MAT540
Week 4 Homework
Chapter 15
2. The manager of the Carpet City outlet needs to make an
accurate forecast of the demand for SoftShag 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 Demand for Soft Shag Carpet (1,000 yd.)
1 8
2 12
3 7
4 9
5 15
6 11
7 10
8 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 nextmonth so that the
proper number ofgallons 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 800
November 725
December 630
January 500
February 645
March 690
April 730
May 810
June 1,200
July 980
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 onthe average price of the fund
during the past 20 months:
Month Fund Price
1 $63 1/4
2 60 1/8
3 61 3/4
4 64 1/4
5 59 3/8
6 57 7/8
7 62 1/4
8 65 1/8
9 68 1/4
10 65 1/2
11 68 1/8
12 63 1/4
13 64 3/8
14 68 5/8
15 70 1/8
16 72 3/4
17 74 1/8
18 71 3/4
19 75 1/2
20 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 nextmost recent month weighted 0.30,and the
third month weighted 0.10,forecast the fundprice for month 21.
c. Compute an exponentially smoothed forecast,using α=0 .40,
and forecast the fund pricefor 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 thatthe store’s sales are
directly related to the number of new housing starts in town.The
manager hasgathered data from county records on monthly house
construction permits and from store recordson monthly sales.These
data are as follows:
Monthly Carpet Sales (1,000 yd.) Monthly ConstructionPermits
5 21
10 35
4 10
3 12
8 16
2 9
12 41
11 15
9 18
14 26
a. Develop a linear regression model for these data and
forecast carpet sales if 30 constructionpermits for new homes are
filed.
b. Determine the strength of the causal relationship between
monthly sales and new homeconstruction 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 losesbusiness, and if it orders too much, the extra must
be thrown away. The manager believes that amajor determinant of ice
cream sales is temperature (i.e., the hotter the weather, the more
icecream 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 Average Temperature
(degrees) Ice Cream Sold
(gal.)
1 73 110
2 65 95
3 81 135
4 90 160
5 75 97
6 77 105
7 82 120
8 93 175
9 86 140
10 79 121
a. Develop a linear regression model for these data and
forecast the ice cream consumption ifthe average weekly daytime
temperature is expected to be 85 degrees.
b. Determine the strength of the linear relationship between
temperature and ice creamconsumption by using correlation.
28. Compute the coefficient of determination for the data in
Problem 27 and explain its meaning.












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