6西格瑪回歸分析ppt課件

1、回歸分析回歸分析Regression Analysis目的目的Objectivesl介紹相關(guān)性及回歸的基本概念介紹相關(guān)性及回歸的基本概念 Introduce The Basic Concepts of Correlation and Regressionl把回歸與六西格瑪路線圖結(jié)合起來把回歸與六西格瑪路線圖結(jié)合起來 Link Regression To The Six Sigma Roadmapl學(xué)習(xí)多元回歸的使用學(xué)習(xí)多元回歸的使用 Review the use of Multiple Regressionl介紹相關(guān)性及回歸的基本概念介紹相關(guān)性及回歸的基本概念 Introduce The Ba

2、sic Concepts of Correlation and Regressionl把回歸與六西格瑪路線圖結(jié)合起來把回歸與六西格瑪路線圖結(jié)合起來 Link Regression To The Six Sigma Roadmapl學(xué)習(xí)多元回歸的使用學(xué)習(xí)多元回歸的使用 Review the use of Multiple Regressionl介紹相關(guān)性及回歸的基本概念介紹相關(guān)性及回歸的基本概念 Introduce The Basic Concepts of Correlation and Regressionl把回歸與六西格瑪路線圖結(jié)合起來把回歸與六西格瑪路線圖結(jié)合起來 Link Regres

3、sion To The Six Sigma Roadmapl學(xué)習(xí)多元回歸的使用學(xué)習(xí)多元回歸的使用 Review the use of Multiple Regression2;.項目跟蹤圖項目跟蹤圖 第五版 項目開始日期21/01/2004項目類別“Y”“Y”變量數(shù)據(jù)變量數(shù)據(jù)采集計劃采集計劃制定項目制定項目 日程日程啟動項目書啟動項目書DMAIC改善定義定義確定”Y”變量和起草項目書項目書得以批準(zhǔn)流程圖流程圖C&EC&E矩陣或矩陣或故障樹分析故障樹分析FTAFTA第三十天第三十天MBBMBB審閱審閱FMEAFMEA或或故障樹分析故障樹分析FTAFTA測量系統(tǒng)分析測量系統(tǒng)分析MS

4、AMSA關(guān)鍵關(guān)鍵”X”X”變量變量 數(shù)據(jù)采集計劃數(shù)據(jù)采集計劃MBBMBB審閱審閱測量測量21/01/200421/01/200404/02/200404/02/200411/02/200411/02/200425/02/200425/02/200409/03/200409/03/200409/03/200409/03/200409/03/200409/03/2004初始能力研究初始能力研究 多元變量流程分析多元變量流程分析MBBMBB審閱審閱 合同批準(zhǔn)合同批準(zhǔn)分析分析22/03/200422/03/200415/04/200415/04/200415/04/200415/04/200415/0

5、4/200415/04/200415/04/200415/04/2004單因子或多因子測試單因子或多因子測試實驗設(shè)計實驗設(shè)計(DOE) (DOE) MBBMBB審閱審閱改善改善31/05/200431/05/200431/05/200431/05/200431/05/200431/05/2004控制計劃控制計劃最終能力研究最終能力研究 控制階段控制階段FMEAFMEA回顧回顧 重新修訂重新修訂RPNRPNMBBMBB審閱審閱項目最終匯報項目最終匯報 及報告及報告項目審核項目審核及項目收尾及項目收尾控制控制21/06/200421/06/200429/06/200429/06/200429/06

6、/200429/06/200405/07/200405/07/200409/07/200409/07/200409/07/200409/07/200419/07/200419/07/2004( (根據(jù)需要使用根據(jù)需要使用) )客戶心聲客戶心聲/ /業(yè)務(wù)之聲調(diào)業(yè)務(wù)之聲調(diào)查查VOC/VOBVOC/VOB需求分析需求分析流程再造流程再造 解決方案設(shè)計解決方案設(shè)計流程再造流程再造在這里輸入開始日期在這里輸入開始日期 確定改善方案確定改善方案由項目發(fā)起人在備選項目數(shù)據(jù)庫中完成由項目發(fā)起人在備選項目數(shù)據(jù)庫中完成在在6 6西格瑪西格瑪數(shù)據(jù)庫數(shù)據(jù)庫查找相似項目查找相似項目實施改善實施改善移交移交培訓(xùn)培訓(xùn)/ /

