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Lecture 16
Readings on Simple & Multiple Regression
Outliers
Interaction Effects
Presidential Popularity and Presidential Vote
by Lewis-Beck and Rice
They use Gallup presidential approval in the
last survey before the election to predict the
percent each incumbent president received
in his re-election bid in the 8 such elections
1940..1980.
The last poll before the election is held at
various times and may be affected by
proximity to the conventions and other
short term forces. So instead they use the
June poll which was possible for all but
1940 and 1944. These war elections may
have been unusual anyway since they are
FDR’s unprecedented 3rd & 4th term
elections.
The paper we just looked at was a very early
publication in this area. Predicting national
presidential vote outcomes has become a
cottage industry with a reasonable number of
scholars submitting their model and prediction of
the result before each election.
This is intrinsically an interesting topic and since
there are very few data points the models must
be kept quite simple with few independent
variables.
Here I’ll just give an example of one model for 2004 by Alan
Abramowitz
V=50.3 + .81*GDP+.113*NETAPP-4.7*TFC
V=predicted major party vote for incumbent party
GDP=growth rate of real gross domestic product during the
first two quarters of the year
NETAPP=incumbent president’s approval-disapproval in the
final Gallup Poll in June
TFC=0 of pres party has controlled the White House for one
term and 1 if two terms or more
The national economy also has an impact
on congressional elections.
Now let’s look at:
Economic Conditions and the Forgotten
Side of Congress: A Foray into US Senate
Elections
Hibbing & Alford
They wish to compare the impact of
economic conditions on the electoral
support for congressional candidates of
the president’s party.
Here they look separately at House and
Senate elections 1946—1980.
If one party is stronger than the other during
the period, we may misestimate the effect
of the economy on vote. When a control
for party is included the coefficient on the
economy is smaller than in the simple
bivariate regression. The coefficients are
still sig although now only at the .1 and .05
levels. The R square increases.
Now the authors change the dependent variable to
look at the percent of seats won by the
president’s party.
Here we see that the coefficient for the economy in
the Senate equation is much larger than in the
House equation.
For the Senate a 1% change in RPCI yields a
3.5% change in the proportion of seats. Or with
about 33 Senate elections in a year—one seat
difference.
For the House a 1% change yields less than half
that % change.
• For an updated model, we can examine
one by Gary Jacobson.
• For the House, he predicts the percentage
of seats gained or lost by the president’s
party.
• %seat change=
• -17.70-.76 Exposure+1.29 change in real
income per capita+.25 pres approval
• Adjusted Rsq=.70 N of elections=29
• Next we can take a look at the final
regression article by Gary Jacobson.
• The Effect of the AFL-CIO’s “Voter
Education” Campaigns on the 1996 House
Elections
Jacobson indicates that the Republican
takeover of the House in 1994 provoked a
swift response from labor.
• Outliers.
• We didn’t have time to cover the section
that dealt with outliers and non-linear
regression
• There is one article in that section that I
did want to mention. Earlier in the course
we read several articles on electoral
competitiveness. One of these was by
Jacobson.
• To refresh your memory, Jacobson argued that
marginals had not vanished. Although
incumbents were winning by larger margins,
vote margins were more variable and just about
as many incumbents were losing office as had
previously.
• Bauer and Hibbing update Jacobson’s data
adding the 1980s. They argue that incumbents
are safer. The 1970s are an outlier—an unusual
decade.
• The 1970s included Watergate, several
House scandals, and a major
redistricting.—altogether an atypical
decade.
• Jacobson’s conclusions rested on few
instances of actual incumbent defeats. A
longer time period provided a better
perspective.
Dummy Variables and Interactive
Terms
Conditional Relationships: Specification is another reason
to control for a third variable
c
a
b
Low
Ed.
High
Ed.
No
83%
70%
Yes
17%
30%
Worked for
Political Candidate
Men
No
Women
Low
Ed.
High
Ed.
75%
70%
Low
Ed.
High
Ed.
No
90%
70%
Yes
10%
30%
Worked
Worked
Yes
25%
30%
Small + Taub
Large + Taub
Relationship between education and working for a
candidate is positive for both men and women, but is
stronger for women than men.
• We haven’t talked about how to look at conditional
relationships with regression.
• We know from our earlier work, that better educated
constituencies are more likely to be represented by
women in the legislature.
• We could ask whether this relationship is stronger in the
South than in the rest of the US.
• Women are more likely to be elected outside the south.
Education might make more difference in the south.
• We could simply do one regression for the south and
another for the rest of the country.
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Linear Regression
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pctwch_1
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pctwch_1 = 0.11 + 0.00 * colleg_1
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R-Square
= 0.04
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0.20
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pctwch_1 = -0.02 + 0.01 * colleg_1
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R-Square
= 0.18
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0.10
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20.00
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colleg_1
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colleg_1
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35.00
• We can look at this by including 3
variables in our equation:
• South 0-1 (1=south)
• Pct college
• South * Pct college
Is the increase in slope in the
South statistically discernable?
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Model
1
Model Summary
R
.582a
R Square
.339
Adjusted
R Square
.318
Std. Error of
the Estimate
.07390
a. Predictors: (Constant), s outh, colleg_1, s_col
Coefficientsa
Model
1
(Constant)
colleg_1
s_col
south
Unstandardized
Coefficients
B
Std. Error
.110
.059
.004
.002
.002
.005
-.133
.112
a. Dependent Variable: pctwch_1
Standardized
Coefficients
Beta
.214
.225
-.658
t
1.842
1.971
.426
-1.189
Sig.
.069
.052
.671
.237
• % w=.11-.133*south+.004*coll+.002*S_c.
• So for the non-south, south=0 and the
equation simplifies to:
• Predicted pct women=.11+.004*college
• In the south, predicted percent of women =
(.11-.133)+(.004+.002)*college
This yields the same two lines we saw in the
scatterplot, but it allows us to test the
hypotheses that the intercept and slope
are different