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# A real estate agent has new clients who are recently married. They are initially interested in purchasing a 1700 square foot home with 3 bedrooms and 2.5 baths.

1. Estimate the regression model below.

Price= β_0+β_1 Living.Area+β_2 Bedrooms+β_3 Bathrooms+ε

The real estate agent is confused as to why the sign on bedrooms in your regression from Part 1 is negative. He says, “Homes with more bedrooms go down in price? That makes no sense.”

2. Explain why it makes perfect sense for bedrooms in the model above to have a negative sign. (Hint: think about what you are controlling in the regression above.)

3. Use the model estimates to predict the price of a 1700 square foot home with 3 bedrooms and 2.5 baths.

The couple would prefer a home with central air. They can either buy a house with central air or have central air installed for \$25,000.

Add Air to the regression you ran in Part 1 and estimate the model below. Note: you will have to first create a dummy variable and recode Air before running the regression.

Price= β_0+β_1 Living.Area+β_2 Bedrooms+β_3 Bathrooms+α_0 Air+ε

Interpret the results of a t-test on the coefficient for Air. Is it statistically significant? Explain.

Does the model in Part 4 do a better job of predicting home prices compared to the model in Part 1? Explain.

Based on the results from Parts 4 and 5, on average, will it be cheaper to purchase a 1700 square foot, 3 bedroom, 2.5 bath home with central air or purchase a 1700 square foot, 3 bedroom, 2.5 bath without central air and install it for \$25,000? Explain.