BroilerGrowthPerformanceAnalysis:fromCorrelationAnalysis,MultipleLinearRegression,toNeuralNetworkMeiyanXiao,PeijieHuang*,PiyuanLin,ShangweiYanCollegeofInformaticsSouthChinaAgriculturalUniversityGuangzhou,China*CorrespondingAuthor:AbstractThepurposeofthisstudyistoinvestigatethedataWeusethebroilergrowthdatasetofthemostfamousfittingforbroilergrowthperformanceparameters.Inthispaper,poultryraisingcompanyinChinatoevaluateourapproachandthegradualadvancinganalysismethods,fromcorrelationtheresultsshowtheeffectivenessofourapproach.analysis,multiplelinearregression,toneuralnetwork,areproposed.Themeantechnologyroadmapis:firstly,correlationTherestofthispaperisorganizedasfollows.Inthenextanalysisisusedtodetectthedegreeofcorrelationbetweenthesection,wepresentthegradualadvancinganalysismethods.broilergrowthperformanceparameterandthecandidateinputExperimentsarepresentedanddiscussedinSection3.Finally,variables.AndthenchoosethepredictorvariablesthathavegoodSection4listssomeconclusions.correlationwiththedependentvariabletobuildthemultiplelinearregressionorneuralnetworkpredictionmodel,orboth,II.GRADUALADVANCINGANALYSISMETHODSaccordingtothelineardegreeofcorrelations.CombinedpredictionmaybechoseoncebothmodelshavegoodpredictionTheexploremethodsinourstudyofdatafittingforbroilerperformances.Weusethebroilergrowthdatasetofthemostgrowthperformanceparametersisdevelopedstepbystep,fromfamouspoultryraisingcompanyinChinatoevaluateourcorrelationanalysistoMLR,andthentononlinearfittingapproachandtheresultsshowtheeffectivenessofourapproach.meansbyneuralnetwork.Keywords-growthperformance；correlationanalysis；multipleA.TechnologyRoadmaplinearregression；neuralnetwork；broilerbreedingThetechnologyroadmapofourgradualadvancinganalysismethodsisshowninFig.1.I.INTRODUCTIONBioinformatics1isapromisingyoungfieldthatappliescomputertechnologyinbiologyanddevelopsalgorithmsandmethodstomanageandanalyzebiologicaldata2.Forthemodernpoultrybreedingcompanies,itisdeservedtopredictthepoultrygrowthperformanceparameters,suchasrateforsale,feedintake,dailygainandfeedconversionratio,basedonthemassivehistoricaldatagraduallycumulatedinproduction.However,becauseofthecomplexityanduncertaintybringbytheinfluenceofenvironmentalandphysiologicalfactors,informationintegrationofbiologicaldataisachallenge.Inthispaper,thegradualadvancinganalysismethods,fromcorrelationanalysis,multiplelinearregression(MLR)3,toneuralnetwork4,areproposedtostudythedatafittingforbroilergrowthperformanceparameters.Inbroilerbreeding,seasonalfactorplaysanimportantpart.Ontheeffectofseasonalfactors,broilergrowthperformanceFigure1.Technologyroadmapoftheproposedmethodscanbeobviouslydifferent.SobroilergrowthperformanceTheassociationbetweenvariablescanbelinearorparametershaveobviousseasonalvariation.Seasonalfactorsnonlinear.Correlationanalysisismostlyusedtoevaluatelinearincludeairtemperature,precipitation,windspeed,pressure,relationships.Associationsbetweentwovariablescanberelativehumidity,etc.Thispapertakestheinfluenceoftheairanalyzedwithabivariatecorrelationanalysis.Whiletemperaturetotherateforsaleforexampletointroducetheassociationsbetweenone(dependent)variableandasetoftwobroilergrowthperformanceanalysismethods.ormore(independent)variables,whichhavestrongThisworkissupportedbytheSci&TechResearchProjectofGuangdongProvinceunderGrantNo.2007A020300010,theNational863High-TechResearch&DevelopmentPlanofChinaunderGrantNo.2006AA10Z246，andtheNewDisciplineSupportingFundofSouthChinaAgriculturalUniversityunderGrantNo.2007X022.NotlinearenoughDependentvariableIndependentvariablesCorrelationAnalysisComparisonCombinedpredictionwhenbothhavegoodpredictresponsesMultipleLinearRegressionNeuralNetworkStronglinercorrelation978-1-4244-4713-8/10/$25.002010IEEEcorrelationswiththedependentvariable,canbestudiedusingmultiplecorrelation(regression)analysis,suchasMLR.Alternatively,ifthedegreeofcorrelationsisnotlinearenoughbetweenthedependentvariableandtheindependentvariables,somenonlinearfittingsprovidegoodchoose.Inthenonlinearfittingmethods,comparingtoGompertzthatusingleastsquaresinnonlinearregression,neuralnetworkisprovedtohasgoodabilitytopredictresponses5.Finally,inpracticalapplication,ifbothMLRandneuralnetworkhavegoodpredictionperformances,wecanconsiderthecombinedprediction.B.CorrelationAnalysisAcorrelationanalysisisastatisticalprocedurethatevaluatestheassociationbetweenthedependentvariableandtheindependentvariablesrespectively.Thesimplestwaytofindoutqualitativelythecorrelationistoplotthedata.AndwecanquantifythedegreeofcorrelationbyspecifyingthecorrelationcoefficientR,definedasyyinixxiyxnR=111(1)wherexandxdenotethesamplemeanandthesamplestandarddeviationrespectivelyforthevariablexandyandydenotethesamplemeanandthesamplestandarddeviationrespectivelyforthevariabley.Assumethataperfectlinearrelationshipexistsbetweenthevariablesxandy,i.e.,baxyii+=fori=1,2,.,nwith0a.Nowverifyusingthedefinitionsofthemeanandthevariancethatbaxy+=andxya=.Thisimpliesfrom(1)thatR=a/|a|.Orinotherwords,R=1ifa0andR=-1ifa0.ThecaseR=1correspondstothemaximumpossiblelinearpositiveassociationbetweenxandy,meaningthatallthedatapointswilllieexactlyonastraightlineofpositiveslope.Similarly,R=-1correspondstothemaximumpossiblenegativeassociationbetweenthestatisticalvariablesxandy.Ingeneral,-1R1withthemagnitudeandthesignofRrepresentingthestrengthanddirectionrespectivelyoftheassociationbetweenthetwovariables.C.MultipleLinearRegressionOncewehaveestablishedthatastrongcorrelationexistsbetweenthedependentvariableandmorethanoneindependentvariable,wewilluseMLR.AlinearregressionmodelthatcontainsmorethanonepredictorvariableiscalledaMLRmodel.ThefollowingmodelisaMLRmodelwithtwopredictorvariables,1xand2xuxxy+=2210(2)Themodelislinearbecauseitislinearintheparameters,0,1and2.Themodeldescribesaplaneinthethreedimensionalspaceofy,1xand2x.Theparameter0istheinterceptofthisplane.Parameters1and2arereferredtoaspartialregressioncoefficients.Parameter1representsthechangeinthemeanresponsecorrespondingtoaunitchangein1xwhen2xisheldconstant.Parameter2representsthechangeinthemeanresponsecorrespondingtoaunitchangein2xwhen1xisheldconstant.uistherandomerror.D.NeuralNetworkNeuralnetwork4offeranalternativetoregressionanalysisforbiologicalmodeling.Inrelationtosystemmodeling,thedifferencebetweenartificialneuralnetworksandregressionanalysisisthatanequationisnotassumed,tighterfitsofdataarepossible,anditispossibletoworkwith“noisy”data.Verylittleresearchhasbeenconductedtomodelanimalgrowthusingartificialneuralnetworks5,6.Inourstudy,wechoosetheBack-Propagation(BP)neuralnetwork,whichisafeed-forwardmulti-layernetworkbasedontheBack-PropagationalgorithmdevelopedbyRumelhartandMcCelland7andhasbecomeoneofthemostwidelyusedneuralnetworkinpractice.TheActivationTransferFunction(ATF)ofaBPnetwork,usually,isadifferentiableSigmoid(S-shape)function,whichhelpstoapplynon-linearmappingfrominputstooutputs.Atwo-layerBPnetworkwasusedinourmodel.Thegoodnessoffitsfortheobtainedneuralnetworkmodelwascalculatedbymeansquareerror(MSE)andmeanpercentageerror(MPE).TheMPEandMSEarecomputedas=nttttyyynMPE11(3)nyyMSEnttt=12)(4)wheretyequalstheobservedvalueattimet,tyequalstheestimatedvalue,andnequalsthenumberofobservations.III.EXPERIMENTALRESULTSA.ExperimentSetupWetakethebreedingareaofGuangdongprovinceofChinaforexampletoevaluateourapproach.Thedatasetoften-daymeanairtemperatureisprovidedbyGuangdongProvincialClimateandAgrometeorologicalCente.AndthebroilergrowthdatasetisprovidedbyGuangdongWensFoodGroupLimitedCompany,whichisthemostfamouspoultryraisingcompanyinChina.Andwetakehenofshort-feetbuffBforexampletoevaluatetheinfluenceoftheairtemperaturetotherateforsale.Weselecthengrowthdataof2007,whichconsistsof5714data,andremain4209dataafterdatapreprocessing,whichistoeliminateabnormaldata,suchasabnormalrateforsale,nulldayage,andnullweight.FortheMLRandneuralnetworkmodels,weselect70%samplesrandomlyfortraining,andtherestfortesting.B.CorrelationAnalysisConsideringthatthefullgrowingstageofbroilercanbedividedintochicklingstage(thefirst4weeks)andadultchickenstage.Differentstageshavedifferentphysiologicalcharacteristic.So,inourstudy,firstly,weusescatterplotstoshowtherelationshipbetweentherateforsaleandtheten-daymeanairtemperatureofhen,chicklingstage,andadultchickenstagerespectively,whichareshowninFig.2toFig.4.Andthen,thedegreesofcorrelationsarequantifiedbycorrelationcoefficientR,whichisshowninTable1.0.920.930.940.950.960.970.9871217222732Ten-daymeanairtemperature()RateforsaleFigure2.Ten-daymeanairtemperatureofhenVSrateforsale0.940.950.960.970.9871217222732Ten-daymeanairtemperature()RateforsaleFigure3.Ten-daymeanairtemperatureofchicklingstageVSrateforsale0.940.950.960.970.9871217222732Ten-daymeanairtemperature()RateforsaleFigure4.Ten-daymeanairtemperatureofadultchickenstageVSrateforsaleTABLEI.CORRELATIONCOEFFICIENTCaseRTen-daymeanairtemperatureofhenandrateforsale0.8506Ten-daymeanairtemperatureofchicklingstageandrateforsale0.8932Ten-daymeanairtemperatureofadultchickenstageandrateforsale0.8594AswecanseefromTable1,correlationcoefficientRoftherateforsaleandtheten-daymeanairtemperatureofchicklingstageandadultchickenstageisbiggerthanthatoftherateforsaleandtheten-daymeanairtemperatureofhen,whichindicatesthedivisionofchicklingstageandadultchickenstagetodofurtherresearchisarightchoose.C.MultipleLinearRegressionThefollowingMLRequationisfitforthetrainingdata:21057.00755.0367.93xxy+=(5)whereyistherateforsale，and1xand2xaretheten-daymeanairtemperatureofchicklingstageandadultchickenstagerespectively.D.NeuralNetworkSimilartotheMLRmodel,weusetheten-daymeanairtemperatureofchicklingstageandadultchickenstageasinputs,andsettherateforsaleasoutput.Fig.5showstherealobservedvaluesandpredictedrateforsaleforbothMLRandneuralnetwork(labeledas“NN”inFig.5)methods,usingthetestingdata.Figure5.ComparsionofMLRandneuralnetworkinpredictionTable2showsthestatisticsfortheMLRandneuralnetworkforpredictingbroilerrateforsale.TABLEII.MODELSTATISTICSFORMLRANDNEURALNETWORKFORPREDICTINGRATEFORSALEModelStatisticMPEMSEMLR0.52%4.328E-05Neuralnetwork0.47%3.538E-05AswecanseefromTable2,neuralnetworkmodeloutperformsMLRmodelinbothMPEandMSE.Butfromtheresult,wecanseetheMLRmodelalsohasgoodpredictionperformances.IV.CONCLUSIONSInthispaper,wehavedealtwiththeresearchofthedatafittingforbroilergrowthperformanceparameters.Gradualadvancinganalysismethods,fromcorrelationanalysis,MLR,toneuralnetwork,areproposed.WeusethebroilergrowthdatasetofthemostfamouspoultryraisingcompanyinChina,andtakestheinfluenceoftheairtemperaturetotherateforsaleforexampletoevaluateourapproach.Aswecanseefromexperiment,correlationanalysisisusedtodetectthatthedivisionofchicklingstageandadultchickenstageisgoodforfurtherresearch,sincetheten-daymean