Political Science 328
Introduction
Political Science 328
Purpose
Test causal theories
Lots of methods:
Statistics
Experiments
Case studies
All have strengths and weaknesses
328 will help us learn one tool for analyzing
politics
This tool is also

Confidence Intervals for the
Population Mean
Political Science 328
The Logic of a Confidence Interval
We usually do not know population mean
We usually have a sample and wish to make inferences
about the population
Impossible to learn the exact value o

Brief Review
We are trying to learn the essentials for regression:
Measure of centrality: Regression is a type of
conditional mean.
Measure of spread: How close is any observation to the
regression line?
Normal distributions: How likely is that we woul

Exact vs. Approximate
Sampling Distribution
If distribution of is not normal, exact sampling
distribution is difficult
With large sample size, and use sample
approximation (asymptotic distribution):
Approximations become exact in the limit that
Good f

Probability
Political Science 328
Why do we need to know
probability?
We want to distinguish random variation (i.e.
chance) from systematic variation.
Class example: Did you vote in 2012?
What do we do first?
Main point from last class.
0
10
Frequency
20

Simple Linear Regression
Political Science 328
Covariance
A Measure of the extent to which two random variables
move together.
Dispersion
Variance
Relationship
Covariance
Calculating the Covariance
Population covariance:
= cov , =
=
If discrete:
=1

Multiple Linear Regression:
Hypothesis Tests
& Confidence Intervals
Political Science 328
Multiple Regression Assumptions
Why do we have regression assumptions?
= 0 + 1 1 + 2 2 + + + , = 1, ,
1. The conditional distribution of given the s has
mean zero,

Multiple Linear Regression
Political Science 328
Class Objectives
Causality and regression analysis
Omitted variable bias
Multiple regression and OLS
Measures of fit
Causal Relationships
What produces democracy?
How does the effect occur?
What leads

Intuition Behind Sign of Slope
=1
1 =
=1 2
Vote Share
With a neighbor:
Using the least squares
slope equation, figure out
what makes the slope
positive or negative
Y
X
Campaign
Spending
How Do We Evaluate Statistical Models?
A natural question is how w

What do
2
2 tell us?
and
A high 2 (or 2 ) means that the regressors explain
the variation in Y.
A high 2 (or 2 ) does not mean that you have
eliminated omitted variable bias.
A high 2 (or 2 ) does not mean that you have an
unbiased estimator of a causal

Multiple Linear Regression:
Extensions
Political Science 328
Homoskedasticity vs. Heteroskedasticity
What do these two terms mean?
If var(| = ) is constant, then is said to be
homoskedastic.
Otherwise, is said to be heteroskedastic.
Homoskedasticity in