### MAS8403 : Statistical Foundations of Data Science

 Subject MAS8403 : Statistical Foundations of Data Science

Palmer Penguins

The Palmer Station located in the Palmer Archipelago on Anvers Island, Antarctica, has been monitoring the ecology of the Palmer Long-Term Ecological Research (LTER) study area for over 50 years. You can see what’s going on at the Palmer Station currently by clicking here. Being on Antarctica, naturally one of their keen interests is monitoring the local penguin population from which they record data in order to understand their population dynamics, responses to changing climate etc

The Data

The palmerpenguins dataset contains data measured on 333 penguins from the Palmer Archipelago. The variables observed are:

• species: The species of the penguin (Adelie, Chinstrap or Gentoo)

• island: The island on which the penguin lives (Biscoe, Dream or Torgerson)

• bill length mm: The length of the penguin’s bill (in millimetres)

• bill depth mm: The depth of the penguin’s bill (in millimetres)

• flipper length mm: The length of the penguin’s flipper (in millimetres)

• body mass g: The penguin’s body mass (in grams)

• sex: The sex of the penguin (male or female)

• year: The year the measurements were taken

Installing the Data

Install the palmerpenguins package and access the data
install.packages(“palmerpenguins”) # You only need to do this once
library(palmerpenguins)
data(“penguins”)
penguins = na.omit(penguins) # Removes missing rows
Run the following code to access your unique subset of the penguin dataset
my.student.number = 123456789 # Replace this with your student number
set.seed(my.student.number)
my.penguins = penguins[sample(nrow(penguins), 100), ]
the object my.penguins now contains the data on your 100 penguins.

You are to produce a report which comprises of an exploratory data analysis of the data on your sample of 100 penguins. In this exploratory analysis you should include appropriate graphical and numerical summaries for your data, ensuring all summaries/figures are suitably discussed in the report.

We would like to be able to use this sample of data to estimate probabilities/ proportions for the penguin population in general. One way to do this is to fit a probability distribution to our sample,and use this distribution to estimate probabilities/proportions for the population. For at least one of the measurement variables (bill length, bill depth, flipper length and body mass) choose an appropriate probability distribution to represent the variable, and
find estimates for the parameters of the distribution for your data. Comment on the accuracy of your distribution, and whether you feel this is a good method for estimating population proportions.

Sexing (i.e. determining the sex) of a penguin can often be very difficult without causing distress to the penguin. Researchers at the Palmer station would like to be able to estimate the sex of a penguin from measurement data, thereby avoiding the need for invasive procedures. From your data, which variables appear to be the best at distinguishing between male and female
penguins? How reliable do you think they would be at identifying the sex of a penguin?

Similarly, evolutionary biologists are interested in knowing if there is a significant difference in the physical characteristics of penguins living on different islands. From your data, does the island the penguin is from appear to have a significant impact on any of its physical characteristics?