COST BEHAVIOR
BACOSTMX Module 2
Learning Outcomes
The students should be able to:
1.
Define and describe fixed, variable and mixed costs.
2.
Separate mixed costs into their fixed and variable components using the scatter-graph
method, the high-low method, and the method of least squares.
3.
4.
5.
Explain how multiple regression can be used to assess cost behavior
Use Regression Program for separating mixed costs
Discuss the use of managerial judgement in determining cost behavior.
BACOSTMX Module 2
2
DEFINE AND DESCRIBE FIXED,
VARIABLE AND MIXED COSTS.
Learning Outcome 1
BACOSTMX Module 2
3
Cost behavior
 Used to describe whether a cost changes when the level of
output changes
 Fixed costs do not change as output changes
 Variable costs increase in total with an increase in output and
decrease in total with a decrease in output
BACOSTMX Module 2
4
Types of Cost Behavior Patterns –
Variable
A variable cost is a cost whose total dollar
amount varies in direct proportion to changes
in the activity level.
Summary of Variable and Fixed Cost Behavior
Cost
In Total
Per Unit
Variable
Total variable cost is
proportional to the activity
level within the relevant range.
Variable cost per unit remains
the same over wide ranges
of activity.
Total fixed cost remains the
same even when the activity
level changes within the
relevant range.
Fixed cost per unit goes
down as activity level goes up.
Fixed
BACOSTMX Module 2
5
Variable Costs: Illustrative example
 Nooksack Expeditions, a small company that provides daylong whitewater rafting
excursions on rivers in the North Cascade Mountains. The company provides all of the
necessary equipment and experienced guides, and it serves gourmet meals for its
guests. The meals are purchased from an exclusive caterer for $30 a person for a day
long excursion. If we look at the cost of the meals on a per person basis, it remains
constant at $30. This $30 cost per person will not change, regardless of how many
people participate in a daylong excursion. The behavior of this variable cost, on both a
per unit and a total basis, is tabulated as follows:
Number of Guests
Cost of Meals per
Guest
Total Cost of Meals
250
$30
$7,500
500
$30
$15,000
750
$30
$22,500
1,000
$30
$30,000
BACOSTMX Module 2
6
The Activity Base
(also called a cost driver)
Machine
hours
Units
produced
A measure of what
causes the
incurrence of a
variable cost
Miles
driven
Labor
hours
BACOSTMX Module 2
7
True Variable Cost – An Example
Total Overage
Charges on Cell
Phone Bill
As an example of an activity base, consider
overage charges on a cell phone bill. The activity
base is the number of minutes used above the
allowed minutes in the calling plan.
Minutes Talked
BACOSTMX Module 2
8
Types of Cost Behavior Patterns –
Variable
Variable costs remain constant if expressed on
a per unit basis.
Summary of Variable and Fixed Cost Behavior
Cost
In Total
Per Unit
Variable
Total variable cost is
proportional to the activity
level within the relevant range.
Variable cost per unit remains
the same over wide ranges
of activity.
Total fixed cost remains the
same even when the activity
level changes within the
relevant range.
Fixed cost per unit goes
down as activity level goes up.
Fixed
BACOSTMX Module 2
9
Variable Cost Per Unit – An Example
Per Minute
Overage Charge
Referring to the cell phone example, the cost per overage
minute is constant, for example 45 cents per overage minute.
Minutes Talked
BACOSTMX Module 2
10
Examples of Variable Costs
1. Merchandising companies – cost of goods sold.
2. Manufacturing companies – direct materials,
direct labor, and variable overhead.
3. Merchandising and manufacturing companies –
commissions, shipping costs, and clerical costs
such as invoicing.
4. Service companies – supplies, travel, and
clerical.
BACOSTMX Module 2
11
True Variable Costs
The amount of a true variable cost used during the
period varies in direct proportion to the activity level.
The overage charge on a cell phone bill was one
example of a true variable cost.
