Melody Baker has just been appointed director of recreation programs for Highland Park. In the past, the city has sponsored a number of softball leagues in the summer months. From the city’s cost records, Baker has found the following total costs associated with the softball leagues over the past five years:

Number of LeaguesTotal Costs

5. . . . . . . . . . . . . . . . . . . . $13,000

2. . . . . . . . . . . . . . . . . . . . 7,000

4. . . . . . . . . . . . . . . . . . . . 10,500

6. . . . . . . . . . . . . . . . . . . . 14,000

3. . . . . . . . . . . . . . . . . . . . 10,000

Each league requires its own paid supervisor and paid umpires as well as printed schedules and other copy work. Therefore, Baker knows that some variable costs are associated with the leagues. She would like to know the amount of variable cost per league and the total fixed cost per year associated with the softball program. This information would help her plan.

Required:

1. Using the least-squares regression method, estimate the variable cost per league and the total fixed cost per year for the softball program.

2. Express the cost data derived in (1) above in the form Y = a + bX.

3. Assume that Baker would like to expand the softball program during the coming year to involve a total of seven leagues. Compute the expected total cost for the softball program. Can you see any problem with using the cost formula from (2) above to derive this total cost figure? Explain.

4. Prepare a scattergram and fit a line to the plotted points using the cost formula expressed in (2) above.