Shortly after being hired as an analyst with Hire Equip in Hong Kong, Joseph Goh 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. Joseph 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

Joseph 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 July was especially slow because of a paralyzing typhoon, 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 Hire Equip expects to write 2,500 rental invoices.

d. Did Joseph make a mistake 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.