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ECON20003 – QUANTITATIVE METHODS
Please read the following instructions carefully before starting to work on the
assignment.
There is a total of 100 marks for this assignment. It is worth 5% of the final
grade for QM2.
This assignment must be submitted online via the LMS by 10:00AM on
Monday 23 May. Any assignment not submitted by this due date and time
will be given a mark of zero.
Students may work alone and submit their own assignment answers, if they
wish to do so, or they can work on the assignment in pairs. In the latter case,
each assignment pair must submit only one set of assignment answers and
both students of the pair will receive the same mark for their assignment. It
is not allowed to form assignment groups of more than two students.
Please note that the assignment submission process has two stages:
1. Registering your assignment group (only if you work in a pair), and
2. Submitting the assignment online via the LMS.
Students who intend to work on the assignment in pairs must register their
groups. To do so, click the “People” link and then the Groups tab in the
Canvas course navigation menu. The group names (set by default) are A3 1,
A3 2, A3 3 etc. Every assignment pair MUST register as one of these created
groups for submitting the assignment and not create a new group. The
deadline for registering your group is 5:00PM on Friday 13 May. If a pair fails
to register their group before the deadline for group registration, both
students will need to make an individual submission.
Students making an individual submission do not need to register.
Answer the assignment questions using Microsoft Word. Make sure to
include a cover page in the document with the student ID, the name, and the
tutorial group of each group member. Paste your relevant R/RStudio scripts,
screenshots, and printouts (graphs, output tables etc.) in the document.
Convert the whole file to PDF before submitting it online via the LMS.
Do not forget to preview your assignment after uploading on the LMS to
ensure that you have indeed uploaded the correct and complete assignment,
and that its formatting is in order as in their original document. Submissions
2
ECON20003 Semester 1, 2022 Assignment 3
that are late because of formatting issues or because a version is
incomplete, will not be accepted.
Assignment Tasks and Questions
Exercise 1 (34 marks = 4 + 18 + 4 + 8)
One of the issues that usually come up in the US presidential elections is how to deal
with a sluggish economy. Specifically, should the government cut spending, raise
taxes, inflate the economy by printing more money, or do none of the above and let
the deficit rise? And as with most other issues, politicians need to know which parts of
the electorate support these options.
Suppose that a random sample of 1,000 people was asked which option they support
and their political affiliations. The possible responses to the question about the
preferred economic option were the four options mentioned above (i.e., Cut, Raise,
Inflate, and Let), and to the question about political affiliation the respondents could
answer Democrat, Republican, or Independent (which included a variety of political
persuasions). The responses are summarised in the table below.
Do these data allow us to conclude at the 1% significance level that political affiliation
affects support for the economic options?
(a) Describe the variables of interest? Are they qualitative or quantitative? If they are
qualitative, are they ranked or unranked? If they are quantitative, are they discrete
or continuous? What are the levels of measurement? Explain your answers.
(b) Answer the research question by performing all necessary calculations manually.
State the hypotheses, the decision rule, calculate the test statistic showing the
details of your calculations, make a statistical decision with reference to the proper
Option Democrat Republican Independent
Cut 101 282 61
Raise 38 67 25
Inflate 131 88 31
Let 61 90 25
Affiliation
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ECON20003 Semester 1, 2022 Assignment 3
critical value and draw your conclusion. Based on the relevant critical value table,
what can you tell about the p-value of your test? Explain your answer.
(c) Repeat the test you performed in part (b) with R. Evaluate the test using the
reported p-value this time.
(d) List all requirements that must be met to validate the test in parts (b) and (c). Are
they likely satisfied this time? Explain your answers.
Exercise 2 (31 marks: 6 + 4 + 8 + 13)
Consumer Research is an independent agency that conducts research on consumer
attitudes and behaviours for a variety of firms. In one study, a client asked for an
investigation on consumer characteristics that can be used to predict the amount
charged by credit card users. Data were collected on annual income (Income, $1000),
household size (Size), and annual amount of credit charged to the credit card (Credit,
$) for a random sample of 50 customers. These data are saved in the a3e2.xlsx file.
(a) For each of the three variables, answer the following questions. Is the variable
qualitative or quantitative? If it is qualitative, is it ranked or unranked? If it is
quantitative, is it discrete or continuous? What is its level of measurement? Explain
your answers.
(b) Consider the following two pairs of variables: Credit and Income, and Credit and
Size. In each case, do you expect the variables to be related to each other? If yes,
do you expect the relationship to be positive or negative. Explain your answers.
(c) Using R, calculate the Pearson or Spearman correlation coefficient, whichever is
more appropriate, for the two pairs of variables in part (b). In each case, briefly
explain your choice between the Pearson and Spearman correlation coefficients
and comment on the direction and relative strength of the relationship as implied
by the point estimate.
(d) Based on your answers in part (b), perform an appropriate test with R at the 5%
significance level on each pair of variables to determine whether there is a linear,
or at least monotonic, relationship between the variables in the expected direction.
In each case, show the hypotheses and state the statistical decision and the
conclusion.
ECON20003 Semester 1, 2022 Assignment 3
Exercise 3 (35 marks: 4 + 6 + 8 + 6 + 11)
Refer to Exercise 2.
(a) Estimate a multiple linear regression model with R for the annual credit card
charges using annual income and household size as independent variables. Write
out the sample regression equation using the actual variable names.
(b) Interpret the adjusted coefficient of determination. Is the model likely to be useful
in predicting the annual credit card charges? Explain your answer.
(c) Test the overall significance of the model at the 1% significance level. What are
the hypotheses, the observed test statistic, the statistical decision, and the
conclusion? Be precise.
(d) Based on your expectations in part (b) of Exercise 2, test appropriate hypotheses
concerning the slope coefficients using t-tests at the 1% significance level. What
are your decisions and conclusions?
(e) Interpret the slope coefficients that you deemed significant in the expected
direction. Does the y-intercept estimate have a logical interpretation this time? If
yes, what is it? If not, why not?
