need to know the diff between null and alt (1 vs 2 sided)
omitted (bias, decreases SE) vs irrelevant variable (no bias, increases SE)
expected bias = b omitted * alpha omitted
when to keep an x, theory, the t score, bias, r^2
log n ln
ln is the natural lo
ECONOMETRICS COMPREHENSIVE EXAM STUDY GUIDE FOR PART I This portion of the exam will consist of six multi-part questions that will be similar in format to the questions from the midterm and final exams, but shorter: 1) Definitions 2) Short answer 3) Math
ECONOMETRICS TOPICS
Chapter 1: An Overview of Regression Analysis
What is econometrics?
Econometrics: economic measurement
Uses of econometrics:
1. Describing economic reality
2. Testing hypothesis about economic theory
3. Forecasting future economic acti
Econ 081
Introductory Statistics
22
Confidence intervals and
necessary sample size
Recall: The 95% confidence interval
z(.025) = 1.96
Translation: The z-score corresponding to 2.5% of
area in the upper tail is 1.96 (for 2.5% of area in lower tail,
z = -1.
Econ 081
Introductory Statistics
30
Two-sample hypothesis
tests: t-tests and F-tests
Review: Testing hypotheses about variance
in one sample
The chi-square distribution
A family of distributions: one curve for each level of n
Mean of the distribution equa
Econ081
Introductory Statistics
17
The normal distribution
The normal distribution
Also known as the Gaussian distribution
Defined completely by two parameters: m and s
Not defined by some clearly defined process
Denoted N(m, s)
Domain is < X < +
Area un
Econ 081
Introductory Statistics
20
Sampling distributions II:
Making inferences
Recall: The SDSM is the
sampling distribution of the sample
mean
Because the makeup of a random sample is random, the
sample mean is itself a random variable.
Every random va
Econ 081
Introductory Statistics
31
Analysis of variance
(ANOVA)
Example: Airbag inflation times
The first-generation airbag was designed to have an average inflation time of
50 milliseconds, and a standard deviation of 12 milliseconds.
If it inflates too
Econ 081
Introductory Statistics
34
Linear correlation
and the
line of best fit
Recall: Mystery process
The linear relationship generator as a
?
black box: x
y
Linear relationship generator can do several things:
It can output some constant value (an inte
Econ 081
Introductory Statistics
35a
Linear correlation
and the
line of best fit
Recall: Mystery process
The linear relationship generator as a
?
black box: x
y
Linear relationship generator can do several things:
It can output some constant value (an int
Econ 081
Introductory Statistics
33 ANOVA and linear
correlation
Recall: ANOVA
Sometimes we want to test the equality of more than
one mean:
Want to test whether 1 = 2 = 3
We use analysis of variance (ANOVA)
ANOVA is a way to test your hypothesis without
Econ 081
Introductory Statistics
4
Visual depictions of data
Copyright Eirik
Graphs
Visual depictions of data
Many ways to depict data visually
I found all of the following examples on
Google Images.
Copyright Eirik
A very
famous
graph
(known as a
coxco
Chapter2:Data5
Statistics is the science of data so lets start with the terms we use to describe data.
Individuals are the objects described by sets of data. These individuals may or may not
be people. They can also be called respondents, subjects, cases,
Econ 081
Introductory Statistics
39
Linear correlation
revisited
(c) Eirik Evenhouse. Not for distribution outside this course.
2
Recall: linear correlation coefficient
r = cov(x,y) / xy
= E [(X-x)(Y-y)] / xy
= SS(xy) / sqrt [ SS(x) SS(y) ]
(c) Eirik Even
Econ 081
Introductory Statistics
19
Sampling distribution
Flight time example from last lecture
Using the same distribution of flight times
(mean=8 hours and s.d.=1.2 hours), what
fraction of flights are going to be longer than 7
hours but shorter than 8.
Econ 081
Introductory Statistics
11
Discrete distributions
Combining dependent and independent
events in a problem
Two issues: Is the product good? and Did the inspector make a
mistake?
Define 4 events:
Product is good (G)
Product is defective (D)
Inspect
Econ 081
Introductory Statistics
16
Discrete distributions, II
Recall: Binomial distribution
What is a Bernoulli process?
What parameters describe the process?
What is X (the random variable)?
What is the use of the binomial
distribution?
(c) Eirik Evenho
Lecture 1: The Classical Linear Regression Model
(Hayashi, pp. 3-14)
1. Fundamental concepts: Data, Models, Estimation Procedures
2. The Classical Linear Regression Model and OLS: Overview
3. The Classical Linear Regression Model: Details
2
1. Fundamental
Econometrics
A Summary
The Joint Distribution
The joint distribution of discrete RVs X and Y is the
probability that the two RVs simultaneously take on certain
values, say x and y: That is, Pr(X = x, Y = y), like a cross-tab.
Example: weather and commut
Political Economy Group Stanford GSB
Econometrics Qualifying Exam Review Sheet
August 2012
Relevant textbooks: for probability and statistics, DeGroot and Schervish or Casella and
Berger; for linear models and time series, Amemiya, Hayashi, Greene, Wooldr
The simple linear Regression Model
Correlation coefficient is non-parametric and just indicates that two
variables are associated with one another, but it does not give any
ideas of the kind of relationship.
Regression models help investigating bivariat
Study Guide for Econometrics
Unit 1: Ordinary Least Squares Regression
OLS Model: yi = 1 + 2 x2i + 3 x3i + + k xki + e i (Wooldridge 2.1)
(Univariate: yi = 1 + 2 xi + e i )
Econometric model: yi = 1 + 2 x2i + + ki xki , e i = yi yi ; yi = 1 + 2 x2i + + ki
Economics 210 Econometrics Handout # III
The Classical Linear Regression Model
The Classical Linear Regression Model
We make the following assumptions. ( Gujarati pg 65-75): 1. 2. The model is linear in parameters. The explanatory variables are non-stocha
ECONOMETRICS
Bruce E. Hansen
c
2000, 20141
University of Wisconsin
Department of Economics
This Revision: January 3, 2014
Comments Welcome
1
This manuscript may be printed and reproduced for individual or instructional use, but may not be
printed for comm
Econ 81
Statistics
8
Probability
Z-score: Practice problem 1
You know what a z-score (or standard score) is
You know the Empirical Rule
Check your understanding: Street-crossing problem.
Average crossing time: 12.5 seconds. Std deviation in
crossing times
Econ 81
Statistics
10
Probability II
What defines a probability?
A necessary property:
0 P(A) 1
Another necessary property: P(A)=1
Ex: Is the following function a probability
function?
P(x) = x/10
for x=1,2,3,4
Ex: And the following?
(c) Eirik Evenhouse.
Econ 81
Statistics
7
Measures of position
Review
In Excel, you now know how to compute:
Measures of central tendency:
Unweighted mean
Median
Weighted mean
Measures of dispersion:
Variance
(c) Eirik Evenhouse. Not
2
When do you need a weighted
average?
Whe
Econ 81
Intro Statistics
5
Describing a distribution
with numbers
Eirik Evenhouse
Review
A histogram is a _bar_ graph that depicts the
frequency _distribution_ of a _
variable.
What is the difference between a frequency histogram
and a relative frequency
Introduction to Statistics
Econ 081
2
Overview and basic
terminology
Eirik Evenhouse
What is statistics?
What is the point of statistics?
Using reliable data to reach unreliable
conclusions ( how you interrupt the data)
Why make decisions with incomplete