesmighttakeiscenteredaroundthetruevalueoftheparameter Theestimates donotgenerallyequalthetruevaluesofa b arerandomvariablescomputedusingdatafromarandomsample UnbiasedEstimators Anestimatorisunbiasedifitsaveragevalue orexpectedvalue isequaltothetruevalueoftheparameter RelativeFrequencyDistribution Figure4 3 Alsocalledaprobabilitydensityfunction pdf 0 8 2 10 4 6 1 1 3 5 7 9 StatisticalSignificance MustdetermineifthereissufficientstatisticalevidencetoindicatethatYistrulyrelatedtoX i e b 0 Evenifb 0 itispossiblethatthesamplewillproduceanestimatethatisdifferentfromzero Testforstatisticalsignificanceusingt testsorp values Performingat Test FirstdeterminethelevelofsignificanceProbabilityoffindingaparameterestimatetobestatisticallydifferentfromzerowhen infact itiszeroProbabilityofaTypeIError1 levelofsignificance levelofconfidence Performingat Test Uset tabletochoosecriticalt valuewithn kdegreesoffreedomforthechosenlevelofsignificancen numberofobservationsk numberofparametersestimated t ratioiscomputedas Performingat Test Iftheabsolutevalueoft ratioisgreaterthanthecriticalt theparameterestimateisstatisticallysignificantatthegivenlevelofsignificance Usingp Values Treatasstatisticallysignificantonlythoseparameterestimateswithp valuessmallerthanthemaximumacceptablesignificancelevelp valuegivesexactlevelofsignificanceAlsotheprobabilityoffindingsignificancewhennoneexists CoefficientofDetermination R2measuresthepercentageoftotalvariationinthedependentvariable Y thatisexplainedbytheregressionequationRangesfrom0to1HighR2indicatesYandXarehighlycorrelated F Test UsedtotestforsignificanceofoverallregressionequationCompareF statistictocriticalF valuefromF tableTwodegreesoffreedom n k k 1Levelofsignificance F Test IfF statisticexceedsthecriticalF theregressionequationoverallisstatisticallysignificantatthespecifiedlevelofsignificance MultipleRegression UsesmorethanoneexplanatoryvariableCoefficientforeachexplanatoryvariablemeasuresthechangeinthedependentvariableassociatedwithaone unitchangeinthatexplanatoryvariable allelseconstant QuadraticRegressionModels UsewhencurvefittingscatterplotisU shapedor shapedY a bX cX2Forlineartransformationcomputenewvari