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 writtenMatt had analyzed data over the past 12 months

Question

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.

What will be an ideal response?

Answer 1

A. No. The three methods produce equations by different means. Scatter diagrams and least-squares regression rely on an examination of all data points. The scatter diagram, however, requires an analyst to fit a line through the points by visual approximation, or "eyeballing." In contrast, least-squares regression involves the use of statistical formulas to derive the best possible fit of the line through the points. Finally, the high-low method is based on an analysis of only two data points: the highest and the lowest.
B. These amounts represent the fixed and variable elements of the company's order processing cost. Fixed cost totals $59,000, and Hidden Cove incurs $6.75 of variable cost for each invoice written.
C. OP = $56,000 + $6.80RI; OP = $56,000 + ($6.80 × 2,500); OP = $73,000
D. Yes, he did err by including February data. February is not representative because of the effects of the ice storm. The month is an outlier and should be eliminated from the data set.
The equation constructed by using the high-low method is likely to be affected the most since the equation is based on only two data points. One of those two points should have been excluded from the analysis.