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 94.5 , the highest component of which is 97.9 for Food/Dining.
Ship |
Overall |
Shore Excursions |
Food/Dining |
---|---|---|---|
Seabourn Odyssey | 94.5 | 91.1 | 97.9 |
Seabourn Pride | 93.1 | 84.2 | 96.6 |
National Geographic Endeavor | 93.0 | 99.9 | 88.6 |
Seabourn Sojourn | 91.2 | 94.7 | 97.1 |
Paul Gauguin | 90.4 | 87.7 | 91.0 |
Seabourn Legend | 90.3 | 82.0 | 99.0 |
Seabourn Spirit | 90.4 | 86.2 | 92.0 |
Silver Explorer | 89.9 | 92.8 | 88.9 |
Silver Spirit | 89.3 | 85.9 | 91.0 |
Seven Seas Navigator | 89.1 | 83.2 | 90.5 |
Silver Whisperer | 89.1 | 82.2 | 88.6 |
National Geographic Explorer | 89.2 | 92.9 | 89.9 |
Silver Cloud | 88.7 | 78.3 | 91.4 |
Celebrity Xpedition | 87.4 | 91.6 | 73.4 |
Silver Shadow | 87.2 | 75.0 | 89.8 |
Silver Wind | 86.5 | 78.3 | 91.4 |
SeaDream II | 86.3 | 77.3 | 90.8 |
Wind Star | 85.9 | 76.5 | 91.4 |
Wind Surf | 85.9 | 72.3 | 89.4 |
Wind Spirit | 85.0 | 77.6 | 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
c. Predict the overall score for a cruise ship with a Shore Excursions score of 80 and a Food/Dining Score of 90 .
(to 2 decimals)
Store the data in vector name under in R, Overall, Shore_Excursions & Food_Dining
> Overall
[1] 94.5 93.1 93.0 91.2 90.4 90.3 90.4 89.9 89.3 89.1 89.1 89.2 88.7 87.4
[15] 87.2 86.5 86.3 85.9 85.9 85.0
> Shore_Excursions
[1] 91.1 84.2 99.9 94.7 87.7 82.0 86.2 92.8 85.9 83.2 82.2 92.9 78.3 91.6
[15] 75.0 78.3 77.3 76.5 72.3 77.6
> Food_Dining
[1] 97.9 96.6 88.6 97.1 91.0 99.0 92.0 88.9 91.0 90.5 88.6 89.9 91.4 73.4
[15] 89.8 91.4 90.8 91.4 89.4 91.8
Q a)
> lm(Overall ~ Shore_Excursions)
Call:
lm(formula = overall ~ Shore_Excursions)
Coefficients:
(Intercept) Shore_Excursions
68.4581 0.2446
Overall = 68.4581 + 0.2446 * Shore_Excursions
Q b)
> lm(Overall ~ Shore_Excursions + Food_Dining)
Call:
lm(formula = overall ~ Shore_Excursions + Food_Dining)
Coefficients:
(Intercept) Shore_Excursions Food_Dining
45.0082 0.2615 0.2419
Overall = 45.0082 + 0.2615 * Shore_Excursions + 0.2419 * Food_Dining
Q c) Predict the overall score for cruise ship with Shore Excursions score of 80 and Food/Dining Score of 90
We have linear equation
Overall = 45.0082 + 0.2615 * Shore_Excursions + 0.2419 * Food_Dining
Overall = 45.0082 + 0.2615 * 80 + 0.2419 * 90
= 87.6992
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