More on Deriving Odds Ratios

From Applied Logistic Regression, 2nd Edition. Hosmer and Lemeshaw.

This is why you can exponentiate the co-efficients from logistic regression to derive the odds ratio- note we start out with calculating the odds given X =1 and divide that by the odds given X = 0  for exp( Bo + B1X ). See logistic regression and the calculation and interpretation of odds ratios  and analysis of the logistic function for more details.