$3\mathrm{.}8.$ The characterisfic line of modern investment analysis involves running the following regression:

$r_1=B_1+B_2{r}_{m1}+u_1$

where $r=$ the rate of return on a stock or security

$r_m=$ the rate of return on the market portfolio represented by a broad market index such as S&P $500,$ and

$t=$ time

In investment analysis, $B_2$ is known as the beff coefficient of the security and is used as a measure of market risk, that is$,$ how developments in the market affect the fortunes of a given company.

Based on $240$ monthly rates of return for the period $1956$ to $1976,$ Fogler and Ganapathy obtained the following results for IBM stock. The market index used by the authors is the market portfolio index developed at the University of Chicago: ${?}^{19}$

$r_2=0\mathrm{.}7264+1\mathrm{.}0598r_{mt}$

$se=(0\mathrm{.}3001)(0\mathrm{.}0728),r^2=0\mathrm{.}4710$

a$.$ Interpret the estimated intercept and slope.

b$.$ How would you interpret $r^2?$

c$.$ A security whase beta coefficient is greater than $1$ is called a volatile or aggressive security. Set up the appropriate null and alternative hypotheses and test them using the $t$ test. Note: Use $=5\%.$