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.

FirmReturn PE PS

$14\mathrm{.}614\mathrm{.}392\mathrm{.}45$

$2$

$\backslash$vdots

$\backslash$vdots

$30$

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 $3\mathrm{.}30\%,$ holding PE constant.

As the PS ratio increases by $1$ unit, the predicted return of the firm decreases by $33\mathrm{.}47\%,$ holding PE constant.

As the PS ratio decreases by $1$ unit, the predicted return of the firm decreases by $33\mathrm{.}47\%,$ holding PE constant.

As the PS ratio increases by $1$ unit, the predicted return of the firm increases by $3\mathrm{.}30\%,$ 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.$)$

Standard

error

e$.$ Interpret $R^2.$