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 $3\mathrm{.}32\%,$ holding PE constant.

As the PS ratio decreases by $1$ unit, the predicted return of the firm decreases by $33\mathrm{.}17\%,$ holding PE constant.

As the PS ratio increases by $1$ unit, the predicted return of the firm increases by $3\mathrm{.}32\%,$ holding PE constant.

As the PS ratio increases by $1$ unit, the predicted return of the firm decreases by $33\mathrm{.}17\%,$ 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 $R^2.$

$40\mathrm{.}08\%$ of the sample variation in $y$ is explained by the sample regression equation.

$40\mathrm{.}08\%$ of the sample variation in $x$ is explained by the sample regression equation.

$63\mathrm{.}31\%$ of the sample variation in $x$ is explained by the sample regression equation.

$35\mathrm{.}65\%$ of the sample variation in $y$ is explained by the sample regression equation.