Chapter4TheMethodsofDataAnalysis6.1Datanormalization

Datanormalizationisthebasisforcomparingexperimentswithinlargeserieswhenexperimentalconditionsmaynotbeidentical.Normalizationensuresthattheexperimentalqualityofthedataiscomparableand,soundmathematicalalgorithmshavebeenemployed.Normalizationincludesvariousoptionstostandardizedataandtoadjustbackgroundlevelsandcorrectgradients.Thecommonlyusednormalizationfunctionsareasfollows:

Linearnormalization:

(6.1)

Rationormalization:

(6.2)

Z-scorenormalization:

(6.3)Generally,linearnormalizationisrecommended(ifX’max

=1andX’min

=0,x’i

isnormalizedinpercentagebyformula(6.1)).AfterRationormalization,thesumofnormalizedvariableswillbeequalto1.Z-scoreassumesxi

obeysGaussiandistribution.Ifxi

hasadifferentdistribution,thenthenormalizationwilltwistthepattern(variancewillbefarawayfromthestandarddeviation)andleadstoincorrectpatternrecognition.

σIspopulationstandarddeviation,ingeneral,itcanbeapproximatedbysamplestandarddeviation(S)

6.2SimpleLinearRegressionLearningObjectives:1. DescribetheLinearRegressionModel2.ExplainOrdinaryLeastSquares3. ComputeRegressionCoefficients4. Evaluatethelinearregressionmodel5. PredictResponseVariable6.2.1DescribetheLinearRegressionModel

RegressionModels:1. Answer‘WhatIstheRelationshipBetweentheVariables?’2. EquationUsed1NumericalDependent(Response)Variable1orMoreNumericalorCategoricalIndependent(Explanatory)Variables3. UsedMainlyforPrediction&EstimationTypesof

RegressionModelsRegressionModelsTypesof

RegressionModelsRegressionModelsSimple1ExplanatoryVariableTypesof

RegressionModelsRegressionModels2+ExplanatoryVariablesSimpleMultiple1ExplanatoryVariableTypesof

RegressionModelsRegressionModelsLinearSimpleMultiple1ExplanatoryVariable2+ExplanatoryVariableTypesof

RegressionModelsRegressionModelsLinearNon-LinearSimpleMultiple1ExplanatoryVariable2+ExplanatoryVariableTypesof

RegressionModelsRegressionModelsLinearNon-LinearSimpleMultipleLinear1ExplanatoryVariable2+ExplanatoryVariableTypesof

RegressionModelsRegressionModelsLinearNon-LinearSimpleMultipleLinearNon-Linear1ExplanatoryVariable2+ExplanatoryVariableLinearEquationsHighSchoolTeacherYXiii

01LinearRegressionModel

AssumesthattherelationshipbetweenvariablesisalinearfunctionDependent(Response)Variable

(e.g.,properties)Independent(Explanatory)Variable(e.g.,structurerepresentation)PopulationSlopePopulation

Y-InterceptRandomErrorLinearRegressionModelObservedvalueObservedvalue

i

=RandomerrorSimpleLinearRegressionModelUnsampledobservation

i

=RandomerrorObservedvalue^02040600204060XY6.2.2ExplainOrdinaryLeastSquaresScatterGraph:1. Plotofall(Xi,Yi)pairs2. SuggestshowwellmodelwillfitThinkingChallengeHowwouldyoudrawalinethroughthepoints?Howdoyoudeterminewhichline‘fitsbest’?ThinkingChallengeHowwouldyoudrawalinethroughthepoints?Howdoyoudeterminewhichline‘fitsbest’?ThinkingChallengeHowwouldyoudrawalinethroughthepoints?Howdoyoudeterminewhichline‘fitsbest’?ThinkingChallengeHowwouldyoudrawalinethroughthepoints?Howdoyoudeterminewhichline‘fitsbest’?ThinkingChallengeHowwouldyoudrawalinethroughthepoints?Howdoyoudeterminewhichline‘fitsbest’?ThinkingChallengeHowwouldyoudrawalinethroughthepoints?Howdoyoudeterminewhichline‘fitsbest’?ThinkingChallengeHowwouldyoudrawalinethroughthepoints?Howdoyoudeterminewhichline‘fitsbest’?LeastSquares(LS)1. ‘BestFit’MeansDifferenceBetweenActualYValues&PredictedYValuesAreaMinimumButPositiveDifferencesOffSetNegative2. LSMinimizestheSumoftheSquaredDifferences(SSE)LeastSquaresGraphically6.2.3ComputeRegressionCoefficientsGoal:Minimizesquarederror:(6.4)(6.5)(6.6)Where:6.2.4PredictResponseVariableComputationTable1ComputationTable2CoefficientEquationsSampleSlopeSampleY-interceptRegressionEquationExample1:1.

