Presentation is loading. Please wait.

Presentation is loading. Please wait.

Blended Lean Six Sigma Black Belt Training – ABInBev Correlation and Regression ©2010 ASQ. All Rights Reserved.

Similar presentations


Presentation on theme: "Blended Lean Six Sigma Black Belt Training – ABInBev Correlation and Regression ©2010 ASQ. All Rights Reserved."— Presentation transcript:

1 Blended Lean Six Sigma Black Belt Training – ABInBev Correlation and Regression ©2010 ASQ. All Rights Reserved.

2 2 Module Objectives Learn and apply some key Black Belt tools used to analyze your data How to develop and interpret the correlation between variables Develop a mathematical model expressing the relationshipegression o Regression o Simple Linear Regression o Multiple Linear Regression o Logistic Regression This review module is aligned with your Moresteam Web Training, Session 7: Identifying Root Cause

3 © 2010 ASQ. All Rights Reserved. 3 So Where Are We Now? We have understood our process using process maps and FMEA. Created graphs and charts to visualize what is happening in our processseven basic tools. Validated our measurement system to ensure our data is both precise and accurateGage R&R. Collected data to establish our process performance using process capability analysis. Now we are going to use the statistical tools to infer cause and effect/uncover underlying relationships.

4 © 2010 ASQ. All Rights Reserved. 4 Terms Correlation Used when both Y and X are continuous Measures the strength of linear relationship between Y and X Metric: Pearson Correlation Coefficient, r (r varies between -1 and +1) o Perfect positive relationship: r = 1 o No relationship: r = 0 o Perfect negative relationship: r = -1 Regression Simple linear regression used when both Y and X are continuous Quantifies the relationship between Y and X (Y = 0 + 1 X) Metric: Coefficient of Determination, R-Sq (varies from 0.0 to 1.0 or zero to 100%) o None of the variation in Y is explained by X, R-Sq = 0.0 o All of the variation in Y is explained by X, R-Sq = 1.0

5 © 2010 ASQ. All Rights Reserved. 5 Correlation Coefficients: Illustration r = 0.0 r = -1.0 1031021011009998 103 102 101 100 99 98 X Y SCATTERPLOT OF Y VERSUS X r = +1.0

6 © 2010 ASQ. All Rights Reserved. 6 Correlation: Minitab Example Voltage for the same power supply is measured at Station 1 and Station 2. Determine the correlation for voltage between the two stations. Approach: Open Datafile:CORRELAT.mtw (the data are displayed in the Data Window) Go to Stat > Basic Statistics > Correlation…

7 © 2010 ASQ. All Rights Reserved. 7 Correlation: Minitab Example (Continued) 1.Select C1 Station 1 and C2 Station 2 2.Select Display p-values 2 1 Graph > Scatterplot…Simple

8 © 2010 ASQ. All Rights Reserved. 8 Correlation: Minitab Example (Continued) From Minitab Session Window Null Hypothesis: no correlation between Station 1 and Station 2 (H 0 is false because p is less than 0.05)

9 © 2010 ASQ. All Rights Reserved. 9 ABI Example 1 – Correlation This project related to measuring client satisfaction in the BSC. Client satisfaction was measured by a monthly survey of five general questions Four answers could be given for each question: very dissatisfied, dissatisfied, satisfied, and very satisfied. The questions were about response time, language knowledge, helpfulness, quality of solution, and knowledge. A correlation test was run to determine if there is a relationship between the questionsmeaning that if a low score in one area might mean a low score in another, and so on… Isabelle Verdoodt and Matthias Pindur Belt Project, Zone WE © Anheuser-Busch InBev. All Rights Reserved.

10 © 2010 ASQ. All Rights Reserved. 10 © 2010 ASQ. All Rights Reserved. ABI Example 1 – Correlation (Continued) Is there a correlation betweeen customer satisfaction questions? Isabelle Verdoodt and Matthias Pindur Belt Project, Zone WE © Anheuser-Busch InBev. All Rights Reserved. There is only correlation between the questions Helpfulness and Knowledge.

11 © 2010 ASQ. All Rights Reserved. 11 © 2010 ASQ. All Rights Reserved. ABI Example 2 – Correlation POC buyout is a type of trade investment to POC with the agreement about volume commitment, loyalty request, or other conditionality. POC buyout is a key driver of core+ and premium business in the restaurant channel and the nightlife channel. It is the single biggest investment in China, accounting for 45% of total China commercial investments (2.4 billion RMB in 2011). A correlation test was run to determine if there was any correlation between the volume sold and investment made for four different brands. Luke Zhou Belt Project, Zone APAC © Anheuser-Busch InBev. All Rights Reserved.

