excel data analysis

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Microsoft Excel 2003

Data Analysis

Larry F. Vint, Ph.D

[email protected]

815-753-8053

Technical Advisory Group

Customer Support Services

Northern Illinois University

120 Swen Parson Hall

DeKalb, IL 60115

© Copyright 2004 Northern Illinois University Information Technology Services



© Copyright 2004 Northern Illinois University Information Technology Services 1

Microsoft Excel 2003

Data Analysis

Using Excel’s Data Analysis Tools 2

Tables 6

Evaluating Trends 11

Using Excel's Goal Seek 17

Using Solver 20

Creating Scenarios 23




Using Excel’s Data Analysis Tools

Excel includes a number of add-in tools to assist with a number of data handling,reporting and analysis functions.

1. Click on the worksheet tab labeled Data Analysis

2. Click on the Tools pull-down menus

3. Click on Add-Ins

4. Check Analysis ToolPak as in FigureDA-01

5. Also Check Solver as we will beusing the Solver in a later exercise

6. Click OK

This unpacks the chosen Excel Add-in toolsand makes them available for use. If the Add-in list is empty, there may have been a limitedinstallation of MS Office. If this is the case,the MS Office CDs will be needed to installthese Add-in tools.

7. Click on the Tools pull-down menusagain

8. Click on DataAnalysis

9. Select Descriptive

Statistics from theAnalysis Tools as inFigure DA-02

10. Click OK

The Descriptive Statisticsbox is shown in Figure DA-03.

Figure DA-01

Figure DA-02

Fi ure DA-03




11. Click on the contract button for the Input Range box.

12. Highlight B1 through C7

13. Click the expand button

14. Check the Labels in First Row box

15. Click on the contract button for the Output Range box

16. Click on cell A11


18. Check the SummaryStatistics box

The Descriptive Statistics windowshould now look like Figure DA-04.

19. Click OK

20. The output will becrowded so highlight thecolumn headings for columns A through D

21. Position the cursor over the right-hand border of one of the highlightedcolumns and double-clickto increase the width of each column to the widest cell in the column.

The resulting Descriptive Statistics should look like Figure DA-05.

Figure DA-05

Figure DA-04




Let’s try another analysis. Regression statistics can be useful in evaluating pasttrends and predicting future consequences. Using the data in the Data Analysisworksheet, let’s compute the regression of Expenditure increases as a function of the number of Students.

22. Click on the Tools pull-down menus again

23. Click on Data Analysis

24. Select Regression from the Analysis Tools

25. Click OK

26. Click on the contract button for the Input Y Range box.

27. Highlight B1 through B7


29. Click on the contract button for the Input X Range box.

30. Highlight C1 through C7


32. Check the Labels box

33. Click on the contract button for the Output Range box

34. Click on cell E1


The Regression window should now look like Figure DA-06.

36. Click OK 37. The output will be

crowded so highlight thecolumn headings for columns E through M

38. Position the cursor over the right-hand border of one of the highlightedcolumns and double-clickto increase the width of

each column to thewidest cell in the column.

The resulting RegressionStatistics should look likeFigure DA-07.

Figure DA-06




The coefficient for STUDENTS, 5069.547647, indicates that every student adds$5,069.55 to EXPENDITURES and that even with no students there would be$12,763.11 in EXPENDITURES. Let’s use these coefficients to set up anequation to predict EXPENDITURES based upon student numbers.

39. Click on cell P3

40. Type =

41. Click on cell F17

42. Type +

43. Click on cell F18

44. Type *

45. Click on cell O3

46. Press Enter

These steps have created a prediction equation based upon the regressionanalysis that can be used to predict expenditures for varying numbers of students. Care must be taken in interpreting results greatly beyond the range of existing data; i.e. the prediction may be reasonable for 20 students, but notrealistic for 100 students.

47. Click on cell O3

48. Type 20

49. Press Enter

The equation predicts that if we had 20 students we could expect expenditures to be $114,154.06. The above examples illustrate some of the types of statistical analysis that can be

performed with Excel’s Add-in Analysis ToolPak.

