Regression with a single regressor

An application to the Capital Asset Pricing Model (CAPM)
[1] Theory
From riskreturn tradeoff analysis in finance, the CAPM model is a regression model with no intercept:
(
)
Where is the return of an individual asset
Econ 3334
Topic 6: Multiple Regression
Estimation
1
Econ 3334
We covered
Yi 0 1 X i u i
where we only have one regressor (explanatory variable,
independent variable) Xi
But what if true specification is
Yi 0 1 X 1i 2 X 2i . . . k X ki u i
e.g. Y is wage
Econ 3334
Topic 4: Simple Linear
p
p
RegressionEstimation
Part B
1
3) Fit
Econ 3334
So how well does the estimated model explain the
dependant variable?
R is the fraction of the variation of Y that is
explained by the model
Here model is linear functiona
Econ 3334
Topic 7
p
Multiple Regression (Part B)
Application
1
Beauty and the Labor Market
Econ 3334
Are goodlooking people paid more in the labor market?
Daniel S. Hamermesh and Jeff E. Biddle (1994) Beauty and the
labor market, American Economic Review
Econ 3334
Topic 7: Multiple Regression
Inference
1
1) Hypothesis tests
Econ 3334
Yi 0 1 X 1i 2 X 2i . . . k X ki u i
Everything from simple regression extends here to multiple
regression
Each OLS estimator 0, 1, 2, . . . , k will have a standard
erro
Econ 3334
Topic 4: Simple Linear
p
p
RegressionEstimation
Part A
1
Who Invented Regression ?
http:/en.wikipedia.org/wiki/Francis_Galton
Econ 3334
2
1) Linear Regression Model
Econ 3334
Here we are interested in estimating a linear equation that
describes
Standard Normal Probabilities
Table entry
Table entry for z is the area under the standard normal curve
to the left of z.
z
z
.00
.01
.02
.03
.04
.05
.06
.07
.08
.09
3.4
3.3
3.2
3.1
3.0
2.9
2.8
2.7
2.6
2.5
2.4
2.3
2.2
2.1
2.0
1.9
1.8
1.7
1.6
1.5
1.4
1.3
1
Econ 3334
Topic 9: Carrying Out an
Empirical Project Using
Regression
(Part B)
1
Econ 3334
1.
2.
3.
4.
5.
Posting a Specific Questions
Literature Review
Data Collection
Econometric Analysis
Writing an Empirical Paper
Econ 3334
1. Posting a Specific Questi
Econ 3334
Topic 9: Carrying Out an
Empirical Project Using
Regression
(Part A)
1
1) Using Regression
Econ 3334
the main workhorse of applied empirical research in
economics is still linear regression by ordinary least
squares (OLS).
But we know regressi
Answers to Quiz Questions
Chapter 2: Review of Probability
1. See Glossary.
2. a.
Employed (X = 0) Unemployed (X = 1) Total
0.55
0.04
.59
No College Degree (Y = 0)
0.39
0.02
0.41
College Degree (Y = 1)
0.94
0.06
1.00
Total
b. Pr(X = 1) = .06
c. .02/.41 =
Answers to Quiz Questions
Chapter 1: Economic Questions and Data
1. See the Glossary.
2. a. time series data, b. panel data, c. crosssectional data.
3. They can be unethical, impossible to execute, or too expensive.
4. This is a poor estimate. Many thing
Quiz Questions
Chapter 2: Review of Probability
1. Provide a definition for each of the Key Terms at the end of the chapter.
2. The table below shows the joint probability distribution employment status (employed and
unemployed) and education (no college
Quiz Questions
Chapter 3: Review of Statistics
1. Provide a definition for each of the Key Terms at the end of the chapter.
2. A student achievement test is constructed so that the mean score is 1000 for the population of
all 6th grade students in the Uni
Econ 3334
Topic 5: Simple Linear
RegressionInference
1
Econ 3334
We have estimated 1 which is the OLS estimator of
the slope coefficient.
