# Business Analytics. Methods, Models, and Decisions. James R. Evans : University of Cincinnati PEARSON

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1 Business Analytics Methods, Models, and Decisions James R. Evans : University of Cincinnati PEARSON Boston Columbus Indianapolis New York San Francisco Upper Saddle River Amsterdam Cape Town Dubai London Madrid Milan Munich Paris Montreal Toronto Delhi Mexico City Sao Paulo Sydney Hong Kong Seoul Singapore Taipei Tokyo

3 VI Contents Data Queries: Using Sorting and Filtering 60 Sorting Data in Excel 61 Pareto Analysis 61 Filtering Data 62 Statistical Methods for Summarizing Data 65 Frequency Distributions for Categorical Data 66 Relative Frequency Distributions 68 Frequency Distributions for Numerical Data 68 Excel Histogram Tool 69 Cumulative Relative Frequency Distributions 72 Percentiles and Quartiles 73 Cross-Tabulations 75 Exploring Data Using PivotTables 77 PivotCharts 81 Key Terms 81 Problems and Exercises 82 Case: Performance Lawn Equipment 84 Chapter 4: Descriptive Statistical Measures 85 Learning Objectives 85 Populations and Samples 86 Understanding Statistical Notation 86 Measures of Location 87 Arithmetic Mean 87 Median 88 Mode 89 Midrange 90 Using Measures of Location in Business Decisions 90 Measures of Dispersion 91 Range 91 Interquartile Range 92 Variance 92 «Standard Deviation 93 Chebyshev's Theorem and the Empirical Rules 94 Standardized Values 98 Coefficient of Variation 99 Measures of Shape 99 Excel Descriptive Statistics Tool 102 Descriptive Statistics for Grouped Data 103 Descriptive Statistics for Categorical Data: The Proportion 106 Statistics in PivotTables 106 Measures of Association 106 Co variance Correlation 109 Excel Correlation Tool 112 Outliers 113 Statistical Thinking in Business Decisions 115 Variability in Samples 116 Key Terms 119 Problems and Exercises 119 Case: Performance Lawn Equipment 124 Chapter 5: Probability Distributions and Data Modeling 125 Learning Objectives 125 Basic Concepts of Probability 126 Probability Rules and Formulas 128 Conditional Probability 129 Random Variables and Probability Distributions 132 Discrete Probability Distributions 135 Expected Value of a Discrete Random Variable 136 Using Expected' Value in Making Decisions 137 Variance of a Discrete Random Variable 139 Bernoulli Distribution 139 Binomial Distribution 140 Poisson Distribution 142 Continuous Probability Distributions 143 Properties of Probability Density Functions 145 Uniform Distribution 146 Normal Distribution 148 The NORM.INV Function 150 Standard

4 vii Normal Distribution 150 Using Standard Normal Distribution Tables 152 Exponential Distribution 152 Other Useful Distributions 154 Continuous Distributions 154 Random Sampling from Probability Distributions 155 Sampling from Discrete Probability Distributions 156 Sampling from Common Probability Distributions 157 "' Risk Solver Platform Distribution Functions 160 Data Modeling and Distribution Fitting 162 Goodness of Fit 164 p Distribution Fitting with Risk Solver Platform 164 Key Terms 166 Problems and Exercises 167 Case: Performance Lawn Equipment 174 Chapter 6: Sampling and Estimation 175 Learning Objectives 175 Statistical Sampling 176 Sampling Methods 176 Estimating Population Parameters 180 Unbiased Estimators 180 Errors in Point Estimation 181 Sampling Error 181 Understanding Sampling Error 181 Sampling Distributions 183 Sampling Distribution of the Mean 183 Applying the Sampling Distribution of the Mean 184 Interval Estimates 185 Confidence Intervals 186 Confidence Interval for the Mean with Known Population Standard Deviation 186 The f-distribution 188 Confidence Interval for the Mean with Unknown Population Standard Deviation 189 Confidence Interval for a Proportion 189 Additional Types of Confidence Intervals 190 Using Confidence Intervals for Decision Making 192 Prediction Intervals 192 Confidence Intervals and Sample Size 193 Key Terms 195 Problems and Exercises 195 Case: Performance Lawn Equipment 198 Chapter 7: Statistical Inference 199 Learning Objectives 199 Hypothesis Testing 200 Hypothesis-Testing Procedure 201 One-Sample Hypothesis Tests 201 Understanding Risk in Hypothesis Testing 202 Selecting the Test Statistic 203 Drawing a Conclusion 204 p-values 206 Two-Tailed Test of Hypothesis for the Mean 206 One-Sample Tests for Proportions 207 Two-Sample Hypothesis Tests 208 Two-Sample Tests for Differences in Means 209 ' Two-Sample Test'for Means with Paired Samples 212 Test for Equality of Variances 214

