ECON 335 – Homework 5 – 100 pointsModel Specification and HeteroscedasticityInitial Steps:For this problem go to RamCT, download the Gretl data set named “homeprice.gdt” included with this homework...

SUMMER 2012 - ONLINE
ECON 335 – Homework 5 – 100 points
Model Specification and Heteroscedasticity
Initial Steps:
For this problem go to RamCT, download the Gretl data set named “homeprice.gdt” included with this homework assignment, and save it to your computer. Then Open Gretl and click file > open data > user file,
owse for the file and double click on it. It should load into Gretl.
This is a data set of home prices and various characteristics of each home. The data is from home prices in Baton Rouge, LA in mid-2005. The variable names should be self explanatory as we go along but you can get a feel for what the data looks like by viewing summary statistics of the variables. I will assume that you are familiar with much of the basic commands in Gretl which we’ve used to date, but I’ll help a little.
First click on the “price” variable so that it is highlighted. In the Gretl toolbar, click Variable > Frequency Distribution. Then just click ‘OK’ in the dialogue box. What pops up is called a “Histogram” and shows the distribution of the prices of the home. Notice that it almost looks like a “standard” normal distribution except it seems to be skewed to the right with a long tail on the right side. In this situation we typically transform our dependent variable by taking the natural log of the value. So generate the natural log of home price by again selected the “price” variable and clicking Add > logs of selected variables. What we will be regressing then is a log-lin model as we discussed in our lecture notes.
1. [50 points] Select the sqft variable in your variable list. Click Variable > Summary Statistics. Notice that this variable is in thousands. To have a more meaningful interpretation of the coefficient let’s scale it to be a smaller number (note that this does not change the estimation of the relationship only the value of the coefficient that would be estimated otherwise – you can try to see for yourself by running a regression with the unscaled and scaled version of sqft). For now, generate a new variable by dividing the sqft variable by 100. Call it sqft_100.
Answer:
Summary statistics, using the observations 1 - 1080
for the variable 'sqft' (1080 valid observations)
Mean 2325.9
Median 2186.5
Minimum 662.00
Maximum 7897.0
Standard deviation 1008.1
C.V. 0.43342
Skewness 1.5996
Ex. kurtosis 4.5427
Summary statistics, using the observations 1 - 1080
for the variable 'sqft_100' (1080 valid observations)
Mean 23.259
Median 21.865
Minimum 6.6200
Maximum 78.970
Standard deviation 10.081
C.V. 0.43342
Skewness 1.5996
Ex. kurtosis 4.5427
a) [18 points] Now, regress l_price on the sqft_100, the number of bedrooms (bedrooms), the number of bathrooms (baths), the age of the house in years (age), the dummy for whether the owner lives in the house (owner), a dummy for whether there is a pool (pool), the dummy for whether the house has a traditional design (traditional), the dummy for whether there is a fireplace (fireplace), and the dummy for whether the property is waterfront property or not (waterfront). Display your results.
Use your econometric knowledge to comment on how well the model fits the data, including a discussion of the interpretation, signs (Are the signs what you expect?), and statistical significance of the estimated coefficients. [HINT: Note that the dependent variable has been transformed, so interpret co
ectly!]. You can do this in a congenial way, no need to list things unless you wish to – just make sure you provide a fully formed analysis of your results!
Answer:
Model 1: OLS, using observations 1-1080
Dependent variable: l_price
coefficient std. e
or t-ratio p-value
--------------------------------------------------------------
const 10.8886 0.0458947 237.3 0.0000 ***
sqft_100 0.0299011 0.00140588 21.27 5.30e-084 ***
bedrooms -0.0315060 0.0166109 -1.897 0.0581 *
baths 0.190119 0.0205579 9.248 1.20e-019 ***
age -0.00621453 0.000517940 -12.00 3.29e-031 ***
owner 0.0674654 0.0177460 3.802 0.0002 ***
pool -0.00427481 0.0315812 -0.1354 0.8924
traditional -0.0560926 0.0170267 -3.294 0.0010 ***
fireplace 0.0842748 0.0190150 4.432 1.03e-05 ***
waterfront 0.109970 0.0333550 3.297 0.0010 ***
Mean dependent var 11.79518 S.D. dependent var 0.524535
Sum squared resid 77.98093 S.E. of regression 0.269962
R-squared 0.737325 Adjusted R-squared 0.735116
F(9, 1070) 333.7195 P-value(F) 2.6e-303
Log-likelihood -113.1975 Akaike criterion 246.3950
Schwarz criterion ...