If you examine my post, Predicting Obama Victory in Each County with the Gini Coefficient, you will see a reader’s comment wondering if State Gini coefficients predict state presidential outcomes. After merging a couple files I have sufficient information to run a regression analysis to answer the reader’s question.
Before we look at the formal regression results let’s examine scatter plots of the two variables with a linear fit with the percent of votes President Obama received in each State with 95% confidence intervals displayed.
It appears that both variables are directly related to the percentage of votes President Obama received in each state. What happens when we simultaneously use these variables in a multiple regression to understand each variable’s influence on the election?
Here are the regression results of “percentage votes Obama received in each state” on the state’s Gini coefficient and the percent of the state’s population with a baccalaureate degree or more. (Recall, the Gini coefficient measures income inequality. The greater the Gini coefficient the higher the level of income inequality.)
It’s observed that the two independent variables, gini and bac_more, are statistically significant and reveal a direct direct relationship with the percentage of votes Obama received in state elections in 2012. The model is statistically significant (Prob > F = 0.000) and the model accounts for a surprising 57% of the variance in percentage votes received by the incumbent President.
As inequality increases, as measured by the Gini coefficient, Obama’s percent of favorable votes increases. After controlling for state level higher education attainment, a one unit increase in the State’s Gini coefficient is associated with a 1.22% increase in the percentage of votes favorable to President Obama
Likewise, the greater the percentage of people with a baccalaureate degree or more, the greater the percent of votes going to President Obama. A one unit increase in the percent of people in the state with a baccalaureate degree is associated with a 1.43 percent increase in Obama votes, after controlling for the effect of inequality.
So, yes, income inequality and educational attainment are important predictors of the 2012 presidential election.
You state these two variables are independent, I’m not so sure. Do you have a reference showing the cross-correlation analysis?
I used the term “independent variables” in the context of identifying the right-hand side of the regression equation. To answer your question about the correlation of two variables, the Pearson zero-order correlation is .24, meaning they share less than 6% of the variance. This is a low level of collinearity, meeting the assumption of ordinary least squares analysis. A high level of collinearity could cause the standard errors of the regression coefficients to be inflated. But that is not a problem in this analysis.