西格玛回归分析课件

1、回归分析Regression Analysis目的Objectives介绍相关性及回归的基本概念 Introduce The Basic Concepts of Correlation and Regression把回归与六西格玛路线图结合起来 Link Regression To The Six Sigma Roadmap学习多元回归的使用 Review the use of Multiple Regression介绍相关性及回归的基本概念 Introduce The Basic Concepts of Correlation and Regression把回归与六西格玛路线图结合起来 Li

2、nk Regression To The Six Sigma Roadmap学习多元回归的使用 Review the use of Multiple Regression介绍相关性及回归的基本概念 Introduce The Basic Concepts of Correlation and Regression把回归与六西格玛路线图结合起来 Link Regression To The Six Sigma Roadmap学习多元回归的使用 Review the use of Multiple Regression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

3、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21/01/200404/02/200411/02/200425/02/200409/03/200409/03/200409/03/2004初始能力研究 多元变量流程分析MBB审阅合同批准分析22/03/200415/04/200415/04/200415/04/200415/04/2004单因子或多因子测试实验设计(DOE) MBB审阅改善31/05/200431/05/2

4、00431/05/2004控制计划最终能力研究 控制阶段FMEA回顾 重新修订RPNMBB审阅项目最终汇报 及报告项目审核及项目收尾控制21/06/200429/06/200429/06/200405/07/200409/07/200409/07/200419/07/2004(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2/1/020022/

5、3/02完成画钩分析路线图Analyze Roadmap 单一因子 X -单一因子 Y Single X - Single Y输入变量 X X Data离散Discrete 连续Continuous 输出变量 Y Y Data离散Discrete 连续Continuous 卡方相关性分析Chi-Square逻辑回归Logistic Regression方差分析，均值/中位数测试ANOVAMeans / Medians Tests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 #1 Scenario #1管理者想知道接线员

6、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 ? What is correlation?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? Have you ever measured something and then shipped to your customer only for them to tell you it doesnt meet spec?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? How well correlated do you think two ice s

7、kating judges are at the Olympics?相关性Correlation路线分析图Analyze Roadmap 画出点阵图Produce Scatter Plot计算相关性Calculate Correlation评估r 和 P值 Evaluate r and P value相关系数Correlation Coefficients什么是相关系数? So what is the Correlation Coefficient supposed to be anyway?相关系数 (r)介于-1和1之间 The Correlation Coefficient (r) li

8、es between -1 and 1一般规则:General Rules 相关系数 (r) .80 或 .80 or BASIC STATS CORRELATION.不选择p值选项Uncheck p value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The Year and Marketing$ Variables are highly correlated! We will have to choose one or the other of the correlated pre

9、dictor variables (but not both) to use in a regression fit.Possible that marketing$ is a function of the year - so keep the marketing $ and eliminate year. 基本原则, 如果相关性 0.8 or Regression Best Subsets.最佳子集回归：刹车板销售 注意”年度”从模式中去掉了.Best Subsets Regression: Sales versus Mktg$, Sales Rep, .Response is Sales

10、 S L a Y P l ( r M e S o k s a d t l u g R e c Vars R-Sq R-Sq(adj) C-p S $ e s t 1 79.0 77.8 156.0 12.841 X 1 20.9 16.6 631.3 24.910 X 2 90.1 89.0 66.8 9.0570 X X 2 85.2 83.5 107.0 11.084 X X 3 98.2 97.8 3.0 4.0222 X X X 3 90.5 88.7 65.8 9.1570 X X X 4 98.2 97.7 5.0 4.1540 X X X X 多元回归Multiple Regre

11、ssion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Analyze Using Regression or Best Subsets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Run Multiple Regression Reduced Model因为有多条线，就不再使用拟合线图，No longer fitted line plot due to multiple lines回归:刹车板销售Regression: Brake Sales 选择所有四个预测变量

12、和响应变量.Select all four predictor variables and the response variable.使用 Minitab 菜单, STAT Regression Regression回归分析:刹车板销售Regression Analysis: Brake Sales 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 = No relationship between variables Ha = Some relationship exists between variablesRegression Analysis: Sales versus

