STATS 201 University of Sydney R Studio Questions

STATS 201/208 Data Analysis
Assignment 5, Summer Semester, 2023
Due: 3pm Tuesday 7th February
Instructions concerning this assignment:
A major purpose of this assignment is to ease you into the assignment procedures and the use of
the statistical package R. We will be doing this through the use of R Studio and using R
Markdown.
We are providing you an R Markdown document called STATS20x_2023_SS_A5.Rmd
(available on Canvas) which will have some answers already filled in. You will need to fill in and
complete the rest of the document. The data files you will be using for the assignment are
described in the questions and are available from Canvas. Make sure you put these data files in the
same place you put the R Markdown document because it is going to look for them there. The first
change you need to make to the markdown document is put your name and ID number at the top.
Notes:
• This assignment is worth 6% of your final mark and requires a substantial amount of work. Do not
leave it until the last few days.
• Assignments must be submitted online to the Canvas dropbox PRIOR to the deadline. You will need
to submit your knitted document as either a Word, HTML or PDF file. Assignments more than 30
minutes late are not accepted unless there is a good reason for an extension being granted (usually
medical requiring a medical certificate). Canvas automatically closes submissions after the 30
minute grace period so you will be unable to submit after then.
• The total marks for this assignment will be 44 (this includes 4 marks for presentation and
communication). Most of the marks for assignments will tend to be for interpretation. For
questions where R code is required, there will be additional marks for ensuring that the R output you
produce is consistent with your written answers.
• There are 4 Presentation and Communication marks for this assignment as follows:
• Name, ID number and Space Saving, Name and ID number at top of R Markdown document.
Not printing out unnecessary output (listing data sets or showing erroneous R output).
• Readability. This is for your general communication ability in the assignment. This includes
sentences clearly conveying the correct idea; sentences making sense; comments not being
excessively long or short; conclusions following logically from previous statements.
• Use of Natural Language in Executive Summaries. In executive summaries, this is for
discussing the analysis in context, not using variable names, using units when known and
rounding sensibly.
• Keeping to the Point in Executive Summaries. In executive summaries this is for not going
into far more detail than required.
• It is your responsibility to back up your computer files. If you are using your own computer, it is
your responsibility to ensure that you can access the data and run R and R Studio well ahead of the
assignment due date. Technical problems outside our control are not accepted as excuses for
submitting coursework late.
• We encourage working together. Working together is discussing assignments with other students
or getting help in understanding from staff and tutors. You must write up your final assignment
individually, in your own words. We view cheating on assignment work seriously! Cheating is:
copying all or part of another student’s assignment or allowing another student to copy all or part of
your assignment. A student who allows someone else to copy their work is treated identically to the
student who did the copying. Penalties include: the student’s name will be entered on the universitywide Register of Academic Misconduct; loss of some or all marks for the assignment; the student(s)
involved taken to the University Discipline Committee.
Question 1. [22 Marks]
The northern hairy-nosed wombat is one of the world’s rarest mammals, and also the largest burrowing
herbivore in the world. Its natural range has been reduced to just one reserve in Queensland, Australia.
With the help of intensive management, the population has recovered from a low point of just 30
animals in the 1980s, to over 300 animals today. One major step was to install a dog-proof fence
around the reserve, to keep the wombats safe from predation by dingos (Australian wild dogs). The
fence was completed in 2002.
The number of wombats in the population was estimated in 13 surveys that took place from 1982 to
2021. The survey data can be found in the file Wombats.csv, with the following variables:
nWombat
Year
Fence
A count of the estimated number of wombats alive in the corresponding year.
Numeric variable denoting the year of the survey.
Factor with levels Y and N, indicating whether or not the wombat population was
protected by the dog-proof fence in the corresponding year.
Our aims are firstly to describe the wombat population dynamics from 1982 to 2021, and secondly to
quantify the impact (if any) of installing the dog-proof fence.
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Comment on the data and the initial plot.
Fit an appropriate Poisson GLM to answer the questions of interest.
o Check the model assumptions.
o If necessary, change the model and repeat the checks as needed.
o Decide upon an appropriate final model. This should be the simplest adequate
model. (Hint: you should find that your final model includes an interaction term.)
Plot the data with the fitted line from your final model superimposed.
Explain what the two curves represent in the additional plot shown, and interpret what the
plot describes in terms of the wombat population and its management.
Generate appropriate numeric output for interpretation from your final model. In particular,
you should generate confidence intervals that provide a suitable way of quantifying each of
the following items of interest:
a. annual percentage population increase before the fence was installed;
b. annual percentage population increase after the fence was installed;
c. how the population trajectory changed after the fence was installed.
Note: all of these confidence intervals are available directly from R. You should not attempt
to find CIs by performing arithmetic calculations on other CIs; instead, you need to decide
upon R commands and outputs that deliver these CIs directly.
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Write a Methods and Assumption Checks section.
Write an Executive Summary. Remember to address all the questions asked, including
quantifications.
Reference: Horsup AB, Austin JJ, Fewster RM, Hansen BD, Harper DE, Molyneux JA, White LC, and
Taylor AC. Demographic trends and reproductive patterns in the northern hairy-nosed wombat
Lasiorhinus krefftii at Epping Forest National Park (Scientific), Central Queensland. Australian
Mammalogy, 43, 72–84, 2021.
Question 2. [18 Marks]
What’s the secret to long life and happiness? Could it be … chocolate? Indeed, chocolate may
have pronounced health benefits, although we hasten to add that a sane level of moderation is
advised. The idea is that chocolate – especially dark chocolate – contains compounds called
flavanols which help to lower blood pressure and thus reduce the risk of having a heart attack or
stroke. (If you don’t like chocolate, don’t despair! Other flavanol-rich foods include berries,
onions, and broccoli, which make great substitutes. Seriously.)
A European study investigated the impact of chocolate consumption on the long-term risk of
having a stroke. They were also interested in whether the relationship between chocolate
consumption and stroke risk differed according to the level of education of their subjects. A
dataset constructed from their report is found in Stroke.csv. The following variables were
measured for more than 19,000 participants with low to moderate chocolate intake:
Stroke
Chocolate
Degree
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A binary variable specifying whether the subject did (1) or did not (0) suffer a
stroke in the 8-year period of the study.
Numeric variable giving the amount of chocolate consumed daily (g/day).
Categorical variable with levels Y and N specifying whether or not the subject
had a university degree.
Comment on the plot and the numeric summaries of the data.
Fit an appropriate logistic regression model to investigate the relationship between stroke
incidence and the two predictors. If necessary, change the model until you are satisfied
you have found the simplest adequate model.
Generate quantifications for the estimated probability of suffering a stroke given
chocolate consumptions of (a) 2 g/day, and (b) 10 g/day. Include the interpretation of
these in your Executive Summary.
Write a Method and Assumption Checks section.
Write an Executive Summary to summarise all your findings and quantifications from
the model.
Reference: Buijsse B, Weikert C, Drogan D, Bergmann M, Boeingoth H. Chocolate consumption in
relation to blood pressure and risk of cardiovascular disease in German adults. European Heart Journal
31, 1616–1623, 2010.