The Hard Rock Mining Company
SuperClassEXERCISE 3A–2 Least-Squares Regression [LO4]
The Hard Rock Mining Company is developing cost formulas for management planning and de-
cision making. The company’s cost analyst has concluded that utilities cost is a mixed cost, and he is attempting to find a base with which the cost might be closely correlated. The controller has
100 Chapter 3 Cost Behaviour: Analysis and Use
suggested that tonnes mined might be a good base to use in developing a cost formula. The pro- duction manager disagrees; she thinks that direct labour-hours would be a better base. The cost analyst has decided to try both bases and has assembled the following information:
Quarter | TonnesMined | DirectLabour-Hours | UtilitiesCost |
Year 1: |
|
|
|
First | 15,000 | 5,000 | $50,000 |
Second | 11,000 | 3,000 | 45,000 |
Third | 21,000 | 4,000 | 60,000 |
Fourth | 12,000 | 6,000 | 75,000 |
Year 2: |
|
|
|
First | 18,000 | 10,000 | $100,000 |
Second | 25,000 | 9,000 | 105,000 |
Third | 30,000 | 8,000 | 85,000 |
Fourth | 28,000 | 11,000 | 120,000 |
Required:
1. Using tonnes mined as the independent (X) variable:
a. Determine a cost formula for utilities cost using the least-squares regression method. Calculate the R2 as part of your analysis.
b. Prepare a scattergram and plot the tonnes mined and utilities cost.
2. Using direct labour-hours as the independent (X) variable, repeat the computations in 1(a) and (b) above.
3. Would you recommend that the company use tonnes mined or direct labour-hours as a base for planning utilities cost?
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