1
SIM/UB Undergraduate Program
Economics 480, Econometrics I
Spring 2013
Answers to Midterm Test One
The maximum possible score is 23 points.
Question 1. (5 points) In a certain city 28% of all of the
ECO480 Econometrics 1
Class Note 2
Xu Guo
2-3 Spread of a distribution
A. The range = the largest - the smallest observation
Just depends on two observations. When the largest or the smallest changes,
African Journal of Mathematics and Computer Science Research Vol. 2(8), pp. 179-183, September, 2009
Available online at http:/www.academicjournals.org/ajmcsr
2009 Academic Journals
Full Length Resea
ECO480 Econometrics 1
Class Note 5
Xu Guo
Chapter 4 Probability Distributions
4-1 Discrete Random Variables
An example. A family plans to have 3 children and want to know the number
of girls they migh
ECO480 Econometrics 1
Class Note 3
Xu Guo
Chapter 3 Probability
3-1 Definition of probability
Definition of probability, when sample size goes to positive infinite (very large),
the relative frequency
ECO480 Econometrics 1
Class Note 4
Xu Guo
3-4 Conditional Probability
A. Definition for conditional probability
Outcome is restricted by a condition
Pr(H|G) =
Pr(G and H)
Pr(G)
B. An application of co
ECO480 Econometrics 1
Class Note 1
Xu Guo
Chapter 2 Descriptive Statistics
One important purpose of statistics is to infer whole population information
from a sample. What we can get from sample are s
ECO480 - Econometrics 1
Dr. McLaughlin
Computer Assignment 1
Due date: Friday, October 14, 2016 at the beginning of class
Instructions: The objective of computer assignments are to teach you how to ap
2
2
F(n1k),(n2k) (8.8.8)
follows the Fdistribution with (n1k)and(n2k)df in the numerator and
the denominator, respectively, in our example k=2, since there are only two
parameters in each subregressi
2
2
are unbiased estimators of
the true variances in the two subperiods. As a result, it can be shown that if
2
1 =
2
2
that is, the variances in the two subpopulations are the same (as
assumed by the
the true error variances, we can obtain their estimates from the RSS given
in the regressions (8.8.1a) and (8.8.2a), namely,
2
1=
RSS1
n12
=
1785.032
10
=178.5032 (8.8.6)
2
2=
RSS2
n22
=
10,005.22
142
hypothesis on the basis of the t test, and do not reject the other individual hypotheses on the basis of
the ttest.
3.Reject the joint null hypothesis on the basis of the Fstatistic, and
reject each s
hypothesis that there are constant returns to scale, i.e., (2+3)=1?
b.If there are constant returns to scale, how would you interpret regression (3)?
c.Does it make any difference whether we divide (1
se=(0.91) (0.32) (0.20)
R
2 =0.27
whereC=cigarette consumption, packs per year
P=real price per pack
Y=real disposable income per capita
a.What is the elasticity of demand for cigarettes with respect
ECO480 Econometrics 1
Class Note 8
Xu Guo
5-3 Covariance
A. Definition
X,Y = Covariance of X and Y
P P
= E(X X )(Y Y ) = x y (x x )(y y )p(x, y)
To measure how two variables X and Y vary together.
Bas
ECO480 Econometrics 1
Class Note 7
Xu Guo
Chapter 5 Two Random Variables
5-1 Distributions
A. Joint Distributions
In the planning of 3 children, let us define two random variables:
X = number of girls
Sample Exam and Questions for Practices
DO NOT PANIC! THE NON-MULTIPLE-CHOICE
QUESTIONS ARE NOT GOING TO BE ON THE FINAL EXAM.
THEY ARE HERE FOR YOU TO PRACTICE.
MULTIPLE CHOICE. Choose the one altern
# 4.12
n
n
n
i =1
i=1
i=1
^ iY )2= ( ^ 0+ ^1 X i Y )2= [ ^ 1( X i X ) ]2
ESS=
(
Y
a)
n
)2
^ 21 ( X i X
i=1
n
(X i X )(Y iY )
Since we know that:
^ 1= i=1
n
( X i X )2
i=1
Y iY
n
( X i X )2
i=1
X
Y
( i=0)=1 p
# 3.2 ( Y i=1)= p Pr
Pr
E ( Y i )=0 Pr ( Y =0 ) +1 Pr(Y =1)= p
Var ( Y i )=E [ ( Y i r )2 ]
( Y i=0 ) +(1p)2 Pr (Y i=1)
2
(0 p) Pr
2
2
p ( 1 p )+(1 p) p= p(1 p)
n
(a)
^p =
Yi
succes
#5.7 a)
1
^
SE
t statistic=
^
1 1,0
The tstatistic is 2.13 with a pvalue of 0.03 . The null hypothesis is rejected
At the 5 level because pvalue isless than 0.05 .
^
^
b) 95 confidence interval for
#2.7 (a) C = M (male) + F (female)
c = M + F
C =40,000+45,000=$ 85,000 Per year.
(b) cor r ( M , F )=
cov (M , F)
M F
cov ( M , F )=cor ( M , F ) M F =0.8 12,000 18,000=172,800,000
172,800,000
2
(c)
A Guide to Modern Econometrics / 2ed
Answers to selected exercises - Chapter 2
Exercise 2.1
a. See page 8-9.
b. Assumption (A1) and (A2), see page 17.
c. See page 25. We also require assumptions (A3)
Eco 480 Homework 1
Due 2/7 before class
1. Suppose we have the following linear transformations for sample X with
sample size N
Yi = a + bXi
prove
Y = a + bX
sy = |b|sx
is the average of the original
Eco 480 Homework 1
Due 2/7 before class
1. Suppose we have the following linear transformations for sample X with
sample size N
Yi = a + bXi
prove
Y = a + bX
sy = |b|sx
is the average of the original
ECO480 Econometrics 1
Class Note 6
Xu Guo
4-4 Continuous Distributions
We already learnt the discrete random variable and its distribution.
Y = the number of girls in 3 children family
y P(y)
0
1
2
3
ECO480 Econometrics 1
Class Note 10
Xu Guo
REVIEW
A very simple random sample (VSRS) is a sample whose n observations X1 , X2 , X3 , ., Xn are independent. Then the distribution of each
X is the popul
ECO480 Econometrics 1
Class Note 9
Xu Guo
Chapter 6 Sampling
6-1 Random sampling
A. The population
The word population has a very specific meaning in statistics. It is the total
collection of objects
ECO480 Econometrics 1
Class Note 11
Xu Guo
Chapter 7
7-1 Population and sample
Table 1. Review of Population versus Sample
Random sample is a random subset of the population
Relative frequencies f/n a
Companies, 2004
290 PART ONE: SINGLE-EQUATION REGRESSION MODELS
You are to consider the following model:
Yi =1+2X2t +3X3t +4X4t +5X5t +6X6t +ut
a.Estimate the preceding regression.
b.What are the expe