Suggested answers, Problem Set 1
ECON 375
1. (See page 2 of the statistics handout)
The probability the tire will fail after 30 thousand miles is the Pr(x>30) which is evaluated as one minus the
CDF or 1-Pr(x30)=1-F(30).
From the handout, we know that the
Problem Set 3, ECO375
(Due at the start of class, Monday, October 12th)
[Must show all work for credit. For STATA work, include a print out of the answer and do file of commands used.]
1.
Consider a multivariate regression model of the form yi = 0 + x1i 1
Suggested Answers, Problem Set 2
ECO375
n
1.
1 =
( y y )( x x )
i
i
i =1
n
(x x )
=
2
18
= 0.05
360
0 = y x 1 = 6 14(0.05) = 5.3
i
i =1
R2 = 1
SSE
, SSE = 12
SSTy
n
SSTy = ( yi y ) 2 = 13 so R 2 = 1
i =1
2.
12
= 0.077
13
In class, we demonstrated that
ECON 375: Introduction to Econometrics Spring 2010
Problem Set 1 Due: April 12, 2010
NOTE: All assignments must be typed if you can not write it legibly. Graphs and calculations may be handwritten. No late homework will be accepted.
Exercise 1 (10 Points)
Econ 375 Study Problems
Burhan Biner January 25, 2010 You can have a cheat sheet for the midterm exam. Please write whatever you deem necessary on both sides of an A4 paper. I am going to list a few problems that might be helpful for the exam. Mind you, y
Some important properties of summations
ECON 375
Definition: The summation sign () adds up a series of numbers
Suppose there is a sample with n observations and two variables (xi and yi). Then
n
x
i
= x1 + x 2 + x3 + x n
i =1
We can represent sample means
How to Interpret Regression Coefficients
ECO375
How one interprets the coefficients in regression models will be a function of how the dependent (y) and
independent (x) variables are measured. In general, there are three main types of variables used in
ec
The Multivariate Regression
Model
1
Example 1
Determinants of College GPA
Sample of 141 Freshman
Collect data on College GPA (4.0 scale)
Look at importance of ACT
Consider the following model
CGPAi 0 ACTi 1 i
2
ACT
4 tests
English/math/reading/science r
Moving from Correlation
to Causation
1
Statistics Emphasizes
The properties of random variables
Given some known distribution
For example, what is the probability of getting exactly
(k=)4 heads if you flip a fair coin (n=)10 times?
=
What if we wanted
Notes on Assumptions of
ECO375
1.
E [i ] = E [i | xi ] = 0
From this we showed that [remember (1) always conditioning on xi and (2) i and xi are independent.]
E [i xi ] = E [i xi | xi ] = xi E [i | xi ] = E [i ] = 0
That allows us to look at the relation
Why Econometrics?
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What Statistics do I need for ECO 375?
(Use Appendix B and Appendix C of the textbook for additional reference.)
Random variables are variables whose outcome is determined in part by chance. There are two types of random variables
Discrete a countable num
Correction for Variance of 1
ECO375
Let's start from the beginning.
"
Var 1 = E $ 1 E 1
#
( )
(
2
%
( ) '
&
Remember the definition for 1
n
1 = 1 +
( x x )
i
i
i=1
n
( x x )
2
i
i=1
n
1 1 =
( x x )
i
i
i=1
n
( x x )
2
i
i=1
This can be substituted bac
Problem Set 1
ECON 375
Due at the start of class, Wednesday, September 16th
1.
Suppose the distance (in thousands of miles) until a tire fails (x) can be described by the exponential
distribution, f(x) = e-x, for >0 and x>0. Suppose =0.025 and the tire is
Problem Set 2 ECO375
(Due by the start of class, Monday, October 5, 2015)
[Must show all work for credit. For STATA work, include a print out of the answer and do file of commands used.]
1.
Suppose a researcher is interested in estimating the linear regre
Tests of multiple parameters
F-Tests
1
Null hypothesis
Model
yi= 0+x1i 1+x2i 2+x3i 3+xki k+i
Ho: 1= 2= 3= .q=0
Subset of the parameters all equal zero
q restrictions in total (count the equal signs)
2
3
And two more definitions
(Chi) 2 Distribution
A
Hypothesis tests for one
parameter
1
Few more definitions
Standard normal distribution
zi ~ N(0,1)
Normal distribution
yi ~ N(, 2)
Normal can always be turned into a standard
normal by subtracting mean and dividing by
standard deviation
zi = (yi- )/ ~
Problem Set 4, ECO375
(Due at the start of class, Monday, November 2, 2015)
1.
To test a set of q restrictions in a linear regression model, we use the F-statistic
which is constructed as
( SSEr SSEu ) / q
F=
SSEu / (n k 1)
Show that the test statistic c
ECON 375: Introduction to Econometrics Spring 2010
Problem Set 2 Due: April 29, 2010, 9:00PM
NOTE: All assignments must be typed if you can not write it legibly. Graphs and calculations may be handwritten. No late homework will be accepted.
Exercise 1 (10
ECON 375 SAMPLE MIDTERM EXAM, MAY 03, SPRING 2010
Name
ID
90 Minutes Instructions: 1. This is a closed book exam. 2. You are allowed to have a cheat sheet. 3. Please show all your work. 4. Fully label all graphs.
Good Luck
1
(1) (20 points) In a given pop