12 © 2010 ASQ. All Rights Reserved. 12 © 2010 ASQ. All Rights Reserved. ABI Example 2 – Correlation (Continued) Pearson CorrelationP-Value Volume vs. Investment / case – Bud SBT 0.8190.000 Volume vs. Investment / case – HICE 500 0.5940.000 Volume vs. Investment / case - Bud BBT.8900.000 Volume vs. Investment / case – HICE 600.1390.312 Is there a correlation? What is the strength of the relationship? Is there a correlation? What is the strength of the relationship? Luke Zhou Belt Project, Zone APAC © Anheuser-Busch InBev. All Rights Reserved.

13 © 2010 ASQ. All Rights Reserved. 13 © 2010 ASQ. All Rights Reserved. Testing Method Selection Matrix Variable TypeAttribute YCount YContinuous Y Discrete X 1 or 2 Treatments Proportions 3+ Treatments Chi Square 1 or 2 Treatments Poisson 3+ Treatments Chi Square 1 or 2 Treatments T tests 3+ Treatments ANOVA Continuous X Logistic Regression Least Squares Regression

14 © 2010 ASQ. All Rights Reserved. 14 Simple Linear Regression Analysis Used to fit lines and curves to data when the parameters ( s) are linear The fitted lines: o Quantify the relationship between the predictor (input) variable (X) and response (output) variable (Y) o Help to identify the vital few Xs o Enable predictions of the response Y to be made from a knowledge of the predictor X o Identify the impact of controlling a process input variable (X) on a process output variable (Y) Produces an equation of the form:

15 © 2010 ASQ. All Rights Reserved. 15 Regression: Minitab Example 1 A Black Belt in the Supply department is tracking the output of voltage at two different stations. Voltage is measured at Station 1 and Station 2. A Black Belt is given the task of predicting the voltage at Station 2 from the voltage measured at Station 1. Stat>Regression>Fitted Line Plot Approach: Open Datafile: CORRELAT.mtw (the data are displayed in the Data Window) Go to Stat > Regression > Fitted Line Plot…

16 © 2010 ASQ. All Rights Reserved. 16 Regression: Minitab Example 1 (Continued)

17 © 2010 ASQ. All Rights Reserved. 17 Regression: Minitab Example 1 (Continued) Prediction equation Coefficient of Determination: use R- Sq for simple linear regression (one X) Fitted line: obeys the prediction equation

18 © 2010 ASQ. All Rights Reserved. 18 Regression: Minitab Example 1 (Continued) From the Session Window, the regression equation is: Station 2 = -0.3402 + 1.054 Station 1 o The intercept (b 0 ) is where the fitted line (regression line) crosses the Y-axis when X = 0. o The slope, b 1, is rise over run, or Y/ X. The coefficients b 0 and b 1 are estimates of the population parameters 0 and 1 : they are linear coefficients. Intercept, b 0 Slope, b 1 Practically, what does this mean? You can measure the voltage only at Station 1 and plug it into the equation. You can then predict the voltage at Station 2.. Practically, what does this mean? You can measure the voltage only at Station 1 and plug it into the equation. You can then predict the voltage at Station 2.. As a result of the regression equation, you no longer need to measure the voltage at Station 2.

19 © 2010 ASQ. All Rights Reserved. 19 © 2010 ASQ. All Rights Reserved. Statistical Significance – Minitab Example 2 An analysis of variance (ANOVA) table informs us about the statistical significance of the regression analysis. Hypothesis for Regression: o H 0 : The regression results from common cause variationwhen H 0 is true, there is no statistically significant regression, and the best prediction of Y is the mean of Y. o Ha: The regression is statistically significant. o Look at the p-value used to evaluate the null hypothesis; in this case, alpha = 0.05. So if p is less than alpha, then reject the null hypothesis. You can conclude that the regression is statistically significant Approach: Use Datafile:REGRESSANOVA.mtw Go to Stat > Regression… >Regression

20 © 2010 ASQ. All Rights Reserved. 20 ANOVA for Simple Linear Regression – Minitab Example 2 (Continued) REGRESSANOVA.mtw Stat > Regression… >Regression

21 © 2010 ASQ. All Rights Reserved. 21 © 2010 ASQ. All Rights Reserved. ANOVA for Simple Linear Regression – Minitab Example 2 (Continued) Regression is significant: p < 0.05 What is R-sq value telling us?

