Mat 540 week 4 homework (chapter 15)

Chapter 15

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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 1500 July 1200

a.       Compute an exponential smoothed forecast, using an α value of 0.4

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

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 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

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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