Data:

Firm Return PE PS

$14\mathrm{.}414\mathrm{.}352\mathrm{.}42$

$2-4\mathrm{.}210\mathrm{.}990\mathrm{.}78$

$36122\mathrm{.}27$

$44\mathrm{.}611\mathrm{.}31\mathrm{.}37$

$5-11\mathrm{.}69\mathrm{.}791\mathrm{.}85$

$620\mathrm{.}715\mathrm{.}630\mathrm{.}82$

$764\mathrm{.}216\mathrm{.}071\mathrm{.}62$

$818\mathrm{.}68\mathrm{.}990\mathrm{.}99$

$9-15\mathrm{.}311\mathrm{.}392\mathrm{.}8$

$104813\mathrm{.}721\mathrm{.}42$

$117\mathrm{.}411\mathrm{.}441\mathrm{.}2$

$1220\mathrm{.}714\mathrm{.}341\mathrm{.}29$

$13-17\mathrm{.}98\mathrm{.}160\mathrm{.}79$

$143\mathrm{.}19\mathrm{.}482\mathrm{.}71$

$1511\mathrm{.}911\mathrm{.}191\mathrm{.}96$

$16-3\mathrm{.}812\mathrm{.}622\mathrm{.}76$

$171\mathrm{.}79\mathrm{.}662$

$1815\mathrm{.}713\mathrm{.}431\mathrm{.}14$

$1923\mathrm{.}114\mathrm{.}963\mathrm{.}35$

$20-1\mathrm{.}68\mathrm{.}932\mathrm{.}37$

$21-8\mathrm{.}210\mathrm{.}553\mathrm{.}71$

$22-3\mathrm{.}57\mathrm{.}892\mathrm{.}19$

$2315\mathrm{.}516\mathrm{.}374\mathrm{.}62$

$2421\mathrm{.}616\mathrm{.}280\mathrm{.}86$

$256\mathrm{.}415\mathrm{.}052\mathrm{.}29$

$2612\mathrm{.}19\mathrm{.}170\mathrm{.}99$

$2713\mathrm{.}514\mathrm{.}941\mathrm{.}37$

$281615\mathrm{.}60\mathrm{.}92$

$291\mathrm{.}312\mathrm{.}620\mathrm{.}47$

$3016\mathrm{.}413\mathrm{.}971\mathrm{.}96$

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.

Firm Return PE PS

$14\mathrm{.}414\mathrm{.}352\mathrm{.}42$

$24\mathrm{.}210\mathrm{.}990\mathrm{.}78$

$$

$3016\mathrm{.}413\mathrm{.}971\mathrm{.}96$

a$-1.$ Estimate: Return $=\backslash$beta $0+\backslash$beta $1$PE $+\backslash$beta $2$PS $+\backslash$epsi $.($Negative values should be indicated by a minus sign. Round your answers to $2$ decimal places.$)$

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

multiple choice $1$

Yes

No

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

multiple choice $2$

As the PS ratio increases by $1$ unit, the predicted return of the firm increases by $3\mathrm{.}41\%,$ holding PE constant.

As the PS ratio increases by $1$ unit, the predicted return of the firm decreases by $33\mathrm{.}27\%,$ holding PE constant.

As the PS ratio decreases by $1$ unit, the predicted return of the firm decreases by $33\mathrm{.}27\%,$ holding PE constant.

As the PS ratio increases by $1$ unit, the predicted return of the firm decreases by $3\mathrm{.}41\%,$ 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.$)$