Problem Set 1 - Solutions
MATH 386-1: Econometrics I
Titan Alon
January 24, 2015
Question 1 (Wooldridge 2.2)
Dene the random variable v where v = u 0 . Then, the regression model y =
to y = 0 + 1 educ + v, where 0 = 0 + 0 and E[v] = E[u] 0 = 0.
0 + 1 educ
Problem Set 5 - Solutions
MATH 386-1: Econometrics I
Titan M Alon
March 5, 2015
Question 1
(a) The condence interval is given by the usual expression, namely
[
s
c(1
/2)
se(), s
s
c(1
/2)
se()].
s
Since s = 1 + 2 , the natural estimate for s is s = 1 +
Math 386-1: MMSS Econometrics
Final Examination
Tuesday, March 16, 2011
This is a two hour, open book and notes exam. Budget your time carefully. You may refer to
the Wooldridge text, and to two pages of notes. You will not receive credit for answering an
Math 386-1: MMSS Econometrics
Midquarter Examination
Monday, February 8, 2010
This is an 80 minute, open book and notes exam. Budget your time carefully. You will
not receive credit for answering any questions that have not been asked. Remember to write
y
Math 386-1: MMSS Econometrics
Final Examination
Tuesday, March 16, 2010
This is a two hour, open book and notes exam. Budget your time carefully. You will not receive
credit for answering any questions that have not been asked. Remember to write your name
2010 Midterm Examination - Solutions
MATH 386-1: Econometrics I
David A. Ovadia
February 16, 2010
Question 1 (18 points)
(a) 6 points. If log y and x have a linear relationship, then y and x have an exponential relationship. Thus,
a linear regression of y
Math 386-1: MMSS Econometrics
Midquarter Examination
Wednesday, February 2, 2011
This is an 80 minute, open book exam. Budget your time carefully. You may refer to the
Wooldridge text, and to one page of notes. You will not receive credit for answering an
MATH 386-1: Econometrics for MMSS
Chris Lau
February 2, 2611
Solutions to Midterm 2011
P1. Suppose that a random sample of 200 twenty year oid 1men is selected from a population and that
the men’s height and weight are recorded. A regression of weight o
Problem Set 4 - Solutions
MATH 386-1: Econometrics I
February 19, 2015
Question 1
The predictions given by the regression equation may
8
< a 1 + b1 Y i
a 2 + b2 Y i
Bi =
:
a 3 + b3 Y i
be expressed as
if Yi 300
if 300 < Yi 100
if 1000 < Yi
To determine th
Problem Set 2 - Solutions
MATH 386-1: Econometrics I
Titan Alon
January 24, 2015
Question 1
(a) The standard OLS estimate for
1
is given by
d
1 = Cov(C, YD)
d
V ar(YD)
which, after some expansion, can be expressed in terms of the given data:
1 =
=
=
1
n 1
Problem Set 3 - Solutions
MATH 386-1: Econometrics I
Titan M. Alon
January 30, 2015
Question 1
(a) To estimate the mean of a random variable within the linear regression framework, we set
2
6
6
=6
4
(N 1)
y
3
Z1
Z2
.
.
.
Zn
(b) The OLS estimator of the me
MATH 386-1: Econometrics for MMSS
Joe Hardwick
January 31, 2016
Solutions to Midterm 2004
P1. Suppose that you observe two sample points for the variables y and x, (1, 0) and (3, 2), where in
each ordered pair y is reported first and x second.
(a) Plot th
MATH 386-1: Econometrics for MMSS
Joe Hardwick
February 9, 2016
Solutions to Midterm 2016
P1. Suppose that you observe three sample points for the variables y and x, (4, 0), (2, 1) and (4, 2),
where in each ordered pair y is reported first and x second.
(
MATH 386-1: Econometrics for MMSS
Joe Hardwick
February 26, 2016
Solutions to Problem Set 5
P1. (a) A 95% confidence interval for s = 1 + 2 is given by:
h
i
CI = s t253 (0.975)
s , s + t253 (0.975)
s
Here, s = 1 + 2 = 0.3 0.3 = 0, t22 (0.975) = 2.074 an
MATH 386-1: Econometrics for MMSS
Joe Hardwick
January 31, 2016
Solutions to Midterm 2010
P1. Answer the following questions.
(a) Suppose that sample data on the variables x and y are generated according to the log-linear
relationship log y = 4 + 2x + u,
MATH 386-1: Econometrics for MMSS
Joe Hardwick
January 31, 2016
Solutions to Midterm 2011
P1. Suppose that a random sample of 200 twenty year old men is selected from a population and that
the mens height and weight are recorded. A regression of weight on
MATH 386-1 Solutions 3
Joe Hardwick
January 2017
1.
(a) For i = 1, .n, we can write Zi = + ui , where = E(Z), E(ui ) = E(Zi ) = 0 and V ar(Zi ) =
V ar(ui ) = 2 . Stacking these equations in the usual manner, we get:
Z1
1
u1
Z2 1
u2
. = . + .
.
MATH 386-1 Solutions 1
Joe Hardwick
January 2017
1. Wooldridge, Problem 2.2
The given model is:
y = 0 + 1 x + u
= (0 + E(u) + 1 x + (u E(u)
+ 1 x + v
where v = u E(u) has zero expectation and = 0 + E(u) is the new intercept. The slope is still 1 .
2. Woo
MATH 386-1: Econometrics for MMSS
Joe Hardwick
January 31, 2016
Solutions to Midterm 2003
P1. Answer the following questions.
(a) Outline a procedure for a two sided test of the hypothesis that the mean of y is zero, based on
a random sample of n observat
MATH 386-1 Solutions 2
Joe Hardwick
January 2017
1.
Pn
xi yi n
xy
. Compute
We have n = 15 observations. It is convenient to use the form 1 = Pi=1
n
2
x2
i=1 xi n
Y D = 770.72, S = 68.72 and C = 702. Hence we find:
8, 297, 772.87 15 702 770.72
0.9282 and
MATH 386-1: Econometrics for MMSS
Joe Hardwick
January 31, 2016
Solutions to Midterm 2015
P1. Assume that yi = 0 + 1 xi + ui for i = 1, 2, ., n, where the unobservable errors ui are independent
normally distributed random variables with mean zero and vari
MATH 386-1: Econometrics for MMSS
Joe Hardwick
March 4, 2016
Solutions to Problem Set 6
P1. (Wooldridge, Problem 4.8)
(i) The variance of 1 32 is given by
Var(1 32 ) = Var(1 ) + Var(32 ) 2Cov(1 , 32 )
= Var(1 ) + 9Var(2 ) 6Cov(1 , 2 ).
The standard error