7、流程所有人簽準(zhǔn)流程所有人簽準(zhǔn)再造路線圖的日程是獨立計算的與以上DMAIC的日期不相關(guān)實際完成日期 計劃完成日期圖例圖例2/1/020022/3/022/3/02完成畫鉤3;.分析路線圖分析路線圖Analyze Roadmap 單一因子 X -單一因子 Y Single X - Single Y輸入變量輸入變量 X X X Data離散離散Discrete 連續(xù)連續(xù)Continuous 輸出變量輸出變量 Y Y Y Data離散離散Discrete 連續(xù)連續(xù)Continuous 卡方相關(guān)性分析卡方相關(guān)性分析Chi-Square邏輯回歸邏輯回歸Logistic Regression方差分析，方差分

8、析，均值均值/ /中位數(shù)測試中位數(shù)測試ANOVAMeans / Medians Tests回歸回歸Regression4;.什么是什么是 Y ? _ Y ? _ 數(shù)據(jù)類型數(shù)據(jù)類型? ? _什么是什么是 X ?X ? _ 數(shù)據(jù)類型數(shù)據(jù)類型 ? _? _應(yīng)該使用何種工具應(yīng)該使用何種工具? ? _案例案例 #1 #1 Scenario #1管理者想知道接線員的經(jīng)驗管理者想知道接線員的經(jīng)驗( (以月為單位衡量以月為單位衡量) )是否會對接聽顧客熱線電話需要的時間有影響是否會對接聽顧客熱線電話需要的時間有影響5;.相關(guān)性相關(guān)性Correlation 什么是相關(guān)性什么是相關(guān)性 ? What is corr

9、elation? 你是否有過如此經(jīng)驗?zāi)闶欠裼羞^如此經(jīng)驗: :測量某些產(chǎn)品并送至顧客處測量某些產(chǎn)品并送至顧客處，但他們回來告訴你的產(chǎn)品，但他們回來告訴你的產(chǎn)品不符規(guī)格不符規(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(rèn)為兩個裁判成績之相關(guān)性有多高在奧林匹克溜冰比賽上，你認(rèn)為兩個裁判成績之相關(guān)性有多高? ? How well correlated do you think two i

10、ce skating judges are at the Olympics?6;.相關(guān)性相關(guān)性Correlation路線分析圖路線分析圖Analyze Roadmap 畫出點陣圖畫出點陣圖Produce Scatter Plot計算相關(guān)性計算相關(guān)性Calculate Correlation評估評估r r 和和 P P值值 Evaluate r and P value7;.相關(guān)系數(shù)相關(guān)系數(shù)Correlation Coefficients 什么是相關(guān)系數(shù)什么是相關(guān)系數(shù)? ? So what is the Correlation Coefficient supposed to be anyway?

11、相關(guān)系數(shù)相關(guān)系數(shù) (r) (r)介于介于-1-1和和1 1之間之間 The Correlation Coefficient (r) lies between -1 and 1 一般規(guī)則一般規(guī)則:General Rules 相關(guān)系數(shù)相關(guān)系數(shù) (r) .80 (r) .80 或或 -0.8 .80 or 剎車距離Braking Distance = 182.8 + 0.4763 速度速度SpeedS = 13.5571 R-Sq = 69.5% R-Sq(adj) = 67.9%方差分析方差分析Analysis of VarianceSource DF SS MS F PRegression 1

12、7955.9 7955.91 43.29 0.000Error 19 3492.1 183.79Total 20 11448.0Minitab Minitab 更多輸出更多輸出R2 (Same one as before)28;.R2 - R2 - 有何意義有何意義? ?R2與P值，有助我們以統(tǒng)計做決策。R2被稱為 判斷判斷系數(shù)系數(shù)R2 and P , help us put some statistical backing behind our decisions. The R2 is called the coefficient of determinationR2 值代表“多少”輸出變異

13、總量可由回歸模式所解釋，其值介于 0 到 1 (0% 到 100%)。此值越高代表對該模式的可信度越高.R2 is a measure of the amount of variation in the output that is explained by the regression model. It will always be a value between 0 and 1 (0% to 100%). The higher this amount, the greater confidence we have in the model itself. R2100%0%29;.R2 -