Cost
Direct material is
another example
of a cost that
behaves in a true
variable pattern.
Volume
BACOSTMX Module 2
12
Step-Variable Costs
Cost
A step-variable cost is a resource that is obtainable only
in large chunks (such as maintenance workers) and
whose costs change only in response to fairly wide
changes in activity.
Volume BACOSTMX Module 2
13
Step-Variable Costs
Cost
Small changes in the level of production are not
likely to have any effect on the number of
maintenance workers employed.
Volume
BACOSTMX Module 2
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Step-Variable Costs
Cost
Only fairly wide changes
in the activity level will
cause a change in the
number of maintenance
workers employed.
Volume
BACOSTMX Module 2
15
The Linearity Assumption and the Relevant
Range
Total Cost
Economist’s
Curvilinear Cost
Function
Relevant
Range
A straight line
closely
approximates a
curvilinear
variable cost
line within the
relevant range.
Accountant’s Straight-Line
Approximation (constant
unit variable cost)
Activity
BACOSTMX Module 2
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Types of Cost Behavior Patterns –
Fixed
A fixed cost is a cost whose total dollar amount
remains constant as the activity level changes.
Summary of Variable and Fixed Cost Behavior
Cost
In Total
Per Unit
Variable
Total variable cost is
proportional to the activity
level within the relevant range.
Variable cost per unit remains
the same over wide ranges
of activity.
Total fixed costs remain the
same even when the activity
level changes within the
relevant range.
Fixed cost per unit goes
down as activity level goes up.
Fixed
BACOSTMX Module 2
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Total Fixed Cost – An Example
Monthly Basic
Cell Phone Bill
For example, your cell phone bill probably includes a fixed
amount related to the total minutes allowed in your calling
plan. The amount does not change when you use more or
less allowed minutes.
Number of Minutes Used
within Monthly Plan
BACOSTMX Module 2
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Types of Cost Behavior Patterns –
Fixed
Average fixed costs per unit decrease as the
activity level increases.
Cost
In Total
Per Unit
Variable
Total variable cost is
proportional to the activity
level within the relevant range.
Variable cost per unit remains
the same over wide ranges
of activity.
Total fixed costs remain the
same even when the activity
level changes within the
relevant range.
Average fixed costs per unit
decrease as the activity
level increases.
Fixed
BACOSTMX Module 2
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Fixed Cost Per Unit Example
Cost Per Cell Phone Call
For example, the fixed cost per minute used
decreases as more allowed minutes are used.
Number of Minutes Used
within Monthly Plan
BACOSTMX Module 2
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Types of Fixed Costs
Committed
Discretionary
Long-term, cannot be
significantly reduced in
the short term.
May be altered in the
short-term by current
managerial decisions
Examples
Examples
Depreciation on Buildings
and Equipment and Real
Estate Taxes
Advertising and
Research and
Development
BACOSTMX Module 2
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Rent Cost in Thousands
of Dollars
Fixed Costs and the Relevant
Range
90
Relevant
60
Range
30
0
0
The relevant range
of activity for a fixed
cost is the range of
activity over which
the graph of the
cost is flat.
1,000
2,000
3,000
Rented Area (Square Feet)
BACOSTMX Module 2
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Fixed Costs and the Relevant
Range
For example, assume office space is available at
a rental rate of $30,000 per year in increments of
1,000 square feet.
Fixed costs would increase
in a step fashion at a rate of
$30,000 for each additional
1,000 square feet.
BACOSTMX Module 2
23
Fixed Costs and the Relevant
Range
How does this
step-function
pattern differ from a
step-variable cost?
BACOSTMX Module 2
Step-variable costs
can be adjusted more
quickly as conditions
change and . . .
The width of the activity
steps is much wider for
the fixed cost.
24
Mixed Costs
(also called semivariable costs)
A mixed cost contains both variable and fixed
elements. Consider the example of utility cost.
