Question - Amanda King has just been appointed director of recreation programs for Highland Park, a rapidly growing community in Connecticut. In the past, the city has sponsored a number of softball leagues in the summer months. From the city's cost records, Amanda has found the following total costs associated with the softball leagues over the last five years:
Number of Leagues Total Cost
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, Amanda 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 for planning purposes.
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 Amanda 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.