Figure DA-07




Tables

Most people familiar with databases will mistakenly assume the Tables feature inExcel is used similarly but they are mistaken. The Tables feature in Excel isanother What-If analysis tool that displays the result of a formula with differentsets of input values.

For this example we will create a formula that determines the monthly paymentsfor the principal of an investment given a fixed interest rate. We will use thePPMT function that is one of the financial functions provided by Excel to calculatethe monthly payments to be made on an investment over a specified period of time. We will enter the interest rate,

Let’s first go to the Payment Table worksheet for the function and ensuing table.

1. Click on the Payment Table worksheet tab

Let’s enter the input values for the function first and then create the function.

2. Click on cell B1

3. Type 7.5

4. Click on cell B2

5. Type 5

6. Click on cell B3

7. Type 18000

These three values will be used by the PMT function to calculate the monthlypayments. Let’s enter the formula.

8. Click on cell B6

9. Click on the Paste Function toolbar button

10. From popup Insert Function window click on the Financial categoryfrom the select a category picklist

11. Scroll down the list box labeledSelect a function until you seethe PMT function and click on itas in Figure PT-01

12. Click on the OK button

The formula box appears listing thearguments needed by the PMT function.The three required arguments, Rate,Nper, and Pv, are indicated in boldface.Two optional arguments are Fv andType. Figure PT-01




13. To better understand the arguments needed for the PMT function clickon Help on this function.

We can now see that Fv and Type are the future value and payment method,respectively. The future value is the balanced desired after the last payment wasmade. If no argument is supplied to this argument the default is zero. The Type

argument is used to indicate when the payment is made. A value of Trueindicates the payment is made at the beginning of the period and a value of False or if this value is not supplied the payment is made at the end of the period.

We will supply the three required arguments since we want to attain a zerobalance after all payments are made and the payments are made at the end of each pay period.

14. Click within the box labeled Rate

15. Type (B1/12)/100

Cell B1 contains the annual interest rate. Since we wish to determine the

monthly payments we must express on all arguments in monthly units. Sodividing the annual rage by 12 months will give us the monthly interest rate. Wethen divided the monthly interest rate by 100 to express on the percentage as adecimal number.

16. Click within the box labeled Nper

17. Click on the Contract dialog box button to the right of this box

The formula box will be temporarily suppressed and the box containing the Nper argument is displayed. Whenever we click on a cell Excel will fill the cell addressinto the Nper argument box.

18. Click on cell B2

The cell address B2 is placed within the Nper argument box.

19. Click on the Expand dialog box button

The Nper argument box will contain the cell address B2 that contains the payperiod that is expressed in years. Just like the Rate argument we must expressthe Nper argument in months. So we must multiply the contents of cell B2 by 12.

20. Click on the End key tomove the insertion pointto the end of theargument

21. Type *12

The Nper argument should nowread B2*12.

22. Click within the boxlabeled Pv and click onthe Contract button

Figure PT-02




23. Click on cell B3 and then click on the Expand dialog box button

The Pv argument is the principal value. We will not supply any arguments for theFv and Type arguments because we want the future value of this investment toequal zero when the pay period ends and we are paying at the end of eachmonth, which are the defaults when an argument is not supplied. Figure 4 shows

the formula box now. Compare your formula box to the figure and correct anymistakes. The value of each argument is evaluated and displayed to the right of the argument boxes. The monthly interest rate, which is expressed as a decimalvalue, is .00625. The number of periods is 60 months and the principal value is18000.

24. Click OK

A negative value of $360.68 is displayed in cell B6. The payment is negativebecause it is the amount we must pay each month to pay off an $18,000investment at 7.5% for 5 years.

Suppose you want to see how the monthly payments will change when theannual interest rate and pay period are modified. We can set up a table toperform this what-if analysis. The table will display the input parameters alongthe top row and left-most column with each cell within the table displaying theformula result for each combination of input values.