22 © 2010 ASQ. All Rights Reserved. 22 © 2010 ASQ. All Rights Reserved. Analysis of Residuals – Minitab Example 2 (Continued) Residuals are used to test the adequacy of the prediction equation (model) In residual plots, three types of plots indicate model inadequacy The plots will be dramaticnot subtle! 1. Fans2. Bands sloping up or down 3. Curved bands

23 © 2010 ASQ. All Rights Reserved. 23 © 2010 ASQ. All Rights Reserved. Analysis of Residuals – Minitab Example 2 (Continued) Do you see any patterns in the residuals that might indicate model inadequacy?

24 © 2010 ASQ. All Rights Reserved. 24 Regression: Minitab Example 3 Illustrating the analysis of residuals Use Datafile: RESIDUALS.mtw Go to Stat > Regression… >Fitted Line Plot Linear

25 © 2010 ASQ. All Rights Reserved. 25 © 2010 ASQ. All Rights Reserved. Regression: Minitab Example 3 (Continued) R-Sq is 89.7%. The regression is significant. Can we do better? How do the residuals look?

26 © 2010 ASQ. All Rights Reserved. 26 © 2010 ASQ. All Rights Reserved. Regression: Minitab Example 3 (Continued) Not quite random! What do the Residuals look like? Is the straight line a best fit? What do you suggest?

27 © 2010 ASQ. All Rights Reserved. 27 Regression: Minitab Example 3 (Continued) Continuing with the same example ….. Use Datafile: RESIDUALS.mtw Go to Stat > Regression… >Fitted Line Plot > Quadratic Illustrating the analysis of residuals

28 © 2010 ASQ. All Rights Reserved. 28 Regression: Minitab Example 3 (Continued) Improving the model adequacy increased R-Sq from 89.7% to 95.0% How do the residuals look?

29 © 2010 ASQ. All Rights Reserved. 29 © 2010 ASQ. All Rights Reserved. ABI Example 1: Correlation and Regression Trying to determine if there is a relationship between Customer Delivery Performance and Forecast Accuracy? What is the Regression Equation? UKI Forecast Accuracy (FA) © Anheuser Busch InBev. All Rights Reserved. Gustavo Burger Belt Project – Zone WE

30 © 2010 ASQ. All Rights Reserved. 30 © 2010 ASQ. All Rights Reserved. Bud SBT Pearson correlation: 0.819 P value:0.00 Legend: Volume is units sold Investment per case is how much money is paid to the POC Legend: Volume is units sold Investment per case is how much money is paid to the POC Luke Zhou Belt Project - Zone APAC ABI Example 2: Correlation and Regression © Anheuser Busch InBev. All Rights Reserved.

31 © 2010 ASQ. All Rights Reserved. 31 © 2010 ASQ. All Rights Reserved. The regression equation is: Gross Inv Val = 3,531,232 + 854,979 Vol pack (MM bbl) Predictor Coef SE Coef T P Constant 3531232 1751989 2.02 0.072 Vol pack (MM bbl) 854979 191217 4.47 0.001 S = 2079206 R-Sq = 66.7% R-Sq(adj) = 63.3% Analysis of Variance Source DF SS MS F P Regression 1 8.64274E+13 8.64274E+13 19.99 0.001 Residual Error 10 4.32310E+13 4.32310E+12 Total 11 1.29658E+14 Regression Analysis: Gross Inv Val vs. Volume packaged Katie Shiro Belt Project, Zone NA What is the regression equation? What is the Rsq (adj) figure telling you? What is the regression equation? What is the Rsq (adj) figure telling you? ABI Example 3: Correlation and Regression – Spare Parts Inventory Determine whether these is a correlation between the inventory value of spare parts and the volume packaged at each brewery. © Anheuser Busch InBev. All Rights Reserved.

32 © 2010 ASQ. All Rights Reserved. 32 Multiple Linear Regression – Exercise 1 (Continued) Our goal is to fit a multiple regression of the following form: This example will illustrate the following additional aspects of multiple regression: 1. Elimination of X-variables that have no explanatory power 2. Residual analysis

33 © 2010 ASQ. All Rights Reserved. 33 Multiple Factor Correlation and Regression Data on water usage has been collected along with data on factors that may be used to predict water usage. The factors were average temperature, production volume, number of associates, number of days of plant operation, and number of visitors. Data is in Water Usage.mtw

34 © 2010 ASQ. All Rights Reserved. 34 Multiple Factor Regression Stat>Regression>General Regression Recommend you always turn this option on.