14、 有何意義有何意義? ?The R2 = 69.5%這表明有69.5%的Y(剎車距離)的變差可以由X(速度)來解釋.This means 69.5% of the variation in Y (Braking Distance) can be explained by the X (Speed).30.5% 30.5% 是由其他因素引起的是由其他因素引起的.30.5% is due to something else.你的決策是什么?SpeedBraking Distance475450425400375350420400380360340320S13.5571R-Sq69.5%R-Sq(a

15、dj)67.9%Fitted Line PlotBraking Distance = 182.8 + 0.4763 Speed30;.R2-該為多大值? How Big Should It Be ? 視分析對象而定 如對安全系統(tǒng)或回紋針 That answer “depends” on what you are studying, e.g. safety systems or paper clips. 如果你在實驗一個新的安全保障系統(tǒng), 你的數(shù)據(jù)將由交通部審查.你的數(shù)值該需要有多“好”？ If you are experimenting with a new safety restraint

16、system, your numbers will probably be reviewed by the Department of Transportation. How “good” should you be ? 不同的課題會有不同的決策標(biāo)準(zhǔn) (通常為 +80%)。重要的是我們必須認(rèn)識到 R2 越高,統(tǒng)計模式越好。 Different texts suggest different decision criteria (usually +80%). The important thing to realize is that the higher the R2 the better t

17、he model.31;.回歸分析: 剎車距離v. 速度Regression Analysis: Braking Dist versus Speed回歸的等式為The regression equation is剎車距離Braking Distance = 182.8 + 0.4763 速度SpeedS = 13.5571 R-Sq = 69.5% R-Sq(adj) = 67.9%方差分析Analysis of VarianceSource DF SS MS F PRegression 17955.97955.91 43.29 0.000Error 193492.1 183.79Total

18、2011448.0P值里怎么了? What Is Going On Here ?Another P Value !32;.零假設(shè): 線段斜率=0 (無相關(guān)性)Ho: Slope of The Line = 0(No correlation)備擇假設(shè): 線段斜率 = 0(有相關(guān)性)Ha: Slope of The Line 0 (There is correlation)記住P P要小要小, , Ho Ho要倒要倒When P is low, Ho must go !P 值另一個假設(shè)檢定Another Hypothesis Test33;.Minitab 回歸- 殘差&擬合數(shù)Regres

19、sion - Residuals & Fits34;.Speed DistanceRESI1FITS1336325-17.8392342.839418375-6.8948 381.89535536715.1113 351.889445385-9.7546 394.75536537518.3484 356.652455395-4.5175 399.51739539524.0598 370.940405365-10.7031375.7033463557.3979347.60. . . . . . . . .Minitab 更多輸出More Output35;.速度Speed距離Distan

20、ce殘差1 RESI1擬合數(shù)1 FITS1336325-17.8392342.839殘差&擬合數(shù)- 它們是什么? Residual & Fit - What Are They ?擬和線Fitted Line336325實際點Actual Point殘差距離Residual Distance (-17.8392)理論擬合點Theoretical Fit 34236;.速度Speed 距離Distance殘差1 RESI1 擬合數(shù)1 FITS1336325-17.8392 342.839殘差- 點到擬合線的垂直距離 在線下方為負(fù), 在線上方為正.Residual - The ver

21、tical distance to the fitted line Negative is below , positive is above擬合數(shù)擬合數(shù)- - Y值在擬合線上的理論值Fits - The theoretical y value on the fitted line殘差&擬合數(shù)- 它們是什么? Residual & Fit - What Are They ?37;.回歸- 殘差&擬合數(shù)- 圖表總結(jié)Regression - Residuals & Fits Graphical Summary38;.數(shù)據(jù)應(yīng)該通過 “胖鉛筆測試”“Fat Pencil

22、 Test”殘差分析Residual Analysis數(shù)據(jù)應(yīng)該像鐘型分布Data Should Fit A Bell Shaped CurveResidualPercent30150-15-30999050101Fitted ValueResidual40038036034020100-10-20ResidualFrequency20100-10-206.04.53.01.50.0Observation OrderResidual201816141210864220100-10-20Normal Probability Plot of the ResidualsResiduals Versus

23、 the Fitted ValuesHistogram of the ResidualsResiduals Versus the Order of the DataResidual Plots for Braking Distance比較P值與殘差正態(tài)分布測試的結(jié)果Check P value with Normality test on Residuals39;.數(shù)據(jù)應(yīng)在控制線內(nèi),調(diào)查異常點Data Should Be In ControlInvestigate Outliers殘差分析Residual Analysis數(shù)據(jù)應(yīng)無任何規(guī)律Data Should Exhibit No Patter

