Practice, Practice and Practice
Section 1: Cost classification and Cost behaviour
Contents:
1.1 Nature & purpose of management accounting
1.2 Cost Classification
1.3 Cost Behaviour
1.1 Nature & purpose of Management Accounting
Financial accounting provides information to stockholders, creditors and others who are
outside the organization.
Management accounting provides information for managers inside an organization who direct
and control its operations.
Financial Accounting Management Accounting
1. Users
External persons who
make financial decisions
Managers who plan for
and control an organization
Historical perspective
Future emphasis
3. Verifiability
versus relevance
Emphasis on
verifiability
Emphasis on relevance
for planning and control
4. Precision versus
timeliness
Emphasis on
precision
Emphasis on
timeliness
5. Subject
Primary focus is on
the whole organization
Focuses on segments
of an organization
6. Requirements
Must follow GAAP
and prescribed formats
Need not follow GAAP
or any prescribed format
2. Time focus
Formulating long-and
short-term plans
(Planning)
Comparing actual
to planned performance
(Controlling)
Decision
Making
Begin
Implementing
plans (Directing and
Motivating)
Measuring
performance (Controlling)
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set/change
Strategic planning
Senior management
objectives/strategic targets
Tactical planning
(managment control)
decisions about
Efficiency & Effectiveness
Middle management
in using resources to
achieve objectives
Operational planning
(operational control)
ensure specific tasks
front-line managers
carried out effectively and
efficiently
Question 2 – Pilot paper
The following assertions relate to financial accounting and to cost accounting:
(i)
The main users of financial accounting information are external to an organisation.
(ii)
Cost accounting is that part of financial accounting which records the cash received
and payments made by an organisation.
Which of the following statements are true?
A
Assertions (i) and (ii) are both correct.
B
Only assertion (i) is correct.
C
Only assertion (ii) is correct
Question 14 A - Jun-06 exam
The following statements refer to strategic planning:
(i)
It is concerned with quantifiable and qualitative matters.
(ii)
It is mainly undertaken by middle management in an organisation.
(iii)
It is concerned predominantly with the long term.
Which of the statements are correct?
A (i) and (ii) only
B (i) and (iii) only
C (ii) and (iii) only
D (i), (ii) and (iii)
Question 9 A – Dec - 03 exam
Which of the following would be best described as a short term tactical plan?
A Reviewing cost variance and investigate as appropriate
B Comparing actual market share to budget
C Lowering the selling price by 15%
D Monitoring actual sales to budget
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Question 9 A – Jun 05 exam
Which of the following statement are correct?
(i)
Strategic information is mainly used by senior management in an organization.
(ii)
Productivity measurements are examples of tactical information.
(iii)
Operational information is required frequently by its main users.
A (i) and (ii) only
B (i) and (iii) only
C (ii) and (iii) only
D (i), (ii) and (iii)
Question 5 A – Jun 07 exam
The following statements refer to different types of planing within a manufacturing
organisation:
(i)
Operational planning includes the scheduling of work to be done in the short term.
(ii)
Tactical planning includes consideration of ways in which the productivity of the
factory workforce could be improved.
(iii)
Strategic planning includes the setting of the organisation’s long term objectives..
A (i) and (ii) only
B (i) and (iii) only
C (ii) and (iii) only
D (i), (ii) and (iii)
Question 5 A – Dec06 exam
The following statements refer to qualities of good information:
(i)
It should be communicated to the right person.
(ii)
It should always be completely accurate before it is used.
(iii)
It should be understandable by the recipient.
A (i) and (ii) only
B (i) and (iii) only
C (ii) and (iii) only
D (i), (ii) and (iii)
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1.2 Cost Classification
Costs concepts:
Cost object - is any activity for which a separate measurement of costs is desired. eg
cost of product, cost of service
Costs unit - is a unit of product or service to which costs can be related - a basic
control unit for costing purposes
Responsibility centers - a department or organisational functions whose performance is
the direct responsibility of a specific manager
Cost centers - A segment whose manager has control over costs, but not over
revenues or investment funds.
