Serenity Living manufactures gas fireplaces for home use. Each unit produced goes through a complex quality control process. The company has observed quality control costs as follows over the past $16$ weeks:

Week Units Produced Total Quality Control Costs

$134$ $ $690$

$225$ $ $550$

$340$ $ $740$

$422$ $ $500$

$528$ $ $630$

$637$ $ $720$

$730$ $ $621$

$831$ $ $633$

$927$ $ $549$

$1029$ $ $582$

$1132$ $ $647$

$1239$ $ $765$

$1336$ $ $705$

$1424$ $ $485$

$1526$ $ $534$

$1648$ $ $749$

For planning purposes, the company$$s management wants to know the amount of variable quality control costs per unit and the total fixed quality control costs per week.

Required:

$1.$ Using the least$-$squares regression method, estimate the variable and fixed elements of the quality control cost. $($Round variable cost to $2$ decimal places.$)$

$2.$ If the company produces $30$ gas fireplaces next week, what are the expected total quality control costs? $($Round intermediate and final value to $2$ decimal places.$)$

$3.$ This part of the question is not part of your Connect assignment.