Transcript Political Research and Statistics

Multivariate Regression
11/15/2012
Readings
• Chapter 8 Correlation and Linear Regression (Pollock)
(pp 187-199)
• Chapter 9 Dummy Variables and Interaction Effects
(Pollock Workbook)
Homework and Paper
• Due 11/19- Paper Proposal
OPPORTUNITIES TO DISCUSS
COURSE CONTENT
Office Hours For the Week
• When
– Friday 10-11
– Monday 11-12:15
– Tuesday 9-12
Course Learning Objectives
• Students will be able to interpret and explain
empirical data.
• As this course fulfills the Computational Skills
portion of the University degree plan,
students will achieve competency in
conducting statistical data analysis using the
SPSS software program.
Ratio and Intervals!
REGRESSION ANALYSIS
Bivariate Linear Regression
• Bivariate linear regression is an important
statistical technique in the Social Sciences. It
allows us to measure the effects of an
independent variable on a dependent
variable.
• It regresses all the values on to a line that best
describes the relationship.
Rules for Regression
• If you have a Ratio/Interval Dependent
variable that takes on at least 11 values
• You need ratio level independent variables
(some argue that you can use ordinals, but be
careful)
• If you have 30 or more cases (N>30)
• If you have a linear relationship. It will not
work with curvilinear or exponential
relationships.
The Regression Equation!
The
Dependent
Variable
The Constant, where
the line crosses the
y-axis
The
independent
variable
The Slope
and
direction of
the line
The Output
The Constant (Alpha)
• Value is 42.435
• This is the value of the d.v. if the iv is zero
Betas and Independent variables
• this tells us how much change in the dependent variable, is
explained by the independent variable.
• Every increase in religious attendance causes the d.v to move
by .470
• Do we have a positive or negative relationship?
Is it a significant Relationship (TStatistic)
• This gives us a T-Statistic that tells us if we can
reject the null hypothesis.
• You look at the significance value to check to
see if there is a relationship. The magic
number for significance is .05 to reject the null
and say there is a relationship!
• Sig<.05, the independent variable is
significant!
One More
• % without health insurance (DV)
• Unemployment rate (IV)
Cars of the 1970’s
• Lets all try one out with
the Cars database
• Run a regression
MULTIPLE REGRESSION
What we can do with it
• Test the significance, strength and direction of
more than one independent variable on the
dependent variable, while controlling for the
other independent variables.
• We can compare the strength of each
independent variable against each other
• We can examine an entire model at one time!
The Model
• Y is the dependent variable
• a is the constant
• b1x1- first beta coefficient and first
independent variable
• b2x2- Second beta coefficient and Second
independent variable
This allows us to model additive
relationships
Computing a Multiple regression
• You put more than one
independent variable
where you say
"independents“
• D.V. Women09 (% of
women in parliament)
– IV1- womenyear2 (date
of enfranchisement)
– IV2- pr-sys (pr system)
– IV3- pmat12_3
(postmaterialism)
Regression Outputs
• These have 3 parts
1. The Model Summary
2. ANOVA
3. The Variables/Model
Part I
THINGS THAT BEGIN WITH “R”
With So Many, How do we know?
• There are many R's out there:
– lower case "r" for correlation
– upper case "R" for regression
Correlation (small r)
• r- the pearson’s product
movement
• r2- The squared pearson
correlation coefficient.
The R-Square (large R)
• this is a measure of
association for the entire
model
• This is a PRE measure that
tells us what percent of the
total variation in the
dependent variable is
explained by our model.
• The higher the number, the
better our model predicts.
• We can increase the R value
of our model, by increasing
the number of variables,
even insignificant ones!
Adjusted R-Square
• this "adjusts" for the
addition of independent
variables. In equations
with more than 1
independent variable, it
will always be smaller
than the R Square.
• This is the preferred
measure and a PRE
model
What the R’s look like
The R Square
Adj R-Square
Part II
THE ANALYSIS OF VARIANCE
(ANOVA)
ANOVA
• A Way of testing the null hypothesis for the
entire model- We Look at the F-Score
• H0 = that there is not relationship between
our variables and the dependent variable
• HA = There is at least 1 significant variable in
the model
What The F-Score tells us
• It is like a chi-square for
Regression. The F-score tells
us if we have a significant
regression model
• If the F-Score is not significant,
we accept the null hypothesis
(no relationship).
• It usually tells us at least one
of our variables is significant.
• It is a way of examining the
entire regression.
The F-Score
• We look at the Sig value and use the p<.05
measurement
• In the model above, our p value is .001
– We Reject the null hypothesis
– At least one variable is significant
Part III
THE MODEL
The Model
• What it tells us
– Variable relationships and direction
– Variable significance
– Variable Strength
Old Friends
Beta Values
• Measure the change in the
dependent variable
• Show the direction of the
relationship
T-Tests
• Test the significance of each
independent variable on the
dependent variable
• Accept or reject the null for
that variable
Standardized Beta Coefficients
• They show us the
variables which have
the greatest influence.
• These are measured in
absolute value
• The larger the
standardized beta, the
more influence it has on
the dependent variable.
Looking at our Model
Beta Values
T-ScoreSignificance
TRYING IT OUT
Texas Poverty
• Data
•
http://myweb.stedwards.edu/brianws/3328fa12/texas3.sav
• Dependent Variable
– POORKIDS Child Poverty in
254 Texas Counties
• Independent Variables– MANUFACT % of earnings
from manufacturing,
– COLGRAD percent of those
25 or older with college
degree
– HISPPER Hispanic percent
– BLACKPER black percent
Another One
• D.V. Palin_therm-post
(Feeling thermometer for
Palin 0-100)
• IV's
– enviro_jobs (Environment
vs. jobs tradeoff) 0=envir,
1=middle, 2=jobs
– educ_r- education in years
– Gunown- do you own a
gun (1=yes, 5=no)
– relig_bible_word (Is Bible
actual word of God?)
1=yes, 0=No
Another one from the states
• Gay Rights involves many concepts. The Lax-Phillips index
uses content validity to address this issue at the state level.
It examines the support for the following issues
–
–
–
–
–
–
–
–
–
Adoption
Hate Crimes legislation
Health Benefits
Housing Discrimination
Job Discrimination
Marriage Laws
Sodomy Laws
Civil Unions
It then averages these to get a statewide level
State Example
• Dependent Variablegay_support (higher is
more supportive on LaxPhillips)
• Independent Variables
– relig_import (% of people
in state that say religion
provides a great deal of
guidance)
– south (1=south, 0=
NonSouth
– abortlaw (restrictions on
abortion)