西格瑪回歸分析課件

1、回歸分析Regression Analysis目的Objectives介紹相關性及回歸的基本概念 Introduce The Basic Concepts of Correlation and Regression把回歸與六西格瑪路線圖結合起來 Link Regression To The Six Sigma Roadmap學習多元回歸的使用 Review the use of Multiple Regression介紹相關性及回歸的基本概念 Introduce The Basic Concepts of Correlation and Regression把回歸與六西格瑪路線圖結合起來 Li

2、nk Regression To The Six Sigma Roadmap學習多元回歸的使用 Review the use of Multiple Regression介紹相關性及回歸的基本概念 Introduce The Basic Concepts of Correlation and Regression把回歸與六西格瑪路線圖結合起來 Link Regression To The Six Sigma Roadmap學習多元回歸的使用 Review the use of Multiple Regression項目跟蹤圖 第五版 項目開始日期21/01/2004項目類別“Y”變量數(shù)據采集計

3、劃制定項目 日程啟動項目書DMAIC改善定義確定”Y”變量和起草項目書項目書得以批準流程圖C&E矩陣或故障樹分析FTA第三十天MBB審閱FMEA或故障樹分析FTA測量系統(tǒng)分析MSA關鍵”X”變量 數(shù)據采集計劃MBB審閱測量21/01/200404/02/200411/02/200425/02/200409/03/200409/03/200409/03/2004初始能力研究 多元變量流程分析MBB審閱合同批準分析22/03/200415/04/200415/04/200415/04/200415/04/2004單因子或多因子測試實驗設計(DOE) MBB審閱改善31/05/200431/05/2

4、00431/05/2004控制計劃最終能力研究 控制階段FMEA回顧 重新修訂RPNMBB審閱項目最終匯報 及報告項目審核及項目收尾控制21/06/200429/06/200429/06/200405/07/200409/07/200409/07/200419/07/2004(根據需要使用)客戶心聲/業(yè)務之聲調查VOC/VOB需求分析流程再造 解決方案設計流程再造在這里輸入開始日期 確定改善方案由項目發(fā)起人在備選項目數(shù)據庫中完成在6西格瑪數(shù)據庫查找相似項目實施改善移交培訓/流程所有人簽準再造路線圖的日程是獨立計算的與以上DMAIC的日期不相關實際完成日期 計劃完成日期圖例2/1/020022/

5、3/02完成畫鉤分析路線圖Analyze Roadmap 單一因子 X -單一因子 Y Single X - Single Y輸入變量 X X Data離散Discrete 連續(xù)Continuous 輸出變量 Y Y Data離散Discrete 連續(xù)Continuous 卡方相關性分析Chi-Square邏輯回歸Logistic Regression方差分析，均值/中位數(shù)測試ANOVAMeans / Medians Tests回歸Regression什么是 Y ? _ 數(shù)據類型? _什么是 X ? _ 數(shù)據類型 ? _應該使用何種工具? _案例 #1 Scenario #1管理者想知道接線員

6、的經驗(以月為單位衡量)是否會對接聽顧客熱線電話需要的時間有影響相關性Correlation 什么是相關性 ? What is correlation?你是否有過如此經驗:測量某些產品并送至顧客處，但他們回來告訴你的產品不符規(guī)格? Have you ever measured something and then shipped to your customer only for them to tell you it doesnt meet spec?在奧林匹克溜冰比賽上，你認為兩個裁判成績之相關性有多高? How well correlated do you think two ice s

7、kating judges are at the Olympics?相關性Correlation路線分析圖Analyze Roadmap 畫出點陣圖Produce Scatter Plot計算相關性Calculate Correlation評估r 和 P值 Evaluate r and P value相關系數(shù)Correlation Coefficients什么是相關系數(shù)? So what is the Correlation Coefficient supposed to be anyway?相關系數(shù) (r)介于-1和1之間 The Correlation Coefficient (r) li

8、es between -1 and 1一般規(guī)則:General Rules 相關系數(shù) (r) .80 或 .80 or BASIC STATS CORRELATION.不選擇p值選項Uncheck p value年度和市場營銷費用有著很高的相關性！我們必須只能選擇一個作為預測變量在回歸擬合中使用市場營銷費用可能受年度影響，因此我們保留市場營銷費用，而去掉年度變量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. 基本原則, 如果相關性 0.8 or Regression Best Subsets.最佳子集回歸：剎車板銷售 注意”年度”從模式中去掉了.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 多元回歸Multiple Regre

