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.

1. Use minitab to help you do the following questions.

a. Determine an estimated regression equation that can be used to predict the overall score given the score for Shore Excursions.

b. Consider the addition of the independent variable Food/Dining, i.e., develop the estimated regression equation that can be used to predict the overall score given the scores for Shore Excursion and Food/Dining.

c. Predict the overall score for a cruise ship with a Shore Excursions score of 80 and a Food/Dining score of 90.

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

Explanation / Answer

a.

Regression Analysis: Overall versus Shore Excursions

The regression equation is
Overall = 69.3 + 0.235 Shore Excursions

Predictor Coef SE Coef T P
Constant 69.300 4.799 14.44 0.000
Shore Excursions 0.23476 0.05659 4.15 0.001

S = 1.87028 R-Sq = 48.9% R-Sq(adj) = 46.0%

Analysis of Variance

Source DF SS MS F P
Regression 1 60.202 60.202 17.21 0.001
Residual Error 18 62.963 3.498
Total 19 123.166

Unusual Observations

Shore
Obs Excursions Overall Fit SE Fit Residual St Resid
1 91 94.400 90.640 0.554 3.760 2.10R
2 84 93.000 89.067 0.419 3.933 2.16R
14 92 87.200 90.828 0.584 -3.628 -2.04R

R denotes an observation with a large standardized residual.

b.

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

Source DF Seq SS
Shore Excursions 1 60.202
Food/Dining 1 30.752

Unusual Observations

Shore
Obs Excursions Overall Fit SE Fit Residual St Resid
14 92 87.200 86.635 1.126 0.565 0.71 X

X denotes an observation whose X value gives it large influence.

c. Shore Excursions score = 80

Food/Dining score = 90

Overall = 45.2 + 0.253 Shore Excursions + 0.248 Food/Dining

or, Overall = Overall = 45.2 + 0.253*80 + 0.248 *90 = 87.76

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