Is a binary logistic regression the best approach when I have a count predictor and a binary outcome? Can I apply a multiple binary logistic regression model if I have more than 1 predictor that is a count variable?
Additionally, what kind of correlation can I run if one variable is count and the other is binary?
Per your questions...
Is a binary logistic regression the best approach when I have a count predictor and a binary outcome?
Yes. Logistic regression handles any linear equation which requires the outcome to be binary. The types of predictors don't necessarily matter.
Can I apply a multiple binary logistic regression model if I have more than 1 predictor that is a count variable?
Yes. Just like standard regressions, you can include multiple predictors. The type of predictor is, again, not important.
Additionally, what kind of correlation can I run if one variable is count and the other is binary?
Typically the point-biserial correlation is used when one variable is binary and another is continuous/discrete.
Is a binary logistic regression the best approach when I have a count predictor and a binary outcome?
It is certainly one valid approach, probably the most common one. Is it "best"? That depends on your particular situation and what your goals are. You might also consider a classification tree (or one of the offshoots of trees), especially if you have a bunch of predictors, which your next question implies that you do.
(For your other two questions, I agree completely with Shawn's answer).
