My data has three continuous predictors and one binary response. I built a logistic regression model but AUC is only 0.52..it's almost like the model did nothing.. Then I calculated the correlation between the response and predictor. The correlation are all very low, around 0.01, all less than 0.05. That is to say, the predictors and response are actually independent. My question is:
1.is it possible to get high AUC while the predictors and response are almost independent
2.Since my response is binary data 0/1, is the correlation a good measure on independence? If not, what is a better way to test independence?
Thank you everyone!