多元回归分析：深入专题.ppt

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1、1Copyright©2007ThomsonAsiaPte.Ltd.Allrightsreserved.MultipleRegressionAnalysis:FurtherIssuesy=b0+b1x1+b2x2+...bkxk+u2Copyright©2007ThomsonAsiaPte.Ltd.Allrightsreserved.6.1数据的测度单位对OLS统计量的影响Changingthescaleoftheyvariablewillleadtoacorrespondingchangeinthescale

2、ofthecoefficientsandstandarderrors,sonochangeinthesignificanceorinterpretationChangingthescaleofonexvariablewillleadtoachangeinthescaleofthatcoefficientandstandarderror,sonochangeinthesignificanceorinterpretation3Copyright©2007ThomsonAsiaPte.Ltd.Allrightsres

3、erved.4Copyright©2007ThomsonAsiaPte.Ltd.Allrightsreserved.5Copyright©2007ThomsonAsiaPte.Ltd.Allrightsreserved.6Copyright©2007ThomsonAsiaPte.Ltd.Allrightsreserved.7Copyright©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。8Copyr

4、ight©2007ThomsonAsiaPte.Ltd.Allrightsreserved.BetaCoefficientsOccasionalyou’llseereferencetoa“standardizedcoefficient”or“betacoefficient”whichhasaspecificmeaningIdeaistoreplaceyandeachxvariablewithastandardizedversion–i.e.subtractmeananddividebystandarddevia

5、tionCoefficientreflectsstandarddeviationofyforaonestandarddeviationchangeinx9Copyright©2007ThomsonAsiaPte.Ltd.Allrightsreserved.10Copyright©2007ThomsonAsiaPte.Ltd.Allrightsreserved.BetaCoefficients(cont)11Copyright©2007ThomsonAsiaPte.Ltd.Allrightsreserved.Ex

6、ample6.1:EffectsofPollutiononHousingPrices（数据名：HPRICE2）Stata命令语句：regpricenoxcrimeroomsdiststradio,beta(标准化后的回归分析)12Copyright©2007ThomsonAsiaPte.Ltd.Allrightsreserved.6.2对函数形式的进一步讨论OLScanbeusedforrelationshipsthatarenotstrictlylinearinxandybyusingnonlinearfun

7、ctionsofxandy–willstillbelinearintheparametersCantakethenaturallogofx,yorbothCanusequadraticformsofxCanuseinteractionsofxvariables13Copyright©2007ThomsonAsiaPte.Ltd.Allrightsreserved.InterpretationofLogModelsln(y)=b0+b1ln(x)+ub1istheelasticityofywithrespectt

8、oxln(y)=b0+b1x+ub1isapproximatelythepercentagechangeinygivena1unitchangeinxy=b0+b1ln(x)+ub1isapproximatelythechangeinyfora100percentchangeinx14Copyright©2007ThomsonAsiaPte.Ltd.Allrightsreserved.