維尼綸纖維的耐熱水性能好壞可以用指標(biāo)“縮醛化度”來衡量，此指標(biāo)越高，耐熱水性能也越好。下表為測(cè)得的一組數(shù)據(jù)，分別計(jì)算出回歸系數(shù)和相關(guān)系數(shù)。甲醛濃度（g/L）18202224262830縮醛化度

(mol%)26.8628.3528.7528.8729.7530.0030.36

把聚乙烯醇溶解于水中﹐經(jīng)干法紡絲或濕法紡絲合成纖維。聚乙烯醇纖維用甲醛處理制成聚乙烯醇縮甲醛纖維﹐即通常所稱的維尼綸。聚乙烯醇縮醛化反應(yīng)可得到重要的高分子產(chǎn)品縮甲醛：維尼綸縮丁醛：良好的玻璃粘合劑Table1:Table2:6.2.5Evaluatethelinearregressionmodel

MeasuresofVariationinRegression

1. TotalSumofSquares(SSyy)MeasuresVariationofObservedYiAroundtheMean

Y2. ExplainedVariation(SSR)VariationDuetoRelationshipBetween

X&Y3. UnexplainedVariation (SSE)VariationDuetoOtherFactorsVariationMeasuresTotalsumofsquares(Yi-

Y)2

Unexplainedsumofsquares(Yi-

Yi)2

^Explainedsumofsquares(Yi-

Y)2

^Yi

1.

ProportionofVariation‘Explained’byRelationshipBetweenX&YCoefficientofDetermination0

r2

1=0.9211CoefficientofDeterminationExamplesr2=1r2=1r2=.8r2=02. PearsonProductMomentCoefficientofCorrelation,r:SimpleCoefficientofCorrelation

=0.9597CoefficientofCorrelationValues-1.0+1.00-.5+.5-1.0+1.00-.5+.5NoCorrelation-1.0+1.00Increasingdegreeofnegativecorrelation-.5+.5NoCorrelation-1.0+1.00-.5+.5PerfectNegativeCorrelationNoCorrelation-1.0+1.00-.5+.5PerfectNegativeCorrelationNoCorrelationIncreasingdegreeofpositivecorrelation-1.0+1.00PerfectPositiveCorrelation-.5+.5PerfectNegativeCorrelationNoCorrelationCoefficientofCorrelationExamplesr=1r=-1r=.89r=06.2.6IntroductiontoNon-linearregression基本概念非線性模型及其線性化方法非線性回歸1. 因變量y與x之間不是線性關(guān)系2. 可通過變量代換轉(zhuǎn)換成線性關(guān)系用最小二乘法求出參數(shù)的估計(jì)值并非所有的非線性模型都可以化為線性模型幾種常見的非線性模型

指數(shù)函數(shù)線性化方法兩端取對(duì)數(shù)得：lny

=ln

+

x令：y'=lny，則有y'

=ln

+

x基本形式：圖像

<幾種常見的非線性模型

冪函數(shù)線性化方法兩端取對(duì)數(shù)得：lgy=lg

+

lgx令：y'=lgy，x'=lgx，則y'

=lg

+x'基本形式：圖像0<<1

1

=1-1<

<0

<-1

=-1幾種常見的非線性模型

雙曲線函數(shù)線性化方法令：y'=1/y，x'=1/x,則有y'

=

+

x'基本形式：圖像

<0

>0幾種常見的非線性模型

對(duì)數(shù)函數(shù)線性化方法x'=lgx,則有y'

=

+

x'基本形式：圖像

0

<0幾種常見的非線性模型

S型曲線線性化方法令：y'=1/y，x'=e-x,則有y'

=

+

x'基本形式：圖像非線性回歸

（實(shí)例）

【例】為研究生產(chǎn)率與廢品率之間的關(guān)系，記錄數(shù)據(jù)如下表。試擬合適當(dāng)?shù)哪Ｐ汀U品率與生產(chǎn)率的關(guān)系生產(chǎn)率（周/單位)x1000200030003500400045005000廢品率（%）y5.26.56.88.110.210.313.0非線性回歸

