This document provides an overview of simple linear regression modeling. It defines key regression terminology like independent and dependent variables. It explains how to visualize relationships between variables using scatter plots and how to calculate correlation coefficients. While correlation does not necessarily imply causation, regression can be used to generate prediction models. The document reviews best practices like planning data collection and model validation. It provides examples of applying regression in administrative, market research, and hospitality contexts.
This document provides an overview of simple linear regression modeling. It defines key regression terminology like independent and dependent variables. It explains how to visualize relationships between variables using scatter plots and how to calculate correlation coefficients. While correlation does not necessarily imply causation, regression can be used to generate prediction models. The document reviews best practices like planning data collection and model validation. It provides examples of applying regression in administrative, market research, and hospitality contexts.
1) The document describes a training module on analysis of variance (ANOVA), a statistical technique for comparing means across multiple groups.
2) ANOVA can be used to determine if different methods, processes, or treatments result in different average outcomes, such as shipping costs across distribution centers.
3) The training module will provide conceptual understanding of ANOVA, teach how to design single-factor and two-factor experiments, and how to interpret ANOVA results including interactions and follow-up comparisons between groups.
This document discusses rapid improvement events (RIEs) and quick improvement methods for processes. It describes:
1) RIEs as a facilitated event lasting 3-5 days where a cross-functional team makes rapid improvements to an identified process problem. Documentation is completed during the event.
2) Quick improvements called "Just Do Its" that can bypass analysis and implement low-risk, fast changes identified early in a project using basic tools.
3) The criteria for "Just Do Its" as having minimal costs, low risk, quick implementation within 1-2 weeks, and authority to make the changes. Control plans must still be implemented after quick improvements.
This document provides an overview of the measure phase for a National Guard Black Belt training module. It outlines an 8-step process for measuring performance that includes defining problems, identifying gaps, setting targets, determining root causes, developing countermeasures, seeing results, and standardizing processes. Tools for the measure phase are listed, including process mapping, data collection plans, statistical analysis, and tollgate requirements. The tollgate requirements specify deliverables needed for the measure phase such as a value stream map, metrics, operational definitions, baseline statistics, and an estimate of financial and operational benefits.
This document provides information about standardized work processes. It begins with an overview of the 8-step CPI roadmap for process improvement. It then discusses standardized work techniques and tools that can be used to analyze and improve processes. The rest of the document uses an exercise where participants standardize the process of drawing a pig picture to demonstrate how to create a standardized work instruction document. It provides examples of standardized work forms like standard operation sheets that document the best way to complete a task or job through detailed steps and timing. The goal is to achieve consistency in processes to improve safety, quality, productivity and performance.
This document provides an overview of multiple regression analysis techniques. It begins with an introduction to multiple regression, explaining how it allows modeling of a dependent variable (Y) based on multiple independent variables (X1, X2, X3, etc). The document then outlines the basic steps for developing a multiple regression model, including visualizing relationships in the data, assessing correlation, generating a prediction equation, and validating the model. An example involving silver consumption in a production plant is presented to demonstrate these steps. The goal is to help readers understand how to identify correlation between variables, create mathematical models relating multiple inputs to an output, and evaluate models.
The document provides information on conducting a Failure Modes and Effects Analysis (FMEA) to identify potential failures, their causes and effects, and determine appropriate actions. It discusses when an FMEA should be used, the different types (system, design, process), how to link it to other Lean Six Sigma tools like SIPOC, process map and Cause & Effect matrix. The document outlines the FMEA procedure and provides an example of conducting an FMEA on the process of making coffee at the All Ranks Club to improve customer satisfaction.
This document provides an overview of basic design of experiments (DOE). It discusses how DOE is a more effective approach to experimentation than traditional trial and error or one-factor-at-a-time methods. The document reviews full and fractional factorial experimental designs and provides an example exercise involving optimization of a paper helicopter design through experimental testing. The overall goal is to introduce practitioners to DOE methodology and its benefits for process and product improvement.
This document provides an overview of simple linear regression modeling. It defines key regression terminology like independent and dependent variables. It explains how to visualize relationships between variables using scatter plots and how to calculate correlation coefficients. While correlation does not necessarily imply causation, regression can be used to generate prediction models. The document reviews best practices like planning data collection and model validation. It provides examples of applying regression in administrative, market research, and hospitality contexts.
1) The document describes a training module on analysis of variance (ANOVA), a statistical technique for comparing means across multiple groups.
2) ANOVA can be used to determine if different methods, processes, or treatments result in different average outcomes, such as shipping costs across distribution centers.
3) The training module will provide conceptual understanding of ANOVA, teach how to design single-factor and two-factor experiments, and how to interpret ANOVA results including interactions and follow-up comparisons between groups.
This document discusses rapid improvement events (RIEs) and quick improvement methods for processes. It describes:
1) RIEs as a facilitated event lasting 3-5 days where a cross-functional team makes rapid improvements to an identified process problem. Documentation is completed during the event.
2) Quick improvements called "Just Do Its" that can bypass analysis and implement low-risk, fast changes identified early in a project using basic tools.
3) The criteria for "Just Do Its" as having minimal costs, low risk, quick implementation within 1-2 weeks, and authority to make the changes. Control plans must still be implemented after quick improvements.
This document provides an overview of the measure phase for a National Guard Black Belt training module. It outlines an 8-step process for measuring performance that includes defining problems, identifying gaps, setting targets, determining root causes, developing countermeasures, seeing results, and standardizing processes. Tools for the measure phase are listed, including process mapping, data collection plans, statistical analysis, and tollgate requirements. The tollgate requirements specify deliverables needed for the measure phase such as a value stream map, metrics, operational definitions, baseline statistics, and an estimate of financial and operational benefits.
This document provides information about standardized work processes. It begins with an overview of the 8-step CPI roadmap for process improvement. It then discusses standardized work techniques and tools that can be used to analyze and improve processes. The rest of the document uses an exercise where participants standardize the process of drawing a pig picture to demonstrate how to create a standardized work instruction document. It provides examples of standardized work forms like standard operation sheets that document the best way to complete a task or job through detailed steps and timing. The goal is to achieve consistency in processes to improve safety, quality, productivity and performance.
