INFORMS Transactions on Education

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1 This article was downloaded by: [4..3.3] On: 0 September 0, At: 0: Publisher: Institute for Operations Research and the Management Sciences (INFORMS) INFORMS is located in Maryland, USA INFORMS Transactions on Education Publication details, including instructions for authors and subscription information: Developing a Scalable Model to Analyze Expanding Data Sets Donald D. Conant To cite this article: Donald D. Conant (0) Developing a Scalable Model to Analyze Expanding Data Sets. INFORMS Transactions on Education (3):-3. Full terms and conditions of use: This article may be used only for the purposes of research, teaching, and/or private study. Commercial use or systematic downloading (by robots or other automatic processes) is prohibited without explicit Publisher approval, unless otherwise noted. For more information, contact permissions@informs.org. The Publisher does not warrant or guarantee the article s accuracy, completeness, merchantability, fitness for a particular purpose, or non-infringement. Descriptions of, or references to, products or publications, or inclusion of an advertisement in this article, neither constitutes nor implies a guarantee, endorsement, or support of claims made of that product, publication, or service. Copyright 0, INFORMS Please scroll down for article it is on subsequent pages INFORMS is the largest professional society in the world for professionals in the fields of operations research, management science, and analytics. For more information on INFORMS, its publications, membership, or meetings visit

2 Vol., No. 3, May 0, pp. 3 ISSN 3-04 (online) I N F O R M S Transactions on Education 0 INFORMS Developing a Scalable Model to Analyze Expanding Data Sets Donald D. Conant School of Business, Saint Martin s University, Lacey, Washington 03, dconant@stmartin.edu Ioffer a workbook to teach the scalable analysis of expanding data sets. When analyzing data sets, function ranges are often statically defined. As a result, when new data are appended to the data set, the appended data are beyond the static ranges. This paper uses a basic time series regression analysis to show how to access data in expanding data sets and analyze data periods that expand and contract. Keywords: teaching data analysis; time series regression analysis; data sets; statistical process control; spreadsheet modeling History: Received: September 04; accepted: December 04.. Introduction Workbooks (sometimes referred to as spreadsheets) have long been regarded as important tools for business managers (Coles and Rowley 6). Workbook application software, in particular, Microsoft Excel, is used by businesses around the world to provide managers with decision support information (LeBlanc and Grossman 00, Pemberton and Robson 000). It is important that business students and managers develop the skills to use workbooks and worksheets effectively to remain competitive in today s business environment (Coles and Rowley 6). Often in business, it is necessary to glean information from a data set (Pemberton and Robson 000). When training users to work with data sets, there is frequently an assumption that the data set is fixed. The models that are designed based on a fixed data set assumption are constructed using Excel functions that are oriented to a fixed set of rows and columns. Problems can arise when new data become available and are added to the data set. The new data are outside of the ranges assigned to the functions used in the analysis. The fixed data set assumption results in worksheets that are not scalable. Savage (7) was among the first to draw attention to the problems of scalability in spreadsheet models. Savage observed that an action as routine as adding a new product could result in hours of work reformatting a worksheet, and in some cases, result in models that provide incorrect answers. In addition, when analyzing a data set, both the number of periods to analyze and the starting period for analysis may vary. This was the case in the study by Agrawal et al. (), which examined the preand postmerger performance of the stock of acquiring firms. By varying the analysis period length and selecting periods before and after the acquisitions, they were able to test the assumption of efficient capital markets. In a recent conversation with Walker (04), the call center director for the Washington Health Benefits Exchange, the need to analyze an