Chapter 6.A, Problem 6P

Least-Square. 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 that correlates with the cost. 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:

Required:
1. Using torn mined as the independent variable, prepare a scattergraph that plots tons mined on the horizontal axis and utilities cost on the vertical axis Using the least-squares regression method, estimate the variable utilities cost per ton mined and the total fixed utilities cost per quarter. Express these estimates in the form Y = a + bX.
2. Using direct labor-hours as the independent variable, prepare a scattergraph that plots direct labor-hours on the horizontal axis and utilities cost on the vertical axis. Using the least-squares regression method, estimate the variable utilities cost per direct labor-hour and the total fixed utilities cost per quarter. Express these estimates in the form Y = a+ bX.
3. Would you recommend that the company use tons mined or direct labor-hours as a base for planning utilities cost?