Problem 2A-4 (45 minutes)
1. a.
Quarter
Tons
Mined
(X)
Utilities
Cost
(Y)
Year 1:
1st
15,000
$50,000
2nd
11,000
$45,000
3rd
21,000
$60,000
4th
12,000
$75,000
Year 2:
1st
18,000
$100,000
2nd
25,000
$105,000
3rd
30,000
$85,000
4th
28,000
$120,000
The least-squares regression results are as follows:
Intercept (fixed cost) …………….
$28,352
Slope (variable cost per unit) ….
$2.58
R2 …………………………………….
0.47
Therefore, the cost formula using tons mined as the activity base is
$28,352 per quarter plus $2.58 per ton mined, or
Y = $28,352 + $2.58X.
Note that the R2 is 0.47, which means that only 47% of the variation in
utility costs is explained by the number of tons mined.
