During June, July, and early August $1981,$ DuPont, Seagram, and Mobil made $10$ bids to take over Conoco. Finally, on August $5,$ DuPont announced success. The total value of the offer accepted by Conoco was $$7\mathrm{.}54$ billion, making it the largest takeover in the history of American business at that time. A study of Conoco takeover used regression analysis to examine whether movements in the rate of return of the contending companies$$ common stock could be explained by movements in the return of the stock market. The model was $,$ where y is the daily rate of return of a stock, x is the daily rate of return of the stock market, and $$ is the error term. $($This model is known in the finance literature as the market model. Note that the parameter reflects the sensitivity of the stock$$s return rate to movements in the stock market as a whole. $)$

Daily data from early $1979$ through $1980($n$=504),$ yielded the least squares lines shown in the table for the four firms in question. The t statistics and p$-$values associated with the values of are also shown.

Firm Estimated Market Model t Statistics p$-$Values SSE R$-$Square

Conoco

$21\mathrm{.}93\mathrm{.}000$

DuPont

$18\mathrm{.}76\mathrm{.}000$

Mobil

$16\mathrm{.}21\mathrm{.}0000\mathrm{.}074\mathrm{.}343$

Seagram

$6\mathrm{.}05\mathrm{.}000$

a$.$ Is the market model useful for predicting the daily return on a stock in each case? Explain why?

b$.$ Compute the standard error of regression for Mobil.

c$.$ Set up a $95\%$ confidence interval for Mobil return on a day when the market returned $2$ percent.