# ng bb 36 simple linear regression

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- 1. UNCLASSIFIED / FOUO UNCLASSIFIED / FOUO National GuardBlack Belt TrainingModule 36Simple Linear RegressionUNCLASSIFIED / FOUO This material is not for general distribution, and its contents should not be quoted, extracted for publication, or otherwisecopied or distributed without prior coordination with the Department of the Army, ATTN: ETF. UNCLASSIFIED / FOUO

2. UNCLASSIFIED / FOUOCPI Roadmap Analyze 8-STEP PROCESS 6. See 1.Validate2. Identify 3. Set4. Determine5. Develop 7. Confirm8. StandardizeCounter-the Performance ImprovementRoot Counter- ResultsSuccessfulMeasuresProblem GapsTargetsCause Measures & ProcessProcessesThroughDefineMeasureAnalyzeImproveControlACTIVITIES TOOLS ValueStream Analysis Identify Potential Root Causes Process Constraint ID Reduce List of Potential Root Takt Time Analysis Causes Cause and Effect Analysis Brainstorming Confirm Root Cause to Output 5 Whys Relationship Affinity Diagram Estimate Impact of Root Causes Pareto on Key Outputs Cause and Effect Matrix FMEA Prioritize Root Causes Hypothesis Tests Complete Analyze Tollgate ANOVA Chi Square Simple and Multiple Regression Note: Activities and tools vary by project. Lists provided here are not necessarily all-inclusive. UNCLASSIFIED / FOUO 3. UNCLASSIFIED / FOUO Learning Objectives Terminology and data requirements for conducting a regression analysis Interpretation and use of scatter plots Interpretation and use of correlation coefficients The difference between correlation and causation How to generate, interpret, and use regression equationsSimple Linear Regression UNCLASSIFIED / FOUO 3 4. UNCLASSIFIED / FOUO Application Examples Administrative A financial analyst wants to predict the cash needed to support growth and increases in training Market/Customer Research The main exchange wants to determine how to predict a customers buying decision from demographics and product characteristics Hospitality The MWR Guest House wants to see if there is a relationship between room service delays and order size Simple Linear Regression UNCLASSIFIED / FOUO 4 5. UNCLASSIFIED / FOUO When Should I Use Regression? Independent Variable (X) Continuous Attribute ContinuousDependent Variable (Y)RegressionANOVA AttributeLogistic Chi-Square (2) Regression Test The tool depends on the data type. Regression is typically used with a continuousinput and a continuous response but can also be used with count or categorical inputs and outputs. Simple Linear RegressionUNCLASSIFIED / FOUO 5 6. UNCLASSIFIED / FOUO General Strategy for Regression Modeling Planning and What variables?Data Collection How will I get the data? How much data do I need? Initial Analysis and What input variables have the biggestReduction of Variableseffect on the response variable? What are some candidate predictionmodels?Select and Refine What is the best model? Models Validate How well does the model predict newModel observations?Simple Linear RegressionUNCLASSIFIED / FOUO 6 7. UNCLASSIFIED / FOUO Regression Terminology Types of Variables Input Variable (Xs) These are also called predictor variables or independent variables Best if the variables are continuous,Error but can be count or categorical X1 Output Variable (Ys)Process or X2Y These are also called response Product X3 variables or dependent variables (what were trying to predict) Best if the variables are continuous, but can be count or categoricalSimple Linear RegressionUNCLASSIFIED / FOUO 7 8. UNCLASSIFIED / FOUO Visualize the Data A Good Start!Scatter Plot: A graph showing a relationship (or correlation)between two factors or variables Lets you see patterns in data Supports or refutes theories about the data Helps create or refine hypotheses Predicts effects under other circumstances (be careful extending predictions beyond the range of data used) Be Careful Correlation does not guarantee causation! Simple Linear RegressionUNCLASSIFIED / FOUO 8 9. UNCLASSIFIED / FOUO Correlation vs. Causation Correlation by itself does not imply a cause and effect relationship! Other examples? Average life expectancy Gas mileage # divorces/10,000 Price of automobiles Lurkingvariables!When is it correct to infer causation? Simple Linear RegressionUNCLASSIFIED / FOUO 9 10. UNCLASSIFIED / FOUO Example: Mortgage Estimates A Belt is trying to reduce the call length for military clients calling for a good faith estimate on a VA loan The Belt thinks that there is a relationship between broker experience and call length, and creates a scatter plot to visualize the relationshipSimple Linear Regression UNCLASSIFIED / FOUO 10 11. UNCLASSIFIED / FOUO Example: Mortgage Estimate Scatter PlotHypothesis:Brokers with more experience can provide estimates in a shorter time.6050Call Length403020 10 20 30 Broker ExperienceDoes it look like a relationship exists between Broker Experience and Call Length?Simple Linear RegressionUNCLASSIFIED / FOUO 11 