Total Utility Cost
Y
Variable
Cost per KW
X
Activity (Kilowatt Hours)
BACOSTMX Module 2
Fixed Monthly
Utility Charge
25
Mixed Costs
The total mixed cost line can be expressed
as an equation: Y = a + bX
Where:
Y
Y
a
Total Utility Cost
b
X
= The total mixed cost.
= The total fixed cost (the
vertical intercept of the line).
= The variable cost per unit of
activity (the slope of the line).
= The level of activity.
Variable
Cost per KW
X
Activity (Kilowatt Hours)
BACOSTMX Module 2
Fixed Monthly
Utility Charge
26
Mixed Costs – An Example
If your fixed monthly utility charge is $40, your
variable cost is $0.03 per kilowatt hour, and your
monthly activity level is 2,000 kilowatt hours, what is
the amount of your utility bill?
Y = a + bX
Y = $40 + ($0.03 × 2,000)
Y = $100
BACOSTMX Module 2
27
SEPARATE MIXED COSTS INTO THEIR FIXED AND
VARIABLE COMPONENTS USING THE SCATTER-GRAPH
METHOD, HIGH-LOW METHOD,, AND METHOD OF LEAST
SQUARES.
Learning Outcome 2
BACOSTMX Module 2
28
Method of Separating Mixed Costs
Scattergraph
method
High-low
method
Account
analysis
Least-square
regression
method
Engineering
approach
BACOSTMX Module 2
29
The Scatter-graph Method
Plot the data points on a graph
(Total Cost Y vs. Activity X).
Maintenance Cost
1,000’s of Dollars
Y
20
* *
* *
10
0
0
1
2
* ** *
**
3
4
X
Patient-days in 1,000’s
BACOSTMX Module 2
30
The Scatter-graph Method
Draw a line through the data points with about an
equal numbers of points above and below the line.
Maintenance Cost
1,000’s of Dollars
Y
20
* *
* *
10
0
0
1
2
* ** *
**
3
4
X
Patient-days in 1,000’s
BACOSTMX Module 2
31
The Scatter-graph Method
Maintenance Cost
1,000’s of Dollars
Use one data point to estimate the total level of activity
and the total cost.
Y Total maintenance cost = $11,000
20
* *
* *
10
* ** *
**
Intercept = Fixed cost: $10,000
0
0
1
Patient days = 800
2
3
4
X
Patient-days in 1,000’s
BACOSTMX Module 2
32
The Scatter-graph Method
Make a quick estimate of variable cost per unit and
determine the cost equation.
Total maintenance at 800 patients
Less: Fixed cost
Estimated total variable cost for 800 patients
Variable cost per unit = $1,000
800
$ 11,000
10,000
$ 1,000
= $1.25/patient-day
Y = $10,000 + $1.25X
Total maintenance cost
Number of patient days
BACOSTMX Module 2
33
Method of Separating Mixed Costs
Scattergraph
method
High-low
method
Account
analysis
Least-square
regression
method
Engineering
approach
BACOSTMX Module 2
34
The High-Low Method – An Example
Assume the following hours
of maintenance work and
the total maintenance costs
for six months.
BACOSTMX Module 2
35
The High-Low Method – An Example
The variable cost
per hour of
maintenance is
equal to the change
in cost divided by
the change in hours.
$2,400
= $6.00/hour
400
BACOSTMX Module 2
36
The High-Low Method – An Example
Total Fixed Cost = Total Cost – Total Variable Cost
Total Fixed Cost = $9,800 – ($6/hour × 850 hours)
Total Fixed Cost = $9,800 – $5,100
Total Fixed Cost = $4,700
BACOSTMX Module 2
37
The High-Low Method – An Example
The Cost Equation for Maintenance
Y = $4,700 + $6.00X
BACOSTMX Module 2
38
Method of Separating Mixed Costs
Scattergraph
method
High-low
method
Account
analysis
Least-square
regression
method
Engineering
approach
BACOSTMX Module 2
39
Least-Squares Regression Method
A method used to analyze mixed costs if a
scattergraph plot reveals an approximately linear
relationship between the X and Y variables.
