In a recent survey concerning company sales and net earnings, $15$ companies responded with the following information.

Company Sales

$($$ thousands$)$ Net Earnings

$($$ thousands$)$

Classic Coverings $58\mathrm{.}710\mathrm{.}9$

Financial Services $40\mathrm{.}77\mathrm{.}0$

SouthCo $53\mathrm{.}89\mathrm{.}4$

Swan Furnace Cleaners $48\mathrm{.}38\mathrm{.}2$

Universal Maintenance Co$.35\mathrm{.}66\mathrm{.}3$

DigiCom $52\mathrm{.}39\mathrm{.}8$

Southwest Consulting $45\mathrm{.}08\mathrm{.}6$

Softouch Co$.44\mathrm{.}47\mathrm{.}8$

The Grayson Group $44\mathrm{.}07\mathrm{.}5$

Second Time Around Clothing $47\mathrm{.}48\mathrm{.}0$

PhotoFinish Co$.48\mathrm{.}28\mathrm{.}2$

SunBlush Technologies $23\mathrm{.}54\mathrm{.}3$

JenStar $38\mathrm{.}66\mathrm{.}7$

Cola Company $35\mathrm{.}46\mathrm{.}6$

Cantu Excavating $43\mathrm{.}57\mathrm{.}4$

a$)$ Using a statistical computing tool, find the equation of the regression line.

For full marks your answer should be accurate to at least three decimal places.

b$)$ Use the regression line from part a to estimate the net earnings for a company with sales of $$54\mathrm{.}9$ thousand.

For full marks your answer should be accurate to at least one decimal place.

c$)$ Given the regression equation from part a$,$ which of the following statements is most appropriate regarding company sales and earnings?

$-$ Positive sales means positive net earnings for any business.

Sales have no effect on net revenues.

Insufficient sales can lead to net losses for some businesses.

After a certain level of sales has been reached, net earnings stop growing entirely.