生產(chǎn)率與廢品率的散點(diǎn)圖非線性回歸

（實(shí)例）用線性模型：y

=

0

1x+

，有y=2.671+0.0018x用指數(shù)模型：y=

x

，有y

=4.05

(1.0002)x3.用指數(shù)模型：y=4.003e0.000219x4.比較5.直線的殘差平方和＝5.3371<指數(shù)模型2的殘差平方和＝6.11。直線模型略好于指數(shù)模型6.指數(shù)模型3的殘差平方和＝2.8459，因此指數(shù)模型3最吻合。6.3MultipleLinearRegressionLearningObjectives:DescribetheMultipleLinearRegressionModelExplainOrdinaryLeastSquaresand ComputeRegressionCoefficientsEvaluatethelinearregressionmodelPredictResponseVariableAssumesthattheregressionfunctionE(Y|X)islinearLinearmodelsareoldtoolsbut…StillveryusefulSimpleAllowaneasyinterpretationofregressorseffectsVerywidesinceXi’scanbeanyfunctionofothervariables(quantitativeorqualitative)Usefultounderstandbecausemostothermethodsaregeneralizationsofthem.6.3.1DescribetheMultipleLinearRegressionModel6.3.2ExplainOrdinaryLeastSquaresandComputeRegressionCoefficientsXisn(p+1)ofinputvectorsyisthen-vectorofoutputs(labels)

isthe(p+1)-vectorofparametersMatrixNotation:Lesastsquaresestimation:Thelinearregressionmodelhastheform theβj’sareunknownparametersorcoefficients.Typicallywehaveasetoftrainingdata(x1,y1),…,(xn,yn)fromwhichwewanttoestimatetheparametersβ.ThemostpopularestimationmethodisleastsquaresLeastSquares:findsolution,,byminimizingtheresidualsumofsquares(RSS):Trainingsamplesarerandom,OR,yi’sareconditionallyindependentgivenxiLinearregressionandleastsquares:Reasonablecriterionwhen…GeometricalviewofleastsquaresSimplyfindthebestlinearfittothedataeiistheresidualofobservationiOnecovariateTwocovariatesSolvingLeastSquaresAccordingtothemathematicsextremetheories:Then,SettingtheFirstDerivativetoZero:6.3.3PredictResponseVariableAssumingthat(XTX)isnon-singular,thenormalequationsgivestheuniqueleastsquaressolution:LeastsquarespredicitonsWhen(XTX)issingulartheleastsquarescoefficientsarenolongeruniquelydefined.Somekindofalternativestrategyisneededtoobtainasolution:Recodingand/ordroppingredundantcolumnsFilteringControlfitbyregularizationGeometricalinterpretationofleastsquaresestimatesPredictedoutcomes

?aretheorthogonalprojectionofyontothecolumnspaceofX(thatspansasubspaceofRn).TechniqueforMultipleRegressionComputingdirectlyhaspoornumericpropertiesQRDecompositionofXDecomposeX=QRwhereQisN(p+1)orthogonalmatrix(QTQ=I(p+1))Risan(p+1)(p+1)uppertriangularmatrixThen1)ComputeQTy2)SolveR=QTybyback-substitutionSubsetselectionGoal:toeliminateunnecessaryvariablesfromthemodel.Wewillconsiderthreeapproaches:BestsubsetregressionChoosesubsetofsizekthatgiveslowestresidualsumofsquares(RSS).ForwardstepwiseselectionContinuallyaddfeatureswiththelargestF-ratioBackwardstepwiseselectionRemovefeatureswithsmallF-ratioGreedytechniques–notguaranteedtofindthebestmodelBestsubsetregressionForeachfindthesubsetofsizekthatgivesthesmallestRSS.Leapsandboundsprocedureworkswithp

≤40.Howtochoosek?Choosemodelthatminimizespredictionerror(notatopichere).Whenpislargesearchingthroughallsubsetsisnotfeasible.Canweseekagoodpaththroughsubsetsinstead?ForwardStepwiseselectionMethod:Startwithinterceptmodel. SequentiallyincludevariablethatmostimprovetheRSS(β)basedontheFstatistic:StopwhennonewvariableimprovesfitsignificantlyBackwardStepwiseselectionMethod:StartwithfullmodelSequentiallydeletepredictorsthatproducesthesmallestvalueoftheFstatistic,i.e.increasesRSS(β)least.StopwheneachpredictorinthemodelproducesasignificantvalueoftheFstatisticHybridsbetweenforwardandbackwardstepwiseselectionexistsSubsetselectionProducesmodelthatisinterpretableandhaspossiblylowerpredictionerrorForcessomedimensionsofXtozero,thusprobablydecreaseVar(β)Optimalsubsetmustbechosentominimizepredicionerror(modelselection:notatopichere)6.3.4Evaluatethelinearregressionmodel1.determinationcoefficient(Rsquare)2.multiplecorrelationcoefficient3.修正多重判定系數(shù)

