Transcript July 23

Data Lab #8
July 23, 2008
Ivan Katchanovski, Ph.D.
POL 242Y-Y
Multiple Regression: SPSS Commands
• SPSS Command: Analyze-Regression-Linear
• “Dependent” box: Select the dependent
variable
• “Independent” box: Select independent
variables
• Method: “Enter”
• Statistics:
– “Estimates” of “Regression Coefficients”
– “Model fit”
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Example: Multiple Research
Hypotheses
• First Research Hypothesis: The level of economic
development has a positive effect on the level of
democracy
• Second Research Hypothesis: Former British colonies
are more likely to be democratic compared to other
countries
• Third Research Hypothesis: Protestant countries are
more likely to be democratic compared to other
countries
• Dataset: World
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Example: Variables
• Dependent Variable:
– Freedom House democracy rating reversed:
• Interval-ratio
• Independent Variables:
– GDP per capita ($1000)
• Interval-ratio
• Colony variable
– Nominal
– Has to be transformed into dummy variables
• Religious culture variable
– Nominal
– Has to be transformed into dummy variables
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Example: Dummy Independent Variables
• Former British colony
– Recode into new variable: UK=1; All other values=0
– Omitted from multiple regression
• Former French colony
– Recode into new variable: France=1; All other values=0
• Former Spanish colony
– Recode into new variable: Spain=1; All other values=0
•
Other countries
– Recode into new variable: UK, France, Spain=0; All other
values=1
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Example: Dummy Independent Variables
• Protestant
– Recode into new variable: Protestant=1; All other values=0
– Omitted from regression
• Roman Catholic
– Recode into new variable: Catholic=1; All other values=0
• Muslim
– Recode into new variable: Muslim=1; All other values=0
•
Other
– Recode into new variable: Protestant, Catholic, Muslim=0;
All other values=1
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Table: Determinants of democracy
GDP per cap ($1000)
French colony
Spanish colony
Other country
Catholic
Muslim
Other religion
Constant
Adjusted R square
N
Unstandardized regression
coefficients (Standard error)
.199***
(.027)
-.885*
(.353)
.038
(.308)
.196
(.409)
1.008**
(.296)
-.257
(1.300)
.747*
(.329)
3.660***
(.289)
.481
Standardized regression
coefficients
.563
-.204
.011
.042
.284
-.014
.178
111
*** Statistically significant at the .001 level, ** statistically significant at the .01 level, *
statistically significant at the .05 level
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Example: Statistical Significance
• Number of cases: N=111
• .1 or 10% significance level can be used
• Regression coefficient of the GDP variable:
• SPSS: p(obtained)=.000 <p(critical)=.001=.1%
• Statistically significant at the .001 or .1% level
• Regression coefficient of the French colony variable:
• SPSS: p(obtained)=.014<p(critical)=.05
• Statistically significant at the .05 or 5% level
• Regression coefficient of the Catholic country variable:
• SPSS: p(obtained)=.001<p(critical)=.01
• Statistically significant at the .01 or 1% level
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Example: Statistical Significance
• Regression coefficient of the Other religion variable:
• SPSS: p(obtained)=.025<p(critical)=.05
• Statistically significant at the .05 or 5% level
• Regression coefficient of the Constant:
• SPSS: p(obtained)=.000<p(critical)=.001
• Statistically significant at the .001 or .1% level
– Regression coefficients of all other variables:
• SPSS: p(obtained) ranges from .634 to .902>p(critical)=.1
• Statistically insignificant
– Statistical significance of the regression model:
• SPSS: p(obtained).000<p(critical)=.001
• Statistically significant at the .001 or .1% level
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Example: Interpretation of Unstandardized
Regression Coefficients
• GDP per capita variable:
– Increase of $1000 in the GDP per capita increases the democracy score
on a scale from 1 to 7 by .199 units keeping other variables constant
• French colony variable:
• The average former French colony has democracy score which is .885
units smaller compared to the average former British colony keeping
other variables constant
• Catholic country variable:
– The average Catholic country has democracy score which is about
1unit higher compared to the average Protestant country keeping other
variables constant
• Other religion variable:
– The average Other religion country has democracy score which is .747
units higher compared to the average Protestant country keeping other
variables constant
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Example: Interpretation
• Standardized Regression Coefficient of GDP per
capita variable=.563
– The absolute value much higher compared to other
variables
• GDP per capita variable has the biggest effect on the
level of democracy
– Effects of the colonial dummy variables and religious
dummy variables are much smaller
• Adjusted R square=.481
• GDP per capita, colonial dummy variables, and religious
dummy variables explain about 48% of variation in the
Freedom House democracy scale
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Interpretation of Results
• The first research hypothesis is supported by multiple
regression analysis
• The level of economic development has a positive and
statistically significant effect on democracy
• The second research hypothesis is partly supported by
multiple regression analysis
• The former British colonies have higher levels of democracy
compared to former French colonies
• The third research hypothesis is not supported by
multiple regression analysis
• Protestant countries do not have higher levels of democracy
compared to other countries keeping other variables constant
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