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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:

Required:

$1$a$.$ Using tons mined as the independent variable, prepare a scattergraph that plots tons mined on the horizontal axis and utilities cost on the vertical axis.

$1$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$.$

Round the variable cost per unit to $2$ decimal places and Fixed Cost to the nearest whole dollar amount.