(adjustedmultiplecoefficientofdetermination)

用樣本容量n和自變量的個(gè)數(shù)p去修正R2得到計(jì)算公式為避免增加自變量而高估R2意義與R2類似數(shù)值一般小于R2Example2:根據(jù)給定的數(shù)據(jù)進(jìn)行多元線性回歸，分別計(jì)算出回歸系數(shù)和相關(guān)系數(shù)。其中C1,C2,C3分別為混合物各組分的濃度，已知它們與粘度之間成線性關(guān)系。C1C2C3粘度0.4020.1530.0580.6250.5030.3010.1830.8260.3060.1090.2241.1820.2960.3650.0091.9440.3090.4050.1092.3720.0550.1530.1563.243y(粘度)=2.5447-6.8794*C1+4.2240*C2+2.0547*C3R=0.9926,R2=0.9852

Theindependentvariablesarenotnormalized:Theindependentvariablesarenormalized,andthenormalizedintervalis[-1,1]:y(粘度)=1.9503-1.5410*C1+0.6252*C2+0.2209*C3R=0.9926,R2=0.9852=0.963，n=6，p=36.4PrincipalComponentAnalysisPrincipalpurpose:Reducingdimensionality:largebodyofdatatomanageableset.Rotatesmultivariatedatasetintoanewconfigurationwhichiseasiertointerpret.simplifydatalookatrelationshipsbetweenvariableslookatpatternsofresearchsystemsPCA:GeneralmethodologyFromporiginalvariables:x1,x2,...,xp: Producek(k<=p)newvariables:y1,y2,...,yk:

y1=a11x1+a12x2+...+a1pxp

y2=a21x1+a22x2+...+a2pxp ...

yk=ak1x1+ak2x2+...+akpxpPCA:Generalmethodologysuchthat:yk'sareuncorrelated(orthogonal)y1explainsasmuchaspossibleoforiginalvarianceindatasety2explainsasmuchaspossibleofremainingvarianceetc.PrincipalComponentsAnalysis1stPrincipalComponent,y12ndPrincipalComponent,y2PrincipalComponentsAnalysis{a11,a12,...,a1p}is1stEigenvectorof correlation/covariancematrix,andcoefficientsoffirstprincipalcomponent

{a21,a22,...,a2p}is2ndEigenvectorof correlation/covariancematrix,andcoefficientsof2ndprincipalcomponent…{ak1,ak2,...,akp}iskthEigenvectorof correlation/covariancematrix,and coefficientsofkthprincipalcomponentPrincipalComponentsAnalysisSo,principalcomponentsaregivenby:

y1=a11x1+a12x2+...+a1pxp

y2=a21x1+a22x2+...+a2pxp ...

yk=ak1x1+ak2x2+...+akpxpxj’sarestandardizedifcorrelationmatrixisused(mean0.0,SD1.0)PrincipalComponentsAnalysisScoreofithunitonjthprincipalcomponent yi,j=aj1xi1+aj2xi2+...+ajkxipPCAScoresxi2xi1yi,1yi,2PrincipalComponentsAnalysisAmountofvarianceaccountedforby:1stprincipalcomponent,λ1,1steigenvalue2ndprincipalcomponent,λ2,2ndeigenvalue...

λ1

>

λ2

>

λ3

>λ4

>...Averageλj=1(correlationmatrix)PrincipalComponentsAnalysis:Eigenvaluesλ1λ2PCA:Terminologyjthprincipalcomponentisjtheigenvectorof correlation/covariancematrixcoefficients,ajk,areelementsofeigenvectorsandrelateoriginalvariables(standardizedifusingcorrelationmatrix)tocomponentsscoresarevaluesofunitsoncomponents(producedusingcoefficients)amountofvarianceaccountedforbycomponentisgivenbyeigenvalue,λjproportionofvarianceaccountedforbycomponentisgivenbyλj/Σλjloadingofkthoriginalvariableonjthcomponentisgivenbyajk%λj--correlationbetweenvariableandcomponent

Howmanycomponentstouse?

