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a. Prepare line graphs of each of the six expenditure categories. Indicate whether each category appears to be stationary or nonstationary.b. Use Holt’s method to create models for each expenditure category. Use Solver to estimate the values of α and β that minimize the MSE. What are the optimal values of α and β and the MSE for each model? What is the forecast for next year for each expenditure category?c. Estimate linear regression models for each expenditure category. What is the estimated regression equation and MSE for each model? What is the forecast for next year for each expenditure category?d. Fysco’s Vice President of Marketing has a new idea for forecasting market demand. For each expenditure category, she wants you to estimate the growth rate represented by g in the following equation: Ŷt+1 = Yt(1 + g). That is, the estimated value for time period t + 1 is equal to the actual value in the previous time period (t) multiplied by one plus the growth rate g. Use Solver to identify the optimal (minimum MSE) growth rate for each expenditure category. What is the growth rate for each category? What is the forecast for next year for each expenditure category?e. Which of the three forecasting techniques considered here would you recommend that Fysco use for each expenditure category?

a. Prepare line graphs of each of the six expenditure categories. Indicate whether each category appears to be stationary or nonstationary. b. Use Holts method to create models for each expenditure category. Use Solver to estimate the values of and that minimize the MSE. What are the optimal values of and and the MSE for each model? What is the forecast for next year for each expenditure category? c. Estimate linear regression models for each expenditure category. What is the estimated regression equation and MSE for each model? What is the forecast for next year for each expenditure category? d. Fyscos Vice President of Marketing has a new idea for forecasting market demand. For each expenditure category, she wants you to estimate the growth rate represented by g in the following equation: t+1 = Yt(1 + g). That is, the estimated value for time period t + 1 is equal to the actual value in the previous time period (t) multiplied by one plus the growth rate g. Use Solver to identify the optimal (minimum MSE) growth rate for each expenditure category. What is the growth rate for each category? What is the forecast for next year for each expenditure category? e. Which of the three forecasting techniques considered here would you recommend that Fysco use for each expenditure category? Fysco Foods, Inc. is one of the largest suppliers of institutional and commercial food products in the United States. Fortunately for Fysco, the demand for food away from home has been growing steadily over the past 22 years as shown in the following table (and the file FyscoFoods.xls on your data disk). This table breaks the total expenditures on food away from home (shown in the final column) into six component parts (e.g., eating & drinking places, hotels & motels, etc). As part of its strategic planning process, each year Fsyco generates forecasts of the total market demand in each of the six food away from home expenditure categories. This helps the company allocate its marketing resources among the various customers represented in each category.

(a)

See the Next sheets for the explaination. All six series are nonstationary.

(b)

Series Eating & drinking places Hotels & motels Retail stores, direct selling Recreational places Schools & colleges Eating & drinking places

a 1 0.758 1 0.852 0.95 1

b 0.491 0.698 0.059 0.111 0.584 0.501

MSE 39171511.4 157086.1 940813 822724 87677.7 492037.9

(c ) Series Eating & drinking places Hotels & motels Retail stores, direct selling Recreational places Schools & colleges Eating & drinking places Intercept -19682495.4 -1073108.6 -744887.2 -933269.2 -1659605.4 -1722215.6 Slope 9976.6 545.2 380.9 472.4 843 878.1 MSE 48497973.7 230616 1439823.2 806761.7 614900.8 520190.6

(d)

Series Eating & drinking places Hotels & motels Retail stores, direct selling Recreational places Schools & colleges Eating & drinking places

Growth rate 0.0553 0.0433 0.0266 0.0472 0.0446 0.0339

MSE 34744362.4 149423.1 868556.9 790450.3 69928.3 382278.3

Forecast 306749.8 18675.4 17330.7 12366.7 29263 36191.9

(e)

For each series, the growth rate approach had the smallest MSE. The moral of the case is that so

Forecast 304879 18599.5 17153.7 12155.3 28956.3 35827.8

Forecast 290609.6 18400.8 17578.7 12501.2 27992.4 35652.3

moral of the case is that sometimes the simplest forecasting method is the best!

