Please Answer using EXCEL: A data set containing information for $14$ mutual funds that are part of the Morningstar Funds $500$ is listed below. f$.$ Use $=0\mathrm{.}05$ to test if the independent variables type of fund and expense ratio in the estimated

regression equation from $($e$)$ are significant. Provide your reason. $[15$ pts$]$

g$.$ Using the estimated regression equation from part $($e$),$ predict the $5-$year average return for the

following record: $10pts[70$ pts$]$ A data set containing information for $14$ mutual funds that are part of the Morningstar Funds

$500$ is listed below.

Fund Name Fund Type Net Asset Value $($$$)5$ Year Average Return $(\%)$

$($Y$)$ Expense Ratio

$(\%)$

$($x$)$ Morningstar Rank

Amer Cent Inc & Growth Inv DE $28\mathrm{.}8812\mathrm{.}390\mathrm{.}672-$Star

American Century Intl. Disc IE $14\mathrm{.}3730\mathrm{.}531\mathrm{.}413-$Star

American Century Tax$-$Free Bond FI $10\mathrm{.}733\mathrm{.}340\mathrm{.}494-$Star

American Century Ultra DE $24\mathrm{.}9410\mathrm{.}880\mathrm{.}993-$Star

Ariel DE $46\mathrm{.}3911\mathrm{.}321\mathrm{.}032-$Star

Artisan Intl Val IE $25\mathrm{.}5224\mathrm{.}951\mathrm{.}233-$Star

Artisan Small Cap DE $16\mathrm{.}9215\mathrm{.}671\mathrm{.}183-$Star

Baron Asset DE $50\mathrm{.}6716\mathrm{.}771\mathrm{.}315-$Star

Brandywine DE $36\mathrm{.}5818\mathrm{.}141\mathrm{.}084-$Star

Brown Cap Small DE $35\mathrm{.}7315\mathrm{.}851\mathrm{.}204-$Star

Buffalo Mid Cap DE $15\mathrm{.}2917\mathrm{.}251\mathrm{.}023-$Star

Delafield DE $24\mathrm{.}3217\mathrm{.}771\mathrm{.}324-$Star

DFA U$.$S$.$ Micro Cap DE $13\mathrm{.}4717\mathrm{.}230\mathrm{.}533-$Star

Dodge & Cox Income FI $12\mathrm{.}514\mathrm{.}310\mathrm{.}444-$Star

a$.$ Develop a $95\%$ confidence interval to predict the mean $5-$year average return given expense ratio $1\mathrm{.}25\%.$

b$.$ Develop an estimated regression equation that can be used to predict the $5-$year average return given the type of fund and the expense ratio as the independent variables. You don$$t need to remove any insignificant variables. What is the estimated regression equation? $[10$ pts$]$

To incorporate the effect of quality, a categorical variable with three levels, we used two dummy variables, Fund$-$IE and Fund$-$FI$.$ Each variable is coded $0$ or $1$ as follows.

Fund$-$IE $=\{1$ if fund type is IE$,0$ otherwise$)$

Fund$-$FI $=\{1$ if fund type is FI$,0$ otherwise$)$

c$.$ Use $\backslash$alpha $=0\mathrm{.}05$ to test if the independent variables type of fund and expense ratio in the estimated regression equation from $($e$)$ are significant. Provide your reason.

d$.$ Using the estimated regression equation from part $($e$),$ predict the $5-$year average return for the following record: $[10$ pts$]$

Fund Type Net Asset Value $($$$)$ Expense Ratio $(\%)$ Morningstar Rank

DE $20\mathrm{.}211\mathrm{.}233-$Star