13、 Mktg$, Sales Rep, .The regression equation isSales = - 66.6 + 11.8 Mktg$ + 1.18 Sales Rep + 2.70 LY(SalesRep) - 0.007 ProductPredictor Coef SE Coef T PConstant -66.64 19.17 -3.48 0.003Mktg$ 11.838 1.494 7.92 0.000 HaSales Re 1.1751 0.1224 9.60 0.000HaLY(Sales 2.7023 0.1154 23.42 0.000HaProduct -0.0

14、068 0.2337 -0.03 0.977HoS = 4.154 R-Sq = 98.2% R-Sq(adj) = 97.7%回归/简化模式:刹车板销售Regression/Reduced Model: Brake Sales 选择所剩三个预测变量和响应变量.Select the three remaining predictor variables and the response variable.Using Minitab Menu, STAT Regression Regression记住检查残差图Remember to check your residual plots回归分析:刹

15、车板销售Regression Analysis: Brake Sales 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 = No relationship between variables Ha = Some relationship exists between variables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Regression Analysis: Sales versus Mktg$, Sales Rep, LY(SalesRep)The regression equation isSales = - 66.9 + 11.8 Mktg$

16、+ 1.18 Sales Rep + 2.70 LY(SalesRep)Predictor Coef SE Coef T PConstant -66.91 16.22 -4.12 0.001Mktg$ 11.847 1.414 8.38 0.000HaSales Re 1.1764 0.1106 10.64 0.000HaLY(Sales 2.7027 0.1106 24.44 0.000HaS = 4.022 R-Sq = 98.2% R-Sq(adj) = 97.8%刹车板销售案例的其他MiniTab 输出The Rest of Mini Tab Output Brake Sales An

17、alysis of VarianceSource DF SS MS F PRegression 3 13870.1 4623.4 285.78 0.000Residual Error 16 258.8 16.2Total 19 14128.9Source DF Seq SSMktg$ 1 893.9Sales Re 1 3313.2LY(Sales 1 9663.0Unusual ObservationsObs Mktg$ Sales Fit SE Fit Residual St Resid 10 11.1 204.000 196.236 2.161 7.764 2.29R R denotes

18、 an observation with a large standardized residual刹车板销售R-Sq (修正后)Brake Sales R-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% of the variation in Y is explained by the Three factors included in the regression.尽管结果不错,但仍有2.2%刹车板销售的变差不能解释(While good, this still means that about 2.2%

19、of the variation in Brake Sales is still unexplained.)S = 4.022 R-Sq = 98.2% R-Sq(adj) = 97.8%多元回归Multiple Regression路线分析图Analyze Roadmap规划分析内容收集数据利用回归或最佳子集分析Analyze Using Regression or Best Subsets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Run Multiple Regr

20、ession Reduced Model因为有多条线，就不再使用拟合线图，No longer fitted line plot due to multiple lines刹车板销售残差Brake Sales Residuals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least squares 拟合规律.以此可以指导我们改进回归拟合模式.Not to be overlooked is residual analysis. Careful analysis of residuals tells whether any assumptions of the least s

21、quares fit are violated. This will guide us in improving the regression fit. 最小二乘方的假设Least Squares Assumptions:残差的变差不是由任何预测变量X引起的 The variance of the residuals do not depend upon any predictor variable, X.残差有着正态分布. Residuals are normally distributed.以时间为序,各残差间互不倚靠 Arranged in time order, the residua

22、ls are independent of each other.刹车板销售量的拟合及残差Brake Sales Fits & Residuals多元回归总结Multiple Regression Summary 这是用来建立Y = f(X1, X2, X3, . . .)该形式非常有用的统计工具 A powerful statistical tool that is used to build models of the form Y = 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. The best model is the

23、one with the fewest factors that explains the most variation in the response Y.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. Best Subsets is a useful technique to quickly zero in on potential good models回归里应避免没有价值的残差及元素间的共线性. Pitfalls to avoid in regression are poorly-behaved residuals and factor collinearity.多元回归

24、Multiple Regression路线分析图Analyze Roadmap规划分析内容收集数据利用回归或最佳子集分析Analyze Using Regression or Best Subsets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Run Multiple Regression Reduced Model因为有多条线，就不再使用拟合线图，No longer fitted line plot due to multiple lines多元回归的练习3-4人分为一组,记录下列数据:Y = 组里每人的