To accompany Quantitative Analysis for
Management, 7e by Render/ Stair
5-1 © 2000 by Prentice Hall, Inc. ,Upper Saddle River,
N.J. 07458
Quantitative Analysis
for Management
Forecasting

To accompany Quantitative Analysis for
Management, 7e by Render/ Stair
5-2 © 2000 by Prentice Hall, Inc. ,Upper Saddle River,
N.J. 07458
Forecasting Models
Moving
Average
Exponential
Smoothing
Trend Projections
Time Series
Methods
Forecasting
Techniques
Delphi
Methods
Jury of Executive
Opinion
Sales Force
Composite
Consumer
Market Survey
Qualitative
Models
Causal
Methods
Regression
Analysis
Multiple
Regression

To accompany Quantitative Analysis for
Management, 7e by Render/ Stair
5-3 © 2000 by Prentice Hall, Inc. ,Upper Saddle River,
N.J. 07458
Scatter Diagram for Sales
0
50
100
150
200
250
300
350
400
450
0 2 4 6 8 10 12
Time (Years)
Annual
Sales
Televisions

To accompany Quantitative Analysis for
Management, 7e by Render/ Stair
5-4 © 2000 by Prentice Hall, Inc. ,Upper Saddle River,
N.J. 07458
Decomposition of Time
Series
Time series can be decomposed into:
Trend (T): gradual up or down movement
over time
Seasonality (S): pattern of fluctuations above
or below trend line that occurs every year
Cycles(C): patterns in data that occur every
several years
Random variations (R): “blips”in the data
caused by chance and unusual situations

To accompany Quantitative Analysis for
Management, 7e by Render/ Stair
5-5 © 2000 by Prentice Hall, Inc. ,Upper Saddle River,
N.J. 07458
Product Demand
Showing Components
-150
-50
50
150
250
350
450
550
650
0 1 2 3 4 5
Time (Years
Demand
Trend
Actual Data
Cyclic
Random

To accompany Quantitative Analysis for
Management, 7e by Render/ Stair
5-6 © 2000 by Prentice Hall, Inc. ,Upper Saddle River,
N.J. 07458
Moving Averages
n
n)
period
in
(demand
:
average
Moving


To accompany Quantitative Analysis for
Management, 7e by Render/ Stair
5-7 © 2000 by Prentice Hall, Inc. ,Upper Saddle River,
N.J. 07458
Calculation of Three-Month
Moving Average
Month Actual Shed
Sales
Three-Month Moving
Average
January 10
February 12
March 13
April 16
3
2
11
13)/3
12
(10 =
+
+
May 19
3
2
13
16)/3
13
(12 =
+
+
June 23 16
19)/3
16
(13 =
+
+
July 26
3
1
19
23)/3
19
(16 =
+
+

To accompany Quantitative Analysis for
Management, 7e by Render/ Stair
5-8 © 2000 by Prentice Hall, Inc. ,Upper Saddle River,
N.J. 07458
Weighted Moving Averages
weights
)
period
in
)(demand
period
for
(weight
average
moving
Weighted


=
n
n

To accompany Quantitative Analysis for
Management, 7e by Render/ Stair
5-9 © 2000 by Prentice Hall, Inc. ,Upper Saddle River,
N.J. 07458
Calculating Weighted
Moving Averages
Weights Applied Period
3 Last month
2 Two months ago
1 Three months ago
3*Sales last month +
2*Sales two months ago +
1*Sales three months ago
6 Sum of weights

To accompany Quantitative Analysis for
Management, 7e by Render/ Stair
5-10 © 2000 by Prentice Hall, Inc. ,Upper Saddle River,
N.J. 07458
Calculation of Three-Month
Moving Average
Month Actual
Shed
Sales
Three-Month Moving
Average
January 10
February 12
March 13
April 16
6
1
12
10)]/6
*
(1
12)
*
(2
13)
*
[(3 =
+
+
May 19
3
1
14
12)]/6
*
(1
13)
*
(2
16)
*
[(3 =
+
+
June 23 17
13)]/6
*
(1
16)
*
(2
19)
*
[(3 =
+
+
July 26
2
1
20
16)]/6
*
(1
19)
*
(2
23)
*
[(3 =
+
+

To accompany Quantitative Analysis for
Management, 7e by Render/ Stair
5-11 © 2000 by Prentice Hall, Inc. ,Upper Saddle River,
N.J. 07458
Exponential Smoothing
New forecast =
previous forecast + (previous actual - previous)
or:
where
( )
1
1
1  -
-
- -
+
= t
t
t
t F
A
F
F
actual
period
previous
constant between 0~1
smoothing
forecast
previous
forecast
new
=
=
=
=
-1
1

t
t-
t
A
F
F

To accompany Quantitative Analysis for
Management, 7e by Render/ Stair
5-12 © 2000 by Prentice Hall, Inc. ,Upper Saddle River,
N.J. 07458
Table 5.5

