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Unformatted text preview: say that OLS is asymptotically efficient
• Important to remember our assumptions though: If the error terms are not
homoscedastic, then the asymptotic efficiency is no longer true VER. 10/23/2012. © P. KOLM 17 Multiple Regression Analysis: Dummy Variables VER. 10/23/2012. © P. KOLM 18 Example: C7.10 in Wooldridge
(For you: Review the following example on your own using dummy variables.
There is “nothing new here” besides the use of dummy variable. Think about
other situations where you might be using dummy variables. It is a useful tool
from the “econometrician’s toolbox.”) VER. 10/23/2012. © P. KOLM 19 We use the data in NBASAL.RAW for this exercise.
(i) Estimate a linear regression model relating points per game to experience in the league and position (guard, forward, or center). Include
experience in quadratic form and use centers as the base group. Report the
results in the usual form.
Solution:
The estimated regression equation and output are shown below: points = 4.815 + 1.264exper − 0.07045exper 2 + 2.336guard + 1.590 forward
(1.18) (0.328) (0.0240) n = 269, R2 = 0.091, VER. 10/23/2012. © P. KOLM (0.997) (0.999) R2 = 0.077 20 Ordinary Leastsquares Estimates
Dependent Variable =
points
Rsquared
=
0.0910
Rbarsquared
=
0.0772
sigma^2
=
31.9327
DurbinWatson =
2.2214
Nobs, Nvars
=
269,
5
***************************************************************
Variable
Coefficient
tstatistic
tprobability
intercept
4.814859
4.097752
0.000056
exper
1.264197
3.859862
0.000143
expersq
0.070452
2.935740
0.003621
guard
2.336508
2.342856
0.019880
forward
1.589599
1.590907
0.112827 VER. 10/23/2012. © P. KOLM 21 (ii) Why do you not include all three position dummy variables in part (i)? Solution:
Including all three position dummy variables would be redundant, and result in
the dummy variable trap. Each player falls into one of the three categories, and
the overall intercept is the intercept for centers. VER. 10/23/2012. © P. KOLM 22 (iii) Holding experience fixed, does a guard score more than a center? How much more? Is the difference statistically significant?
Solution:
A guard is estimated to score about 2.3 points more per game, holding experience
fixed. The t statistic is 2.34, with a pvalue of 0.0199, so the difference is
statistically different from zero at the 5% level, against a twosided alternative. VER. 10/23/2012. © P. KOLM 23 (iv) Now, add marital status to the equation. Holding position and experience fixed, are married players more productive (based on points per
game)?
Solution:
The estimated regression equation and output are shown below: points = 4.759 + 1.219exper − 0.0690exper 2
(1.18) (0.333) (0.0241) −2.309guard − 1.586 forward + 0.5598marr (1.00) (1.00) n = 269, R2 = 0.093, VER. 10/23/2012. © P. KOLM (0.738) R2 = 0.076 24 Ordinary Leastsquares Estimates
Dependent Variable =
points
Rsquared
=
0.0929
Rbarsquared
=
0.0757
sigma^2
=
31.9842
DurbinWatson =
2.2287
Nobs, Nvars
=
269,
6
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This document was uploaded on 02/17/2014 for the course COURANT G63.2751.0 at NYU.
 Fall '14

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