expanding data set using a scalable model in a quality management setting was illustrated. The call center keeps a weekly record of customer wait times. Each record consists of two measurements per day taken during designated peak periods. The 4 measurements for each week are added to the call center data set. The desire is to analyze the data to better determine the effects of training, workspace configuration, call triage methods, and supervisor involvement on customer wait times. For example, data collected for a selected period before training was conducted could be compared with data collected for a period afterward to determine significant variations in customer wait times. The conversation with Walker (04) involved an examination of a data set that is similar to that used in statistical process control. Shewhart (3) developed control charts to differentiate between a process experiencing random variation and one that was out of control. Operations management students may be presented with cases where customers have reported receiving product that is not within the

3 6 INFORMS Transactions on Education (3), pp. 3, 0 INFORMS specified range for a specific characteristic (weight, height, etc.). To find the source of the quality issue, control charts may be constructed from quality samples taken over varying periods. Students may compare quality samples from various shifts, from before and after a scheduled maintenance, or from before and after receipt of raw materials from a new vendor. These periods will begin at different places in the data set and may be of differing lengths. In a realworld setting, new samples will be added regularly to the data set causing the data set to expand... The Pedagogy I have used the material presented in this paper to teach quantitative methods and advanced financial modeling techniques to undergraduate business students and operations management and business analytics to graduate students. Beyond the obvious pedagogical goal of teaching students to create spreadsheet models, my objective is to teach students to formulate problems in a way that assumes a spreadsheet model as part of the solution. Problem formulation is the bridge between our verbal or conceptual understanding of the problem and an automated solution. Students must have an indepth understanding of what a spreadsheet can do if they are to think about problems in terms of an automated solution. I use a series of exercises to separately introduce each of the functions that make up the model I present in this paper. Students document the steps they would use to manually find the answer to a simple problem. Then, they automate each of the steps using a spreadsheet function and test the model. As the process builds toward the final project, students gain a deeper understanding of how functions are used to answer simple questions and how functions can be used together to find more complex answers. The concept is that, in the same way we ask questions of others to get the information we need to answer questions; functions can ask questions of other functions to get the information they need to answer questions. To demonstrate as many of the functions associated with the use of a scalable model to analyze an expanding data set as possible, this article uses a basic time series regression analysis of the financial performance of a company that was acquired twice during a 4-year period beginning in. The purpose is to examine the effect of the acquisitions on company sales. Figure presents the time line of the company s decision to analyze the effects of acquisitions on sales. This is accomplished by calculating the slope (the increase or decrease in sales) and the coefficient of determination (how well the data fit the model) for each period. The first acquisition occurred at the end of 00 and the second at the end of 007. The initial Figure Timeline of the Company s Decision to Analyze the Effects of Acquisitions on Sales Analysis period Acquisition Original sales data Analysis period Year Decision to analyze effect of acquisitions on sales Acquisition Additional sales data Analysis period 3 Follow-up analysis analysis begins with a nine-year data set. To continue the analysis beyond the second acquisition, an additional five years of data will be added. The first period of analysis is a three-year period beginning in and ending with the first acquisition at the end of 00. The second period is a six-year period beginning in 00 and ending with