35 © 2010 ASQ. All Rights Reserved. 35 Session Window Regression Equation Water Usage = 6805.38 + 17.2286 Average Temp + 0.221781 Production - 138.578 Operating Days - 26.4302 Associates - 1.59134 Visitors Coefficients Term Coef SE Coef T P VIF Constant 6805.38 1461.69 4.65583 0.001 Average Temp 17.23 6.64 2.59330 0.025 1.26281 Production 0.22 0.05 4.41450 0.001 6.74070 Operating Days -138.58 55.09 -2.51543 0.029 1.27287 Associates -26.43 9.27 -2.85192 0.016 6.77552 Visitors -1.59 3.19 -0.49900 0.628 1.03867 Visitors are not significant and should be removed from the model.

36 © 2010 ASQ. All Rights Reserved. 36 Reduced Model Coefficients Term Coef SE Coef T P VIF Constant 6687.10 1396.48 4.78854 0.000 Average Temp 16.96 6.41 2.64580 0.021 1.25479 Production 0.22 0.05 4.53564 0.001 6.71249 Operating Days -138.35 53.34 -2.59393 0.023 1.27278 Associates -25.89 8.91 -2.90510 0.013 6.68148 Variance Inflation Factor (VIF) checks for factors that are co-linear. Co-linear factors may cause invalid models and should be avoided. Rule of thumb: VIFs < 8 are not a problem. If factors are highly correlated, try removing one from the model or using Partial Least Squares Regression. Regression Equation Water Usage = 6687.1 + 16.9643 Average Temp + 0.220159 Production - 138.354 Operating Days - 25.8854 Associates

37 © 2010 ASQ. All Rights Reserved. 37 The Rest of the Session Window Summary of Model S = 276.626 R-Sq = 76.10% R-Sq(adj) = 68.14% PRESS = 1588865 R-Sq(pred) = 58.65% Analysis of Variance Source DF Seq SS Adj SS Adj MS F P Regression 4 2924259 2924259 731065 9.5537 0.0010367 Average Temp 1 315092 535674 535674 7.0003 0.0213440 Production 1 1562688 1574213 1574213 20.5720 0.0006830 Operating Days 1 400666 514877 514877 6.7285 0.0234871 Associates 1 645813 645813 645813 8.4396 0.0132008 Error 12 918264 918264 76522 Total 16 3842523 Standard deviation of the error term How well the model is expected to predict new observations.

38 © 2010 ASQ. All Rights Reserved. 38 Residual Analysis The residuals are normally distributed with a mean of zero and a constant variance. There is no reason to reject the model.

39 © 2010 ASQ. All Rights Reserved. 39 Lets Use the Model to Predict Usage You have been asked to predict the amount of usage for a month with an average temperature of 68, production of 1400, 20 days of operation, and 175 associates. Do Control + E to bring back previous dialog box

40 © 2010 ASQ. All Rights Reserved. 40 The Prediction Predicted Values for New Observations New Obs Fit SE Fit 95% CI 95% PI 1 851.869 666.567 (-600.455, 2304.19) (-720.553, 2424.29) The predicted value However, because of the low r 2 Predicted the prediction intervals are very wide. However, because of the low r 2 Predicted, the prediction intervals are very wide.

41 © 2010 ASQ. All Rights Reserved. 41 Multiple Regression: ABI Example 1 – Brand Health Pedro Lozada Belt Project – Zone GHQ This output is from Excel. What is the significance telling us? How do you interpret the Rsq? This output is from Excel. What is the significance telling us? How do you interpret the Rsq? - 1.76 = Increase of 10% in price will decrease the share by – 17.6% Is there a relationship between price and market share? © Anheuser Busch InBev. All Rights Reserved.