This method uses all of the
data points to estimate
the fixed and variable
cost components of a
mixed cost.
The goal of this method is
to fit a straight line to the
data that minimizes the
sum of the squared errors.
BACOSTMX Module 2
40
Least-Squares Regression Method
 Software can be used to
fit a regression line
through the data points.
 The cost analysis
objective is the same:
 Y = a + bX
Least-squares regression also provides a statistic, called
the R2, which is a measure of the goodness
of fit of the regression line to the data points.
BACOSTMX Module 2
41
Regression Analysis Assumptions
Independent variable must be a valid predictor of
the dependent variable
Coefficient of correlation
Reliable only within the relevant range
Useful only as long as circumstances existing at
the time of its development remain constant
Strategic Cost Management
PARAMETERS
 The coefficients in an equation that determine the exact
mathematical relation among the variables.
Sample:
𝐶 = 𝑎 + 𝑏𝑄 + 𝑐𝑄2 + 𝑑𝑄 3
Parameters
Illustration
 Suppose the values of the parameters of the cost equation
are determined to be:
a = 1,262, b = 1.0, c = -0.03 and d = 0.005
 The cost equation can be expressed as:
𝟐
𝑪 = 𝟏, 𝟐𝟔𝟐 + 𝟏𝑸 − 𝟎. 𝟎𝟑𝑸 + 𝟎. 𝟎𝟓𝑸
𝟑
Illustration
𝑪 = 𝟏, 𝟐𝟔𝟐 + 𝟏𝑸 − 𝟎. 𝟎𝟑𝑸𝟐 + 𝟎. 𝟎𝟓𝑸𝟑
 If, for example, the manager wishes to produce 30 units of output,
the total cost can be calculated as:
 𝑪 = 𝟏, 𝟐𝟔𝟐 + 𝟑𝟎 − 𝟎. 𝟎𝟑 𝟑𝟎𝟐 + 𝟎. 𝟎𝟎𝟓 𝟑𝟎𝟑 = 𝟏, 𝟒𝟎𝟎
Simple linear regression model
In the simple linear regression model, the
dependent variable Y is related to only one
explanatory variable X, and the relation
between X and Y is linear:
Y = a + bX
Dependent variable
Slope
Independent variable
Illustration:
Month
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
Σ
Average
n
Units
Produced
X
21,000
33,000
38,000
20,000
18,000
44,000
27,000
23,000
45,000
31,000
31,500
23,500
355,000
29,583
12
Maintenance
Costs
Y
$79,000
83,000
84,000
60,000
59,000
102,000
81,000
74,000
106,000
90,000
98,000
94,000
1,010,000
84,167
Strategic Cost Management
XY
$1,659,000,000
$2,739,000,000
$3,192,000,000
$1,200,000,000
$1,062,000,000
$4,488,000,000
$2,187,000,000
$1,702,000,000
$4,770,000,000
$2,790,000,000
$3,087,000,000
$2,209,000,000
31,085,000,000
x2
441,000,000
1,089,000,000
1,444,000,000
400,000,000
324,000,000
1,936,000,000
729,000,000
529,000,000
2,025,000,000
961,000,000
992,250,000
552,250,000
11,422,500,000
Simple Linear Regression Graph
Regression Line
MAINTENANCE COSTS
120 000,00
Maintenance Costs
100 000,00
80 000,00
y = 1.3101x + 45410
R² = 0.6381
60 000,00
40 000,00
20 000,00
0
5000
10000
15000
20000
25000
30000
Units Produced
Strategic Cost Management
35000
40000
45000
50000
INTERCEPT PARAMETER
 The parameter that gives the value of Y at the point where the
regression line crosses the Y-axis
Y = a + bX
Parameter a
Simple Linear Regression GraphY-intercept
or Parameter
a
MAINTENANCE COSTS
120 000,00
Maintenance Costs
100 000,00
80 000,00
y = 1.3101x + 45410
R² = 0.6381
60 000,00
40 000,00
20 000,00
0
5000
10000
15000
20000
25000
30000
Units Produced
Strategic Cost Management
35000
40000
45000
50000
Slope parameter
 the slope of the regression line,
𝑏 =
∆𝑌
∆𝑋
 or the change in Y associated with a one-unit change in X.