the second acquisition at the end of 007. To followup on the initial analysis, an additional five years of data were added. The final period is a five-year period beginning in 00. The variation in starting years and period length demonstrate the importance of a scalable model. The addition of five years of data leading up to the follow-up analysis shows the importance of the model s ability to manage data sets where new data may become available.. The Data Set Figure shows a data set containing the monthly sales figures for a nine-year period beginning in January and ending in December 007. I assume that no additional columns (months) will be added. However, as data becomes available for future months or if data are discovered for prior years, the year and corresponding month s data can be appended to or inserted into the table. I entered the table shown in Figure in the Data worksheet in the Expanding- DataSets.xlsx workbook. 3. The Analysis Model Figure 3 illustrates the scalable model. The model performs a times series regression analysis on an expanding data set for periods from three to seven years in length. The user selects the number of years to analyze and the most recent year of the analysis. The model requires that all months of data are available before including a year in the list of years for analysis. The regression analysis is based on the annual totals with each year representing one period. Based on these parameters, the model creates a table that shows the monthly sales figures by year; calculates annual totals; calculates the intercept (a), slope (b),

4 INFORMS Transactions on Education (3), pp. 3, 0 INFORMS 7 Figure This Sample Data Set Contains Sales Amounts for the Calendars Years A B C D E F G H I J K L M Year Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec,3,3 3,063,00,7 3,04,760,36,63,,400,00 000,77,6,6,0,0,7,6 3,43,707,,,3 00 3,066,43,473,44,7 3,73 3,000 3,6,43 3,46,40,67 00,66,60,3,3,63,70,0 3,,6,77,3, 003 3,00,60 3,70 3,0,7 3, 3,0 3, 3,0 3,64,, ,4,7 4,0 3,430 3, 4,0 3,476 3,6 3,743 3,4 4,64 3,6 00 3,4 3,40 4,7 3,0 4,7 4,6 3,666 4,34 3, 3,44 3,4 3, 006 3, 3, 4, 4,400 4,7 4,04 4,6,7 4, 4,70 4,0 3, ,4 4,436 4,73 4, 4,0,,777,476 4,73 4,77 4,3 3,36 correlation coefficient (r), and coefficient of determination (r ); and graphs, with trend line, the annual totals for the period selected. The table assumes that there will always be a period. It is important that the list of months in column A match the list of months in Figure row. The number of years to analyze input is limited to three to seven years using data validation. Data validation is also used to limit the most recent year in analysis input. The title, to 00 Annual Sales changes to reflect the years in the analysis selected by the user. This title is used in the chart to ensure that the chart title reflects the current data in the analysis. The periods, years, monthly totals, and annual totals in the table expand and contract to reflect the number of years to analyze and the years in the analysis. The forecast data (slope, intercept, r, and r ) are calculated based on the data in the table. The model shown in Figure 3 is in worksheet Annual in Expanding- DataSets.xlsx. 4. User Input The user needs to provide the model with two pieces of data. The first is the number of periods (years) to analyze. The second is the most recent year in the analysis. 4.. Number of Periods to Analyze Data validation is an important tool for ensuring that only data that fits the model is entered by the user. The data validation option is found on the Data menu ribbon. To validate the first piece of user input, I placed the cursor in cell A3, selected the Data menu ribbon, and selected Data Validation. In the Allow combo box, I selected List. In the Source field, I entered 3, 4,, 6, 7 and clicked OK. This limits the values for cell A3 to the integers 3 7 inclusive. 4.. Most Recent Year in Analysis I used a data validation list to restrict user input for the most recent year in analysis value. The list should Figure 3 The Model with Graph and Regression Analysis A B C D E F G H I J K L M N Annual regression analysis for periods from 3 to 7 years in length 3 = Number of years to analyze 00 = Most recent year in analysis to 00 annual sales Jan,3,77 3,066 Feb,3,6,43 Mar 3,063,6,473 Apr,00,0,44 May,7,0,7 Jun 3,04 3,7 3,73 Jul,760,6 3,000 Aug,36 3,43 3,6 Sep,63,707,43 Oct,, 3,46 Nov,400,,40 Dec,00,3,67 Total Slope = Intercept = r = r = 3,074 34,0 33,4 70 3, ,00 34,000 33,00 33,000 3,00 3,000 3,00 3,000 to 00 annual sales

