A portion of a data set containing information for 14 mutual funds that are part of the Morningstar Funds 500 for 2008 follows. 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, 2007. 5-YearAverageReturn(\%): Theaverageannualreturnforthefundoverthepast5years. 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 1Star to a high of 5-Stars. a. Develop an estimated regression equation that can be used to predict the 5-year average return given expense ratio. (If you use Excel, you have to upload the file. Otherwise, no points will be given) [15 pts] c. Use
α=0.05
to test if the independent variable in the estimated regression equation from (a) is significant. Provide your reason. [15 pts] d. Is there any outlier in the dataset for the estimated regression equation in part (a)? Provide your reason. [10 pts] e. Use the estimated regression equation from part (a) to estimate the expected 5-year average return given expense ratio
1.25%
. [15 pts] f. Develop a
95%
confidence interval to predict the mean 5-year average return given expense ratio
1.25%
. [10 pts] Hint: Use the regression equation from part (a). (1) Write down the formula calculating the confidence interval estimate of the mean 5-year average return given expense ratio
1.25%
: (2) Start your calculation here: g. 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. You don't need to remove any insignificant variables. What is the estimated regression equation? [5 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
(If you use Excel, you have to upload the file. Otherwise, no points will be given) h. (1) What is the value of adjusted
r 2
for the estimated regression equation in part (g)? [3 pts] (2) Explain the meaning of adjusted
r 2
:
[2 pts] i. Use
α=0.05
to test if the independent variables in the estimated regression equation from (g) are significant. Provide your reason. [5 pts] j. Using the estimated regression equation from part
(g)
, predict the 5-year average return for the following record: [5 pts]
