Interprete estimates of model with two categorical independent variables in binomial regression (GLM) I use R for a binomial regression (GLM) to test for a difference in whether people voted (coded as 0/1) in an election based on race (6 categories) and religion (3 categories), see structure of dataset and output below.
Structure of dataset:

GLM Binomial regression:

ANOVA - Test predictors relative to the full model:


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*How can I understand the estimate of the intercept of this model since the model contains two categorical independent variables? Does the estimate for the intercept somehow represent both the first categories for both variable (Religion: catholic; Race: Asian)? How can I understand the P-value of the intercept?


*As I run an ANOVA for the model both categorical variables render statistically significant P-values but the summary of the regression does only show statistically significant P-values for Religion. How can I understand the result of the ANOVA? Does it provide anything in terms of understanding the relationship between voting behavior and the two categorical variables?
 A: 
How can I understand the estimate of the intercept of this model since the model contains two categorical independent variables? Does the estimate for the intercept somehow represent both the first categories for both variable (Religion: catholic; Race: white)? How can I understand the P-value of the intercept?

The intercept includes the reference level of both of the variables, so that will be the level of each variable that does not have it's own estimate. The reference level for Religion appears to be catholic - but there isn't enough info provided to see what the reference level for Race is.

As I run an ANOVA for the model both categorical variables render statistically significant P-values but the summary of the regression does only show statistically significant P-values for Religion. How can I understand the result of the ANOVA? Does it provide anything in terms of understanding the relationship between voting behavior and the two categorical variables?

The ANOVA tests are for the whole variables, whereas the tests in the lm() summary output are for individual levels of each variable compared to the reference level for that variable. So you can't really comapare them.