5 INFORMS Transactions on Education (3), pp. 3, 0 INFORMS only contain years that are preceded by enough years to satisfy the user s selected number of periods. For example, if the user selected three years to analyze, the list of most recent years should begin with 00 and end with 007. Allowing the user to select a year earlier than 00 would not allow for enough data to provide three years to analyze. I used a combination of the OFFSET and COUNTA functions to create a list that is limited to years that satisfy the years in analysis criteria. Pre-00 versions of Excel required the use of named ranges to access data from another worksheet in the Source field. This limitation is removed in Excel 00, allowing me to illustrate the use of the OFFSET function in data validation by entering the function into the Source field The OFFSET Function. Figure 4 shows the resulting list of years in cell A4 and the data validation dialog box. In cell A4, I selected data validation using a list. I entered =OFFSET(Data!$A$,$A$3-, 0,COUNTA(Data!$M:$M)-$A$3,) in the Source field. The OFFSET function has five arguments: reference, rows, columns, height, and width. For the reference argument, I entered Data!$A$. Column A of the data set contains the titles (years) for each record in the table. However, the first row of the data set contains titles for the fields (months) in each record. The data begins in the second row and the second column. The cell reference Data!$A$ indicates the first year () of data in the table. For the rows argument, I entered the number of periods analyzed by the user on the Annual worksheet in cell $A$3 minus. This moves the cursor from the reference argument position (Data!$A$) down four rows. This ensures that the first choice on the list of years in the analysis has the required number of years available (the reference row plus four rows provides the selected five periods for analysis). I left the columns argument at the default value of 0. The height and width are optional arguments used to return a range of values rather than a single value. For the height argument, I entered COUNTA(Data!$M:$M)-$A$3. The COUNTA function returns the number of nonempty cells in a range. By setting the range column to M, the list waits until the last month s data are entered before adding the year to the list. By omitting the row portion of the cell references, the COUNTA function evaluates the entire M column. The height argument determines how many years to include in the range starting at the reference. The reference has been moved down five rows. Therefore the height or number of rows remaining must be decreased by. This is accomplished by subtracting the number of years to analyze as indicated by the user in $A$3 (). I left the width argument at the default value of, indicating a single column list.. Annual Sales Table Based on user input, the model creates a table consisting of periods, years, monthly sales values, and yearly totals. The formula in cell A6, =A4 A3+ & "to" & A4 & "Annual Sales," creates the title for the table and the chart. I used data concatenation to calculate the years in the analysis and combine those with the title... Periods It is preferable to number the years sequentially beginning with when designing a regression analysis model. These numbers serve as x in the formula y = a + bx, which is used to calculate a trend line or to forecast y for future years. Using numbers for these calculations is much more convenient than using the years. Row 7 assigns a number beginning with to each year. The model assumes that there will always be a period. Period, cell C7 and the remaining periods are calculated with the formula, =IF(B7="","",IF(B7+<=$A$3,B7+,"")). In this formula for period, the cell to the left of the current Figure 4 Data Validation for the Most Recent Year in Analysis

