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
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
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
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
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)
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
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
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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
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
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
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
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
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
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- )/ ~
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