Forecasting
4
PowerPoint presentation to accompany
Heizer and Render
Operations Management, Eleventh Edition
Principles of Operations Management, Ninth Edition
PowerPoint slides by Jeff Heyl
© 2014
© 2014
Pearson
Pearson
Education,
Education,
Inc.Inc.
4-1
What is Forecasting?
►
Process of predicting a
future event
►
Underlying basis
of all business
decisions
►
Production
►
Inventory
►
Personnel
►
Facilities
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??
4-2
Forecasting Time Horizons
1. Short-range forecast
►
Up to 1 year, generally less than 3 months
►
Purchasing, job scheduling, workforce levels,
job assignments, production levels
2. Medium-range forecast
►
3 months to 3 years
►
Sales and production planning, budgeting
3. Long-range forecast
►
3+ years
►
New product planning, facility location,
research and development
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4-3
Distinguishing Differences
1. Medium/long range forecasts deal with more
comprehensive issues and support
management decisions regarding planning
and products, plants and processes
2. Short-term forecasting usually employs
different methodologies than longer-term
forecasting
3. Short-term forecasts tend to be more
accurate than longer-term forecasts
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4-4
Company Strategy/Issues
Product Life Cycle
Introduction
Growth
Best period to
increase market
share
Practical to change
price or quality
image
R&D engineering is
critical
Strengthen niche
Maturity
Decline
Poor time to
change image,
price, or quality
Cost control
critical
Competitive costs
become critical
Defend market
position
Drive-through
Internet search engines
restaurants
DVDs
Xbox 360
iPods
Boeing 787
Sales
3D printers
3-D game
players
Electric vehicles
Analog
TVs
Figure 2.5
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4-5
Product Life Cycle
OM Strategy/Issues
Introduction
Product design and
development
critical
Frequent product
and process
design changes
Short production
runs
High production
costs
Limited models
Attention to quality
Growth
Forecasting critical
Product and
process reliability
Competitive
product
improvements and
options
Increase capacity
Shift toward
product focus
Enhance
distribution
Maturity
Standardization
Fewer product
changes, more
minor changes
Optimum capacity
Increasing stability
of process
Long production
runs
Product
improvement and
cost cutting
Decline
Little product
differentiation
Cost
minimization
Overcapacity in
the industry
Prune line to
eliminate items
not returning
good margin
Reduce
capacity
Figure 2.5
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4-6
Types of Forecasts
1. Economic forecasts
►
Address business cycle – inflation rate, money
supply, housing starts, etc.
2. Technological forecasts
►
Predict rate of technological progress
►
Impacts development of new products
3. Demand forecasts
►
Predict sales of existing products and services
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4-7
Strategic Importance of
Forecasting
►
►
►
Supply-Chain Management – Good
supplier relations, advantages in product
innovation, cost and speed to market
Human Resources – Hiring, training,
laying off workers
Capacity – Capacity shortages can result
in undependable delivery, loss of
customers, loss of market share
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4-8
Seven Steps in Forecasting
1. Determine the use of the forecast
2. Select the items to be forecasted
3. Determine the time horizon of the
forecast
4. Select the forecasting model(s)
5. Gather the data needed to make the
forecast
6. Make the forecast
7. Validate and implement results
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4-9
Forecasting Approaches
Qualitative Methods
►
►
Used when situation is vague and
little data exist
►
New products
►
New technology
Involves intuition, experience
►
e.g., forecasting sales on Internet
© 2014 Pearson Education, Inc.
