QM2 Assignment 2,

| January 30, 2016

QM2 Assignment 2,
Assignment 2
Due by: 9am Friday 5 February
This assignment must be submitted by 9am on the above due date. Any assignment
submitted after the due date and time will be given a mark of zero.
The purpose of this assignment is to give you practice in using the regression technique, to
build and estimate regression models, and to test certain hypotheses taken from “theory”.
Lectures 5-9 provide information to complete the tasks set out in this Assignment.
This is a group assignment. A group up to three students may work together and submit one
assignment for the group. All members of the group, however, MUST be enrolled in the
same tutorial. For assignments submitted as a group, all students in the group, as long as
they are all enrolled in the same tutorial, will receive the same mark for the assignment. Any
student, who attempts to submit an assignment with a group that is not in their own
tutorial, or in a group with more than three members, will not receive any credit for that
assignment. Students should form their own groups. Individuals may work alone if they wish
and submit their own answers, but I would urge students to work in groups.
Your assignment answers must be no more than ten pages in total, including all graphs
tables, and written responses. Any assignments in excess of this length will be ignored
during assignment marking. Answer the questions directly. Do not undertake inappropriate
tests or discuss irrelevant matters.
Students should form groups via the LMS groups sign up link and one member submits the
assignment on behalf of the group. More instructions will be provided on the LMS.
Students must copy and paste the template provided with the assignment into the top of
the first page of their assignment answers, and complete the template before submitting
their answers. It is essential that you include the name of your tutor and your allocated
tutorial day and time at the top of your assignment answers in order for your assignment to
be graded in a timely manner.
Dr Wasana Karunarathne
Department of Economics
The University of Melbourne
QM2 Assignment 2, Summer Semester 2016 Page 2
Question 1 (50 Marks)
Background:
Research findings on the impact of class attendance of university students on their exam
performance provide ambiguous conclusions. Some research suggests a strong positive association
between students attending lectures and their performance in exams. However, others suggest that
the positive impact of lecture attendance reported in the literature may be overestimated as it
reflects the impact of unobservable factors on exam marks. (Feel free to search the web to read up
on journal articles written in this area of research).
Suppose that we are also interested in estimating the impact of lecture attendance on the final exam
marks of university students. We have been given a dataset collected for a sample of 680 university
students. Our data set includes the variables described below.
attend Number of classes attended out of 32 classes during the semester
attend_rate Percentage of classes attended during the semester
prior_GPA Cumulative GPA prior to the semester of interest
UAE Score of a university admissions examination, consisting of 4 subject areas. Range of
marks: 1-36
finalscore Final exam score for the semester
skipped Number of classes skipped
std_score Standardised exam score calculated as: (final exam score for each student – mean of
final exam score)/standard deviation of final exam score
gender Takes value 1 if the student is a male
Notes:
1. It is sensible to use standardised exam score in your regression since it is easier to interpret
a student’s performance relative to the rest of the class. For a similar reason, we would
prefer to include the attendance rate into the regression rather than the number of classes
attended.
2. There are evidence to suggest that UAE and Prior_GPA have quadratic relationship with the
final scores and there is an interaction effect of Prior_GPA and attendance rate on scores.
Make sure that you only include relevant variables into your regression.
3. Students must follow all the 6 steps when they do hypothesis testing. When necessary,
students must provide EViews outputs as evidence (these include the regression output).
QM2 Assignment 2, Summer Semester 2016 Page 3
Questions:
(a) Provide descriptive statistics for all the variables given in the data set. Discuss these statistics.
[4 Marks]
(b) Before estimating the regression, we are interested in looking at the impact of a range of factors
(including class attendance given by attendance rate) on the standardised final score for the
term. Using appropriate graphs, depict the relationship between each of the independent
variable with the dependent variable. Also using appropriate statistics to estimate the linear
relationships, discuss the nature of relationship between these variables.
[2 Marks]
(c) From the graphs in part (b), identify if there is any violation of the six OLS assumptions discussed
in class. Also clearly explain why you think the assumption(s) might be violated.
[3 Marks]
(d) Write down a population regression model for the final score (not the standardised score) using
the variables in the data set (use all the relevant variables even if you believe they may not have
an impact of the final score. Use attendance rate to estimate the impact of attendance on final
score).
[2 Marks]
(e) Estimate the population regression model in part (d) above. Report the results.
[2 Marks]
(f) Conduct any statistical tests to determine if OLS assumptions (for the error variable) are
violated. If any of the assumptions is violated, take necessary action and re-estimate the
regression (otherwise you can leave it as it is). If you have a new regression model, report the
results and provide the EViews output as well.
[4 Marks]
(g) Tom believes that gender explains the variation in exam scores. Interpret the coefficient on
gender and test his claim.
[4 Marks]
(h) Using the appropriate model, write an equation to show the impact of attendance on final exam
score.
[2 Marks]
(i) What is the impact of lecture attendance on final scores for students who have average prior
cumulative GPA?
[2 Marks]
(j) Is there any statistical evidence to suggest that the attendance in lectures affect exam scores?
[4 Marks]
QM2 Assignment 2, Summer Semester 2016 Page 4
(k) Using the p-value approach, test for the overall utility of the model you estimated.
[3 Marks]
(l) Is this regression a reasonable fit?
[2 Marks]
(m) Suppose that you are now interested in estimating the impact of the given variables on the
standardised exam scores (rather than raw scores). Re-write the population regression model
with the new dependent variable. If you estimate this regression model, what changes do you
expect to have on the estimated regression coefficients?
[3 Marks]
(n) Estimate the regression for part (m) without the variable “gender”. Report the results.
[4 Marks]
(o) Interpret the goodness of fit of the new model. Based on the coefficient for goodness of the fit
of the model, can we say that model 1 (estimated in part e) is better at explaining the variation
in test scores than model 2 (estimated in part n)?
[4 Marks]
(p) Do you agree with the concern of some researchers that the estimated effect of attendance on
test scores is overestimated? Using the regression models estimated above, clearly explain your
reasoning.
[5 Marks]
END OF ASSIGNMENT

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