uestion $2[10$ points$]$

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

Company Sales

$($$ thousands$)$ Net Earnings

$($$ thousands$)$

The Grayson Group $44\mathrm{.}72\mathrm{.}1$

XYZ Co$.51\mathrm{.}32\mathrm{.}6$

PhotoFinish Co$.40\mathrm{.}71\mathrm{.}4$

Cantu Excavating $47\mathrm{.}01\mathrm{.}9$

Swan Furnace Cleaners $37\mathrm{.}01\mathrm{.}4$

JenStar $30\mathrm{.}20\mathrm{.}5$

Text Tech $37\mathrm{.}60\mathrm{.}7$

EastCo $20\mathrm{.}0-0\mathrm{.}4$

Pace Design $51\mathrm{.}61\mathrm{.}7$

Antique Accents $40\mathrm{.}51\mathrm{.}5$

The Party Place $49\mathrm{.}51\mathrm{.}7$

Stiller Co$.42\mathrm{.}00\mathrm{.}9$

Financial Services $57\mathrm{.}12\mathrm{.}1$

Second Time Around Clothing $36\mathrm{.}81\mathrm{.}2$

JenCo $32\mathrm{.}10\mathrm{.}2$

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 $$30\mathrm{.}8$ 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.