To set up the table, the formula must be in the top, leftmost column. Then theinput values are entered on the same row beginning in the next cell to the right of the formula and on the same column beginning with the next cell below theformula.

25. Position the cursor on cell B7 then continuously hold the left mousebutton down

26. Drag the mouse pointer down to cell B9 and then release the mousebutton

The cell range B7:B9 should be highlighted.

27. Type 3 and press Enter



We will use the leftmost column to supply different number of pay period valuesto the PMT function.

30. Now position the cursor on cell C6 then continuously hold the left mousebutton down

31. Drag the mouse pointer to cell D6 and then release the mouse button

The cell range C6:D6 should be highlighted.


33. Type 6.5 and click on the fill handle of the highlighted range C6:D6




34. Continuously holding down on the left mouse button, drag the fill handleto column K, until the number 10 appears, and release the mouse button

We allowed Excel to use the pattern of 0.5 percent increases to set up a list of interest rates from six to ten in 0.5 increments. Now we can use row six tosupply these different interest rate values to the PMT function. Figure PT-03

shows the column and row input values for this table along with the function. Toset up the What-if table showing what payments would be across this range of payment periods and interest rates:

35. Position the cursor on cell B6 and hold the left mouse button down

36. Drag the mouse pointer to cell K9 and release the mouse button

The cell range B6:K9 should be highlighted and if is not then repeat steps 35 and36 above. You must highlight the entire cell range that will display the results of the table and the formula must be in the top, leftmost cell of the table.

37. Click on Data in the dropdown menus

38. Click on Table

A dialog box entitled Table appears with two options labeled Row input cell andColumn input cell . We must specify the cell range containing the row inputvalues within the table and the cell range containing the column input values.

39. Click within the box labeled Row input cell

40. Click on the Contract button


The cell address $B$1 should be filled into the Row input cell box. Cell B1contains the annual interest rate and the table will replace the interest rate usingthe five values entered in cells C6, D6, E6, F6, and G6.

42. Click on the Expand button to return to the Table dialog box

43. Click within the Column input cell box

44. Click on the Contract button


Figure PT-03




The cell address $B$2 is filled into the Column input cell box. Cell B2 containsthe number of periods and Excel will use the values supplied in cells B7, B8, andB9 to for the number of periods.

46. Click on the Expand button to return to the Table dialog box

47. Click on theOK

button

The table should result like Figure PT-04. Cell F9 displays the result of the PMTfunction using an annual interest rate of 7.5% and a pay period of 5 years.

This is the same result as cell B6 because these were the original values

supplied to the function. Now you can compare the different payment valuesacross different interest rates and pay periods. For example, cell E7 shows themonthly payment amount if the interest rate is 7% and the pay period is only 3years. Cell G8 shows the monthly payment amount if the interest rate is 8% andthe pay period is 4 years. The formatting of the monthly payments in the newlycreated table can be easily set using the Format Painter.


49. Click on the Format Painter

50. Swipe the Format Painter across cells C7 through K9

The table will now look like Figure PT-05.

Fi ure PT-04

Figure PT-05




Evaluating Trends

Excel has a number of tools to assist in analyzing trends in data. Trend analysiscan be utilized to predict future results. In this section we will use Excel’sTrendline tool to analyze several possible trends in a department’s tuitionincome. We will then utilize Excel’s Linear and Growth Trend tools to predictfuture tuition income based upon past results.

1. Click on the Trends worksheet tab

A chart has been created from the data range B7:C11. We will add a series of trendlines to this chart and evaluate how well they describe the existing data.

2. Right-click on one of the blue columns representing a data point in thechart

3. Click on Add Trendline from the popup menu as shown in Figure ET-01

Figure ET-02 shows the types of trendlines that can be to the chart.Excel offers six choices of typesof trendlines that might be appliedto charted data. We will examinevisually how well each fits thedata. We will also display thestatistical formulas Excel has

computed to calculate data pointson the trendline and the R2 valueswhich statistically represent howwell the trendline formuladescribes the data.

