You are working for Zillow and building a model to predict housing prices based on characteristicsof a house. You have data from 55 houses with the following variables:

lprice: Log of price of the house, in thousands of dollars

area: Square footage of the house

land: Square footage of the lot around the house

age: Age of the house, in years

rooms: Total number of rooms in the house (aside from bathrooms)

baths: Total number of bathrooms in the house

Your initial model contained the independent variablesareaandland. The second model addsthree more variables (age of house, rooms and baths) to the model. The regression output isbelow.

1.You want to jointly test whether the square footage of the house (area) and square footageof the lot around the house (land) aect the house price. State the null and alternativehypotheses, making sure to be precise in your statements.

2.What is the result of that test at a 5% signicance level?

3.You want to jointly test whether the age of the house, number of rooms in a house andnumber of bathrooms have an eect on the price of the house after you have controlledforlandandarea. State the null and alternative hypotheses, making sure to be precise inyour statements.

4.Test this hypothesis using an F-test at a 5% signicance level from the output below.

5.How would you test the hypothesis that the eect of an additional room on house priceis the same as the eect of an additional bathroom? Show how you would set up thetest, making sure to precisely state the null and alternative hypotheses. Then describe theregression output that you would generate to conduct the test.

- regress lprice area land age rooms baths - regress lprice area land age rooms baths