book

JMP® Means Business: Statistical Models for Management

by Josef Schmee, Jane Oppenlander

July 2010

Beginner

608 pages

13h 56m

English

SAS Institute

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1.1 Introduction1.2 Why Data Are Needed1.3 Sources of Data1.3.1 Existing Data versus New Data1.3.2 Existing DataSourcesUses of Existing Data1.3.3 New DataFocus GroupsSurveysCensusSample SurveysDesigned ExperimentsObservational StudiesComputer Simulation1.4 Data Scales1.4.1 Ratio Scale1.4.2 Interval Scale1.4.3 Ordinal Scale1.4.4 Nominal Scale1.4.5 Likert Scale1.5 Summary1.6 Problems1.7 Case Study: Green's Gym–Part 1Business GoalsStrategyTasks
2.1 Introduction2.2 Questionnaires2.2.1 Layers of a QuestionnaireWordsQuestionsFormatHypothesis2.2.2 How to Ask QuestionsPersonal InterviewsTelephone InterviewsSelf-Administered QuestionnairesMailed QuestionnairesOnline SurveysDirect Observation2.2.3 Questionnaire Design2.2.4 Guidelines for Writing QuestionsQuestions to AvoidOpen versus Closed ResponsesQuestion by Type of Response2.3 Sampling2.3.1 Sampling ConceptsExample: Customer Satisfaction after On-Board Program in a Bank2.3.2 Probability SamplesSampling ErrorsNon-Sampling Errors2.3.3 Probability versus Non-Probability Samples2.3.4 Common Types of Probability SamplingSimple Random SamplingSystematic SamplingStratified SamplingCluster Sampling2.3.5 Other Sampling Methods2.4 Summary2.5 Problems2.6 Case Study: Green's Gym–Part 2Business GoalsStrategyTasks
3.1 Introduction3.1.1 Graphs for Continuous Data3.1.2 Numerical Summaries for Continuous Data3.1.3 Data Descriptions for Nominal and Ordinal Data3.2 Example: Order Processing in an Herbal Tea Mail Order Business3.3 Descriptive Statistics with the JMP Distribution Platform3.3.1 Describing a Continuous Variable3.3.2 Describing a Nominal Variable3.4 Interpretation of Descriptive Statistics3.4.1 Histogram3.4.2 Box Plot3.4.3 CDF Plot3.4.4 Quantiles3.4.5 Moments3.5 Practical Advice and Potential Problems3.5.1 Features of Good Graphs3.5.2 Example: Izod Impact Strength of Two Suppliers3.5.3 Simple Improvements to Histograms3.5.4 Potential Problems with Box Plots and HistogramsData Sets Are SmallData Are Rounded or Have Very Few Distinct ValuesThe Distribution of Data Is Highly Asymmetric3.6 Summary3.7 Problems3.8 Case Study: New Web Software Testing
4.1 Introduction4.1.1 Building Statistical Models4.1.2 Examining Examples of Statistical Models4.1.3 Evaluating Statistical Models4.2 Classification of Statistical Models4.2.1 Models with a Single Y-Variable and No X-Variables4.2.2 Models with a Single Y-Variable and a Single X-Variable4.2.3 Models with a Single Y-Variable and Multiple X-Variables4.2.4 Models with Multiple Y-Variables and No X-Variables4.2.5 Models with Continuous Multiple Y-Variables and Some X-Variables4.2.6 Other Approaches to Models4.2.7 Other Models4.3 Model Validation4.3.1 Pitfalls of Model Building4.3.2 Model Validation4.3.3 Residuals in Model Validation4.4 Summary4.5 Problems4.6 Case Study: Models of Advertising EffectivenessBusiness ProblemTasks
5.1 Introduction to Distributions5.1.1 Random Variables5.1.2 Independent Events5.1.3 Discrete or Continuous Distributions5.1.4 Characteristics of Distributions5.1.5 General Shape of Distributions5.2 Discrete Distributions5.2.1 Probability Function p(y)5.2.2 Cumulative Distribution Function F[y)5.2.3 Mean, Variance, and Standard Deviation5.3 Binomial Distribution5.3.1 Binomial Distribution Characteristics5.3.2 Calculating Binomial Probabilities in JMP5.3.3 Practical Advice5.4 Distributions of Two Discrete Random Variables (Y1, Y2)5.4.1 Return of Two Stocks under Different Economic Conditions5.4.2 Joint and Marginal Probability Functions5.4.3 Covariance Cov[Y1, Y2] and Correlation Coefficient p125.4.4 Calculating E[Y1], E[Y1], E[Y12], E[Y22] and E[Y1,·Y2]5.4.5 Variance and Standard Deviation of a Portfolio of Two Stocks5.5 Summary5.6 Problems5.7 Case Study: Assessing Financial InvestmentsBackgroundBusiness Problem

