Reference no: EM13971155

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?