4. Click on the Linear boxas in Figure ET-02

Figure ET-01

Figure ET-02




Figure TL6

5. Click OK

A linear trendline has been applied to the chart.

6. Right-click on the trendline. The menu that pops up will allow you toeither Format trendline or Clear the trendline

7. Click on Format Trendline The Format Trendline window that pops up has three tabs. The first, Patterns,will allow you to change the line style, color and weight of the trendline. Thesecond, Type, will allow you to change the type of trendline being established.

8. Click on the third, the Options tab

The Options window in Figure ET-03will allow us to apply a customtrendline name, forcast forward or backward, reset the intercept on they-axis, display the trendline equation

on the chart and display the R-squared value on the chart:

9. Check the Display equationthen check the Display R-squared value boxes

10. Click OK

The formula y = 146.88x + 231.68and R2 = 0.9831 appears above thetrendline (Figure ET-04). This is thelinear regression formula Excel has

calculated to describe the tuitionincome data. The R2 value isthe percent of variation in thedata that is described by theregression equation. A value of 1.0 means the equation cancompletely account for variationin the data. The smaller the R2

value the less useful theequation is in describing thedata.

11. Click in cell C31 (besideLinear)

12. Type in value .9831

13. Press Enter

Figure ET-04

Figure ET-03




Since it is so easy to allow Excel to compute various types of regressionequations we will proceed to look at each of the various types of equations andenter their R2 values beside the Trendline Type name in the table in cells B31 toC36.

14. Right-click on the trendline.

15. Click on the Type tab

16. Choose the next Trendline Type

17. Click OK

18. Click in the cell in column C corresponding to the trendline type andenter the R2 value

19. Repeat steps 28 through 32 until R2 values for all trendline types havebeen calculated.

Note that the Moving Average does not compute a regression equation or R 2

value. This trendline type is based upon the moving average, not a regressionequation; therefore, no regression equation or R2 value is relevant to thistrendline type. Note in the Trendline Descriptive Accuracy table (Figure ET-05)that all of the variation in the data is described by the exponential equation. Thesecond degree polynomial equation also does an excellent job of describing thedata, accounting for 99.99 percent of the variation. Different datasets will yielddifferent results.

Let’s use the exponential equation to forecast for the next ten years.

20. Right-click on the trendline.

21. Click on the Type tab

22. Choose the Exponential trendline

type23. Click on the Options tab

24. Click in the Forecast Forward: boxand enter 10 as in Figure TL9

25. Click OK

Figure ET-05

Figure ET-06




The result of Excel’s forward forecasting using the exponential equation is shownin Figure ET-07. This gives us a clear visual image of predicted future tuitionincome. However, we have no accompanying data points to use for other evaluation purposes. To illustrate methods compute these data points proceedto the next page.

One method of predicting future data points in our data is to use the regressionequation that Excel has computed for us. To do so we must understand that in

our data the X in Excel’s equation represents an incremental counter starting atone and ending at five for the five data points in our data. The value of e (thebase of natural logarithms) is 2.71828183. The * is used in Excel to multiplyvalues. The ^ is used in Excel to raise values to a power. The formula Exceldisplays as y = 327.68e0.2231x is already coded in cell E7 as =327.68*2.71828183^(0.2231*D7). In the following steps we will use Excel’s exponentialprediction equation calculated from our data y = 327.68e0.2231x to predict futuredata points. First we must unhide cell E7.

26. Highlight column headings C through F

27. Right-click then click Unhide in the popup menu

28. Click in cell E7

29. Position the cursor over the fill handle

30. Hold the left mouse button down and drag the fill handle to cell E21 andrelease it

Figure ET-07




The computed data points now appear in columns E8 through E21 (Figure ET-08).