This document provides an overview of multiple regression analysis techniques. It begins with an introduction to multiple regression, explaining how it allows modeling of a dependent variable (Y) based on multiple independent variables (X1, X2, X3, etc). The document then outlines the basic steps for developing a multiple regression model, including visualizing relationships in the data, assessing correlation, generating a prediction equation, and validating the model. An example involving silver consumption in a production plant is presented to demonstrate these steps. The goal is to help readers understand how to identify correlation between variables, create mathematical models relating multiple inputs to an output, and evaluate models.
The document provides information on conducting a Failure Modes and Effects Analysis (FMEA) to identify potential failures, their causes and effects, and determine appropriate actions. It discusses when an FMEA should be used, the different types (system, design, process), how to link it to other Lean Six Sigma tools like SIPOC, process map and Cause & Effect matrix. The document outlines the FMEA procedure and provides an example of conducting an FMEA on the process of making coffee at the All Ranks Club to improve customer satisfaction.
This document provides an overview of basic design of experiments (DOE). It discusses how DOE is a more effective approach to experimentation than traditional trial and error or one-factor-at-a-time methods. The document reviews full and fractional factorial experimental designs and provides an example exercise involving optimization of a paper helicopter design through experimental testing. The overall goal is to introduce practitioners to DOE methodology and its benefits for process and product improvement.
This document provides an overview of hypothesis testing basics and introduces related concepts. It discusses:
1) The difference between population parameters and sample statistics, and how samples are used to estimate populations.
2) Key terms like means, medians, standard deviations, and how samples provide statistic estimates of population parameters.
3) The Central Limit Theorem and how the distribution of sample means approaches normality as sample size increases.
4) Examples of applying hypothesis testing to compare processes and identify statistical differences in metrics like cycle time, accuracy, and quality of service.
This document provides requirements and templates for a project analyze tollgate. It lists mandatory and optional deliverables including root cause validation, cause and effect diagrams, failure mode and effects analysis, hypothesis testing summaries, and process constraint identification. Templates are provided for project charter, measure overview, Pareto analysis, and hypothesis testing. The document aims to guide black belts through requirements for certification at the analyze phase tollgate.
This document provides an overview of process mapping and value stream mapping techniques used in process improvement. It outlines an 8-step process improvement roadmap and discusses activities like process mapping, value stream mapping, and developing future state maps. The goal is to develop skills in process analysis to identify waste and improvement opportunities by mapping material, information, and workflow. Process mapping helps analyze problems, identify gaps, and plan improvement projects.
This document provides information on the improve phase of the CPI roadmap for a National Guard Black Belt training module. It outlines an 8-step process for improvement that includes identifying performance gaps, determining root causes, developing and testing countermeasures, and standardizing successful processes. The document also lists activities and tools that can be used in the improve phase, as well as mandatory and recommended deliverables for the improve tollgate, such as a future state process map, implementation plan, pilot results, and storyboard.
This document provides an overview of the Theory of Constraints (TOC). It defines key TOC concepts like constraints, throughput, inventory, operating expense, and the five focusing steps. It also explains tools like the drum-buffer-rope concept, Little's Law, takt time, and cycle time. An example shows how to identify the constraint in a process. The goal of TOC is to strengthen the weakest link in a system by first identifying and then improving the constraint.
This document provides an overview of control charts for continuous data. It discusses control chart fundamentals like control limits and distinguishing between common and special cause variation. It introduces the X-bar and R chart used for variable data with subgroup sizes of 3-9. An example X-bar and R chart is presented using data on customer hold times. The document also covers the Individuals and Moving Range chart which can be used when the subgroup size is 1. Control chart assumptions and interpretation of control limits are explained.
The document discusses process measurement and improvement techniques. It introduces an 8-step process for measuring performance, identifying issues, and improving processes. Key tools for measurement include process mapping, data collection plans, statistical analysis methods like measures of central tendency, control charts and process capability analysis. Learning objectives focus on understanding the importance of measurement in process improvement and applying statistical process control methods to understand common and special cause variation.
The document discusses change management and outlines an 8-step process for continuous process improvement. It identifies common cultural types in organizations and how they can present barriers to change. The document also examines the characteristics of successful and unsuccessful change initiatives, barriers to change, and elements needed to successfully implement change.
This document discusses quick changeover techniques to improve process efficiency. It begins by outlining an 8-step process improvement methodology. It then defines changeover times and differentiates between traditional and continuous process improvement thinking regarding changeovers. The document explains that quick changeovers can decrease downtime and waste, allowing for increased flexibility through smaller batch sizes. It provides steps to identify internal and external changeover activities, convert internal activities to external to reduce downtime, and further reduce all remaining activities through techniques like parallel operations and automation.
This document discusses takt time, which is a key concept for understanding and improving processes. It defines takt time as the time required to produce components to meet customer demand. An example is provided to demonstrate how to calculate takt time using available operating time and customer requirements. The relationship between takt time and theoretical minimum staffing is explained. Finally, cycle time bar charts are introduced as a way to visualize production lines and identify opportunities for improvement by comparing operator cycle times to the takt time.
The document provides an overview of project management concepts and tools for a National Guard Black Belt training module. It discusses the define stage of the CPI roadmap, key drivers of project success, roles and expectations of a project manager, effective communication, and developing a communication plan. Templates are provided for a stakeholder analysis and communication plan to help project managers identify stakeholders, assess their level of influence and concerns, and develop targeted messaging. The overall aim is to help trainees understand project management responsibilities and optimize performance.
This document discusses sustaining process improvements through project closeout and transitioning to process owners. It outlines the timeline for project closeout, including transitioning to the final process owner at a commissioning meeting and subsequent review meetings. Maintaining improvements requires executing process management, with elements like process maps, monitoring, and response plans. Process owners must institutionalize changes through cultural shifts and updated systems to drive permanent behavior changes.
This document provides an introduction to using Minitab statistical software. It outlines the Minitab layout, menus, and some basic tools. Specifically, it discusses the file, edit, data, calc, stat, and graph menus. It provides an example using the data and calculator tools to calculate total defects by summing defect columns. The goal is to familiarize users with navigating Minitab and using some common tools.
Here are the key steps in developing operational definitions:
1. Identify the factor or variable you want to measure
2. Write a draft definition in your own words
3. Review the definition with others to refine language and ensure common understanding
4. Finalize the definition and document it clearly for those collecting data
5. Periodically review definitions and refine as needed over time
Clear, precise operational definitions are essential to ensure consistent and accurate measurement. Taking the time up front to develop them pays off in the quality of the data collected and insights generated.