4 - 10
Forecasting Approaches
Quantitative Methods
►
►
Used when situation is ‘stable’ and
historical data exist
►
Existing products
►
Current technology
Involves mathematical techniques
►
e.g., forecasting sales of color
televisions
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4 - 11
Overview of Qualitative Methods
1. Jury of executive opinion
►
Pool opinions of high-level experts,
sometimes augment by statistical
models
2. Delphi method
►
Panel of experts, queried iteratively
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4 - 12
Overview of Qualitative Methods
3. Sales force composite
►
Estimates from individual salespersons
are reviewed for reasonableness, then
aggregated
4. Market Survey
►
Ask the customer
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4 - 13
Jury of Executive Opinion
►
Involves small group of high-level experts
and managers
►
Group estimates demand by working
together
►
Combines managerial experience with
statistical models
►
Relatively quick
►
‘Group-think’
disadvantage
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4 - 14
Delphi Method
Iterative group
process, continues
until consensus is
reached
Staff
► 3 types of
(Administering
survey)
participants
►
►
Decision makers
►
Staff
►
Respondents
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Decision Makers
(Evaluate responses
and make decisions)
Respondents
(People who can make
valuable judgments)
4 - 15
Sales Force Composite
►
Each salesperson projects his or her
sales
►
Combined at district and national
levels
►
Sales reps know customers’ wants
►
May be overly optimistic
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4 - 16
Market Survey
►
Ask customers about purchasing
plans
►
Useful for demand and product
design and planning
►
What consumers say, and what they
actually do may be different
►
May be overly optimistic
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4 - 17
Overview of Quantitative
Approaches
1. Moving averages
2. Exponential
smoothing
3. Linear regression
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4 - 18
Time-Series Forecasting
►
Set of evenly spaced numerical data
►
►
Obtained by observing response
variable at regular time periods
Forecast based only on past values, no
other variables important
►
Assumes that factors influencing past
and present will continue influence in
future
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4 - 19
Moving Average Method
►
►
►
MA is a series of arithmetic means
Used if little or no trend
Used often for smoothing
►
Provides overall impression of data
over time
demand in previous n periods
å
Moving average =
n
© 2014 Pearson Education, Inc.
4 - 20
Moving Average Example
MONTH
ACTUAL SHED SALES
January
10
February
12
March
13
April
16
(10 + 12 + 13)/3 = 11 2/3
May
19
(12 + 13 + 16)/3 = 13 2/3
June
23
(13 + 16 + 19)/3 = 16
July
26
(16 + 19 + 23)/3 = 19 1/3
August
30
(19 + 23 + 26)/3 = 22 2/3
September
28
(23 + 26 + 30)/3 = 26 1/3
October
18
(29 + 30 + 28)/3 = 28
November
16
(30 + 28 + 18)/3 = 25 1/3
December
14
(28 + 18 + 16)/3 = 20 2/3
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3-MONTH MOVING AVERAGE
4 - 21
Weighted Moving Average
►
Used when some trend might be
present
►
►
Older data usually less important
Weights based on experience and
intuition
((
)(
))
Weighted å Weight for period n Demand in period n
moving =
å Weights
average
© 2014 Pearson Education, Inc.
4 - 22
Weighted Moving Average
MONTH
ACTUAL SHED SALES
January
10
February
12
March
13
April
16
May
[(3 x 13) + (2 x 12) + (10)]/6 = 12 1/6
19
WEIGHTS
APPLIED
23
June
3-MONTH WEIGHTED MOVING AVERAGE
PERIOD
July
26
3
Last month
August
30
2
Two months ago
September
28
1
Three months ago
October
November
18 6
Forecast for
16this month =
December
Sum of the weights
3 x14
Sales last mo. + 2 x Sales 2 mos. ago + 1 x Sales 3 mos. ago
Sum of the weights
© 2014 Pearson Education, Inc.
4 - 23
Weighted Moving Average
MONTH
ACTUAL SHED SALES
January
10
February
12
March
13
April
16
[(3 x 13) + (2 x 12) + (10)]/6 = 12 1/6
May
19
[(3 x 16) + (2 x 13) + (12)]/6 = 14 1/3
June
23
[(3 x 19) + (2 x 16) + (13)]/6 = 17
July
26
[(3 x 23) + (2 x 19) + (16)]/6 = 20 1/2
August
30
[(3 x 26) + (2 x 23) + (19)]/6 = 23 5/6
September
28
[(3 x 30) + (2 x 26) + (23)]/6 = 27 1/2
October
18
[(3 x 28) + (2 x 30) + (26)]/6 = 28 1/3
November
16
[(3 x 18) + (2 x 28) + (30)]/6 = 23 1/3
December
14
[(3 x 16) + (2 x 18) + (28)]/6 = 18 2/3
