Least-Squares Regression ; Scattergraph; Comparison of Activity Bases
The Hard Rock Mining Company is developing cost formulas for management planning and decision-making purposes. 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 suggested that tons mined might be a good base to use in developing a cost formula. The production superintendent disagrees; she thinks that direct labor-hours would be a better base.The cost analyst has decided to try both bases and has assembled the following information:
Quarter | Tons Mined | Direct Labour-Hours | Utilities Cost |
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 |
Yea r 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 tons mined as the independent (X) variable:
a.Determine a cost formula for utilities cost using the least-squares regression method.
b.Prepare a scattergraph and plot the tons mined and utilities cost. (Place cost on the vertical axis and tons mined on the horizontal axis.) Fit a straight line to the plotted points using the cost formula determined in (a) above.
2. Using direct labor-hours as the independent (X) variable, repeat the computations in (a)and (b) above.
3. Would you recommend that the company use tons mined or direct labor-hours as a base for planning utilities cost?
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