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” 2

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 3

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 4

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 5

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 6

Table: Determinants of democracy Unstandardized regression coefficients (Standard error) Standardized regression coefficients GDP per cap ($1000).199*** (.027).563 French colony-.885* (.353) Spanish colony.038 (.308).011 Other country.196 (.409).042 Catholic1.008** (.296).284 Muslim-.257 (1.300) Other religion.747* (.329).178 Constant3.660*** (.289) Adjusted R square.481 N111 7 *** Statistically significant at the.001 level, ** statistically significant at the.01 level, * statistically significant at the.05 level

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 8

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 9

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 10

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 11

Interpretation of Result s 12 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