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3-MONTH WEIGHTED MOVING AVERAGE
4 - 24
Potential Problems With
Moving Average
Increasing n smooths the forecast but
makes it less sensitive to changes
► Does not forecast trends well
► Requires extensive historical data
►
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4 - 25
Exponential Smoothing
►
►
►
Form of weighted moving average
►
Weights decline exponentially
►
Most recent data weighted most
Requires smoothing constant ()
►
Ranges from 0 to 1
►
Subjectively chosen
Involves little record keeping of past
data
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4 - 26
Exponential Smoothing
New forecast = Last period’s forecast
+  (Last period’s actual demand
– Last period’s forecast)
Ft = Ft – 1 + (At – 1 - Ft – 1)
where
Ft =
Ft – 1 =
 =
new forecast
previous period’s forecast
smoothing (or weighting) constant (0 ≤  ≤ 1)
At – 1 =
previous period’s actual demand
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4 - 27
Exponential Smoothing
Example
Predicted demand = 142 Ford Mustangs
Actual demand = 153
Smoothing constant  = .20
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4 - 28
Exponential Smoothing
Example
Predicted demand = 142 Ford Mustangs
Actual demand = 153
Smoothing constant  = .20
New forecast
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= 142 + .2(153 – 142)
4 - 29
Exponential Smoothing
Example
Predicted demand = 142 Ford Mustangs
Actual demand = 153
Smoothing constant  = .20
New forecast
= 142 + .2(153 – 142)
= 142 + 2.2
= 144.2 ≈ 144 cars
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4 - 30
Choosing 
The objective is to obtain the most
accurate forecast no matter the
technique
We generally do this by selecting the
model that gives us the lowest forecast
error
Forecast error = Actual demand – Forecast value
= At – Ft
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4 - 31
Common Measures of Error
Mean Absolute Deviation (MAD)
Actual - Forecast
å
MAD =
n
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4 - 32
Common Measures of Error
Mean Squared Error (MSE)
Forecast errors)
å
(
MSE =
2
n
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4 - 33
Common Measures of Error
Mean Absolute Percent Error (MAPE)
n
MAPE =
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å100 Actual -Forecast
i
i
/ Actuali
i=1
n
4 - 34
Values of Dependent Variable (y-values)
Least Squares Method
Actual observation
(y-value)
Deviation7
Deviation5
Deviation3
Deviation1
(error)
Deviation6
Least squares method minimizes the
sum of Deviation
the squared
errors (deviations)
4
Deviation2
Trend line, y^ = a + bx
|
|
|
|
|
|
|
1
2
3
4
5
6
7
Time period
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Figure 4.4
4 - 35
Least Squares Method
Equations to calculate the regression variables
ŷ = a+ bx
xy - nxy
å
b=
å x - nx
2
2
a = y - bx
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4 - 36
Least Squares Example
YEAR
ELECTRICAL
POWER DEMAND
YEAR
ELECTRICAL
POWER DEMAND
1
74
5
105
2
79
6
142
3
80
7
122
4
90
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4 - 37
Least Squares Example
YEAR (x)
ELECTRICAL POWER
DEMAND (y)
x2
xy
1
74
1
74
2
79
4
158
3
80
9
240
4
90
16
360
5
105
25
525
6
142
36
852
7
122
49
854
Σx = 28
Σy = 692
x 28
å
x=
=
=4
n
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7
Σx2 = 140
Σxy = 3,063
y 692
å
y=
=
= 98.86
n
7
4 - 38
Least Squares Example
YEAR (x)
1
2
xy - nxy 3,063 - ( 7) ( 4) (98.86) 295
å
ELECTRICAL
b=
= POWER
=
= 10.54
DEMAND (y) 140 - ( 7) 4
xy
å x - nx
( ) x 28
2
2
2
2
74
79
()
3
a = y - bx = 98.8680
-10.54 4 = 56.70
4
90
1
74
4
158
9
240
16
360
Thus,
105 ŷ = 56.70 +10.54x25
5
525
6
142
36
852
7
122
49
854
Σx = 28
Σy = 692
Σx2 = 140
Σxy = 3,063
x in
y+ 10.54(8)
Demand
å
å
28year 8 = 56.70
692
x=
=
=4
y=
=
= 98.86
=
141.02,
or
141
megawatts
n
7
n
7
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4 - 39
Power demand (megawatts)
Least Squares Example
160
150
140
130
120
110
100
90
80
70
60
50
Trend line,
y^ = 56.70 + 10.54x
–
–
–
–
–
–
–
–
–
–
–
–
|
1
|
2
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|
3
|
4
|
5
Year
|
6
|
7
|
8
|
9
Figure 4.5
4 - 40
Least Squares Requirements
1. We always plot the data to insure a
linear relationship
2. We do not predict time periods far
beyond the database
3. Deviations around the least squares
line are assumed to be random
© 2014 Pearson Education, Inc.