The document provides information on analyzing processes to determine root causes of issues. It discusses an 8-step process that includes identifying performance gaps, determining root causes, developing countermeasures, and standardizing successful processes. Basic analysis tools covered are brainstorming, cause-and-effect diagrams, affinity diagrams, Pareto charts, and using Minitab. The tools help generate and organize ideas to identify potential root causes and improvements to address issues.
The document discusses mistake proofing (Poka Yoke) techniques. It provides examples of mistake proofing devices used in various processes to prevent defects from occurring. The key steps in mistake proofing are to identify the defect, its root cause, and develop a device to prevent mistakes and signal errors. Mistake proofing aims to prevent defects at the source of production to improve quality and reduce waste from rework and inspection.
NG BB 25 Measurement System Analysis - AttributeLeanleaders.org
This document discusses measurement system analysis for attribute data. It explains that attribute or ordinal measurement systems use accept/reject criteria or ratings to determine quality levels. The Kappa and Kendall techniques can be used to evaluate attribute and ordinal measurement systems, respectively. These methods assess consistency between raters when classifying units. Having clear operational definitions is important for attribute measurements, as poor agreement between raters usually stems from unclear definitions. Failing to evaluate attribute measurement systems before using the data can lead to making flawed decisions if the system is inconsistent.
This document provides an overview of project chartering for continuous process improvement (CPI) projects. It discusses selecting CPI projects, developing a project charter, and who is responsible for chartering a project. The project charter defines the team's mission and includes the opportunity/problem statement, business case, goal statement, project scope, timeline, and team selection. It is a living document that may change over time. Developing an effective charter involves scoping the project based on the identified problem and determining proportional benefits, measurements, and boundaries.
The document outlines the Define, Measure, Analyze, Improve, and Control (DMAIC) process for a Lean Six Sigma project. It provides details on the key deliverables for the Define phase, including:
1) Define VOC, VOB, and CTQs to understand the customer problem and specifications;
2) Define the project boundaries and scope through a problem statement, process mapping, and project charter;
3) Quantify the project value by calculating the costs of poor quality;
4) Develop a project management plan identifying stakeholders, communication plans, milestones, and timelines.
The document provides an introduction to Six Sigma, defining it as a management philosophy that aims to reduce defects in processes. It discusses the Six Sigma definition and process, including the DMAIC and DMADV methodologies. It also outlines the roles of Green Belts, Black Belts, and Master Black Belts in executing Six Sigma projects and processes.
This document provides an overview of Project Management Deliverable 4D, which is to develop a project management plan. It lists the primary and secondary tools used, including developing a communication plan, creating a project schedule in Excel or MS Project, establishing team consensus, and facilitating effective meetings. The goals are to identify team members, interface with stakeholders, and develop a project plan with milestones and timelines to effectively manage the project.
This document provides an overview of hypothesis testing basics and introduces related concepts. It discusses:
1) The difference between population parameters and sample statistics, and how samples are used to estimate populations.
2) Key terms like means, medians, standard deviations, and how samples provide statistic estimates of population parameters.
3) The Central Limit Theorem and how the distribution of sample means approaches normality as sample size increases.
4) Examples of applying hypothesis testing to compare processes and identify statistical differences in metrics like cycle time, accuracy, and quality of service.
This document provides requirements and templates for a project analyze tollgate. It lists mandatory and optional deliverables including root cause validation, cause and effect diagrams, failure mode and effects analysis, hypothesis testing summaries, and process constraint identification. Templates are provided for project charter, measure overview, Pareto analysis, and hypothesis testing. The document aims to guide black belts through requirements for certification at the analyze phase tollgate.
This document provides an overview of process mapping and value stream mapping techniques used in process improvement. It outlines an 8-step process improvement roadmap and discusses activities like process mapping, value stream mapping, and developing future state maps. The goal is to develop skills in process analysis to identify waste and improvement opportunities by mapping material, information, and workflow. Process mapping helps analyze problems, identify gaps, and plan improvement projects.
This document provides information on the improve phase of the CPI roadmap for a National Guard Black Belt training module. It outlines an 8-step process for improvement that includes identifying performance gaps, determining root causes, developing and testing countermeasures, and standardizing successful processes. The document also lists activities and tools that can be used in the improve phase, as well as mandatory and recommended deliverables for the improve tollgate, such as a future state process map, implementation plan, pilot results, and storyboard.
This document provides an overview of the Theory of Constraints (TOC). It defines key TOC concepts like constraints, throughput, inventory, operating expense, and the five focusing steps. It also explains tools like the drum-buffer-rope concept, Little's Law, takt time, and cycle time. An example shows how to identify the constraint in a process. The goal of TOC is to strengthen the weakest link in a system by first identifying and then improving the constraint.
This document provides an overview of control charts for continuous data. It discusses control chart fundamentals like control limits and distinguishing between common and special cause variation. It introduces the X-bar and R chart used for variable data with subgroup sizes of 3-9. An example X-bar and R chart is presented using data on customer hold times. The document also covers the Individuals and Moving Range chart which can be used when the subgroup size is 1. Control chart assumptions and interpretation of control limits are explained.
The document discusses process measurement and improvement techniques. It introduces an 8-step process for measuring performance, identifying issues, and improving processes. Key tools for measurement include process mapping, data collection plans, statistical analysis methods like measures of central tendency, control charts and process capability analysis. Learning objectives focus on understanding the importance of measurement in process improvement and applying statistical process control methods to understand common and special cause variation.
The document discusses change management and outlines an 8-step process for continuous process improvement. It identifies common cultural types in organizations and how they can present barriers to change. The document also examines the characteristics of successful and unsuccessful change initiatives, barriers to change, and elements needed to successfully implement change.
This document discusses quick changeover techniques to improve process efficiency. It begins by outlining an 8-step process improvement methodology. It then defines changeover times and differentiates between traditional and continuous process improvement thinking regarding changeovers. The document explains that quick changeovers can decrease downtime and waste, allowing for increased flexibility through smaller batch sizes. It provides steps to identify internal and external changeover activities, convert internal activities to external to reduce downtime, and further reduce all remaining activities through techniques like parallel operations and automation.
This document discusses takt time, which is a key concept for understanding and improving processes. It defines takt time as the time required to produce components to meet customer demand. An example is provided to demonstrate how to calculate takt time using available operating time and customer requirements. The relationship between takt time and theoretical minimum staffing is explained. Finally, cycle time bar charts are introduced as a way to visualize production lines and identify opportunities for improvement by comparing operator cycle times to the takt time.
