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1、Leaf-Mass&LeavesClassificationFebruary14,2012AbstractInthispaper,wepresentastatisticalmodeltoestimatetheleafmassandclassifyvariousleafshapesbasedonthedataobtainedthroughtreeharvestandleafremovalof21urbantrees.Wefirstexplainthediversificationofleafshapesanddescribetherelationshipbetweenleafshape
2、sandtreeprofileinordertodefinethecorrelationbetweentreeprofileandleafshapes.Inordertoestimateleafmass,weapplytheregressionanalysiswithfourobservedindependentvariables,whichallowsustoestimatetheleaf-massofawhole-tree.Inordertoclassifyleaves,weusehierarchicalclusteringmethodaccordingtothedryleaf-
3、massbyWard'sMethod.InthismethodweusethestandardEuclideandistanceasourprincipleofclassification.Finallyweobtainaregressionmodelwithvaryhighcoefficientofdeterminationandagoodwaytoclassifyleaves.ForofficeuseonlyTeamControlNumberForofficeuseonlyT1________________T2________________T3________________
4、T4________________ ProblemChosenAF1________________F2________________F3________________F4________________2012MathematicalContestinModeling(MCM)SummarySheet(Attachacopyofthispagetoeachcopyofyoursolutionpaper.)Typeasummaryofyourresultsonthispage.Donotincludethenameofyourschool,advisor,orteammembe
5、rsonthispage.DearEditors,Byoperatingandanalyzingtheexperimentaldata,wehavesetupanoptimizedregressionmodeltoestimateleafmass,andhaveclassifiedleavesintoseveralspecificgroupsdependingonareasonablecriterion.Moreimportantly,wehavenoticedsomereasonableresults.Tobeginwith,aclassicregressionmodeliscit
6、edtouncovertheambiguousrelationshipbetweentreeformsandleafshapes.Asamatteroffact,theleafshapesarenegativelycorrelatedtothetreeforms,andtheresultenablestoexposethetruthwhynarrowerleavesonlower-crowntreesarecomparativelyprolific.Moreover,comparedwithotherregressionmodels,anoptimalregressionmodele
7、stimatingleafmasswasproposed.Underthespecificsignificancelevel,treemassiscloselyrelevanttosometreecharacteristicsincludingcrownheight(m),crownradius(m)andleafmassperareaofcrownprojection().Therefore,iftheseparametersaremeasured,th
