Description
Instructions
This assignment involves linear regression. The data can be found on Sakai: go to Resources → Data Analysis Assignment Datasets → Assignment 1. Please type your solutions using R Markdown. The final output file should be “.pdf”. Submissions should be made on gradescope: go to Assignments → Data Analysis Assignment 1.
DO NOT INCLUDE R CODE OR OUTPUT IN YOUR SOLUTIONS/REPORTS All R code must be included in an appendix, and R outputs should be converted to nicely formatted tables. Feel free to use R packages such as kable, xtable, stargazer, etc.
Also, you can round up ALL numbers/estimates to 2 decimal places (4 decimal places at the most to avoid exact zeros when possible).
Reminder: You are allowed and even encouraged to talk to each other about general concepts, or to the instructor/TAs. However, the write-ups, solutions, and code MUST be entirely your own work.
Questions
Question 1 below is taken and adapted from Chapter 7 of Ramsey, F.L. and Schafer, D.W. (2013), “The Statistical Sleuth: A Course in Methods of Data Analysis (3rd ed).”.
Side Note: We will use textbook datasets on some of the data analysis assignments. This is intentional as a way to start with clean and small datasets. Projects will focus a bit more on “messy” datasets.
1. RESPIRATORY RATES FOR CHILDREN. A high respiratory rate is a potential diagnostic indicator of respiratory infection in children. To judge whether a respiratory rate is truly “high,” however, a physician must have a clear picture of the distribution of “normal” respiratory rates. To this end, Italian researchers measured the respiratory rates of 618 children that are at most 3 years old. The data for this question can be found in the file “Respiratory.csv” on Sakai.
a. Do exploratory analysis on the data and include a useful plot that a physician could use to assess
a “normal” range of respiratory rates for children of any age between 0 and 3.
b. Write down a regression model for predicting respiratory rates from age. Make sure to use the
right mathematical notation.
c. Fit the model to the data. Include a table showing the output from the regression model including the estimated intercept, slope, residual standard error, and proportion of variation explained by the model.
d. Interpret your results. In the context of the problem, what do you conclude? Your interpretation
should mention an appropriate p-value, 95% confidence interval, and R2 value.
e. Is there enough evidence that the model assumptions are reasonable for this data? Include ap-
propriate plots in your answer.
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2. AIRBNB LISTINGS FOR SEATTLE, WA. AirBnB is a rental online marketplace. The company itself is based in San Francisco CA, and there are millions of listings in cities across the world. In this problem, you will only focus on data for AirBnB listings in Queen Anne, Seattle, WA. Specifically, you will try to understand how certain factors influence the price of a listing. The data we will use here is a very small subset of the overall available data. For more on the data, or if you are interested in using AirBnB data, see http://insideairbnb.com/get-the-data.html. The data for this question can be found in the file “Listings_QueenAnne.txt” on Sakai.
a. Analyze the data using host_is_superhost,host_identity_verified, room_type, accommodates, bathrooms and bedrooms as predictors. You should start by doing EDA, then model fitting, and model assessment. You should consider transformations if needed.
b. Include the output from the final regression model that you used, as well as evidence that the model fits the assumptions reasonably well. Your regression output should includes a table with coefficients and SEs, p-values, and confidence intervals.
c. Interpret the results of your fitted model in the context of the data. d. Are there any (potential) outliers, leverage points or influential points? Provide evidence to support your response. Also, if there are influential points and/or outliers, exclude the points, fit your model without them, and report the changes in your overall conclusions.
e. Overall, are there any potential limitations of this analysis? If yes, what are two potential limi-
tations?
Code Book
Variable
id host_is_superhost
host_identity_verified
room_type accommodates bathrooms bedrooms price
Grading
40 points: 20 points for each question
Description
Unique identifier for listings Whether or not the host is a “superhost,” meaning they satisfy AirBnB’s criteria for high-quality listings, high response rate, and reliability Whether or not the host has verified their identity with AirBnB Entire home/apt, private room, or shared room Number of people that the listing can accommodate Number of bathrooms in the listing Number of bedrooms in the listing Price of the listing for one night (Use this as the response variable)
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