Holiday Cruise Lines is evaluating the cost of operating its newest ship, the Caribbean Summer. In its first year of operation, the Caribbean Summer completed 25 short cruises along the same route, but with varying numbers of passengers on board. The chief operating officer of Holiday Cruise Lines collected the total cost of operating each short cruise, as well as the num- ber of passengers on board, and summarized the data:

Assume that Y in this information is the total cost of operating the ship on a short cruise, in millions of US dollars, while X is the number of passengers on that cruise stated in thousands.

Questions 

1. According to the information, what was the average total cost of operating the Carib- bean Summer on one of its 25 short cruises? 

2. Use this information to find the linear regression equation that best explains the relationship of the total cost of a short cruise to the number of passengers on that cruise. What is that equation? Using that equation, what total cost would you pre- dict for a Caribbean Summer short cruise carrying 2,500 passengers? 

3. What percent of the variation in the total cost of operating the ship on these 25 short cruises is explained by your regression equation? 

4. The chief operating officer is particularly interested in understanding the fixed cost of operating the Caribbean Summer on a short cruise, which represents the expenses that would be incurred regardless of whether there are no, few, or many passengers aboard. The Caribbean Summer was built to eventually replace its sister ship the Tropical Equinox, which requires a fixed cost of about $2 million to complete a short cruise similar to those being evaluated here. What does your regression equation indicate about this issue? Does the newer Caribbean Summer have lower fixed costs than the Tropical Equinox?

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= 25 = 31.17 X=3.28 Y-1.25 EX = 82.03 . = 39.38 = 104.39 EX = 280.07