11、ssion路線分析圖規(guī)劃分析內容收集數(shù)據利用回歸或最佳子集分析Analyze Using Regression or Best Subsets評估殘差制定決策評估 R2 及 P值的顯著性多元共線性分析（相關性）Multicollinearity “X” Check (correlation)使用多元回歸簡化模式Run Multiple Regression Reduced Model因為有多條線，就不再使用擬合線圖，No longer fitted line plot due to multiple lines回歸:剎車板銷售Regression: Brake Sales 選擇所有四個預測變量

12、和響應變量.Select all four predictor variables and the response variable.使用 Minitab 菜單, STAT Regression Regression回歸分析:剎車板銷售Regression Analysis: Brake Sales 零假設 = 變量間沒有任何關系備擇假設= 變量間有一些關系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%回歸/簡化模式:剎車板銷售Regression/Reduced Model: Brake Sales 選擇所剩三個預測變量和響應變量.Select the three remaining predictor variables and the response variable.Using Minitab Menu, STAT Regression Regression記住檢查殘差圖Remember to check your residual plots回歸分析:剎

15、車板銷售Regression Analysis: Brake Sales 零假設 = 變量間沒有任何關系備擇假設= 變量間有一些關系Ho = No relationship between variables Ha = Some relationship exists between variables回歸分析:銷售量v.市場營銷費用,銷售人員數(shù),去年銷售人員數(shù)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%剎車板銷售案例的其他MiniTab 輸出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剎車板銷售R-Sq (修正后)Brake Sales R-Sq (Adjusted)R-Sq (Adj)= 97.8%Y的變差可由回歸里的三個元素解釋.R-Sq (Adj) = 97.8% of the variation in Y is explained by the Three factors included in the regression.盡管結果不錯,但仍有2.2%剎車板銷售的變差不能解釋(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%多元回歸Multiple Regression路線分析圖Analyze Roadmap規(guī)劃分析內容收集數(shù)據利用回歸或最佳子集分析Analyze Using Regression or Best Subsets評估殘差制定決策評估 R2 及 P值的顯著性多元共線性分析（相關性）Multicollinearity “X” Check (correlation)使用多元回歸簡化模式Run Multiple Regr

20、ession Reduced Model因為有多條線，就不再使用擬合線圖，No longer fitted line plot due to multiple lines剎車板銷售殘差Brake Sales Residuals殘差分析同樣不容忽視. 對殘差進行仔細分析會幫助我們確定我們沒有違反least squares 擬合規(guī)律.以此可以指導我們改進回歸擬合模式.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. 最小二乘方的假設Least Squares Assumptions:殘差的變差不是由任何預測變量X引起的 The variance of the residuals do not depend upon any predictor variable, X.殘差有著正態(tài)分布. Residuals are normally distributed.以時間為序,各殘差間互不倚靠 Arranged in time order, the residua

22、ls are independent of each other.剎車板銷售量的擬合及殘差Brake Sales Fits & Residuals多元回歸總結Multiple Regression Summary 這是用來建立Y = f(X1, X2, X3, . . .)該形式非常有用的統(tǒng)計工具 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來解釋響應變量Y的絕大多數(shù)變異的模式. The best model is the

23、one with the fewest factors that explains the most variation in the response Y.最好子集回歸是一個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回歸里應避免沒有價值的殘差及元素間的共線性. Pitfalls to avoid in regression are poorly-behaved residuals and factor collinearity.多元回歸

24、Multiple Regression路線分析圖Analyze Roadmap規(guī)劃分析內容收集數(shù)據利用回歸或最佳子集分析Analyze Using Regression or Best Subsets評估殘差制定決策評估 R2 及 P值的顯著性多元共線性分析（相關性）Multicollinearity “X” Check (correlation)使用多元回歸簡化模式Run Multiple Regression Reduced Model因為有多條線，就不再使用擬合線圖，No longer fitted line plot due to multiple lines多元回歸的練習3-4人分為一組,記錄下列數(shù)據:Y = 組里每人的