Homework 4 Questions Please submit relevant STATA output Data hrprice xls 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, Sqft 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 multiple regression models a) Price i 1 2 Sqft i 3 Bedrooms i 4 Baths i 5 Age i 6 Pool i 7 Waterfront i u t b) 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 c) 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 Estimation 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 Hints For model (a), Elasticity for sqft 2 , Standard error for sqft 2 ) In stata, you can use the mfx command after regress For example, mfx, eyexcalculate elasticities in the form of d(lny) d(lnx) mfx, dyexcalculate elasticities in the form of d(y) d(lnx) mfx, eydxcalculate elasticities in the form of d(lny) d(x) Interpretation 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 Hypothesis Testing 6 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 the test command to calculate the F statistic when doing this test Goodness of Fit 7 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 Multicollinearity and Heteroskedasticity 8 Apply two diagnostic procedures that are often used to detect multicollinearity Do these procedures indicate that you may have severe multicollinearity 9 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 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

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Homework 4 Questions [Please submit relevant STATA output] Data: hrprice.xls You have been hired as a consultant by the City Council of Baton Rouge, Louisiana

Homework 4 Questions

[Please submit relevant STATA output]

Data: hrprice.xls

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,

Sqft 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 multiple regression models:

a)Price_i = ₁ + ₂ Sqft_i + ₃Bedrooms_i +₄Baths_i + ₅Age_i + ₆Pool_i+₇Waterfront_i + u_t

b)ln(Price_i )= ₁ + ₂ ln(Sqft_i )+ ₃Bedrooms_i +₄Baths_i + ₅Age_i + ₆Pool_i+₇Waterfront_i + u_t

c)ln(Price_i )= ₁ + ₂ ln(Sqft_i )+ ₃Bedrooms_i +₄Baths_i + ₅ln(Age_i)+ ₆Pool_i+₇Waterfront_i + u_t

Estimation

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.

Hints: For model (a),

Elasticity for sqft = ₂ *,

Standard error for sqft = ₂ )*

In stata, you can use the mfx command after regress. For example,

mfx, eyexcalculate elasticities in the form of d(lny)/d(lnx)

mfx, dyexcalculate elasticities in the form of d(y)/d(lnx)

mfx, eydxcalculate elasticities in the form of d(lny)/d(x)

Interpretation

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?

Hypothesis Testing

6.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 the test command to calculate the F-statistic when doing this test.

Goodness-of-Fit

7.Interpret the R² statistic.Given your Adjusted R²statistic 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 Multicollinearity and Heteroskedasticity

8. Apply two diagnostic procedures that are often used to detect multicollinearity. Do these procedures indicate that you may have severe multicollinearity

9. 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? 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.