42 © 2010 ASQ. All Rights Reserved. 42 © 2010 ASQ. All Rights Reserved. ABI Example 2 – UK CDP Performance (Multiple Regression Analysis) What is the prediction model between Customer Delivery Performance in the UK and line efficiency (LEF)? © Anheuser Busch InBev. All Rights Reserved. Gustavo Burger Belt Project – Zone WE

43 © 2010 ASQ. All Rights Reserved. 43 © 2010 ASQ. All Rights Reserved. ABI Example 3 – Multiple Regression Price Change vs. Ad Feature Use multi-variable regression to separate the impact of a price decrease vs. placing the product in the ad feature. Source: NC Food Lion Natural Light 24pks © Anheuser Busch InBev. All Rights Reserved. Mike Zacharias Belt Project – Zone NA

44 © 2010 ASQ. All Rights Reserved. 44 Practically what does this mean? ABI Example 3 (Continued) What is the regression equation? From the regression equation: A $1 price decrease is worth 1.8 share points, and an ad feature is worth 6.0 share points. © Anheuser Busch InBev. All Rights Reserved. Mike Zacharias Belt Project – Zone NA

45 © 2010 ASQ. All Rights Reserved. 45 © 2010 ASQ. All Rights Reserved. Logistic Regression Logistic regression is a variation of ordinary regression which is used when: o The dependent (response) variable is a dichotomous variable (i.e., it takes only two values, which usually represent the occurrence or non-occurrence of some outcome event, usually coded as 0 or 1). o The independent (input) variables are continuous, categorical, or both.

46 © 2010 ASQ. All Rights Reserved. 46 © 2010 ASQ. All Rights Reserved. Testing Method Selection Matrix Variable TypeAttribute YCount YContinuous Y Discrete X 1 or 2 Treatments Proportions 3+ Treatments Chi Square 1 or 2 Treatments Poisson 3 + Treatments Chi Square 1 or 2 Treatments T tests 3 + Treatments ANOVA Continuous X Logistic Regression Least Squares Regression

47 © 2010 ASQ. All Rights Reserved. 47 © 2010 ASQ. All Rights Reserved. Logistic Regression Logistic Regression evaluates the occurrence of the event in terms of its probability. o If an event happens (success), the probability is p o The probability of the event not happening is given by (1-p) Odds of success relative to failure is the ratio of p/(1-p) The logistic regression model is fitted to the natural logarithm of the odds Ln {p/(1-p)} The statistical model for logistic regression is: Log (p/1 p) = β0 + β1x o where p is a binomial proportion and x is the input factor. o The parameters of the logistic model are β0 and β1.

48 © 2010 ASQ. All Rights Reserved. 48 © 2010 ASQ. All Rights Reserved. The Logistic Function The logistic function starts very close to 0, then rises rapidly as the event probability threshold is approached, then asymptotically approaches 1. Datafile/EXHREG.XLS Probability of event

49 © 2010 ASQ. All Rights Reserved. 49 © 2010 ASQ. All Rights Reserved. An Example A cereal company want to determine the factors that increase the probability a consumer will purchase their product. Data was collected on 71 consumers to determine the effect of whether they had seen an advertisement, whether they have children, their income, and if they purchased the cereal. Data is in Logistic Regression Cereal Ad.mtw.

50 © 2010 ASQ. All Rights Reserved. 50 © 2010 ASQ. All Rights Reserved. Set Up the Analysis Discrete factors that are included in the model are entered in the Factors box. Stat>Regression>Binary Logistics Regression

51 © 2010 ASQ. All Rights Reserved. 51 © 2010 ASQ. All Rights Reserved. Option and Graphs

52 © 2010 ASQ. All Rights Reserved. 52 © 2010 ASQ. All Rights Reserved. Logistic Regression Output Variable Value Count Bought Yes 34 (Event) No 37 Total 71 Logistic Regression Table Odds 95% CI Predictor Coef SE Coef Z P Ratio Lower Upper Constant -5.21059 1.31033 -3.98 0.000 Income 0.0563140 0.0230953 2.44 0.015 1.06 1.01 1.11 Children Yes 2.69208 1.13832 2.36 0.018 14.76 1.59 137.43 ViewAd Yes 1.76941 0.658335 2.69 0.007 5.87 1.61 21.32 Log-Likelihood = -30.480 Test that all slopes are zero: G = 37.341, DF = 3, P-Value = 0.000 The null hypothesis is that the factor has no effect on the event probability. All three factors are statistically significant

53 © 2010 ASQ. All Rights Reserved. 53 © 2010 ASQ. All Rights Reserved. Model Integrity Goodness-of-Fit Tests Method Chi-Square DF P Pearson 45.1757 49 0.629 Deviance 44.8648 49 0.641 Hosmer-Lemeshow 6.4373 8 0.598 Measures of Association: (Between the Response Variable and Predicted Probabilities) Pairs Number Percent Summary Measures Concordant 1105 87.8 Somers' D 0.76 Discordant 145 11.5 Goodman-Kruskal Gamma 0.77 Ties 8 0.6 Kendall's Tau-a 0.39 Total 1258 100.0 The null hypothesis for goodness of fit is that the model fits. Do not reject the null hypothesis and conclude the model fits.

