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Every weeks word count must must be more than 1200 words excluding questions. ISBN-13: ISBN-10: 978-0-13-449716-7 0-13-449716-3 9 7 8 0 1 3 4 4 9 7 1 6 7 9 0 0 0 0 Get the Most Out of MyStatLab® R O B E R T S T I N E D E A N F O S T E R S T I N E F O S T E R Statistics for Business S tatistics fo r B usiness Decision Making and Analysis D ecision M aking and A nalysis Third Edition Third Edition MyStatLab is available for this textbook. To learn more, visit www.mystatlab.com S Personalized and adaptive learning S Interactive practice with immediate feedback S Multimedia learning resources S Complete eText S Mobile-friendly design S Full access to StatCrunch MyStatLab is the leading online homework, tutorial, and assessment program designed to help you learn and understand statistics. Statistics for Business DECISION MAKING AND ANALYSIS ROBERT STINE Wharton School of the University of Pennsylvania DEAN FOSTER Emeritus, Wharton School of the University of Pennsylvania 330 Hudson Street, NY NY 10013 THIRD EDITION A01_STIN7167_03_SE_FM.indd 1 12/11/16 10:03 AM For permission to use copyrighted material, grateful acknowledgment has been made to the copyright holders listed on p. C-1 and C-2, which is hereby made part of the copyright page. Many of the designations by manufacturers and sellers to distinguish their products are claimed as trade- marks. Where those designations appear in this book, and the publisher was aware of a trademark claim, the designations have been printed in initial caps or all caps. Microsoft® and Windows® are registered trademarks of the Microsoft Corporation in the U.S.A. and other countries. Screen shots and icons reprinted with permission from the Microsoft Corporation. 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Title: Statistics for business : decision making and analysis / ROBERT STINE, Wharton School of the University of Pennsylvania, DEAN FOSTER, Wharton School of the University of Pennsylvania. Description: Third Edition. | Boston : Pearson, 2016. | Revised edition of the authors’ Statistics for business, 2013. | Includes index. Identifiers: LCCN 2016016748| ISBN 9780134497167 (hardcover) | ISBN 0134497163 (hardcover) Subjects: LCSH: Commercial statistics. | Statistics. Classification: LCC HF1017 .S74 2016 | DDC 519.502/465--dc23 LC record available at https://lccn.loc.gov/2016016748 Copyright © 2018, 2014, 2011 Pearson Education, Inc. All rights reserved. No part of this publication may be re- produced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, pho- tocopying, recording, or otherwise, without the prior written permission of the publisher. Printed in the United States of America. For information regarding permissions, request forms and the appropriate contacts within the Pearson Education Global Rights & Permissions department, please visit www.pearsoned.com/permissions/. 1 16 Director, Portfolio Management, Math & Statistics: Deirdre Lynch Portfolio Management Assistant: Justin Billing Managing Producer, Math/Stats: Karen Wernholm Content Producer: Peggy McMahon Producer, Production & Digital Studio, Math & Statistics: Aimee Thorne Manager, Courseware Content Develop- ment, Math & Stats: Robert Carroll Manager, Courseware QA: Mary Durnwald Director, Product Marketer, Math & Sta- tistics: Erin Kelly Product Marketing Assistant: Jennifer Myers Senior Author Support/Technology Spe- cialist: Joe Vetere Manager, Rights and Permissions: Gina Cheselka Manufacturing Buyer: Carol Melville/ LSC Communications Production Coordination, Composition, Text Design, Illustrations: Cenveo® Publisher Services Associate Director of Design: Blair Brown Program Design Lead: Barbara Atkinson Cover Design: Tamara Newnam Cover Photo: Getty Images/BeholdingEye Student Edition: ISBN-13: 978-0-13-449716-7 ISBN-10: 0-13-449716-3 A01_STIN7167_03_SE_FM.indd 2 12/11/16 10:03 AM https://lccn.loc.gov/2016016748 http://www.pearsoned.com/permissions/ iii Robert Stine holds a Ph.D. from Princeton University. He has taught at the Whar- ton School since 1983, during which time he has regularly taught business statis- tics. During his tenure, Bob has received a variety of teaching awards, including regularly winning the MBA Core Teaching Award, which is presented to faculty for outstanding teaching of the required curriculum at Wharton. He also received the David W. Hauck Award for Outstanding Teaching, awarded to the most highly rat- ed faculty member teaching in the Wharton undergraduate program. Bob active- ly consults for industry. His clients include the pharmaceutical firms Merck and Pfizer, and he regularly works with the Federal Reserve Bank of Philadelphia on models for retail credit risk. This collaboration has produced three well-received conferences held at Wharton. His areas of research include computer software, time series analysis and forecasting, and general problems related to model iden- tification and selection. Bob has published numerous articles in research journals, including the Journal of the American Statistical Association, Journal of the Royal Statistical Society, Biometrika, and The Annals of Statistics. Dean Foster holds