Chapter 3 Cost Behavior Cornerstones of Managerial Accounting

Chapter 3: Cost Behavior Cornerstones of Managerial Accounting, 4 e © 2012 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use.

Learning Objectives 1. Explain the meaning of cost behavior, and define and describe fixed and variable costs. 2. Define and describe mixed and step costs. 3. Separate mixed costs into their fixed and variable components using the high-low method, the scattergraph method, and the method of least squares. 4. (Appendix 3 A) Use a personal computer spreadsheet program to perform the method of least squares. © 2012 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use.

1 Basics of Cost Behavior ► Cost behavior is the foundation upon which managerial accounting is built. ► Cost behavior is the general term for describing whether a cost changes when the level of output changes. ► Costs can be variable, fixed, or mixed. ► A cost that does not change in total as output changes is a fixed cost. ► A variable cost, on the other hand, increases in total with an increase in output and decreases in total with a decrease in output. ► Knowing how costs change as output changes is essential to planning, controlling, and decision making. © 2012 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use.

1 Measures of Output and the Relevant Range ► Fixed and variable costs have meaning only when related to some output measure. ► A cost driver is a causal factor that measures the output of the activity that leads (or causes) costs to change. ► Identifying and managing drivers helps managers better predict and control costs. ► For example, weather is a significant driver in the airline industry. © 2012 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use.

1 Relevant Range and Cost Relationships ► The relevant range is the range of output over which the assumed cost relationship is valid for the normal operations of a firm. ► The relevant range limits the cost relationship to the range of operations that the firm normally expects to occur. As this graph shows, the concept of the relevant range allows managerial accountants to assume a linear cost relationship. © 2012 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use.

1 Fixed Costs ► Fixed costs are costs that in total are constant within the relevant range as the level of output increases or decreases. ► In this example of Colley Computers, notice while the total fixed cost of supervision remains the same, the unit cost decreases as more computers are produced. © 2012 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use.

1 ► ► Fixed Costs (continued) The number of computers produced is called the output measure, or driver. Even though fixed costs may change, this possibility does not make them variable. They are fixed at a new higher (or lower) rate. A graph of Colley’s fixed supervision costs is shown below: Supervision cost is fixed with respect to the number of computers produced. © 2012 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use.

1 Discretionary Fixed Costs and Committed Fixed Costs ► Two types of fixed costs are commonly recognized: discretionary fixed costs and committed fixed costs. ► Discretionary fixed costs are fixed costs that can be changed or avoided relatively easily at management discretion. ► Committed fixed costs, on the other hand, are fixed costs that cannot be easily changed. Advertising is a discretionary fixed cost, because it depends on a management decision. Lease cost is a committed fixed cost because it involves a long-term contract. © 2012 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use.

1 Variable Costs ► Variable costs are costs that in total vary in direct proportion to changes in output within the relevant range. ► Variable costs can also be represented by a linear equation. ► Total variable costs depend on the level of output. ► This relationship can be described by the following equation or graphs: Total variable costs = Variable rate x Amount of output © 2012 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use.

The Reasonableness of 1 Straight-Line Cost Relationships ► Caution should be taken when applying cost behavior assumptions to output levels that fall outside of the company’s relevant range of operations. ► Straight-line cost relationships that are assumed within the relevant range may actually be semi-variable costs. For example, at extremely low levels of output, workers often use more materials per unit or require more time per unit than they do at higher levels of output. Likewise, as the level of output increases, workers learn how to use materials and time more efficiently so that the variable cost per unit decreases as more and more output is produced. © 2012 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use.

2 Mixed Costs ► Mixed costs are costs that have both a fixed and a variable component. For example, overhead for a company may consist of a fixed supervisor salary plus the cost of supplies that vary with the quantity of output produced. The formula and graph depiction for a mixed cost is as follows: Total cost = Total fixed cost + Total variable cost Volume © 2012 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use.

2 Step Costs: Narrow Steps ► Some cost functions may be discontinuous. ► These costs are known as step costs (or semi-fixed). ► A step cost displays a constant level of cost for a range of output and then jumps to a higher level (or step) of cost at some point, where it remains for a similar range of output. ► If a step cost has relatively narrow steps, it means that the cost changes in response to fairly small changes in output and we can approximate it as a variable cost (i. e. , the red line). © 2012 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use.

2 Step Costs: Wide Steps ► Step cost with relatively wide steps are more characteristic of fixed costs. ► For example, a company may have to lease production machinery. If the machine can only produce 1, 000 units and the company grows, they will have to lease additional machines for each 1, 000 units of production needed (resulting in the wide steps shown in the graph). © 2012 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use.

