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CHAPTER 14 Building Multiple Regression Models LEARNING OBJECTIVES This chapter presents several advanced topics in multiple regression analysis, enabling you to: 1. Generalize linear regression models as polynomial regression models using model transformation and Tukey’s ladder of transformation, accounting for possible interaction among the independent variables 2. Examine the role of indicator, or dummy, variables as predictors or independent variables in multiple regression analysis 3. Use all possible regressions, stepwise regression, forward selection, and backward elimination search procedures to develop regression models that account for the most variation in the dependent variable and are parsimonious 4. Recognize when multicollinearity is present, understanding general techniques for preventing and controlling it Panoramic Images/Getty Images
Determining Compensation for CEOs Chief executive officers for large companies receive widely varying amounts of compensation for their work. Why is the range so wide? What are some of the variables that seem to contribute to the diversity of CEO compensation packages? As a starting place, one might examine the role of company size as measured by sales volume, number of employees, number of plants, and so on in driving CEO compensation. It could be argued that CEOs of larger companies carry larger responsibilities and hence should receive higher compensation. Some researchers believe CEO compensation is related to such things as industry performance of the firm, percentage of stock that has outside ownership, and proportion of insiders on the board. At least a significant proportion of CEOs are likely to be compensated according to the performance of their companies during the fiscal period preceding compensation. Company performance can be measured by such variables as earnings per share, percentage change in profit, sales, and profit. In addition, some theorize that companies with outside ownership are more oriented toward declaring dividends to stockholders than toward large CEO compensation packages. Do CEOs’ individual and family characteristics play a role in their compensation? Do such things as CEO age, degrees obtained, marital status, military experience, and number of children matter in compensation? Do type of industry and geographic location of the company matter? What are the significant factors in determining CEO compensation? What follow are CEO compensation data generated by using management compensation models published by Wyatt Data Services. In the first column on the left are cash compensation figures (in $1,000) for 20 CEOs. Those figures represent salary, bonuses, and any other cash remuneration given to the CEO as part of compensation. The four columns to the right contain data on four variables associated with each CEO’s company: sales, number of employees, capital investment, and whether the company is in manufacturing. Sales figures and capital investment figures are given in $ millions. Cash Number of Capital Compensation Sales Employees Investment Manufacturing 212 35.0 248.00 10.5 1 226 27.2 156.00 3.8 0 237 49.5 348.00 14.9 1 239 34.0 196.00 5.0 0 242 52.8 371.00 15.9 1 245 37.6 216.00 5.7 0 253 60.7 425.00 18.3 1 262 49.2 285.00 8.0 0 271 75.1 524.00 22.6 1 285 69.0 401.00 12.3 0 329 137.2 947.00 41.4 1 340 140.1 825.00 30.3 0 353 162.9 961.00 36.7 0 384 221.7 1517.00 67.1 1 405 261.6 1784.00 79.2 1 411 300.1 1788.00 79.8 0 456 455.5 2733.00 135.7 0 478 437.6 2957.00 132.7 1 525 802.1 4857.00 278.4 0 564 731.5 4896.00 222.2 1 Managerial and Statistical Questions 1. Can a model be developed to predict CEO compensation? 2. If a model is developed, how can the model be evaluated to determine whether it is valid? 3. Is it possible to sort out variables that appear to be related to CEO compensation and determine which variables are more significant predictors? 4. Are some of the variables related to CEO compensation but in a nonlinear manner? 5. Are some variables highly interrelated and redundant in their potential for determining CEO compensation? Sources: Adapted from Jeffrey L. Kerr and Leslie Kren,“Effect of Relative Decision Monitoring on Chief Executive Compensation,” Academy of Management Journal, vol. 35, no. 2 (June 1992). Used with permission. Robin L. Bartlett, James H. Grant, and Timothy I. Miller,“The Earnings of Top Executives: Compensating Differentials for Risky Business,” Quarterly Reviews of Economics and Finance, vol. 32, no. 1 (Spring 1992). Used with permission. Database derived using models published in 1993/1994 Top Management Compensation Regression Analysis Report, 44th ed. Fort Lee, NJ: Wyatt Data Services/ECS, December 1994. 547
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With WileyPLUS: This online teachin
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6 TH EDITION Business Statistics Fo
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Vice President & Publisher George H
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BRIEF CONTENTS UNIT I UNIT II UNIT
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x Contents 3.5 Descriptive Statisti
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xii Contents Statistical Hypotheses
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xiv Contents Forward Selection 572
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PREFACE The sixth edition of Busine
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Preface xix all of the inferential
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Preface xxi very limited access to
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Preface xxiii Interpreting the Outp
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Preface xxv ACKNOWLEDGMENTS John Wi
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UNIT I INTRODUCTION The study of bu
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Statistics Describe the State of Bu
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1.2 Basic Statistical Concepts 5 In
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1.3 Data Measurement 7 FIGURE 1.1 P
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1.3 Data Measurement 9 In addition,
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1.3 Data Measurement 11 Statistical
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Analyzing the Databases 13 1.3 Give
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Case 15 ASSIGNMENT Use the database
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Energy Consumption Around the World
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2.1 Frequency Distributions 19 TABL
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2.2 Quantitative Data Graphs 21 cla
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2.2 Quantitative Data Graphs 23 FIG
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2.2 Quantitative Data Graphs 25 FIG
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2.3 Qualitative Data Graphs 27 2.9
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2.3 Qualitative Data Graphs 29 FIGU
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2.3 Qualitative Data Graphs 31 STAT
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2.4 Graphical Depiction of Two-Vari
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Problems 35 Pie Charts for World Oi
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Supplementary Problems 37 2.19 Cons
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Supplementary Problems 39 include t
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Using the Computer 41 In 1983, the
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Using the Computer 43 ■ ■ ■ t
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CHAPTER 3 Descriptive Statistics LE
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48 Chapter 3 Descriptive Statistics
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ƒ ƒ 58 Chapter 3 Descriptive Stat
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CHAPTER 4 Probability LEARNING OBJE
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94 Chapter 4 Probability FIGURE 4.1
