MAT540
MAT540
Week 4 Homework
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1. The manager of
the Carpet City outlet needs to make an accurate forecast of the demand for
Soft Shag carpet (its biggest seller). If the manager does not order enough
carpet from the carpet mill, customer
will buy their
carpet from one
of Carpet City’s
many competitors. The
manager has
collected the following demand data for the past 8 months:
Month
Demand for Soft Shag
Carpet (1,000 yd.)
1
10
2
9
3
8
4
9
5
10
6
12
7
14
8 11
a. Compute a 3-month moving average forecast
for months 4 through 9.
b. Compute
a weighted 3-month
moving average forecast
for months 4
through 9. Assign weights of
0.55, 0.35, and 0.10 to the
months in sequence, starting with
the most recent month.
c. Compare the two forecasts by using MAD.
Which forecast appears to be more accurate?
2. The manager
of the Petroco
Service Station wants
to forecast the demand
for unleaded gasoline next month so that the proper number
of gallons can be ordered from the distributor. The owner has accumulated the
following data on
demand for unleaded
gasoline from sales
during the past
10 months:
Month Gasoline
Demanded (gal.) October
775
November 835
December
605
January
450
February
600
March
700
April
820
May
925
June
July
1500
1200
a. Compute an exponential smoothed forecast,
using an α value of 0.4
b. Compute the MAD.
3. Emily Andrews
has invested in
a science and
technology mutual fund.
Now she is
considering liquidating and investing in another fund. She would like to
forecast the price of the science and technology fund for the next month before
making a decision. She has collected the following data on the average price of
the fund during the past 20 months:
Month Fund
Price
1
$55 ¾
2
54 ¼
3
55 1/8
4
58 1/8
5
53 3/8
6
51 1/8
7
56 ¼
8
59 5/8
9
62 ¼
10
59 ¼
11
62 3/8
12
57 1/1
13
58 1/8
14
62 ¾
15
64 ¾
16 66 1/8
17
68 ¾
18
60.5
19
65.875
20
72.25
a. Using a 3-month average, forecast the fund
price for month 21.
b. Using a 3-month weighted average with the
most recent month weighted 0.5, the next most recent month weighted 0.30, and
the third month weighted 0.20, forecast the fund price for month 21.
c. Compute an
exponentially smoothed forecast, using α=0.3, and forecast the fund price for
month 21.
d. Compare the forecasts in (a), (b), and (c),
using MAD, and indicate the most accurate.
4. Carpet City wants to develop
a means to forecast its carpet sales. The store manager believes that the
store’s sales are directly related to the number of new housing starts in town.
The manager has gathered data from county records on monthly house construction
permits and from store records
on monthly sales. These data are as follows:
Monthly
Carpet Sales
(1,000 yd.)
Monthly
Construction
Permits
9
17
14
25
10 8
12
7
15
14
9
7
24
45
21
19
20 28
29
28
a. Develop
a linear regression model
for these data and forecast
carpet sales if 30 construction permits for new homes are filed.
b. Determine
the strength of the causal
relationship between monthly
sales and new
home construction by using correlation.
5. The manager of Gilley’s Ice Cream Parlor
needs an accurate forecast of the demand for ice cream.
The store orders ice
cream from a distributor a week ahead; if the store orders too little, it loses
business, and if it
orders too much, the
extra must be
thrown away. The manager
belives that a major determinant
of ice cream sales is temperature (i.e.,the hotter the weather, the more ice
cream people buy). Using an almanac, the manager has determined the average day
time temperature for
14 weeks, selected at random, and from store records
he has determined the ice cream consumption
for the same 14 weeks. These data are
summarized as follows:
Week
Average Temperature
(Degrees)
Ice Cream Sold
(gal.)
1
68
80
2
70
115
3
73 91
4
79
87
5
77
110
6
82
128
7
85
164
8
90 178
9
85
144
10
92
179
11 90
144
12
95
197
13
80
144
14 75
123
a. Develop a linear regression model for these
data and forecast the ice cream consumption if the average weekly daytime
temperature is expected to be 85 degrees.
b. Determine
the strength of the linear
relationship between temperature
and ice cream consumption by using correlation.
c. What is the coefficient of determination?
Explain its meaning.
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