For the past $2$ years, Teagan has worked in a machining facility, helping the company track and record its wide variety of costs. She has organized the data quarterly, to correspond with the quarterly budget$/$actual meetings, with the following data obtained for power costs.

Quarter

Machine Hours

Power Cost

$1$

$28,000$ $$36,400$

$2$

$35,00053,200$

$3$

$42,00059,500$

$4$

$30,80051,800$

$5$

$29,40047,600$

$6$

$25,20040,600$

$7$

$33,60050,400$

$8$

$39,20053,400$

$9$

$37,00052,000$

$10$

$34,50048,500$

Power costs used to be a mystery to the company before the new production supervisor came on board, just $6$ months after Teagan started. Teagan heard through the grapevine that employees and management in the factory used to leave equipment running even when there was not an active production run in process. In other cases, they shut everything down right in the middle of a shift to celebrate employee milestones with cake. There are no such activities now, as the new supervisor is running a tight ship.

Create a scatter plot of the data in Excel. Does the data exhibit a linear relationship within this range of activity? What is the expected production range given this data for the past ten quarters?