The Data Below Were Gathered on a Random Sample of 5

question 37

Essay

The data below were gathered on a random sample of 5 basking sharks, swimming through the water and filter-feeding, i.e. passively letting the water bring food into their mouths. ​
a) What is the value of the correlation coefficient for these data?
b) What is the equation of the least squares line describing the relationship between x = body length and y = mean speed.
c) If these sharks are representative of the population of basking sharks, what would you predict is the mean speed for a filter-feeding basking shark that is 5.0 meters in length? Show any calculations below.
d) The largest basking shark in the sample is measured as 6.5 meters long. Theory predicts a maximum length of about 12.26 meters. Would it be reasonable to use the equation from part (b) above to predict the mean filter-feeding speed for a 12 meter long basking shark? Why or why not?

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Definitions:

Interindustry Competition

Competition that occurs between companies in different industries or sectors offering substitute goods or services.

Oligopolistic Industries

Market structures characterized by a small number of firms that dominate the industry, leading to competition primarily on factors other than price, such as innovation or advertising.

Product Price

The amount of money required to purchase a good or service, determined by factors such as production costs, demand, and supply.

Herfindahl Index

A gauge of company sizes within their market and a marker for the degree of rivalry between them.