4 - 41
Associative Forecasting
Used when changes in one or more independent
variables can be used to predict the changes in
the dependent variable
Most common technique is linear
regression analysis
We apply this technique just as we did
in the time-series example
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4 - 42
Associative Forecasting
Forecasting an outcome based on predictor
variables using the least squares technique
y^ = a + bx
where y^ = value of the dependent variable (in our example,
sales)
a = y-axis intercept
b = slope of the regression line
x = the independent variable
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4 - 43
Associative Forecasting
Example
NODEL’S SALES
(IN $ MILLIONS), y
AREA PAYROLL
(IN $ BILLIONS), x
NODEL’S SALES
(IN $ MILLIONS), y
AREA PAYROLL
(IN $ BILLIONS), x
2.0
1
2.0
2
3.0
3
2.0
1
2.5
4
3.5
7
Nodel’s sales
(in$ millions)
4.0 –
3.0 –
2.0 –
1.0 –
0
|
|
|
|
|
|
|
1
2
3
4
5
6
7
Area payroll (in $ billions)
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4 - 44
Associative Forecasting
Example
SALES, y
Σy =
PAYROLL, x
xy
2.0
1
1
2.0
3.0
3
9
9.0
2.5
4
16
10.0
2.0
2
4
4.0
2.0
1
1
2.0
3.5
7
49
24.5
Σx =
15.0
6
Σx2 =
18
x 18
å
x=
=
=3
6
2
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2
Σxy =
80
51.5
y 15
å
y=
=
= 2.5
xy - nxy 51.5 - (6)(3)(2.5)
å
b=
=
= .25
80 - (6)(3 )
å x - nx
2
x2
6
6
a = y - bx = 2.5 - (.25)(3) = 1.75
4 - 45
Associative Forecasting
Example
SALES, y
Σy =
PAYROLL, x
2.0
1
3.0
3
2.5
4
2.0
2
2.0
3.5
Σx =
15.0
2
© 2014 Pearson Education, Inc.
1
2.0
9
ŷ = 1.75
+ .25x
9.0
10.0
1
1
2.0
7
49
24.5
Sales = 1.75
4 + .25(payroll)
4.0
Σx2 =
18
6
2
Σxy =
80
51.5
y 15
å
y=
=
= 2.5
xy - nxy 51.5 - (6)(3)(2.5)
å
b=
=
= .25
80 - (6)(3 )
å x - nx
2
xy
16
x 18
å
x=
=
=3
6
x2
6
6
a = y - bx = 2.5 - (.25)(3) = 1.75
4 - 46
Associative Forecasting
Example
SALES, y
2.0
Nodel’s sales
(in$ millions)
3.0
Σy =
PAYROLL, x
4
3.5
Σx =
1
1
2.0
7
49
24.5
Sales = 1.75
4 + .25(payroll)
4.0
Σx2 =
18
|
x 1 18 2
å
x=
=
=3
6
6
|
|
å
Σxy =
80
|
|
51.5
|
3
4 y 5 15 6
7
y =(in $ billions)
=
= 2.5
Area payroll
xy - nxy 51.5 - (6)(3)(2.5)
å
b=
=
= .25
80 - (6)(3 )
å x - nx
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9.0
10.0
2
0
2
2.0
16
|
2
1
9
ŷ = 1.75
+ .25x
3
2.5 3.0 –
2.0
2.0 2.0 –
15.0
xy
1
4.0 –
1.0 –
x2
2
6
6
a = y - bx = 2.5 - (.25)(3) = 1.75
4 - 47
Associative Forecasting
Example
If payroll next year is estimated to be $6 billion,
then:
Sales (in $ millions) = 1.75 + .25(6)
= 1.75 + 1.5 = 3.25
Sales = $3,250,000
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4 - 48
Associative Forecasting
Example
Nodel’s sales
(in$ millions)
If payroll4.0
next
– year is estimated to be $6 billion,
then: 3.25
3.0 –
2.0 –
Sales (in$ millions) = 1.75 + .25(6)
1.0 –
= 1.75 + 1.5 = 3.25
|
0
© 2014 Pearson Education, Inc.
1
|
|
|
|
|
2
3
4
5
6
Sales
= $3,250,000
Area payroll
(in $ billions)
|
7
4 - 49
Standard Error of the Estimate
►
A forecast is just a point estimate of a
future value
►
This point is
actually the
mean of a
probability
distribution
Nodel’s sales
(in$ millions)
4.0 –
3.25
3.0 –
Regression line,
1.0 –
0
Figure 4.9
© 2014 Pearson Education, Inc.
