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1、多元数据分析刘国庆Question?Howtodetermineafairmarketvaluefortheproperty?Inbuildingthemodel,thegoalistopredictthemarketvalueoftheLeslieSaltproperty,usingtheinformationavailable.DataLeslieSaltData.txtRegressionAnalysisItisusedtoexploretherelationshipbetweenasetofindependentvariables(X’s)
2、andasingledependentvariable(Y).Aregressionmodelisalinearcombinationofindependentvariablesthatcorrespondsaspossibletothedependentvariable.RegressionforansweringquestionsHowcanwedescribetherelationshipbetweenthedependentvariableandtheindependentvariables?Istherelationshipdescrib
3、edbythemodelstatisticallysignificant?Whichindependentvariablesaremostimportant?Howwelldoesthemodelgeneralizetoobservationsoutsidethesample?资料预处理大多数的销售价格低于$10,000,但是有一些价格甚至高于$20,000or$30,000每亩；一般地，这种价值的差别会带来问题。为此，采用log函数。一些特殊的点需要排除VariablesDescriptionVariables.txtCorrelationMat
4、rixCorrMatData.txt分析从表3中可以看出与log(Price)高度关联的变量是Elevation,Sewer,Date,Flood.从表格中我们也可以看到在独立的变量之间也存在着相关性。比如，Elevation,County.回归模型ResultsofRegressionResultsRegress.txtHowgoodistheFit?HowgoodistheFit(continueI)OneofthedrawbacksofR^2isthatwheneveranindependentvariableisaddedtothemode
5、litalwaysincreases,nomatterhowsmallthecontributioninfit.Ingeneral,whenbuildingmodels,onewantstomakeatrade-offbetweenparsimonyandimprovementinfit.HowgoodistheFit(continueII)IsitSignificant?Testtheerrortermsarenormallydistributed;thatisTestingthemodelF-TestFTest.txtThecriticalva
6、luefortheF-distributionatthe0.01levelisF(4,26)=4.14,whichsuggeststhatourmodelishighlysignificant.DetectingproblemswiththemodelOnemeasureofmulticollinearityiscalledtheconditionindex(CI)Heteroscedasticity(异方差性)Wehaveassumedthattheerrortermsallhavethesamevariance.Thisassumptionis
7、sometimescalledhomoscedasticity.Whentheassumptionisviolated(i.e.,thevariancesarenotallthesame),wehavewhatiscalledheteroscedasticity.Weightedleastsquares(WLS)InfluentialObservationsSometimesregressionmodelresultscanbeinordinatelyinfluencedbyoneorafewobservationsinthedata.Thisty
8、peofobservationasanoutlier.DFBETAsWecanlookattheimpactoftheob