a Ph.D. from the University of Maryland. He has taught at the Wharton School since 1992 and previously taught at the University of Chicago. Dean has taught courses in introductory business statistics, probability and Markov chains, statistical computing, and advanced statistics for managers. Dean’s research areas are statistical inference for stochastic processes, game theory, ma- chine learning, and variable selection. He is published in a wide variety of jour- nals, including The Annals of Statistics, Operations Research, Games and Economic Behaviour, Journal of Theoretical Population Biology, and Econometrica. Currently Senior Principal Scientist at Amazon; Dean Foster is working on big data there, and his goal is to predict the sales of each and every product that Amazon sells. Bob Stine and Dean Foster (along with Richard Waterman) have co-authored two casebooks: Basic Business Statistics (Springer-Verlag) and Business Analysis Using Regression (Springer-Verlag). These casebooks offer a collection of data analysis examples that motivate and illustrate key ideas of statistics, ranging from standard error to regression diagnostics and time series analysis. They also have collabo- rated on a number of research articles. ABOUT THE AUTHORS A01_STIN7167_03_SE_FM.indd 3 12/11/16 10:03 AM 561590_MILL_MICRO_FM_ppi-xxvi.indd 2 24/11/14 5:26 PM This page intentionally left blank v Preface xi Index of Application xxi PART I Variation 1 Introduction 2 1.1 What Is Statistics? 2 1.2 Previews 4 2 Data 10 2.1 Data Tables 11 2.2 Categorical and Numerical Data 12 2.3 Recoding and Aggregation 14 2.4 Time Series 17 2.5 Further Attributes of Data 18 Chapter Summary 22 3 Describing Categorical Data 26 3.1 Looking at Data 27 3.2 Charts of Categorical Data 28 3.3 The Area Principle 33 3.4 Mode and Median 38 Chapter Summary 42 4 Describing Numerical Data 51 4.1 Summaries of Numerical Variables 52 4.2 Histograms 57 4.3 Boxplots 59 4.4 Shape of a Distribution 62 4.5 Epilog 68 Chapter Summary 72 5 Association between Categorical Variables 80 5.1 Contingency Tables 81 5.2 Lurking Variables and Simpson’s Paradox 89 CONTENTS A01_STIN7167_03_SE_FM.indd 5 18/11/16 2:22 PM vi CONTENTS 5.3 Strength of Association 92 Chapter Summary 100 6 Association between Quantitative Variables 109 6.1 Scatterplots 110 6.2 Association in Scatterplots 111 6.3 Measuring Association 114 6.4 Summarizing Association with a Line 120 6.5 Spurious Correlation 123 6.6 Correlation Matrix 126 Chapter Summary 129 CASE: STATISTICS IN ACTION Financial Time Series 140 CASE: STATISTICS IN ACTION Executive Compensation 148 PART II Probability 7 Probability 156 7.1 From Data to Probability 157 7.2 Rules for Probability 161 7.3 Independent Events 166 Chapter Summary 170 8 Conditional Probability 179 8.1 From Tables to Probabilities - 180 8.2 Dependent Events 184 8.3 Organizing Probabilities 187 8.4 Order in Conditional Probabilities 190 Chapter Summary 195 9 Random Variables 202 9.1 Random Variables 203 9.2 Properties of Random Variables 205 9.3 Properties of Expected Values 211 9.4 Comparing Random Variables 214 Chapter Summary 216 10 Association between Random Variables 224 10.1 Portfolios and Random Variables 225 10.2 Joint Probability Distribution 227 10.3 Sums of Random Variables 230 10.4 Dependence Between Random Variables 232 10.5 IID Random Variables 236 10.6 Weighted Sums 239 Chapter Summary 243 A01_STIN7167_03_SE_FM.indd 6 12/11/16 10:03 AM viiCONTENTS 11 Probability Models for Counts 251 11.1 Random Variables for Counts 252 11.2 Binomial Model 254 11.3 Properties of Binomial Random Variables 255 11.4 Poisson Model 259 Chapter Summary 265 12 The Normal Probability Model 270 12.1 Normal Random Variable 271 12.2 The Normal Model 274 12.3 Percentiles 280 12.4 Departures from Normality 282 Chapter Summary 290 CASE: STATISTICS IN ACTION Managing Financial Risk 298 CASE: STATISTICS IN ACTION Modeling Sampling Variation 306 PART III Inference 13 Samples and Surveys 314 13.1 Two Surprising Properties of Samples 315 13.2 Variation 320 13.3 Alternative Sampling Methods 323 13.4 Questions to Ask 326 Chapter Summary 329 14 Sampling Variation and Quality 334 14.1 Sampling Distribution of the Mean 335 14.2 Control Limits 340 14.3 Using a Control Chart 344 14.4 Control Charts for Variation 347 Chapter Summary 354 15 Confidence Intervals 362 15.1 Ranges for Parameters 363 15.2 Confidence Interval for the Mean 368 15.3 Interpreting Confidence Intervals 372 15.4 Manipulating Confidence Intervals 373 15.5 Margin of Error 376 Chapter Summary 384 16 Statistical Tests 391 16.1 Concepts of Statistical Tests 392 16.2 Testing the Proportion 397 16.3 Testing the Mean 404 A01_STIN7167_03_SE_FM.indd 7 12/11/16 10:03 AM viii 16.4 Significance versus Importance 408 16.5 Confidence Interval or Test? 409 Chapter Summary 413 17 Comparison 420 17.1 Types of Comparisons 421 17.2 Data for Comparisons 421 17.3 Two-Sample z-Test for Proportions 424 17.4 Two-Sample Confidence Interval for Proportions 425 17.5 two-Sample t-Test 429 17.6 Confidence Interval for the Difference Between Means 433 17.7 Paired Comparisons 436 Chapter Summary 446 18 Inference for Counts 453 18.1 Chi-Squared Tests 454 18.2 Test of