$[70$ pts$]$ A data set containing information for $14$ mutual funds that are part of the Morningstar Funds $500$ is listed below.

$\backslash$table$[[$Fund Name,$\backslash$table$[[$Fund$],[$Type$]],\backslash$table$[[$Net Asset$],[$Value $($$$)]],\backslash$table$[[5$ Year$],[$Average$],[$Return$],[(\%)]],\backslash$table$[[$Expense$],[$Ratio$],[(\%)]],\backslash$table$[[$Morningstar$],[$Rank$]]],[$Amer Cent Inc & Growth Inv,$DE,28\mathrm{.}88,12\mathrm{.}39,0\mathrm{.}67,2-$Star$],[$American Century Intl. Disc,IE$,14\mathrm{.}37,30\mathrm{.}53,1\mathrm{.}41,3-$Star$],[$American Century Tax$-$Free Bond,FI$,10\mathrm{.}73,3\mathrm{.}34,0\mathrm{.}49,4-$Star$],[$American Century Ultra,$DE,24\mathrm{.}94,10\mathrm{.}88,0\mathrm{.}99,3-$Star$],[$Ariel$,DE,46\mathrm{.}39,11\mathrm{.}32,1\mathrm{.}03,2-$Star$],[$Artisan Intl Val,IE$,25\mathrm{.}52,24\mathrm{.}95,1\mathrm{.}23,3-$Star$],[$Artisan Small Cap,$DE,16\mathrm{.}92,15\mathrm{.}67,1\mathrm{.}18,3-$Star$],[$Baron Asset,$DE,50\mathrm{.}67,16\mathrm{.}77,1\mathrm{.}31,5-$Star$],[$Brandywine$,DE,36\mathrm{.}58,18\mathrm{.}14,1\mathrm{.}08,4-$Star$],[$Brown Cap Small,$DE,35\mathrm{.}73,15\mathrm{.}85,1\mathrm{.}20,4-$Star$],[$Buffalo Mid Cap,$DE,15\mathrm{.}29,17\mathrm{.}25,1\mathrm{.}02,3-$Star$],[$Delafield$,DE,24\mathrm{.}32,17\mathrm{.}77,1\mathrm{.}32,4-$Star$],[$DFA U$.$S$.$ Micro Cap,$DE,13\mathrm{.}47,17\mathrm{.}23,0\mathrm{.}53,3-$Star$],[$Dodge & Cox Income,FI$,12\mathrm{.}51,4\mathrm{.}31,0\mathrm{.}44,4-$Star$]]$

The data set above includes the following five variables:

Type: The type of fund, labeled DE $($Domestic Equity$),$ IE $($International Equity$),$ and FI $($Fixed Income$).$ Net Asset Value $($$$)$: The closing price per share on December $31.$

$5-$YearAverageReturn$(\%)$: Theaverageannualreturnforthefundoverthepast$5$years.

ExpenseRatio$(\%)$: The percentage of assets deducted each fiscal year for fund expenses.

Morningstar Rank: The risk adjusted star rating for each fund; Morningstar ranks go from a low of $1$Star to a high of $5-$Stars.

e$.$ 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$-IE=\{\begin{array}{ccc}1& if\text{f}\text{u}\text{n}\text{d}\text{t}\text{y}\text{p}\text{e}is& IE\end{array}$

$0$ otherwise

Fund$-FI=\{\begin{array}{ccc}1& if\text{f}\text{u}\text{n}\text{d}\text{t}\text{y}\text{p}\text{e}is& FI\end{array}$

$0$ otherwise

$($If you use Excel, you have to upload the file, Otherwise, no points will be given$)q,$

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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: $[10$ pts$]$

$\backslash$table$[[$Fund Type,Net Asset Value $($$$),$Expense Ratio $(\%),$Morningstar Rank$],[$DE$,20\mathrm{.}21,1\mathrm{.}23,3-$Star$]]$

$7$