Revenue centers - similar to cost centers but accountable for revenue
Profit centers - A segment whose manager has control over both costs and revenues,
but no control over investment funds.
Investment centers - is profit centers with additional responsibilities for capital
investment - measure it's performance by ROI
Cost
Center
Revenue
Center
Profit
Center
Investment
Center
Responsibility
Center
Question 6 A - Jun-06 exam
The following statements relate to responsibility centres:
(i)
Return on capital employed is a suitable measure of performance in both profit
and investment centres.
(ii)
Cost centres are found in manufacturing organisations but not in service
organisations.
(iii)
The manager of a revenue centre is responssible for both sales and costs in a
part of an organisation.
Which of the statements, if any, is true?
A (i) only
B (ii) only
C (iii) only
D None of them
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Question 12 A - Dec-06 exam
A paint manufacturer has a number of departments. Each department is located in a separate
building on the same factory site. In the mixing department the basic raw materials are mixed
together in very large vessels. These are then moved on to the colour adding department
where paints of different colours are created in these vessels. In the next department – the
pouring department – the paint is poured from these vessels into litre sized tins. The tins then
go on to the labelling department prior to going on to the finished goods department.
The following statements relate to the paint manufacturer:
(i)
The mixing department is a cost centre.
(ii)
A suitable cost unit for the colour department is a litre tin of paint.
(iii)
The pouring department is a profit centre.
Which statement or statements is/are correct?
A (i) only
B (i) and (ii) only
C (i) and (iii) only
D (ii) and (iii) only
Costs classified by function
Production - this is the most important of all in cost accounting. It is incurred in
producing a product
•Direct materials:
–Those materials that become an integral part of the product and that can be
conveniently traced directly to it.
•Direct labor:
–Those labor costs that can be easily traced to individual units of product.
•Manufacturing overhead:
–Manufacturing costs that cannot be traced directly to specific units produced.
Administration - This cost is connected to the office and is generally for clerical
work
Eg, Reception, photocopy, fax,...
Selling and distribution - This cost is incurred when selling and distributing
products to the customer
Eg, salesman's salaries, carriage outwards, advertising, promotion...
Financing - This cost is connected to the reporting and maintaining of the
accounts,
Eg, Interest, audit fees, accountant's salary...
Research and development - This cost is incurred in processes of research and
develop a new product, patent or formulae of new product....
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Costs classification for production of a product/ service
Direct
Material
Direct
Labor
Manufacturing
Overhead
Conversion
Prime
Cost
Cost
Question 17 – Pilot Paper
A manufacturing organisation incurs costs relating to the following:
(i) Commission payable to salespersons
(ii) Inspecting all products
(iii) Packing the products at the end of manufacturing process prior to moving them to the
warehouse
Which of these costs are classified as production costs?
A (i) and (ii) only
B (i) and (iii) only
C (ii) and (iii) only
D (i), (ii) and (iii)
Product cost and period cost (for prepare financial statements)
•
Product costs are costs identified with a finished product/ produced costs
–Inventoried
–Expensed as product sold
•
Period costs are costs that are deducted as expenses in the P&L.
–Not inventoried
–Expensed as incurred
Costs
Material
Raw Materials
Direct Labor
Work in
Process
Manufacturing
Overhead
Selling and
Administrative
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Balance Sheet
Inventories
Finished
Goods
Period Costs
Income
Statement
Expenses
Cost of
Goods
Sold
Selling and
Administrative
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Direct Costs vs. Indirect Costs
• Direct costs are costs that can be easily and conveniently traced to a unit of
product or other cost object.
Examples: direct material and direct labor
• Indirect costs are costs cannot be easily and conveniently traced to a unit of
product or other cost object.
Example: manufacturing overhead
Question 21 A - Jun-07 exam
Which of the following should be classified as indirect labour?
