A portion of a data set containing information for $45$ mutual funds that are part of the Morningstar Funds $500$ follows. The complete data set is available in the file named MutualFunds. The data set includes the following five variables:

Fund 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 $31,2007$

$5-$Year Average Return $(\%)$: The average annual return for the fund over the past five years

Expense Ratio $(\%)$: 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

a$.$ Develop an estimated regression equation that can be used to predict the $5-$yearaverage return given the type of fund. At the $\mathrm{.}05$ level of significance, test for a significant relationship.

b$.$ Did the estimated regression equation developed in part $($a$)$ provide a good fit to the data? Explain.

c$.$ Develop the estimated regression equation that can be used to predict the $5-$year average return given the type of fund, the net asset value, and the expense ratio. At the $\mathrm{.}05$ level of significance, test for a significant relationship. Do you think any variables should be deleted from the estimated regression equation? Explain.

d$.$ Morningstar Rank is a categorical variable. Because the data set contains only

funds with four ranks $(2-$Star through $5-$Star$),$ use the following dummy variables:

$3$StarRank $=1$ for a $3-$Star fund, $0$ otherwise; $4$ StarRank $=1$ for a $4-$Star fund, $0$

otherwise; and $5$StarRank $=1$ for a $5-$Star fund, $0$ otherwise. Develop an estimated regression equation that can be used to predict the $5-$year average return given the type of fund, the expense ratio, and the Morningstar Rank. Using $=\mathrm{.}05,$ remove any independent variables that are not significant.

e$.$ Use the estimated regression equation developed in part $($d$)$ to predict the $5-$year average return for a domestic equity fund with an expense ratio of $1\mathrm{.}05\%$ and a

$3-$Star Morningstar Rank.