第六讲 多元回归分析深入专题ppt课件.pptVIP

1 MultipleRegressionAnalysis FurtherIssues y b0 b1x1 b2x2 bkxk u 2 Copyright 2007ThomsonAsiaPte Ltd Allrightsreserved 6 1数据的测度单位对OLS统计量的影响 Changingthescaleoftheyvariablewillleadtoacorrespondingchangeinthescaleofthecoefficientsandstandarderrors sonochangeinthesignificanceorinterpretationChangingthescaleofonexvariablewillleadtoachangeinthescaleofthatcoefficientandstandarderror sonochangeinthesignificanceorinterpretation 3 Copyright 2007ThomsonAsiaPte Ltd Allrightsreserved 4 Copyright 2007ThomsonAsiaPte Ltd Allrightsreserved 5 Copyright 2007ThomsonAsiaPte Ltd Allrightsreserved 6 Copyright 2007ThomsonAsiaPte Ltd Allrightsreserved 7 Copyright 2007ThomsonAsiaPte Ltd Allrightsreserved 因变量或自变量以对数形式出现 改变度量单位不会影响斜率系数 只会改变截距项 8 Copyright 2007ThomsonAsiaPte Ltd Allrightsreserved BetaCoefficients Occasionalyou llseereferencetoa standardizedcoefficient or betacoefficient whichhasaspecificmeaningIdeaistoreplaceyandeachxvariablewithastandardizedversion i e subtractmeananddividebystandarddeviationCoefficientreflectsstandarddeviationofyforaonestandarddeviationchangeinx 9 Copyright 2007ThomsonAsiaPte Ltd Allrightsreserved 10 Copyright 2007ThomsonAsiaPte Ltd Allrightsreserved BetaCoefficients cont 11 Copyright 2007ThomsonAsiaPte Ltd Allrightsreserved Example6 1 EffectsofPollutiononHousingPrices 数据名 HPRICE2 Stata命令语句 regpricenoxcrimeroomsdiststradio beta 标准化后的回归分析 12 Copyright 2007ThomsonAsiaPte Ltd Allrightsreserved 6 2对函数形式的进一步讨论 OLScanbeusedforrelationshipsthatarenotstrictlylinearinxandybyusingnonlinearfunctionsofxandy willstillbelinearintheparametersCantakethenaturallogofx yorbothCanusequadraticformsofxCanuseinteractionsofxvariables 13 Copyright 2007ThomsonAsiaPte Ltd Allrightsreserved InterpretationofLogModels ln y b0 b1ln x ub1istheelasticityofywithrespecttoxln y b0 b1x ub1isapproximatelythepercentagechangeinygivena1unitchangeinxy b0 b1ln x ub1isapproximatelythechangeinyfora100percentchangeinx 14 Copyright 2007ThomsonAsiaPte Ltd Allrightsreserved Whyuselogmodels 1 使用自然对数使得对系数的解释颇具有吸引力 可以直接以弹性的形式体现出来 2 斜率系数不随测量单位的变化而变化 3 取对数后 即使不能消除异方差的影响 但可以使之有所缓解 4 取对数通常会缩小变量的取值范围 在某些情况下还相当可观 5 缺点 变量不能取零和负值 更难预测原变量的值 原模型使我们预测log y 而不是y 15 Copyright 2007ThomsonAsiaPte Ltd Allrightsreserved QuadraticModels 二次式模型 Foramodeloftheformy b0 b1x b2x2 uwecan tinterpretb1aloneasmeasuringthechangeinywithrespecttox weneedtotakeintoaccountb2aswell since 16 Copyright 2007ThomsonAsiaPte Ltd Allrightsreserved MoreonQuadraticModels Supposethatthecoefficientonxispositiveandthecoefficientonx2isnegativeThenyisincreasinginxatfirst butwilleventuallyturnaroundandbedecreasinginx 