STAT330/430 -Assignment 4 Solved

Question 1
In each assignment you will be able to earn up to 5 marks based on your engagement on the moodle Discussion forums from the topics associated with the given assignment. See the Assignment assessment criteria document for more details.


Question 2
Spinner dolphins are a small delphinid that reside in subtropical and tropical waters. I collected data on spinner dolphins in Fiji to explore characteristics of their whistles. The type of whistle (e.g., concave, constant, convex, downsweep, sine, and upsweep) along with a variety of other acoustic properties of individual whistles was measured and is summarised in the Spinner_dolphin data-set.

Variable
Description
Whistle
Whistle classification (Concave, Constant, Convex,

Downsweep, Sine or Upsweep)
Duration
The time span of the whistle (seconds)
Centre_Freq
The frequency recorded at the midpoint (centre) of the whistle (kHz)
Low_Freq
The lowest frequency recorded during a whistle

(kHz)
Delta_Freq
The range in frequency recorded during a whistle

(kHz)
Max_Freq
Maximum frequency (kHz) recorded during a whistle (kHz)
Range_50
Centre frequency [minus] minimum frequency
Range_100
Maximum frequency [minus] centre frequency
Inflections
Number of points of change in whistle curvature
(a)     Conduct an exploratory data analysis and present a summary of the Spinner_dolphin data-set.

(b)    Find a low-dimensional representation of the numerical variables in the Spinner_dolphin data-set. Provide carefully labeled and well-formatted tables and/or figures - as well as an informative summary of your model and results. In addition, provide a visualisation and brief summary of whistle type in the context of your low-dimensional representation.

Question 3
The Pacific Islands region stretches from the eastern coast of Australia all the way to French Polynesia and is comprised of a wide variety of island countries and territories. Exploring the similarities and characteristics of these nations is useful for environmental management and planning. A summary of the variables contained in the Pacific_Islands data-set is listed below.

Variable
Description
PICT
Pacific Island Country or Territory
Land_area
Total land area (km2)
Coastline
Total distance of coastlines (km)
EEZ
Economic Exclusive Zone area (km2)
Shelf_Area
Continental shelf area (km2)
Inshore_fishing_area
Continental shelf area accessible for inshore fishing (km2)
Coral_reefs
Percentage of the world’s coral reefs contained in this PICT
Seamounts
Percentage of the world’s seamounts contained in this PICT
Primary_production
Estimated primary production for the marine environment (mg of carbon/m2/day)
MPA
“Marine protected areas” (km2)
PA
Terrestrial “protected areas” (km2)
Pop
Population size of the PICT
Total_spp
Total number of animal species listed for this

PICT
Region
Melanesia, Polynesia or Micronesia
(a)    Use k-means clustering to identify the optimal number of clusters for the Pacific_Islands data-set. Visualise your results, provide some broad insights into cluster membership in relation to Region, and provide a brief summary of your results.

(b)    Create at least two different types of dendrograms based on the Pacific_Islands data-set. Use PICT as your label on each leaf for these plots. Using the same number of clusters in each dendrogram compare and contrast your results. Provide a general interpretation of groupings seen in each of the dendrograms you produce.