A
Machine operators in a factory producing furniture
B
Lawyers in a legal firm
C
Maintenance workers in a power generation organization
D
Lorry drivers in a road haulage company
Avoidable vs. unavoidable costs (involve with activity of business)
Avoidable costs are specific costs of an activity or business, that would be avoided if
the activity or business did not exits. This cost can be eliminated by changing the
operation.
Eg, If a factory decide to stop produce a product, avoidable costs likely to be direct
material, labor, expenses. These costs will no longer be incurred once production stops
Unavoidable costs are costs that would be incurred whether or not an activity or
sector existed
Eg, If a factory decide to stop produce a product, Direct costs/ Prime costs are not
incurred -> Avoidable but the rent cost are unchanged. -> Un-avoidable
Controllable vs. noncontrollable cost (Influenced by management decisions)
A controllable cost is a cost which ran be influenced by management decisions and
actions
Eg. if you decide not to use taxi if no rain or if not necessary -> taxi cost is controlled.
If you strictly control your office calls/ no personal calls allowed -> Tel, cost is
controlled.
A non-controllable cost is any cost that cannot be affected by management within
a given time span.
Eg. the office renting fee is noncontrollable. But this is for a period of time... 1 year or
some years. This can be changed if you have chance to move to other premises/ places.
But this rent fee can be controllable by manager at higher levels - as he can decide the
rank of your office renting fees...
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Can You Apply these to Exam type questions?
Question 1
Classify the following items into categories
of;
a.
Prime cost
b.
Production OH
c.
Administration expenses
d.
Selling & Distribution expenses
1. Factory storekeeper's wage
2. Repairs to factory roof
3, Traveling expenses of salesman
4. Road tax for delivery vehicles
5. Costs of paper for firm's computer
6. Debt collection cost
7. Machinist wages
8. Carriage inwards on materials
9. Advertising agency fees
10. Depreciation of office equipment
11. Depreciation of car for directors use
12. Accommodation cost for salesman
13. Accountant salary
14. Showroom rent
Question 2
Catergorise the following into;
a. Production cost
b. Administration cost
c. Marketing cost
Question 3
Classify the following into groups of:
a. Direct materials
b. Direct labor
c. Production overhead
d. Research and development cost
e. Selling and distribution cost
f.
Administration cost
g. Finance cost
1. lubricant for sewing machine
2. floppy disks for general office computer
3. maintenance contract for general office
copying
4. interest on bank overdraft
5. wages of security guards for factory
6. Carriage on purchases of basic materials
7. road license for delivery vehicle
8. cost of advertising products on television
9. chief accountant's salary
10. wages of operatives in cutting
department
11. wages of storekeepers in materials store
1 2 . wages of fork lift truck drivers who
handle raw materials
13. developing new product in the laboratory
1.
2.
3.
4,
5.
6.
7.
fire insurance of factory buildings
chairman's remuneration
duty on raw materials
electricity cost for office machines
rent of stall for exhibition
printing cost of sales brochures
shipping cost of sending goods to
overseas
8. repairs to computer
9. audit fees
10. diesel for running machinery
11. maintenance of delivery vans
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Question 4
Over which of the following is the manager of a profit center likely to have control?
(i) Selling prices
(ii) Controllable costs
(iii) Apportioned head office costs
(iv) Capital investment in the centre.
A All of the above
B (i), (ii) and (iii)
C (i), (ii) and (iv)
D (i) and (ii)
Question 5
Which of the following best describes a period costs?
A A cost that relates to a time period which is recorded as expenses for the period and is not
included in the stock evaluation.
B A cost that can be easily allocated to a particular period, without the need for arbitrary
apportionment between periods.
C A cost that is identified with a unit produced during the period, and is included in the value
of stock. The cost is treated as an expenses for the period when the stock is actually sold.
D A cost that is incurred regularly every period, eg.. every month or quarter.
Question 23 A - Jun-05 exam
Reginald is the manager of production department M in a factory which has ten other
production departments. He receives monthly information that compares planned and actual
expenditure for department M. After department M, all production goes into other factory
departments to be completed prior to being despatched to customers. Decisions involving
capital expenditure in department M are not taken by Reginald.
