MATH 503 Coursework 2
Submission deadline: 9 am Wednesday of Week 6
(17/11/2021).
� You should answer both questions. The total marks is 30. However,
the weight is 15% towards your total marks in this module.
� Solutions should be typed and should be uploaded via M503 Moodle
in its designated CW2 space. If possible, submit a pdf file, which is
knitted from a Rmarkdown file.
� Note that you are allowed to upload only one file in moodle.
� I will give you a letter grade in Qn 1 as this is an open-ended question.
Qn 1 has a total of 25 and Qn 2 has a total of 5 marks. I will then
convert it to a mark out of 15.
� Order your solutions following the order of the questions and provide
page numbers. For example, solution to Qn 1(a) should be placed
immediately before that to Qn 1(b) and so on.
� Any graphs should be interpreted with a sentence or two to summarise
key findings.
� Plagiarism: Please be aware of the difference between a general dis-
cussion on possible approaches to the coursework and working closely
together on detailed solutions. The latter is most certainly poor aca-
demic practice. You should implement and interpret all solutions on
your own. All writing should be your own. In particular, please do not
fall into the trap of ‘patchwork writing’: taking another person’s work
and restructuring their sentences by changing some of their words.
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1. Consider the following data on the mean annual temperature records
at 20 different weather stations in Virginia as a function of the north
latitude (in degrees) and a categorical variable indicating low elevation
(if it is less than 2200 ft) or high elevation (if it is more than 2200 ft)
above the sea level.
North latitude Elevation Temperature
47.5 2 39.27
52.3 1 39.00
54.8 1 38.35
48.4 2 37.58
54.2 1 39.38
54.8 1 39.05
54.4 1 39.65
48.8 2 38.66
50.5 2 37.97
52.7 1 40.10
46.5 2 37.05
46.9 2 37.19
45.1 2 36.92
45.9 2 36.70
50.7 1 38.01
48.5 2 37.26
48.3 2 36.97
48.1 1 36.95
48.8 1 37.68
49.4 1 37.55
(a) Suggest a generalised linear model (GLM) for the response to anal-
yse this data. Use forward selection to select covariates as well as
interaction among the covariates if interaction turns out to be sig-
nificant. Present diagnostics based on your final model. At the
end, you should state your final model clearly by expressing the
response in terms of the covariates and corresponding parameter
estimates.
(b) Write down at least two interpretations of the relation between
the response and covariates in plain language based on the values
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and signs of the corresponding parameter estimates.
Your answer to 1(a) should not be more than two and half typed pages
of standard size. Marks will be allocated for structure, logic and pre-
sentation in addition to the ”correct” answer. [25]
2. The following data concern the occurrence of pneumoconiosis among
a group of coalminers as a function of the number (No.) of years of
exposures.
Years of exposure No. of coalminers exposed No. affected by pneumoconiosis
5.8 98 0
15.0 54 3
21.5 43 9
27.5 48 13
33.5 51 19
39.5 38 15
46.0 28 16
51.5 11 7
A generalised linear model (GLM) for the response ‘proportion of coalmin-
ers affected by pneumoconiosis’ is used to describe its relation with the
covariate ‘years of exposure’.
(a) Suggest two different link functions (which are sensible) to analyse
the above data.
(b) Test the validity of your model under first and second link func-
tion. Show your R-code and the corresponding R-output
as part of the solution.
(c) Provide your estimates of the proportion affected with an exposure
for 25 years; give two answers corresponding to two link functions.
Show your R-code and the corresponding R-output as
part of the solution.
[5]
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