The document provides an overview of project management concepts and tools for a National Guard Black Belt training module. It discusses the define stage of the CPI roadmap, key drivers of project success, roles and expectations of a project manager, effective communication, and developing a communication plan. Templates are provided for a stakeholder analysis and communication plan to help project managers identify stakeholders, assess their level of influence and concerns, and develop targeted messaging. The overall aim is to help trainees understand project management responsibilities and optimize performance.
This document discusses sustaining process improvements through project closeout and transitioning to process owners. It outlines the timeline for project closeout, including transitioning to the final process owner at a commissioning meeting and subsequent review meetings. Maintaining improvements requires executing process management, with elements like process maps, monitoring, and response plans. Process owners must institutionalize changes through cultural shifts and updated systems to drive permanent behavior changes.
This document provides an introduction to using Minitab statistical software. It outlines the Minitab layout, menus, and some basic tools. Specifically, it discusses the file, edit, data, calc, stat, and graph menus. It provides an example using the data and calculator tools to calculate total defects by summing defect columns. The goal is to familiarize users with navigating Minitab and using some common tools.
Here are the key steps in developing operational definitions:
1. Identify the factor or variable you want to measure
2. Write a draft definition in your own words
3. Review the definition with others to refine language and ensure common understanding
4. Finalize the definition and document it clearly for those collecting data
5. Periodically review definitions and refine as needed over time
Clear, precise operational definitions are essential to ensure consistent and accurate measurement. Taking the time up front to develop them pays off in the quality of the data collected and insights generated.
The document provides information on analyzing processes to determine root causes of issues. It discusses an 8-step process that includes identifying performance gaps, determining root causes, developing countermeasures, and standardizing successful processes. Basic analysis tools covered are brainstorming, cause-and-effect diagrams, affinity diagrams, Pareto charts, and using Minitab. The tools help generate and organize ideas to identify potential root causes and improvements to address issues.
The document discusses mistake proofing (Poka Yoke) techniques. It provides examples of mistake proofing devices used in various processes to prevent defects from occurring. The key steps in mistake proofing are to identify the defect, its root cause, and develop a device to prevent mistakes and signal errors. Mistake proofing aims to prevent defects at the source of production to improve quality and reduce waste from rework and inspection.
NG BB 25 Measurement System Analysis - AttributeLeanleaders.org
This document discusses measurement system analysis for attribute data. It explains that attribute or ordinal measurement systems use accept/reject criteria or ratings to determine quality levels. The Kappa and Kendall techniques can be used to evaluate attribute and ordinal measurement systems, respectively. These methods assess consistency between raters when classifying units. Having clear operational definitions is important for attribute measurements, as poor agreement between raters usually stems from unclear definitions. Failing to evaluate attribute measurement systems before using the data can lead to making flawed decisions if the system is inconsistent.
This document provides an overview of project chartering for continuous process improvement (CPI) projects. It discusses selecting CPI projects, developing a project charter, and who is responsible for chartering a project. The project charter defines the team's mission and includes the opportunity/problem statement, business case, goal statement, project scope, timeline, and team selection. It is a living document that may change over time. Developing an effective charter involves scoping the project based on the identified problem and determining proportional benefits, measurements, and boundaries.
The document outlines the Define, Measure, Analyze, Improve, and Control (DMAIC) process for a Lean Six Sigma project. It provides details on the key deliverables for the Define phase, including:
1) Define VOC, VOB, and CTQs to understand the customer problem and specifications;
2) Define the project boundaries and scope through a problem statement, process mapping, and project charter;
3) Quantify the project value by calculating the costs of poor quality;
4) Develop a project management plan identifying stakeholders, communication plans, milestones, and timelines.
The document provides an introduction to Six Sigma, defining it as a management philosophy that aims to reduce defects in processes. It discusses the Six Sigma definition and process, including the DMAIC and DMADV methodologies. It also outlines the roles of Green Belts, Black Belts, and Master Black Belts in executing Six Sigma projects and processes.
This document provides an overview of Project Management Deliverable 4D, which is to develop a project management plan. It lists the primary and secondary tools used, including developing a communication plan, creating a project schedule in Excel or MS Project, establishing team consensus, and facilitating effective meetings. The goals are to identify team members, interface with stakeholders, and develop a project plan with milestones and timelines to effectively manage the project.
This document appears to be a template for Lean event documentation. It includes sections for defining the problem and goals, documenting the current process, identifying areas for improvement, planning the new process, ensuring implementation of changes, and controlling the new process. The template provides guidance on the type of information, format, and level of detail needed for each section to fully capture the Lean event and ensure successful implementation and sustainability of improvements.
AFSO21 is the Air Force's standardized approach to continuously improve processes through lean principles in order to increase productivity, equipment availability, response time, safety, and energy efficiency. It utilizes lean methodology including specifying value, identifying the value stream, establishing flow without waste, pursuing perfection, and engaging Airmen. The goal is to eliminate non-value added activities and waste through relentless process improvement.
1.Class presentation.About the job and correct attitude in working
2. Please contact with me (sujack@outlook.com) if you want to discuss detail with me.
This certificate from the International Six Sigma Institute certifies that the individual with the provided ID number has successfully completed the requirements for Six Sigma Black Belt and is awarded the Certified Six Sigma Black Belt designation as of March 31, 2016.
This document summarizes statistical hypothesis testing methods for continuous variables, including t-tests, F-tests, and z-tests. It provides examples of applying one-sample and two-sample t-tests to compare means from randomized experiments. It also discusses using F-tests to compare variances and z-tests for proportions from binomial and Poisson distributions with large samples. The document includes step-by-step solutions to examples testing differences in weights after treatment, red blood cell counts between males and females, biochemical indexes between patients and healthy people, positive testing rates between physicians and the general population, and measuring radioactivity levels.
The document discusses the process for identifying and selecting projects for black belts. It provides criteria for project selection such as the problem being related to key business issues and having organizational support. It also describes documenting potential projects with a project charter that includes details like the customer and process owner. Project ideas are evaluated based on their estimated financial impact and strategic importance to prioritize resources.
8. testing of hypothesis for variable & attribute dataHakeem-Ur- Rehman
The document discusses hypothesis testing for continuous variable and attribute data. It begins by defining key concepts in statistical inference like the null and alternative hypotheses. The three types of hypotheses are explained - two-tailed, left-tailed, and right-tailed. The document then discusses hypothesis testing steps including defining the hypotheses, determining the sampling risk of type I and type II errors, calculating the p-value, and making a decision to accept or reject the null hypothesis based on the p-value and significance level. Specific parametric statistical tests are explained like the one sample t-test, two sample t-test, and ANOVA. Examples of each test are provided and how to interpret the results.