Which of the following describes Reginald's role in department M?
A
A cost centre manager
B
An investment centre manager
C
A profit centre manager
D
A revenue centre manager
Question 18A - Jun-07 exam
The following statements relate to responsibility centers:
(i) The manager of a revenue centre is responsible for sales and costs in a segment of an
organisation.
(ii) Return on capital employed is a suitable measure of performance in a profit centre.
(iii) Cost centres are found in manufacturing and service organisations.
Which of the statements, if any, is correct?
A (i) only
B (ii) only
C (iii) only
D None of them
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Question 24 A - Dec-04 exam
Which one of the following groups of workers would be classified as indirect labour?
A
Machinists in an organisation manufacturing cloths
B
Bricklayers in a house building company
C
Maintenance workers in a shoe factory
D
Assembly workers in a vehicle manufacturing business
Question 5A - Dec-05 exam
The following statements relate to financial accounting or to cost and management
accounting:
(i) The main users of financial accounting information are external to an organization.
(ii) Cost accounting is a part of financial accounting and establishes costs incurred by an
organisation.
(iii) Management accounting is used to aid planning, control and decision making.
Which of the statements are correct?
A (i) and (ii) only
B (i) and (iii) only
C (ii) and (iii) only
D (i), (ii) and (iii) only
1.3 Cost Behaviour
Types of costs:
+ Variable costs
+ Fixed costs
+ Step costs
Fixed costs are costs that in total are constant within the relevant range as the level of the
activity driver varies.
Example: Days Computers, Inc.
Two production lines can process 10,000 computers per year each. The workers on each line
are supervised by a production-line manager who is paid $54,000 per year. For production up
to 10,000 units, only one supervisor is needed. When production is between 10,001 and
20,000 units, two supervisors are required.
Days Computers, Inc.
Supervision
$54,000
54,000
54,000
108,000
108,000
108,000
Computers
Processed
4,000
8,000
10,000
12,000
16,000
20,000
Unit Cost
$13.50
6.75
5.40
9.00
6.75
5.40
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Variable costs are costs that in total vary in direct proportion to changes in an activity
driver.
Example: Days Computers, Inc.
A CD-ROM disk drive is added to each computer at a cost of $30 per computer. The total cost
of disk drives for each level of production varies.
Days Computers, Inc.
Total Cost of
CD-ROMs
$120,000
240,000
360,000
480,000
600,000
Number of
Computers
Processed
4,000
8,000
12,000
16,000
20,000
Unit Cost of
CD-ROMs
$30.00
30.00
30.00
30.00
30.00
Semi-variable costs (mixed costs) are costs that have both a fixed and a variable
component.
Example: Days Computers, Inc.
Ten sales representatives each earn an annual salary of $30,000 plus a commission of $50
per computer sold. 10,000 computers are sold.
Y = Fixed cost + Total variable cost
Y = F + VX
where
Y = Total cost
For Days Computer, the selling cost is:
Y = $300,000 + $50X
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Days Computers, Inc.
Variable
Fixed Cost of
Selling
$300,000
300,000
300,000
300,000
300,000
Cost of
Computers Selling Cost
Selling
Total Cost
$200,000 $500,000
400,000
700,000
600,000
900,000
800,000 1,100,000
1,000,000 1,300,000
Sold
4,000
8,000
12,000
16,000
20,000
per Unit
$125.00
87.50
75.00
68.75
65.00
Step cost behavior displays a constant level of cost for a range of output and then jumps to
a higher level of cost at some point
Step-Variable costs
- Narrow increments
- Approximate as a strictly variable assumption
Step-Fixed costs
- Wide increments
- Assigned to the fixed cost category
Methods for Separating Mixed Costs into Fixed and Variable Components
•The High-Low Method
•The Scatterplot Method
•The Method of Least Squares
Straight-line equation: Y = F + VX
where
Y = Total activity cost
F = Fixed cost component
V = Variable cost per unit
X = Measure of activity output
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High – Low method
Month
January
February
March
April
May
June
July
August
September
October
Materials
Number of
Handling Cost
Moves
$2,000
3,090
2,780
1,990
7,500
5,300
4,300
6,300
5,600
6,240
100
125
175
200
500
300
250
400
475
425
Low
High
Step 1: Solve for variable cost (V)
V = Change in cost ÷ Change in activity
Step 2: Using either the high cost or low cost,
solve for the total fixed costs F
S te p 1 : V =
$ 7 ,5 0 0 - $ 2 ,0 0 0
= $ 1 3 .7 5
500 - 100
Low cost
Y = F +V( X )
$2,000 = F + $13.75(100)
$625 = F
High cost
Y = F +V( X )
$7,500 = F + $13.75(500)
$625 = F
Step 3: Cost fuction Y = 625 + 13.75 X
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Scatterplot Method
Step 1: Plot the data points on a scattergraph
Step 2: Choose the two data points most representative of the data to describe
the cost behavior line
Can You Apply These to Exam type Questions?
