STAT3010/6075 Statistical Methods in Insurance
Assignment 2
This assignment is worth 10% of the overall mark for STAT3010/6075.
The deadline for submission is 16.00 on Thursday 4 May 2023.
Standard University policies and procedures will be followed for late submission, extensions and
academic integrity (see the Module Outline for details).
Submission is via Blackboard. You must submit a report of at most six pages (in pdf format),
containing your answers, and a separate R script, containing the code that you used to obtain
your results.
– Your should submit your report via TurnitinUK on Blackboard (see Module Outline for
details) in a file called report-ID.pdf, where ID is your student ID number, for example
report-12345678.pdf. In the Assignments folder, click on Assignment 2 report submission
to submit your report. Please enter this file name as the Submission Title.
– You should not include R code used in your analysis in your report, but you must submit
a separate R script via Blackboard containing your code called code-ID.R, for example
code-12345678.R. Please rename and use the R template code-yyy.R provided. In the
Assignments folder, click on Assignment 2 code submission to submit your code.
? The page limit is strict and is easily sufficient to receive full credit. If your report is more than
six pages of A4, only the first six pages will be marked.
Recall from Assignment 1 that a health insurance company is developing a model to assess the risk of
its policy holders having diabetes based on the following data from the file diabetes.csv:
Diabetes Binary variable indicating diabetes diagnosis, either positive (pos) or negative (neg)
Age Age of individual, recorded in years
BMI Body mass index (weight in kg/(height in m)2)
Glucose Plasma glucose concentration
Pressure Diastolic blood pressure (mm Hg)
Pregnant Number of times pregnant
Use the code in the R template to:
(a) Set the seed to be your student ID number with the command set.seed(ID ), for example
set.seed(12345678).
(b) Select a random training data set (train=1) of size 450 and test data set (train=0) of size 274
with the command train <- sample(c(rep(0,274), rep(1,450))).
1
Tasks
1. Calculate the diabetes rate in the test and training data sets, and hence calculate the classification
rate of the na¨?ve classifier. Comment on the usefulness of this classifier for identifying cases of
diabetes.
[4 marks]
2. Fit a logistic regression model to predict Diabetes from Age, BMI, Glucose, Pressure and
Pregnant using the training data set and calculate its classification rate using the test data
set.
[4 marks]
3. Fit ridge regression models with λ = 0.1, 0.2, 0.3 and 0.4 to predict Diabetes from Age, BMI,
Glucose, Pressure and Pregnant using the training data set and calculate their classification
rates using the test data set.
[8 marks]
4. Fit logistic regression models using LASSO with λ = 0.01, 0.02, 0.03 and 0.04 to predict Diabetes
from Age, BMI, Glucose, Pressure and Pregnant using the training data set and calculate their
classification rates using the test data set.
[8 marks]
5. Calculate the classification rates on the test data set for the K-nearest neighbours classifiers with
K = 1 to 15 to predict Diabetes from Age, BMI, Glucose, Pressure and Pregnant trained on
the training data set.
[8 marks]
6. Produce a classification tree to predict Diabetes from Age, BMI, Glucose, Pressure and Pregnant
grown on the training data set.
[4 marks]
7. The R function predict can be used on a classification tree to classify new observations contained
in a dataframe unseen: predict(tree, unseen, type="class"). Use this function to calculate
the classification rate for the tree produced in part 6.
[4 marks]
8. Which of the above classifiers would you recommend the company uses? Justify your answer.
Start by selecting a value for λ for the ridge regression model and logistic regression model using
LASSO, and a value for K for the K-nearest neighbours classifier.
[10 marks]