6.1 Introduction to Continuous Distributions6.2 Characteristics of Continuous Distributions6.2.1 Density Function f(y)6.2.2 Cumulative Distribution Function F[y)6.2.3 General Shape of Continuous Distributions6.2.4 Measures of Location and Spread6.3 Uniform Distribution6.4 The Normal Distribution6.4.1 General Normal Distribution with Mean[Y] = μ and SD[Y] = σStandardizing Random VariablesExample: Lifetime of Light Bulbs6.4.2 Standard Normal DistributionCalculating Normal Probabilities in JMPCalculating Normal Distribution Quantiles in JMPDistribution of the Mean of Normally Distributed Outcomes6.5 Central Limit Theorem6.6 Sampling Distributions6.6.1 Student's t-Distribution6.6.2 Chi-Square Distribution6.6.3 F-Distribution6.7 Summary6.8 Problems6.9 Case Study: Julie's Lakeside CandyBusiness Problem
7.1 Introduction7.2 Point Estimates of Mean and Standard Deviation7.2.1 What Is a Point Estimate?Example: Estimating the Mean Number of Orders per7.2.2 Parameters and Estimates7.2.3 Standard Error of Estimate7.3 Confidence Intervals for Mean and Standard Deviation7.3.1 What Is a Confidence Interval?7.3.2 (1 - α) 100% Confidence Level7.4 Detail Example: Package Delivery Times of Herbal Teas7.5 JMP Analysis of Herbal Tea Package Delivery Times7.5.1 Confidence Intervals for Mean and Standard Deviation7.6 Prediction and Tolerance Intervals7.6.1 Prediction IntervalsPrediction Interval for a Single Future ObservationExample: Delivery TimesPrediction Intervals for k Future Observations7.6.2 Tolerance IntervalsConclusion7.7 Summary7.8 Problems
8.1 Introduction to Hypothesis Testing8.1.1 Accept or Reject Decisions for the Mean: H0 versus HALeft-Sided Alternative HypothesisRight-Sided Alternative HypothesisTwo-Sided Alternative HypothesisHypothesis Testing StepsCourt Decisions and Hypothesis Testing8.1.2 Significance Level α8.1.3 Test Statistic8.1.4 p-Value8.1.5 Decision Rule to Accept or Reject H08.1.6 Example: Order Processing TimesLeft-Sided Alternative HypothesisRight-Sided Alternative HypothesisTwo-Sided Alternative Hypothesis8.1.7 Test Statistic, Significance Level, Critical Value, and p-Value8.1.8 Example: Order Processing with JMP8.1.9 Confidence Intervals and Two-Sided Hypothesis TestingExample: Herbal Tea Mail Order8.2 Sample Size Needed to Test H0: Mean = Mean0 versus HA: Mean = MeanA8.2.1 Introduction8.2.2 Example: Sample Size Calculations for Mama Mia's Pizza Parlor8.2.3 Sample Size in JMP8.2.4 Approximate Formulas for Sample Size8.2.5 Power Curves8.2.6 Sample versus Process Standard Deviation (s versus σ)Standard Deviation σ Is Unknown–Use Sample Standard Deviation sStandard Deviation σ Is KnownConfidence Interval for the Standard Deviation σ8.2.7 Hypothesis Test for the Standard Deviation σNormal Quantile Plot8.3 Summary8.4 Problems8.5 Case Study: Traffic Speed Limit ChangeBusiness ProblemStrategyTasks
9.1 Introduction9.1.1 Hypotheses for Comparing Two Means9.1.2 Paired t-Test versus Two-Sample t-Test9.2 Two-Sample t-Test9.2.1 Detail Example: Comparing Processor Speeds of Two Brands9.2.2 Two-Sample t-Test in JMP9.2.3 Interpretation of Two-Sample Results9.3 Paired t-Test9.3.1 Detail Example: Advertising Effect in Test Markets9.3.2 Paired t-Test in JMP9.3.3 Interpretation of Paired t-Test Results9.4 Paired t-test versus Two-Sample t-test on the Same Data9.4.1 Example: Abrasion Resistance9.4.2 Summary of Differences between the Paired and Two-Sample t-test9.5 Summary9.6 Problems9.7 Case Study: Westville Meat Processing PlantBusiness ProblemStrategyTask