Question 6
Fixed costs are conventionally deemed to be:
A Constant per unit of output
B Constant in total when production volume changes
C Outside the control of management
D Those unaffected by inflation
Question 7
The following data relate to the overheads expenses of a contract cleaners at two activity
levels
Square meters cleaned
12,750
15,100
Overheads
73,950$
83,585$
What is the estimate of the overheads if 16,200 square meters are to be cleaned?
A 66,420 $
B 88,095$
C 89,674$
D 83,960$
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Question 8
B Limited has recorded the following data in the two most recent periods
Total costs of production
13,500$
18,300$
Volume of production (units)
700
1,100
What is the best estimate of the company's fixed cost per period
A 13,500 $
B 13,200 $
C 5,100 $
D 4,500 $
Question 9
A production worker is paid a salary of 650 $ per month, plus an extra 5 pence for each unit
produced during the month. This labor cost is best described as:
A
a variable cost
B
a fixed cost
C
a step cost
D
a semi-variable cost
Question 10
What type of cost is supervisor salary costs, where one supervisor is needed for every ten
employees added to the staff?
A
B
C
D
a variable cost
fixed cost
a step cost
a semi-variable cost
Question 1 A - Jun-04 exam
The following diagram represents the behaviour of one element of cost:
$
Total
cost
Volume of activity
Which ONE of the following statements is consistent with the above diagram?
A. Annual factory power cost where the electricity supplier sets a tariff based on a fixed
charge plus a constant unit cost for consumption but subject to a maximum annual
charge.
B. Weekly total labour cost when there is a fixed wage for a standard 40 hour week but
overtime is paid at a premium rate
C. Total direct material cost for a period if the supplier charges a lower unit cost on all
units once a certain quantity has been purchased in that period.
D. Total direct material cost for a period where the supplier charges a constant amount
per unit for all units supplied up to a maximum charge for the period.
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Question 21 A - Dec-02 exam
A company achieves bulk buying discounts on quantities above a certain level. These
discounts are only available for the units above the specified level and not on all the units
purchased.
Which of the following graphs of total purchase cost against units best illustrated the above
situation?
B
A
$
$
Units
Units
D
C
$
$
Units
Units
Question 1 A- Jun-06 exam
A supplier of telephone services charges a fixed line rental per period. The first 10 hours of
telephone calls by the customer are free, after that all calls are charged at a constant rate per
minute up to a maximum, thereafter all calls in the period are again free.
Which of the following graphs depicts the total cost to the customer of the
telephone services in a period?
B
A
$
$
Hours
Hours
C
C
$
$
Hours
Hours
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Question 1 A- Dec-04 exam
When total purchases of raw material exceed 30,000 units in any one period then all units
purchased, including the initial 30,000, are invoiced at a lower cost per unit.
Which of the following graphs is consistent with the behavior of the total materials
cost in a period?
Question 1 A – Dec05 exam
Up to a given level of activity in each period the purchase price per unit of a raw material is
constant. After that point a lower price per unit applied both to further units purchased and
also retrospectively to all units already purchased.
