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 $19,0005,400$ $ $54,000$

Second $14,0003,400$ $ $49,000$

Third $24,0004,400$ $ $64,000$

Fourth $16,0006,400$ $ $79,000$

Year $2$:

First $22,00010,800$ $ $120,000$

Second $29,00010,200$ $ $125,000$

Third $34,0008,800$ $ $89,000$

Fourth $32,00011,800$ $ $128,000$

$1-$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.