6160sigma160bb黑带培训资料-160160booster_wk1_08_regression1(编辑修改稿)

6160sigma160bb黑带培训资料-160160booster_wk1_08_regression1(编辑修改稿)内容摘要：

ear?  One X or more Xs?  Transform?  Discrete X, discrete Y?  Do the regression  Look at residuals plots  Look at unusual observations  Look at RSq  Look at Pvalues for b 1  Make predictions for Xvalues of interest 1. Get Familiar With Data 2. Formulate Model 3. Fit Model to Data 5. Report Results and Use Equation 4. Check Model and Assumptions Good Fit Inadequate Fit 31 Five Step Regression Procedure With Minitab (Simple Linear: One X) 32 Checking Assumptions About Residuals 33 Exercise: Simple Linear Regression (One X) Objective: Practice doing a regression analysis for one X. Time: 30 mins. Data: c:\BoosterData\ Background: The production manager of a custom job shop is plaining to the sales manager that customers are being promised production cycle times that are unrealistic. The sales manager explains how he estimates the production times. The production manager indicates that some jobs require more equipment setup changes than others and it was not included in the estimation.  They agree to select and research 50 jobs already delivered and collect data on the production cycle time (hrs) and the number of setups required.  If the production manager can demonstrate that variation in production cycle times can be explained by number of equipment setups, the sales manager agrees to list the number of setups required for certain jobs and use it to estimate production cycle time for customers. This will help him set prices better and improve scheduling and delivery time estimates.  They give you the data (listed by order date) and ask you to analyze it. Job Time(hrs) Setups1 61 62 129 143 77 5… … …48 107 949 112 750 72 1034 Exercise: Simple Linear Regression (One X), cont. Instructions: 1. Pair up and decide whether the managers should restrict the sample of 50 jobs to the most recent, or to those that took a long time, or would 50 jobs from a wide variety of production cycle times be more useful? 2. Use the “Five Step Regression Procedure with Minitab” to analyze the data. Record on a flipchart: a. Identity of X, Y. Can you control X? b. Data type for X, Y c. Impressions from plots d. Range of X, Y e. Correlation, r f. Conclusions from residuals plots (Do assumptions hold?) g. Unusual observations (Will you leave them in or take them out?) h. Final regression equation i. Rsq j. Pvalue for slope 35 Exercise: Simple Linear Regression (One X), cont. 3. The managers ask you to predict the production cycle time (hrs) for a job that has 10 equipment setups. 4. Be prepared to explain the regression equation. 36 Exercise: Answers 1: Jobs chosen from a wide variety of production cycle times will give you a better chance of seeing a relationship with the number of setups. 2: Summary • Y = production cycle time (hrs), continuous, range 0 to 187 • X = of setups, discretecount。 range = 2 to 15 • Correlation, r = .634 • Residuals seem OK。 Outlier with st. resid. of removed • One influential observation retained because it extends range • Final equation: Cycletime = + Setups • Rsq = 57% • Pvalue for slope = .000, meaning a significant relationship 37 Exercise: Answers 38 Exercise: Answers, cont. 2a, b (X and Y data types): Y = production cycle time (hrs), continuous X = number of setups, discretecount, you can39。 t really control the number of setups, but you could manage it for improvement and you could definitely use it for prediction 2c, d, e (interpretation of plots and output): Time plots of both variables showed no obvious trends. (Control charts were also checked because the mean and control limits make it easier to look for trends and other special causes。 none were seen). Dotplots and histograms show roughly Normal distributions, no interesting shapes. Unfortunately, there are no other factors in the data set that can be used to make stratified plots. Descriptive statistics show the number of setups ranged from 2 to 15 and the cycle time ranged from 0 to 187 hours. A scatter plot shows a moderately positive relationship. The correlation, r =.634 39 Exercise: Answers, cont. 2f, g (conclusions): The residuals plots all look good except for one outlier that appears on each plot (observation number 11, setups = 13, cycletime = 0). It’s also identified on the regression output. Its st. resid. value is . After identifying it on the scatter plot it clearly looks unusual. It is probably a mistake since it makes no sense for cycletime = 0. We will remove it by recoding the ―Prodtime‖ on row 11 in the worksheet to ―*‖ (missing). 40 Exercise: Answers, cont. 2h (final equation): The regression analysis was run again with the outlier removed. All the residuals plots look good and the assumptions seem to hold (residuals are Normal with mean of 0, constant, stable, and not related to X=setups). There is one influential observation now (row 15, setups = 15, prodtime = 187). After identifying it on the scatter plot you can see it’s flagged as influential because it’s the only point in the upper right corner. Keep it in the regression to get representation in that range. The final equation: “Prodtime” = + Setups 41 Exercise: Answers, cont. 2i (Rsq): The Rsq value is 57% (it was % with the outlier included). 2j (Pvalue): The Pvalue for the slope is .000, meaning there is a significant positive relationship. 3: The predicted production cycletime for 10 setups is 98 hours. A 95% prediction interval is from 49 to 147 hours. 42 Exercise: Answers, cont. 4: Explanation of regression equation • 57% of the variation in production time can be explained by the number of setups required for the job. • For every setup required, th。