ANL 2216 Group Project Mini-Case 5 Requirements: 1) The purpose of the project is to find some applications of regression techniques and model building in business area. Each group member is supposed to choose TWO questions from the list. All students are supposed to use PowerPoint to prepare their oral presentation files and use MS Word to prepare their answer files for the questions and submit their answer doc-files through the group project submission link in Blackboard. If the group members prefer to compile a single written report file, the group should specify who is responsible got which two questions. 2) The Group's combined effort at the end of Question 6 is optional: if it is done correctly, each group member will earn 2 extra points. 3) If there are more than 6 x-variables in the group, the stepwise regression output is provided at the last page. Mini-Case 5 Study on Mutual Fund Performance Many international funds offer more reasonable equity valuations than those found in the United States. Because international markets often move in different directions than the U.S. market, investments in foreign markets can also reduce an investor's overall risk. The information in the data set mini-case5.xls shows the fund type (load or no-load), expense ratio (%), safety rating (0=riskiest, 10=safest), and the one-year performance (measured by the annual return rate in percentage) through December 10, 1999, for 20 international funds (Mutual Funds, February 2000). The purpose of this study is to develop a regression model to characterize how the independent variables: Safety Rating, Expense Ratio (%), and the Fund Type may affect the dependent variable: Mutual Fund Performance. The Fund Type is a dummy variable whose value can be assigned as follows. 0, if it is No - load, x1 Numerical Fund Type 1, if it is Load. Define x2=Expense Ratio, x3=Safety Rating, and y=Mutual Fund Performance (%). Do data analysis on the following questions: Question 1. Set up an appropriate regression model between the dependent variable (y) and the independent variables (x1, x2, and x3). Fit the model by the data and write down the estimated regression model and the hypothesis for testing the significance of each independent variable. Question 2. Point out which independent variable is the most significant and which independent variable is the least significant. Use level 10% to summarize all significant variables. Use only the significant variables as the independent variables, fit the model between the dependent variable and these significant independent variables. Write down the estimated regression model. Question 3. Use the stepwise regression technique to select significant variables (alpha=10%) from all of the independent variables as provided above. Write down the final estimated regression model after the stepwise regression. Compare this model with the estimated regression model in Question 1 by using the three criteria: 1) the F-test for model assessment; 2) the t-test for significance of each independent variable; and 3) the R-square. Summarize some benefits for the model after the stepwise regression. Question 4. In the final estimated regression model in Question 3, please try to improve the model by considering the quadratic term x22. Provide statistical analysis on whether it is necessary to add this term to the final model in Question 3 at level 10% by defining the hypothesis for adding this quadratic term and point out the p-value for this hypothesis. Question 5. In the final estimated regression model in Question 4, please try to improve the model by considering the quadratic term x32. Provide statistical analysis on whether it is necessary to add this term to the final model in Question 4 at level 10% by defining the hypothesis for adding this quadratic term and point out the p-value for this hypothesis. Question 6. In the final estimated regression model in Question 5, please try to improve the model by considering the interaction term x2x3. Provide statistical analysis on whether it is necessary to add this term to the final model in Question 5 at level 10% by defining the hypothesis for adding this interaction term and point out the p-value for this hypothesis. Group's combined effort: Based on the analysis in Questions 1-6, please give your group's recommendation for the final model to be used for this study on the mutual fund performance and summarize some evidence for your recommendation. The evidence should be based on a comparison of the models by considering the three criteria: 1) the F-test for model assessment; 2) the t-test for significance of each independent variable; and 3) the R-square. Numerical Expense Fund Fund Type Fund Type Ratio Concert Inv "A" Int'l Equity Load 1 2.16 Guardian Baillie Fifford Int'l "A Load 1 1.62 Pilgrim Interntational Value "A" Load 1 1.8 Putnam "A" Int'l Grth Load 1 1.59 Touchstone Int'l Eauity "A" Load 1 1.6 United Int'l Growth "A" Load 1 1.28 Waddell & Reed Int'l Growth "B Load 1 2.46 ABN AMRO Int'l Equity "Com" No-load 0 1.38 Accessor Int'l Equity "Adv" No-load 0 1.59 Artisan Int'l No-load 0 1.45 Columbia Int'l Stock No-load 0 1.56 Diversified Invstr Int'l Eqty No-load 0 1.4 Driehaus Interntaional Growth No-load 0 1.88 Founders Passport No-load 0 1.52 Jamestown Int'l Equity No-load 0 1.56 Julius Baer Int'l Equity No-load 0 1.79 Aetna "I" Int'l No-load 0 1.35 Fidelity Diversified Int'l No-load 0 1.48 Sit Int'l Growth No-load 0 1.5 Vontobel Int'l Equity No-load 0 1.5 Safety Rating Performance 6.3 116 7.1 37 7.1 42 6.9 55 7.5 35 7.1 47 7 75 6.9 36 7.1 42 6.8 72 7.1 54 7.3 54 6.5 92 7 86 7.1 35 6.9 71 7.3 46 7.5 42 6.9 49 7 43