# Odd Ratio and logistic regression [duplicate]

Say, I am trying to predict likelihood to buy ice cream (event =1 , non-event = 0) using logistic regression.

I have only one variable "Gender" (2 value= Male/Female), so, the formula would be like this.

$logit(p)=β_0+β_1∗female$

Odd ratio for female with reference to $male (A) = \frac{odd(female)}{odd(male)}$

Next, I added in "TodayWeather" (2 $value = \frac{Sun}{Rain}$).

$logit(p)=β_0+β_1∗female+β_2*SUN$

Q1) Why does the Odd ratio for A with reference to male change? Shouldn't my Odd ratio for female still be the same as (A) above? Since it is still comparing female and male (i.e. the odd of female to buy ice cream if increase by one unit)?

Q2) Say (A) above is < 1, is it possible that once i added "TodayWeather", the odd ratio become > 1? Why?

## marked as duplicate by kjetil b halvorsen, Michael Chernick, jbowman, Stephan Kolassa, Peter Flom♦Nov 29 '17 at 11:35

• Your first $\beta_1$ may or may not the same as the second $\beta_1$ since your first $\beta_1$ might be confounded by SUN (the second variable), such as males are more exposed to SUN and expose to SUN may relate to your outcome variable, buying ice cream. You may read something on cofounding, I think. – Deep North Nov 28 '17 at 4:58