2 Accounting Records and Need for Cost Separation ► Only through a formal effort to separate costs can all costs be classified into the appropriate cost behavior categories. ► If mixed costs are a very small percentage of total costs, formal cost separation may be more trouble than it’s worth. ► In this case, mixed costs could be assigned to either the fixed or variable cost category without much concern for the classification error or its effect on decision making. ► Alternatively, the total mixed cost could be arbitrarily divided between the two cost categories. (This is rarely done and not a good option. ) ► Typically, mixed costs for many firms are large enough to call for separation. © 2012 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use.

Methods for Separating Mixed Costs 3 into Fixed and Variable ►Three methods of. Components separating a mixed cost into its fixed and variable components are commonly used: ►the high-low method ►the scattergraph method ►the method of least squares ►Each method requires the simplifying assumption of a linear cost relationship. © 2012 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use.

Methods for Separating Mixed Costs 3 into Fixed and Variable Components (continued) ► Recall the expression of cost as an equation for a straight line is: ►Total cost = Fixed cost + (Variable rate x Output) ► The dependent variable is a variable whose value depends on the value of another variable. In the previous equation, total cost is the dependent variable; it is the cost we are trying to predict. ► The independent variable is a variable that measures output and explains changes in the cost or other dependent variable. ► A good independent variable is one that causes or is closely associated with the dependent variable. ► Therefore, many managers refer to an independent variable as a cost driver. ► The intercept corresponds to fixed cost. ► The slope of the cost line corresponds to the variable rate. © 2012 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use.

3 Cornerstone 3 -1 Creating and Using A Cost Formula © 2012 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use.

3 Cornerstone 3 -1 Creating and Using A Cost Formula (continued) © 2012 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use.

3 The High-Low Method ► Given two points, the slope and the intercept can be determined. ► The high-low method is method of separating mixed costs into fixed and variable components by using just the high and low data points. ► To demonstrate, we will use data from materials handling costs at Anderson Company: © 2012 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use.

3 The High-Low Method ► Four steps must be taken in the high-low method: ►Step 1: Find the high point and the low point for a given data set. ►Step 2: Using the high and low point, calculate the variable rate. ►Variable rate = (High point cost - Low point cost) ÷ (High point output - Low point output) ►Step 3: Calculate the fixed cost using the variable rate (from Step 2) and either the high point or low point. ►Fixed cost = Total cost at high point - (Variable rate x Output at high point) ►Step 4: Form the cost formula for materials handling based on the high-low method. © 2012 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use.

Cornerstone 3 -2 Using The High-Low Method to Calculate Fixed Cost and the Variable Rate and to Construct a Cost Formula Solution: Step 1—Find the high and low points: The high number of machine hours is in March, and the low number of machine hours is in June. (Hint: Did you notice that the high cost of $4, 200 was for August? Yet August is not the high point because its number of machine hours is not the highest activity level. Remember, the high point is associated with the highest activity level; the low point is associated with the lowest activity level. ) © 2012 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use.

3 Cornerstone 3 -2 Using The High-Low Method to Calculate Fixed Cost and the Variable Rate and to Construct a Cost Formula (continued) © 2012 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use.

3 Cornerstone 3 -3 Using The High-Low Method to Calculate Predicted Total Variable Cost and Total Cost for Budgeted Output Information: Recall that Blue. Denim Company constructed the following formula for monthly electricity cost. (Refer to Cornerstone 3 -2 to see how the fixed cost per month and the variable rate were computed. ) Total electricity cost = $440 + ($6. 10 x Machine hours) Required: Assume that 550 machine hours are budgeted for the month of October. Use the previous cost formula for the following calculations: 1. Calculate total variable electricity cost for October. 2. Calculate total electricity cost for October. Solution: 1. Total variable electricity cost = Variable rate x Machine hours = $6. 10 x 550 = $3, 355 2. Total electricity cost = Fixed cost + (Variable rate x Machine hours) = $440 + ($6. 10 x 550) = $440 + $3, 355 = $3, 795 © 2012 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use.

3 Cornerstone 3 -4 Using The High-Low Method to Calculate Predicted Total Variable Cost and Total Cost for A Time Period that Differs from the Data Period © 2012 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use.

3 Cornerstone 3 -4 Using The High-Low Method to Calculate Predicted Total Variable Cost and Total Cost for A Time Period that Differs from the Data Period (continued) © 2012 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use.

