PROBLEM 2A–4 Least-Squares Regression; Scattergraph; Comparison of Activity Bases [LO3, LO8] 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 con- troller 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:

 

 

 

 

 

 

 

 

 

 

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 verti- cal 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?