A research analyst is trying to determine whether a firm's price$-$earnings $($PE$)$ and price$-$sales $($PS$)$ ratios can explain the firm's stock

performance over the past year. A PE ratio is calculated as a firm's share price compared to the income or profit earned by the firm per

share. Generally, a high PE ratio suggests that investors are expecting higher earnings growth in the future compared to companies

with a lower PE ratio. The PS ratio is calculated by dividing a firm's share price by the firm's revenue per share for the trailing $12$

months. In short, investors can use the PS ratio to determine how much they are paying for a dollar of the firm's sales rather than a

dollar of its earnings $($PE ratio$).$ In general, the lower the PS ratio, the more attractive the investment. The accompanying table shows a

portion of the year$-$to$-$date returns $($Return in $\%)$ and the PE and PS ratios for $30$ firms.

Click here for the Excel Data File

a$-1.$ Estimate: Return $={}_0+{}_1$ PE $+{}_{2}PS+.($Negative values should be indicated by a minus sign. Round your answers to $2$

decimal places.$)$

Predicted Return $=$

a$-2.$ Are the signs on the coefficients as expected?

Yes

No

b$.$ Interpret the slope coefficient of the PS ratio.

As the PS ratio increases by $1$ unit, the predicted return of the firm decreases by $3\mathrm{.}37\%,$ holding PE constant.

As the PS ratio increases by $1$ unit, the predicted return of the firm decreases by $33\mathrm{.}51\%,$ holding PE constant.

As the PS ratio decreases by $1$ unit, the predicted return of the firm decreases by $33\mathrm{.}51\%,$ holding PE constant.

As the PS ratio increases by $1$ unit, the predicted return of the firm increases by $3\mathrm{.}37\%,$ holding PE constant.

c$.$ What is the predicted return for a firm with a PE ratio of $10$ and a PS ratio of $2?($Negative value should be indicated by a minus sign. Do not round intermediate calculations. Round final answer to $2$ decimal places.$)$

d$.$ What is the standard error of the estimate? $($Round your answer to $2$ decimal places.$)$

e$.$ Interpret R$2.$

multiple choice $3$

$40\mathrm{.}53\%$ of the sample variation in y is explained by the sample regression equation.

$40\mathrm{.}53\%$ of the sample variation in x is explained by the sample regression equation.

$63\mathrm{.}67\%$ of the sample variation in x is explained by the sample regression equation.

$36\mathrm{.}13\%$ of the sample variation in y is explained by the sample regression equation.

DATA:

Firm, Return, PE$,$ PS

$1.4\mathrm{.}2,14\mathrm{.}36,2\mathrm{.}41$

$2.-4\mathrm{.}111\mathrm{.}030\mathrm{.}8$

$3\mathrm{.}6\mathrm{.}211\mathrm{.}962\mathrm{.}26$

$44\mathrm{.}911\mathrm{.}281\mathrm{.}36$

$5-119\mathrm{.}841\mathrm{.}86$

$620\mathrm{.}915\mathrm{.}650\mathrm{.}78$

$764\mathrm{.}516\mathrm{.}071\mathrm{.}63$

$818\mathrm{.}89\mathrm{.}010\mathrm{.}99$

$9-15\mathrm{.}611\mathrm{.}342\mathrm{.}79$

$1048\mathrm{.}513\mathrm{.}751\mathrm{.}46$

$117\mathrm{.}611\mathrm{.}441\mathrm{.}24$

$122114\mathrm{.}341\mathrm{.}3$

$13-18\mathrm{.}48\mathrm{.}160\mathrm{.}81$

$1439\mathrm{.}482\mathrm{.}7$

$151211\mathrm{.}191\mathrm{.}99$

$16-4\mathrm{.}212\mathrm{.}632\mathrm{.}75$

$171\mathrm{.}79\mathrm{.}672$

$1815\mathrm{.}913\mathrm{.}451\mathrm{.}16$

$1923\mathrm{.}1153\mathrm{.}38$

$20-1\mathrm{.}68\mathrm{.}912\mathrm{.}39$

$21-810\mathrm{.}513\mathrm{.}72$

$22-3\mathrm{.}47\mathrm{.}942\mathrm{.}21$

$2315\mathrm{.}616\mathrm{.}364\mathrm{.}6$

$2421\mathrm{.}516\mathrm{.}290\mathrm{.}88$

$255\mathrm{.}915\mathrm{.}072\mathrm{.}34$

$2611\mathrm{.}89\mathrm{.}170\mathrm{.}99$

$2713\mathrm{.}714\mathrm{.}911\mathrm{.}39$

$2815\mathrm{.}915\mathrm{.}580\mathrm{.}91$

$291\mathrm{.}212\mathrm{.}590\mathrm{.}47$

$3016\mathrm{.}713\mathrm{.}961\mathrm{.}95$