Problem Set 1 Answer Key
Problem 2
Joint Probability Distribution
Y=0
Y=1
Total
X=0
0.045
0.709
0.754
X=1
0.005
0.241
0.246
Total
0.05
0.95
1
a)
E[Y]
= Prob(Y=1)*1 + Prob(Y=0)*0
= 0.95
b) To calculate the conditional mean E[Y|X=1] and condition variance V
Econometrics: Homework 3
1. Consider the regression model Y i 0 1 X 1i 2 X 2i 3 X 1i X 2i u i . Please show: Y (a) X 1 1 3 X 2 (effect of change in X 1 holding X 2 constant). (b)
Y X 2
2 3 X 1 (effect of change in X 2 holding X 1 constant).
(c) If X 1 ch
Economics 180.334
Spring 2013
Johns Hopkins University
Prof. Jorge Balat
459 Mergenthaler Hall
[email protected]
Problem Set # 3
The linear model with multiple regressors
Due on March 26, at the beginning of class. The purpose of this assignment is to r
Economics 180.334
Spring 2013
Johns Hopkins University
Prof. Jorge Balat
459 Mergenthaler Hall
[email protected]
Problem Set # 1
Review of Statistics and Probability
Due on Feb 7, at the beginning of class. This problem set is a hands-on review of stati
1. (a) there is a selection problem. People are not being treated but rather selecting
into the drinking diet soda and not drinking diet soda groups. Who typically drinks diet
soda? Perhaps people who are trying to lose weight (people making other life de
Econometrics
Johns Hopkins University
Prof. Minicozzi
Fall 2007-2008
Answers for Final Tuesday, December 11, 2007
1. 15 points Suppose that X and Y are iid (independently, and identically distributed), each
with probability .5 of equaling 1 and probabilit
Review of Probability Theory
Random variable multiple possible outcomes, cannot predict an outcome on the basis of
information available at a given moment
Discrete
Continuous
Definition
Finite number of outcomes
Continuum of outcomes
Example
Bernoulli ran
University of Pennsylvania
Economics 6, Fall 2003
Introduction
What is Econometrics?
Example: The Mayor of Philadelphia wants to introduce a city gasoline tax to
reduce the automobile trac and emissions within the city by 30%. He asks his
advisor to analy
Solution to Practical Problems (Quiz 3)
April 21, 2015
1 P ROBLEM 1
1.1
H0 : 3 = 0
H1 : 3 = 0
3
0.058
P-value = prob(| 0 | | 3,ac t |) = 2prob( 3 0.017 )
3
3,ac t
3
1.2
g r ad e2 = 0 + 1 (g r ad e1 + ) + 2 post + 3 si ze (g r ad e1 + ) + u i 0 1 g r ad e1
Introduction to Linear Regression
Empirical problem: Class size and educational output
Policy question: What is the effect of reducing class
size by one student per class? by 8 students/class?
What is the right output (performance) measure?
parent satis
Review of Statistics
Random Sampling and i.i.d Random Variables
X is a random variable
F(.) is cumulative distribution function of X
f(.) is probability density of X
E[X] =
Var[X] = 2
Suppose that we take n records (draws of X)
Before the value of each d
Suggested Solution for Sample Quiz 2
March 26, 2015
Problem 1
(a)
Yes. From the table we know the t-statistic is 11.85 > 2.58, so we can reject H0 : 1 =
0 at 1% level. Alternatively, we can see the p-value for testing H0 is as low as 0.000, so
that we can
Solutions
Problem 1
(a) If class size increases by 1 student then the number of applications increases by
1.69 applications. The intercept does not have a good interpretation in this
environment. Formally, it implies that the college with zero class size
J OHNS H OPKINS U NIVERSITY
Solution to Problem Set 3
Introduction to Econometrics Spring 2015
March 28, 2015
Notation:Unless otherwise noted, all summation signs
denote summing from i = 1 to n.