Ifλj<1thencomponentexplainslessvariancethanoriginalvariable(correlationmatrix)Use2components(or3)forvisualeaseScorediagram:PrincipalComponentsAnalysison:

CovarianceMatrix:VariablesmustbeinsameunitsEmphasizesvariableswithmostvarianceMeaneigenvalue…1.0Usefulinmorphometrics,afewothercasesCorrelationMatrix:Variablesarestandardized(mean0.0,SD1.0)VariablescanbeindifferentunitsAllvariableshavesameimpactonanalysisMeaneigenvalue=1.0RotationsofPrincipalComponents(ExploratoryFactorAnalysis)Factorsarerotatedcomponents(justrotateafewprincipalcomponents)Varimax:triestomaximizevarianceofsquaredloadingsforeachfactor(orthogonal):linesupfactorswithoriginalvariablesimprovesinterpretabilityoffactorsQuartimax:triestominimizesumsofsquaresofproductsofloadings(orthogonal)Procedureforprincipalcomponentsanalysis1.Decidewhethertousecorrelationorcovariancematrix2.Findeigenvectors(components)andeigenvalues(varianceaccountedfor)3.Decidehowmanycomponentstousebyexaminingeigenvalues(perhapsusingscreediagram)4.Examineloadings(perhapsvectorloadingplot)5.Plotscores6.Tryrotation--gotostep4Singularvaluedecomposition(SVD)TheSVDofthematrixhastheform whereandareorthogonalmatricesandD=diag(d1,…..,dr)arethenon-zerosingularvaluesofX.r≤min(n,p)istherankofXTheeigenvectorsviarecalledtheprincipalcomponentsofX.1.

Example3:

下表為n個(gè)組分5個(gè)不同濃度的混合物在10個(gè)波長下測(cè)定的吸光光度值，利用主成分分析來確定它的特征值，并以此判斷該混合物的主成分?jǐn)?shù)。5.31.16.14.112.117.440.626.353.260.418.657.327.572.665.621.952.231.368.774.37.255.215.263.240.28.339.414.545.333.218.475.429.590.871.720.611.126.324.357.328.425.336.944.580.227.336.335.153.580.6c1c2c3c4c5特征值分別為：96610.99,4308.51,3.7543,2.5971,1.7262,主成分?jǐn)?shù)為2。Firstpc:96610.99/(99610.99+4308.51+3.7543+2.5971+1.7262)=0.9572Secondpc:4308.51/(96610.99+4308.51+3.7543+2.5971+1.7262)=0.0427Pc1+pc2=0.99996.5PrincipalComponentRegression

PCR,orprincipalcomponentregression,isasimpleextensionofMLRandPCA.Inthefirststep,theprincipalcomponentsarecalculated.ThescoresofthemostimportantprincipalcomponentsareusedasthebasisforthemultiplelinearregressionwiththetargetdatayThemostimportantpointinPCRistheproperselectionoftheeigenvectorstobeincluded.Aplotoftheeigenvaluesusuallyindicatestothe"best"numberofeigenvectors.AdvantagesofPCRoverMLR:

Noiseremainsintheresiduals,sincetheeigenvectorswithloweigenvaluesrepresentonlypartsofthedatawithlowvariance.Theregressioncoefficientsaremorestable.Thisisduetothefactthattheeigenvectorsareorthogonaltoeachother.TheflowchartofPCR:LinearregressionbySVDAgeneralsolutiontoy=XβcanbewrittenasThefilterfactorsωideterminestheextentofshrinking,0≤ωi≤1,orstretching,ωi>1,alongthesingulardirectionsuiFortheOLSsolutionωi=1,i=1,…,p,i.e.allthedirectionsuicontributeequallyPCRUselinearcombinationszm=Xvasnewfeaturesvjistheprincipalcomponent(columnofV)correspondingtothejthlargestelementofD,e.g.

thedirectionsofmaximalsamplevarianceForsomeM≤pformthederivedinputvectors [z1…zM]=[Xv1……XvM]Regressyonz1…zM,givesthesolutionwherePCRcontinuedThem’thprincipalcomponentdirectionvmsolves:Filterfactorsbecome

e.g.itdiscardsthep-MsmallesteigenvaluecomponentsfromtheOLSsolution.Ifp=MitgivestheOLSsolution6.6IntroductionofOrigin6.6.1introduction

