Question

The Condé Nast Traveler Gold List provides ratings for the top 20 small cruise ships. 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 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 94.2, the highest component of which is 97.8 for Food/Dining. Shore Ship Overall Food/Dining Excursions Seabourn Odyssey 94.2 90.8 97.8 96.6 Seabourn Pride 93.1 84.1 100.0 88.6 National Geographic Endeavor 93.0 Seabourn Sojourn 91.1 94.9 97.3 Paul Gauguin 90.7 87.7 91.2 82.0 98.9 Seabourn Legend 90.4 Seabourn Spirit 90.2 86.4 91.8 Silver Explorer 92.7 89.9 88.8 Silver Spirit 86.0 89.6 90.8 Seven Seas Navigator 89.0 83.1 90.5 Silver Whisperer 88.8 89.1 81.9 National Geographic Explorer 93.2 89.2 89.7 Silver Cloud 88.9 78.3 91.2 Celebrity Xpedition 91.6 73.8 87.3 Silver Shadow 87.3 75.2 89.7 Silver Wind 86.7 78.2 91.6 77.5 SeaDream II 86.4 90.7 Wind Star 76.4 91.6 86.1 Wind Surf 85.9 72.2 89.2 Wind Spirit 85.3 77,4 91.8 a. Determine an estimated regression equation that can be used to predict the overall score given the score for Shore Excursions (to 3 decimals). Overall Shore Excursions b. Consider the addition of the independent variable Food/Dining. Develop the estimated regression equation that can be used to predict the overall score given the scores for Shore Excursions and Food/Dining (to 3 decimals). Overall Shore Excursions Food/Dining Determine an estimated regression equation that can be used to predict the overall score given the score for Shore Excursions (to 3 decimals). Overall Shore Excursions . Consider the addition of the independent variable Food/Dining. Develop the estimated regression equation that can be used to predict the overall score given the scores for Shore Excursions and Food/Dining (to 3 decimals). Overall Shore Excursions + Food/Dining Predict the overall score for a cruise ship with a Shore Excursions score of 80 and 90. Food/Dining Score (to 2 decimals)

Answer 1

Following is the output of regression analysis:

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.698856408
R Square	0.488400279
Adjusted R Square	0.459978073
Standard Error	1.852499415
Observations	20
ANOVA
	df	SS	MS	F	Significance F
Regression	1	58.97042654	58.97042654	17.18375651	0.000607752
Residual	18	61.77157346	3.431754081
Total	19	120.742
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	69.55251282	4.750525671	14.64101399	1.93192E-11	59.57202875	79.53299689
Shore Excursions	0.232214574	0.056018363	4.145329482	0.000607752	0.114524359	0.349904788

(a)

overall = 69.553 +0.232 *  Shore Excursions

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(b) Following is the output of multiple regression:

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.854862957
R Square	0.730790675
Adjusted R Square	0.69911899
Standard Error	1.382769436
Observations	20
ANOVA
	df	SS	MS	F	Significance F
Regression	2	88.23712766	44.11856383	23.07394342	1.43142E-05
Residual	17	32.50487234	1.912051314
Total	19	120.742
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	46.04821114	6.976144844	6.600810643	4.49684E-06	31.3298322	60.76659007
Shore Excursions	0.248497213	0.042020648	5.913693012	1.70064E-05	0.159841396	0.33715303
Food/ Dinning	0.243119581	0.062141656	3.912344726	0.001121263	0.112012148	0.374227015

The regression equation is:

overall = 46.048 + 0.248 * Shore-Excursions + 0.243 * Food/Dinning

(c)

The required predicted value is

overall = 46.048 + 0.248 * 80 + 0.243 * 90 = 87.758

Answer: 87.76