Independence 454 18.3 General versus Specific Hypotheses 466 18.4 Tests of Goodness of Fit 467 Chapter Summary 477 CASE: STATISTICS IN ACTION Rare Events 484 CASE: STATISTICS IN ACTION Data Mining Using Chi-Squared 491 PART IV Regression Models 19 Linear Patterns 498 19.1 Fitting a Line to Data 499 19.2 Interpreting the Fitted Line 501 19.3 Properties of Residuals 506 19.4 Explaining Variation 508 19.5 Conditions for Simple Regression 510 Chapter Summary 520 20 Curved Patterns 528 20.1 Detecting Nonlinear Patterns 529 20.2 Transformations 531 20.3 Reciprocal Transformation 532 20.4 Logarithm Transformation 538 Chapter Summary 550 21 The Simple Regression Model 557 21.1 The Simple Regression Model 558 21.2 Conditions for the SRM 562 21.3 Inference in Regression 565 21.4 Prediction Intervals 573 Chapter Summary 587 CONTENTS A01_STIN7167_03_SE_FM.indd 8 12/11/16 10:03 AM ix 22 Regression Diagnostics 596 22.1 Changing Variation 597 22.2 Outliers 607 22.3 Dependent Errors and Time Series 611 Chapter Summary 622 23 Multiple Regression 630 23.1 The Multiple Regression Model 631 23.2 Interpreting Multiple Regression 632 23.3 Checking Conditions 640 23.4 Inference In Multiple Regression 642 23.5 Steps In Fitting A Multiple Regression 646 Chapter Summary 656 24 Building Regression Models 667 24.1 Identifying Explanatory Variables 668 24.2 Collinearity 673 24.3 Removing Explanatory Variables 678 Chapter Summary 694 25 Categorical Explanatory Variables 703 25.1 Two-Sample Comparisons 704 25.2 Analysis of Covariance 706 25.3 Checking Conditions 711 25.4 Interactions and Inference 712 25.5 Regression with Several Groups 719 Chapter Summary 726 26 Analysis of Variance 736 26.1 Comparing Several Groups 737 26.2 Inference in ANOVA Regression Models 744 26.3 Multiple Comparisons 748 26.4 Groups of Different Size 754 Chapter Summary 759 27 Time Series 768 27.1 Decomposing a Time Series 769 27.2 Regression Models 772 27.3 Checking the Model 782 Chapter Summary 797 CASE: STATISTICS IN ACTION Analyzing Experiments 807 CASE: STATISTICS IN ACTION Automated Modeling 815 CONTENTS A01_STIN7167_03_SE_FM.indd 9 12/11/16 10:03 AM x Appendix: Tables 823 Answers A-1 Credits C-1 Index I-1 Supplementary Material (online-only) S1 Alternative Approaches to Inference S1-1 S2 Two-Way Analysis of Variance S2-1 S3 Regression with Big Data S3-1 CONTENTS A01_STIN7167_03_SE_FM.indd 10 12/11/16 10:03 AM xi PREFACE Knowledge of statistics is a great asset in business, but getting the most value from this asset requires knowing how to ask and answer the right questions. Choosing the right question and solving the problem correctly require an appreciation of business as well as the subtleties of statistics. Unless you understand the business issue from a finance, marketing, management, or accounting per- spective, you won’t see how statistics can help solve the problem. Performing the statistical analysis must wait until you have grasped the issue facing the business. Solving Business Problems This application-directed approach is key to business analytics and shapes our examples. We open each chap- ter with a business question that motivates the contents of the chapter. For extra practice, worked-out examples within each chapter follow our 4M (Motivation, Method, Mechanics, Message) problem-solving strategy. The mo- tivation sets up the problem and explains the relevance of the question at hand. We then identify the appropri- ate statistical method and work through the mechanics of its calculation. Finally, the message answers the ques- tion in language suitable for a business presentation or report. Through the 4Ms, we’ll show you how a business context guides the statistical procedure and how the re- sults determine a course of action. Motivation and Mes- sage are critical. The Motivation answers the question “Why am I doing this analysis?”. If you cannot answer that question, it’s hard to get the statistics correct. The Message has to express your answer in language that is used in the business world. Understand the business first, then use statistics to help formulate your conclu- sion. Notice that we said “help.” A statistical analysis by itself is not the final answer. You must frame that analy- sis in terms that others in the business will understand and find persuasive. Our emphasis on the substantive use of statistics in business shapes our view that the ideal reader for this text is someone with an interest in learning how statis- tical thinking improves the ability of a manager to run or contribute to a business. Whether you’re an under- graduate with an interest in business, an MBA looking to improve your skills, or a business owner looking for another way to get ahead of the competition, the key is a desire to learn how statistics can produce better de- cisions and insights from the growing amount of data generated in modern businesses. We don’t assume that readers have mastered the do- mains of a business education, such as economics, fi- nance, marketing, or accounting. We do assume, though, that you care how ideas from these areas can improve a business. If you’re interested in these applications—and we think you will be—then our examples