24、nsResidualPercent30150-15-30999050101Fitted ValueResidual40038036034020100-10-20ResidualFrequency20100-10-206.04.53.01.50.0Observation OrderResidual201816141210864220100-10-20Normal Probability Plot of the ResidualsResiduals Versus the Fitted ValuesHistogram of the ResidualsResiduals Versus the Orde

25、r of the DataResidual Plots for Braking Distance40;.其他案例Other Examples使用Minitab Project: 練習(xí) #1: Analyze worksheet Y = 油漆厚度Paint Thickness X1 = 氣壓Air Pressure X2 = 黏度Viscosity練習(xí) #2: Analyze worksheet Y = 客戶回應(yīng)時間Customer Response TimeX1 = 代理人有經(jīng)驗程度Experience Level of AgentX2 = 與客戶的距離Distance From Custom

26、er Site練習(xí) #3: Analyze 41;.注意陳述中的注意陳述中的因果關(guān)系因果關(guān)系Beware of Stating Causality即使我們建立了Y與X之相關(guān)性，但并不能確定X之變異將一定導(dǎo)致Y之變異。If we establish a correlation between Y and a X, that doesnt necessarily mean variation in X caused variation in Y.其它潛藏的變量，可能造成X與Y之改變。 Other variables may be lurking that cause both X and Y to

27、 vary.42;.研究指出當(dāng)醫(yī)院規(guī)模增加，病人死亡率亦顯著提升。這么說來，我們應(yīng)該避免去大型醫(yī)院就診嗎？Research has consistently shown that as the hospital size increases, the death rate of patients dramatically increases. So, should we avoid large hospitals?回歸問題探討：回歸問題探討：Xs Xs 缺失缺失 Regression Issues - Missing Xs0 1 2 4 5 X =醫(yī)院規(guī)模Y =死亡率1510543;.有關(guān)一個

28、城市的數(shù)據(jù)顯示，當(dāng)城市里鸛的數(shù)量增加時，城市人口也增加鸛真的影響城市人口嗎？Data on a city showed that as population density of storks increased, so did the towns population. Did storks influence the population ?0 1 2 4 5 X= X= 鸛的數(shù)量鸛的數(shù)量Y =Y =城市人口城市人口15105回歸問題探討：回歸問題探討：Xs Xs 缺失缺失 Regression Issues - Missing Xs44;.回歸問題探討回歸問題探討Regression I

29、ssues 研究范圍太狹窄研究范圍太狹窄Range Of Study Too Small0 1 2 4 5 X= X= 車齡車齡Age of CarY =Y =車值車值 Sales Value1510545;.$ $ 車值車值Value of Car車齡車齡Age of Car現(xiàn)在的數(shù)據(jù)看來如何？What Would This Look Like Now ?0 15 10 15 20 25 30 35 40 45 50回歸問題探討回歸問題探討Regression Issues 研究范圍太狹窄Range Of Study Too Small46;.分析路線圖分析路線圖Analyze Roadma

30、p 輸入變量輸入變量 X X X Data單一因子單一因子 XSingle X多因子多因子 XsMultiple Xs 輸出變量輸出變量 Y Y Y Data單一輸出單一輸出 Y Single Y 多元輸出多元輸出 Y Multiple Ys 多變量分析Multivariate Analysis(注意: 這與多元變量分析不同)(Note: This Is Not The Same As Multi-Vari Analysis)輸入變量輸入變量 X X Data離散 Discrete 連續(xù) Continuous 輸出變量輸出變量 Y Y Y Data卡方相關(guān)性分析Chi-Square邏輯回歸Lo

31、gistic RegressionT T 測試，方差分析，均值/中位數(shù)測試T-test, ANOVAMeans/Medians Tests回歸Regression多元回歸Multiple RegressionMedians Tests2, 3, 4 way.ANOVAMultiple Logistic Regression多元邏輯回歸離散 Discrete 連續(xù) Continuous 離散 Discrete 連續(xù) Continuous 離散 Discrete 連續(xù) Continuous 2, 3, 4 因子方差分析中位數(shù)測試多元邏輯回歸Multiple Logistic Regression輸

32、入變量輸入變量 X X Data輸出變量輸出變量 Y Y Data47;.多元回歸分析Multiple Regression Analysis 兩個或多個流程變量（Xs)可能對流程表現(xiàn)產(chǎn)生影響(Y). Two or more process variables (Xs) may have an influence upon process performance (Y). 多元回歸應(yīng)用于有兩個或多個可能的預(yù)測變量的情況Multiple regression is used whenever there are two or more possible predictor variables.

