Data Lab

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Data Lab 8July 23, 2008

• Ivan Katchanovski, Ph.D.
• POL 242Y-Y

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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 UK1 All other
  values0
• Omitted from multiple regression
• Former French colony
• Recode into new variable France1 All other
  values0
• Former Spanish colony
• Recode into new variable Spain1 All other
  values0
• Other countries
• Recode into new variable UK, France, Spain0
  All other values1

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Example Dummy Independent Variables

• Protestant
• Recode into new variable Protestant1 All other
  values0
• Omitted from regression
• Roman Catholic
• Recode into new variable Catholic1 All other
  values0
• Muslim
• Recode into new variable Muslim1 All other
  values0
• Other
• Recode into new variable Protestant, Catholic,
  Muslim0 All other values1

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Table Determinants of democracy
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 N111
• .1 or 10 significance level can be used
• Regression coefficient of the GDP variable
• SPSS p(obtained).000 ltp(critical).001.1
• Statistically significant at the .001 or .1
  level
• Regression coefficient of the French colony
  variable
• SPSS p(obtained).014ltp(critical).05
• Statistically significant at the .05 or 5 level
• Regression coefficient of the Catholic country
  variable
• SPSS p(obtained).001ltp(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).025ltp(critical).05
• Statistically significant at the .05 or 5 level
• Regression coefficient of the Constant
• SPSS p(obtained).000ltp(critical).001
• Statistically significant at the .001 or .1
  level
• Regression coefficients of all other variables
• SPSS p(obtained) ranges from .634 to
  .902gtp(critical).1
• Statistically insignificant
• Statistical significance of the regression model
• SPSS p(obtained).000ltp(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