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1、6LinearRegressionAnalysisIntheVisualizationtechniquesforcontinuousvariabledatasectionofChapter3,DataVisualization,wehaveseendifferentdatavisualizationtechniqueswhichhelpinunderstandingthedatavariables(boxplotsandhistograms)andtheirinterrelationships(ma
2、trixofscatterplots).WehadseeninExample4.6.1.ResistantlinefortheIO-CPUtimeanillustrationoftheresistantline,whereCPU_TimedependslinearlyontheNo_of_IOvariable.Thepairfunction'soutputinExample3.2.9.Octaneratingofgasolineblendsindicatedthatthemileageofacarh
3、asstrongcorrelationswiththeengine-relatedcharacteristics,suchasdisplacement,horsepower,torque,thenumberoftransmissionspeeds,andthetypeoftransmissionbeingmanualorautomatic.Further,themileageofacaralsostronglydependsonthevehicledimensions,suchasitslength
4、,width,andweight.Thequestionaddressedinthischapterismeanttofurthertheseinitialfindingsthroughamoreappropriatemodel.Now,wetakethenextstepforwardandbuildlinearregressionmodelsfortheproblems.Thus,inthischapterwewillprovidemoreconcreteanswersforthemileagep
5、roblem.LinearRegressionAnalysisThefirstlinearregressionmodelwasbuiltbySirFrancisGaltonin1908.Thewordregressionimpliestowards-the-center.Thecovariates,alsoknownasindependentvariables,features,orregressors,havearegressiveeffectontheoutput,alsocalleddepen
6、dentorregressandvariable.Sincethecovariatesareallowed,actuallyassumed,toaffecttheoutputinlinearincrements,wecallthemodelthelinearregressionmodel.Thelinearregressionmodelsprovideananswerforthecorrelationbetweentheregressandandtheregressors,andassuchdono
7、treallyestablishcausation.Asitwillbeseenlaterinthechapter,usingdata,wewillbeabletounderstandthemileageofacarasalinearfunctionofthecar-relateddynamics.Fromapurescientificpointofview,themileageshouldreallydependoncomplicatedformulasofthecar'sspeed,roadco
8、nditions,theclimate,andsoon.However,itwillbeseenthatlinearmodelsworkjustfinefortheproblemdespitenotreallygoingintothetechnicaldetails.However,therewillalsobeapricetopay,inthesensethatmostregressionmodelsworkwellwhentherangeofthevariable
