# Logistic regression coefficients and exp(coefficients) meaning and relationship

Suppose that we have this output for Logistic Regression:

     Coef   EXP(Coef)
X1   2.45     11.67
X2   0.40     1.449
X3  -4.1401   0.0159


Here X3 has highest absolute Coefficient value but lowest EXP(coef) values.

• If we want ranking these variables based on importance we should rank based on Coef or EXP(Coef)?

• As we can see all Exp(Coef) are positive. How we can consider negative coefs here?

For the second question, "EXP(Coef)", i.e., (estimated) odds ratio, is of course always positive regardless the "Coef" is positive or negative. However, if "Coef" is negative, then "EXP(Coef)" is between $(0, 1)$, representing the response and covariate is partially negatively correlated. As above, when viewing it, you should compare it with 1 (instead of 0) to assess the covariate's effect. For example, 0.0159 should be considered a very strong association, as $1/0.0159 = 62.89$ is way bigger than 1.