Excel Data

https://docs.google.com/spreadsheets/d/1UvM8fLdmbBpoSWeI6SkHqFUoJQLEOvcz9neGjU-uPDM/edit?usp=sharing

The file problem2.xlsx contains data on 250 locations of Airbnb service in San Francisco,

Dependent variable:

VariableDescription

PricePrice of staying per night

Independent variables:

VariableDescription

Room_typeType of accommodation, =0 if it is a "shared room",

=1 if it's an entire home or apartment

ReviewsNumbers of reviews on website

Overall_SatisfactionAverage satisfaction rated by customers

NightsNumber of nights stayed by customers

BedroomNumber of bedrooms

Estimate the following model.

Ln(Price) = ₀ + ₁Room_type + ₂Reviews + ₃Overall_Satisfaction + ₄Nights + ₅Bedroom

(Note: The dependent variable is Ln(Price) and not Price)

(a) (3 points) Report and interpret your estimates for ₁,₂ and ₅.

(b) (2 points) Based on the estimated regression model predict the price (in $) per night for an "entire home or apartment" in a 4-bedroom apartment that has received 15 reviews. The overall satisfaction is 4.5, number of nights is equal to 3.

(c) (3 points) Construct a 95% confidence interval for your prediction done in part (b).

(d) (3 points) Using the estimated regression, test the hypothesis that "entire home or apartment" price is two-and-a-half times higher than a "shared room". Write down the null and alternate hypothesis and report your conclusions.

(e) (4 points) In the regression model that you have estimated, the impact of number of reviews on price is the same irrespective of room_type. Modify your regression model to answer the following question...

Is the impact of number of reviews on price the same for "shared rooms" versus "entire home or apartment"?

Please write down your modified regression model and based on the results of this modified model answer the question asked with a brief explanation.

(f) (5 points) There is a belief amongst customers that staying in a "non-shared room" ("entire home or apartment") in a facility with certain number of bedrooms costs the same as a "shared room" in a facility with two additional bedrooms. Given your data, do you have support for this belief. Justify your answer with an appropriate test.