In: Statistics and Probability
The Condé Nast Traveler Gold List provides ratings for the top 20 small cruise ships. The data shown below are the scores each ship received based upon the results from Condé Nast Traveler's Annual Readers' Choice Survey. Each score represents the percentage of respondents who rated a ship as excellent or very good on several criteria, including Shore Excursions and Food/Dining. An overall score was also reported and used to rank the ships. The highest ranked ship, the Seabourn Odyssey, has an overall score of 94.4, the highest component of which is 97.8 for Food/Dining.
Ship | Overall | Shore Excursions |
Food/Dining |
---|---|---|---|
Seabourn Odyssey | 94.4 | 90.9 | 97.8 |
Seabourn Pride | 93.0 | 84.2 | 96.7 |
National Geographic Endeavor | 92.9 | 100.0 | 88.5 |
Seabourn Sojourn | 91.3 | 94.8 | 97.1 |
Paul Gauguin | 90.5 | 87.9 | 91.2 |
Seabourn Legend | 90.3 | 82.1 | 98.8 |
Seabourn Spirit | 90.2 | 86.3 | 92.0 |
Silver Explorer | 89.9 | 92.6 | 88.9 |
Silver Spirit | 89.4 | 85.9 | 90.8 |
Seven Seas Navigator | 89.2 | 83.3 | 90.5 |
Silver Whisperer | 89.2 | 82.0 | 88.6 |
National Geographic Explorer | 89.1 | 93.1 | 89.7 |
Silver Cloud | 88.7 | 78.3 | 91.3 |
Celebrity Xpedition | 87.2 | 91.7 | 73.6 |
Silver Shadow | 87.2 | 75.0 | 89.7 |
Silver Wind | 86.6 | 78.1 | 91.6 |
SeaDream II | 86.2 | 77.4 | 90.9 |
Wind Star | 86.1 | 76.5 | 91.5 |
Wind Surf | 86.1 | 72.3 | 89.3 |
Wind Spirit | 85.2 | 77.4 | 91.9 |
(a)
Determine an estimated regression equation that can be used to predict the overall score given the score for Shore Excursions. (Round your numerical values to two decimal places. Let x1 represent the Shore Excursions score and y represent the overall score.)
ŷ =
(b)
Consider the addition of the independent variable Food/Dining. Develop the estimated regression equation that can be used to predict the overall score given the scores for Shore Excursions and Food/Dining. (Round your numerical values to two decimal places. Let x1 represent the Shore Excursions score, x2 represent the Food/Dining score, and yrepresent the overall score.)
ŷ =
(c)
Predict the overall score for a cruise ship with a Shore Excursions score of 82 and a Food/Dining Score of 91. (Round your answer to one decimal place.)