Part 1:
You have learned about multiple regression, and now please answer the following questions in detail by applying the knowledge that you have gained from readings and lectures this week. It is important to include hypothetical examples whenever applicable.
· Describe the distinction between a quantitative (continuous) variable and a categorical variable, how several dummy variables can be incorporated in the regression model to represent the categorical variables, and provide a hypothetical formulation of a regression which incorporates several categorical variables.
· Explain the hypotheses on the coefficients of the regression and how the results of testing these hypotheses are interpreted about significance of these coefficients, including possible interactions. Include both unidirectional and bidirectional situations.
· Explain and provide a hypothetical example of how a regression model which incorporates dummy variables enables prediction.
· Define logistic regression model, the nature of the independent variable, dependent variable, assumptions of the model, and the objectives.
· Please explain if a categorical variable can be the independent variable in a logistic regression; the LOGIT transformation of a logistic regression and its advantage, the hypotheses on coefficients of the regression, how the results of testing these hypotheses are interpreted about significance of these coefficients in both unidirectional and bidirectional situations, the effect of significant variables in the LOGIT formulation and consequently in the original logistic formulation, how logistic regression model can be used for prediction, accompany a hypothetical example for better clarity.
Part 2:
A data set containing information for nine (9) mutual funds provided in Table 6 are part of the Morningstar Funds 500. The data set includes the following five variables:
1. Fund Type: The type of fund, labeled DE (Domestic Equity), IE (International Equity), and FI (Fixed Income).
2. Net Asset Value ($): The closing price per share on December 31, 2007.
3. 5-Year Average Return (%): The average annual return for the fund over the past five consecutive years ending in 2007.
4. Expense Ratio (%): The percentage of assets deducted each fiscal year for fund expenses.
5. Morningstar Rank: The risk adjusted star rating for each fund; Morningstar ranks go from a low of 1-Star to a high of 5-Stars.
Table 6
Data on Performance and Morningstars Ranking of 9 Mutual Funds
|
Fund Name |
Fund Type |
Net Asset value ($) |
5 Year Average Return (%) |
Expense Ratio (%) |
Morningstar Rank |
|
Amer Cent Inc & Growth Inv |
DE |
28.88 |
12.39 |
.67 |
2-Star |
|
American Century Intl. Disc |
IE |
14.37 |
30.53 |
1.41 |
3-Star |
|
American Century Tax-Free Bond |
FI |
10.73 |
3.34 |
.49 |
4-Star |
|
American Century Ultra |
DE |
24.94 |
10.88 |
.99 |
3-Star |
|
Ariel |
DE |
46.39 |
11.32 |
1.03 |
2-Star |
|
Artisan Intl Va |
IE |
25.52 |
24.95 |
1.23 |
3-Star |
|
Artisan Small Cap |
DE |
16.92 |
15.67 |
1.18 |
3-Star |
|
Baron Asset |
DE |
50.67 |
16.77 |
1.31 |
5-Star |
|
Brandywine |
DE |
36.58 |
18.14 |
1.0 |
4-Star |
Use the sample data provided in the Table 5 to answer the following questions:
a. Provide descriptive statistics of the data classified according to the divisions in the values of categorical variables.
b. Develop a regression model in which the 5-year average return is the dependent variable. State the hypotheses on the coefficients, justify formulation of these hypotheses, and interpret the results. Use ? = .05. Include all phases of assessment of the model and do not forget to check multicollinearity.
c. Use the estimated regression equation developed in part b to predict the expected 5-year return for a combination of values not given in the above table for the independent variables.
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