Question

A quick answer is appreciated. Thank you!

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.

Ship	Overall	Shore Excursions	Food/Dining
Seabourn Odyssey	94.4	90.9	97.8
Seabourn Pride	93.0	84.2	96.7
National Geographic Endeavor	92.9	100.0	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
Seabourn Spirit	90.2	86.3	92.0
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	82.0	88.6
National 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	75.0	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

(a)

Determine an estimated regression equation that can be used to predict the overall score given the score for Shore Excursions. (Round your numerical values to two decimal places. Let x₁ represent the Shore Excursions score and y represent the overall score.)

ŷ = __________

(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. (Round your numerical values to two decimal places. Let x₁ represent the Shore Excursions score, x₂ represent the Food/Dining score, and y represent the overall score.)

ŷ = ________

(c)

Predict the overall score for a cruise ship with a Shore Excursions score of 80 and a Food/Dining Score of 91. (Round your answer to one decimal place.)

_________

Answer 1

Ans:

A)

The calculation for the predicted regression line is given below,

Therefore, the required answer in 2 decimal place is obtained by use of Excel and online calculator y^ = 0.23X + 69.30.

B)

Therefore, the required for part (B) is Y^ = 0.25*X1 + 0.25*X2 + 45.18.

C)

When x1 = 80,and X2 = 91 then the value of Y^ is given as,

Y^ = 0.25*X1 + 0.25*X2 + 45.18

  = 0.25*80 + 0.25*91 + 45.18

= 87.93

Therefore, the predicted overall score is 87.9 .