Regression computations, ethics. (Chapter Appendix) Cambridge Engineering manufac¬

tures small electric motors. Data on manufacturing labour costs and units produced for the last four quarters are as follows:

Quarter Manufacturing Labour Costs Units Produced 1 $211,200 9,000 2 208,800 10,000 3 198,000 9,000 4 246,000 12,000 Total $864,000 40,000 Peter Smith, the manufacturing manager, is evaluated on how labour costs in a quarter com¬

pare with labour costs in the previous four quarters. In the recently concluded Quarter 5, Cambridge Engineering produced 12,000 motors and incurred manufacturing labour costs of $249,600. Smith is very happy with the results. Over the previous four quarters, the aver¬

age manufacturing labour cost per unit is $21.60 ($864,000 h- 40,000 units) resulting in a benchmark for Quarter 5 of $21.60 X 12,000 = $259,200. Just as Smith is thinking about what he might do with the bonus, Allison Hart, the plant controller, knocks on Smith’s door.

Allison Hart:

Peter Smith:

Allison Hart:

Q Peter Smith:

I am sorry that we couldn’t beat the benchmark over the last four quarters. We certainly gave it our best shot.

What do you mean we didn’t beat the benchmark? Here are the numbers I just calculated. Against a benchmark of $259,200, we achieved $249,600.

No, that’s not how the calculations are done. Some of the labour costs are fixed and others vary with production. My analysis here first separates out the fixed from the variable components. My calculations then show that our Quarter 5 performance was worse than the previous four quarters.

Please review your calculations. I am sure you can report better numbers than that. This regression approach you are using is subject to estimation error. You should make some adjustment for that. If we don’t show senior management that we are succeeding in reducing labour costs, they might shut us down because they do not believe that we can be competitive. I am sure that no one in this plant wants that to happen.

Required 1.Verify, either by using the actual formulae given in the Appendix, or by using a software program on a computer, that the regression equation is given by y — $78,000 + ($13.80 X Units produced)

with an r2 = 0.88. Adjusted R2 = 0.819 2. What is the benchmark for Quarter 5 that Allison Hart had calculated?

3. Why is there a difference between the benchmark calculated by Peter $mith and the benchmark calculated in requirement 2? Which benchmark do you prefer? Explain your answer.

4. Identify the steps that Allison Hart should follow in attempting to resolve the situation created by Peter $mith’s comment about adjusting the benchmark.