Now we are going to see how we can use the estimated
results from a sample to draw inferences about the
population p
Econ 3334
Welcome to
Econ 3334
Introductory Econometrics
1
Teaching Team
Econ 3334
Instructor: Xun (Sean) Lu ()
Assistant Professor, Department of Economics
Specialty: Econometrics
Teaching Assistant: TBA
2
Lecture and Tutorial Information:
Econ 3334
Le
Econ 3334
Review of Probability TheoryPart B
1
4) Distribution
Normal Distribution
Econ 3334
X N, 2
Pr 1. 96 X 1. 96 0. 95
4) Distribution
Econ 3334
In general, we standardize the Normal R.V. by subtracting
and dividing by .
Prc X d
c X d
Pr
Z
wher
Documentation for CPS04 Data
Each month the Bureau of Labor Statistics in the U.S. Department of Labor conducts the
Current Population Survey (CPS), which provides data on labor force characteristics of the
population, including the level of employment, u
THE CALIFORNIA TEST SCORE DATA SET
The California Standardized Testing and Reporting (STAR) dataset contains data on test performance, school characteristics and student demographic backgrounds. The data used here are from all 420 K6 and K8 districts in
PROBLEM SET ONE (PS1)
(Due on Feb 25, Tuesday)
Chapter 2 (Review of Probability)
Exercises: 2.4, 2.6, 2.14, 2.15, and 2.19, and 2.23
For Exercise 2.4, a Bernoulli random variable X is defined as:
X=1 with probability p and X=0 with probability 1p.
All of
PROBLEM SET FOUR (PS4)
(Due on 8 April, Tuesday)
Part I:
Exercises 5.1, 6.1, 6.2, 6.3, and 6.4
Part II:
Empirical Exercise: E.5.1. For this question, you need to submit your Stata outputs
by printing out the regression outputs directly. Then you need answ
PROBLEM SET THREE (PS3)
(Due on March 20, Thursday)
Chapter 4: Linear Regression with One Regressor
Part One:
Exercises: 4.1, 4.5, and 4.9
Part Two:
Empirical Exericse: E4.1. For this question, you need to submit your Stata outputs
by printing out the reg
ECON3334, Spring, 2014, HKUST
Information on the Midterm
1. Time and Venue:
Time: 7:008:30pm, March 20, Thursday
Venue: LTB
Please hand in your PS3 before or after the midterm.
2. We will NOT have class on March 20 (Thursday).
3. Format of the Midterm:
PROBLEM SET FIVE (PS5)
(Due on April 24, Thursday)
Part 1: Questions from the textbook
Chapter 7
Exercises: 7.1, 7.2, 7.3(a) (skip (b), and 7.9(b)(c) (skip (a)
Part 2: Stata questions
1. Replicate Table 7.1 in the textbook (page 280). The data is download
A quick review of calculus
Econ 3334
Use calculus to find Min or Max of functions
Multivalue functions
z = 5x 2 + 10xy 20x 7y 2 + 240y 5300
Find the x & y that gives the Max z
z
z
= 0 and y = 0 are the first order conditions (FOCs)
x
Solve simultaneously
Econ 3334
Review of Statistics
1
Econ 3334
The reality we dont know the population (e.g., and
in the normal population).
population)
. . . .
. .
. . .
.
.
.
. . . . .
. . .
. .
.
POPULATION
Sampling
p g
(X1 ,X2 , . ,Xn )
[A simple random sample]
Statisti
Answers to Quiz Questions
Chapter 3: Review of Statistics
1. See Glossary.
1010 1000
= 1.43
98 / 196
a.  t  < 1.96, so H0 is not rejected at the 5% level.
b. Pr( t  1.43) = 0.15
c. SE(Y ) = 98/ 196 = 7; 95% confidence interval is 1010 1.967 = (996.3 t