To accompany Quantitative Analysis for
Management, 7e by Render/ Stair
5-13 © 2000 by Prentice Hall, Inc. ,Upper Saddle River,
N.J. 07458
Table 5.5 Continued  =0.50
Qtr Actual Tonnage
Unloaded
Forecast using  =0.50
1 180 175
2 168 177.50 =175.00+0.50(180-175)
3 159 172.75 =177.50+0.50(168-177.50)
4 175 165.38 =172.25+0.50(159-172.25)
5 190 170.19 =165.38+0.50(175-165.38)
6 205 179.09 =170.19+0.50(190-170.19)
7 180 179.54 =179.09+0.50(180-179.09)
8 182 182.00 =179.54+0.50(182-179.54)
9 ?

To accompany Quantitative Analysis for
Management, 7e by Render/ Stair
5-14 © 2000 by Prentice Hall, Inc. ,Upper Saddle River,
N.J. 07458
Trend Projection
General regression equation:
+
=
2
X
2 n
X
Y
X
n
XY
b
Y
a
Y
where
bX
a
Y
-
-
=
=
=


intercept
axis
-
variable)
(dependent
predicted
be
to
variable
the
of
value
computed

To accompany Quantitative Analysis for
Management, 7e by Render/ Stair
5-15 © 2000 by Prentice Hall, Inc. ,Upper Saddle River,
N.J. 07458
Table5.7

To accompany Quantitative Analysis for
Management, 7e by Render/ Stair
5-16 © 2000 by Prentice Hall, Inc. ,Upper Saddle River,
N.J. 07458
Solved Formula

To accompany Quantitative Analysis for
Management, 7e by Render/ Stair
5-17 © 2000 by Prentice Hall, Inc. ,Upper Saddle River,
N.J. 07458
Midwestern Manufacturing’s
Demand
60
70
80
90
100
110
120
130
140
150
160
1993 1994 1995 1996 1997 1998 1999 2000 2001
Forecast points
Trend Line
Actual demand line
X
y 54
.
10
70
.
56 +
=

To accompany Quantitative Analysis for
Management, 7e by Render/ Stair
5-18 © 2000 by Prentice Hall, Inc. ,Upper Saddle River,
N.J. 07458
Computing Seasonality Indices
Using Answering Machine Sales

To accompany Quantitative Analysis for
Management, 7e by Render/ Stair
5-19 © 2000 by Prentice Hall, Inc. ,Upper Saddle River,
N.J. 07458
Trend Analysis with Seasonal
Indices
Y = 1150 + 20x
Where x=1,2,…12 for Jan, Feb,….Dec
So;
Jan =[1150+20(1)]*.957 = 1119.69
Feb =[1150+50(2)]*.851 = 1012.69
Mar =[1150+20(3)]*.904 = 1093.84
.
.
Dec = [1150*20(12)]*.851 = 1182.89

To accompany Quantitative Analysis for
Management, 7e by Render/ Stair
5-20 © 2000 by Prentice Hall, Inc. ,Upper Saddle River,
N.J. 07458
Trend Analysis Example
with Seasonality:
 Trend analysis was used to forecast the number of new hotel
registrants (in ooo’s). The following data was used.
yr1 yr2
1 Jan 17 17
2 Feb 16 15
3 Mar 16 17
4 Apr 25 24
5 May 24 23
6 June 25 25
7 July 23 24
8 Aug 20 19
9 Sep 20 20
10 Oct 16 15
11 Nov 16 15
12 Dec 17 17

To accompany Quantitative Analysis for
Management, 7e by Render/ Stair
5-21 © 2000 by Prentice Hall, Inc. ,Upper Saddle River,
N.J. 07458
The trend analysis, using year1 data was
Y= 20.5 + 0.1455X
a) Compute the seasonal index
b) Forecast July of year3, October of year3
c) What is the forecast for December if the
average yearly demand for year is thought to
increase by 10% higher than year1?
Trend Analysis Example :

To accompany Quantitative Analysis for
Management, 7e by Render/ Stair
5-22 © 2000 by Prentice Hall, Inc. ,Upper Saddle River,
N.J. 07458
Using Regression Analysis to
Forecast(Causal)
Y
Triple A' Sales
($100,000's)
X
Local Payroll
($100,000,000)
2.0 1
3.0 3
2.5 4
2.0 2
2.0 1
3.5 7

To accompany Quantitative Analysis for
Management, 7e by Render/ Stair
5-23 © 2000 by Prentice Hall, Inc. ,Upper Saddle River,
N.J. 07458
Using Regression Analysis to
Forecast - continued
Sales, Y Payroll, X X2
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
S Y = 15.0 SX = 18 SX2
= 80 SXY = 51.5

