Mehmet Soytas
Applied Econometrics I, Summer, 2009
Wednesday, May 21, 2009
(due: Wednesday, May 27, 2009)
Homework Assignment 2
1.
Show that the OLS formula for the coe¢ cient
1
in the multiple regression model
Y
i
=
&
0
+
1
X
1
i
+
1
X
2
i
+
u
i
reduces to the OLS formula of
1
in the one regressor case if the correlation between
X
1
i
and
X
2
i
is zero.
2.
For this question, use the California Testscore Data Set and your regression package (STATA).
a. First perform a multiple regression of testscores on a constant, the studentteacher ratio, and the
percent of English learners. Record the coe¢ cients.
Next, do the following three step procedure instead:
b. First, regress the testscore on a constant and the percent of English learners. Calculate the residuals
and store them under the name resYX2.
c. Second, regress the studentteacher ratio on a constant and the percent of English learners. Calculate
the residuals from this regression and store these under the name resX1X2.
d. Finally regress resYX2 on resX1X2. Explain intuitively why the simple regression coe¢ cient in the
last regression is identical to the regression coe¢ cient on the studentteacher ratio in the multiple
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 Summer '08
 Staff
 Statistics, Econometrics, Regression Analysis, dence level

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