Originisprofessionalgraphinganddataanalysissoftwareforscientistsandengineers.Origin,hasbeengrowinginpopularityamongscientistsandengineersasaseriousdataanalysisandgraphingsoftwaresince1991.Originisusedinhundredsoflargecorporationsandaroundathousandcollegesanduniversitiesworldwide.Therearevariousversion,itremainscommittedtothemissionofmakingOriginthebestscientificgraphingsoftwareanddataanalysissoftware.Alongwithitseasy-to-usegraphicalinterface,Originoffersintuitive,yetpowerful,researchtoolsforthedailyneedsoftheresearcher.ThelatestversionisOrigin7.5.MenusandMenuCommands

Origin'smenubarprovidescommandstoperformoperationsontheactivewindowandtoperformgeneraloperationssuchasopeningaHelpfileorturningonthedisplayofatoolbar.Themenubarchangesasyouchangetheactivewindow.Forexample,thefollowingfigurescomparetheworksheetandgraphmenubars.

Origin是美國OriginLab公司（其前身為Microcal公司）開發(fā)的圖形可視化和數(shù)據(jù)分析軟件，是科研人員和工程師常用的高級(jí)數(shù)據(jù)分析和制圖工具。自1991年問世以來，由于其操作簡(jiǎn)便，功能開放，很快就成為國際流行的分析軟件之一，是公認(rèn)的快速、靈活、易學(xué)的工程制圖軟件。在國內(nèi)，其使用范圍也越來越廣泛，目前的最高版本為Origin7.5。當(dāng)前流行的圖形可視化和數(shù)據(jù)分析軟件有Matlab，Mathmatica和Maple等。這些軟件功能強(qiáng)大，可滿足科技工作中的許多需要，但使用這些軟件需要一定的計(jì)算機(jī)編程知識(shí)和矩陣知識(shí)，并熟悉其中大量的函數(shù)和命令。而使用Origin就像使用Excel和Word那樣簡(jiǎn)單，只需點(diǎn)擊鼠標(biāo)，選擇菜單命令就可以完成大部分工作，獲得滿意的結(jié)果。

像Excel和Word一樣，Origin是個(gè)多文檔界面應(yīng)用程序。它將所有工作都保存在Project(*.OPJ)文件中。該文件可以包含多個(gè)子窗口，如Worksheet，Graph，Matrix，Excel等。各子窗口之間是相互關(guān)聯(lián)的，可以實(shí)現(xiàn)數(shù)據(jù)的即時(shí)更新。子窗口可以隨Project文件一起存盤，也可以單獨(dú)存盤，以便其他程序調(diào)用。

Origin具有兩大主要功能：數(shù)據(jù)制圖和數(shù)據(jù)分析。Origin數(shù)據(jù)制圖主要是基于模板的，提供了50多種2D和3D圖形模板。用戶可以使用這些模板制圖，也可以根據(jù)需要自己設(shè)置模板。Origin數(shù)據(jù)分析包括排序、計(jì)算、統(tǒng)計(jì)、平滑、擬合和頻譜分析等強(qiáng)大的分析工具。這些工具的使用也只是單擊工具條按鈕或選擇菜單命令。

在Origin7.0的基礎(chǔ)上，OriginLab公司開發(fā)了Originpro和附加模塊(Addonmodules)。用戶可以在Originpro中建立自己需要的特殊工具。Originpro的靈活界面使用起來快捷方便，這樣用戶可以將精力集中到圖形的數(shù)據(jù)分析上，而不是處理圖形本身。Addonmodules為Origin和Originpro添加了特殊的高級(jí)數(shù)據(jù)分析功能，可以彌補(bǔ)Origin7.0相對(duì)Matlab和Mathmatica的不足。用戶可以自定義數(shù)學(xué)函數(shù)和制圖模板，添加菜單命令和命令按鈕，調(diào)用OriginC和NAG函數(shù)。Origin界面6.6.2數(shù)據(jù)分析繪圖工具Origin§1概述§2數(shù)據(jù)文件的建立§3數(shù)據(jù)的編輯§4繪制圖形§5圖形的編輯和格式化§6Tools工具欄的使用§7數(shù)據(jù)分析——曲線擬合§8Origin圖形文件的輸出1.1Origin的主要功能由數(shù)據(jù)或函數(shù)作圖圖形的擬合1.2Origin的工作界面（Workspace）工作表窗口子窗口工程管理器圖形窗口1.標(biāo)題欄

