Shortly After Being Hired as an Analyst with Hidden Cove

question 48

Essay

Shortly after being hired as an analyst with Hidden Cove Rentals in Coastal North Carolina, Matt Loman 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. Matt 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
Matt 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 "tend to even out." He observed that February was especially slow because of a paralyzing ice storm, 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 Hidden Cove expects to write 2,500 rental invoices.
D. Did Matt 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:

Complement

In probability theory, the complement of an event is the set of all outcomes that are not in the event.

Event A

A specified occurrence or outcome, often used in probability and statistics to denote a specific set of results within an experiment.

Sample Space

The collection of all potential results or outcomes from a probabilistic experiment.

Discrete Random Variables

Random variables that take on a countable number of distinct values.