Which of the following graphs depict the total costs of the raw materials for a
period?
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Question 4 A – June - 06 exam
The following production and total cost information relates to a single product organisation for
the last three months:
Month
Production
Total cost
units
$
1
1,200
66,600
2
900
58,200
3
1,400
68,200
The variable cost per unit is constant up to a production level of 2,000 units per month but a
step up of $6,000 in the monthly total fixed cost occurs when production reaches 1,100 units
per month.
What is the total cost for a month when 1,000 units are produced?
A. $54,200
B. $55,000
C. $59,000
D. $ 60,200
Question 14 A - Dec-02 exam
A company has been reviewing its total costs over the last few periods and has established
the following:
Period
Sales
Total cost
(units)
$
1
225
2,300
2
150
1,500
3
350
2,800
The company is aware that fixed costs increase by $500 when sales exceed 200 units.
What would be the total cost at a sales level of 180 units?
A. $2,120
B. $1,800
C. $1,695
D. $ 1,620
Question 7 – Pilot paper
An organisation has the following total costs at two activity levels
Activity level (units)
16,000
22,000
Total costs (£)
135,000
170,000
Variable cost per unit is- constant within this range of activity but there is a step up of
£5,000 in the total fixed costs when the activity exceeds 17,500 units.
What is the total cost at an activity level of 20,000 units?
A
£155,000
B
£158,000
C
£160,000
E
£163,000
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Question 4 B - Jun-05 exam
Archibald Ltd manufactures and sells one product, its budgeted profit statement for the first
month of trading is as follows:
Sales (1,200 units at £ 180 per unit)
£
£
Less: Cost of sales:
216,000
Production (1,800 units at £100 per unit)
180,000
Less Closing stock (600 units at £100 per unit) (60,000)
(120,000)
Gross profit
96,000
Less Fixed selling and distribution costs
(41,000)
Net profit
55,000
The budget was prepared using absorption costing principles. If budgeted production in
the first month had been 2,000 units then the total production cost would have been
£188,000.
Required:
(a) Using the high-low method, calculate:
(i) the variable production cost per unit; and
(ii) the total monthly fixed production cost.
(4 marks)
Solution:
Question 45 – Pilot paper
A semi-variable cost is one that, in the short term, remains the same over a given range of
activity but beyond that increased and then remains constant at the higher level of activity.
Is this statement true or false?
A
True
B
False
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Question 5 A - Dec-04 exam
The total cost of production for two levels of activity is as follows:
Level 1
Level 2
Production (units)
3,000
5,000
Total cost (£)
6,750
9,250
The variable production cost per unit and the total fixed production cost both remain constant
in the range of activity shown.
What is the variable production cost per unit?
A
£0.80
B
£1.25
C
£1.85
D
£2.25
Question 6 A - Jun-04 exam
An organisation manufactures a single product. The total cost of making 4,000 units is
£20,000 and the total cost of making 20,000 units is £40,000. Within this range of activity the
total fixed costs remain unchanged.
What is the variable cost per unit of the product?
A £0.80
B £1.20
C £1.25
D £2.00
Question 23 A – June - 03 exam
The following information for advertising and sales has been established over the past six
months:
Month
Sales revenue
Advertising exp.
$’000
$’000
1
155
3
2
125
2.5
3
200
6
4
175
5.5
5
150
4.5
6
225
6.5
Using the High – Low method which of the following is correct equation for linking advertising
and sales from the above data?
