Suppose you have been hired as a consultant by the City Council of Baton Rouge, Louisiana to
Question:
Suppose you have been hired as a consultant by the City Council of Baton Rouge, Louisiana to analyze the characteristics of a house that affect its market price in the city of Baton Rouge. It wants you to obtain estimates of how much a typical buyer is willing to pay for an additional square foot of space, an additional bedroom, an additional bathroom, a pool, a newer home, and a home located on the waterfront. It wants to know whether square footage, bedrooms, or bathrooms has the biggest effect on the price of a house. It also wants you to predict the price of a house with a particular set of these characteristics.
The data for your study is contained in the data set HPRICE. The data are a cross section of 1080 home sales during year 2015 in Baton Rouge, Louisiana. The variables are as follows.
Price is the sale price in dollars,
Sq ft is total square feet,
Bedrooms is the number of bedrooms,
Baths is the number of full bathrooms,
Age is the age of the house in years,
Pool is a dummy variable that equals 1 if the house has a pool and 0 otherwise, and
Waterfront is a dummy variable that equals 1 if the house is located on the waterfront and 0 otherwise.
Statistical Model
You specify the following alternative regression models:
- Price i = ? 1 + ? 2 Sqft i + ? 3 Bedrooms i + ? 4 Baths i + ? 5 Age i + ? 6 Pool i + ? 7 Waterfront i + u t
- ln(Price i )= ? 1 + ? 2 ln(Sqft i )+ ? 3 Bedrooms i + ? 4 Baths i + ? 5 Age i + ? 6 Pool i + ? 7 Waterfront i + u t
- ln(Price i )= ? 1 + ? 2 ln(Sqft i )+ ? 3 Bedrooms i + ? 4 Baths i + ? 5 ln(Age i )+ ? 6 Pool i + ? 7 Waterfront i + u t
Requirements:
1. Use the regress command in Stata to estimate your model. Report the results. Which model do you prefer and why. Use your favorite model to answer the rest of the questions.
2. Calculate estimates of elasticities for the quantitative variables sqft, bedrooms, baths, and age. Calculate estimates of the standard errors of the elasticity estimates. Show your work. 3. Interpret the estimate of the coefficient of each variable. Are the algebraic signs of each of the estimates consistent with your prior expectations? Yes/no. Explain. (If “yes” explain why it is; if “no” explain why it isn’t).
4. Interpret the elasticity estimates for sqft, bedrooms, baths, and age. Which variable has the biggest effect on price? Which variable has he smallest effect?
Precision of Estimates
5. Rank the estimates of the coefficients in descending order of their precision; that is, from most precise to least precise. What measure did you use to create this ranking? Which estimate is most precise? Which estimate is least precise? In your opinion, are any of these estimates relatively imprecise? Justify your answer.
Strength of Evidence of an Effect
6. Discuss the factors that affect the precision of the estimate of a slope coefficient, such as the estimate of the coefficient of the variable sqft. How does each of these factors affect the precision of the estimate?
Hypothesis Testing
7. Use an F-Test to test the hypothesis that the effect on price of one additional bathroom is the same as the effect on price of a home located on the waterfront. You may use thetestcommand to calculate the F-statistic when doing this test.
Goodness-of-Fit
8. Interpret the R 2 statistic. Given your Adjusted R 2 statistic and RMSE, how well do you think your model fits the data? How well do you think your model will predict the price of a house?
Checking for Multi collinearity and Heteroskedasticity
9. Apply two diagnostic procedures that are often used to detect multicollinearity. Do these procedures indicate that you may have severe multicollinearity
Test for heteroskedasticity. Do these procedures indicate that you may have severe heteroskedasticity?
Conclusions
10. What conclusions can you draw about how much a typical consumer is willing to pay for characteristics of houses in Baton Rouge, Louisiana?
11. Use your model to predict the price of a house with 3,000 square feet, 4 bedrooms, 3 bathrooms, that is 10 years old with no pool and located on the waterfront.
Cost Accounting Foundations and Evolutions
ISBN: 978-1111626822
8th Edition
Authors: Michael R. Kinney, Cecily A. Raiborn