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?
Definitions:
Total Utility
The cumulative satisfaction or value a consumer receives from consuming a particular quantity of goods or services.
Money Income
The total income a person or entity receives in monetary form, including wages, salaries, benefits, and income from investments.
Marginal Rate
A term used to describe the rate at which one variable changes as another variable changes by a single unit, often applied in economic analysis like the marginal tax rate or marginal rate of substitution.
Substitution
The act of replacing one good or service with another due to changes in price or preference.
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