# A Quantitative Approach to Commercial Damages. Applying Statistics to the Measurement of Lost Profits + Website

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2 Type of Interruption 9 Length of Period of Interruption 10 Availability of Historical Data 10 Regularity of Sales Trends and Patterns 10 Ease of Explanation 10 Conventional Forecasting Models 11 Simple Arithmetic Models 11 More Complex Arithmetic Models 11 Trendline and Curve-Fitting Models 12 Seasonal Factor Models 12 Smoothing Methods 12 Multiple Regression Models 13 Other Applications of Statistical Models 14 Conclusion 14 Notes 15 CHAPTER 1 Case Study 1 Uses of the Standard Deviation 17 The Steps of Data Analysis 17 Shape 18 Spread 19 Conclusion 23 Notes 23 CHAPTER 2 Case Study 2 Trend and Seasonality Analysis 25 Claim Submitted 25 Claim Review 26 Occupancy Percentages 26 Trend, Seasonality, and Noise 28 Trendline Test 33 Cycle Testing 33 Conclusion 34 Note 36 CHAPTER 3 Case Study 3 An Introduction to Regression Analysis and Its Application to the Measurement of Economic Damages 37

3 What Is Regression Analysis and Where Have I Seen It Before? 37 A Brief Introduction to Simple Linear Regression 38 I Get Good Results with Average or Median Ratios Why Should I Switch to Regression Analysis? 40 How Does One Perform a Regression Analysis Using Microsoft Excel? 43 Why Does Simple Linear Regression Rarely Give Us the Right Answer, and What Can We Do about It? 51 Should We Treat the Value Driver Annual Revenue in the Same Manner as We Have Seller s Discretionary Earnings? 60 What Are the Meaning and Function of the Regression Tool s Summary Output? 68 Regression Statistics 69 Tests and Analysis of Residuals 75 Testing the Linearity Assumption 77 Testing the Normality Assumption 78 Testing the Constant Variance Assumption 80 Testing the Independence Assumption 83 Testing the No Errors-in-Variables Assumption 84 Testing the No Multicollinearity Assumption 84 Conclusion 87 Note 87 CHAPTER 4 Case Study 4 Choosing a Sales Forecasting Model: A Trial and Error Process 89 Correlation with Industry Sales 89 Conversion to Quarterly Data 89 Quadratic Regression Model 92 Problems with the Quarterly Quadratic Model 92 Substituting a Monthly Quadratic Model 94 Conclusion 95 Note 99 CHAPTER 5 Case Study 5 Time Series Analysis with Seasonal Adjustment 101 Exploratory Data Analysis 101 Seasonal Indexes versus Dummy Variables 102 Creation of the Optimized Seasonal Indexes 103 Creation of the Monthly Time Series Model 108 Creation of the Composite Model 108

4 Conclusion 115 Notes 115 CHAPTER 6 Case Study 6 Cross-Sectional Regression Combined with Seasonal Indexes to Determine Lost Profits 117 Outline of the Case 117 Testing for Noise in the Data 119 Converting to Quarterly Data 119 Optimizing Seasonal Indexes 119 Exogenous Predictor Variable 124 Interrupted Time Series Analysis 124 But For Sales Forecast 126 Transforming the Dependent Variable 130 Dealing with Mitigation 130 Computing Saved Costs and Expenses 133 Conclusion 137 Note 138 CHAPTER 7 Case Study 7 Measuring Differences in Pre- and Postincident Sales Using Two Sample t-tests versus Regression Models 139 Preliminary Tests of the Data 139 Using the t-test Two Sample Assuming Unequal Variances Tool 141 Regression Approach to the Problem 141 A New Data Set Different Results 143 Selecting the Appropriate Regression Model 143 Finding the Facts Behind the Figures 148 Conclusion 151 Notes 153 CHAPTER 8 Case Study 8 Interrupted Time Series Analysis, Holdback Forecasting, and Variable Transformation 155 Graph Your Data 155 Industry Comparisons 155 Accounting for Seasonality 157 Accounting for Trend 161 Accounting for Interventions 161

5 Forecasting Should Be Sales 164 Testing the Model 167 Final Sales Forecast 169 Conclusion 169 CHAPTER 9 Case Study 9 An Exercise in Cost Estimation to Determine Saved Expenses 171 Classifying Cost Behavior 171 An Arbitrary Classification 172 Graph Your Data 172 Testing the Assumption of Significance 174 Expense Drivers 174 Conclusion 177 CHAPTER 10 Case Study 10 Saved Expenses, Bivariate Model Inadequacy, and Multiple Regression Models 179 Graph Your Data 179 Regression Summary Output of the First Model 181 Search for Other Independent Variables 183 Regression Summary Output of the Second Model 185 Conclusion 188 CHAPTER 11 Case Study 11 Analysis of and Modification to Opposing Experts Reports 189 Background Information 189 Stipulated Facts and Data 190 The Flaw Common to Both Experts 194 Defendant s Expert s Report 196 Plaintiff s Expert s Report 199 The Modified-Exponential Growth Curve 201 Four Damages Models 208 Conclusion 208 CHAPTER 12 Case Study 12 Further Considerations in the Determination of Lost Profits 209 A Review of Methods of Loss Calculation 210 A Case Study: Dunlap Drive-In Diner 211 Skeptical Analysis Using the Fraud Theory Approach 212 Revenue Adjustment 212

6 Officer s Compensation Adjustment 214 Continuing Salaries and Wages (Payroll) Adjustment 215 Rent Adjustment 215 Employee Bonus 216 Discussion 216 Conclusion 217 CHAPTER 13 Case Study 13 A Simple Approach to Forecasting Sales 221 Month Length Adjustment 221 Graph Your Data 221 Worksheet Setup 222 First Forecasting Method 227 Second Forecasting Method 227 Selection of Length of Prior Period 228 Reasonableness Test 228 Conclusion 229 CHAPTER 14 Case Study 14 Data Analysis Tools for Forecasting Sales 231 Need for Analytical Tests 231 Graph Your Data 231 Statistical Procedures 233 Tests for Randomness 235 Tests for Trend and Seasonality 240 Testing for Seasonality and Trend with a Regression Model 246 Conclusion 249 Notes 249 CHAPTER 15 Case Study 15 Determining Lost Sales with Stationary Time Series Data 251 Prediction Errors and Their Measurement 251 Moving Averages 252 Array Formulas 254 Weighted Moving Averages 256 Simple Exponential Smoothing 260 Seasonality with Additive Effects 263

7 Seasonality with Multiplicative Effects 268 Conclusion 272 CHAPTER 16 Case Study 16 Determining Lost Sales Using Nonregression Trend Models 273 When Averaging Techniques Are Not Appropriate 273 Double Moving Average 275 Double Exponential Smoothing (Holt s Method) 277 Triple Exponential Smoothing (Holt-Winter s Method) for Additive Seasonal Effects 279 Triple Exponential Smoothing (Holt-Winter s Method) for Multiplicative Seasonal Effects 285 Conclusion 288 APPENDIX The Next Frontier in the Application of Statistics 291 The Technology 291 EViews 291 Minitab 292 NCSS 292 The R Project for Statistical Computing 293 SAS 294 SPSS 295 Stata 296 WINKS SDA 7 Professional 298 Conclusion 299 Bibliography of Suggested Statistics Textbooks 301 Glossary of Statistical Terms 303 About the Authors 317 Index 319 Ordering: Order Online - Order by Fax - using the form below Order by Post - print the order form below and send to Research and Markets, Guinness Centre, Taylors Lane, Dublin 8, Ireland.

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