EXERCISE 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
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?