Forecasting Problem of Arnold Tofu

1. Arnold Tofu owns and operates a chain of 12 vegetable protein "hamburger" restaurants in northern Louisiana. Sales figures and profits for the stores are in the table below. Sales are given in millions of dollars; profits are in hundred of thousands of dollars. Calculate a regression line for the data. What is your forecast of profit for a store with sales of $24 million? $30 million?
Store Sales Profits Store Sales Profits
1 7 15 7 16 24
2 2 10 8 12 20
3 6 13 9 14 27
4 4 15 10 20 44
5 14 25 11 15 34
6 15 27 12 7 17

2. Favors Distribution Company purchases small imported trinkets in bulk, packages them, and sells them to retail stores. They are conducting an inventory control study of all their items. The following data are for one such item, which is not seasonal.
a. Use trend projection to estimate the relationship between time and sales (state the equation).
b. Calculate forecasts for the first four months of the next year.

1 2 3 4 5 6 7 8 9 10 11 12
Month Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
Sales 51 55 54 57 50 68 66 59 67 69 75 73

3. The quarterly sales for specific educational software over the past three years are given in the following table. Compute the four seasonal indices.

YEAR 1 YEAR 2 YEAR 3
Quarter 1 1690 1800 1850
Quarter 2 940 900 1100
Quarter 3 2625 2900 2930
Quarter 4 2500 2360 2615

4. Calculate three forecasts using the following data. First, for periods 4 through 11, develop the exponentially smoothed forecasts using a forecast for period 3 (F3) of 45.0 and an alpha of 0.4. Second, calculate the three-period moving average forecast for periods 4 through 11. Third, calculated the weighted moving average for periods 4 through 11,using weights of .70, .20, and .10. Calculate the mean absolute deviation (MAD) and the cumulative sum of forecast error (CFE) for each forecasting procedure. Which forecasting procedure would you select? Why?
Month Demand
1 45
2 48
3 43
4 48
5 49
6 54
7 47
8 50
9 46
10 47