17 Copyright 2007ThomsonAsiaPte Ltd Allrightsreserved MoreonQuadraticModels Supposethatthecoefficientonxisnegativeandthecoefficientonx2ispositiveThenyisdecreasinginxatfirst butwilleventuallyturnaroundandbeincreasinginx 18 Copyright 2007ThomsonAsiaPte Ltd Allrightsreserved Howtodescribedecreasingeffect 19 Copyright 2007ThomsonAsiaPte Ltd Allrightsreserved Howtodescribeincreasingeffect 20 Copyright 2007ThomsonAsiaPte Ltd Allrightsreserved 二次项模型案例 污染对住房价格的影响 数据名 HPRICE2 0 57 0 115 0 043 0 165 0 013 0 006 N 506 R2 0 603 在room 0 545 2 0 062 4 4的右边 增加一个卧室对价格的百分比变化具有递增的影响 21 Copyright 2007ThomsonAsiaPte Ltd Allrightsreserved 比如 rooms从5增加到6会导致价格提高约为 54 5 12 4 5 7 5 rooms从6增加到7会导致价格提高约为 54 5 12 4 6 19 9 这是一个很强的递增影响 STATA命令语句 genrooms2 rooms roomsgenldist log dist reglpricelnoxldistroomsrooms2stratiodisplay 1 b rooms 2 b rooms2 求转折点 display100 b rooms 2 b rooms2 6 求rooms从6增加到7会导致价格提高的百分比 22 Copyright 2007ThomsonAsiaPte Ltd Allrightsreserved InteractionTerms 有交互作用项的模型 Foramodeloftheformy b0 b1x1 b2x2 b3x1x2 uwecan tinterpretb1aloneasmeasuringthechangeinywithrespecttox1 weneedtotakeintoaccountb3aswell since 23 Copyright 2007ThomsonAsiaPte Ltd Allrightsreserved 交互效应通常需将模型重新参数化 原模型 是x2 0时 X2对y的偏效应 这通常没有什么意义 我们转而将模型重新参数化为 其中 和分别是x1和x2的总体均值 很容易计算出 我们立即得到在均值的偏效应 24 Copyright 2007ThomsonAsiaPte Ltd Allrightsreserved Example EffectsofAttendanceonFinalExamPerformance 数据名 ATTEND DTA atndrte系数为负 是否意味着听课对期末考试分数具有负面影响 b1仅考虑了priGPA 0时的影响 atndrte和priGPA atndrte系数估计值t值不显著 是否意味着两者对期末考试分数无影响 F检验的p值为0 014 25 Copyright 2007ThomsonAsiaPte Ltd Allrightsreserved Atndrte对stndfnl的偏效应 其含义是 在priGPA的平均水平 2 59 上 atndrte提高10个百分点 使stndfnl比期末考试平均分数高出0 078倍 26 Copyright 2007ThomsonAsiaPte Ltd Allrightsreserved STATA命令语句 sumpriGPAgenpriGPA2 priGPA priGPAgenACT2 ACT ACTgenpriatn priGPA atndrteregstndfnlatndrtepriGPApriGPA2ACT2priatn 27 Copyright 2007ThomsonAsiaPte Ltd Allrightsreserved 6 3拟合优度和回归元选择的进一步探讨 RecallthattheR2willalwaysincreaseasmorevariablesareaddedtothemodelTheadjustedR2takesintoaccountthenumberofvariablesinamodel andmaydecrease 28 Copyright 2007ThomsonAsiaPte Ltd Allrightsreserved 调整R方的作用 为在一个模型中另外增加自变量施加了惩罚 随着一个新的自变量加入回归方程 SSR下降 但回归中的自由度df n k 1也下降 因此 SSR n k 1 可能上升 也可能下降 作为一个结论有 在回归中增加一个新变量 当且仅当新变量的t统计量在绝对值上大于1 调整R方才会有所提高 在回归中增加一组变量时 当且仅当这组新变量联合显著性的F统计量大于1 调整R方才会有所提高 29 Copyright 2007ThomsonAsiaPte Ltd Allrightsreserved AdjustedR Squared cont It seasytoseethattheadjustedR2isjust 1 R2 n 1 n k 1 butmostpackageswillgiveyoubothR2andadj R2Youcancomparethefitof2models withthesamey bycomparingtheadj R2Youcannotusetheadj R2tocomparemodelswithdifferenty s e g yvs ln y 30 Copyright 