54 © 2010 ASQ. All Rights Reserved. 54 © 2010 ASQ. All Rights Reserved. The Chi-Square vs. Probability Graph Right-click on the graph and brush the outliers. Note them in the data sheet.

55 © 2010 ASQ. All Rights Reserved. 55 © 2010 ASQ. All Rights Reserved. Prepare a Graph of the Results Do Control + e to bring back previous dialog box

56 © 2010 ASQ. All Rights Reserved. 56 © 2010 ASQ. All Rights Reserved. Storing the Data

57 © 2010 ASQ. All Rights Reserved. 57 © 2010 ASQ. All Rights Reserved. Preparing the Graph Graph>Scatterplot

58 © 2010 ASQ. All Rights Reserved. 58 © 2010 ASQ. All Rights Reserved. Presenting the Results

59 © 2010 ASQ. All Rights Reserved. 59 Exercise – Your Turn Data was collected for the outcome of emergency room admissions. A hospital administrator would like help determining if any of the factors collected could be used to predict the probability of dying in the hospital. The data is in Datafile/Emergency.MTW. A definition of the terms is given in Datafile/EmergencyFileTerms.DOC.

60 © 2010 ASQ. All Rights Reserved. 60 What Have We Covered? Learned and applied key tools to analyze your data How to develop and interpret the correlation between variables Develop a mathematical model expressing the relationshipregression o Regression o Simple Linear Regression o Multiple Linear Regression o Logistic Regression

61 © 2010 ASQ. All Rights Reserved. 61 © 2010 ASQ. All Rights Reserved. In the Next Module... We will learn how to determine the proper sample size and the power of the test We will use Minitab to determine: o Sample size o Delta o Power

62 © 2010 ASQ. All Rights Reserved. 62 Supplemental Material

63 © 2010 ASQ. All Rights Reserved. 63 Exercise Solution – Emergency Room

64 © 2010 ASQ. All Rights Reserved. 64 Exercise Solution – Emergency Room (Continued) Odds 95% CI Predictor Coef SE Coef Z P Ratio Lower Upper Constant -5.74590 1.27590 -4.50 0.000 Age 0.0342199 0.0117207 2.92 0.004 1.03 1.01 1.06 Sex 1 -0.374718 0.411645 -0.91 0.363 0.69 0.31 1.54 Race 2 -1.16640 1.09116 -1.07 0.285 0.31 0.04 2.64 3 0.269519 0.907951 0.30 0.767 1.31 0.22 7.76 Ser 1 -0.394346 0.432915 -0.91 0.362 0.67 0.29 1.57 Can 1 1.83110 0.849745 2.15 0.031 6.24 1.18 33.00 PRE 1 0.571998 0.546810 1.05 0.296 1.77 0.61 5.17 TYP 1 2.87674 0.918809 3.13 0.002 17.76 2.93 107.51 Age, TYP, and Can are significan t

65 © 2010 ASQ. All Rights Reserved. 65 Exercise Solution – Emergency Room (Continued)

66 © 2010 ASQ. All Rights Reserved. 66 Exercise Solution – Emergency Room (Continued) Logistic Regression Table Odds 95% CI Predictor Coef SE Coef Z P Ratio Lower Upper Constant -6.20134 1.17173 -5.29 0.000 Age 0.0352979 0.0109595 3.22 0.001 1.04 1.01 1.06 Can 1 1.57914 0.808289 1.95 0.051 4.85 0.99 23.65 TYP 1 3.02273 0.873298 3.46 0.001 20.55 3.71 113.79 Even though Can is slightly over.05, lets keep it in the model.

67 © 2010 ASQ. All Rights Reserved. 67 Exercise Solution – Emergency Room (Continued)

68 © 2010 ASQ. All Rights Reserved. 68 Exercise Solution – Emergency Room (Continued)


Download ppt "Blended Lean Six Sigma Black Belt Training – ABInBev Correlation and Regression ©2010 ASQ. All Rights Reserved."

Similar presentations


Ads by Google