Y = a + bX
Parameter b
Simple Linear Regression GraphSlope or
Parameter b
MAINTENANCE COSTS
120 000,00
Maintenance Costs
100 000,00
80 000,00
y = 1.3101x + 45410
R² = 0.6381
60 000,00
40 000,00
20 000,00
0
5000
10000
15000
20000
25000
30000
Units Produced
Strategic Cost Management
35000
40000
45000
50000
Strategic Cost Management
Illustration:
Month
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
Units
Produced
X
21,000
33,000
38,000
20,000
18,000
44,000
27,000
23,000
45,000
31,000
31,500
23,500
Maintenance
Costs
Y
$79,000
83,000
84,000
60,000
59,000
102,000
81,000
74,000
106,000
90,000
98,000
94,000
Strategic Cost Management
Illustration:
Month
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
Σ
Average
n
Units
Produced
X
21,000
33,000
38,000
20,000
18,000
44,000
27,000
23,000
45,000
31,000
31,500
23,500
355,000
29,583
12
Maintenance
Costs
Y
$79,000
83,000
84,000
60,000
59,000
102,000
81,000
74,000
106,000
90,000
98,000
94,000
1,010,000
84,167
XY
$1,659,000,000
$2,739,000,000
$3,192,000,000
$1,200,000,000
$1,062,000,000
$4,488,000,000
$2,187,000,000
$1,702,000,000
$4,770,000,000
$2,790,000,000
$3,087,000,000
$2,209,000,000
31,085,000,000
Strategic Cost Management
x2
441,000,000
1,089,000,000
1,444,000,000
400,000,000
324,000,000
1,936,000,000
729,000,000
529,000,000
2,025,000,000
961,000,000
992,250,000
552,250,000
11,422,500,000
Simple Linear Regression:
b
1.310095066
Illustration:
Month
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
Σ
Average
n
Units
Produced
X
21,000
33,000
38,000
20,000
18,000
44,000
27,000
23,000
45,000
31,000
31,500
23,500
355,000
29,583
12
Maintenance
Costs
Y
$79,000
83,000
84,000
60,000
59,000
102,000
81,000
74,000
106,000
90,000
98,000
94,000
1,010,000
84,167
a
r
r2
XY
$1,659,000,000
$2,739,000,000
$3,192,000,000
$1,200,000,000
$1,062,000,000
$4,488,000,000
$2,187,000,000
$1,702,000,000
$4,770,000,000
$2,790,000,000
$3,087,000,000
$2,209,000,000
31,085,000,000
Strategic Cost Management
45,409.69
0.798820062
64%
x2
441,000,000
1,089,000,000
1,444,000,000
400,000,000
324,000,000
1,936,000,000
729,000,000
529,000,000
2,025,000,000
961,000,000
992,250,000
552,250,000
11,422,500,000
Simple Linear Regression Graph
MAINTENANCE COSTS
120 000,00
Maintenance Costs
100 000,00
80 000,00
y = 1.3101x + 45410
R² = 0.6381
60 000,00
40 000,00
20 000,00
0
5000
10000
15000
20000
25000
30000
Units Produced
Strategic Cost Management
35000
40000
45000
50000
Lines
 Another way to evaluate the relationships between two
variables is to compute the coefficient of correlation.
 This measure expresses the degree or strength of the linear
relationship.
 Usually identified as r, the coefficient of correlation can be
any number between +1 and -1.
