6西格玛回归分析.ppt

回归分析RegressionAnalysis,目的Objectives,介绍相关性及回归的基本概念IntroduceTheBasicConceptsofCorrelationandRegression把回归与六西格玛路线图结合起来LinkRegressionToTheSixSigmaRoadmap学习多元回归的使用ReviewtheuseofMultipleRegression,介绍相关性及回归的基本概念IntroduceTheBasicConceptsofCorrelationandRegression把回归与六西格玛路线图结合起来LinkRegressionToTheSixSigmaRoadmap学习多元回归的使用ReviewtheuseofMultipleRegression,介绍相关性及回归的基本概念IntroduceTheBasicConceptsofCorrelationandRegression把回归与六西格玛路线图结合起来LinkRegressionToTheSixSigmaRoadmap学习多元回归的使用ReviewtheuseofMultipleRegression,项目跟踪图,第五版,项目开始日期,21/01/2004,项目类别,“Y”变量数据,采集计划,制定项目,日程,启动项目书,DMAIC改善,定义,确定”Y”变量和,起草项目书,项目书,得以批准,流程图,C&E矩阵或,故障树分析FTA,第三十天MBB审阅,FMEA,或故障树分析FTA,测量系统分析MSA,关键”X”变量,数据采集计划,MBB审阅,测量,21/01/2004,04/02/2004,11/02/2004,25/02/2004,09/03/2004,09/03/2004,09/03/2004,初始能力研究,多元变量流程分析,MBB审阅,合同批准,分析,22/03/2004,15/04/2004,15/04/2004,15/04/2004,15/04/2004,单因子或多因子测试,实验设计(DOE),MBB审阅,改善,31/05/2004,31/05/2004,31/05/2004,控制计划,最终能力研究,控制阶段FMEA回顾,重新修订RPN,MBB审阅,项目最终汇报,及报告,项目审核,及项目收尾,控制,21/06/2004,29/06/2004,29/06/2004,05/07/2004,09/07/2004,09/07/2004,19/07/2004,(根据需要使用),客户心声/业务之声调查VOC/VOB,需求分析,流程再造,解决方案设计,流程再造,在这里输入开始日期,确定改善方案,由项目发起人在备选项目数据库中完成,在6西格玛,数据库,查找相似项目,实施改善,移交培训/,流程所有人签准,再造路线图的日程是独立计算的,与以上DMAIC的日期不相关,实际完成日期,计划完成日期,图例,2/1/02002,2/3/02,完成,画钩,分析路线图AnalyzeRoadmap单一因子X-单一因子YSingleX-SingleY,输入变量XXData,离散Discrete,连续Continuous,输出变量YYData,离散Discrete,连续Continuous,卡方相关性分析Chi-Square,逻辑回归LogisticRegression,方差分析，均值/中位数测试ANOVAMeans/MediansTests,回归Regression,什么是Y?_数据类型?_,什么是X?_数据类型?_,应该使用何种工具?_,案例#1Scenario#1,管理者想知道接线员的经验(以月为单位衡量)是否会对接听顾客热线电话需要的时间有影响,相关性Correlation,什么是相关性?Whatiscorrelation?你是否有过如此经验:测量某些产品并送至顾客处，但他们回来告诉你的产品不符规格?Haveyouevermeasuredsomethingandthenshippedtoyourcustomeronlyforthemtotellyouitdoesntmeetspec?在奥林匹克溜冰比赛上，你认为两个裁判成绩之相关性有多高?HowwellcorrelateddoyouthinktwoiceskatingjudgesareattheOlympics?,相关性Correlation,路线分析图AnalyzeRoadmap,画出点阵图ProduceScatterPlot,计算相关性CalculateCorrelation,评估r和P值EvaluaterandPvalue,相关系数CorrelationCoefficients,什么是相关系数?SowhatistheCorrelationCoefficientsupposedtobeanyway?相关系数(r)介于-1和1之间TheCorrelationCoefficient(r)liesbetween-1and1一般规则:GeneralRules相关系数(r).80或.80orBASICSTATSCORRELATION.不选择p值选项Uncheckpvalue,年度和市场营销费用有着很高的相关性！我们必须只能选择一个作为预测变量在回归拟合中使用市场营销费用可能受年度影响，因此我们保留市场营销费用，而去掉年度变量TheYearandMarketing$Variablesarehighlycorrelated!Wewillhavetochooseoneortheotherofthecorrelatedpredictorvariables(butnotboth)touseinaregressionfit.Possiblethatmarketing$isafunctionoftheyear-sokeepthemarketing$andeliminateyear.,基本原则,如果相关性0.8orRegressionBestSubsets.,最佳子集回归：刹车板销售,注意”年度”从模式中去掉了.,BestSubsetsRegression:SalesversusMktg$,SalesRep,.ResponseisSalesSLaYPl(rMeSoksadtlugRecVarsR-SqR-Sq(adj)C-pS$est179.077.8156.012.841X120.916.6631.324.910X290.189.066.89.0570XX285.283.5107.011.084XX398.297.83.04.0222XXX390.588.765.89.1570XXX498.297.75.04.1540XXXX,多元回归MultipleRegression,路线分析图,规划分析内容,收集数据,利用回归或最佳子集分析AnalyzeUsingRegressionorBestSubsets,评估残差,制定决策,评估R2及P值的显著性,多元共线性分析（相关性）Multicollinearity“X”Check(correlation),使用多元回归简化模式RunMultipleRegressionReducedModel,因为有多条线，就不再使用拟合线图，Nolongerfittedlineplotduetomultiplelines,回归:刹车板销售Regression:BrakeSales,选择所有四个预测变量和响应变量.Selectallfourpredictorvariablesandtheresponsevariable.,使用Minitab菜单,STATRegressionRegression,回归分析:刹车板销售RegressionAnalysis:BrakeSales,零假设=变量间没有任何关系备择假设=变量间有一些关系Ho=NorelationshipbetweenvariablesHa=Somerelationshipexistsbetweenvariables,RegressionAnalysis:SalesversusMktg$,SalesRep,.TheregressionequationisSales=-66.6+11.8Mktg$+1.18SalesRep+2.70LY(SalesRep)-0.007ProductPredictorCoefSECoefTPConstant-66.6419.17-3.480.003Mktg$11.8381.4947.920.000HaSalesRe1.17510.12249.600.000HaLY(Sales2.70230.115423.420.000HaProduct-0.00680.2337-0.030.977HoS=4.154R-Sq=98.2%R-Sq(adj)=97.7%,回归/简化模式:刹车板销售Regression/ReducedModel:BrakeSales,选择所剩三个预测变量和响应变量.Selectthethreeremainingpredictorvariablesandtheresponsevariable.,UsingMinitabMenu,STATRegressionRegression,记住检查残差图Remembertocheckyourresidualplots,回归分析:刹车板销售RegressionAnalysis:BrakeSales,零假设=变量间没有任何关系备择假设=变量间有一些关系Ho=NorelationshipbetweenvariablesHa=Somerelationshipexistsbetweenvariables,回归分析:销售量v.市场营销费用,销售人员数,去年销售人员数RegressionAnalysis:SalesversusMktg$,SalesRep,LY(SalesRep)TheregressionequationisSales=-66.9+11.8Mktg$+1.18SalesRep+2.70LY(SalesRep)PredictorCoefSECoefTPConstant-66.9116.22-4.120.001Mktg$11.8471.4148.380.000HaSalesRe1.17640.110610.640.000HaLY(Sales2.70270.110624.440.000HaS=4.022R-Sq=98.2%R-Sq(adj)=97.8%,刹车板销售案例的其他MiniTab输出TheRestofMiniTabOutputBrakeSales,AnalysisofVarianceSourceDFSSMSFPRegression313870.14623.4285.780.000ResidualError16258.816.2Total1914128.9SourceDFSeqSSMktg$1893.9SalesRe13313.2LY(Sales19663.0UnusualObservationsObsMktg$SalesFitSEFitResidualStResid1011.1204.000196.2362.1617.7642.29RRdenotesanobservationwithalargestandardizedresidual,刹车板销售R-Sq(修正后)BrakeSalesR-Sq(Adjusted),R-Sq(Adj)=97.8%Y的变差可由回归里的三个元素解释.R-Sq(Adj)=97.8%ofthevariationinYisexplainedbytheThreefactorsincludedintheregression.尽管结果不错,但仍有2.2%刹车板销售的变差不能解释(Whilegood,thisstillmeansthatabout2.2%ofthevariationinBrakeSalesisstillunexplained.),S=4.022R-Sq=98.2%R-Sq(adj)=97.8%,多元回归MultipleRegression,路线分析图AnalyzeRoadmap,规划分析内容,收集数据,利用回归或最佳子集分析AnalyzeUsingRegressionorBestSubsets,评估残差,制定决策,评估R2及P值的显著性,多元共线性分析（相关性）Multicollinearity“X”Check(correlation),使用多元回归简化模式RunMultipleRegressionReducedModel,因为有多条线，就不再使用拟合线图，Nolongerfittedlineplotduetomultiplelines,刹车板销售残差BrakeSalesResiduals,残差分析同样不容忽视.对残差进行仔细分析会帮助我们确定我们没有违反leastsquares拟合规律.以此可以指导我们改进回归拟合模式.Nottobeoverlookedisresidualanalysis.Carefulanalysisofresidualstellswhetheranyassumptionsoftheleastsquaresfitareviolated.Thiswillguideusinimprovingtheregressionfit.,最小二乘方的假设LeastSquaresAssumptions:残差的变差不是由任何预测变量X引起的Thevarianceoftheresidualsdonotdependuponanypredictorvariable,X.残差有着正态分布.Residualsarenormallydistributed.以时间为序,各残差间互不倚靠Arrangedintimeorder,theresidualsareindependentofeachother.,刹车板销售量的拟合及残差BrakeSalesFits&Residuals,多元回归总结MultipleRegressionSummary,这是用来建立Y=f(X1,X2,X3,.)该形式非常有用的统计工具ApowerfulstatisticaltoolthatisusedtobuildmodelsoftheformY=f(X1,X2,X3,.).最好的模式是可以用最少的元素来解释响应变量Y的绝大多数变异的模式.ThebestmodelistheonewiththefewestfactorsthatexplainsthemostvariationintheresponseY.最好子集回归是一个可以快速整合可能的好模式的非常有用的技巧.BestSubsetsisausefultechniquetoquicklyzeroinonpotentialgoodmodels回归里应避免没有价值的残差及元素间的共线性.Pitfallstoavoidinregressionarepoorly-behavedresidualsandfactorcollinearity.,多元回归MultipleRegression,路线分析图AnalyzeRoadmap,规划分析内容,收集数据,利用回归或最佳子集分析AnalyzeUsingRegressionorBestSubsets,评估残差,制定决策,评估R2及P值的显著性,多元共线性分析（相关性）Multicollinearity“X”Check(correlation),使用多元回归简化模式RunMultipleRegressionReducedModel,因为有多条线，就不再使用拟合线图，Nolongerfittedlineplotduetomultiplelines,多元回归的练习