The Data Below Were Gathered on a Random Sample of 7

question 23

Essay

The data below were gathered on a random sample of 7 male black-footed albatrosses of known age. In an effort to monitor diseases of these animals, biologists would like to be able to estimate the age of animals that have died by flattening their gonads and measuring the resulting area. ​
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 = Gonad Size and y = Age.
c) If these albatrosses are representative of the population, what would you predict to be the age of a male albatross with a gonad size of 50 sq. mm? Show any calculations below.
d) The largest albatross gonad size in the sample was 96 sq. mm, with an age of 23.64 years. These animals are thought to live for up to 40 years. Would it be reasonable to use the equation from part (b) above to predict the age for a gonad size of 150 sq. mm? Why or why not?

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Definitions:

Short Run

A period in which at least one factor of production is fixed, limiting the ability of a business to adjust to changing market conditions fully.

Variable Cost

A cost that increases when the firm increases its output and decreases when the firm reduces its output.

Average Total Cost

The total cost divided by the number of units produced, representing the average cost of production per unit.

Purely Competitive Industry

An industry characterized by many firms offering identical products where no single firm can influence the market price.