10.1 Introduction10.1.1 Fixed-Effect One-Way ANOVA10.1.2 One-Way ANOVA Model10.1.3 One-Way ANOVA Hypotheses10.1.4 Sources of Variation10.2 Detail Example: Training Method and Time to Learn10.3 One-Way ANOVA in JMP10.3.1 One-Way ANOVA with Fit Y by X10.3.2 Interpretation of Results10.3.3 Means ComparisonsEach Pair, Student's t Confidence IntervalsOther Compare Means in Fit Y by XCompare Means in Fit ModelCrosstab Report of Fit Model10.4 Checking Assumptions of ANOVA Model10.4.1 Residuals10.4.2 Example: Stock Indices by Industry10.4.3 Side-by-Side Box Plots10.4.4 Tests for Unequal Variances10.4.5 Normal Quantile Plot of Residuals10.5 Summary10.6 Problems10.7 Case Study: Carpal Tunnel Release SurgeryBusiness ProblemTask
11.1 Introduction11.2 Two-Way ANOVA without Replications11.2.1 Model and Sources of Variation11.2.2 Hypotheses for Each Model Term11.2.3 Detail Example: Prices of Wireless Mouse Devices by Brand at Different Stores11.2.4 JMP Analysis of the Wireless Mouse Example Using the Fit Model Platform11.3 Two-Way ANOVA with Equally Replicated Data11.3.1 Model and Sources of Variation11.3.2 Hypotheses for Each Model Term11.3.3 What Is an Interaction Effect?11.3.4 Detail Example: Profitability of Futures Trading Customers of a Financial Institution (Equal Replications)11.3.5 JMP Analysis of Profitability of Futures Trading Customers11.4 Two-Way ANOVA with Unequal Replications11.5 Summary11.6 Problems11.7 Case Study: Fish Catch near Oil RigBusiness ProblemTasks
12.1 Introduction12.2 Proportions from a Single Sample12.2.1 Introduction to Proportions12.2.2 Detail Example: A Survey to Evaluate Brand Preference12.2.3 Sample Size Considerations with Single Proportions12.3 Chi-Square Test for Equality of k Proportions12.3.1 Introduction to Chi-Square12.3.2 Detail Example: Default Rates on a Specific Type of Loan (CBA Loan) by Credit Rating12.3.3 The Pearson Chi-Square Statistic12.4 Summary12.5 Problems12.6 Case Study: Incomplete Rebate Submissions
13.1 Statistical Independence of Two Nominal Variables13.1.1 Introduction13.1.2 Review of Conditional Probability and Independent Events13.1.3 Statistical Hypotheses of Independence of Two Nominal VariablesStatistical Hypotheses and Chi-Square Statistic for Testing Independence13.1.4 Example 1: Executive TransfersAnalysis of Executive Transfer in JMP13.2 Stratification in Cross-Classified Data13.2.1 What Is Stratification of Cross-Classified Data?13.2.2 Example 1: Consumer Preference of Two Cola BrandsAnalysis of Consumer Preference of Two Cola Brands in JMP13.2.3 Example 2: On-Time Performance of Package Delivery CompaniesAnalysis of On Time Performance and Package Companies in JMPStratified Analysis by Regular and Express Mail Packages13.2.4 Example 3: Mortality after a High-Risk Procedure in Two HospitalsAnalysis of Mortality after High Risk Procedure in JMP13.3 Summary13.4 Problems13.5 Case Study: Financial Management Customer Satisfaction SurveyBusiness ProblemTask
14.1 Introduction14.1.1 General Simple Regression Problem and Use14.1.2 Data Requirements14.1.3 Basic Results14.2 Detail Example: Yield in a Chemical Reactor14.2.1 Situation, Research Question, Data Requirements, and Anticipated Results14.2.2 Outputs Related to Problem Statement14.3 JMP Analysis of the Yield in a Chemical Reactor Example14.3.1 Simple Regression Results with the Fit Y by X Platform14.3.2 Fit Y by X Results14.3.3 Summary of Relevant Output14.4 Interpretation of Basic Regression Outputs14.4.1 Estimates of Simple Regression Equation14.4.2 t-Ratios to Test Significance of b0 and b114.4.3 Root