Admission to Ontario Universities and Mutual Funds Analysis

Importance of Ontario Academic Credits (OACs) and Required Courses

Ontario high school students must complete a minimum of six Ontario Academic Credits (OACs) to gain admission to a university in the province.  Most students take more than six OACs because universities take the average of the best six in deciding which students to admit.  Most programs at universities require high school students to select certain courses.  For example, science programs require two of chemistry, biology, and physics.  Students applying to engineering must complete at least two mathematics OACs as well as physics.  In recent years, one business program began an examination of all aspects of its program, including the criteria used to admit students.  Students are required to take English and calculus OACs, and the minimum high school average is about 85%.  Oddly, even though students are required to complete English and calculus, the marks in these subjects are not included in the average unless they are in the top six courses in a student’s transcript.   To examine the impact of this policy on admissions decisions, the program director took a random sample of students who recently graduated with the BBA (Bachelor of Business Administration) degree.  She recorded the university GPA (in the range 0 to 12), the high school average based on the best six courses, and the high school average using English and calculus and the next four best marks.  These data are stored in the worksheet Grades.xls.

a)      Is there a relationship between university GPA and the high school average using the best six OACs?

b)      Is there a relationship between GPA and the high school average using the best four OACs plus calculus and English?

c)      How should the program director interpret the implications of this data for admission purposes?

 

Question 2 (35 marks)

Data for 137 mutual funds are provided in the MutualFunds.xlsx spreadsheet. This file contains the fields described below:

 

In this assignment you will attempt to develop a model for Ret00Q1 returns as a function of the other variables. In the following questions the term ‘variables’ refers to all variables in this data set except the ‘Fund’ name variable.

Use the Excel Tools/Data Analysis/Regression tool to carry out a multiple regression of Ret00Q1 versus all of the other variables. The resulting model will be referred to as the ‘full model’ below. [Note that the built-in Excel tool requires all ‘X’-variables to be in adjacent columns. You may need to move columns around in the data set to carry out some regressions.]

Be sure to use the regression options to calculate residuals and standardized residuals for each of the regressions you carry out. It is not necessary to hand in copies of all of your regression output; limit your submission to exhibits that are directly referenced in your analyses.

a)      Calculate the sample correlations for all pairs of variables.  Briefly comment on any correlations that may be relevant to the regression analysis.

b)      What percentage of the variation in Ret00Q1 is explained by the full model.

c)      Write out a clear interpretation of each significant slope coefficient that you obtain.

d)      When questioned by an investor about a seemingly high expense ratio for a mutual fund, an investment advisor at a bank responded that “this fund is intensively managed to maximize returns, and the management costs are accordingly higher.” Comment on this advisor’s statement, using the regression results to support your statements.

e)      Predict the return in the first quarter of 2000 on a single average-risk, TK fund with a sales charge, an expense ratio of 1.30, and a 10% return in 1999.It is not necessary to generate a prediction interval for this estimate. Examine the original data and comment on any concerns you might have about this prediction.

f)       Run a multiple regression of Ret00Q1 versus only the two Risk indicator variables. Compare the results from this regression with those from the full model. Can you explain any differences?

g)      Conduct additional regressions at your discretion with the objective of obtaining a ‘good’ model in the terms discussed in class. You may choose to use the adjusted R-square as a rough measure of the ‘goodness’ of a model. Prepare a brief summary of your findings (maximum two pages – again, please limit the amount of computer reports you submit).

h)      Graphically examine the residuals from the final model that you select and comment on any concerns you might have. (A plot of standard residuals vs. predicted values is useful for this purpose.)