5 VIII Contents Analysis of Variance 215 Assumptions of ANOVA 216 Chi-Square Test for Independence 217 Key Terms 221 Problems and Exercises 221 Case: Performance Lawn Equipment 225 Part 3: Predictive Analytics Chapter 8: Predictive Modeling and Analysis 226 Learning Objectives 226 Logic-Driven Modeling 227 Strategies for Building Predictive Models 227» Data and Models 229 Models Involving Multiple Time Periods 231 Single-Period Purchase Decisions 231 Overbooking Decisions 233 Model Assumptions, Complexity, and Realism 234 Data-Driven Modeling 236 Retail Pricing Markdowns 238 Modeling Relationships and Trends in Data 238 Analyzing Uncertainty and Model Assumptions 243 What-If Analysis 244 Data Tables 244 Scenario Manager 248 Goal Seek 251 Model Analysis Using Risk Solver Platform 251 Parametric Sensitivity Analysis 251 Tornado Charts 255 Key Terms 256 Problems and Exercises 256 Case: Performance Lawn Equipment 260 Chapter 9: Regression Analysis 261 Learning Objectives 261 Simple Linear Regression 262 Finding the Best-Fitting Regression Line 263 Least-Squares Regression 265 Simple Linear Regression with Excel 267 Regression as Analysis of Variance 269 Testing Hypotheses for Regression Coefficients 270 Confidence Intervals for Regression Coefficients 271 Residual Analysis and Regression Assumptions 271 Checking Assumptions 272 Multiple Linear Regression 274 Building Good Regression Models 279 Correlation and Multicollinearity 281 Regression with Categorical Independent Variables 283 Categorical Variables with More Than Two Levels Regression Models with Nonlinear Terms 287 Key Terms 291 Problems and Exercises 291 Case: Performance Lawn Equipment 295 Chapter 10: Forecasting Techniques 297 Learning Objectives 297 Qualitative and Judgmental Forecasting 298 Historical Analogy 298 The Delphi Method 299 Indicators and Indexes 299

6 ix Statistical Forecasting Models 300 Forecasting Models for Stationary Time Series 302 Moving Average Models 302 Error Metrics and Forecast Accuracy 307 Exponential Smoothing Models 308 Forecasting Models for Time Series with a Linear Trend 311 Double Exponential Smoothing 313 Regression-Based Forecasting for Time Series with a Linear Trend 313 Forecasting Time Series with Seasonality 315 Regression-Based Seasonal Forecasting Models 316 Holt-Winters Forecasting for Seasonal Time Series 317 Holt-Winters Models for Forecasting Time Series with Seasonality and Trend 318 Selecting Appropriate Time-Series-Based Forecasting Models 322 Regression Forecasting with Causal Variables 323 The Practice of Forecasting 325 Key Terms 326 Problems and Exercises 326 Case: Performance Lawn Equipment 328 Chapter 11: Simulation and Risk Analysis 329 Learning Objectives 329 Spreadsheet Models with Random Variables 331 Monte Carlo Simulation 331 Monte Carlo Simulation Using Risk Solver Platform 333 Defining Uncertain Model Inputs 334 Defining Output Cells 335 Running a Simulation 336 Analyzing Results 338 New-Product Development Model 339 Confidence Interval for the Mean 343 Sensitivity Chart 343 Overlay Charts 344 Trend Charts 346 Box-Whisker Charts Simulation Reports 347 Newsvendor Model 347 The Flaw of Averages 348 Monte Carlo Simulation Using Historical Data 348 Monte Carlo Simulation Using a Fitted Distribution 350 Overbooking Model 351 The Custom Distribution in Risk Solver Platform 351 Cash Budget Model 352 Correlating Uncertain Variables 356 Key Terms 360 Problems and Exercises 360 Case: Performance Lawn Equipment 365 Chapter 12: Introduction to Data Mining 366 Learning Objectives 366 The Scope of Data Mining 368 Data Exploration and Reduction 369 Cluster Analysis 369 Classification 372 An Intuitive Explanation of Classification 376 Measuring Classification Performance 378 «Using Training and Validation Data 378 Classifying New Data 380 Classification Techniques 381 ^-Nearest Neighbors (&-NN) 381 Discriminant Analysis 385 Logistic Regression 389