provide the background you will need to appreciate why we want to solve the challenges that we present in each chapter. Readers with more experience will discover that we’ve simplified the technical details of some applications, such as those in finance or marketing. Even so, we think that the examples offer those with substantive experience a new perspective on familiar problems. We hope that you will agree that the examples are realistic and get to the heart of quantitative applications of statistics in business. Technology You cannot do research in modern applied statistics without computing. Data sets have grown in size and complexity, making it impossible to work out the cal- culations by hand. Rather than dwell on routine cal- culations, we rely on software (often referred to as a statistics package) to compute the results. Although we emphasize the use of technology, we give the formulas and illustrate the calculations introduced in each chap- ter so that you will always know what the software is doing. It is essential to appreciate what happens in the calculations: You need to understand how the calcu- lations are done in order to recognize when they are appropriate and when they fail. That does not mean, however, that you need to spend hours doing routine calculations. Your time is precious, and there’s only so much of it to go around. We think it makes good eco- nomic sense to take advantage of modern technology in order to give us more time to think harder and more thoroughly about the motivating context for an applica- tion and to successfully present the business message. When we present results obtained with a calcula- tor or computer, we typically round them. You don’t A01_STIN7167_03_SE_FM.indd 11 12/11/16 10:03 AM xii need to know that the profits from a projected sale are $123,234.32529. It’s usually better to round such a number to $123 thousand. To let you know when we’ve rounded a calculation, we say about or approximately. In expressions, we denote rounding with the symbol < , as in 1/6 < 0.167. To help you learn how to use software, each chapter includes hints on using Excel®, MinitabExpress®, and JMP® for calculations. These hints won’t replace the help provided by your software, but they will point you in the right direction so that you don’t spin your wheels figur- ing out how to get started with an analysis. Supplemental software study cards are available for specific packages. Data Statistical analysis uses data, and we’ve provided lots of data to give you the opportunity to have some real hands-on experience. As you read through the chap- ters, you’ll discover a variety of data sets that include real estate markets, stocks and bonds, technology, retail sales, human resource management, and fundamental economics. These data come from a range of sources, and each chapter includes a discussion about where we found the data used in examples. We hope you’ll use our suggestions and find more. Prerequisite Knowledge To appreciate the illustrative calculations and formulas, readers will need to be familiar with basic algebra. Por- tions of chapters that introduce a statistical method of- ten include some algebra to show where a formula comes from. Usually, we only use basic algebra (up through top- ics such as exponents and square roots). Several chapters make extensive use of the logarithm function. If you’re interested in business and economics, this is a function worth getting to know a lot better. The applications we’ve provided, such as modeling sales or finding the best price, show why the logarithm is so important. Occasion- ally, we give credit to calculus for solving a problem, but we don’t present derivations using calculus. You’ll do fine if you are willing to accept that calculus is a branch of more advanced mathematics that provides, among other things, the ability to derive formulas that have special properties. If you do know calculus, you’ll be able to see where these expressions come from. WHAT’S NEW IN THIS EDITION This edition adds more of what readers have found re- ally useful: ■■ Business analytics relies on linking data to business decisions. Businesses ranging from traditional banks to the latest game developers are clamoring for em- ployees who can connect data and models to substan- tive business problems. This edition adds emphasis, examples, and illustrations that stress the impor- tance of these connections. For example, previous editions introduced the 4M paradigm—motivation, method, mechanics, and message—that shows how to combine data and statistics to solve problems in business. This edition carries this metaphor further. By explicitly linking this paradigm to analytics, this edition shows that business analytics requires blend- ing substantive relevance with statistical analysis. ■■ Up-to-date applications explore problems related to “big data” and introduce hot topics such as A/B test- ing that are popular in today’s businesses. Although the methods behind these new topics are familiar within statistics, the names are new. This edition makes sure students know the new names so that they can link what they learn in the classroom to what they read online. ■■ This