The Hard Rock Mining Company wants to separate its utilities cost into variable and fixed elements for planning purposes. The controller believes tons mined might be a good base for developing a cost formula. The production superintendent disagrees; she thinks direct labor-hours would be a better base. Quarterly data for tons mined, direct labor-hours, and utilities cost are as follows:
Quarter Tons Mined Direct Labor-Hours Utilities Cost
Year 1:
First 19,000 5,400 $ 54,000
Second 14,000 3,400 $ 49,000
Third 24,000 4,400 $ 64,000
Fourth 16,000 6,400 $ 79,000
Year 2:
First 22,000 10,800 $ 120,000
Second 29,000 10,200 $ 125,000
Third 34,000 8,800 $ 89,000
Fourth 32,000 11,800 $ 128,000
1-b. 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.
Note: Round the Variable cost per unit to 2 decimal places and Fixed Cost to the nearest whole dollar amount.