Business
Engineering
Math
Science
Social Science
In Example 7.5, we implied that each of the five observations was from one period of time, such as a particular week. Suppose instead that each is an average over several weeks. For example, the 4.7 million exposures corresponding to one ad might really be an average over 15 different weeks where one ad was shown in each of these weeks. Similarly, the 90.3 million exposures corresponding to 50 ads might really be an average over only three different weeks where 50 ads were shown in each of these weeks. If the observations are really averages over different numbers of weeks, then simply summing the squared prediction errors doesn’t seem appropriate. For example, it seems more appropriate that an average over 15 weeks should get five times as much weight as an average over only three weeks. Assume the five observations in the example are really averages over 15 weeks, 10 weeks, 4 weeks, 3 weeks, and 1 week, respectively. Devise an appropriate fitting function, to replace sum of squared errors or RMSE, and use it to find the best fit. EXAMPLE 7.5 E STIMATING AN A DVERTISING R ESPONSE F UNCTION Recall that the General Flakes Company from Example 4.1 of Chapter 4 sells a brand of low-fat breakfast cereal that appeals to people of all age groups and both genders. The company has advertised this product in various media for a number of years and has accumulated data on its advertising effectiveness. For example, the company has tracked the number of exposures to young men from ads placed on a particular television show for five different time periods. In each of these time periods, a different number of ads was used. Specifically, the numbers of ads were 1, 8, 20, 50, and 100. The corresponding numbers of exposures (in millions) were 4.7, 22.1, 48.7, 90.3, and 130.5. What type of nonlinear response function might fit these data well?
Practical Management Science
Solutions
Practical Management Science
In Example 7.5, we implied that each of the five observations was from one period of time, such as a particular week. Suppose instead that each is an average over several weeks. For example, the 4.7 million exposures corresponding to one ad might really be an average over 15 different weeks where one ad was shown in each of these weeks. Similarly, the 90.3 million exposures corresponding to 50 ads might really be an average over only three different weeks where 50 ads were shown in each of these weeks. If the observations are really averages over different numbers of weeks, then simply summing the squared prediction errors doesn’t seem appropriate. For example, it seems more appropriate that an average over 15 weeks should get five times as much weight as an average over only three weeks. Assume the five observations in the example are really averages over 15 weeks, 10 weeks, 4 weeks, 3 weeks, and 1 week, respectively. Devise an appropriate fitting function, to replace sum of squared errors or RMSE, and use it to find the best fit.
EXAMPLE 7.5 ESTIMATING AN ADVERTISING RESPONSE FUNCTION
Recall that the General Flakes Company from Example 4.1 of Chapter 4 sells a brand of low-fat breakfast cereal that appeals to people of all age groups and both genders. The company has advertised this product in various media for a number of years and has accumulated data on its advertising effectiveness. For example, the company has tracked the number of exposures to young men from ads placed on a particular television show for five different time periods. In each of these time periods, a different number of ads was used. Specifically, the numbers of ads were 1, 8, 20, 50, and 100. The corresponding numbers of exposures (in millions) were 4.7, 22.1, 48.7, 90.3, and 130.5. What type of nonlinear response function might fit these data well?
To devise: An appropriate fitting function.
Non-linear programming (NLP):
Non-linear programming (NLP) is used in complex optimization problems where the objectives or constraints or sometimes both are non-linear functions of the decision variables. A model can be termed as non-linear for more than one reason.
Explanation of Solution
Model:
Formula:
Chapter 7 Solutions
Additional Business Textbook Solutions
Purchasing and Supply Chain Management
Cornerstones of Cost Management (Cornerstones Series)
Corporate Financial Accounting
Economics (MindTap Course List)
PAYROLL ACCT.,2019 ED.(LL)-TEXT
Accounting Information Systems
Fundamentals of Financial Management (MindTap Course List)
Accounting (Text Only)
Essentials of Business Communication (MindTap Course List)
Economics For Today
Fundamentals of Financial Management, Concise Edition (with Thomson ONE - Business School Edition, 1 term (6 months) Printed Access Card) (MindTap Course List)
Corporate Financial Accounting
College Accounting, Chapters 1-27
College Accounting (Book Only): A Career Approach
Fundamentals of Financial Management, Concise Edition (MindTap Course List)
Accounting Information Systems
Management, Loose-Leaf Version
MKTG 12:STUDENT ED.-TEXT
College Accounting (Book Only): A Career Approach
Principles of Macroeconomics (MindTap Course List)
Statistics for Business & Economics, Revised (MindTap Course List)
Macroeconomics
Financial And Managerial Accounting
Financial & Managerial Accounting
Fundamentals of Financial Management (MindTap Course List)
Exploring Economics
STATISTICS F/BUSINESS+ECONOMICS-TEXT
Essentials of Economics (MindTap Course List)
Intermediate Accounting: Reporting And Analysis
Financial Accounting
Brief Principles of Macroeconomics (MindTap Course List)
Financial Accounting
ECON: MICRO4 (New, Engaging Titles from 4LTR Press)
Survey of Accounting (Accounting I)
Contemporary Marketing
College Accounting, Chapters 1-27 (New in Accounting from Heintz and Parry)
Principles of Economics (MindTap Course List)
Principles of Microeconomics (MindTap Course List)
Pkg Acc Infor Systems MS VISIO CD
Principles of Macroeconomics (MindTap Course List)
Managerial Accounting: The Cornerstone of Business Decision-Making
Foundations of Business (MindTap Course List)
Financial & Managerial Accounting
Cornerstones of Financial Accounting
Microeconomics
Macroeconomics: Private and Public Choice (MindTap Course List)
Micro Economics For Today
Managerial Accounting
MACROECONOMICS FOR TODAY
Microeconomics: Private and Public Choice (MindTap Course List)
Understanding Management (MindTap Course List)
Economics: Private and Public Choice (MindTap Course List)
