Shortly After Being Hired as an Analyst with Harbor Rentals

question 57

Essay

Shortly after being hired as an analyst with Harbor Rentals in upstate New York, Raul Gomez was asked to prepare a report that focused on the company's order processing costs-a cost driven largely by the number of rental invoices written. Raul knew that he could use several different tools to analyze cost behavior, including scatter diagrams, least-squares regression, and the high-low method. In addition, he knew that he could present the results of his analysis in the form of algebraic equations. Those equations follow.
Scatter diagram: OP = $56,000 + $6.80RI
Least-squares regression: OP = $59,000 + $6.75RI
High-low method: OP = $53,500 + $7.25RI
where OP = total order processing costs and RI = number of rental invoices written
Raul had analyzed data over the past 12 months and built equations based on these data, purposely including the slowest month of the year and the busiest month so that things would "¼ tend to even out." He observed that February was especially slow because of a paralyzing blizzard, one that forced the company to close for four days.
Required:
A. Will scatter diagrams, least-squares regression, and the high-low method normally result in the same equation? Why?
B. Assuming the use of least-squares regression, explain what the $59,000 and $6.75 figures represent.
C. Assuming the use of a scatter diagram, predict the order processing cost of an upcoming month when Harbor expects to write 2,500 rental invoices.
D. Did Raul err in constructing the equations on data of the past 12 months? Briefly discuss. If "yes," determine which of the three tools is likely to be affected the most and explain why.

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Definitions:

Perfect Substitutes

Goods or services that can be used in exact place of each other with no loss of utility to the consumer, often characterized by a constant marginal rate of substitution.

Production

The process of creating goods or services by combining various inputs like labor, raw materials, and machinery.

Marginal Productivity

Marginal productivity refers to the additional output that is produced by adding one more unit of a factor of production, holding all other factors constant.

Labor

Labor refers to the human effort, both physical and mental, used in the production of goods and services, forming a crucial component of the economic production process.