edition features more than 90 new and updated data sets. The changed data range from examples used within chapters to those underlying exercises. Important, highly visible changes include “through the cycle” finance and economic time series that span the 2008 recession. ■■ More than 100 enhanced exercises remove ambi- guities and capture nuances in revised data. Many of these changes address issues identified by tracking online student performance in completing related exercises in MyStatLab. Problems that were worded in a way that might confuse students were clarified. ■■ Excel is the workhorse tool of many businesses. This edition adds a section to every chapter that shows step by step how to complete analytic exercises with the latest version of Excel. Excel is the most popular software for introductory statistics, but some prefer the features offered by statistics packages such as Minitab or JMP. We’ve retained and updated hints in each chapter for these as well. ■■ It’s the little things. Hundreds of changes have been made throughout this edition to emphasize and clar- ify key points. For example, this edition highlights additional tips throughout the text that help readers recognize important points that might be overlooked. Clarified explanations, analogies, and examples in every chapter encourage students to delve deeper and learn for themselves. COVERAGE AND ORGANIZATION We have organized the chapters of this book into four parts: 1. Variation 2. Probability 3. Inference 4. Regression Models Part I. These chapters introduce summary statistics such as the mean and important graphical summaries, including bar charts, histograms, and scatterplots. Even PREFACE A01_STIN7167_03_SE_FM.indd 12 12/11/16 10:03 AM xiii if you are familiar with these methods, we encourage you to skim the examples in these chapters. These ex- amples introduce important terminology that appears in subsequent chapters. A quick review will introduce the notation that we use (which is rather standard) as well as give you a chance to look at some interesting data. If you do skip past these, take advantage of the index of Key Terms in each chapter to find definitions and examples. Part II. Many courses in mathematics now include topics from probability. Even if you have seen basic probability, you might benefit from reviewing how methods, such as Bayes’ Rule, can be used to improve business processes (Chapter 8). If you plan to skip or move briskly through the rest of the chapters in Part 2, be sure that you’re famil- iar with the concept of a random variable (Chapter 9). Sta- tistical models use random variables to present an ideal- ized description of the data in applications. Unless you’re familiar with random variables, you won’t appreciate the important assumptions that come with their use in prac- tice. Chapter 11 describes special random variables used to model counts, and Chapter 12 defines normal random variables that appear so often in statistical models. Part III. This part presents the foundations for statistical inference, the process of inferring properties of an entire population from those of a subset known as a sample. Even if you are not interested in quality control, we en- courage you to read Chapter 14. Chapter 14 uses quality control to introduce a fundamental concept of inferential statistics, the sampling distribution and standard error. You can get by in statistics with a basic understanding of the concept of a sampling distribution, but the more you know about sampling distributions, the better. Each in- ferential procedure comes with a checklist of conditions that tell you whether your data and situation match up to the various inferential techniques in these chapters. Part IV. The chapters in Part 4 describe regression mod- eling. Regression modeling allows us to associate how differences in data that describe one phenomenon are related to differences in others. Regression models are among the most powerful ways to use statistics in busi- ness, providing methods for assessing profitability, setting prices, identifying anomalies, and generating forecasts. We encourage you to slow down and take your time study- ing these chapters. Even if you don’t see yourself doing statistics in your career in business, you can be sure that you will be presented with the results of regression models. Because the examples in these chapters allow us to describe the interconnectedness of several busi- ness processes at once, they become even more interest- ing than those in prior chapters. Be careful if you skip Chapter 20. The material in this chapter shows how to model a richer set of patterns and is less common in business textbooks, but we think these ideas are an es- sential component of every manager’s tool set. Case Studies Each of the four main parts of this book includes two supplemental case studies called Statistics in Action. Each case study provides an in-depth look at a business application of statistics. Every case uses real data and takes students through the details of using those data to address a business question. For example, a case study for Part 1 explains details of stock market data, such as how stock returns