This certificate certifies that Sandeep Roy has fulfilled the requirements established by GreyCampus Inc. and is hereby granted certification as a GreyCampus Certified Six Sigma Green Belt as of May 30, 2016. GreyCampus is a leading global provider of training and certification.
The document outlines the steps to complete Deliverable 2D - Define Project Boundaries, which includes drafting a problem statement, defining the project scope using tools like SIPOC and a project charter, and estimating benefits. It provides objectives for defining boundaries such as constructing a problem statement and goal statement. It also notes that aspects of other define deliverables may be reflected in the project charter.
This document provides an overview of multiple regression analysis techniques. It begins with an introduction to multiple regression, explaining how it allows modeling of a dependent variable (Y) based on multiple independent variables (X1, X2, X3, etc). The document then outlines the basic steps for developing a multiple regression model, including visualizing relationships in the data, assessing correlation, generating a prediction equation, and validating the model. An example involving silver consumption in a production plant is presented to demonstrate these steps. The goal is to help readers understand how to identify correlation between variables, create mathematical models with multiple inputs, and examine a regression model.
This document provides an overview of basic tools for analyzing processes and identifying root causes of issues. It describes brainstorming, including that it is used to generate unconstrained ideas in both the analyze and improve phases. Guidelines for effective brainstorming are outlined, such as establishing rules, individually writing down ideas before sharing, and using techniques like cause-and-effect diagrams to avoid groupthink. The document also notes that affinity diagrams can help organize the large number of ideas generated through brainstorming.
This document provides an overview of hypothesis testing basics and confidence intervals. It discusses key concepts such as population parameters versus sample statistics, the central limit theorem, and variability of means. It also covers confidence intervals when the population standard deviation is known and unknown. Examples are provided to demonstrate how to calculate confidence intervals for the mean. The goal is to introduce statistical tests and understand how sample sizes influence results.
This document provides information about creating a cause and effect (XY) matrix to analyze processes. It discusses the steps to create a XY matrix, including identifying key customer requirements and process inputs, rating their importance and relationship, and calculating scores to determine which inputs have the largest impact on outputs. An example of using a XY matrix to improve customer satisfaction with coffee at an all ranks club is provided.
This document provides information about creating a cause and effect (XY) matrix for process improvement. It discusses the steps to create a XY matrix, including identifying key customer requirements and process inputs, rating their importance and relationship, and calculating scores to determine which inputs have the largest impact on outputs. An example is provided about using a XY matrix to identify which factors most affect customer satisfaction with coffee at an all ranks club.
NG BB 23 Measurement System Analysis - IntroductionLeanleaders.org
This document discusses measurement system analysis (MSA) and evaluating measurement systems to ensure reliable data collection for process improvement efforts. It introduces the eight-step CPI roadmap and explains why accurate measurements are important. Sources of variation are described, including repeatability, reproducibility, and bias. Conducting a gage R&R study to quantify measurement system variation is recommended so that variation due to the measurement process can be distinguished from natural process variation. The goal is to eliminate measurement system variation and rely on data to make good decisions about process performance and improvement opportunities.
This document discusses tools and methods for assessing risk in projects. It introduces risk assessment and explains that risk management proactively identifies, assesses, and mitigates risks throughout a project. Several tools are described for assessing risk, including a risk standards matrix, risk identification matrix, and controls assessment matrix. The risk standards matrix prompts consideration of how a project may impact various areas. The risk identification matrix involves brainstorming risks, prioritizing their potential impact and likelihood, and focusing on high impact/likelihood risks. The controls assessment matrix identifies controls to mitigate high priority risks and ensures controls are sufficient.
This document discusses quick changeover techniques to improve process efficiency. It begins by outlining an 8-step process improvement methodology. It then defines changeover times and differentiates between traditional and lean thinking regarding changeovers. The key steps to reducing changeover times are identified as separating internal and external changeover activities, converting internal activities to external where possible, and reducing all remaining activities through techniques like parallel operations and automation. The goal is to standardize and simplify changeovers to allow for smaller batch sizes and increased flexibility.
This document discusses visual management techniques used in lean processes. It begins by outlining an 8-step process for improvement and listing common lean tools. It then defines visual management as using visual displays and controls to provide immediate information to guide decisions and work. Examples of visual management in industries and workplaces are presented, such as andon boards, color coding, lines of visibility, and kanban cards. The power of visual cues through various indicators, organization, and displays is explored.
This document provides information about measuring process improvement for the National Guard Black Belt Training Module 15. It outlines an 8-step CPI roadmap for measurement, including defining the problem, identifying performance gaps, setting improvement targets, determining root causes, developing countermeasures, seeing results through countermeasures, confirming results, and standardizing successful processes. It also lists tools that can be used during the measurement process, such as process mapping, data collection plans, control charts, and process capability analysis. Finally, it outlines the mandatory and recommended deliverables required to pass the measure tollgate, including current state process maps, metrics, operational definitions, baseline statistics, estimated benefits, and barriers/risks.
The document provides guidance on using the Power Steering project tracking tool. It outlines how to access Power Steering, navigate the interface, update user profiles, and invite new users. Power Steering is used to track Department of Defense continuous process improvement projects, store associated templates and tools, and share best practices between projects. National Guard students who attend Black Belt training will receive login credentials to enter project details and updates.
The document provides an overview of the Power Steering project tracking tool used by the National Guard for continuous process improvement projects. It describes how to access and navigate Power Steering, the roles and responsibilities of Black Belts in using it to track project progress, and how to invite new users. The learning objectives are to understand how to use Power Steering to navigate, track projects, and share best practices.
This document provides information on the 8-step CPI Roadmap process for improvement projects and the requirements to pass through the "Improve" tollgate. The 8 steps are: 1) Validate the problem 2) Identify performance gaps 3) Set improvement targets 4) Determine root cause 5) Develop countermeasures 6) See countermeasures through 7) Confirm results 8) Standardize successful processes. The tollgate requirements include delivering a solution prioritization, future state process map, implementation plan, pilot plan and results, process capability analysis, control charts, storyboard and barriers/risks identification.
NG BB 24 Measurement System Analysis - ContinuousLeanleaders.org
1. The document discusses how to conduct a measurement system analysis (MSA) using continuous data to determine if a measurement system is acceptable and reliable.