6 INFORMS Transactions on Education (3), pp. 3, 0 INFORMS cell is evaluated to see if it is blank. If it is blank, that indicates the previous period is not in use in the current model, therefore the current period is also not in use. If it is not blank, is added to the period in the cell to the left of the current cell. If the resulting value is less than or equal to the number of years selected to analyze in cell A3, the value is entered into the current cell. If the resulting value is greater than the number of years selected to analyze a blank is entered into the current cell, indicating the period is not used in the current model. Using absolute and relative cell references in the formulas allowed me to copy the formula in C7 and pasted it into cells D7 H7 to allow for seven years of analysis. To expand the model beyond seven years, the formula can be copied and pasted beyond cell H7... Years Row indicates each year that the user has selected for analysis. The model assumes that there will always be a first year. Cell B calculates the first year, =$A$4-($A$3-). First, it reduces the number of years to analyze (3) by to include the first year. The result is subtracted from the most recent year in the analysis (00). The second year in cell C is calculated in the formula, =IF(C7="","",B+). This adds to the year value in the cell to the left of the current cell. Using absolute and relative cell references in the formulas allowed me to copy the formula in cell C and paste it into cells D H to allow for seven years of analysis..3. The Data Table Column A of the data table indicates each month. The sales figures for each month of each year are retrieved from the Data worksheet using the OFFSET, MATCH, and COUNTA functions. The sales figure for January is retrieved using the formula: =IF(B$7="","",OFFSET(Data!$A$,MATCH(Annual!B$, OFFSET(Data!$A$,0,0,COUNTA(Data!$A:$A)-,),0), MATCH(Annual!$A,Data!$B$:$M$,0))). As with the year values in paragraph., an IF function is used to determine if the period for the current cell is in use in this model. If it is, it retrieves the sales amount, if not, it returns a blank. To retrieve the sales amount, the OFFSET function uses MATCH and COUNTA to locate the row and column in the Data worksheet that corresponds to each value. For the OFFSET function s reference argument the cursor is placed in Data!$A$..3.. The MATCH Function. I used the MATCH function to return the row and column arguments for the OFFSET function. The MATCH function allows OFFSET to move the cursor from the reference position to the desired value based on the year (row) and month (column) values in the data table. The MATCH function has three arguments: the lookup value, the lookup array, and the match type. The first use of the MATCH function is to find the row (year) of the value in the data set. For the lookup value argument for January, I used the year value from Annual!B$ (). For the lookup array argument, I nested an OFFSET function, OFF- SET(Data!$A$,0,0,COUNTA(Data!$A:$A)-,). This allows the data set to expand as a user appends additional records to the data set. When a new year of monthly data are added, the MATCH function will include the new year in the lookup array. For the nested OFFSET reference argument, I entered Data!$A$ (the first year in the data set). I left the row and column arguments at the default value of 0. This leaves the cursor in Data!$A$. For the height argument, I entered COUNTA(Data!$A:$A)-. This counts all the nonempty cells in column A and removes the title row. I left the width argument at the default value of. For the MATCH function matchtype argument, I entered 0, indicating an exact match. The second use of the MATCH function is to find the column (month) of the value in the data set. For the lookup value argument for January, I used the month value from Annual!$A (January). For the lookup value argument, I used the month value from Annual!$A (January). For the lookup array argument, I entered Data!$B$:$M$ to indicate the range of cells in the Data worksheet that contain the month values January December For the matchtype argument, I entered 0 to indicate an exact match. Using absolute and relative cell references in the formulas allowed me to copy the formula in B and paste it into cells B0 B0. I then copied the range of cells B:B0 and copied those to the range C:H0 to allow for seven years of analysis..4. Totals Row calculates the totals for each year in the analysis. The formula in B, =IF(B7="","",SUM(B:B0)), checks the period row to see if the period is in use. If the period is not in use, it returns a blank. Otherwise, it calculates the sum of the monthly values for the period. Using relative cell references in the formulas allowed me to copy the formula in B and paste it into cells C H to allow for seven years of analysis. 6. Regression Analysis The regression analysis section uses the totals from the annual sales table to calculate the slope (a), intercept (b), correlation coefficient (r), and coefficient of determination (r ). The slope (SLOPE), intercept (INTER- CEPT), and correlation coefficient (CORREL) functions require similar arguments. The SLOPE and INTER- CEPT functions require known y s and known x s and the CORREL function requires array and array. For the known y s and array, I selected the totals from the annual sales table. I used the OFFSET