If linear or growth equations adequately describe the data there is an even easier

method of computing future data points.31. Click on cell B7

32. Highlight cells B7 through B11 and position the cursor over the fillhandle

33. Hold the left mouse key down and drag the fill handle to cell B21 andrelease it

34. Click on cell C7

35. Highlight cells C7 throughC11 and position the

cursor over the fill handle

36. Hold the RIGHT mousekey down and drag the fillhandle to cell C21 andrelease

The Trends menu that pops up(Figure ET-09) will allow the choiceof either a Linear Trend or GrowthTrend to fill in the future datapoints. Since our data was best

described by either an exponentialor second degree polynomialregression equation we shouldselect the Growth Trend.

37. Click on Growth Trend

Figure ET-08

Figure ET-09




The results (Figure ET-10) using are very close to those calculated using theexponential equation; however, they were more easily obtained. Note: If we hadheld down on the LEFT mouse button instead of the RIGHT mouse button as wewere dragging the fill handle, a linear trend would have been used to populateour future data points by default.

Figure ET-10




Using Goal Seek

Goal Seek is one of Excel’s what-if tools. Goal Seek allows you to

• Specify a single adjustable cell.

• Specify a target value that is dependent upon the adjustable cell.

• Generate a solution by manipulating the value of the adjustable cell.

• Generate a single solution to a problem

Goal Seek is a relatively easy tool to learn how to use and is a useful tool for finding solutions to complex problems involving a single variable. We will use itto find the coefficient required to reach a Department’s goals for growth in tuitionincome over the next ten years. The objective is to predict the coefficient of growth (x) required to achieve a ten-year goal and compute the annual tuitiontargets leading to that objective. It is assumed that the department has

$1,000,000 of tuition income in the current year and that tuition income for eachfuture year will increase by (x) times the previous year’s tuition total. This dataand accompanying chart are present in the Goal Seek worksheet.

1. Click on the Goal Seek worksheet tab

We want use the Goal Seek tool to compute the growth rate required to reach agoal of $10,000,000 of tuition income in the department by year 2011. Thecurrent tuition income in 2002 is $1,000,000. Over the past five years an annualgrowth rate of 125% has been achieved. Using this growth rate the tuition levelsover the next ten years has been predicted in the table in the worksheet andcharted in the accompanying chart. Tuition has been coded to thousands of

dollars. This predicts the department will fail to reach the $10,000,000 tuitionincome target in 2011. We will use Goal Seek to determine what the futuregrowth rate must be to reach the 2011 objective.

2. Click on cell C17.

This is the location of our objective.

3. Click on Tools in the dropdown menus

4. Choose and click on Goal Seek

The Goal Seek box (Figure GS-01) will appear.Our target cell is populated in Set cell: because

we clicked on it (C16) before opening Goal Seek

5. Click in the To value: box and enter 12000, the number of thousands of dollars equivalent to the goal of $12,000,000

Figure GS-01




6. Enter B1 in the By changing cell box as in Figure GS-02.

7. Click OK

The Goal Seek Status window (Figure GS-03) will announce that a solution hasbeen found and that a Current value of $12,000 (thousands) matched the Targetvalue of 12000. This value has been placed in cell C16. Notice that the tuitionvalues for other years have not yet been changed and the chart does not yetreflect the use of the new coefficient of growth in cell B1.

8. Click OK to accept thesolution of 128.21% asthe coefficient of growthnecessary to achieve thetarget of $12,000,000tuition income in year 2012. The newlycalculated coefficient isin cell B1.

Now both the table and the chart reflect the use of the newly computed growthrate in the modified values now present for each year. Next we want to visit analternative way to accomplish the same result.

9. Click the undo button on Excel’s standard Toolbar

10. Position the cursor over the 2012 bar.

In the Department Tuition Incomechart and click the left mousebutton twice. Only the 2012 bar should be active as identified bythe size handles on both ends and

in the middle.11. Position the cursor over

the top of active 2012 bar and hold down the leftmouse button when thetwo pointed arrow appearsas in Figure GS-04.