2. An MSA study involves having multiple appraisers take repeated measurements of samples to analyze variability and ensure it is less than 10% of the process variability or specification limits.
3. The document provides guidelines for planning an MSA study, such as selecting samples, ensuring measurement devices are calibrated, and collecting data.
4. An example is given of conducting an MSA study in Minitab to analyze the reliability of a non-destructive testing method's measurement of inspection
NG BB 53 Process Control [Compatibility Mode]Leanleaders.org
This document provides an overview of process control concepts and tools. It discusses an 8-step process for process improvement that includes control. Control plans are important to ensure improved processes remain stable. Measurement systems should be analyzed and process capability recalculated during control. Cultural issues can impact control and force field analysis can identify drivers and restraints. Standard operating procedures, control charts, and mistake proofing are discussed as control mechanisms.
This document outlines the define phase of an 8-step continuous process improvement (CPI) roadmap. The define phase includes activities like identifying problems, validating the problem statement, establishing strategic alignment, gathering customer input, and creating a goal statement. It also lists required deliverables for the define tollgate, such as a problem statement, goal statement, project scope, timeline, and high-level process map. The document provides an overview of the key elements and documentation needed to properly define a CPI project.
This document outlines the 8-step process and tollgate requirements for the Control phase of a National Guard Black Belt training module on continuous process improvement. The 8-step process includes validating problems, identifying performance gaps, setting improvement targets, determining root causes, developing countermeasures, seeing results through key performance indicators, confirming results, and standardizing successful processes. Tollgate requirements for the Control phase mandate updating benefits, standardizing processes, establishing process owner accountability, achieving results, implementing control plans, and creating a storyboard summary.
The document provides information about selecting solutions for process improvement projects. It discusses an 8-step problem solving process and lists tools that can be used, including brainstorming, process mapping, and selection matrices. The objectives are to understand idea generation principles, apply brainstorming tools, and use methods to select improvement ideas. Sources of solutions are identified, such as root causes, best practices, and past projects. Guidelines are given for generating many ideas through techniques like brainstorming and building on others' suggestions. Rules for effective brainstorming include allowing ideas without criticism and focusing on quantity over quality initially.
This document provides an overview of process mapping using a SIPOC (Supplier, Input, Process, Output, Customer) chart. It discusses how to create a high-level SIPOC that defines the key steps in a process, identifies important inputs and suppliers, and lists the major outputs and customers. The SIPOC is presented as the first step in process mapping to help visualize the current process and identify areas for potential improvement. Examples of completed SIPOCs are also included to demonstrate how they can be used to identify metrics and scope a process improvement project.
This document provides an overview of process capability analysis. It defines key terms like Cp and Cpk, which measure the capability of a process based on its variability compared to specification limits. Cp looks at total variation, while Cpk accounts for dynamic shifts in the process mean. The document reviews how to calculate and interpret Cp and Cpk values using statistical tools. It also provides examples to metaphorically explain Cp, Cpk, and how they indicate if a process is capable of meeting specifications. The learning objectives are to understand how to conduct process capability studies and analyze the results.
This document appears to be a template for documenting a Lean event from start to finish. It includes sections for defining the problem and goals, analyzing the baseline process, planning and executing improvements during the event, and controlling the new process afterwards. The template provides guidance on including details such as metrics, stakeholders, process maps, plans for transitioning and training, and tools for ensuring the benefits are sustained long-term.
The document discusses computer simulation as a tool for process improvement. It defines computer simulation as using a computer model to simulate a real system. The basic steps for computer simulation are: 1) define the problem, 2) map the process, 3) define inputs, 4) build the model, 5) validate the model, 6) perform simulations, 7) interpret results, and 8) recommend and document solutions. Reasons for using simulation include testing changes without risk or time constraints, understanding bottlenecks, and validating expected improvements. Simulation should not be used without proper training or understanding, or when simpler methods can achieve the goal.
This document provides an agenda and overview for a JEA Process Improvement Black Belt training on defining projects using the Six Sigma DMAIC methodology. It outlines the schedule and expectations for the define training week, including introducing the 15 deliverable format, methodology and tools for the define phase. It also covers emergency evacuation procedures and codes of conduct for the training.
This document provides guidance on using statistical tests to determine which process inputs (X's) are critical and influence outcomes (Y's). It outlines common statistical tests for continuous and discrete data, including tests for normality, one-sample t-tests to compare a mean to a target, and one-sample sign tests to compare a median when data is not normal. Examples are provided to illustrate how to use Minitab to conduct these tests and interpret the results.
The document discusses identifying root cause relationships as part of a quality improvement process. It explains that before developing solutions to identified root causes, their relationships to environmental concerns like climate change, conservation, and protecting resources must be examined. A relationship matrix tool is presented for mapping which environmental issues need consideration for each root cause when developing countermeasures. The objective is to ensure improvements also advance the organization's environmental performance.
The document provides guidance for project tollgates, focusing presentations on satisfying 15 deliverables in each project phase and showing the logical thought process. Tollgate presentations should also list tasks and dates for the next phase, as well as barriers and assistance needed to complete the project on schedule. Projects are now performed using a standardized 15 deliverable format to guide tollgate reviews.
This document defines the key deliverables and tasks for quantifying the value of a project. Deliverable 3D involves quantifying the project value by determining the benefits to customers and the organization. This includes calculating the cost of poor quality using baseline data and estimating savings. Project benefits are documented in the project benefit document and summarized in the project charter and final presentation.
The document provides instructions for a team to design and launch a balsa wood airplane to hit a target representing a varmint from 12-20 feet away. The team must use the Six Sigma DMAIC process to develop the airplane and launching system, and document their work in a presentation. They will be scored on accuracy in hitting the target from different distances and involvement of all team members. Payments will be made depending on whether the plane hits the target in flight or after landing.
This document provides a flowchart to guide users in selecting the appropriate hypothesis test based on the type of data (continuous or discrete variables), number of variables, assumptions of the data, and other factors. It outlines hypothesis test categories and provides decision trees to navigate through options for continuous and discrete dependent and independent variables, from parametric to non-parametric tests. It also includes sections on control charts and considerations for chart selection based on data type, subgroup size, and sampling versus census data.
Strategies for Effective Upskilling is a presentation by Chinwendu Peace in a Your Skill Boost Masterclass organisation by the Excellence Foundation for South Sudan on 08th and 09th June 2024 from 1 PM to 3 PM on each day.