7 0 INFORMS Transactions on Education (3), pp. 3, 0 INFORMS function to ensure the size of the selected range matched the number of periods in the analysis, OFF- SET(B,0,0,,A3). For the OFFSET reference argument, I entered B to indicate the annual total of the first period in the table. I left the row and column arguments at the default value of 0. For the height argument, I entered to indicate a single row of values. And, for the width argument, I entered the number of years to analyze value found in cell A3. This scales the range of the function to match the selected range for the analysis. I did almost the same thing for the known x s and array. The only difference is the value in the reference argument of the OFFSET function, OFFSET(B7, 0,0,,A3). I entered B7 in the reference argument to select the periods in the annual sales table. To calculate the coefficient of determination, I squared the correlation coefficient value in cell B6, =B6. 7. Chart Charts and graphs are useful tools for communicating the results of a data series. However, when representing a scalable data series, nonscalable charts can be confusing. Figure illustrates the problem, assuming that the selected years are 00. The nonscalable chart on the left includes the maximum range of seven years and the scalable chart on the right includes only the three selected years. The problem with the nonscalable chart is that the data for the years that are not included are shown as zeros, and these zeros are included if one inserts a trend line into the graph, resulting in a misleading chart. I use a scalable chart in the model. In the remainder of this section, I explain how to use the OFFSET function to make the chart scalable. The chart feature in Excel will not accept the OFF- SET function as the series value for a series. However, it will accept a named range that contains the OFF- SET function. To create a scalable chart, I created two named ranges, Years and Totals. 7.. Named Ranges For the x-axis labels (years), I created a range named Years, =OFFSET(Annual!$B$,0,0,,Annual!$A$3). For the OFFSET reference argument, I entered Annual!$B$, which indicates the first year in the analysis. I left the row, column, and height arguments at their default values of 0, 0, and, respectively. For the width argument, I entered the number of years to analyze value found in cell Annual!$A$3. This scales the named range to match the selected range for the analysis. For the series values (totals), I created a range named Totals, =OFFSET(Annual!$B$,0,0,,Annual!$A$3). For the OFFSET reference argument, I entered Annual!$B$, which indicates the first annual total in the analysis. I left the row, column, and height arguments at their default values of 0, 0, and, respectively. For the width argument, I entered the number of years to analyze value found in cell Annual!$A$3. This scales the named range to match the selected range for the analysis. 7.. Completing the Chart To create a scalable chart, I inserted a blank line chart. In the design chart tools, I opened the select data dialog box and added a legend entry (series). For the series name, I selected the table title in cell Annual!$A$6, (=Annual!$A$6). The series editor will make the series name the title of the chart as well as the series. This will link the chart title to the table title causing the chart title to update each time the periods to analyze change. To enter the series values from a named range, chart requires the name of the workbook and the range, =workbook_name.xlsx!totals. Chart will accept the worksheet name and the name of the range, for this example, =Annual!Totals. If this second option is used, chart will convert the worksheet name to the workbook name. The second option is often easier given the length of some workbook names. For the horizontal (category) axis labels, I clicked on edit and used the same format as the series values to enter the axis labels, =Annual!Years. As with the series values, when I clicked OK, Excel converted Figure A Comparison of Nonscalable and Scalable Charts when Plotting Scalable Data with a Trend Line 40,000 3,000 30,000,000 0,000,000 0,000,000,000 0, to 00 annual sales to 00 annual sales 34,00 34,000 33,00 33,000 3,00 3,000 3,00 3,