33、多元回歸的一般等式為The general form of the multiple regression equation isnnXbXbXbbY.2211048;.案例：剎車板銷售量Example: Brake Sales例中對剎車板銷售量進(jìn)行次的觀察已知有五個流程變量和一個表現(xiàn)變量，：Twenty observations regarding Brake Sales are given. There are Five known process variables and one performance variable, Y:X1 = 年度YearX2 = 市場營銷費用Mktg$X3

34、 = 今年銷售人員數(shù)Sales RepX4 = 去年（銷售人員）數(shù)LY(Sales Rep)X5 = 產(chǎn)品ProductY = 銷售Sales利用數(shù)據(jù)找出可能影響”銷售量”的”重要的幾個”流程變量. .Use the data to mine for the “vital few” process variables that may influence “Sales”. 49;.剎車板銷售量數(shù)據(jù) YearMktg$SalesRep LY(SalesRep)Product Sales 19.63020 18130 210.3203017157 310.2152019129 410.425152

35、2129 510.6302524162 610.7153018154 710.5251517132 810.9352516172 911.0403514207 1011.1204018204 1111.2252022144 1211.2352525175 1311.453527167 1411.21252897 1511.6161218122 1611.7211616139 1711.8222115153 1811.8242216156 1911.8262410172 2012.128261817850;.剎車板銷售量55443322110XbXbXbXbXbbY我們的目的是找到適用于下列形式

36、的多元回歸：Our goal is to fit a multiple regression of the following form這個問題便于闡明下列多元回歸的其他方面：This problem will illustrate the following additional aspects of multiple regression去掉沒有解釋能力的變量 elimination of X-variables that have no explanatory power;殘差分析 residual analysis留在模式里的變量是能控制的在西格瑪里，我們的目標(biāo)就是要控制少數(shù)變量Wha

37、t stays in the model must have controls. In Six Sigma, goal is to control a few. 51;.多元回歸Multiple Regression路線分析圖規(guī)劃分析內(nèi)容收集數(shù)據(jù)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(guān)性）Multicollinearity “X” Check (correlation)使用多元回歸簡化模式Run Multiple Regression Reduced Model因為有多

38、條線，就不再使用擬合線圖，No longer fitted line plot due to multiple lines52;.相關(guān)的預(yù)測變量（多元共線性）相關(guān)的預(yù)測變量（多元共線性）Correlated Predictor Variables (Multicollinearity)nnXbXbXbbY.22110流程結(jié)果（）與預(yù)測變量（s)間的相關(guān)性是有用的它可以幫助我們找出可能的因果關(guān)系 Correlation between the process output (Y) and the predictor variables (Xs) is good - helps us identi

39、fy possible cause and effect relationships.相反，預(yù)測變量間的相關(guān)性卻是一個問題 Correlation between predictors, in contrast, is a problem.計算里的正負(fù)符號和預(yù)測變量間的相關(guān)性大小可能有錯誤.Calculated signs and magnitudes of correlated predictors may be wrong.計算出的P值可能偏大.Calculated P-values may be large.預(yù)測變量間的高相關(guān)性被稱為”共線性”High correlation betwe

40、en predictor variables is called “collinearity”53;.多元共線性：剎車板銷售量Multicollinearity: Brake Sales左側(cè)是前剎車板銷售量預(yù)測變量：Predictor Variables: (1) 年度Year;(2)市場營銷費用Marketing $;(3) 今年銷售人員數(shù)量How many Sales Reps this year;(4)去年銷售人員數(shù)量How many Sales Reps last year.(5) 產(chǎn)品Product YearMktg$SalesRepLY(SalesRep)Product Sales

41、19.6302018130210.3203017157310.2152019129410.4251522129510.6302524162610.7153018154710.5251517132810.9352516172911.04035142071011.12040182041111.22520221441211.23525251751311.4535271671411.212528971511.61612181221611.72116161391711.82221151531811.82422161561911.82624101722012.128261817854;.多元共線性：剎車板

