Homework 1 (4 Points), due at the beginning of class on September
12, 2016. You can help each other!
• Q1 (2 point) Consider a simple regression
Y = E(Y |X) + e
where E(Y |X) is the population regression function, and e is the error term. Please
prove that
E(e|X) = 0
(1)
E(e) = 0
(2)
E(eX) = 0
(3)
cov(e, X) = 0
(4)
Hint: E(e) = E[E(e|X)]; E(eX) = E[E(eX|X)] = E[XE(e|X)]
• Q2 (1 point) Please use grade data posted in my webpage, and use stata to find
E(exam2) and E(exam2|section). Verify that the law of iterated expectation holds
(i.e., E(exam2) = E[E(exam2|section)]). Show me your log file or stata results. Hint,
the stata command to find the distribution for section is
tab section
and the command to find the conditional mean is
sort section
by section: sum exam2
• Q3 (1 point) Continue Q2. Please use stata to find the best linear predictor for exam2
based on exam1 (i.e., use exam1 to predict exam2). Hint, the stata command to find
variance and covariance is
cor exam2 exam1, cov
To learn more about the command cor, type help cor in the command window of
stata.
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