2.菜單欄3.工具欄工具欄的開啟方法4.子窗口子窗口種類5.工程管理器（ProjectExplorer）：

TheProjectExplorerisatooltohelp

youorganizeyourOriginprojects

6.狀態(tài)欄Origin的工作界面工具欄的開啟方法:selectView:Toolbars

fromtheOriginmenubar.Whenaworkbook（Excel）

isactive,select

Window:OriginToolbars.Toolbarsdialogbox

子窗口的種類主要有：TheWorksheetWindow工作表窗口TheExcelWorkbookWindowExcel工作表窗口TheGraphWindow圖形窗口

TheFunctionGraphWindow函數(shù)圖形窗口TheLayoutPageWindow版面編排窗口Attention:Eachchildwindowhasitsownmenustructure,whichisdisplayedwhenthewindowisactive.

1.使用菜單中的相應(yīng)命令2.使用工具按鈕3.右擊鼠標(biāo)，在彈出的快捷菜單中

選相應(yīng)命令4.選定對(duì)象后雙擊，打開對(duì)話框1.3基本操作方法1.Origin的啟動(dòng)桌面快捷圖標(biāo)“開始”→“程序”→“MicrocalOrigin6.0”→快捷圖標(biāo)1.4Origin的啟動(dòng)和退出2.Origin的退出方法有兩種：?jiǎn)螕粲疑辖堑年P(guān)閉按扭；單擊Origin窗口菜單的“File”→“Exit”注意：要區(qū)分Origin的退出和子窗口的退出Saveaproject

保存工程Saveachildwindowseparatelyasafile

單獨(dú)將子窗口作為一個(gè)文件保存Saveatemplateasafile

保存為模板文件可保存的文件類型及文件擴(kuò)展名1.5Origin文件的保存文件類型及文件擴(kuò)展名（fileextension）

Project——OPJ

ItcannotsaveastemplateGraphWorksheet——OGW

TemplateextensionisOTWExcelWorkbook——XLS

ItcannotsaveastemplateLayoutPage——OTPItcannotsaveasfileMatrix——OGMTemplateextensionisOTMFunctionGraph——OGGTemplateextensionisOTPNotes——TXTItcannotsaveastemplate

Originprovidesseveralwaystoadddatatotheworksheet1.Enteringdatausingthekeyboard.鍵盤輸入2.Importingafile.導(dǎo)入文件3.PastingdatafromanotherapplicationusingtheClipboard.4.Pastingdatafromanother(orthesame)Originworksheet

usingtheClipboard.（3）和（4）是粘貼數(shù)據(jù)5.UsingExcelWorkbookWindow.打開或創(chuàng)建Excel工作表6.Usingafunctiontosetcolumnvalues.用函數(shù)設(shè)置列的值§2數(shù)據(jù)文件的建立

§3數(shù)據(jù)的編輯3.1工作表簡(jiǎn)介3.2工作表的選定操作3.3數(shù)據(jù)的編輯修改3.4列的插入、刪除及重排3.5行的插入和刪除3.6刪除工作表3.7格式化數(shù)據(jù)表（Worksheet）3.1工作表簡(jiǎn)介Theworksheetwindowisorganizedinto

verticalcolumnsandhorizontalrows.

工作表由垂直的列和水平的行組成Attheintersectionofeachcolumnandrowisacell.

列與行的交叉處稱為單元格Eachcellcancontainasinglenumeric,text,numericandtext,date,ortimevalue.

每個(gè)單元格內(nèi)可包含數(shù)、文本、日期、時(shí)間等Originprojectscancontainmultipleworksheets.

一個(gè)Originprojects中可以包含多個(gè)工作表3.2工作表的選定操作1.