3 Scattergraph Method ► The scattergraph method is a way to see the cost relationship by plotting the data points on a graph. ► The first step in applying the scattergraph method is to plot the data points so that the relationship between materials handling costs and activity output can be seen. © 2012 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use.

3 Scattergraph Method (continued) ► Then we inspect the scattergraph to see if it reveals one or more points (outliers) that do not seem to fit the general pattern of behavior. ► This knowledge might justify their elimination and perhaps lead to a better estimate of the underlying cost function. © 2012 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use.

3 Scattergraph Method (continued) ► Next, we should question whether the line determined by the high and low points is representative of the overall relationship. ► Notice that three points lie above the high-low line, but five points lie below it. ► This does not give us confidence in the high-low results for fixed and variable costs. ► In particular, we might wonder if the variable cost (slope) is somewhat higher than it should be and the fixed cost is somewhat lower than it should be. © 2012 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use.

3 Scattergraph Method (continued) ► Finally, we can use the scattergraph to visually fit a line to the data points on the graph. ► Of course, the manager or cost analyst will choose the line that appears to fit the points the best, and perhaps that choice will take into account past experience with the behavior of the cost item. ► An infinite number of lines might go through the data, but this one goes through the point for January (100, $2, 000) and intersects the y-axis at $800. © 2012 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use.

3 Scattergraph Method (continued) ► First, remember that our two points are (100, $2, 000) and (0, $800). Next, use these two points to compute the variable rate (the slope): Variable rate = ($2, 000 - $800) $100 - 0 = $1, 200/100 = $12 ► Thus the variable rate is $12 per material move. ► The fixed cost and variable rate for materials handling cost have now been identified. ► The cost formula for the materials handling activity can be expressed as: Total cost = $800 + ($12 x Number of moves) © 2012 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use.

3 Using the Formula from the Scattergraph Method ► Using this formula, the total cost of materials handling for between 100 and 500 moves can be predicted and then broken down into fixed and variable components. ► For example, assume that 350 moves are planned for November. ► Using the cost formula, the predicted cost is: $5, 000 = $800 + ($12 x 350) ► Of this total cost, $800 is fixed, and $4, 200 is variable. ► Unfortunately, the scattergraph method suffers from the lack of any objective criterion for choosing the best-fitting line. ► The quality of the cost formula depends on the quality of the subjective judgment of the analyst. © 2012 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use.

3 The Method of Least Squares ►The method of least squares (regression) is a statistical way to find the best-fitting line through a set of data points. ►One advantage of the method of least squares is that for a given set of data, it will always produce the same cost formula. ►Basically, the best-fitting line is the one in which the data points are closer to the line than to any other line. © 2012 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use.

3 Line Deviations ► The regression line better describes the pattern of the data than other possible lines. ► This best description results because the squared deviations between the regression line and each data point are, in total, smaller than the sum of the squared deviations of the data points and any other line. ► The least squares statistical formulas can find the one line with the smallest sum of squared deviations or the line which minimizes the cost prediction errors or differences between predicted costs (i. e. , on the regression line) and actual costs (i. e. , the actual data points). © 2012 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use.

3 Cornerstone 3 -5 Using The Regression Method to Calculate Fixed Cost and the Variable Rate and to Construct a Cost Formula and to Determine Budgeted Cost © 2012 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use.

3 Cornerstone 3 -5 Using The Regression Method to Calculate Fixed Cost and the Variable Rate and to Construct a Cost Formula and to Determine Budgeted Cost (continued) © 2012 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use.

3 Comparison of Methods ►Knowing how costs change in relation to changes in output is essential to planning, controlling, and decision making. ►Each of the methods for separating mixed costs into fixed and variable components help managers understand cost behavior and consequently make good business decisions. © 2012 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use.

3 Comparison of Methods for Separating Fixed Costs into Fixed and Variable Components © 2012 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use.

3 Managerial Judgment ► Managerial judgment is critically important in determining cost behavior and is by far the most widely used method in practice. ► Many managers simply use their experience and past observation of cost relationships to determine fixed and variable costs. ► This method, however, may take a number of forms. ►Some managers simply assign some costs to the fixed category and others to the variable category and ignore the possibility of mixed costs. ►Other managers may identify mixed costs and divide these into fixed and variable components. © 2012 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use.

3 Managerial Judgment (continued) ► Finally, management may use experience and judgment to refine statistical estimation results. ► Perhaps the experienced manager might ‘‘eyeball’’ the data and throw out several points as being highly unusual or revise the results of estimation account for projected changes in cost structure or technology. ► The advantage of using managerial judgment to separate fixed and variable costs is its simplicity. ► In situations in which the manager has a deep understanding of the firm and its cost patterns, this method can give good results. ► However, if the manager does not have good judgment, errors will occur. © 2012 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use.

