In this exercise, we will use the ‘Airbnb’ dataset we used in class to continue to familiarize ourselves with regressions and data visualization in R. If you already didn’t do so, you can download the dataset here.

Load the dataset and answer the following questions.

Questions:

  1. In class, we plotted and predicted price as a function of reviews. We saw that the relationship is not linear.

    • What happens when you plot log(price) vs number of reviews?
    • What happens when you plot log(price) vs log(number of reviews)?

  2. Now estimate the three linear models below and print the results using the library stargazer:

    • price ~ reviews_count
    • log(price) ~ reviews_count
    • log(price) ~ log(reviews_count)

  3. How do you interpret the coefficient of reviews_count in each one of the models?

  4. What is the R-squared of each model? What do they tell you?

  5. Let’s add more predictors to the model: star_rating, bathrooms, bedrooms, guests_included. Do the coefficient you obtain make intuitive sense? What does it happen to the R-squared? What does it tell you about the model?

  6. Let’s add to the model a categorical variable: city. How many estimates do you get? Why? How do you interpret them? Which is the most and least expensive city in the dataset?

  7. Alternative ways to include factors in the model. Create a dummy variable for each city, i.e., a variable called “Austin” that is 1 if the city is Austin and 0 otherwise. Do the same for Boston, Los Angeles, Miami, and New York City. Estimate the model again by including four of these dummies excluding Austin, and compare the results with the previous one. What do you see?

  8. Let’ assume we can compute listing revenue by multiplying price by the number of reviews. Create a new variable called revenue and predict revenue as a function of the variables used above BUT excluding the number of reviews. Where would you buy an Airbnb property and why?

  9. Now, let’s also add room_type to the model. How do you interpret the coefficients of room_type? Which type of property generates more revenue?

  10. Working with dummy variables. Create a new dummy variable called “highQuality” that is 1 if the star_rating is 4.5 or higher and 0 otherwise. Estimate the model again by including this variable instead of star_rating. How do we interpret the coefficient of highQuality? What does it tell you about the importance of quality on Airbnb when it comes to revenue?