MAT540 Homework
Week 4
Page 1 of 4
MAT540
Week 4 Homework
Chapter 15
2. 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,
customers 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
1
2
3
4
5
6
7
8
Demand for Soft Shag
Carpet (1,000 yd.)
8
12
7
9
15
11
10
12
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, 0.33, and 0.12 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?
6. 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
October
November
December
January
February
March
April
May
June
July
Gasoline Demanded (gal.)
800
725
630
500
645
690
730
810
1,200
980
MAT540 Homework
Week 4
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a. Compute an exponentially smoothed forecast, using an α value of 0.30.
b. Compute the MAPD.
9. 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
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
Fund Price
$63 1/4
60 1/8
61 3/4
64 1/4
59 3/8
57 7/8
62 1/4
65 1/8
68 1/4
65 1/2
68 1/8
63 1/4
64 3/8
68 5/8
70 1/8
72 3/4
74 1/8
71 3/4
75 1/2
76 3/4
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 0.60, the next
most recent month weighted 0.30, and the third month weighted 0.10, forecast the fund
price for month 21.
c. Compute an exponentially smoothed forecast, using α=0 .40, and forecast the fund price for
month 21.
d. Compare the forecasts in (a), (b), and (c), using MAD, and indicate the most accurate.
26. 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
MAT540 Homework
Week 4
Page 3 of 4
on monthly sales. These data are as follows:
Monthly Carpet Sales
(1,000 yd.)
5
10
4
3
8
2
12
11
9
14
Monthly Construction
Permits
21
35
10
12
16
9
41
15
18
26
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.
27. 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 believes 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 daytime
temperature for 10 weeks, selected at random, and from store records he has determined the ice
cream consumption for the same 10 weeks. These data are summarized as follows:
Week
1
2
3
4
5
6
7
8
9
10
Average Temperature
(degrees)
73
65
81
90
75
77
82
93
86
79
Ice Cream Sold
(gal.)
110
95
135
160
97
105
120
175
140
121
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.
MAT540 Homework
Week 4
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b. Determine the strength of the linear relationship between temperature and ice cream
consumption by using correlation.
28. Compute the coefficient of determination for the data in Problem 27 and explain its meaning.
Carpet City
Month
1
2
3
4
5
6
7
8
9
Demand for Soft Shag Carpet (1,000
yd.)
8
12
7
9
15
11
10
12
3 mos moving
Weighted 3 mos moving
average forecast average forecast
Please apply weights
stated in the problem
Compute MAD on 3 mos moving average
Compute MAD on weighted 3 mos moving average
Which is a better forecast method?
Petroco Service Station
alpha =
0,3
Month
October
November
December
January
February
March
April
May
June
July
Gas Demand
800
725
630
500
645
690
730
810
1200
980
7710
Exp Forecast
Error
777,5
0,00
MAPD
0,00%
SUM
Science and Technology Mutual Fund
Month
Fund Price
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
63 1/4
60 1/8
61 3/4
64 1/4
59 3/8
57 7/8
62 1/4
65 1/8
68 1/4
65 1/2
68 1/8
63 1/4
64 3/8
68 5/8
70 1/8
72 3/4
74 1/8
71 3/4
75 1/2
76 3/4
alpha =
3 mos moving average
forecast
0,4
Compute MAD on 3 mos moving average
Compute MAD on weighted 3 mos moving average
Compute MAD on exponentially smoothed forecast
Which is a better forecast method?
Weighted 3 mos
moving average
forecast
Please apply weights
stated in the problem
Exp Forecast
Carpet City Regression
Monthly Carpet Sales Monthly Construction
(1,000 yd.)
Permits
5
10
4
3
8
2
12
11
9
14
21
35
10
12
16
9
41
15
18
26
Place regression output here
If 30 construction permits issued
What is expected carpet sales (1000 yds)?
Correlation Coefficient
Gilley's Ice Cream Parlor
Week
1
2
3
4
5
6
7
8
9
10
x
y
Ave. Temp
(degrees)
73
65
81
90
75
77
82
93
86
79
Ice cream Sold
(gal.)
110
95
135
160
97
105
120
175
140
121
Place regression output here
If average 85 deg weekly daytime temperature
What is expected ice cream sold?
Correlation Coefficient
Coefficient of Determination
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