Overview
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Hypothesis testing about the dierence between two parameters
(Chapter 10)
Today:
Linear regression analysis
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Linear regression
Correlation characterized the linear relationship between two variables:
Cor(X, Y ) =
Cov(X, Y )
X Y
L
Lecture 3: Interpretation and Hypothesis
Tests
Charles J. Saunders
University of Western Ontario
Econometrics
Winter 2017
Interpretation of coefficients
I
We have estimated the following linear model,
Yi = b0 + b1 Xi + i
I
Let Y be $ of consumption and X
# hard code the US repo for CRAN - Used to download packages - Not needed
for the assignment
r <- getOption("repos")
r["CRAN"] <- "http:/cran.us.r-project.org"
options(repos = r)
rm(r)
Z <- rnorm(10000)
# PDF of normal distribution
n = 10000
X <- rnorm(n)
Lecture 4: Multiple Regression
Charles J. Saunders
University of Western Ontario
Econometrics
Winter 2017
Adding Regressors
I
I
Assume we have two variables that affect our dependent
variable
What variables would you use to explain:
I
I
I
I
I
Income of in
Lecture 8: Endogeneity
Charles J. Saunders
University of Western Ontario
Econometrics
Winter 2017
Endogeneity
I
The model:
Yi = 0 + 1 Xi + ui
I
Thus far, assumed exogeneity:
E[ui |X ] = 0
I
Relax this assumption, endogeneity:
E[ui |X ] 6= 0
I
The regresso
Lecture 5: Model Specification
Charles J. Saunders
University of Western Ontario
Econometrics
Winter 2017
Multiple Regression Model
I
Our model so far is:
Yi = 0 + 1 X1,i + 2 X2,i + + K XK ,i + ui
I
Specification of the relationship is linear
I
Can OLS de
Lecture 10: Autocorrelation
Charles J. Saunders
University of Western Ontario
Econometrics
Winter 2017
Time Series
Yt = 0 + 1 Xt + ut
I
OLS assumptions regarding errors:
1. Exogenous: E[ut |X ] = 0 for all t
2. Homoscedastic: E[ut2 |X ] = u2 for all t
3.
# hard code the US repo for CRAN - Used to download packages - Not needed
for the assignment
r <- getOption("repos")
r["CRAN"] <- "http:/cran.us.r-project.org"
options(repos = r)
rm(r)
# Packages and Libraries
install.packages("lubridate")
library(lubrida
Lecture 1: Regression Intuition and
Review
Charles J. Saunders
University of Western Ontario
Econometrics
Winter 2017
Intuition of OLS
I
Ordinary Least Squares (OLS) is drawing the best line in
a bunch of dots (this was my explanation to my 6 year old),
c
Lecture 2: Simple Linear Regression
Charles J. Saunders
University of Western Ontario
Econometrics
Winter 2017
Linear Model
I
We define the linear model as
Yi = 0 + 1 Xi + ui
where observations are indexed by i = 1, . . . , N and
I
I
I
I
Yi dependent vari
FINAL EXAM TOPICS
1. ALL the material from the midterm
2. New material:
Dummy variables: Chapter 5
Interaction terms: Section 4.3
Testing linear restrictions: Section 6.5
Heteroskedasticity: Chapter 7
Omitted variable bias: Section 6.2 and 6.3
Measu
ECON 2223B
Midterm Exam - Winter 2011 - SOLUTIONS
1. TRUE/FALSE:
(a) FALSE. Consider X and Y - two independent variables, and let Z = X + Y .
Then Cov(X, Y ) = 0 (since X and Y are independent), but Cov(X, Z) 6= 0 and
Cov(Y, Z) 6= 0.
(b) FALSE. This is a
Overview
Last time:
Linear regression analysis
Today:
Continue linear regression analysis
1 / 16
1500
q
1000
q
q
q
q
q
q
q
q
500
q
0
Monthly wage
2000
2500
Look again at the relationship between years of education completed and
monthly wage:
10
12
14
16
1
Problem Set 1
Intermediate Econometrics II
ECONOMICS 2223B
Prof. Julio Elias
You have to return your solutions to the problem set on Thursday, January 15 at the
beginning of the class.
Review of Statistics
1. A random variable X is defined to be the diffe
University of Western Ontario
Department of Economics - ECON 2223B Intermediate Econometrics
Instructor: Maria Ponomareva - Midterm Exam - February 16 2012
RULES: This is a closed book, closed notes exam. You are not allowed to use your cell
phones (even
University of Western Ontario
Department of Economics - ECON 2223B Intermediate Econometrics
Instructor: Maria Ponomareva - Midterm Exam - February 14 2011
RULES: This is a closed book, closed notes exam. You are not allowed to use your cell
phones (even
MIDTERM TOPICS
Here is a short summary of the topics for the midterm exam with references to specific
chapters in the textbook:
1. Chapter 1: pages 83-107 (dont need to learn the alternative interpretation of R2 ).
2. Chapter 2: pages 110-121, 125-148.
3.
University of Western Ontario
Department of Economics - ECON 2223B: Intermediate Econometrics
Instructor: Maria Ponomareva - Final Exam - April 14, 2012
RULES: This is a closed book, closed notes exam. You are not allowed to use your cell
phones (even for
Some Useful Formulas
Expected Value and Variance of X:
Sample Correlation:
E(X) = X
rXY =
2
V (X) = X
= E (X X )2
sXY
sX sY
OLS Estimators in simple linear regression model
Y = 0 + 1 X + U :
Law of Iterated Expectations:
n
P
E(Y ) = E (E(Y |X)
1 = i=1
n
P
Midterm Exam, ECON 2223B, Winter 2012: Solution
1. (5 pts. each) TRUE/FALSE: State if the following statements are true or false. Only
clearly explained answers will earn full credit.
(a) FALSE: Ui s here are error terms, not residuals, and we do not obse
University of Western Ontario
Department of Economics - ECON 2223B: Intermediate Econometrics
Instructor: Maria Ponomareva - Final Exam - April 14, 2012
RULES: This is a closed book, closed notes exam. You are not allowed to use your cell
phones (even for