We are studying mutual bond funds for the purpose of investing in several funds. For this particular study, we want to focus on the assets of a fund and its $5-$year performance. The question is: Can the $5-$year rate of return be estimated based on the assets of the fund? Nine mutual funds were selected at random, and their assets and rates of return are as follows:

Fund Assets $($$ millions$)$ Return $(\%)$ Fund Assets $($$ millions$)$ Return $(\%)$

AARP High Quality Bond $ $622\mathrm{.}210\mathrm{.}8$ MFS Bond A $ $494\mathrm{.}511\mathrm{.}6$

Babson Bond L $160\mathrm{.}411\mathrm{.}3$ Nichols Income $158\mathrm{.}39\mathrm{.}5$

Compass Capital Fixed Income $275\mathrm{.}711\mathrm{.}4$ T$.$ Rowe Price Short$-$term $681\mathrm{.}08\mathrm{.}2$

Galaxy Bond Retail $433\mathrm{.}29\mathrm{.}1$ Thompson Income B $241\mathrm{.}36\mathrm{.}8$

Keystone Custodian B$-1437\mathrm{.}99\mathrm{.}2$

Click here for the Excel Data File

a$.$ Draw a scatter diagram.

$1.$ On the graph below, use the point tool to plot the point corresponding to the first Assets and her Return $($Asset $1).$

$2.$ Repeat the process for the remainder of the sample $($Asset $2,$ Asset $3,...).$

$3.$ To enter exact coordinates, double$-$click on the point and enter the exact coordinates of x and y$.$

b$-1.$ Compute the coefficient of correlation. $($Round your answer to $3$ decimal places. Negative amount should be indicated by a minus sign.$)$

b$-2.$ Compute the coefficient of determination. $($Round your answer to $3$ decimal places.$)$

c$.$ Give a description of the degree of association between the variables.

d$.$ Determine the regression equation. Use assets as the independent variable. $($Round your answers to $4$ decimal places. Negative amounts should be indicated by a minus sign.$)$

e$.$ For a fund with $$400\mathrm{.}0$ million in sales, determine the $5-$year rate of return $($in percent$).($Round your answer to $4$ decimal places.$)$