MAS223 Applied Statistics ICT513 Data Analytics

Due: Sunday, 4 September 2022, 5PM

Questions
1. (15 marks)
Visualisations are important for understanding and communicating
data. This article describes some of the important considerations when
selecting data visualisations.
(a) (10 marks)
Read the article and summarise the message provided in the article
in more than 500 words.Your summary should be your own words
and understanding from the article, not copied and pasted from
the article.
(b) (5 marks) Review one visualisation of your choice from this arti-
cle, commenting on how effective or ineffective is the visualisation
to tell the story of the underlying data. Please include the vi-
sualisation in the assignment PDF. The visualisation type does
not need to be one covered in class, just include a brief descrip-
tion of the visualisation itself to demonstrate you understand the
visualisation you are analysing.
2. (8 marks)
To assess the consistency of a packaging machine in filling packets with
sour worms, four packets were produced in succession and the weight
measured. Weights of the packet (in g) were as follows:
251.3 250.6 250.9 249.8
By hand, calculate the jackknife estimator and standard error of the
median of packet weights (to at least three significant digits), showing
all working. Is the estimator unbiased?

3. (20 marks)
In this assignment, we will examine the “Melbourne House Price Subset.csv”
datasets. More information on this data set can be found here. Note
that it has been subset so only a few suburbs have been included.
Consider the variable Price in the “Melbourne House Price Subset’
dataset, which records the sale price of some houses in Melbourne.
(a) Use appropriate graphical displays and measures of centrality and
dispersion to summarise the Price variable. Provide a reasonable
explanation for why the Price data might have the distribution
you observe. (6 marks)
(b) For the most appropriate measure of centrality and measure of
dispersion you have selected for Price, produce a table of the
form shown below that presents:
• the particular measures (i.e., statistics) you have chosen,
• those measures (i.e., statistics) as calculated for the variable
Price,
• the jackknife and bootstrap estimators for those statistics,
• the jackknife and bootstrap standard errors for those statis-
tics, and
• the jackknife and bootstrap estimates of bias for those statis-
tics.
Do these measures of centrality and dispersion appear to be biased
or unbiased estimators? (8 marks)

Measure of Centrality: ăName of measure of centralityą
ăValue of measure of centrality
when applied to original dataą
Jackknife Bootstrap
Estimator
Standard error
Bias
Measure of Dispersion: ăName of measure of dispersioną
ăValue of measure of dispersion
when applied to original dataą
Jackknife Bootstrap
Estimator
Standard error
Bias
(c) Produce graphical displays of the sampling distributions of the
measure of centrality and measure of dispersion you have selected
for Price. Comment on the shapes of these distributions. Addi-
tionally, produce a 95% bootstrap percentile confidence interval
for both your measure of centrality and measure of dispersion and
interpret them. If there is anything unusual about the 95% boot-
strap percentile confidence intervals, comment on that. (6 marks)

4. (10 marks)
The R package gcookbook has a dataset called heightweight which you
can read more about using ?heightweight.
Consider four analyses, detailed below, of the data and state the lin-
ear model which you believe would be best when attempting to assess
the relationship between heightIn and weightLb. Present and dis-
cuss relevant the assumptions, including presenting diagnostic plots for
assessing the assumptions of linear regression for these models. Also
provide the interpretation for all four models.
The four analyses to consider are:
(a) No transform of heightIn and weightLb.
(b) Log transform of heightIn and no weightLb.
(c) No transform of heightIn and log weightLb.
(d) Log transform of heightIn and log weightLb.