8 INFORMS Transactions on Education (3), pp. 3, 0 INFORMS the worksheet name in the reference to the workbook name.. Applying the Scalable Model to the Expanding Data Series The purpose of this article was to examine the effect of the acquisitions on company sales. This was accomplished by calculating the slope (the increase or decrease in sales) and the coefficient of determination (how well the data fit the model) for each period. The first period for analysis was a three-year period ending with the first acquisition in 00. The second period for analysis is a six-year period ending with the second acquisition in 007. The variation in starting years and period lengths demonstrate the importance of a scalable model. Figure 6 The Model with Graph and Regression Analysis for the Period between the First and Second Acquisitions A B C D E F G H I J K L M N Annual regression analysis for periods from 3 to 7 years in length 3 6 = Number of years to analyze = Most recent year in analysis 6 00 to 007 annual sales Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Total 30,44 Slope = Intercept = r = r = ,66 3,00 3,4 3,4 3, 3,4,60,60,7 3,40 3, 4,436,3 3,70 4,0 4,7 4, 4,73,3 3,0 3,430 3,0 4,400 4,,63,7 3, 4,7 4,7 4,0,70 3, 4,0 4,6 4,04,,0 3,0 3,476 3,666 4,6,777 3, 3, 3,6 4,34,7,476,6 3,0 3,743 3, 4, 4,73,77 3,64 3,4 3,44 4,70 4,77,3, 4,64 3,4 4,0 4,3,,0 3,6 3, 3,63 3,36,04 6, , 43,040 47,47, 7,333 Figure 3 provided the slope (70) and coefficient of determination (0.4) for the period leading up to the first acquisition at the end of 00. To use the model to calculate the second period, change the number of years to analyze to 6 and the most recent year in analysis to 007. Figure 6 indicates the slope (,04) and coefficient of determination (0.) for the period following in first acquisition through the second acquisition at the end of 007. To complete the final analysis, five years of data must be appended to the table. The addition of five years of data leading up to the follow up analysis shows the importance of the model s ability to manage data sets where new data may become available. Figure 7 shows the complete sales data set for analysis. After the five years of data have been appended 00 to 007 annual sales 70,000 60,000 0,000 40,000 30,000 0,000 0, Figure 7 The Complete Sales Data Set A B C D E F G H I J K L M Year Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec,3,3 3,063,00,7 3,04,760,36,63,,400, ,77,6,6,0,0,7,6 3,43,707,,, ,066,43,473,44,7 3,73 3,000 3,6,43 3,46,40,67 00,66,60,3,3,63,70,0 3,,6,77,3, ,00,60 3,70 3,0,7 3, 3,0 3, 3,0 3,64,, ,4,7 4,0 3,430 3, 4,0 3,476 3,6 3,743 3,4 4,64 3,6 00 3,4 3,40 4,7 3,0 4,7 4,6 3,666 4,34 3, 3,44 3,4 3, 006 3, 3, 4, 4,400 4,7 4,04 4,6,7 4, 4,70 4,0 3, ,4 4,436 4,73 4, 4,0,,777,476 4,73 4,77 4,3 3, ,64 4,43,376,04,03 4,7 4,0 4,477 4,36,066,4, ,6 4,,,46,4 4,7,03 4,7 4,670,66 3,04, ,67 4,47,66 4,3,644 4,60 4,3 4,63 4,43 4,07,4, , 4,,44,3 6,03 4,,,07 4,7,0 3,4, ,67 4,47,,0, 4,63 4,74 4,6 4,370 4,7 3,04,3

9 INFORMS Transactions on Education (3), pp. 3, 0 INFORMS Figure The Model with Graph and Regression Analysis for the Period Following the Second Acquisition B C D E F G H I J K L M N A Annual regression analysis for periods from 3 to 7 years in length Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Slope = Intercept = r = r = = Number of years to analyze = Most recent year in analysis 6 00 to 0 annual sales Total 3, ,64 4,6 4,67 4, 4,67 4,43 4, 4,47 4, 4,47,376,,66,44,,04,46 4,3,3,0,03,4,644 6,03, 4,7 4,7 4,60 4, 4,63 4,0,03 4,3, 4,74 4,477 4,7 4,63,07 4,6 4,36 4,670 4,43 4,7 4,370,066,66 4,07,0 4,7,4 3,04,4 3,4 3,04,34,44,37,443,3 6 4, ,4 4,4 7,7 3,67,000,000 7,000 6,000,000 4,000 3,000,000, to 0 annual sales to the table, the most recent year in analysis list will expand to include the five additional years. To use the model to calculate the third period, change the number of years to analyze to and the most recent year in analysis to 0. Figure indicates the slope (6) and coefficient of determination (0.06) for the period following the second acquisition in 00.. An Additional Characteristic of the Scalable Model As the data set expands, the scale of the model may need to increase. The current model analyzes periods from three to seven years in length. With an additional five years of data, it may be necessary to increase the scale of the model to analyze periods from 3 to 0 years in length. Three steps need to be followed to expand the scale of the model beyond the