3 Ethical Decisions ► There are ethical implications to the use of managerial judgment. ► Managers use their knowledge of fixed and variable costs to make important decisions, such as whether to switch suppliers, expand or contract production, or lay off workers. ► These decisions affect the lives of workers, suppliers, and customers. ► Ethical managers will make sure that they have the best information possible when making these decisions. © 2012 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use.

3 You Decide Choosing a Cost Estimation Method Assume that you work as a financial analyst for Royal Caribbean Cruises Ltd. The company operates some of the world’s biggest cruise ships, such as The Allure of the Seas, which weighs 222, 000 tons and carries 5, 400 guests, as well as 1, 650 crew members. As an internal financial analyst, one of your most important tasks is to estimate the costs that Royal will incur on the many cruises it offers to customers each year. The accuracy with which you predict Royal’s most important cruiserelated costs will affect many of the strategic and operating decisions made by management. You are familiar with several common cost estimation methods, including scattergraph, high-low, and regression. However, you also are aware that each method has its advantages and disadvantages. Which cost estimation method should you employ? © 2012 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use.

3 You Decide Choosing a Cost Estimation Method (continued) If the scattergraph method were used, the analysis would be quite easy as you could employ Excel to quickly create a plot of the important costs against various potential cost drivers. However, this method does not involve quantitative analysis, which some individuals believe is a significant weakness. If the high-low method were adopted, the analysis would be quantitative in nature and relatively easy to conduct and explain to management. However, this method can be subject to considerable inaccuracy if one or both of the two data points used to construct the cost formula is an outlier. Finally, regression overcomes many of the weaknesses of high-low because it incorporates all of the data into its estimate of the cost formula. Nevertheless, regression can require considerably more time than other methods to collect the necessary input data, ensure their accuracy, and explain the results to the ultimate users of the results. There is no obvious, one-sizefits-all answer as to the best cost estimation method to employ. Instead, you would be wise to consult the managers who will be using your analysis. For example, does management need a general ‘‘ball park’’ estimate or does it need the most accurate estimate possible? The results from your cost analysis, along with the competitive pressures facing Royal, will affect important decisions such as how much to pay cruise ship employees to ensure a high quality customer experience, the prices to charge customers to ensure affordability yet exclusivity, and the types and quantities of food, beverages, and shopping to offer onboard the ships. Regardless of the cost estimation method ultimately selected, you likely will supplement the results with a dose of managerial judgment to help management make the best decisions possible. © 2012 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use.

4 APPENDIX 3 A: Using the Regression Programs ► Computing the regression formula manually is tedious, even with only a few data points. ► As the number of data points increases, manual computation becomes impractical. ► Fortunately, spreadsheet packages like Microsoft Excel have regression routines that perform these computations. ► All you need to do is input the data and the spreadsheet regression program supplies more than the estimates of the coefficients. ► It also provides information that can be used to see how reliable the cost equation is—a feature that is not available for the scattergraph and high-low methods. © 2012 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use.

4 Spreadsheet Data ► The first step in using the computer to calculate regression coefficients is to enter the data. The exhibit here shows the computer screen that you would see if you entered the data on material moves into a spreadsheet. ► It is a good idea to label your variables as is done in the exhibit. © 2012 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use.

4 Regression Output ► Once we run the regression, we find the fixed cost is 789 and the variable rate is 12. 38 (rounded). ► Using this information, the cost formula for materials handling cost is: Materials handling cost = $789 + $12. 38 x number of moves ► For 350 moves, the total materials handling cost predicted by the least squares line is: $5, 122 = $789 + ($12. 38 X 350) © 2012 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use.

4 Goodness of Fit ► Regression routines provide information on goodness of fit. ► Goodness of fit tells us how well the independent variable predicts the dependent variable. ► The percentage of variability in the dependent variable explained by an independent variable (in this case, a measure of activity output) is called the coefficient of determination (R -squared). ► The higher the percentage of cost variability explained, the better job the independent variable does of explaining the dependent variable. ► Since R-squared is the percentage of variability explained, it always has a value between 0 and 1. 00. © 2012 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use.

4 Regression Output ► Note that the summary output shows that the coefficient of determination, labeled as R Square (R 2) is 0. 85. ► In other words, material moves explain about 85 percent of the variability in the materials handling cost. ► This is not bad. ► However, something else explains the remaining 15 percent. The company’s controller may want to keep this in mind when using the regression results. © 2012 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use.