Data Analysis Through Modeling:Thinking and Writing in ContextKris Green and Allen EmersonFall 2011 Edition11c2011 Kris H. Green and W. Allen EmersoniiAbout this textData Analysis Through Modeling is a one-semester data analysis and calculus text that canbe used as part of a one-, two- or three semester sequence of mathematics courses usually re-quired of business and management undergraduate majors. We believe the following featuresdistinguish 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 reportfor business and managementThe increasingly information-driven demands of business in the 21st century require a dif-ferent emphasis in the quantitative skills and ways of thinking than traditional mathematicscourses have provided in the education of managers. This emphasis has to do with becomingcomfortable in the world of data and mathematical models, being able to use technology asa 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 ”Whatcan we find out about this data set relevant to our problem?” Models for us are such thingsas: averages, boxplots, histograms, single- and multivariable regression equations, both linearand nonlinear. These models are proxies for data that are too complex to understand anyother 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 emphasizesbasic concepts, such as rates of change, constrained optimization, and interpretations of areaunder a graph, and their applications to business problems. We use spreadsheets to developnumerical methods for both differentiation and integration while deemphasizing symbolicmanipulation. We use Excel’s Solver routine instead of the simplex method to solve linearprogramming problems. Using Solver has the advantage that we can also solve nonlinearprograms.As we developed this text, we found the introduction of spreadsheet technology for anal-ysis of data not only changed our teaching approach and the content of the course, butit caused us to modify our assignments as well. We found that we simply could not getthe quality and depth of understanding we desired from our students by using conventionalexercises. We found that students have to explain their thinking and make explicit theirassumptions and inferences. In short, we had to supplement our more conventional exerciseswith memoranda problems with accompanying data files that students respond to in an ap-propriate business format that are, in turn, read by their supervisor. Further, we find thatstudents learn more by having a chance to revise their work based on instructor/supervisorfeedback. All of which should give an indication as to why the book is subtitled ”Thinkingand Writing in Context.”Although the text has a unit of descriptive statistics and develops regression all the waythrough multivariable regression with interaction terms, Data Analysis Through Modeling isnot a statistics text. Most one-semester introductory statistics courses do not treat regressionat the level presented in this text. Moreover, most introductory statistics texts do not giveiiithe same emphasis to descriptive statistics that this text does, which is to use these relativelysimple concepts for rather deep analysis. Data Analysis Through Modeling fits well with anintroductory statistics course that primarily deals with probability and hypothesis testing.How this text fits into the curriculumWe recommend the following tracks for a three-credit-hour, semester-long course using DataAnalysis Through Modeling:• For students not having a prior statistics course: Chapters 1-9, 11-12 [11 chapters].This course would not contain calculus and would be the first in either a two- or threesemester sequence: 1) data analysis and statistics or 2) data analysis, statistics, andcalculus. In our experience, students then do quite well in the follow-up statisticscourse after their experience with our approach to data analysis.• With a statistics prerequisite: Chapters 1-3, 7-9, 11-17 [12 chapters]. This coursewould contain calculus and constitute the second course in a two-semester sequencecontaining probability and hypothesis testing, data analysis, and calculus.The basic concepts of calculus are emphasized and applied to business problems involvingmarginal analysis, optimization and area under a curve. As recommended by CRAFTY,formal techniques of symbolic manipulation are kept to a minimum, whereas spreadsheetsare used extensively not only for finding numerical solutions but, equally important, for thedevelopment of the basic concepts of calculus themselves.The Technology Used in this TextIn addition to problem solving in the dynamic environment of spreadsheets, students willhave the opportunity to learn about and use the following Excel tools: pivot tables, sort-ing, stacking and unstacking data, basic statistical functions, frequency tables, sumproduct,building boxplots and histograms, correlation tables, simple regression, multivariable regres-sion (quantitative and qualitative), scatterplots, trendlines, Goal Seek, SOLVER table andgraphing in three dimensions. In addition, students will develop many basic computer liter-acy abilities, such as copying and pasting and integrating numerical, textual and graphicalanalyses into a single Word document. But what is most important about the way studentslearn these tools is that they are all taught in the context of solving business-type problems;this context, we believe, is critical for students learning how to transform these tools from aset of instructions to follow into a method of thinking and analyzing data.The Structure of the BookThis text is organized into five units, not all of which can be covered in one semester, asmentioned above. The chapters in each unit are all connected through a common ”thinkingivUnit Thinking StrategyQuantifying the World Students learn the importance of data and how to locatedata in real world situations.Analyzing Data ThroughSpatial ModelsStudents learn how to use basic charts and graphs todeeply understand a problem situation.Analyzing