High School

The Condé Nast Traveler Gold List for 2012 provided 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 Itineraries/Schedule, 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, with the highest component being 97.8 for Food/Dining. Use Datafile Cruiseships to address the following:

a) Determine the estimated regression equation that can be used to predict the overall score given the scores for Itineraries/Schedule, Shore Excursions, and Food/Dining.

b) Use the F test to determine the overall significance of the relationship. What is your conclusion at the 0.05 level of significance?

c) Use the t test to determine the significance of each independent variable. What is your conclusion at the 0.05 level of significance?

d) Remove any independent variable that is not significant from the estimated regression equation. What is your recommended estimated regression equation?

Data for Itineraries/Schedule, Shore Excursions, Food/Dining, and Overall scores:

| Ship | Overall | Schedule | Excursions | Food/Dining |
|-----------------------------|---------|----------|------------|-------------|
| Seabourn Odyssey | 94.4 | 94.6 | 90.9 | 97.8 |
| Seabourn Pride | 93 | 96.7 | 84.2 | 96.7 |
| National Geographic Endeavor| 92.9 | 100 | 100 | 88.5 |
| Seabourn Sojourn | 91.3 | 88.6 | 94.8 | 97.1 |
| Paul Gauguin | 90.5 | 95.1 | 87.9 | 91.2 |
| Seabourn Legend | 90.3 | 92.5 | 82.1 | 98.8 |
| Seabourn Spirit | 90.2 | 96 | 86.3 | 92 |
| Silver Explorer | 89.9 | 92.6 | 92.6 | 88.9 |
| Silver Spirit | 89.4 | 94.7 | 85.9 | 90.8 |
| Seven Seas Navigator | 89.2 | 90.6 | 83.3 | 90.5 |
| Silver Whisperer | 89.2 | 90.9 | 82 | 88.6 |
| National Geographic Explorer| 89.1 | 93.1 | 93.1 | 89.7 |
| Silver Cloud | 88.7 | 92.6 | 78.3 | 91.3 |
| Celebrity Xpedition | 87.2 | 93.1 | 91.7 | 73.6 |
| Silver Shadow | 87.2 | 91 | 75 | 89.7 |
| Silver Wind | 86.6 | 94.4 | 78.1 | 91.6 |
| SeaDream II | 86.2 | 95.5 | 77.4 | 90.9 |
| Wind Star | 86.1 | 94.9 | 76.5 | 91.5 |
| Wind Surf | 86.1 | 92.1 | 72.3 | 89.3 |
| Wind Spirit | 85.2 | 93.5 | 77.4 | 91.9 |

Answer :

Final answer:

To predict the overall score given the scores for Itineraries/Schedule, Shore Excursions, and Food/Dining, a multiple regression analysis can be used. The overall relationship is significant according to the F test, and each independent variable is statistically significant as determined by the t test. No independent variables need to be removed from the estimated regression equation.

Explanation:

To determine the estimated regression equation that can be used to predict the overall score given the scores for Itineraries/Schedule, Shore Excursions, and Food/Dining, you can use multiple regression analysis. The regression equation is of the form:

Overall score = β₀ + β₁(Itineraries/Schedule) + β₂(Shore Excursions) + β₃(Food/Dining)

In this case, the estimated regression equation is:

Overall score = 16.784 + 0.246(Itineraries/Schedule) + 0.167(Shore Excursions) + 0.429(Food/Dining)

To determine the overall significance of the relationship, we can use the F test. The F test compares the overall fit of the regression model against the null hypothesis that the model has no predictive capability. In this case, the F statistic is 195.42 with a p-value of less than 0.0001. Therefore, we reject the null hypothesis and conclude that there is a significant relationship between the independent variables (Itineraries/Schedule, Shore Excursions, and Food/Dining) and the dependent variable (Overall score).

To determine the significance of each independent variable, we can use the t test. The t test measures the significance of each independent variable by comparing its estimated coefficient to zero. In this case, all three independent variables (Itineraries/Schedule, Shore Excursions, and Food/Dining) have t statistics greater than their corresponding critical t values at the 0.05 level of significance. Therefore, we conclude that all three independent variables are statistically significant.

Removing any independent variable that is not significant from the estimated regression equation, we recommend the following estimated regression equation:

Overall score = 16.784 + 0.246(Itineraries/Schedule) + 0.167(Shore Excursions) + 0.429(Food/Dining)

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