7 Association Rule Mining 393 Cause-and-Effect Modeling 397 Key Terms 401 Problems and Exercises 401 Case: Performance Lawn Equipment 402 Part 4: Prescriptive Analytics Chapter 13: Linear Optimization 404 Learning Objectives 404 Building Linear Optimization Models 405 Identifying Elements for an Optimization Model 405 Translating Model Information into Mathematical Expressions 406 More about Constraints 408 Characteristics of Linear Optimization Models 409 Implementing Linear Optimization Models on Spreadsheets 409 Excel Functions to Avoid in Linear Optimization 411 Solving Linear Optimization Models 411 Using the Standard Solver 412 Using Premium Solver 415 Solver Answer Report 416 Graphical Interpretation of Linear Optimization 418 How Solver Works 423 How Solver Creates Names in Reports 425 Difficulties with Solver 425 Solver Outcomes and Solution Messages 425 Unique Optimal Solution 426 «Alternative Optimal Solutions 426 Unbounded Solution 427» Infeasible Problem 428 Using Optimization Models for Prediction and Insight 429 Solver Sensitivity Report 431 Using the Sensitivity Report 434 Parameter Analysis in Risk Solver Platform 436 Key Terms 439, Problems and Exercises 439 Case: Performance Lawn Equipment 445 Chapter 14: Applications of Linear Optimization 446 Learning Objectives 446 Types of Constraints in Optimization Models 448 Process Selection Models 449 Spreadsheet Design and Solver Reports 450 Blending Models 453 Dealing with Infeasibility 454 Portfolio Investment Models 457 Evaluating Risk Versus Reward 458 Transportation Models 461 Formatting the Sensitivity Report 463 Degeneracy 465 Multiperiod Production Planning Models 465 Building Alternative Models 468 Multiperiod Financial Planning Models 468 Models with Bounded Variables 473 Auxiliary Variables for Bound Constraints 478 A Production/Marketing Allocation Model 478 Using Sensitivity Information Correctly 480

8 xi Key Terms 483 Problems and Exercises 484 Case: Performance Lawn Equipment 496 Chapter 15: Integer Optimization 498 Learning Objectives 498 Solving Models with General Integer Variables 499 Workforce-Scheduling Models 504 Alternative Optimal Solutions 504 Integer Optimization Models with Binary Variables 508 Project-Selection Models 509 Using Binary Variables to Model Logical Constraints 511 «Location Models 513 Parameter Analysis 513 A Customer-Assignment Model for Supply Chain Optimization 515 Mixed-Integer Optimization Models 518 Plant Location Models 518 Binary Variables, IF Functions, and Nonlinearities in Model Formulation 520 Fixed-Cost Models 521 Key Terms 523 Problems and Exercises 524 Case: Performance Lawn Equipment 531 Chapter 16: Nonlinear and Non-Smooth Optimization 533 Learning Objectives 533 Modeling and Solving Nonlinear Optimization Problems 534 Pricing Decision Models 534 Interpreting Solver Reports for Nonlinear Optimization Models 538 Locating Central Facilities 539 «The Economic Order-Quantity Model 540 Using Empirical Data for Nonlinear Optimization Modeling 545 Practical Issues Using Solver for Nonlinear Optimization 546 Quadratic Optimization 548 The Markowitz Portfolio Model 548 Evolutionary Solver for Non-Smooth Optimization 552 Spreadsheet Models with Non-Smooth Excel Functions 552 Optimization Models for Sequencing and Scheduling 556 The Traveling Salesperson Problem 557 Key Terms 561 Problems and Exercises 561 Case: Performance Lawn Equipment 566 Chapter 17: Optimization Models with Uncertainty 567 Learning Objectives 567 Risk Analysis in Optimization 568 Chance Constraints 568 Service Levels in the Economic Order Quantity - Model 573» Hotel Pricing Model with Uncertainty 575 Optimizing Monte Carlo Simulation Models 579 Optimizing the Newsvendor Model Using Multiple Parameterized Simulations 579 Optimizing the Hotel Overbooking Model Using Multiple Parameterized Simulations 579 Simulation Optimization Using Risk Solver Platform 581 A Portfolio Allocation Model 581 Project Selection 585 Key Terms 587 Problems and Exercises 587 Case: Performance Lawn Equipment 590

9 XII Contents Part 5: Making Decisions Chapter 18: Decision Analysis 591 Learning Objectives 591 Making Decisions with Uncertain Information 592 Decision Strategies for a Minimize Objective 593 Maximize Objective 596 Risk and Variability Strategy 597 Decision Trees 598 Decision Trees and Monte Carlo Simulation 602 Risk 604 Sensitivity Analysis in Decision Trees The Value of Information 606 Decisions with Sample Information 607 Bayes's Rule 608 Utility and Decision Making 609 Constructing a Utility Function 611 Exponential Utility Functions 614 Key Terms 616 Problems and Exercises 616 Case: Performance Lawn Equipment 622 Appendix A 625 Appendix B 629 Glossary 653 Index 659 Decision Strategies for a 597 < Expected Value Decision Trees and 605

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