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96 Chapter 4 Probability Subjective
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98 Chapter 4 Probability FIGURE 4.3
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100 Chapter 4 Probability THE mn CO
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102 Chapter 4 Probability FIGURE 4.
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104 Chapter 4 Probability TABLE 4.2
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106 Chapter 4 Probability By the ge
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108 Chapter 4 Probability P (neithe
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110 Chapter 4 Probability 4.10 Use
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ƒ ƒ 112 Chapter 4 Probability ran
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114 Chapter 4 Probability DEMONSTRA
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116 Chapter 4 Probability 4.21 A st
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ƒ 118 Chapter 4 Probability The se
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ƒ 120 Chapter 4 Probability STATIS
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122 Chapter 4 Probability the South
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124 Chapter 4 Probability TABLE 4.8
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126 Chapter 4 Probability Event Pri
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128 Chapter 4 Probability ETHICAL C
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130 Chapter 4 Probability TESTING Y
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132 Chapter 4 Probability 4.49 In a
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UNIT II DISTRIBUTIONS AND SAMPLING
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Life with a Cell Phone As early as
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5.2 Describing a Discrete Distribut
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5.2 Describing a Discrete Distribut
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5.3 Binomial Distribution 143 5.3 T
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5.3 Binomial Distribution 145 selec
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5.3 Binomial Distribution 147 DEMON
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ƒ 5.3 Binomial Distribution 149 TA
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5.3 Binomial Distribution 151 FIGUR
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Problems 153 5.8 Use the probabilit
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5.4 Poisson Distribution 155 time i
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5.4 Poisson Distribution 157 Soluti
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5.4 Poisson Distribution 159 FIGURE
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5.4 Poisson Distribution 161 The Po
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Problems 163 data set as a basis fo
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5.5 Hypergeometric Distribution 165
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Problems 167 5.5 PROBLEMS 5.27 Comp
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Key Terms 169 problem, but it can b
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Supplementary Problems 171 5.36 Use
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Supplementary Problems 173 Suppose
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Case 175 ANALYZING THE DATABASES se
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Using the Computer 177 ■ in a col
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The Cost of Human Resources What is
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6.1 The Uniform Distribution 181 FI
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6.1 The Uniform Distribution 183 DE
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6.2 Normal Distribution 185 FIGURE
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6.2 Normal Distribution 187 TABLE 6
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6.2 Normal Distribution 189 This pr
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6.2 Normal Distribution 191 The pro
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6.2 Normal Distribution 193 DEMONST
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Problems 195 6.9 According to the I
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6.3 Using the Normal Curve to Appro
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6.3 Using the Normal Curve to Appro
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Problems 201 The answer obtained by
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6.4 Exponential Distribution 203 FI
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Problems 205 TABLE 6.6 Excel and Mi
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Summary 207 The area associated wit
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Supplementary Problems 209 6.36 Wor
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Supplementary Problems 211 availabi
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Using the Computer 213 that sales a
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CHAPTER 7 Sampling and Sampling Dis
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218 Chapter 7 Sampling and Sampling
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248 Making Inferences About Populat
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CHAPTER 8 Statistical Inference: Es
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252 Chapter 8 Statistical Inference
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Word-of-Mouth Business Referrals an
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9.1 Introduction to Hypothesis Test
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9.2 Testing Hypotheses About a Popu
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Problems 307 one-tailed hypothesis,
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Problems 313 Excel does not have a
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9.4 Testing Hypotheses About a Prop
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9.5 Testing Hypotheses About a Vari
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Problems 323 DEMONSTRATION PROBLEM
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9.6 Solving for Type II Errors 325
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Problems 333 9.40 The New York Stoc
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Supplementary Problems 335 with an
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Supplementary Problems 337 and she
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Case 339 CASE FRITO-LAY TARGETS THE
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Using the Computer 341 ■ To begin
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Online Shopping The use of online s
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Proportions 2-Samples Chapter 10 St
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10.1 Hypothesis Testing and Confide
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Problems 353 10.2 Use the following
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Problems 363 Test your conjecture,
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10.3 Statistical Inferences for Two
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Problems 373 Client Before After 1
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10.4 Statistical Inferences about T
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Problems 381 b. H 0 : p 1 - p 2 = 0
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10.5 Testing Hypotheses about Two P
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Problems 389 City 1 City 2 3.43 3.3
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Summary 391 SUMMARY Business resear
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Supplementary Problems 393 TESTING
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Supplementary Problems 395 machine
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Case 397 ANALYZING THE DATABASES 1.
