Suppose the Variables X=commuting Distance and Y=commuting Time Are Related $\sigma = 10 .$

question 29

Essay

Suppose the variables x=commuting distance and y=commuting time are related according to the simple linear regression model with $\sigma = 10 .$
a. If n=5 observations are made at the x values $x _ { 1 } = 4 , x _ { 2 } = 9 , x _ { 3 } = 14 , x _ { 4 } = 19 , \text { and } x _ { 5 } = 24$
calculate the standard deviations of the five corresponding residuals.
b. Repeat part (a) for $x _ { 1 } = 4 , x _ { 2 } = 9 , x _ { 3 } = 14 , x _ { 4 } = 19 , \text { and } x _ { 5} = 49$
c. What do the results of parts (a) and (b) imply about the deviation of the estimated line from the observation made at the largest sampled x value?

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Definitions:

Economic Profit

The total revenue of a business minus its explicit and implicit costs, showing the actual financial gain.

Opportunity Costs

The cost of forgoing the next best alternative when making a decision, representing the benefits one misses out on.

Perfectly Competitive

A market structure characterized by many buyers and sellers, all of whom are price takers with the product being homogeneous.

Sunk Costs

Expenses that have already been incurred and cannot be recovered, which should not influence future business decisions.