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MAT540 Homework
Week 4
Page 1 of 5
MAT540
Week 4 Homework
Chapter 15
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:
MAT540 Homework
Week 4
Page 2 of 5
Month
Gasoline Demanded (gal.)
October
775
November
835
December
605
January
450
February
600
March
700
April
820
May
925
June
1500
July
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
MAT540 Homework
Week 4
Page 3 of 5
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
Monthly Construction
(1,000 yd.)
Permits
9
17
14
25
10
8
12
7
15
14
9
7
24
45
21
19
20
28
MAT540 Homework
Week 4
Page 4 of 5
28
29
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:
Average Temperature
Ice Cream Sold
(Degrees)
(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
Week
MAT540 Homework
Week 4
Page 5 of 5
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.
Carpet City
Month
1
2
3
4
5
6
7
8
9
3 mos moving average
Demand for Soft Shag Carpet (1,000 yd.) forecast
10
9
8
9
10
12
14
11
Compute MAD on 3 mos moving average
Compute MAD on weighted 3 mos moving average
Which is a better forecast method?
Weighted 3 mos moving
average forecast
Please apply weights
stated in the problem
Error abs()
Error abs()
Weights: 0.55 (most recent month), 0.35, 0.10
Note: average over month 4 through 8 only. No data available to month 9
Note: average over month 4 through 8 only. No data available to month 9
Petroco Service Station
alpha =
0.4
Month
October
November
December
January
February
March
April
May
June
July
August
Gas Demand
775
835
605
450
600
700
820
925
1500
1200
8410
MAPD
Exp Forecast
—-
Error
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
55 3/4
54 1/4
55 1/8
58 1/8
53 3/8
51 1/8
56 1/4
59 5/8
62 1/4
59 1/4
62 3/8
58
58 1/8
62 3/4
64 3/4
66 1/8
68 3/4
60 1/2
65 7/8
72 1/4
3 mos moving average forecast
———-
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?
alpha =
Weighted 3 mos moving average
forecast
———-
Please apply weights stated in the
problem
0.3
Exp Forecast
—-
Weight 0.5 (most recent), 0.3, 0.2
3 mos MA Weighted 3
error
mos MA error
Exp. Smoothing
error
Carpet City Regression
X – axis
Monthly
Construction
Permits
17
25
8
7
14
7
45
19
28
28
Y – axis
Monthly Carpet Sales
(1,000 yd.)
9
14
10
12
15
9
24
21
20
29
Place regression output here
Y = A + Bx
A=
B=
Forecast Carpet sales for 30 construction permits
Correlation Coefficient
Gilley’s Ice Cream Parlor
Week
1
2
3
4
5
6
7
8
9
10
11
12
13
14
x
y
Ave. Temp
(degrees)
68
70
73
79
77
82
85
90
85
92
90
95
80
75
Ice cream Sold
(gal.)
80
115
91
87
110
128
164
178
144
179
144
197
144
123
Place regression output here
(a)
Y = A + Bx
A=
B=
(b)
Correlation Coefficient
(c’)
Coefficient of Determination
Explain the meaning of the coefficient of Determination below. What does it indicate?
…
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