the r book regression

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1、10RegressionRegressionanalysisisthestatisticalmethodyouusewhenboththeresponsevariableandtheexplanatoryvariablearecontinuousvariables(i.e.realnumberswithdecimalplaces–thingslikeheights,weights,volumes,ortemperatures).Perhapstheeasiestwayofknowingwhenregressionistheappropriateanalysisistoseeth

2、atascatterplotistheappropriategraphic(incontrasttoanalysisofvariance,say,whereitwouldhavebeenabox-and-whiskerplotorabarchart).Wecoversevenimportantkindsofregressionanalysisinthisbook:
linearregression(thesimplest,andmuchthemostfrequentlyused);
polynomialregression(oftenusedtotestfornon-linea

3、rityinarelationship);
piecewiseregression(twoormoreadjacentstraightlines);
robustregression(modelsthatarelesssensitivetooutliers);
multipleregression(wheretherearenumerousexplanatoryvariables);
non-linearregression(to?taspeci?ednon-linearmodeltodata);
non-parametricregression(usedwhenthereis

4、noobviousfunctionalform).The?rst?vecasesarecoveredhere,non-linearregressioninChapter20andnon-parametricregressioninChapter18(wherewedealwithgeneralizedadditivemodelsandnon-parametricsmoothing).Theessenceofregressionanalysisisusingsampledatatoestimateparametervaluesandtheirstandarderrors.Firs

5、t,however,weneedtoselectamodelwhichdescribestherelationshipbetweentheresponsevariableandtheexplanatoryvariable(s).Thesimplestofallisthelinearmodely=a+bx.Therearetwovariablesandtwoparameters.Theresponsevariableisy,andxisasinglecontinuousexplanatoryvariable.Theparametersareaandb:theinterceptis

6、a(thevalueofywhenx=0);andtheslopeisb(thechangeinydividedbythechangeinxwhichbroughtitabout).TheRBook,SecondEdition.MichaelJ.Crawley.?2013JohnWiley&Sons,Ltd.Published2013byJohnWiley&Sons,Ltd.450THERBOOK10.1LinearregressionLetusstartwithanexamplewhichshowsthegrowthofcaterpillarsfedonexperimenta

7、ldietsdifferingintheirtannincontent:reg.data<-read.table("c:\temp\regression.txt",header=T)attach(reg.data)names(reg.data)[1]"growth""tannin"plot(tannin,growth,pch=21,col="blue",bg="red")12102468growth02468tanninThehigherthepercentageoftannininth