A. Sale revenue = 62,500 + (25 x advertising expenditure)
B. advertising expenditure = -2,500 + (0.04 x Sale revenue)
C. Sale revenue = 95,000 + (20 x advertising expenditure)
D. advertising expenditure = -4,750 + (0.05 x Sale revenue)
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Method of Least Squares
•The best-fitting line is the line with the smallest sum of squared deviations
•Regression analysis determines the linear function with the minimum sum of squared
deviations
Y1 = a + bx1
.....
n∑XY -∑X∑Y
b = ---------------n∑X2 – (∑X)2
Yn = a +bxn
a = (∑y - b∑x)/n
n∑XY -∑X∑Y
R = ---------------------------------[n∑X2 – (∑X)2] [n ∑Y2 – (∑Y)2]
Question 11
If ∑x = 100, ∑Y = 400, ∑X2 = 2,040, ∑Y2 = 32,278, ∑XY = 8,104 and n = 5 which of the
following values for a and b are correct in the formula Y = a + bX?
a
b
A
28
-2.6
B
28
+2.6
C
-28
-2.6
D
-28
+2.6
• Correlation Coefficient
– R is the Correlation Coefficient
– Measure the degree of correlation between two variables.
– Must always fall between +1 and –1.
– Two variables are said to be correlated if a change in the value of one variable is
accompanied by a change in the value of another variable.
+ Perfect correlation: all pairs of values lie on a straight line. An exact linear
relationship exists between two variables
Perfect correlation (positive)
x
x
x
x
Perfect correlation (negative)
x
x
x
x
x
x
r=+1
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r=-1
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Practice, Practice and Practice
+ Partial correlation: There is no exact relationship. However, one of following will hold
true.
Low value of X tend to be associated with low values of Y
High value of X tend to be associated with high values of Y
Low value of X tend to be associated with high values of Y
High value of X tend to be associated with low values of Y
Partial correlation (positive)
x
x
x x
x
x
x
x
x
Partial correlation (negative)
x
x
x
x x x
x
+ No correlation means that the values of two variables are totally UNRELATED
No correlation
x
x
x
x
x
x
x
x x
x
r=0
Question 12
The following four data pairs have been obtained: (1,5), (2,6), (4,9), (5,11). Without
carrying out any calculation, which of the following correlation coefficients best
describes the relationship between x and y?
A
-0.98
B
-0.25
C
0.98
D
0.25
Coefficient of determination
,
–R2 is the coefficient of determination
–Measures the proportion of the total variation in the value of one variable that can
explained by variations in the value of the other variable.
–The closer to 100%, the better; no benchmark
Eg.
Between material handling costs and number of moves has
r = 0,9289 -> r2 = 0.8629 = 86.29%
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Practice, Practice and Practice
Sentence to say: !!!
86.29% of the total variation in the value of (Y) material handling costs could be
explained by variance in value of (X) number of moves.
Question 13
Using data from 12 European countries, it has been calculated that the correlation between
the level of car ownership and the number of road deaths is 0.73. Which of the statements
shown follow from this?
(i)
High level of car ownership cause high levels of road deaths
(ii)
There is a strong relationship between the level of car ownership and the
number of road deaths
(iii)
53% of the variation in the levels of road deaths from one country to the next
can be explained by the corresponding variation in the level of car ownership
(iv)
73% of the variation in the levels of road deaths from one country to the next
can be explained by the corresponding variation in the level of car ownership
A (i) and (ii) only
B (i) and (iii) only
C (ii) and (iii) only
D (ii) and (iv) only
Can You Apply These to Exam type Questions?
Question 5 A - Jun-06 exam
Which of the following is NOT a feasible value for the correlation coefficient?
A + 1.2
B + 0.6
C+0
D - 0.6
Question 4 B - Jun-06 exam
The management accountant at Josephine Ltd is trying to predict the quarterly total
maintenance cost for a group of similar machines. She has extracted the following
information for the last eight quarters:
Quarter number
Total maintenance
cost (£'000)
Production units
('000)
1
2
3
4
5
6
7
8
265
302
222
240
362
295
404
400
20
24
16
18
26
22
32
30
The effects of inflation have been eliminated from the above costs.
The management accountant is using linear regression to establish an equation of the
form y = a+bx and has produced the following preliminary calculations:
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Practice, Practice and Practice
Σ (total maintenance cost x production units) = £61,250 million
Σ (total maintenance cost)2 = £809,598 million
Σ (production units)2 = 4,640 million
Required:
(a) Establish the equation which will allow the management accountant to predict
quarterly total maintenance costs for a given level of production. Interpret your answer
in terms of fixed and variable maintenance costs.