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Using the Computer 399 ■ ■ add-
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CHAPTER 11 Analysis of Variance and
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404 Chapter 11 Analysis of Variance
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UNIT IV REGRESSION ANALYSIS AND FOR
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Predicting International Hourly Wag
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12.1 Correlation 467 FIGURE 12.1 Fi
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12.2 Introduction to Simple Regress
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12.3 Determining the Equation of th
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12.3 Determining the Equation of th
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Problems 475 Using these values, th
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12.4 Residual Analysis 477 Raw Stee
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12.4 Residual Analysis 479 FIGURE 1
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12.4 Residual Analysis 481 DEMONSTR
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Problems 483 Cost of Milk (per gall
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12.5 Standard Error of the Estimate
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12.6 Coefficient of Determination 4
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12.7 Hypothesis Tests for the Slope
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Page 553 and 554: Problems 523 Solution The following
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Page 569 and 570: Summary 539 SUMMARY OUTPUT Regressi
Page 571 and 572: Supplementary Problems 541 TESTING
Page 573 and 574: Case 543 ANALYZING THE DATABASES 1.
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596 Chapter 15 Time-Series Forecast
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CHAPTER 16 Analysis of Categorical
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646 Chapter 16 Analysis of Categori
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CHAPTER 17 Nonparametric Statistics
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672 Chapter 17 Nonparametric Statis
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Italy’s Piaggio Makes a Comeback
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18.1 Introduction to Quality Contro
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18.2 Process Analysis 733 18.2 PROC
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18.2 Process Analysis 735 FIGURE 18
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18.2 Process Analysis 737 FIGURE 18
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18.3 Control Charts 739 charts are
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18.3 Control Charts 741 UCL and LCL
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18.3 Control Charts 743 Using the s
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18.3 Control Charts 745 Compute R R
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18.3 Control Charts 747 Sample n Ou
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18.3 Control Charts 749 In computin
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18.3 Control Charts 751 below the c
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Problems 753 18.6 A machine operato
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Problems 755 a. 125 X bar Chart 3.0
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Formulas 757 identifying the effect
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Supplementary Problems 759 five con
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Analyzing the Databases 761 12.5 X
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Using the Computer 763 Sample Mean
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APPENDIX A Tables Table A.1: Random
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Appendix A Tables 767 TABLE A.2 Bin
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Appendix A Tables 775 TABLE A.3 Poi
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Appendix A Tables 777 TABLE A.3 Poi
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Appendix A Tables 779 TABLE A.4 The
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Appendix A Tables 781 TABLE A.6 Cri
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Appendix A Tables 783 TABLE A.7 Per
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Appendix A Tables 793 TABLE A.9 Cri
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Appendix A Tables 797 n 2 n 1 = .02
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Appendix A Tables 799 TABLE A.13 p-
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APPENDIX B Answers to Selected Odd-
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Appendix B Answers to Selected Odd-
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GLOSSARY A a posteriori After the e
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Glossary 817 decision table A matri
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Glossary 819 the statistic below th
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Glossary 821 ratio level data Highe
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Glossary 823 W weighted aggregate p
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826 Index Centerline. See also Cont
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828 Index DMAIC (Define, Measure, A
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830 Index Law of improbable events,
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832 Index Populations accessing for
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834 Index Samples defined, 5 depend
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836 Index grouped data versus, 17-1
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Decision Making at the CEO Level CE
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19.1 The Decision Table and Decisio
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19.2 Decision Making Under Uncertai
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Problems C19-13 d. Compute an oppor
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19.3 Decision Making Under Risk C19
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Problems C19-21 Much information ha
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19.4 Revising Probabilities in Ligh
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Problems C19-29 The worth of the sa
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Problems C19-31 Decision Making at
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Supplementary Problems C19-33 for e
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Supplementary Problems C19-35 Decis
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Case C19-37 Following these initiat
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Critical Values from the t Distribu
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