The Condé Nast Traveler Gold List for 2012 provided ratings for the top 20 small
ID: 3363594 • Letter: T
Question
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, the highest component of which is 97.8 for food/dining. Click on the webfile logo to reference the data.
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. Round your answers to three decimal places.
The regression equation is
Overall = ______ + _________ Itineraries/Schedule ____________ + Shore Excursions __________ + ___________ Food/Dining
b. Use the F test to determine the overall significance of the relationship. Round your answers to two decimal places.
What is the conclusion at the .05 level of significance?
- Select your answer -
The overall model is significant.
The overall model is not significant.
c. Use the t test to determine the significance of each independent variable.
- Select your answer -
This variable is significant.
This variable is not significant.
- Select your answer -
This variable is significant.
This variable is not significant
- Select your answer -
This variable is significant.
This variable is not significant.
What is your conclusion at the .05 level of significance?
- Select your answer -
Greater than the level of significance.
Less than the level of significance.
- Select your answer -
Greater than the level of significance.
Less than the level of significance.
- Select your answer -
Greater than the level of significance.
Less than the level of significance.
d. Remove any independent variable that is not significant from the estimated regression equation. What is your recommended estimated regression equation? Round your answers to three decimal places.
Overall = _________ + ___________ - Select your answer
Itineraries/Schedule
Shore Excursions
Food/Dining
+ Select your answer -
Itineraries/Schedule
Shore Excursions
Food/Dining
Itineraries/Schedule- Select your answer -
This variable is significant.
This variable is not significant.
Shore Excursions- Select your answer -
This variable is significant.
This variable is not significant
Food/Dining- Select your answer -
This variable is significant.
This variable is not significant.
Explanation / Answer
Multiple regression output for the data is given below.
Based on these we will answer all of our questions.
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. Round your answers to three decimal places.
The regression equation is
Overall =35.618 + 0.110 Itineraries/Schedule +0.245 Shore Excursions + 0.247 Food/Dining
b. Use the F test to determine the overall significance of the relationship. Round your answers to two decimal places.
The F-statistic is found to be 15.98
What is the conclusion at the .05 level of significance?
Since the p-value is less than significance level we will reject the null hypothesis. Hence the correct option is ,
The overall model is significant.
c. Use the t test to determine the significance of each independent variable.
If a variable has p-value less than 0.05 then we will reject the null hypothesis and hence that variable will be significant.
This variable is not significant.
This variable is significant.
This variable is significant.
What is your conclusion at the .05 level of significance?
Itineraries/Schedule
Greater than the level of significance.
Less than the level of significance.
Less than the level of significance.
d. Remove any independent variable that is not significant from the estimated regression equation. What is your recommended estimated regression equation? Round your answers to three decimal places.
We have found that the variable Itineraries/Schedule is not sigificant. So we will carry out the regression once more without the variable Itineraries/Schedule.
Hence the regression equation would be given by,
Overall = 45.178 + 0.253Shore Excursions+ 0.248Food/Dining
SUMMARY OUTPUT Regression Statistics Multiple R 0.87 R Square 0.75 Adjusted R Square 0.70 Standard Error 1.39 Observations 20 ANOVA df SS MS F Significance F Regression 3 92.35 30.78 15.98 0.00005 Residual 16 30.81 1.93 Total 19 123.17 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 35.618 13.23 2.69 0.02 7.57 63.67 Itineraries/Schedule 0.110 0.13 0.85 0.41 -0.16 0.39 Shore Excursions 0.245 0.04 5.64 0.00 0.15 0.34 Food/Dining 0.247 0.06 3.98 0.00 0.12 0.38Related Questions
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