account for dividends, and elabo- rates the nuances of financial data beyond the coverage in the surrounding chapters. We’ve found that it is easy to have a “chapter-centric” view of any subject; you know how to approach a prob- lem if the question identifies a chapter. Executing the right approach is more difficult without that sort of clue. Case studies allow us to extend the statistical con- cepts introduced in the accompanying chapters in the context of a longer, more complex case. For example, the second case in Part 1 carefully explains how to in- terpret and use logarithms in the context of executive salaries. A case in Part 3 explores the use of many chi- squared tests in an operations management problem that resembles data mining. While logs, chi-squared tests, and issues of multiple testing all appear in the regular flow of the main … WEEK 6: Assignment: 1. Case: Data Mining using Chi Squared Part 1 in the textbook.  Study the case carefully and then answer one of the first four questions from the Questions for Thought section. 2. Case: Data Mining using Chi Squared Part 2 in the textbook.  Using the same case answer one question from questions 5-8 from the Questions for Thought section.  3. Select one of the following: a. Review your chosen thesis and check if the topics from module have been used in the thesis. How has it been used and discuss any improvements. Or b. Damaged Machines - Problem 39 in Chapter 16. An appliance manufacturer stockpiles washers and dryers in a large warehouse for shipment to retail stores. Some appliances get damaged in handling. The long-term goal has been to keep the level of damaged machines below 2\%. In a recent test, an inspector randomly checked 60 washers and discovered that 5 of them had scratches or dents. Test the null hypothesis: p  0.02 in which p represents the probability of a damaged washer. (a) Do these data supply enough evidence to reject? Use a binomial model from Chapter 11 to obtain the p-value. (b) What assumption is necessary in order to use the binomial model for the count of the number of damaged washers? (c) Test by using a normal model for the sampling distribution of. Does this test reject? (d) Which test procedure should be used to test? Explain your choice. 4. New Contact Lens - Problem 24 in Chapter 17. Doctors tested a new type of contact lens. Volunteers who normally wear contact lenses were given a standard type of lens for one eye and a lens made of the new material for the other. After a month of wear, the volunteers rated the level of perceived comfort for each eye. (a) Should the new lens be used for the left or right eye for every patient? (b) How should the data on comfort be analyzed? 5. Stock Movement - Problem 27 in Chapter 17. A stock market analyst recorded the number of stocks that went up or went down each day for 5 consecutive days, producing a contingency table with 2 rows (up or down) and 5 columns (Monday through Friday). Are these data suitable for applying the chi-squared test of independence? WEEK 7: Assignment: 1. Case: Analyzing Experiments in the textbook.  Study the case carefully and then answer question 1 and one other from question 2 through question 5 of the Questions for Thought section.  2. Select one of the following: a. Study your chosen thesis and find out if any of the topics covered in this module are applicable. Has they been applied correctly? What improvements would you suggest and why. Support your thinking. Or b. OECD Part 1 - Problem 45 in Chapter 19. The Organization for Economic Cooperation and Development (OECD) tracks various summary statistics of the member economies. The countries lie in Europe, parts of Asia, and North America. Two variables of interest are GDP (gross domestic product per capita, a measure of the overall production in an economy per citizen) and trade balances (measured as a percentage of GDP). Exporting countries tend to have large positive trade balances. Importers have negative balances. These data are from the 2005 report of the OECD. (a) Describe the association in the scatterplot of GDP on Trade Balance. Does the association in this plot move in the right direction? Does the association appear linear? (b) Estimate the least squares linear equation for GDP on Trade Balance. Interpret the fitted intercept and slope. Be sure to include their units. Note if either estimate represents a large extrapolation and is consequently not reliable. (c) Interpret and associated with the fitted equation. Attach units to these summary statistics as appropriate. (d) Plot the residuals from this regression. After considering this plot, does it provide an adequate summary of the residual variation? (e) Which country has the largest values of both variables? Is it the country that you expected? (f) Locate the United States in the scatterplot and find the residual for the United States. Interpret the value of the residual for the United States. 