1 P ROBLEM 1
1. 1.1
1
n
i X i Yi
1
2
n i Xi
1
n i X i (X i +
Consistency of OLS estimator
We want to show that
p
1
1
or
as
n
p
1 1
0
as
n
We will need to use Mathematical Results:
(1) Law of Large Numbers (LLN)
cfw_Zi i =1,.,n , E[ Z i ] = Z < , Var ( Z i ) <
1 i=n
p
Z
Zi
n i =1
as
n
(2) Continuous Mapping
Properties of OLS coefficients
Yi 0 1 X i U i ,
Assumption 1:
i=1,n
E[U i | X i xi ] 0, for all possible realizations of Xi
Assumption 2: cfw_(Yi,Xi)i=1,.,n are i.i.d.
Assumption 3:cfw_ E[ X ir ], E[U ir ] i=1,.4, are non-zero and finite.]
Note that since
Introduction to Econometrics
Syllabus for Spring 2015
Instructor:
Professor Elena Krasnokutskaya
Office:
Mergenthaler Hall, room 460
Office Hours:
Wednesday, 1:30-2:30PM and by appointment
Email:
[email protected]
TA (section 1):
Jianhui Li ([email protected]
Econometrics
Johns Hopkins University
Prof. Minicozzi
Spring Semester 2004-2005
Questions for Midterm Thursday, February 24, 2005
Answer Key
1. (10 points) We want to measure the responsiveness of working married mothers work hours
to the cost of childcar
Econometrics
Johns Hopkins University
Prof. Minicozzi
Fall 2010-2011
Questions for Final Tuesday, December 7, 2010
Your name:
Instructions: You will have 180 minutes for the exam. There are a total of 150 possible points.
Please sit in alternate seats whe
NAME:
Econ 334: Practice Final Exam
1. Of the four assumptions for simple linear regression, which is most directly connected with estimating the slope coecient?
2. Suppose you run a regression of students nal exam scores on their previous previous grades
Economics 180.334
Spring 2013
Johns Hopkins University
Prof. Jorge Balat
459 Mergenthaler Hall
[email protected]
Problem Set # 2
The two-variable linear model
Due on Feb 14, at the beginning of class. The purpose of this assignment is to review some
bas
Economics 180.334
Spring 2013
Johns Hopkins University
Prof. Jorge Balat
459 Mergenthaler Hall
[email protected]
Problem Set # 2
The two-variable linear model
Due on Feb 14, at the beginning of class. The purpose of this assignment is to review some
bas
Answer Key for Midterm
Jong Jae Lee
Feb.25, 2013
General Deduction rule: Even if the questions are concatenated, mistakes in one question will not be penalized for in the questions after it once was penalized.
1. [12] h: height of college students in inc
Practice Exercises
Economics 180.334
Spring 2013
1. This problem is based on the study of the housing market. The researcher has data
on 300 transactions in the Chicago area. For each transaction she knows the price and
some of the important characteristi
Practice Exercises
Economics 180.334
Spring 2013
1. This problem is based on the study of the housing market. The researcher has data
on 300 transactions in the Chicago area. For each transaction she knows the price and
some of the important characteristi
Answers to Review Questions for Econometrics Final
Question 1
Saunders (1993) tested the null hypothesis that the New York Stock Exchange (NYSE) is unaffected by
the weather on Wall Street (because security markets behave rational). Using daily data from
Review Questions for Econometrics Final
Question 1
Saunders (1993) tested the null hypothesis that the New York Stock Exchange (NYSE) is unaffected by
the weather on Wall Street (because security markets behave rational). Using daily data from 1962 to
198
Economics 281: Introduction to Applied Econometrics
Northwestern University
Prof. Minicozzi
Winter Quarter 2001-2002
Questions for Midterm Monday, February 11, 2002
Your name:
Instructions: You will have 50 minutes for the exam. Please sit in alternate se
Statistics Questions:
1. The probability that David gets a good golf shot if he uses the correct club is 1/2, and the probability of
a good shot with an incorrect club is . In Davids bag are 5 different clubs, only one of which is correct
for the shot in