## Transcribed Text

Need Stata Do file
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
otherwise.
Statistical Model
You specify the following alternative multiple regression models:
a) Pricei = B1 + B2 Sqfti + B3 Bedrooms; + B4 ,Baths + Bs + Bo Pooli + B7 Waterfront, + ut
b) B4 ,Baths; + ß5Agei + Bo Pooli + B7 Waterfront, +
ut
c) B4 Baths; + Bs In(Agei+ Bo Pooli + B7 Waterfronti
+ u,
Estimation
1. Use the regress command in Stata to estimate your model. Report the results. Which model do you
prefer and why.
Use model (a) 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 =
Average of sqfit
Average of Price,
Standard error for sqft=s.e(B2) =
Average of Sqfit
Average of Price.
In stata, you can use mfx, eyex or margins command after regress. The command margins
computes marginal effects or elasticities after estimation. The option eyex (varlist) computes the
elasticity of y with respect to variables in varlist.
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 R² 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.
Note on elasticity from regressions
Log-log model:
When we use the log-log model,
In (y) = b0 + b1*1n (x)
(1)
the slope coefficient of In(x) is the elasticity estimate. In other words, we use the term elasticity to
describe the coefficient of the model (1). Of course, here the elasticity is constant. This is called a
constant elasticity model.
Linear model:
In contrast, when we estimate
y = c0 + cl*x
(2)
and compute d(ln(y))/d(In(x)), we can calculate elasticity at any values of x. For example, the margin
command is calculating the elasticity at the mean, which will not be the same as the slope from the log-
log model. The elasticity from (2) will vary depending on what value of x we are using. In fact, the
standard practice is to calculate the elasticity from (2) as a function of x. For example, if the min of x is
100 and max is 1000, we can create 10 increments, and calculate 10 elasticity estimates from (2). The
constant elasticity from (1) will be in that range of varying elasticity estimates. Since we can evaluate this
function at any value of x, this is a varying elasticity model.
Related STATA commands
constant elasticity model
gen lny=ln (y)
gen lnx=ln (x)
regress lny lnx
gen marg_cons = b [lnx]
*
varying elasticity model
reg y x
elasticity at the mean
margins, eyex (x) atmeans
*
elasticity at different values of weight -
margins, eyex (x) at (x = (min (increment)max)) noatlegend
*---a linear model again
reg y x
summarize y
local meany=r (mean)
summarize x
local meanx=r (mean)
local f=`meanx'*b_[x]
margins, eyex (x) atmeans

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