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

Company Sales

$($$ thousands$)$ Net Earnings

$($$ thousands$)$

Swan Furnace Cleaners $36\mathrm{.}71\mathrm{.}5$

WestCo $22\mathrm{.}4-0\mathrm{.}7$

EastCo $29\mathrm{.}50\mathrm{.}1$

The Grayson Group $37\mathrm{.}10\mathrm{.}6$

XYZ Co$.47\mathrm{.}32\mathrm{.}5$

Second Time Around Clothing $58\mathrm{.}83\mathrm{.}2$

Cola Company $45\mathrm{.}42\mathrm{.}0$

Apex Consulting $25\mathrm{.}40\mathrm{.}4$

Capital Consultants $32\mathrm{.}40\mathrm{.}9$

Pace Design $47\mathrm{.}52\mathrm{.}1$

Text Tech $26\mathrm{.}8-0\mathrm{.}4$

Southwest Consulting $59\mathrm{.}63\mathrm{.}0$

CanTech Supply $29\mathrm{.}40\mathrm{.}0$

JenStar $51\mathrm{.}32\mathrm{.}8$

Stiller Co$.43\mathrm{.}61\mathrm{.}8$

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 $$71\mathrm{.}4$ 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.