2007ThomsonAsiaPte Ltd Allrightsreserved UsingadjustedR squaredtochoosebetweennonnestedmodels 31 Copyright 2007ThomsonAsiaPte Ltd Allrightsreserved 32 Copyright 2007ThomsonAsiaPte Ltd Allrightsreserved Controllingtoomanyfactorsinregressionanalysis 回归分析中控制了过多的因素 Importantnottofixatetoomuchonadj R2andlosesightoftheoryandcommonsenseIfeconomictheoryclearlypredictsavariablebelongs generallyleaveitinDon twanttoincludeavariablethatprohibitsasensibleinterpretationofthevariableofinterest rememberceterisparibusinterpretationofmultipleregression 33 Copyright 2007ThomsonAsiaPte Ltd Allrightsreserved 在研究啤酒税对交通死亡率影响的回归模型中 是否应该将人均啤酒消费量变量包括在模型之中 在保持beercons不变的情况下 死亡率因tax提高1个百分点而导致的差异 这一说法是否有意义 34 Copyright 2007ThomsonAsiaPte Ltd Allrightsreserved Addingregressorstoreducetheerrorofvariance 增加回归元以减少误差方差 在回归中增加一个新的自变量会加剧多重共线性问题 另一方面 从误差项中取出一些因素作为解释变量可以减少误差方差 应该将那些影响y而又与所有我们关心的自变量都无关的自变量包括进来 35 Copyright 2007ThomsonAsiaPte Ltd Allrightsreserved 6 4预测和残差分析 Supposewewanttouseourestimatestoobtainaspecificprediction First supposethatwewantanestimateofE y x1 c1 xk ck q0 b0 b1c1 bkckThisiseasytoobtainbysubstitutingthex sinourestimatedmodelwithc s butwhataboutastandarderror Reallyjustatestofalinearcombination 36 Copyright 2007ThomsonAsiaPte Ltd Allrightsreserved Predictions cont Canrewriteasb0 q0 b1c1 bkckSubstituteintoobtainy q0 b1 x1 c1 bk xk ck uSo ifyouregressyion xij cij theinterceptwillgivethepredictedvalueanditsstandarderrorNotethatthestandarderrorwillbesmallestwhenthec sequalthemeansofthex s 37 Copyright 2007ThomsonAsiaPte Ltd Allrightsreserved Example CIforpredictedcollegeGPA 38 Copyright 2007ThomsonAsiaPte Ltd Allrightsreserved Predictions cont ThisstandarderrorfortheexpectedvalueisnotthesameasastandarderrorforannewoutcomeonyWeneedtoalsotakeintoaccountthevarianceintheunobservederror 39 Copyright 2007ThomsonAsiaPte Ltd Allrightsreserved 40 Copyright 2007ThomsonAsiaPte Ltd Allrightsreserved 41 Copyright 2007ThomsonAsiaPte Ltd Allrightsreserved 42 Copyright 2007ThomsonAsiaPte Ltd Allrightsreserved Predictioninterval Usuallytheestimateofs2ismuchlargerthanthevarianceoftheprediction thusThispredictionintervalwillbealotwiderthanthesimpleconfidenceintervalfortheprediction 43 Copyright 2007ThomsonAsiaPte Ltd Allrightsreserved ResidualAnalysis Informationcanbeobtainedfromlookingattheresiduals i e predictedvs observed Example Regresspriceofcarsoncharacteristics bignegativeresidualsindicateagooddealExample Regressaverageearningsforstudentsfromaschoolonstudentcharacteristics bigpositiveresidualsindicategreatestvalue added 44 Copyright 2007ThomsonAsiaPte Ltd Allrightsreserved 例如 HPRICE1 RAW的