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:

Test Statistic

A value calculated from sample data that is used to make decisions about a population parameter in hypothesis testing.

Kruskal-Wallis Test

A statistical test that doesn't rely on parameter assumptions to evaluate if notable differences exist between two or more independent variable groups, focusing on a continuous or ordinal dependent variable.

Distribution

The spread of values of a variable or the frequencies of occurrence of different possible outcomes in a dataset.

Sign Test Statistic

A test that does not assume a specific data distribution, employed to evaluate if paired observations have a median that differs.