$\backslash$table$[[$Firm$,$Return,PE$,$PS$],[1,4\mathrm{.}8,14\mathrm{.}36,2\mathrm{.}42],[2,-4\mathrm{.}7,11\mathrm{.}04,0\mathrm{.}82],[3,6\mathrm{.}1,11\mathrm{.}98,2\mathrm{.}28],[4,5\mathrm{.}2,11\mathrm{.}28,1\mathrm{.}35],[5,-11\mathrm{.}2,9\mathrm{.}84,1\mathrm{.}83],[6,21,15\mathrm{.}69,0\mathrm{.}84],[7,64\mathrm{.}4,16\mathrm{.}08,1\mathrm{.}61],[8,18\mathrm{.}4,8\mathrm{.}96,1\mathrm{.}02],[9,-15\mathrm{.}1,11\mathrm{.}36,2\mathrm{.}77],[10,48\mathrm{.}4,13\mathrm{.}72,1\mathrm{.}42],[11,7\mathrm{.}6,11\mathrm{.}45,1\mathrm{.}22],[12,20\mathrm{.}9,14\mathrm{.}32,1\mathrm{.}31],[13,-18,8\mathrm{.}21,0\mathrm{.}85],[14,3\mathrm{.}3,9\mathrm{.}51,2\mathrm{.}66],[15,12\mathrm{.}3,11\mathrm{.}17,2\mathrm{.}01],[16,\backslash$table$[[-3\mathrm{.}8]],12\mathrm{.}62,2\mathrm{.}74],[17,1\mathrm{.}6,9\mathrm{.}71,2\mathrm{.}01],[18,16\mathrm{.}1,13\mathrm{.}48,1\mathrm{.}12],[19,23\mathrm{.}3,14\mathrm{.}94,3\mathrm{.}36],[20,,8\mathrm{.}91,2\mathrm{.}42],[21,,10\mathrm{.}51,3\mathrm{.}73],[22,\backslash$table$[[-3\mathrm{.}9]],7\mathrm{.}89,2\mathrm{.}21],[23,15\mathrm{.}3,16\mathrm{.}37,4\mathrm{.}58],[24,21\mathrm{.}3,16\mathrm{.}33,0\mathrm{.}87],[25,6\mathrm{.}5,15\mathrm{.}03,2\mathrm{.}35],[26,11\mathrm{.}8,9\mathrm{.}16,0\mathrm{.}98],[27,13\mathrm{.}4,14\mathrm{.}91,1\mathrm{.}37],[28,15\mathrm{.}9,15\mathrm{.}62,0\mathrm{.}95],[29,1\mathrm{.}2,12\mathrm{.}6,0\mathrm{.}47],[30,16\mathrm{.}5,13\mathrm{.}95,1\mathrm{.}92]]$ 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.$)$

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 increases by $3\mathrm{.}42\%,$ holding PE constant.

As the PS ratio increases by $1$ unit, the predicted return of the firm decreases by $3\mathrm{.}42\%,$ holding PE constant.

As the PS ratio decreases by $1$ unit, the predicted return of the firm decreases by $33\mathrm{.}24\%,$ holding PE constant.

As the PS ratio increases by $1$ unit, the predicted return of the firm decreases by $33\mathrm{.}24\%,$ 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.$)$

Predicted Return

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

Standard error

e$.$ Interpret $R^2.$

$40\mathrm{.}75\%$ of the sample variation in $y$ is explained by the sample regression equation.

$40\mathrm{.}75\%$ of the sample variation in $x$ is explained by the sample regression equation.

$63\mathrm{.}83\%$ of the sample variation in $x$ is explained by the sample regression equation.

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