STA220H1 The Practice of Statistics I (Fall 2024)

Assignment 1 Instructions

Due Date: October 18, 2024 at 11:59 on Crowdmark

Instructions

This is an individual assignment. You are expected to work on this independently. While you may discuss ideas and concepts, please do not share your code or written answers. It is expected   that all code and written work should be written by yourself. Please note, this assignment is fairly open, so the context of most of the work completed here should not match your peers.

Submission Format and Instructions

Your final submission will be in PDF file. You will submit your solutions on Crowdmark. There will be a different upload box for each question, so it is recommended that you place each question on different pages or files.

For question 1, your PDF file will need to show (1) R code, (2) R output/figures, and (3) your written answers. Here are some suggested ways you can create your final submission:

•   Use Microsoft Word to type out your answers. Screenshot your R output and place these images throughout the document. For the R code, either copy/paste as text or screenshot.

•   Use an app like Notability, OneNote, etc., where you can write/type your answers and include screenshots of your R code and output.

•   Use RMarkdown and knit to a PDF. Alternatively, you can knit to an HTML file and then save it as a PDF.

How you create the final file is up to you, as long as it is clear and organized. You don’t want the TA to be frustrated while marking your work! 

Late Penalty

As described on the course syllabus, late work will be deducted 10% per hour.

Question 1 (30 marks)

Consider the Airbnb dataset provided for this assignment. The provided Airbnb dataset offers insights into the listing activity of homestays in New York City, including essential information such as the geographical location, pricing, reviews, and host details. Below is a description of the variables included in the dataset:

•    Name: The name of the property listing.

•    host_identity_verified: Indicates whether the host's identity has been verified.

•    host.name: The name of the host.

•    neighbourhood.group: The larger neighborhood group where the listing is located.

•    neighbourhood: The specific neighborhood where the listing is located.

•    lat: The latitude of the listing, based on the WGS84 geographic coordinate system.

•    long: The longitude of the listing, based on the WGS84 geographic coordinate system.

•    instant_bookable: Specifies whether the listing can be instantly booked.

•    cancellation_policy: The type of cancellation policy applied to the listing.

•    room.type: The type of room available for the listing (e.g., entire home, private room).

•    construction.year: The year the property was constructed.

•    price: The price of the listing per night, in USD.

•     service.fee: The service fee per night, in USD.

•    minimum.nights: The minimum number of nights required to book the listing.

•    number.of.reviews: The total number of reviews received in the last 12 months.

•    reviews.per.month: The average number of reviews received each month over the listing’s lifetime.

•    review.rate.number: The average review rating of the listing.

•    calculated.host.listings.count: The number of listings managed by the host, as calculated by Airbnb.

•     availability.365: The number of days the listing is available for booking within the next 365 days.

Your task is to explore and analyze the Airbnb dataset using graphical summaries created using R. Create a minimum of 4 properly labelled plots/graphs/figures that summarize some of the patterns in the data. It is recommended that you use at least 3 different types of plots. For each plot, write a few sentences explaining the patterns and/or trends you see in the plot.

You will be graded on not only your ability to create plots in R, but also your ability to use the plots to highlight important and/or compelling information in the data.

Question 1 Rubric

Question 2 (30 marks)

Consider a study evaluating the effectiveness of two treatments (A and B) for a particular disease. The effectiveness of these treatments is measured under two different conditions: mild and severe. The outcome for each patient is classified into one of two categories: survived or   deceased. The following table summarizes the observed results:

a)  For each treatment, draw a tree diagram illustrating the problem (2pts)

b)  Calculate all the conditional probabilities appear on your tree diagrams (4pts)

c)  For each treatment, what’s the conditional probabilities of survival under either

condition? (2pt) Briefly summarize the findings based on your results. Which treatment has a better effect and why? (2pts)

d)  For each treatment, what’s the marginal probabilities of survival? (2pts) Briefly

summarize the findings based on your results. Based on this new result, which treatment has a better effect and why? (2pts)

e)  For each treatment, conditioning on a patient survived, what’s the probability that the patient is under mild condition? (4pts)

f)   For patient under either mild or severe conditions, conditioning on a patient survived, what’s the probability that the patient receives treatment A? (4pts)

g)  From your results above, could you explain the reasons why there are contradict findings

between (c) and (d). Overall, which treatment is better? (4pts)

h)  Suggest any possible solutions to avoid the confusions induced by contradict findings. (4pts)