To accompany Quantitative Analysis for
Management, 7e by Render/ Stair
5-24 © 2000 by Prentice Hall, Inc. ,Upper Saddle River,
N.J. 07458
Using Regression Analysis to
Forecast - continued
Calculating the required parameters:
( )( )( )
( )( )
( )( )
X
.
.
Ŷ
.
.
.
X
b
Y
a
.
.
.
X
n
X
Y
X
n
XY
b
.
Y
Y
X
X
25
0
75
1
75
1
3
25
0
5
2
25
0
6
80
5
2
3
6
5
51
5
2
6
15
6
3
6
18
6
3 2
2
2
+
=
=
-
=
-
=
=
-
-
=
-
-
=
=
=
=
=
=
=





To accompany Quantitative Analysis for
Management, 7e by Render/ Stair
5-25 © 2000 by Prentice Hall, Inc. ,Upper Saddle River,
N.J. 07458
Regression Equation
0
1
2
3
4
0 1 2 3 4 5 6 7 8
Area Payroll ($100,000,000)
Triple
A's
Sale
s
($100,000)

To accompany Quantitative Analysis for
Management, 7e by Render/ Stair
5-26 © 2000 by Prentice Hall, Inc. ,Upper Saddle River,
N.J. 07458
Methods to evaluate the
Casual Regression Equation
 Standard Error of the Estimate (the standard
deviation)
 Correlation Coefficient
-1 < r <1
 Coefficient of Determination
0 < r <1
the percent of variation in Y ( the dependent
variable ) that is described by the X’s
(independent variables )
2

To accompany Quantitative Analysis for
Management, 7e by Render/ Stair
5-27 © 2000 by Prentice Hall, Inc. ,Upper Saddle River,
N.J. 07458
Standard Error of the
Estimate - continued
( )
points
data
of
number
equation
regression
the
from
computed
variable
dependent
the
of
value
point
data
each
of
value
=
=
-
=
-
-
=

n
Y
Y
Y
where
n
Y
Y
S
c
c
X
,
Y 2
2
This is the standard deviation of the regression
For Payroll example, S = 0.306
Y,X

To accompany Quantitative Analysis for
Management, 7e by Render/ Stair
5-28 © 2000 by Prentice Hall, Inc. ,Upper Saddle River,
N.J. 07458
Correlation Coefficient
=
( )
[ ]
 
- 2
2 ( )
[ ]
 
-
-

2
2
2
Y
Y
(
Y
n
X
X
n
 
-
 Y
X
XY
n
r
For Payroll example, r = 0.91

To accompany Quantitative Analysis for
Management, 7e by Render/ Stair
5-29 © 2000 by Prentice Hall, Inc. ,Upper Saddle River,
N.J. 07458
Coefficient - Four Values
Fig. 5.7

To accompany Quantitative Analysis for
Management, 7e by Render/ Stair
5-30 © 2000 by Prentice Hall, Inc. ,Upper Saddle River,
N.J. 07458
Multiple Regression to
Forecast #5-32
SUMMARY OUTPUT
Regression Statistics
Multiple R 0.656652082
R Square 0.431191956
Adjusted R Square 0.374311152
Standard Error 8.302983493
Observations 12
ANOVA
df SS MS F Significance F
Regression 1 522.6046512 522.6046512 7.580623398 0.020362831
Residual 10 689.3953488 68.93953488
Total 11 1212
Coefficients Standard Error t Stat P-value Lower 95% Upper 95%
Intercept 6.441860465 5.476681644 1.176234239 0.266742687 -5.760948796 18.64466973
# Tourists 1.23255814 0.447666868 2.753293191 0.020362831 0.235094026 2.230022253

To accompany Quantitative Analysis for
Management, 7e by Render/ Stair
5-31 © 2000 by Prentice Hall, Inc. ,Upper Saddle River,
N.J. 07458
Multiple Regression to
Forecast #5-32
SUMMARY OUTPUT
Regression Statistics
Multiple R 0.673989793
R Square 0.454262242
Adjusted R Square 0.332987184
Standard Error 8.572787458
Observations 12
ANOVA
df SS MS F Significance F
Regression 2 550.5658367 275.2829184 3.745718626 0.065528166
Residual 9 661.4341633 73.49268481
Total 11 1212
Coefficients Standard Error t Stat P-value Lower 95% Upper 95%
Intercept 7.720611916 6.022703676 1.281917944 0.231907613 -5.903700728 21.34492456
Year -0.54576985 0.884817709 -0.616816147 0.552637609 -2.547368093 1.455828393
# Tourists 1.438808374 0.570482864 2.522088682 0.032656541 0.148285494 2.729331253

To accompany Quantitative Analysis for
Management, 7e by Render/ Stair
5-32 © 2000 by Prentice Hall, Inc. ,Upper Saddle River,
N.J. 07458
Regression SAS printout
Problem
Attendance Wins
40,000 6
60,000 11
60,000 9
50,000 9
45,000 8
55,000 8
50,000 10
a) What is the dependent variable?
b) Plot the data is it correlated?