ŷ =1.75+.25x
2.0 –
|
1
|
2
|
3
|
4
|
5
|
6
|
7
Area payroll (in $ billions)
4 - 50
Standard Error of the Estimate
Sy,x =
where
2
(
y
y
)
å
c
n- 2
y = y-value of each data point
yc = computed value of the dependent variable,
from the regression equation
n = number of data points
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4 - 51
Standard Error of the Estimate
Computationally, this equation is
considerably easier to use
Sy,x =
2
y
å - aå y - bå xy
n- 2
We use the standard error to set up
prediction intervals around the point
estimate
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4 - 52
Standard Error of the Estimate
Sy,x =
2
y
å - aå y - bå xy
n- 2
39.5 -1.75(15.0) - .25(51.5)
=
6-2
= .09375
= .306 (in $ millions)
Nodel’s sales
(in$ millions)
The standard error
of the estimate is
$306,000 in sales
4.0 –
3.25
3.0 –
2.0 –
1.0 –
0
|
1
|
2
|
3
|
4
|
5
|
6
|
7
Area payroll (in $ billions)
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4 - 53
Correlation
►
►
►
How strong is the linear relationship
between the variables?
Correlation does not necessarily imply
causality!
Coefficient of correlation, r, measures
degree of association
►
Values range from -1 to +1
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4 - 54
Correlation Coefficient
r=
nå xy - å xå y
é
2
êënå x -
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ùé
2
å x úûêënå y -
( )
2
(
ù
å y úû
)
2
4 - 55
Correlation Coefficient
Figure 4.10
y
y
x
x
(a) Perfect negative
correlation
y
(e) Perfect positive
correlation
y
y
x
x
(b) Negative correlation
(d) Positive correlation
x
(c) No correlation
High
Moderate
|
|
|
–1.0
–0.8
–0.6
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|
Low
|
Low
Moderate
|
|
–0.4
–0.2
0
0.2
0.4
Correlation coefficient values
High
|
|
0.6
0.8
1.0
4 - 56
Correlation Coefficient
y
Σy =
x
x2
xy
y2
2.0
1
1
2.0
4.0
3.0
3
9
9.0
9.0
2.5
4
16
10.0
6.25
2.0
2
4
4.0
4.0
2.0
1
1
2.0
4.0
3.5
7
49
24.5
12.25
15.0
Σx =
18
Σx2 =
80
Σxy =
51.5
Σy2 =
39.5
(6)(51.5) – (18)(15.0)
é(6)(80) – (18)2 ùé(16)(39.5) – (15.0)2 ù
ë
ûë
û
r=
=
309 - 270
(156)(12)
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=
39
1,872
=
39
= .901
43.3
4 - 57
Correlation
►
Coefficient of Determination, r2,
measures the percent of change in y
predicted by the change in x
►
Values range from 0 to 1
►
Easy to interpret
For the Nodel Construction example:
r = .901
r2 = .81
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4 - 58
Multiple-Regression Analysis
If more than one independent variable is to be
used in the model, linear regression can be
extended to multiple regression to accommodate
several independent variables
ŷ = a+ b1x1 + b2 x2
Computationally, this is quite
complex and generally done on the
computer
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4 - 59
Multiple-Regression Analysis
In the Nodel example, including interest rates in the
model gives the new equation:
ŷ = 1.80 +.30x1 - 5.0x2
An improved correlation coefficient of r = .96 suggests
this model does a better job of predicting the change
in construction sales
Sales = 1.80 + .30(6) - 5.0(.12) = 3.00
Sales = $3,000,000
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Forecasting in the Service
Sector
►
Presents unusual challenges
►
Special need for short term records
►
Needs differ greatly as function of
industry and product
►
Holidays and other calendar events
►
Unusual events
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Percentage of sales by hour of day
Fast Food Restaurant Forecast
20% –
Figure 4.12
15% –
10% –
5% –
11-12
1-2
12-1
(Lunchtime)
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3-4
2-3
5-6
4-5
7-8
6-7
(Dinnertime)
Hour of day
9-10
8-9
10-11
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FedEx Call Center Forecast
12% –
Figure 4.12
10% –
8% –
6% –
4% –
2% –
0% –
2
4
6
8
A.M.
10
12
2
4
6
8
P.M.
10
12
Hour of day
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