Year 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22

Eating & drinking places 75,883 83,358 90,390 98,710 105,836 111,760 121,699 146,194 160,855 171,157 183,484 188,228 183,014 195,835 205,768 214,274 221,735 235,597 248,716 260,495 275,695 290,655

Hotels & motels 5,906 6,639 6,888 7,660 8,409 9,168 9,665 11,117 11,905 12,179 12,508 12,460 13,204 13,362 13,880 14,195 14,504 15,469 15,800 16,623 17,440 17,899

Retail stores, direct selling 8,158 8,830 9,256 9,827 10,315 10,499 11,116 12,063 13,211 14,440 16,053 16,750 13,588 13,777 14,210 14,333 14,475 14,407 15,198 16,397 16,591 16,881

Recreational Schools & places colleges All other 3,040 11,115 16,194 2,979 11,357 17,751 2,887 11,692 18,663 3,271 12,338 19,077 3,489 12,950 20,047 3,737 13,534 20,133 4,059 14,401 20,755 4,331 14,300 21,122 5,144 14,929 22,887 6,151 15,728 24,581 7,316 16,767 26,198 8,079 17,959 27,108 8,602 18,983 27,946 9,275 19,844 28,031 9,791 21,086 28,208 10,574 22,093 28,597 11,354 22,993 28,981 8,290 24,071 30,926 9,750 25,141 31,926 10,400 26,256 33,560 11,177 27,016 34,508 11,809 28,012 35,004

Total 120,296 130,914 139,776 150,883 161,046 168,831 181,695 209,127 228,930 244,236 262,326 270,584 265,338 280,124 292,943 304,066 314,043 328,760 346,530 363,730 382,427 400,259

350,000 300,000

14,000

Expenditures

Expenditures

250,000 200,000 150,000 100,000 50,000 0 1 4

Eating & drinking places

12,000 10,000 8,000 6,000 4,000 2,000 0

7

10

13

16

19

22

Year20,000 18,000 16,000 14,000 12,000 10,000 8,000 6,000 4,000 1 4 7 10 13 16 19 22 30,000

Expenditures

Expenditures Year

Hotels & motels

25,000 20,000 15,000 10,000 5,000

18,000

40,000

Expenditures13 16 19 22

16,000

Expenditures

Retail stores, direct selling

35,000 30,000 25,000 20,000 15,000 10,000 5,000

14,000 12,000 10,000 8,000 6,000 1 4 7 10

Year

14,000 12,000 10,000 8,000 6,000 4,000 2,000 0 1 4 7 10 13 16 19 22

Recreational places

Year30,000 25,000 20,000 15,000 10,000 5,000 0 1 4 7 10 13 16 19 22

Schools & colleges

Year40,000 35,000 30,000 25,000 20,000 15,000 10,000 5,000 0 1 4 7 10 13 16 19 22

All other

Year

Series 1 - Holts

Eating & drinking Year places 75,883 1 83,358 2 90,390 3 98,710 4 105,836 5 111,760 6 121,699 7 146,194 8 160,855 9 171,157 10 183,484 11 188,228 12 183,014 13 195,835 14 205,768 15 214,274 16 221,735 17 235,597 18 248,716 19 260,495 20 275,695 21 290,655 22 23 --

Base Level 75883 83358 90390 98710 105836 111760 121699 146194 160855 171157 183484 188228 183014 195835 205768 214274 221735 235597 248716 260495 275695 290655 --

Trend 0.00 3673.30 5323.81 6796.17 6958.25 6450.01 8164.54 16189.52 15438.39 12914.31 12625.70 8752.54 1889.21 7261.22 8574.17 8540.67 8010.11 10885.80 11983.22 11882.86 13512.94 14224.04 --

Predicted Expenditures -75883.0 87031.3 95713.8 105506.2 112794.3 118210.0 129863.5 162383.5 176293.4 184071.3 196109.7 196980.5 184903.2 203096.2 214342.2 222814.7 229745.1 246482.8 260699.2 272377.9 289207.9 304879.0

alpha = beta = MSE =350,000 300,000 250,000 Expenditures 200,000 150,000 100,000 50,000 0

Page 13

Series 1 - Holts

1 0.491 39171511.4350,000 300,000 250,000

Minimize: H6 By Changing: H3:H4 Subject To: 0