This presentation includes basic of PCOS their pathology and treatment and also Ayurveda correlation of PCOS and Ayurvedic line of treatment mentioned in classics.
A review of the growth of the Israel Genealogy Research Association Database Collection for the last 12 months. Our collection is now passed the 3 million mark and still growing. See which archives have contributed the most. See the different types of records we have, and which years have had records added. You can also see what we have for the future.
বাংলাদেশের অর্থনৈতিক সমীক্ষা ২০২৪ [Bangladesh Economic Review 2024 Bangla.pdf] কম্পিউটার , ট্যাব ও স্মার্ট ফোন ভার্সন সহ সম্পূর্ণ বাংলা ই-বুক বা pdf বই " সুচিপত্র ...বুকমার্ক মেনু 🔖 ও হাইপার লিংক মেনু 📝👆 যুক্ত ..
আমাদের সবার জন্য খুব খুব গুরুত্বপূর্ণ একটি বই ..বিসিএস, ব্যাংক, ইউনিভার্সিটি ভর্তি ও যে কোন প্রতিযোগিতা মূলক পরীক্ষার জন্য এর খুব ইম্পরট্যান্ট একটি বিষয় ...তাছাড়া বাংলাদেশের সাম্প্রতিক যে কোন ডাটা বা তথ্য এই বইতে পাবেন ...
তাই একজন নাগরিক হিসাবে এই তথ্য গুলো আপনার জানা প্রয়োজন ...।
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The simplified electron and muon model, Oscillating Spacetime: The Foundation...RitikBhardwaj56
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Physiology and chemistry of skin and pigmentation, hairs, scalp, lips and nail, Cleansing cream, Lotions, Face powders, Face packs, Lipsticks, Bath products, soaps and baby product,
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How to Manage Your Lost Opportunities in Odoo 17 CRMCeline George
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Digital Artefact 1 - Tiny Home Environmental Design
NG BB 36 Simple Linear Regression
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National Guard
Black Belt Training
Module 36
Simple Linear Regression
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This material is not for general distribution, and its contents should not be quoted, extracted for publication, or otherwise
copied or distributed without prior coordination with the Department of the Army, ATTN: ETF. UNCLASSIFIED / FOUO
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CPI Roadmap – Analyze
8-STEP PROCESS
6. See
1.Validate 2. Identify 3. Set 4. Determine 5. Develop 7. Confirm 8. Standardize
Counter-
the Performance Improvement Root Counter- Results Successful
Measures
Problem Gaps Targets Cause Measures & Process Processes
Through
Define Measure Analyze Improve Control
ACTIVITIES TOOLS
• Value Stream 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
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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
equations
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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 customer’s
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
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When Should I Use Regression?
Independent Variable (X)
Continuous Attribute
Continuous
Dependent Variable (Y)
Regression ANOVA
Attribute
Logistic Chi-Square (2)
Regression Test
The tool depends on the data type. Regression is typically used with a continuous
input and a continuous response but can also be used with count or categorical
inputs and outputs.
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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 biggest
Reduction of Variables effect on the response variable?
• What are some candidate prediction
models?
Select and Refine • What is the best model?
Models
Validate • How well does the model predict new
Model observations?
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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
X2 Y
These are also called response
Product
X3
variables or dependent variables
(what we’re trying to predict)
Best if the variables are continuous,
but can be count or categorical
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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!
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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
Lurking
variables!
When is it correct to infer causation?
Simple Linear Regression UNCLASSIFIED / FOUO 9
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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 relationship
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Example: Mortgage Estimate Scatter Plot
Hypothesis:
Brokers with more experience can provide
estimates in a shorter time.
60
50
Call Length
40
30
20
10 20 30
Broker Experience
Does it look like a relationship exists between Broker Experience and Call Length?
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Scatter Plot - Structure
Y Axis
60
Paired
(Result?) Data
50
Call Length
40
X Axis
30 ( 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 broker’s experience). You have to
make sure that the data “pair-up” properly in Minitab, or the diagram will be meaningless.
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Input, Process, Output Context
PREDICTOR MEASURES RESULTS MEASURES
Y (X) (X) (Y)
Input Process Output
• Arrival • Customer
Time Satisfaction
• Accuracy • Total
• Cost Defects
• Key Specs • Cycle Time
• Cost
• Time Per Task
• In-Process Errors
• Labor Hours
• Exceptions
X Axis – Y Axis –
Independent Variable Dependent Variable
X
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Scatter Plots
No Correlation Negative Curvilinear 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
Don’t assume a causal relationship!
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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
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Example One
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Example Two
Simple Linear Regression UNCLASSIFIED / FOUO 17
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Example Three
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Minitab Example: Scatter Plot
Next, we will work through a Minitab example using
data collected at the Anthony’s Pizza company
The Belt suspects that the customers have to wait too
long on days when there are many deliveries to make
at Anthony’s Pizza
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Minitab Example: Pizza Scatter Plot
A month of data was collected, and stored in the
Minitab file Regression-Pizza.mtw
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Pizza Scatter Plot (Cont.)
When you click on Scatterplots,
this is the first dialog box that
comes up
3. Select the Simple Scatterplot
4. Click on OK to move to the
next dialog box
Simple Linear Regression UNCLASSIFIED / FOUO 22
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Pizza 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
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Pizza Scatter Plot (Cont.)
Does it look like the number of Deliveries
influences the customer’s Wait Time?
Scatterplot of Wait Time vs Deliveries
55
50
Wait Time
45
40
35
10 15 20 25 30 35
Deliveries
Simple Linear Regression UNCLASSIFIED / FOUO 24
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Pizza Scatter Plot (Cont.)
Note: Hold your cursor over any
point on the Scatterplot and Minitab will identify the
Row, X-Value and Y-Value for that point
Simple Linear Regression UNCLASSIFIED / FOUO 25
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Correlation Coefficients (r & r2)
Numbers that indicate the strength of the correlation
between two factors
r - strength and the direction of the relationship
Also called Pearson’s Correlation Coefficient
r2 - percentage of variation in Y attributable to the
independent variable X.