Mean Square Error (RMSE)14.4.4 Additional Simple Regression ResultsYhat: Estimated Average or Predicted Value of Y at X0Obtaining Yhat in JMPConfidence Intervals for the Mean of Y at X0Obtaining Confidence Intervals in JMP using Fit Y by XObtaining Confidence Intervals in JMP Using Fit ModelPrediction Intervals for a Single Future Y at X014.5 How Good Is the Regression Line?14.5.1 Scatterplot14.5.2 Significance of Slope Coefficient14.5.3 RMSE Relative to Std Dev[Mean]14.5.4 RSquare: Coefficient of Determination R214.5.5 Plots to Verify Simple Regression Assumptions14.5.6 Residual Plots14.6 Important Considerations14.6.1 Slope Estimates b. Are Sensitive to Outliers14.6.2 Hazards of Extrapolation Beyond the Range of the Data14.6.3 Confidence Intervals for b0 and b114.7 Summary14.8 Problems14.9 Case Study: Lost Time Occupational InjuriesBusiness ProblemStrategyTasks
15.1 Simple Correlation15.1.1 IntroductionSample Correlation Coefficient and Sample Covariance15.1.2 Example: Correlation of Financial IndicesCorrelation Coefficients in JMPCovariances in JMPTesting Significance of a Correlation Coefficient15.1.3 Data Patterns and Correlation CoefficientsRelation of Correlation Coefficient r with Simple Regression R2 and Slope b115.2 Regression and Stock Market Returns15.2.1 IntroductionExample: Comparing the Risk of General Electric, SP500 and 13-week Treasury BillAsset Variability as a Measure of Total Risk15.2.2 Capital Asset Pricing Model (CAPM)Expected Return on MarketExpected Return on Individual StockExample: GE and Its Three-Month Daily Beta for 2006Interpreting the Slope CoefficientsA Hypothesis Test Associated with BetaUsing Covariance and Variance of Returns to Estimate Beta15.3 Curvilinear Regression15.3.1 Introduction15.3.2 Quadratic Regression with Fit PolynomialExample: Detecting Possible Voting Irregularities15.3.3 Fitting Curves with Fit Special15.3.4 Detail Example: Price Elasticity of DemandPoint Price Elasticity EPMeaning of EPElasticity and RegressionElasticity under Unitary DemandExample: Demand for Chicken15.4 Summary15.5 Problems15.5.1 Correlation15.5.2 Stock Market Returns15.5.3 Curvilinear Regression15.6 Case Studies15.6.1 Case Study 1: Comparing Correlation between Individual Stocks and an Index15.6.2 Case Study 2: Comparing the Risk of Two Market Sectors15.6.3 Case Study 3: Experience Curve15.6.4 Case Study 4: Engel's Law
16.1 Introduction16.1.1 Data Requirements for Multiple Regression16.1.2 Multiple Regression Analysis Process16.1.3 Multiple Regression Model16.2 Detail Example: Profits of Bank Branches16.3 JMP Analysis of Bank Branch Profits Example16.3.1 Preliminary Fitting of Single X-Variables to YSimple CorrelationsScatterplot MatrixSimple Regression Analysis with Individual Independent Variables16.3.2 Fitting Several X-Variables to YMultiple Regression Model with All Three Independent VariablesSummary of Fit from Fit ModelParameter Estimates Table16.3.3 What Do t-Ratios Measure?16.3.4 Conclusions from the Three X-Variable Model16.3.5 Regression Model Using Total Sales per Year = X1 and Total Sqft = X2Conclusions from Two X-Variable Model16.4 Evaluating Model Assumptions and Goodness of Fit16.4.1 Residuals ei16.4.2 Residuals ei and RMSE16.4.3 Residuals and R216.4.4 R2 and RMSE16.4.5 R2adj16.4.6 Plot of Residuals versus Predicted Y (Yhat) or versus Time Order16.4.7 Durbin-Watson Test for the Independence of ResidualsExample: Dow Jones 30 Industrials Adjusted Close16.5 Model Interpretation16.5.1 Leverage Plots and the Importance of X16.5.2 Standardized Beta and the Importance of X16.5.3 Understanding the Role of X-Variables: Column DiagnosticsCheck the Slopes of the EquationCheck for Multi-Collinearity Variance Inflation Factors (VIFs)Global Statistical Test in Multiple Regression16.6 Summary16.7 Problems16.8 Case Study: Forbes Global 2000 High PerformersTasks