Figure GS-02

Figure GS-03

Fi ure GS-04




12. Continuously hold down the left mouse button and drag the top of thebar upwards until the number $12,000 appears then release

13. The Goal Seek box reappears with the Set cell: and To value: boxesfilled in (Figure GS-05). Enter B1 in the By changing cell:

14.Click

OKThe Goal Seek Status window will againannounce that a solution has been found andthat a Current value of $12,000 (thousands)matched the Target value of 12000. Thisvalue has been placed in cell C17. Noticethat the tuition values for other years havenot yet been changed and the chart does notyet reflect the use of the new coefficient of growth in cell B1.

15. Click OK to accept the solution of 128.21% as the coefficient of growthnecessary to achieve the target of $12,000,000 tuition income in year 2011. The newly calculated coefficient is in cell B1.

Both the table and the chart again reflect the use of the newly computed growthrate in the modified values now present for each year. For some this alternativeway to access Goal Seek through charts may be a more convenient approach.Note: Goal Seek and the chart modification method of activating Goal Seek only work with data cells created with consistent formulas that rely on singleadjustable cell.

Figure GS-05




5. Click on the contract button in the By Changing Cells: box

6. Highlight cells E4 through E13


8. Click on the Add button beside the Subject to the Constraints: box

The Add Constraint box pops up as in Figure SO-03. This allows us to placelimits or restrictions on the solutions; e.g. that Numbers Starting on a given Hour not be less than zero.

9. Click on the contract button in the Cell Reference: box

10. Highlight cells F4 through F13


12. Change theconstraint to >= fromthe combo box picklist

13. Click in theConstraint: box andenter 0 as in FigureSO-04

14. Click OK

15. Make certainthe Min buttonis checked and

that 0 is in theValue of: boxas in FigureSO-05

Figure SO-03

Figure SO-04

Fi ure SO-5




16. Click Solve

Solver will announce if it has found a solution in the Solver Results window. If this case Solver has found a solution. Make sure the Keep Solver Solution buttonis checked as in Figure SO-06.

17. Click OK

Solver has changed the adjustable cells in E4 to E13 to the solution it found for minimizing the total number of staff that needs to be scheduled. As shown inFigure SO-07, a total of 72 people need to be scheduled. The timing of whenvarying numbers of staff must start their three-hour shifts has been optimized tominimize the total number of staff that needing to be scheduled. At timesadditional constraints must be assigned to insure that partial people or negativenumbers are rejected as solutions. If Solver fails to find a solution, recheck entryparameters and constraints.

Fi ure SO-06

Figure SO7

Figure SO-07




Creating Scenarios

Scenarios are a tool Excel has to allow us to look and be able to recall the effectsof making multiple changes to cells affecting the results of our worksheet.

Excel's Scenario Manager feature makes it easy to automate your what-if models. You can store different sets of input values (called changing cells byScenario Manager) for any number of variables and give a name to each set.You can then select a set of values by name, and Excel displays the worksheetby using those values. Next we will try out the Scenario Manager.

1. Click on the Scenario worksheet tab

2. Click on Tools in the dropdown menus

3. Click on Scenarios as in Figure SC-01

4. Click on Add in the Scenario Manager windowShown in Figure SC-02

5. Click in the Scenario name: box of The Edit Scenario window that popsup

6. Type in Loan_175_30_700

7. Click in the Changing cells: box

8. Click on the contact button

9. Click on cell C4 10. Type in a comma


12. Type in a comma


14. Click on the expand button

Figure SC-01

Figure SC-02



35. Click Add to add a sixth scenario

36. Type in Loan_160_15_650 in the Scenario name: box

37. Uncheck the Prevent changes box

38. In the Scenario Values window type 160000 in the Purchase_Price box

39. In the Scenario Values window type 15 in the Loan_Term box

40. In the Scenario Values window type 0.065 in the Interest_Rate box

41. Click OK

The Scenario Manager now looks like Figure SC-05

42. Click the Summary button43. In the Scenario Summary window that pops up leave the Scenario

summary box checked

44. Click in the Result Cells box and highlight cells C10 through C13

45. Click OK

Excel has added a worksheet called Scenario Summary containing the resultsof the various summaries we have built. (Figure SC-06).

Fi ure SC-05

Fi ure SC-06

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