MAT 540 Homework Week 4 Homework

1. 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 hascollected the following demand data for the past 8 months:Demand for Soft ShagMonth Carpet (1,000 yd.)1 92 83 74 85 106 117 138 12a. 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. Assignweights of 0.50, 0.30, and 0.20 to the months in sequence, starting with the most recentmonth.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 gasolinenext month so that the proper number of gallons can be ordered from the distributor. The ownerhas accumulated the following data on demand for unleaded gasoline from sales during the past 10months:Month Gasoline Demanded (gal.)October 800November 725December 600January 500February 625March 690April 810May 935June 1,200July 1,100Page 2 of 4a. Compute an exponentially smoothed forecast, using an a value of 0.30.b. Compute the MAPD.3. Emily Andrews has invested in a science and technology mutual fund. Now she is consideringliquidating and investing in another fund. She would like to forecast the price of the science andtechnology fund for the next month before making a decision. She has collected the following dataon the average price of the fund during the past 20 months:Month Fund Price1 $57 3/42 541/43 551/84 581/85 533/86 511/87 561/48 595/89 621/410 59 1/411 62 3/812 57 1/113 58 1/814 62 3/415 64 3/416 66 1/817 68 3/418 65 1/219 69 7/820 70 1/4a. 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 a=0 .40, and forecast the fund price formonth 21.U. 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 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 ConstructionPermits9 1714 2510 812 715 149 724 4521 1920 2829 28a. 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.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 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 daytimetemperature for 14 weeks, selected at random, and from store records he has determined the icecream consumption for the same 14 weeks. These data are summarized as follows:Average Temperature Ice Cream SoldWeek (degrees) (gal.)1 68 802 70 1153 73 914 79 875 77 1106 82 1287 85 1648 90 1789 85 14410 92 17911 90 14412 95 19713 80 14414 75 123a. Develop a linear regression model for these data and forecast the ice cream consumption ifthe average weekly daytime temperature is expected to be $5 degrees.b. Determine the strength of the linear relationship between temperature and ice creamconsumption by using correlation.6. Report the coefficient of determination for the data in Problem 5 and explain its meaning.