initial seven years. First, in the Annual worksheet, select and copy the cells in the range H7:H. Paste the copied cells to the range I7:K. Second, open the data validation dialogue box for cell A3 (number of years to analyze) and add,, 0 to the list in the Source field. Finally, in cell A change the title from 3 to 7 years in length to 3 to 0 years in length. Using these steps, the model can just as easily be scaled to 0 or 00 periods. Figure The Model with Graph and Regression Analysis for the Most Recent 0 Years A B C D E F G H I J K L M N O P Annual regression analysis for periods from 3 to 0 years in length 0 = Number of years to analyze 0 = Most recent year in analysis 003 to 0 annual sales Jan 003 3, , , , 007 3, , ,6 00 4,67 0 4, 0 0 4,67 Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec,60 3,70 3,0,7 3, 3,0 3, 3,0 3,64,,0,7 4,0 3,430 3, 4,0 3,476 3,6 3,743 3,4 4,64 3,6 3,40 4,7 3,0 4,7 4,6 3,666 4,34 3, 3,44 3,4 3, 3, 4, 4,400 4,7 4,04 4,6,7 4, 4,70 4,0 3,63 4,436 4,73 4, 4,0,,777,476 4,73 4,77 4,3 3,36 4,43,376,04,03 4,7 4,0 4,477 4,36,066,4,34 4,,,46,4 4,7,03 4,7 4,670,66 3,04,44 4,47,66,3,644 4,60 4,3 4,63 4,43 4,07,4,37 4,,44,3 6,03 4,,,07 4,7,0 3,4,443 4,47,,0, 4,63 4,74 4,6 4,370 4,7 3,04,3 Total Slope = Intercept = r = r = 37, 43,040 47,47, 7,333 3,7 6,4 4,4 7,7 3,67,77 4, to 0 annual sales 70,000 60,000 0,000 40,000 30,000 0,000 0,

10 INFORMS Transactions on Education (3), pp. 3, 0 INFORMS 3 To test the increased scale, change the number of years to analyze to 0 and select 0 as the most recent year in analysis. Figure shows the results of the model analyzing the most recent 0 years. The regression calculations for the slope, intercept, correlation coefficient, and coefficient of determination adjust to the increased scale like the chart. 0. Conclusion Grossman (006) noted the importance of spreadsheets to an organization. Grossman (006) suggested that managers treat spreadsheets as valuable organizational assets rather than mere personal productivity tools (p. 4). A well-developed Excel workbook is the ideal solution for many management applications. Excel is on business desktops around the world. An application developed in one work setting can be easily shared with others. Workbooks can be developed with intuitive worksheets to help users and managers enter and analyze data. It is not uncommon for such management tools to be used periodically. Even though managers may use a particular workbook infrequently, they use Excel regularly. This regular use of Excel helps flatten the learning curve. When managers return to workbooks they have not used in awhile, they do not have to relearn the application. They just need to follow the prompts provided in the workbook. The data sets of Agrawal et al. () may have contained fields (columns) of stock symbols and records (rows) of months or weeks. The data set for the Washington Health Benefits Exchange Call may contain fields of peak period measurements and records for each week. The regression data for this article contained fields of monthly data and records for each year. With minor modifications to account for 0 stocks or 4-peak period measurements instead of months, the scalable model in this article provides managers with a tool they can use to ask questions of an expanding data set without being required to modify functions to account for new data. The answers to these questions will help managers better understand the effects of acquisitions, training, quality initiatives, and other factors on the processes they monitor. References Agrawal A, Jaffe J, Mandelker G () The post-merger performance of acquiring firms: A re-examination of an anomaly. J. Finance 47(4):60 6. Coles S, Rowley J (6) Spreadsheet modelling for management decision making. Indust. Management + Data Systems 6(7): 7 3. Accessed September, 04, Grossman TA (006) Integrating spreadsheet engineering in a management science course: A hierarchical approach. Informs Trans. Ed. 7(): 36. LeBlanc L, Grossman T (00) Introduction: The use of spreadsheet software in the application of management science and operations research. Interfaces (4): 7. Pemberton J, Robson A (000) Spreadsheets in business. Indust. Management + Data Systems 00(): Accessed September, 04, accountid=7. Savage S (7) Weighing the pros and cons of decision technology in spreadsheets. OR/MS Today 4():4 4. Shewhart W (3) Economic Control of Quality of Manufactured Product (Van Nostrand, New York). Walker B (04) Personal communications, November.