(7 marks)
(b) Using the equation established in (a), predict the total maintenance cost for the next
quarter when planned production is 44,000 units. Suggest a major reservation, other than
the effect of inflation, you would have about this prediction.
(3 marks)
Question 18 A- Dec-05 exam
The following statements relate to the calculation of the regression line y = a + bx using the
information on the formulae sheet at the end of this examination paper:
(i) n represents the number of pairs of data items used
(ii) (Σx)2 is calculated by multiplying Σx by Σx
(iii) Σxy is calculated by multiplying Σx by Σy
Which statements are correct?
A (i) and (ii) only
B (i) and (iii) only
C (ii) and (iii) only
D (i), (ii) and (iii)
Question 19 A-Dec-05 exam
The correlation coefficient (r) for measuring the connection between two variables (x and y)
has been calculated as 0.6.
How much of the variation in the dependent variable (y) is explained by the variation in the
independent variable (x)?
A 36%
B 40%
C 60%
D 64%
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Practice, Practice and Practice
Question 6 A - Jun-05 exam
An organisation is using linear regression analysis to establish an equation that shows a
relationship between advertising expenditure and sales. It will then use the equation to
predict sales for given levels of advertising expenditure. Data for the last five periods are as
follows:
Period
Number
1
2
3
4
5
Advertising
expenditure
£000
17
19
24
22
18
Sales
£000
108
116
141
123
112
What are the values of 'Σx', 'Σy' and `n' that need to be inserted into the appropriate
formula?
Σx
Σy
n
A
£600,000
£100,000
5
B
£100,000
£600,000
5
C
£600,000
£100,000
10
D
£100,000
£600,000
10
Question 17 A-Jun-07 exam
Which of the following correlation coefficients indicates the weakest relationship between
two variables?
A + 0.9
B –0.6
C - 0.8
D - 1.0
Question 3 A- Dec-04 exam
Which of the following is a feasible value for the correlation coefficient?
A - 2.0
B - 1.2
C0
D + 1.2
Question 3 – Pilot Paper
Regression analysis is being used to find the line of best fit (y= a + bx) from eleven pairs
of data. The calculations have produced the following information:
Σx = 440, Σy = 330, Σx2 = 17,986, Σy2 = 10,366, Σxy = 13,467 and b = 0.69171
What is value of “a” in the equation for the line of best fit (to 2 decimal places)?
A 0.63
B 0.69
C 2.33
D 5.33
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Practice, Practice and Practice
Question 14 A – June - 03 exam
A company uses regression analysis to establish a total cost equation for budgeting purposes.
Data for the past four months is as follows:
Month
Total costs
Quantity produced
$’000
‘000
1
57.5
1.25
2
37.5
1.00
3
45.0
1.50
4
60.0
2.00
5.75
200.0
The gradient of the regression line is 17.14. What is value of “a”?
A. 25.36
B. 48.56
C. 74.64
D. 101.45
Question 14
A regression equation Y = a + bX is used to forecast the value of Y for a given value of X.
Which of the following increase the reliability of the forecast?
(i)
A correlation coefficient numerically close to 1
(ii)
Working to a higher number of decimal places of accuracy
(iii)
Forecasting for values of x outside the range of those used in the sample
(iv)
A large sample is used to calculate the regression equation
A (i) only
B (i) and (ii) only
C (i) and (iii) only
D (i) and (iv) only
Question 15
A regression equation Y = 3 + 2X has been calculated from 6 pairs of values, with X ranging
from 1 to 10. The correlation coefficient is 0.8. It is estimated that Y = 43 when X = 20.
Which of the following are true?
(i)
The estimate is not reliable because X is outside the range of the data
(ii)
The estimate is not reliable because the correlation coefficient is low
(iii)
The estimate is reliable
(iv)
The estimate is not reliable because the sample is small
A (i) and (ii) only
B (i) and (iii) only
C (ii) and (iv) only
D (i) and (iv) only
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