Strategic Cost Management
Coefficient of Correlation
 To compute r, we use much of the same data needed earlier
to calculate a and b for the regression line. The rather lengthy
equation for r is:
Strategic Cost Management
Simple Linear
Regression:
b
1.310095066
Simple Linear Regression Graph
A
r
r2
MAINTENANCE COSTS
120 000,00
45,409.69
0.798820062
64%
Maintenance Costs
100 000,00
80 000,00
y = 1.3101x + 45410
R² = 0.6381
60 000,00
40 000,00
20 000,00
0
5000
10000
15000
20000
25000
30000
Units Produced
Strategic Cost Management
35000
40000
45000
50000
Coefficient of Correlation
Strategic Cost Management
Coefficient of Determination
 The coefficient of determination is simply the square of the coefficient of
correlation – namely, r2.
 The value of r2 will always be a positive number in the range 0 ≤ r2 ≤ 1. The
coefficient of determination is the percent of variation in the dependent variable
(y) that is explained by the regression equation.
Strategic Cost Management
Simple Linear
Regression:
b
1.310095066
Simple Linear Regression Graph
a
r
r2
MAINTENANCE COSTS
120 000,00
45,409.69
0.798820062
64%
Maintenance Costs
100 000,00
80 000,00
y = 1.3101x + 45410
R² = 0.6381
60 000,00
40 000,00
20 000,00
0
5000
10000
15000
20000
25000
30000
Units Produced
Strategic Cost Management
35000
40000
45000
50000
Least-Squares Regression
Method
 Software can be used to
fit a regression line
through the data points.
 The cost analysis
objective is the same:
 Y = a + bX
Least-squares regression also provides a statistic, called
the R2, which is a measure of the goodness
of fit of the regression line to the data points.
Strategic Cost Management
Least-Squares Regression
Method
Total Cost
R2 is the percentage of the variation in the dependent
variable (total cost) that is explained by variation in the
independent variable (activity).
Y
20
* *
* *2
10
* ** *
**
R varies from 0% to 100%, and
the higher the percentage the better.
0
0
1
2
3
Activity
BACOSTMX Module 2
4
X
66
Comparing Results From the Three
Methods
The three methods just discussed provide
slightly different estimates of the fixed and
variable cost components of the mixed cost.
This is to be expected because each method
uses differing amounts of the data points to
provide estimates.
Least-squares regression provides the most
accurate estimate because it uses all the data
points.
BACOSTMX Module 2
67
EXPLAIN HOW MULTIPLE REGRESSION
CAN BE USED TO ASSESS COST
BEHAVIOR
Learning Outcome 3
BACOSTMX Module 2
68
Multiple Regression
• Used whenever least squares is used to fit an equation
involving two or more independent variables
• Linear equation is expanded to include the additional variable
when there are two explanatory variables
Y = F + V1X1 + V2X2
 Where
 X1 = Number of moves
 X2 = Number of pounds moved
BACOSTMX Module 2
69
USE REGRESSION PROGRAM FOR
SEPARATING MIXED COSTS
Learning Outcome 4
BACOSTMX Module 2
70
Simple Regression Analysis – An
Example
Matrix, Inc. wants to
know its average
fixed cost and
variable cost per unit.
Using the data to the
right, let’s see how to
do a regression using
Microsoft Excel.
BACOSTMX Module 2
71
Simple Regression Using Excel
– An Example
You will need three pieces of
information from your
regression analysis:
1. Estimated Variable Cost Per
Unit (line slope)
2. Estimated Fixed Costs (line
intercept)
3. Goodness of fit, or R2
To get these three pieces
information we will need to
use three Excel functions.
SLOPE, INTERCEPT, and RSQ
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Simple Regression Using Excel –
An Example
Place your cursor in
cell F4 and press the
= key. Click on the
pull down menu and
scroll down to “More
Functions . . .”