Adds precision to a person’s visual judgment about
correlation
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
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Interpreting Correlation Coefficients
r falls on or between -1 and 1
Calculate in Minitab
Figures below -0.65 and above
0.65 indicate a meaningful
correlation
1 = “Perfect” positive correlation
r=0
-1 = “Perfect” negative
correlation
Use to calculate r2
r=-.8
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Pearson Correlation Coefficient (r) – Mortgage
Betty Black Belt used the scatter plot to get a visual
picture of the relationship between broker experience
and call length
Now she uses the Pearson Correlation Coefficient, r,
to quantify the strength of the relationship
60
50
Call Length
40
r = - 0.896
30
(a strong negative correlation)
20
10 20 30
Broker Experience
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Exercise: Correlation
The scatter plot shows that the customers are waiting
longer when Anthony’s Pizza has to make more
deliveries
Next, the Belt wants to quantify the strength of that
relationship
To do that, we will calculate the Pearson Correlation
Coefficient, r
Simple Linear Regression UNCLASSIFIED / FOUO 29
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Correlation Input Window
2. Double click on C5 Wait
Time and C6 Deliveries
to add them to the
Variables box
3. Uncheck the box,
Display p-values
4. Click OK
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Correlation Coefficient
Since r, the Pearson correlation, is 0.970, there is a meaningful
correlation between the wait time and number of deliveries
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Interpreting Coefficients – r2
First, we obtained r from the Correlation analysis
Next, in Regression, we will look at r2 to see how good our
model (regression equation) is
r2: Compute by multiplying r x r (Pearson correlation
squared)
Example: With an r value of .970, in the Pizza example,
the team computed r2 :
.970 x .970 = .941 or 94.1%
So, 94% of the variation in wait time is explained by the
variability in deliveries
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Regression Analysis
Regression Analysis is used in conjunction with
Correlation and Scatter Plots to predict future
performance using past results
While Correlation shows how much linear relationship
exists between two variables, Regression defines the
relationship more precisely
Use this tool when there is existing data over a
defined range
Regression analysis is a tool that uses data on
relevant variables to develop a prediction equation, or
model
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Linear Regression
In Simple Linear Regression, a single variable “X” is
used to define/predict “Y”
e.g.; Wait Time = B1 + (B2) x (Deliveries) + (error)
Simple Regression Equation: Y = B1 + (B2) x (X) +
Y B2 = Slope
y
x
X
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Exercise: Regression
Since the Pearson Correlation (r) was .970, we know
that there is a strong positive correlation between the
number of deliveries and the wait time
Next, the Belt would like to get an equation to predict
how long the customers will be waiting
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Regression (Cont.)
1. Choose Stat>Regression>Fitted Line Plot
Simple Linear Regression UNCLASSIFIED / FOUO 37
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Fitted Line Input Window
2. Double click on
C5 Wait Time to enter it as
the Response (Y) variable
3. Double click on
C6 Deliveries to enter it as
the Predictor (X) variable
4. Make sure Linear is checked
for the type of Regression
5.Edit dialog box options
(Optional)
6. Click OK
Simple Linear Regression UNCLASSIFIED / FOUO 38
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Pizza Regression Plot
Fitted Line Plot
Wait Time = 32.05 + 0.5825 Deliveries
55
S 1.11885
R-Sq 94.1%
R-Sq(adj) 93.9%
50
Wait Time
45
40
35
10 15 20 25 30 35
Deliveries
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Regression Analysis Results – Session Window
Prediction Equation
(Regression Model)
R-Sq is the amount of variation in the data explained by the model.
Notice that 94.1 = .970 * .970. R-Sq is the square of the Pearson
correlation from the previous analysis.
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Using the Prediction Equation
If we have 20 deliveries to make, how long will the
customer have to wait for their order?
Based on our 30 minute guarantee, how acceptable is
our performance?
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Method of “Least Squares”
Regression – Technical Note
Fitted Line Plot
Wait Time = 32.05 + 0.5825 Deliveries
55
ˆ
Y
50
“fitted” observation
(the line)
Wait Time
45
Y
40
true observation
(the data point)
35
10 15 20 25 30 35
Deliveries
Minitab will find the “best fitting” line for us. How does it do that?
•We want to have as little difference as possible between the true observations and
the fitted line
•Minitab minimizes the sums of squares of the distance between the fitted and true
observations
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Multiple Regression
Use this when you want to consider more than one
predictor variable
The benefit is that you might need more predictors to
create an accurate model
In the case of our Anthony’s Pizza example, we may
want to look at the impact that incorrect orders,
damaged pizzas, and cold pizzas have on wait time
Simple Linear Regression UNCLASSIFIED / FOUO 43
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Individual Exercise: Pizza
As a Anthony’s Pizza Belt, you suspect that the number of
pizza defects increases when more pizzas are ordered.
You want to visualize the data and quantify the relationship
Use the Minitab file Pizza Exercise.mtw data to
investigate the relationship between “Total Pizzas” and
“Defects”
Create a scatter plot
Determine correlation
Create a fitted line plot
Determine the prediction equation
How many defects do we usually have when 50 pizzas are
on order? What do you think of this model?
Simple Linear Regression UNCLASSIFIED / FOUO 44
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Another Exercise: Absentee Rate
The human resources director of a chain of fast-food
restaurants studied the absentee rate of employees.
Whenever employees called in sick, or simply did not
show up, the restaurant manager had to find
replacements in a hurry, or else work short-handed
The director had data on the number of absences per
100 employees per week (Y) and the average number
of months’ experience at the restaurant (X) for 10
restaurants in the chain. The director expected that
long-term employees would be more reliable and
absent less often
Simple Linear Regression UNCLASSIFIED / FOUO 45
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Absentee Rate
1. Open an blank Minitab worksheet Experience Absences
and input the data 18.1 31.5
2. Create a scatter plot and decide 20.0 33.1
whether a straight line is a 20.8 27.4
reasonable model 21.5 24.5
3. Conduct a regression analysis and 22.0 27.0
get the linear prediction equation 22.4 27.8
4. Predict the number of absences for 22.9 23.3
employees with 19.5 months of 24.0 24.7
experience
25.4 16.9
27.3 18.1
Simple Linear Regression UNCLASSIFIED / FOUO 46
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Takeaways
Start with a visual tool – create a scatter plot
Determine the Pearson correlation coefficient, r, to
determine the strength of the relationship
Remember that correlation does not guarantee
causation!
Create and interpret the Regression Plot
Use the prediction equation
Validate the prediction model’s r-squared using new
data (not part of the data set used in creating the
prediction equation)
Simple Linear Regression UNCLASSIFIED / FOUO 47
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What other comments or questions
do you have?
UNCLASSIFIED / FOUO