2. Exercise 13.25 eBook The Condé Nast Traveler Gold List for 2012 provided rati

Question

2. Exercise 13.25 eBook 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 following data shown 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 WEB Food Itineraries/ Schedule Shore Excursions 90.9 Overall Dining Seabourn Odyssey Seabourn Pride National Geographic Endeavor Seabourn Sojourn Paul Gauguin Seabourn Legend Seabourn Spirit Silver Explorer Silver Spirit Seven Seas Navigator Silver Whisperer National Geographic Explorer Silver Cloud Celebrity Xpedition Silver Shadow Silver Wind 96.7 88.5 91.2 92.0 92.9 100.0 100.0 94.8 82.1 96.0 88.9 90.6 82.0 88.6 78.3 94.4 90.9 Wind Star Wind Surf Wind Spirit 92.1 93.5 85.2 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 (to 4 decimals) Itineraries/Schedule + Shore Excursions Food/Dining b. Use the F test to determine the overall significance of the relationship. What is your conclusion at the .05 level of significance? Select c. Use the t test to determine the significance of each independent variable. What is your conclusion at the.05 level of significance? Itineraries/Schedule Select Shore Excursions: Select Select d. Remove any independent variable that is not significant from the estimated regression equation. What is your recommended estimated regression equation (to 4 decimals)? y= Shore Excursions+ Food/Dining

Explanation / Answer

SUMMARY OUTPUT: Regression of Overall Score on Itineraries Schedule, Shore and Food

Regression Statistics

Multiple R

0.796087

R Square

0.633755

Adjusted R Square

0.565084

Standard Error

1.679077

Observations

20

ANOVA

df

SS

MS

F

Significance F

Regression

3

78.0567

26.0189

9.228853

0.000887

Residual

16

45.1088

2.8193

Total

19

123.1655

Coefficients

Standard Error

t Stat

P-value

Lower 95%

Upper 95%

Intercept

37.26987

16.95863

2.197693

0.043038

1.31918

73.22056

Itineraries Schedule

0.162503

0.157927

1.028974

0.318797

-0.17229

0.497292

Shore

0.235583

0.052309

4.503724

0.000361

0.124694

0.346472

Food

0.185002

0.077074

2.400325

0.028901

0.021613

0.348391

Overall Score = 37.26987 + 0.162503 * Itineraries Schedule + 0.235583 * Shore + 0.185002 * Food

Independent variable

P value

Remark

Itineraries Schedule

0.318797 > 0.05

Non-Significant

Shore

0.000361 < < 0.05

Highly Significant

Food

0.028901 < 0.05

Significant

Hence Shore and Food are the only significant variables

SUMMARY OUTPUT: Regression of Overall Score on Shore and Food

Regression Statistics

Multiple R

0.780717

R Square

0.609519

Adjusted R Square

0.56358

Standard Error

1.681978

Observations

20

ANOVA

df

SS

MS

F

Significance F

Regression

2

75.07166

37.53583

13.268

0.000338

Residual

17

48.09384

2.829049

Total

19

123.1655

Coefficients

Standard Error

t Stat

P-value

Lower 95%

Upper 95%

Intercept

52.33973

8.564851

6.110991

1.15E-05

34.26947

70.40999

Shore

0.247139

0.051177

4.829103

0.000157

0.139165

0.355113

Food

0.175812

0.076687

2.292596

0.034899

0.014017

0.337607

The revised regression model is

Overall Score = 52.33973 + 0.247139 * Shore + 0.175812 * Food

SUMMARY OUTPUT: Regression of Overall Score on Itineraries Schedule, Shore and Food

Regression Statistics

Multiple R

0.796087

R Square

0.633755

Adjusted R Square

0.565084

Standard Error

1.679077

Observations

20

ANOVA

df

SS

MS

F

Significance F

Regression

3

78.0567

26.0189

9.228853

0.000887

Residual

16

45.1088

2.8193

Total

19

123.1655

Coefficients

Standard Error

t Stat

P-value

Lower 95%

Upper 95%

Intercept

37.26987

16.95863

2.197693

0.043038

1.31918

73.22056

Itineraries Schedule

0.162503

0.157927

1.028974

0.318797

-0.17229

0.497292

Shore

0.235583

0.052309

4.503724

0.000361

0.124694

0.346472

Food

0.185002

0.077074

2.400325

0.028901

0.021613

0.348391

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