The Condé Nast Traveler Gold List for 2012 provided ratings for the top 20 small

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.

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.Item 6

c. Use the t test to determine the significance of each independent variable.

What is your conclusion at the .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? Round your answers to three decimal places.

Overall =  +  - Select your answer -Itineraries/ScheduleShore ExcursionsFood/DiningItem 15 +  - Select your answer -Itineraries/ScheduleShore ExcursionsFood/Dining

Itineraries/Schedule - Select your answer -This variable is significant.This variable is not significant.Item 7 Shore Excursions - Select your answer -This variable is significant.This variable is not significant.Item 8 Food/Dining - Select your answer -This variable is significant.This variable is not significant.Item 9 Itineraries/ Shore Ship Overall Schedule Excursions Food Dining Seabourn Odyssey 90.9 Seabourn Pride 84.2 National Geographic Endeavor 92.9 100.0 100.0 88.5 Seabourn Sojourn 91.3 Paul Gauguin 90.5 95.1 87.9 91.2 Seabourn Legend 90.3 92.5 Seabourne Spirit 90.2 96.0 86.3 92.0 Silver Explorer 89.9 92.6 92.6 88.9 Silver Spirit 89.4 85.9 90.8 Seven Seas Navigator 89.2 90.6 90.5 Silver Whisperer 89.2 90.9 82.0 Natural Geographic Explorer 89.1 93.1 89.7 Silver Cloud 92.6 91.3 Celebrity Xpedition 87.2 Silver Shadow 87.2 91.0 89.7 Silver Wind 86.6 91.6 SeaDream II 86.2 95.5 90.9 Wind Star 949 91.5 Wind Surf 921 723 89.3 Wind Spirit 85.2 93.5 91.9 998908893999999 76871828008913910191 99899998998897899989 04047262532381587627 9809888988897977777 67061 0676 4 6 99089999999999999999 40935329422172262112 799999998888888888888

Explanation / Answer

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.

This is the problem of regression.

We can do regression in MINITAB.

steps :

ENTER data into MINITAB sheet --> STAT --> Regression --> Regression --> Response : overall --> Predictors : select all the remaining variables --> Results : select second option --> ok --> ok

  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 = 35.6 + 0.110 Itineraries/schedule + 0.245 Shore excursions
+ 0.247 food/dining

Use the F test to determine the overall significance of the relationship. Round your answers to two decimal places.

Here we have to test the hypothesis that,

H0 : Bj = 0 Vs H1 : Bj not= 0

where Bj is the population slope for jth independent variable.

Assume alpha = level of significance = 0.05

Here test statistic follows F-distribution.

Analysis of Variance

Source DF SS MS F P
Regression 3 92.352 30.784 15.98 0.000
Residual Error 16 30.813 1.926
Total 19 123.166

Test statistic (F) = 15.98
P-value = 0.000

P-value < alpha

Reject H0 at 5% level of significance.

Conclusion : Atleast one of the slope is differ than 0.

We get significant result about overall significance.

Therefore the overall model is significant.

Use the t test to determine the significance of each independent variable.

Here we have to test,

H0 : B = 0 Vs H1 : B not= 0

where B is population slope for independent variable.

Procedure :

Here test statistic follows t-distribution.

Decision rule :

If P-value < alpha

Reject H0 at 5% level of significance.

Conclusion : The population slope for independent variable is differ than 0.

Predictor Coef SE Coef T P
Constant 35.62 13.23 2.69 0.016
Itineraries/schedule 0.1105 0.1297 0.85 0.407
Shore excursions 0.24454 0.04336 5.64 0.000
food/dining 0.24736 0.06212 3.98 0.001

Here we see that P-value for Shore excursions and food/dining are 0.000 and 0.001 respectively.

Therefore these two variables are significant.

And P-value for Itineraries/schedule is 0.407.

P-value > alpha

We get insignificant result about Itineraries/schedule.

Now we included significant variables in the model and excluded insignificant variables.

Therefore we delete Itineraries/schedule from the model.

And recalculate the model so we get the following output.

Regression Analysis: overall versus Shore excursions, food/dining

The regression equation is
overall = 45.2 + 0.253 Shore excursions + 0.248 food/dining

Predictor Coef SE Coef T P
Constant 45.178 6.952 6.50 0.000
Shore excursions 0.25289 0.04189 6.04 0.000
food/dining 0.24819 0.06161 4.03 0.001

S = 1.37650 R-Sq = 73.8% R-Sq(adj) = 70.8%

Analysis of Variance

Source DF SS MS F P
Regression 2 90.955 45.477 24.00 0.000
Residual Error 17 32.211 1.895
Total 19 123.166

Now we get significant result for both the test F and t.

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