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 94.4, the highest component of which is 97.8 for Food/Dining.

overall	shore	food
94.4	90.9	97.8
93	84.2	96.7
92.9	100	88.5
91.3	94.8	97.1
90.5	87.9	91.2
90.3	82.1	98.8
90.2	86.3	92
89.9	92.6	88.9
89.4	85.9	90.8
89.2	83.3	90.5
89.2	82	88.6
89.1	93.1	89.7
88.7	78.3	91.3
87.2	91.7	73.6
87.2	75	89.7
86.6	78.1	91.6
86.2	77.4	90.9
86.1	76.5	91.5
86.1	72.3	89.3
85.2	77.4	91.9

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. Develop the estimated regression equation that can be used to predict the overall score given the scores for Shore Excursions 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.

Answer 1

I used R software to solve this problem,

R codes:

> overall=scan('clipboard')
Read 20 items
> shore=scan('clipboard')
Read 20 items
> food=scan('clipboard')
Read 20 items
> overall
[1] 94.4 93.0 92.9 91.3 90.5 90.3 90.2 89.9 89.4 89.2 89.2 89.1 88.7 87.2 87.2
[16] 86.6 86.2 86.1 86.1 85.2
> shore
[1] 90.9 84.2 100.0 94.8 87.9 82.1 86.3 92.6 85.9 83.3 82.0 93.1
[13] 78.3 91.7 75.0 78.1 77.4 76.5 72.3 77.4
> food
[1] 97.8 96.7 88.5 97.1 91.2 98.8 92.0 88.9 90.8 90.5 88.6 89.7 91.3 73.6 89.7
[16] 91.6 90.9 91.5 89.3 91.9
> fit1=lm(overall~shore)
> fit1

Call:
lm(formula = overall ~ shore)

Coefficients:
(Intercept) shore
69.2998 0.2348

> fit2=lm(overall~shore+food)
> fit2

Call:
lm(formula = overall ~ shore + food)

Coefficients:
(Intercept) shore food
45.1780 0.2529 0.2482

a)

Overall = 69.2998 + 0.2348 shore

b)

  Overall =  45.1780 + 0.2529 shore + 0.2482 food  

c) put shore = 80 and food= 90 in above equation we get,

Overall score for a cruise ship is 87.748