3. OECD Part 2 - Problem 45 in Chapter 19. The Organization for Economic Cooperation and Development (OECD) tracks various summary statistics of its member economies. The countries lie in Europe, parts of Asia, and North America. Two variables of interest are GDP (gross domestic product per capita, a measure of the overall production in an economy per citizen) and trade balances (measured as a percentage of GDP). Exporting countries tend to have large positive trade balances. Importers have negative balances. These data are from the 2005 report of the OECD. Formulate the SRM with GDP as the response and Trade Balance as the explanatory variable.  (a) On average, what is the per capita GDP for countries with balanced imports and exports (i.e., with trade balance zero)? Give your answer as a range, suitable for presentation.  (b) The foreign minister of Krakozia has claimed that by increasing the trade surplus of her country by 2\%, she expects to raise GDP per capita by $4,000. Is this claim plausible given this model?  (c) Suppose that OECD uses this model to predict the GDP for a country with balanced trade. Give the 95\% prediction interval.  (d) Do your answers for parts (a) and (c) differ from each other? Should they?  4. OECD Part 3 - Problem 45 in Chapter 19. The Organization for Economic Cooperation and Development (OECD) tracks summary statistics of the member economies. The countries are located in Europe, parts of Asia, and North America. Two variables of interest are GDP (gross domestic product per capita, a measure of the overall production in an economy per citizen) and trade balance (measured as a percentage of GDP). Exporting countries have positive trade balances; importers have negative trade balances. These data are from the 2005 report of the OECD. Formulate the SRM with GDP as the response and Trade Balance as the explanatory variable. (a) On average, what is the per capita GDP for countries with balanced imports and exports (i.e., with trade balance zero)? Give your answer as a range, suitable for presentation. (b) The foreign minister of Krakozia has claimed that by increasing the trade surplus of her country by 2\%, she expects to raise GDP per capita by $4,000. Is this claim plausible given this model? (c) Suppose that OECD uses this model to predict the GDP for a country with balanced trade. Give the 95\% prediction interval. (d) Do your answers for parts (a) and (c) differ from each other? Should they? 5. OECD Part 4 - Problem 45 in Chapter 19. An analyst at the United Nations is developing a model that describes GDP (gross domestic product per capita, a measure of the overall production in an economy per citizen) among developed countries. She is using national data for 29 countries from the 2005 report of the Organization for Economic Cooperation and Development (OECD). She started with the equation (estimated by least squares): Estimated per capita GDP = $26,714 +$1.441 Trade Balance The trade balance is measured as a percentage of GDP. Exporting countries tend to have large positive trade balances. Importers have negative balances. This equation explains only 37\% of the variation in per capita GDP, so she added a second explanatory variable, the number of kilograms of municipal waste per person. (a) Examine scatterplots of the response versus the two explanatory variables as well as the scatterplot between the explanatory variables. Do you notice any unusual features in the data? Do the relevant plots appear straight enough for multiple regression? (b) Do you think, before fitting the multiple regression, that the partial slope for trade balance will be the same as in the equation shown? Explain. (c) Fit the multiple regression that expands the one-predictor equation by adding the second explanatory variable to the model. Summarize the estimates obtained for the fitted model. (d) Does the estimated model appear to meet the conditions for the use of the MRM? (e) Draw the path diagram for this estimated model. Use it to explain why the estimated slope for the trade balance has become smaller than in the simple regression shown. (f) Give a confidence interval, to presentation precision, for the slope of the municipal waste variable. Does this interval imply that countries can increase their GDP by encouraging residents to produce more municipal waste?  WEEK 8: Benchmark Assignment This is a benchmark assignment for DCS students. Store your submission with any grading feedback in your Professionals Portfolio and use the following tag: DCS-PG3 Assignment: 1. Case: Automated Modeling in the textbook. Study the case carefully and then answer question 1 and one other from questions 2-8 from the Questions for Thought section. 