17.1 Introduction17.2 Detail Example: Loan Amount versus Sales Revenues17.3 Difference of Intercepts of Two Parallel Lines17.3.1 Using JMP for Regression Analysis with a Nominal Variable17.3.2 Interpretation of Parameter Estimates and Associated Hypothesis Tests17.4 Regression Models Including Nominal Variables with Three or More Levels17.5 Both Intercept and Slope of Two Lines Are Different17.5.1 Detail Example: Growth versus General Equity Fund17.5.2 Using JMP to Model Two Slopes and Two Intercepts17.6 Summary17.7 Problems17.8 Case Study: Coffee Sales
18.1 Introduction18.2 Detail Example: Profit of Bank Branches18.3 All Possible Regression Models18.3.1 R2 Criterion18.3.2 RMSE Criterion18.4 Stepwise Regression18.4.1 Stepwise Regression Algorithms18.4.2 Stepwise Regression in JMPChoice of Prob to Enter and Prob to LeaveForward Stepwise RegressionBackward Stepwise RegressionMixed Stepwise Regression18.5 Candidate ModelsEvaluating Candidate ModelsModel with Five Variables from Forward Stepwise RegressionModel with Four Variables from Backward Stepwise RegressionModel with Three Variables from All Possible Models18.6 Model Recommendation18.6.1 Recommended Model for the Bank Branch Profits Example18.6.2 Other Criteria for Including or Excluding X-VariablesNon-Statistical ReasonsOverriding Statistical Criteria18.7 Summary18.8 Problems18.9 Case Studies18.9.1 Case Study 1: Real Estate AppraisalTasks18.9.2 Case Study 2: Discrimination in Compensation?
19.1 IntroductionData Requirements for Exponential Smoothing19.2 Detail Example: 10-Year Treasury Note Closing PricesDescribing Time Series Data in JMPOther Time Series MethodsDifferences19.3 Smoothing Models19.3.1 Simple Moving AveragesSimple Moving Average CalculationWeights of Observations in a MA(k)Average Age of Observations in a MA(k)Example of MA(3): EDO Stock Price19.3.2 Exponential Smoothing ModelsEstimates and Smoothing Weights19.3.3 Simple Exponential Smoothing (SES)SES WeightsSimple Exponential Smoothing in JMP19.3.4 Double Exponential Smoothing (DES) For Linear TrendDES Example: ABC Stock PriceSES and DES Behavior When the Level Changes19.3.5 Winters' Additive Seasonal MethodExample: Monthly Sales of High End Audio ComponentsWinters' Additive Method in JMP19.4 Summary19.5 Problems19.6 Case Study: Lockheed Martin Stock in Changing TimesBusiness ProblemStrategyTasks

Content preview from JMP® Means Business: Statistical Models for Management

Chapter 12. Proportions

12.1 Introduction 316
12.2 Proportions from a Single Sample 317
- 12.2.1 Introduction to Proportions 317
- 12.2.2 Detail Example: A Survey to Evaluate Brand Preference 318
- 12.2.3 Sample Size Considerations with Single Proportions 323
12.3 Chi-Square Test for Equality of k Proportions 327
- 12.3.1 Introduction to Chi-Square 327
- 12.3.2 Detail Example: Default Rates on a Specific Type of Loan (CBA Loan) by Credit Rating 327
- 12.3.3 The Pearson Chi-Square Statistic 331
12.4 Summary 334
12.5 Problems 335
12.6 Case Study: Incomplete Rebate Submissions 337

12.1 Introduction

The next two chapters deal with categorical data. As discussed in Chapter 1, JMP uses the terms nominal or ordinal for such data. Categorical data occur regularly in many business ...