Question

6. The following regression equation examines the relation between hotel prices (in dollars per night) and the number of short-term rental listings (e.g., Airbnb) in the city hotel price 150 0.018 x ST rentals a) Interpret the coefficient on the number of short-term rentals. b) How would these coefficients change if the number of rentals was expressed in thousands? c) What is the predicted hotel price in a city with 1,000 short-term listings? d) How many listings would there need to be in a city in order for the predicted hotel price to be 50 dollars? Suppose that a hotel in a city with 1,500 short term listings costs $110 dollars. What is the error in the predicted hotel price? e) f) Can you conclude from this regression that short-term rentals cause a decrease in hotel prices? Explain your answer. Next, you regress the natural log of hotel prices on the natural log of the number of short- term rentals and obtain the regression equation shown below: InChotel price) 5.2-0.046 x In(ST_rentals) g) Interpret the coefficient on short-term rentals in a sentence. h) What is the predicted hotel price (in dollars per night) in a city with 1,000 short-term listings?

Answer 1

(a) The coefficient of short-term rental is -0.018, which signifies that as number of short-term rental increases (decreases) by 1 unit, hotel rent decreases (increases) by $0.018. The two variables are inversely related.

(b) If number of rentals is expressed in thousands (i.e. ST_rentals is multiplied by 1,000), its coefficient has to be divided by 1,000 and new coefficient will be (0.018/1,000) = 0.000018. Intercept will remain unchanged.

(c) When ST_rentals = 1,000,

Hotel price ($) = 150 - (0.018 x 1,000) = 150 - 18 = 132

(d) When hotel price = $50,

50 = 150 - 0.018 x ST_rental

0.018 x ST_rental = 100

ST_rental = 5,555.56

NOTE: As per Answering Policy, 1st 4 parts are answered.