選定若干單元格（SelectingCells）Click-and-dragtoselectthecells.2.選定若干行（SelectingRows）Selecttherowheading,dragthemouseOrSelecttherowheading,Click+SHIFTkey

3.選相鄰的列（SelectingAdjacentColumns）Selectthefirstcolumnheading,Click-and-dragOrSelectthecolumnheading,Click+SHIFTkey4.選不相鄰的列（SelectingNonadjacentColumns）Selectthecolumnheading,

+CTRLkey

1.數(shù)據(jù)的修改Tochangeavalue,selectthecellandtypethecorrectvalue.(Originautomaticallyoverwritesthevalueinthecell)

替換單元格中的數(shù)據(jù)，點(diǎn)擊該單元格，輸入新的值Toeditacellvalue,pressF2orclickatthedesiredposition

修改單元格中的數(shù)據(jù)，點(diǎn)擊該單元格后，在擬修改的位置單擊鼠標(biāo)Delete:Deleteonevaluetotherightofthecursor,

ordeleteallhighlightedvalues.3.3數(shù)據(jù)的編輯修改2.在列中插入數(shù)據(jù)（InsertingDatawithinaColumn）①Toinsertacellinacolumn,selectthecell

thatisdirectlybelowwhereyouwantto

insertthenewcell.

選定擬插入新單元格下方的單元格②ThenselectEdit:Insert

orright-click→selectInsertfromtheshortcutmenu.

執(zhí)行編輯菜單中的插入命令③Thenewcellinsertsabovetheselectedcell.

新單元格將插在所選定單元格的上方3.刪除數(shù)據(jù)（DeletingData）Tocleartheentirecontentsofaworksheet,

selectEdit:ClearWorksheet.刪除整個(gè)工作表中的內(nèi)容Todeletethecontentsofarangeofcellsfromtheworksheet,

selectEdit:Clear.刪除單元格或單元格區(qū)域中的內(nèi)容，格子保留Todeletearangeofcellsfromtheworksheet,

selectEdit:Delete.內(nèi)容和單元格同時(shí)刪除Attention:Delete(1)TheEdit:Delete

deletesaselectedvaluesandcells(2)Thekeyboard:Deletedeletestheworksheetvaluesonly.4.列的插入、刪除和重排AddingColumns：增加列Performoneofthefollowingoperations:

SelectColumn:AddNewColumns.ClicktheAddNewColumnsbuttonontheStandardtoolbar.Right-clickinsidetheworksheetwindowbuttotherightoftheworksheetgrid.SelectAddNewColumnfromtheshortcutmenu.InsertingColumns：插入列SelectEdit:InsertRight-click→selectInsertfromtheshortcutmenu..DeletingColumns：刪除列SelectEdit:DeleteRight-click→selectDelete.Note:Toclearthecolumnvaluesbutremainthecolumns,selectEdit:Clear.MovingColumns：移動(dòng)列

SelectColumn:MovetoFirst.Column:MovetoLast.先選定后操作5.行的插入和刪除InsertingRows：插入行selectEdit:Insert

orright-clickandselectInsert

DeletingRows：刪除行Edit:Deleteorright-clickandselectDelete.先選定后操作6.刪除工作表（DeletingaWorksheetfromaProject）

Todeleteaworksheetfromtheproject,performoneofthefollowingoperations:ClicktheCloseWindowbutton

intheupper-rightcorneroftheworksheet.

點(diǎn)擊工作表右上方的關(guān)閉窗口按扭Right-clickontheworksheetwindowiconinProjectExplorerandselectDeleteWindowfromtheshortcutmenu.

在工程管理器中右擊工作表圖標(biāo)，在快捷菜單中選DeleteWindowClickontheworksheetwindowiconinProjectExplorerandthenpressDelete.

在工程管理器中點(diǎn)擊工作表圖標(biāo)，按Delete鍵作用：1.

改變列的名稱（ColumnName）2.改變列的標(biāo)識(shí)（PlotDesignation）3.改變數(shù)據(jù)的類型（Display）4.改變數(shù)的格式（Format）5.改變數(shù)的顯示格式（NumericDisplay）6.改變列寬（ColumnWidth）7.為列標(biāo)簽添加說明（ColumnLabel）7.數(shù)據(jù)表的格式化方法：雙擊工作表的列標(biāo)簽打開WorksheetColumnFormat5.改變數(shù)的顯示格式（NumericDisplay）4.改變數(shù)的格式（Format）十進(jìn)制格式科學(xué)記數(shù)格式工程記數(shù)格式有千位分隔符的十進(jìn)制格式默認(rèn)的十進(jìn)制顯示數(shù)據(jù)設(shè)置小數(shù)點(diǎn)的位置設(shè)置有效數(shù)字的位數(shù)§4繪制圖形4.1圖形窗口中的基本術(shù)語4.2繪圖的方法4.1圖形窗口中的基本術(shù)語Page:Eachgraphwindowcontainsasingleeditable

page.Thepageserves