12. UNCLASSIFIED / FOUO Scatter Plot - StructureY Axis60 Paired (Result?)Data50Call Length40X Axis30( Suspected Influence )20 10 20 30 Broker Experience Paired Data? To use a scatter plot, you must have measured two factors for a single observation or item (ex: for a given measurement, you need to know both the call length and the brokers experience). You have to make sure that the data pair-up properly in Minitab, or the diagram will be meaningless.Simple Linear RegressionUNCLASSIFIED / FOUO 12 13. UNCLASSIFIED / FOUO Input, Process, Output ContextPREDICTOR MEASURES RESULTS MEASURESY (X) (X)(Y) Input Process Output Arrival CustomerTimeSatisfaction Accuracy Total CostDefects Key Specs Cycle Time Cost Time Per Task In-Process Errors Labor Hours ExceptionsX Axis Y Axis Independent VariableDependent VariableXSimple Linear RegressionUNCLASSIFIED / FOUO 13 14. UNCLASSIFIED / FOUO Scatter PlotsNo Correlation NegativeCurvilinear Positive See how one factor relates to changes in another Develop and/or verify hypotheses Judge strength of relationship by width or tightness of scatter Dont assume a causal relationship!Simple Linear Regression UNCLASSIFIED / FOUO 14 15. UNCLASSIFIED / FOUO Exercise: Interpreting Scatter Plots 1. As a team, review assigned Scatter Plots see next pages 2. What kind of correlation do you see? (Name) 3. What does it mean? 4. What can you conclude? 5. What data might this represent? (Example) Simple Linear Regression UNCLASSIFIED / FOUO 15 16. UNCLASSIFIED / FOUO Example OneSimple Linear Regression UNCLASSIFIED / FOUO 16 17. UNCLASSIFIED / FOUO Example TwoSimple Linear Regression UNCLASSIFIED / FOUO 17 18. UNCLASSIFIED / FOUO Example ThreeSimple Linear Regression UNCLASSIFIED / FOUO 18 19. UNCLASSIFIED / FOUO Minitab Example: Scatter Plot Next, we will work through a Minitab example using data collected at the Anthonys Pizza company The Belt suspects that the customers have to wait too long on days when there are many deliveries to make at Anthonys Pizza Simple Linear Regression UNCLASSIFIED / FOUO 19 20. UNCLASSIFIED / FOUO Minitab Example: Pizza Scatter Plot A month of data was collected, and stored in the Minitab file Regression-Pizza.mtw Simple Linear Regression UNCLASSIFIED / FOUO 20 21. UNCLASSIFIED / FOUO Pizza Scatter Plot (Cont.) 1. Open worksheetRegression-Pizza.mtw 2. Choose Graph>Scatterplot Simple Linear Regression UNCLASSIFIED / FOUO 21 22. UNCLASSIFIED / FOUOPizza Scatter Plot (Cont.)When you click on Scatterplots,this is the first dialog box thatcomes up3. Select the Simple Scatterplot4. Click on OK to move to thenext dialog boxSimple Linear Regression UNCLASSIFIED / FOUO 22 23. UNCLASSIFIED / FOUOPizza Scatter Plot (Cont.) 5. Double click on C5 Wait Time to enter it as the Y variable, then double click on C6 Deliveries to enter it as the X variable 6. Edit dialog box options(Optional) 7. Click OK Simple Linear Regression UNCLASSIFIED / FOUO 23 24. UNCLASSIFIED / FOUO Pizza Scatter Plot (Cont.) Does it look like the number of Deliveriesinfluences the customers Wait Time? Scatterplot of Wait Time vs Deliveries5550Wait Time454035 1015 2025 30 35 Deliveries Simple Linear RegressionUNCLASSIFIED / FOUO 24 25. UNCLASSIFIED / FOUOPizza Scatter Plot (Cont.)Note: Hold your cursor over anypoint on the Scatterplot and Minitab will identify theRow, X-Value and Y-Value for that point Simple Linear RegressionUNCLASSIFIED / FOUO 25 26. UNCLASSIFIED / FOUO Correlation Coefficients (r & r2) Numbers that indicate the strength of the correlationbetween two factors r- strength and the direction of the relationship Also called Pearsons Correlation Coefficient r2- percentage of variation in Y attributable to theindependent variable X. Adds precision to a persons visual judgment aboutcorrelation Test the power of your hypothesis How much influence does this factor have? Are there other, more important, vital few causes? Simple Linear Regression UNCLASSIFIED / FOUO 26 27. UNCLASSIFIED / FOUO Interpreting Correlation Coefficients r falls on or between -1 and 1Calculate in Minitab Figures below -0.65 and above 0.65 indicate a meaningful correlation 1 = Perfect positive correlationr=0-1 = Perfect negative correlation Use to calculate r2 r=-.8Simple Linear Regression UNCLASSIFIED / FOUO 27 28. UNCLASSIFIED / FOUO Pearson Correlation Coefficient (r) MortgageBetty Black Belt used the scatter plot to get a visual picture of the relationship between broker experience and call lengthNow she uses the Pearson Correlation Coefficient, r, to quantify the strength of the relationship6050Call Length40r = - 0.89630(a strong negative correlation)20 1020 30Broker ExperienceSimple Linear RegressionUNCLASSIFIED / FOUO 28 29. UNCLASSIFIED / FOUO Exercise: Correlation The scatter plot shows that the customers are waiting longer when Anthonys Pizza has to make more deliveries Next, the Belt wants to quantify the strength of that relationship To do that, we will ca

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