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MATH3030: Coursework, Spring 2025
17/03/2025
• If you are a MATH4068 student, please stop reading and go and find the coursework for
MATH4068. This assessment is for MATH3030 students only.
• This coursework is ASSESSED and is worth 20% of the total module mark. It is split into two questions,
of equal weight.
• Deadline: Coursework should be submitted via the coursework submission area on the Moodle page
by Wednesday 30 April, 10am.
• Do not spend more time on this project than it merits - it is only worth 20% of the module mark.
• Format: Please submit a single pdf document. The easiest way to do this is to use R Markdown or
Quarto in R Studio. Do not submit raw markdown or R code - raw code (i.e. with no output,
plots, analysis etc) will receive a mark of 0.
• As this work is assessed, your submission must be entirely your own work (see the University’s policy
on Academic Misconduct).
• Submissions up to five working days late will be subject to a penalty of 5% of the maximum mark
per working day. Deadline extensions due to Support Plans and Extenuating Circumstances can be
requested according to School and University policies, as applicable to this module. Because of these
policies, solutions (where appropriate) and feedback cannot normally be released earlier than 10 working
days after the main cohort submission deadline.
• Report length: Your solution should not be too long. You should aim to convey the important
details in a way that is easy to follow, but not excessively long. Avoid repetition and long print-outs of
uninteresting numerical output.
• Please post any questions about the coursework on the Moodle discussion boards. This will ensure that
all students receive the same level of support. Please be careful not to ask anything on the discussion
boards that reveals any part of your solution to other students.
• I will be available to discuss the coursework at our Tuesday or Thursday sessions during the semester. I
will not be meeting students 1-1 to discuss the coursework outside of these times.
Plagiarism and Academic Misconduct For all assessed coursework it is important that you submit
your own work. Some information about plagiarism is given on the Moodle webpage.
Grading The two questions carry equal weight, and both will be marked out of 10. You will be assessed on
both the technical content (use of R, appropriate choice of method) and on the presentation and interpretation
of your results.
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Coursework
The file UN.csv is available on Moodle, and contains data from the United Nations about 141 different
countries from 1952 to 2007. This includes the GDP per capita, the life expectancy, and the population.
Load the data into R, and extract the three different types of measurement using the commands below:
UN <- read.csv('UN.csv')
gdp <- UN[,3:14] # The GDP per capita.
years <- seq(1952, 2007,5)
colnames(gdp) <- years
rownames(gdp) <- UN[,2]
lifeExp <- UN[,15:26] # the life expectancy
colnames(lifeExp) <- years
rownames(lifeExp) <- UN[,2]
popn <- UN[,27:38] # the population size
colnames(popn) <- years
rownames(popn) <- UN[,2]
In this project, you will analyse these data using the methods we have looked at during the module.
Question 1
Exploratory data analysis
Begin by creating some basic exploratory data analysis plots, showing how the three variables (GDP, life
expectancy, population) have changed over the past 70 years. For example, you could show should how the
average life expectancy and GDP per capita for each continent has changed through time. Note that there
are many different things you could try - please pick a small number of plots which you think are most
informative.
Principal component analysis
Carry out principal component analysis of the GDP and life expectancy data. Analyse the two variable types
independently (i.e. do PCA on GDP, then on life-expectancy). Things to consider include whether you use
the sample covariance or correlation matrix, how many principal components you would choose to retain in
your analysis, and interpretation of the leading principal components.
Use your analysis to produce scatter plots of the PC scores for GDP and life expectancy, labelling the names
of the countries and colouring the data points by continent. You can also plot the first PC score for life
expectancy against the first PC score for GDP (again colouring and labelling your plot). Briefly discuss these
plots, explaining what they illustrate for particular countries.
Canonical correlation analysis
Perform CCA using log(GDP) and life expectancy as the two sets of variables. Provide a scatter plot of the
first pair of CC variables, labelling and colouring the points. What do you conclude from your canonical
correlation analysis? What has been the effect of using log(gdp) rather than gdp as used in the PCA?
Multidimensional scaling
Perform multidimensional scaling using the combined dataset of log(GDP), life expectancy, and log(popn),
i.e., using
UN.transformed <- cbind(log(UN[,3:14]), UN[,15:26], log(UN[,27:38]))
Find and plot a 2-dimensional representation of the data. As before, colour each data point by the continent
it is on. Discuss the story told by this plot in comparison with what you have found previously.
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Question 2
Linear discriminant analysis
Use linear discriminant analysis to train a classifier to predict the continent of each country using gdp,
lifeExp, and popn from 1952-2007. Test the accuracy of your model by randomly splitting the data into test
and training sets, and calculate the predictive accuracy on the test set.
Clustering
Apply a selection of clustering methods to the GDP and life expectancy data. Choose an appropriate number
of clusters using a suitable method, and discuss your results. For example, do different methods find similar
clusters, is there a natural interpretation for the clusters etc? Note that you might want to consider scaling
the data before applying any method.
UN.scaled <- UN[,1:26]
UN.scaled[,3:26] <- scale(UN[,3:26])
Linear regression
Finally, we will look at whether the life expectancy in 2007 for each country can be predicted by a country’s
GDP over the previous 55 years. Build a model to predict the life expectancy of a country in 2007 from its
GDP values (or from log(gdp)). Explain your choice of regression method, and assess its accuracy. You
may want to compare several different regression methods, and assess whether it is better to use the raw gdp
values or log(gdp) as the predictors.
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