42、銷售量多元共線性：剎車板銷售量選擇所有五個預(yù)測變量和響應(yīng)變量Select all five predictor variables and the response variable.使用 Minitab 菜單, STAT BASIC STATS CORRELATION.不選擇p值選項Uncheck p value55;.年度和市場營銷費用有著很高的相關(guān)性！我們必須只能選擇一個作為預(yù)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 wi

43、ll have to choose one or the other of the correlated predictor 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. 基本原則基本原則, , 如果相關(guān)性如果相關(guān)性 0.8 or0.8 or - 0.8 Regression Best Subsets.59;.最佳子集回歸：剎車板銷售 注意”年度

44、”從模式中去掉了.Best Subsets Regression: Sales versus Mktg$, Sales Rep, .Response is Sales 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

45、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 60;.多元回歸Multiple Regression路線分析圖規(guī)劃分析內(nèi)容收集數(shù)據(jù)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(guān)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

46、longer fitted line plot due to multiple lines61;.回歸:剎車板銷售Regression: Brake Sales 選擇所有四個預(yù)測變量和響應(yīng)變量.Select all four predictor variables and the response variable.使用 Minitab 菜單, STAT Regression Regression62;.回歸分析:剎車板銷售Regression Analysis: Brake Sales 零假設(shè) = 變量間沒有任何關(guān)系備擇假設(shè)= 變量間有一些關(guān)系Ho = No relationship bet

47、ween variables Ha = Some relationship exists between variablesRegression Analysis: Sales versus 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

48、.92 0.000 HaSales Re 1.1751 0.1224 9.60 0.000 HaLY(Sales 2.7023 0.1154 23.42 0.000 HaProduct -0.0068 0.2337 -0.03 0.977 HoS = 4.154 R-Sq = 98.2% R-Sq(adj) = 97.7%63;.回歸/簡化模式:剎車板銷售Regression/Reduced Model: Brake Sales 選擇所剩三個預(yù)測變量和響應(yīng)變量.Select the three remaining predictor variables and the response var

49、iable.Using Minitab Menu, STAT Regression Regression記住檢查殘差圖記住檢查殘差圖Remember to check your residual plots64;.回歸分析:剎車板銷售Regression Analysis: Brake Sales 零假設(shè) = 變量間沒有任何關(guān)系備擇假設(shè)= 變量間有一些關(guān)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)Regre

50、ssion Analysis: Sales versus Mktg$, Sales Rep, LY(SalesRep)The regression equation isSales = - 66.9 + 11.8 Mktg$ + 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 0.000 HaSales Re 1.1764 0.1106 10.64 0.000 HaLY(Sales 2.7027 0.1106

51、24.44 0.000 HaS = 4.022 R-Sq = 98.2% R-Sq(adj) = 97.8%65;.剎車板銷售案例的其他MiniTab 輸出The Rest of Mini Tab Output Brake Sales Analysis 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 96

52、63.0Unusual ObservationsObs Mktg$ Sales Fit SE Fit Residual St Resid 10 11.1 204.000 196.236 2.161 7.764 2.29R R denotes an observation with a large standardized residual66;.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 explai

53、ned by the Three factors included in the regression.盡管結(jié)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% of the variation in Brake Sales is still unexplained.)S = 4.022 R-Sq = 98.2% R-Sq(adj) = 97.8%67;.多元回歸多元回歸Multiple Regression路線分析圖路線分析圖Analyze Roadmap規(guī)劃分析內(nèi)容收集數(shù)據(jù)利用回歸或最佳子集分析Analy

54、ze 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(guān)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，因為有多條線，就不再使用擬合線圖就不再使用擬合線圖，No longer fitted line plot due to multiple lines68;.剎車板銷售殘差Brake Sales Residuals殘差分析同樣不容忽視. 對殘差進(jìn)行仔細(xì)分析會幫助我們確定我們

55、沒有違反least squares 擬合規(guī)律.以此可以指導(dǎo)我們改進(jìn)回歸擬合模式.Not to be overlooked is residual analysis. Careful analysis of residuals tells whether any assumptions of the least squares fit are violated. This will guide us in improving the regression fit. 最小二乘方的假設(shè)Least Squares Assumptions:殘差的變差不是由任何預(yù)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 distri