15. Multiple Regression

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15. Multiple Regression
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• How do we actually request the regressions in
  SPSS?
• How do we use regression to explicate a bivariate
  relationship with a third variable?
• What do we look for once we have run the relevant
  regressions?

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Example of Simple and Multiple Regression
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DV (Effect)
IV (Cause)
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SPSS OutputPart 1 First Part Shown
Multiple R
R Squared Percent Variance Explained (0.49
0.49)
Corrects for small n
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SPSS OutputPart 2 ANOVA
Well ignore this part
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SPSS OutputPart 3 The Coefficients
Almost all of this is important. Here we show
one Independent variable.
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SPSS OutputPart 3(i) The Coefficents - B

• B is shown for each independent variable and the
  constant.

• B for books is the increase in grade when you
  read one more book
• Constant is the estimated grade when you read no
  (0) books.

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Prediction Equation

• Estimating the DV
• OR

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Add a Line
80 60 40 20





Here we can draw the line for the
Equation. These are the predicted Valuesor
best fit line.
0 1 2 3 4
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SPSS OutputPart 3 The Coefficients
Sig. tests the null hypotheses that B is equal to
0. This is a two-tail test. For directional
hypotheses, Divide by 2 to get the sig. level.
Two-tail--the B for BOOKs is sig. at the .001
level--about one in 1/000 times would we observe
a B as large or if there were no relationship
Between BOOKS and grades.
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• Most of these previous 8 slides were adapted from
  Jeremy Miles notes on line.
• Now lets look at explicating a bivariate
  relationship with a third variable.

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Explicating a bivariate relationship with a third
variable

• A misspecified relationship is when the magnitude
  or direction of the relationship you observe
  between a and b is not due to a causing b, but to
  c partly or wholly causing both a and b. When
  you control for c the relationship between a and
  b changes in magnitude or direction.

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• Suppose we hypothesize that respondents affect
  for Clinton (thermometer score) causes their
  affect for Gore (thermometer score).
• But we wish to consider the alternative
  explanation that partisanship is a cause of both.
  By ignoring the effect of partisanship on both
  we can overestimate the effect of feelings
  towards Clinton impacting feelings towards Gore

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• Here we might find

Here we would have overestimated the impact of C
on G. C does cause G, but controlling for P we
realize the effect is less than we initially
thought.
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• So yes we did overestimate the effect of Clinton
  on Gores thermometer score, but the effect of
  Clinton on Gore is still quite substantial, and
  statistically sig. at the .01 level.
• The coefficient on Clinton is reduced from .689
  to .560.
• The first equation G.689 C 17.489 becomes G
  .560 C 8.575 P 40.952.
• Note what assumption was I making about party
  id to have included it in this equation when I
  used party3? (R3, I2, D1).
• What would you predict G to be for a Dem who
  rated Clinton at 60?

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• G .560 C 8.575 P 40.952.
• What would you predict G to be for a Dem (P1)
  who rated Clinton at 60?
• G.560 60 8.575 1 40.952.
• G66
• For an Independent, G57
• For a Republican, G49

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Now we might also have started by examining the
effect of partisanship on Gores thermometer
score and then asking whether Clintons score was
an intervening variable.
G
P causes G. All or some of the way P causes G is
through C.
Gore
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• Most, but not all, of the impact of party on
  Gores thermometer score is due to Clintons
  score. Perception of Clinton mostly explains the
  way in which party affects perception of Gore
• Remember party is still the cause, we are looking
  at the mechanism.

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• Now there is a danger that there is a reciprocal
  relationship. Perhaps Gore also causes
  perception of Clinton. We are assuming that
  perception of Clinton is more important and
  dominant in this relationship. A simple
  correlation doesnt give us the answerwe are
  making an assumption.

This we dont think this
C
G
But rather this
C
G
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3D Relationship
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3D Linear Relationship
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Multiple Causes (Enhancement) Two variables may
be causes of a third variable, while the two are
unrelated to each other. Turning to the
legislative data set Suppose we think that
states with higher levels of average education
are more likely to elect women to the state
legislature either because more women are likely
to run or because electorates are more likely to
vote for the ones that do. Suppose you also
hypothesize that women are more likely to be
elected to lower rather than upper chambers.
E college ed in state Cchamber
(2upper)(1lower) W women in chamber
0

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Now lets look at the correlations among these
three variables

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• Now lets look at a misspecified relationship

Here we would thought that professionalization
(P) had no effect on the percent of women in the
chamber (W). But when we control for South (S)
we see that there may be an effect of prof that
was concealed because of the relationship
Southern state region and both P and W.
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First I computed a var for southern
statecompute south0.if (state eq 'AL' or
state eq 'AR' or state eq 'FL' or state eq 'GA'
or state eq 'KY or state eq 'LA' or state eq
'MS' or state eq 'NC' or state eq 'OK' or state
eq 'SC' or state eq 'TN' or state eq 'TX' or
state eq 'VA')south1.
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