Question

History Bookmarks Window Help page 6 of Question 4 A real estate developer is interested in the relationship between the price of houses in Melbourne and their distance to the CBD. Using data collected from real estate agents, he performed the following simple linear regression model: where the dependent variable (Y) is the price of houses (measured in thousands of Australian dollars); the explanatory variable (X) is the distance to the CBD (measured in km);尻and β1 are unknown parameters, and e is the disturbance term. The regression results are given in the following Table. Table: Excel Output for Linear Regression Model Regression Statistics R Square Standard 0.4615 Error 137.1313 Observations 10 Standard Coefficients Error t StatP-value Intercept 16.30 0.00 Distance -14.75 3.01 0.00 a) What are the values of A and B? b) What is the interpretation of the two parameter estimates? Do they correspond to your expectation? c) What are the predicted prices for a house in Burwood, which is 15 km from the CBD and a house in Yarra Glen, which is 60 km from the CBD? Are these predictions reliable? d) Is this prediction of above Table reliable? Explain.

Answer 1

a) The value of A can be derived from the given values in the table.i.e.t statistic = coefficient divided by standard error

A= 865.87/ 16.30

A=53.12

B= - 14.75/ 3.01

B= - 4.9

b) The slope coefficient implies that when the distance to the CBD increases by one km then ceteris paribus, on an average price of the houses in Melbourne decreases by 14.75 thousand Australian dollars.

The intercept has no economic interpretation and it implies that price of houses in Melbourne on average is 865.85 Australian dollars.

c) If X= 15 then Y = 865.87- 14.75 (15) = 644.62

If X= 60 then Y= 865.87-14.75(60) = 19.13

d) The given predictions are reliable as the p values of the intercept as well as the slope are zero which implies that variables are statistically significant.