【導(dǎo)讀】RegressionAnalysis. 2. ANALYZE. Goal. Identifyrootcauses. andconfirmthemwith. data. Output. Atheorythathasbeen. testedandconfirmed. IMPROVE. 3. YouAreHere. Developa. focusedproblem. statement. ProcessDoor. Versus. DataDoor. Organize. potential. causes. Hypothesis. Testingand. Regression. Analysis. Designof. Experiments. andResponse. Surface. SimpleRegression–。TheoryReview. BridgeMaterials. TransformedData. MLR. Curvilinear. DiscreteXs. Logistic. 4. TableofContents. ReviewofRegression. Appendix. LogisticRegression(DiscreteYs). Introductionto. LinearRegression. 6. 1. 2. 3. 4. 5. 6. 7. 8. X(input). InRegression. DataTypeMinitab. Format. Discrete-Ordinal. ranks1,2,...,5. Numerical. Discrete-Countor. Percents. #ofdefects,%defective. Numerical. Continuous. Amounts. Cycletime. Numerical. 7. Caution!DataIsRisky. 203040. 250. 300. 350. FeedScrew(rpm). Carton. Weight. (grams)??XandYforX>30?Rangeofdata. oftheXdata. groundontothinice. observeddata. 8. TheResiduals. X. 051015. 0. 5. 10. 15. Y. residual2. residual7. ObservedY(actualY). oPredictedY(fittedorexpectedY—ontheline). Aresidual. theregressionline. -Equals(ObservedY–。PredictedY). -Representsmon. cause(=random=. unexplained)variation. 9. IsDetermined. Findsthelinewhere. Restated…minimizesthe. ―square‖ofalltheresiduals. Leastsquaresmethod. toline. 2.Squarethefigures. 10. ANoteonT

　　

【正文】 atrix Scatter Plot: Shows the Relationships of Several Xs and Ys Definition A matrix plot contains scatter plots for all pairs of variables anized in a matrix. 50150500100020060020 60250007500050 150 500 1000 200 600X1X2X3Y1Y2Don’t strain your eyes trying to pick out details about individual points on a matrix plot! The goal is to get a quick visual impression of the patterns showing how the variables are related to each other. 60 Practice: Understand the Matrix Plot Objective: Practice interpreting a matrix plot to increase your understanding of it. Time: 10 mins. Instructions: Pair up and help each other answer questions about the matrix plot on the previous page. Be prepared to discuss 9, 10, and 11. 61 Practice: Answers Check the scale: 1. What are the values labeled on the scale for Y1? 200 – 600 2. What are the values labeled on the scale for X3? 500 – 1000 Assess Y1: 3. Does X1 help to explain Y1? No. 4. Does X2 help to explain Y1? Yes. 5. Does X3 help to explain Y1? Yes. Assess Y2: 6. Does X1 help to explain Y2? No. 7. Does X2 help to explain Y2? Yes. 8. Does X3 help to explain Y2? Yes. 62 Practice: Answers, cont. Conclusion: 9. Conclusion so far? X1 is not useful X2 and X3 are useful for explaining variation in both Y1 and Y2 Assess other relationships: 10. Is X2 related to X3? Yes. 11. Are Y1 and Y2 related? Yes. 63 Correlation Matrix: Quantifies the Strength of the Relationships Between Several Xs and Ys Definition A correlation matrix contains the correlation coefficient, r, for all pairs of variables anized in a matrix. Minitab menu for making a correlation matrix Stat Basic Statistics Correlation Minitab output Correlations (Pearson) X1 X2 X3 Y1X2 X3 Y1 Y2 64 Relating the Matrix Plot to the Correlation Matrix 65 Multiple Regression: Quantifies the Relationship Between Several Xs and One Y Regression equation for one X: Y = b0 + b1 X (Multiple) Regression equation for several Xs: Y = b0 + b1 X1 + b2 X2 + b3 X3 + … + b k Xk 66 Practice: Use the Multiple Regression Equation Objective: Practice using a multiple regression equation. Time: 10 mins. Background: Here is a summary of the data obtained for 50 jobs. A multiple regression analysis produced this equation: ProdTime = + (Setups) + ($Price) + (Features) + (Labels) Job ProdTime Setups $Price Features Labels 1 61 6 8299 7 5 2 129 14 48835 31 2 3 77 5 45848 18 1 ? … … … … …49 112 7 73518 29 150 72 10 50508 21 4Y = P r o d u ct io n cyc le t im e ( h r s)X 1 = Nu m b e r o f e q u ip m e n t se t u p sX 2 = B o o kin g p r ice ( d o ll a r s)X 3 = Nu m b e r o f cu st o m f e a t u r e sX 4 = Nu m b e r o f u n iq u e la b e ls67 Practice: Use the Multiple Regression Equation, cont. Instructions: Pair up and answer the following questions. 1. Fill in the grid: 2. Predict the production time for a job order with 20 custom features, 7 labels, needs 10 equipment setups, booked at $35,000. 3. Is this prediction within the range of all the Xs or are you extrapolating? 4. Explain the coefficients (slope) of each X. N a meT y p e o f D a t aC a n y o u ma n a g e o r c o n t rol Xoru s e i t o n l y t o p red i c t ?Y P r o d T i meX1S e t u p sX2$ P r i ceX3F e a t u r e sX4L a b e l s68 Practice: Answers 1. Data table 2. Prediction for 20 features, 7 labels, 10 setups, and $35,000. = + (10) + (35,000) + (20) + (7) = + + + + = hours N ame Ty pe of D ataC an yo u m an ag e or co nt rol X orus e i t on l y t o pred i ct?Y P r odT i m e C onti nuo usX1S etups C oun t C an possi bl y manag e t he nu m ber ofequ i pment setups , o r use i t t o pre di ctX2$P r i ce C onti nuo us C an manag e t he pri ce, or use i t t opred i ctX3Fe atur es C oun t U se i t t o p redic tX4Lab el s C oun t U se i t t o p redic t69 Practice: Answers, cont. 3. Evaluation of prediction From the data excerpt provided, the prediction is within the range of the data for Setups, $Price, and Features. But you cannot determine if it’s within the range of the data for Labels。 you39。d need to examine all the data. 4. Explain the coefficients b1: for each additional setup, you can expect an increase of production hours b2: for every $10,000 increase in the booked price, you can expect an additional production hours b3: for each additional custom feature ordered, you can expect an increase of production hours b4: for each additional unique label needed in the order, you can expect an increase of production hours 70 Caution! Don’t Compare Coefficients to Each Other Size of coefficients ?The coefficient value (size) does not indicate which X has the biggest effect on Y ?Each X is on a different scale Example ?The coefficient of $Price = .000151 is in units of hours/dollar ?The coefficient of Setups = is in units of hours/setup ?Just because is larger than .000151 doesn’t necessarily mean Setups is more influential than $Price (it depends on how easy it is to manage or control the Xs) 71 Visualizing the Multiple Regression Equation F o r o n e XY = 3 ? 3X0 1 2 36543210123XYFor two Xs Y = 3 – 3X 1 + 2 X 2 5 0 5 10 0 1 2 3 0 1 2 3 Y X 1 X 2 72 Exercise: Multiple Linear Regression Objective: Practice doing a multiple regression in Minitab. Time: 10 mins. Data: c:\Boosterdata\ Background: Recall the data for 50 jobs. Job ProdTime Setups $Price Features Labels 1 61 6 8299 7 5 2 129 14 48835