4. The Condé Nast Traveler Gold List for 2012 provided ratings for the top 20 small cruise ships (Condé Nast Traveler website, March 1, 2012). 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:

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?

The estimated regression equation that can be used to predict the overall score given the scores for Itineraries/Schedule, Shore Excursions, and Food/Dining is: Overall Score = b0 + b1(Itineraries/Schedule) + b2(Shore Excursions) + b3(Food/Dining). The F test is used to determine the overall significance of the relationship between the independent variables and the dependent variable. The t test is used to determine the significance of each individual independent variable. If a variable is found to be not significant, it can be removed from the estimated regression equation.

Explanation:

a) Estimated Regression Equation:

To determine the estimated regression equation, we need to use the given data from the Condé Nast Traveler Gold List for 2012. The scores for Itineraries/Schedule, Shore Excursions, and Food/Dining are the independent variables, and the overall score is the dependent variable.

We can use statistical software or calculators to perform the regression analysis. The estimated regression equation will be in the form:

Overall Score = b0 + b1(Itineraries/Schedule) + b2(Shore Excursions) + b3(Food/Dining)

where b0, b1, b2, and b3 are the regression coefficients.

b) F Test:

The F test is used to determine the overall significance of the relationship between the independent variables and the dependent variable. The null hypothesis is that there is no relationship between the variables.

We can perform the F test using statistical software or calculators. The test will provide an F statistic and a p-value. If the p-value is less than the significance level (0.05 in this case), we reject the null hypothesis and conclude that there is a significant relationship between the independent variables and the dependent variable.

c) t Test:

The t test is used to determine the significance of each individual independent variable. The null hypothesis is that the coefficient of the independent variable is zero, indicating no significant effect on the dependent variable.

We can perform the t test for each independent variable using statistical software or calculators. The test will provide a t statistic and a p-value. If the p-value is less than the significance level (0.05 in this case), we reject the null hypothesis and conclude that the independent variable has a significant effect on the dependent variable.

d) Removing Non-Significant Variables:

If any independent variable is found to be not significant (p-value > 0.05), it can be removed from the estimated regression equation. This means that the variable does not have a significant effect on the dependent variable and including it in the equation does not improve the model's predictive power.

Recommended Estimated Regression Equation:

Based on the results of the F test and t tests, we can determine which variables are significant and should be included in the estimated regression equation. The recommended estimated regression equation will only include the significant variables.

Learn more about regression analysis and significance testing in predicting overall score of small cruise ships here:

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