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Simple Regression Using Excel – An Example
Scroll down to the
“Statistical”,
functions. Now
scroll down the
statistical
functions until you
highlight
“SLOPE”
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Simple Regression Using Excel – An Example
1. In the Known_y’s box, enter C4:C19 for the range.
2. In the Known_x’s box, enter D4:D19 for the range.
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Simple Regression Using Excel – An Example
Here is the
estimate of the
slope of the line.
1. In the Known_y’s box, enter C4:C19 for the range.
2. In the Known_x’s box, enter D4:D19 for the range.
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Simple Regression Using Excel – An Example
With your cursor in
cell F5, press the =
key and go to the pull
down menu for
“Special Functions.”
Select Statistical and
scroll down to
highlight the
INTERCEPT function.
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Simple Regression Using Excel – An Example
Here is the
estimate of the
fixed costs.
1. In the Known_y’s box, enter C4:C19 for the range.
2. In the Known_x’s box, enter D4:D19 for the range.
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Simple Regression Using Excel – An Example
Finally, we will
determine the
“goodness of
fit”, or R2, by
using the RSQ
function.
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Simple Regression Using Excel – An Example
Here is the
estimate of R2.
1. In the Known_y’s box, enter C4:C19 for the range.
2. In the Known_x’s box, enter D4:D19 for the range.
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Using Data Analysis using Excel
 Enter the data
 Choose “Data Analysis” option from the “Tools” menu
 If not available, choose "Add-ins" and select "Analysis ToolPak" to add the data
analysis tools
 Click on “Regression”
 Click on “Input Y Range” and highlight the dependent variables
column
 Click on “Input X Range” and highlight the independent variables
column
 Choose preferred location for output
 Click “OK”
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Spreadsheet Data – Simple Linear
Regression
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Simple Linear Regression Result
𝑌 = 2,618.72 + 2.77𝑥
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Reliability of Cost Formulas
 Statistical assessments concerning the cost formula’s
reliability
 Hypothesis test of cost parameters: Indicates whether the
parameters are different from zero
 Goodness of fit: Measures the degree of association between cost
and activity output
 Confidence intervals - Provide a range of values for the actual cost
with a prespecified degree of confidence
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Hypothesis test of cost parameters
t Stat tests the hypothesis that the parameters
are different from zero
P-value is the level of significance achieved
 P-value of 0.05 or less is needed for significance
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Hypothesis test of cost parameters
 Rule of Thumb for Using t-Statistics
 When the absolute value of the t-statistic is greater than 2,
the manager can be 95 percent confident that the true value
of the underlying parameter in the regression is not zero.
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Goodness of fit measures
Coefficient of determination (R2)
 Percentage of variability in the dependent variable
explained by an independent variable
 R2 always has a value between 0 and 1.00
 Adjusted R Square is used because R2 value has been
adjusted for the number of variables included in the
equation
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Coefficient of Correlation
 Square root of the coefficient of determination when there is
one independent variable
 Ranges between −1 and +1
 Higher the magnitude, the greater the correlation
 Value close to zero indicates no correlation
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Spreadsheet Data – Multiple Regression
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Multiple Regression Result
𝑌 = 507.31 + 7.84𝑥 1 + 0.11𝑥 2
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DISCUSS THE USE OF MANAGERIAL
JUDGEMENT IN DETERMINING COST
BEHAVIOR.
Learning Outcome 4
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Analysis of Mixed Costs
Account Analysis and the Engineering Approach
In account analysis, each account is
classified as either variable or fixed based
on the analyst’s knowledge of how
the account behaves.
The engineering approach classifies
costs based upon an industrial
engineer’s evaluation of production
methods, and material, labor and
overhead requirements.
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References:
 Raiborn and Kinney (2011) Cost
Accounting: Foundations and Evolution
8th edition, Cengage Learning
 Hansen, Don R. and Mowen, Maryanne
M. (2018) Cost Accounting and Control.
Cengage Learning: Boston, USA.
 Garrison, Noreen, and Brewer (2010)
Cost Accounting and Control 13th edition,
McGraw-Hill
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