2. Select one of the following: a. Review your chosen thesis and assess if the topics covered in this module have been used. Discuss the application and how they can be improved. Or b. R & D Expenses - Problem 43 in Chapter 19. This data file contains a variety of accounting and financial values that describe 493 companies operating in several technology industries in 2004: software, systems design, and semiconductor manufacturing. One column gives the expenses on research and development (R&D), and another gives the total assets of the companies. Both columns are reported in millions of dollars. (a) Scatterplot R&D Expense on Assets. Does a line seem to you to be a good summary of the relationship between these two variables? Describe the outlying companies. (b) Estimate the least squares linear equation for R&D Expense on Assets. Interpret the fitted intercept and slope. Be sure to include their units. Note if either estimate represents a large extrapolation and is consequently not reliable. (c) Interpret the summary values r2 and se associated with the fitted equation. Attach units to these summary statistics as appropriate. Does the value of r2 seem fair to you as a characterization of how well the equation summarizes the association? (d) Inspect the histograms of the x- and y-variables in this regression. Do the shapes of these histograms anticipate some aspects of the scatterplot and the linear relationship between these variables? (e) Plot the residuals from this regression. Does this plot reveal patterns in the residuals? Does se provide an adequate summary of the residual variation? 3. R & D Expenses - Problem 43 in Chapter 19. This data file contains a variety of accounting and financial values that describe 324 companies operating in the information sector in 2010. The largest of these provide telephone services. One column gives the expenses on research and development (R&D), and another gives the total assets of the companies. Both columns are reported in millions of dollars. These data need to be expressed on a log scale; otherwise, outlying companies dominate the analysis. Use the natural logs of both variables rather than the original variables in the data table. (Note that the variables are recorded in millions, so 1,000  = 1 billion.) (a) What difference in R&D spending (as a percentage) is associated with a 1\% increase in the assets of a firm? Give your answer as a range, rounded to meaningful precision. (b) Revise your model to use base 10 logs of assets and R&D expenses. Does using a different base for both log transformations affect your answer to part (a)? (c) Find a 95\% prediction interval for the R&D expenses of a firm with $1 billion in assets. Be sure to express your range on a dollar scale. Do you expect this interval to have 95\% coverage?  4. R & D Expenses - Problem 43 in Chapter 22. This table contains accounting and financial data that describe 324 companies operating in the information sector in 2010. The largest of these provide telephone services. One column gives the expenses on research and development (R&D), and another gives the total assets of the companies. Both columns are reported in millions of dollars. Use the logs of both variables rather than the originals. (That is, set Y to the natural log of R&D expenses, and set X to the natural log of assets. Note that the variables are recorded in millions, so 1,000  = 1 billion.) (a) What problem with the use of the SRM is evident in the scatterplot of y on x as well as in the plot of the residuals from the fitted equation on x? (b) If the residuals are nearly normal, of the values that lie outside the 95\% prediction intervals, what proportion should be above the fitted equation? (c) Based on the property of residuals identified in part (b), can you anticipate that these residuals are not nearly normal—without needing the normal quantile plot? 5. R & D Expenses - Problem 43 in Chapter 23. This data table contains accounting and financial data that describe 324 companies operating in the information sector. The variables include the expenses on research and development (R&D), total assets of the company, and the cost of goods sold (CGS). All columns are reported in millions of dollars; the variables are recorded in millions, so 1,000  = 1 billion. Use natural logs of all variables rather than the originals. (a) Examine scatterplots of the log of spending on R&D versus the log of total assets and the log of the cost of goods sold. Then consider the scatterplot of the log of total assets versus the log of the cost of goods sold. Do you notice any unusual features in the data? Do the relevant plots appear straight enough for multiple regression? (b) Fit the indicated multiple regression and show a summary of the estimated features of the model. (c) Does the estimated model appear to meet the conditions for the use of the MRM? (d) Does the fit of this model explain statistically significantly more variation in the log of spending on R&D than a model that uses the log of assets alone? The multiple regression in part (b) has all variables on a natural log scale. To interpret the equation, note that the sum of natural logs is the log of the product,   and that  Hence, the equation is equivalent to The slopes in the log-log regression are exponents in an equation that describes y as the product of the explanatory variables raised to different powers. These powers are the partial elasticities of the response with respect to the predictors. (See Chapter 20 for a discussion of elasticities.) (e) Interpret the slope for the log of the cost of goods sold in the equation estimated by the fitted model in part (b). Include the confidence interval in your calculation. (f) The marginal elasticity of R&D spending with respect to CGS is about 0.60. Why is the partial elasticity in the multiple regression for CGS so different? Is it really that different?