Chapter 4: Forecasting
Problem 1: Auto sales at Carmen’s Chevrolet are shown below. Find a Naive forecast
for week 7. Compute the MAD, MAPE and MSE values.
t
Auto
Sales (At)
1
8
2
10
3
9
4
11
5
10
6
13
Forecast
(Ft)
Error (Et) = At – Ft
1
|Et|
|Et|/At
Et2
Problem 2: Auto sales at Carmen’s Chevrolet are shown below. Find a 2 and 3-week and
moving average forecasts for week 7. Compute the MAD and MAPE values.
t
Sales
1
8
2
10
3
9
4
11
5
10
6
13
t
Sales
1
8
2
10
3
9
4
11
5
10
6
13
Forecast 2-MA
Forecast 3-MA
Error (Et)
Error (Et)
2
|Et|
|Et|/At
|Et|
|Et|/At
Problem 3: Carmen’s decides to forecast auto sales by weighting the three weeks with a
weight of 2 for last week, and 1 for each of the two weeks prior.
t
Auto Sales
1
8
2
10
3
9
4
11
5
10
6
13
Forecast
Error (Et)
3
|Et|
Problem 4: Exponential smoothing is used to forecast automobile battery sales with  =
0.8. Evaluate the accuracy of each smoothing constant. Which is preferable? (Assume
the forecast for January was 22 batteries.) Actual sales are given below.
Sales
Forecast with  = 0.8
January
20
Given: F1 = 22
February
21
March
15
April
14
May
13
June
16
Month
4
Error (Et)
Problem 5: Use the sales data given below to determine: (a) the least squares trend line,
and (b) the predicted value for 2003 and 2004 sales. To minimize computations,
transform the value of x (time) to simpler numbers. In this case, designate year 1996 as
year 1, 1997 as year 2, etc.
Year
t
Demand
1996
100
1997
110
1998
122
1999
130
2000
139
2001
152
2002
164
X2
XY
Sum =
5
Problem 6: The following table shows sales data for water pumps sold by Meredith and
Smunt Manufacturing. Compute the quarterly index.
Quarter
Year 1
Year 2
Year 3
Year 4
Spring
3750
3890
4150
4210
Summer
2850
2990
3060
3100
Fall
1820
1970
2020
2190
950
990
1010
1050
Winter
Quarter
Average
Index
Spring
Summer
Fall
Winter
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Problem 7: Using the data in Problem #6, Meredith and Smunt Manufacturing expects
annual sales of pumps to grow by 10% next year. Compute next year’s sales and the sales
for each quarter.
Problem 8: A large metropolitan county developed a forecasting model for the number
of daily arrests for public drunkenness for use in scheduling officers. The arrest trend line
is given by 50 + 0.2t, where t = 1 for day 1 of week 1 of the fiscal year. In addition, the
multiplicative seasonal factors for the seven weekdays are as follows:
Monday
0.9
Tuesday
0.8
Wednesday
0.6
Thursday
0.9
Friday
1.3
Saturday
1.4
Sunday
1.1
The supervising officer is developing schedule for week 25 and wishes to develop
forecast for the expected number of arrests for the seven days of week 25. Find these
forecasts.
t
Trend
Factor
Monday
Tuesday
Wednesday
Thursday
Friday
Saturday
Sunday
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Forecast
Problem 9: Given the forecast demand and demand for fishing boats, compute the
tracking signal.
Week
Demand
Forecast
1
71
78
2
80
75
3
101
101
4
60
88
Et
|Et|
CFEt
CAEt
MADt
Error (Et)
CFEt
|Et|
CAEt
= Error = Demand - Forecast
= Absolute error = |Demand – Forecast|
= Running Sum of Et
= Running Sum of |Et|
= Running MAD for period t = CAEt/ No. of error
Tracking Signal = CFEt/MADt
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No. of
Error
MADt
Tracking Signal =
CFEt/MADt
Problem 10: Regional Foods, Inc. sells organic soap products. A random sample of
advertising expense in thousand dollars for eight randomly selected months and
corresponding sales in million dollars is given below.
Sales
($Million)
Advertising
expense (000 $)
1
2.56
25.0
2
1.74
17.0
3
2.11
21.0
4
1.37
15.0
5
1.42
13.0
6
1.66
14.0
7
1.01
10.0
8
2.26
20.0
Month
XY
X2
Y2
a. Develop a linear regression equation for predicting sales using the amount spent on
advertising.
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b. Determine the coefficient of correlation and the standard error of the estimate.
c. Find a forecast for the sales next month if the company is considering spending
$15,000 on advertising. If the company spends $22,500 on advertising what will be
the expected sales?
d. Find a forecast for the sales next month if the company spends $22,500 on
advertising.
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Problem #11: The multiple regression equation Ŷ = 16.4 – 4.2X1 + 1.5X2 was developed
to forecast daily milk sales in 1,000 gallons with X1 = Price per gallon and X2 =
Advertising expense in $1,000. Calculate the estimated weekly milk sales milk in gallons
if (a) the price per gallon is set at $4.50 and $3000 was spent on advertising, and (b) the
price per gallon is set at $5.00 and $4400 was spent on advertising. Which of the two
alternative strategies will generate more revenue net of the advertising expense?
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