Problem Set #2
Solutions
(1) Stock and Watson 2.2: (a) First,
E (W ) = 3 + 6E (X ) and E (V ) = 20 7E (Y ).
From table 2.2,
E (X ) = 0(.3) + 1(.7) = .7
and
E (Y ) = 0(.22) + 1(.78) = .78.
Therrefore,
E (W ) = 3 + 6(.7) = 7.2
and
E (V ) = 20 7(.78) = 14.54
Solutions: Problem Set #3
(4.1) Throughout this exercise, let T S denote the test score and CS denote class
size.
(a) We seek E (T S |CS = 22):
E (T S |CS = 22) = 1 + 222
= 520.4 22(5.82)
= 392.36
(b) Note that (in terms of the population regression funct
Solutions: Problem Set #4
(1) Taking the derivative of the objective function with respect to 1 gives the rst
order condition:
n
2
(yi 1 ) = 0.
i=1
Cleaning this expression up a bit, we obtain
n
yi n1 = 0
i=1
which implies
1n
1 = y
yi .
n i=1
The R2 for
Solutions: Problem Set #5
(1) (a)To calculate the 95 percent condence interval, we should use critical values
from the t1002 = t98 table. Looking this up in your textbook (page 645) we nd the
appropriate critical value to be 1.99. Therefore, our 95 percen
Solutions: Problem Set #6
(1) The regression output is provided in the other le. The coecient estimates are
the same as presented in class.
(2) The coecient estimates are provided in the other le. These are the same as
reported in the textbook.
(2a) In cl
Solutions: Problem Set #7
(1) The regression output and STATA code are provided in the other le.
(1b) To implement this test, we need to get the R2 values from both the restricted
and unrestricted models. We see that
2
Ru = .889,
2
Rr = .570,
p = 1,
n = k
Solutions: Problem Set #8
(1) The regression output is provided in the other le. Increasing team batting
average by, say, 10 points will lead to about 5 more wins per season. Hitting 10
more home runs in a season will lead to about 1.2 more wins in that s
Solutions: Problem Set #10
(1a) Mean-independence could be violated for a variety of reasons. First, highlymotivated students may be more likely to purchase computers. (They decide to
purchase a computer, simply because they think it will give them an edg
Solutions: Problem Set #1
(1) The following table gives the joint probability distribution p(X, Y ) of random variables
X and Y .
Y
1
2
3
4
1
.02
.03
.00
.09
X
2
.04
.18
.02
.18
3
.12
.04
.10
.18
Determine the following:
(a) Do the entries of the table sa