Logistic regression 2 x 2 table equivalent for continuous covariate

Question

I am giving a talk about logistic regression and I am trying to go back to basics with explaining what odds are in the context of model estimation using logodds and calculation of probabilities which is what one is ultimately wanting with a logistic model.

I can explain the concept of odds (and odds ratio) simply enough for the case of the binary outcome with a single binary predictor. But, is there a way to reduce the case of the continuous covariate to a 2 x 2 table as well? i.e. I might be missing something simple but I can't intuit what are the odds of an outcome for a specific value of a continuous covariate. It's not the number of observations above that value with the outcome vs the number below with the outcome, is it? (i.e. where you consider that value a threshold).

Would appreciate any tips for how I might be able to explain this.

Answer 1

I have such examples worked out in https://hbiostat.org/rmsc/lrm . The approach is used only for explanation, as binning of a continuous variable is a terrible idea.