Data Analysis Through Modeling is a one-semester data analysis and calculus text that can be used as part of a one-, two- or three semester sequence of mathematics courses usually required of business and management undergraduate majors. We believe the following features distinguish this text from other texts in the curriculum:
Data-driven, open-ended problems
Extensive use of spreadsheets throughout the text as more than just a calculator
Key problems framed as realistic business memos
Follows recommendations of MAA’s Curriculum Foundations Project CRAFTY report for business and management
The increasingly information-driven demands of business in the 21st century require a different emphasis in the quantitative skills and ways of thinking than traditional mathematics courses have provided in the education of managers. This emphasis has to do with becoming comfortable in the world of data and mathematical models, being able to use technology as a tool through which to think, and expressing one’s thinking effectively in writing.
The key, we believe, is data analysis through modeling. Data analysis for us means ”What can we find out about this data set relevant to our problem?” Models for us are such things as: averages, boxplots, histograms, single- and multivariable regression equations, both linear and nonlinear. These models are proxies for data that are too complex to understand any other way. We think of calculus as a way of analyzing certain kinds of models, which in turn, reveals something about underlying data structures. Our treatment of calculus emphasizes basic concepts, such as rates of change, constrained optimization, and interpretations of area under a graph, and their applications to business problems. We use spreadsheets to develop numerical methods for both differentiation and integration while deemphasizing symbolic manipulation. We use routines like Excel’s Solver routine instead of the simplex method to solve linear programming problems. Using Solver has the advantage that we can also solve nonlinear programs.
As we developed this text, we found the introduction of spreadsheet technology for analysis of data not only changed our teaching approach and the content of the course, but it caused us to modify our assignments as well. We found that we simply could not get the quality and depth of understanding we desired from our students by using conventional exercises. We found that students have to explain their thinking and make explicit their assumptions and inferences. In short, we had to supplement our more conventional exercises with memoranda problems with accompanying data files that students respond to in an appropriate business format that are, in turn, read by their supervisor. Further, we find that students learn more by having a chance to revise their work based on instructor/supervisor feedback. All of which should give an indication as to why the book is subtitled ”Thinking and Writing in Context.”
Although the text has a unit of descriptive statistics and develops regression all the way through multivariable regression with interaction terms, Data Analysis Through Modeling is not a statistics text. Most one-semester introductory statistics courses do not treat regression at the level presented in this text. Moreover, most introductory statistics texts do not give the same emphasis to descriptive statistics that this text does, which is to use these relatively simple concepts for rather deep analysis. Data Analysis Through Modeling fits well with an introductory statistics course that primarily deals with probability and hypothesis testing.