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. Write the regression equation. 2. Interpret the regression constant and regression coefficient, forecast a value for the dependent variable, 3.Test the significant of the regression coefficient at an alpha level of .05, 4.Test the overall significant of the regression model,and Interpret the coefficient of determination

Ship 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 SeaDream II Wind Star Wind Surf Wind Spirit Overall 94.4 93.0 92.9 91.3 90.5 90.3 90.2 89.9 89.4 89.2 89.1 88.7 87.2 87.2 86.6 86.2 86.1 86.1 Shore Excursions Food/Dining 90.9 97.8 84.2 96.7 100.0 88.5 94.8 97.1 87.9 91.2 82.1 98.8 86.3 92.0 92.6 88.9 85.9 90.8 90.5 82.0 88.6 89.7 93.1 78.3 91.3 91.7 73.6 89.7 75.0 78.1 91.6 77.4 90.9 76.5 91.5 72.3 89.3 774 91.9

Explanation / Answer

Residuals:
Min 1Q Median 3Q Max
-2.360 -1.075 0.411 0.622 2.529

Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 45.17796 6.95185 6.499 5.46e-06 ***
x1 0.25289 0.04189 6.037 1.33e-05 ***
x2 0.24819 0.06161 4.029 0.000871 ***
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Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 1.377 on 17 degrees of freedom
Multiple R-squared: 0.7385, Adjusted R-squared: 0.7077
F-statistic: 24 on 2 and 17 DF, p-value: 1.119e-05

1) regression equation:

overall = 45.1780 + 0.2529*shore excursions + 0.2482*Food(dinning)

2) prediction using model

  92.43876 90.47137 92.43193 93.25131 90.04204 90.46150 89.83596 90.65980 89.43698 88.70500 87.90468 90.98479 87.63909 86.63490 86.40744 87.66297 87.31221 87.23352 85.62536 87.56040

Constant = 45.170 i.e. if the shore excurssion and dinning rating is 0 then overall rating will be 45.17

slope = average change in overall rating when one unit change in shore excurssion and dinning occur

3) significance of regression coefficient:

since p value fro all the coefficient is < 0.05 i.e. coefficient is significant

4) on the basis of p vaue and f statistics we can infer that model is good fit and adjR2 = 70.77% i.e 70.77 % variability is explainned by predictors

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