25. The significance Condé List for 2012 provided ratings for the top 20 small c

Question

25. The significance Condé List for 2012 provided ratings for the top 20 small cruise ships Nast website, The data are the scores each shi received based upon the results from Condé shown Readers' Choice Survey Each score represents the Travelers annual good on several criteria, percentage of respondents who rated a ship as excellent or very including Shore Excursions, and Food/Dining. An overall score was also reported and used to rank the ships. The highest rank ship, the Seaboum Odyssey, has an overall score of 94.4, the highest component of which is 97.8 for Food Dining.

Explanation / Answer

Solution:-

a) The regression equation to predict the overall score is

Regression equation is given by:-

Y = a + b*X1 + c*X2 + d*X2

Where X1 = Scores for itineraries/schedule

X2 = Shore excursions

X3 = Food/Dinning

a = 35.6183

b = 0.11045

c = 0.24453

d = 0.24735

Y = 35.62 + 0.1104*X1 + 0.2446*X2 + 0.248*X2

b) We can conclude that atleast one of the independent variables affects Y.

The hypotheses for the F-test of the overall significance are as follows:

Null hypothesis: There is no linear relationship between all varibles considering together X and Y.

Alternative hypothesis: Atleast one of the independent variables affects Y.

Significance level = 0.05

Test statitics:-

F = 15.9847 (given)

P value = 4.51 × 10-5

P Since p value of the test is very less than the significance level(0.05) so we have to neglect the null hypothesis.

From this we can conclude that atleast one of the independent variables affects Y.

c)

For Itineraries/schedule

Null hypothesis : H0: There is no linear relationship.

Alternate hypothesis : HA: Theer is linear relationship between X and Y.

t-test = 0.85185

p-value = 0.4069

Since p value(0.4069) is greater than significance level (0.05), so we he to accept the null hypothesis

From this we can conclude that independence variable is not signifant and there is no relationship betweeen overall scores and Itineraries scores.

For Shore excursions

Null hypothesis : H0: There is no linear relationship.

Alternate hypothesis : HA: Theer is linear relationship between X and Y.

t-test = 5.64

p-value = 3.69 × 10-5

Since p value(3.69 × 10-5) is less than significance level (0.05), so we he to reject the null hypothesis

From this we can conclude that independence variable is signifant and there is linear relationship betweeen overall scores and Shore excursions.

For Food/Dinning

Null hypothesis : H0: There is no linear relationship.

Alternate hypothesis : HA: Theer is linear relationship between X and Y.

t-test = 3.9821

p-value = 0.001072

Since p value(0.001072) is less than significance level (0.05), so we he to reject the null hypothesis

From this we can conclude that independence variable is signifant and there is linear relationship betweeen overall scores and food/dinnning.

d) We can remove scores for Itineraries /schedule becuase it does not have any affect on overall scores.

Y = a + b*X1 + c*X2

Where X1 = Shore excursions

X2 = Food/Dinning

a = 35.6183

b = 0.24453

c = 0.24735

Y = 35.62 + 0.245*X1 + 0.2474*X2

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