StatsModel Logistic Regression I am running a fairly simple Logistic Regression model y= (1[Positive Savings] ,0]) X = (1[Treated Group],0)
 I got a coefficient of Treated -.64 and OR of .52. 
My question is how to interpret the meaning of the coefficient?
Is y base 1 and X base 0
My thoughts are that the treatment X 0 is .47% less likely to show positive savings? 
Is it always 0 being the base in the binary or categorical? 
can I get stats model to give 0- 2 or 0-3 as Odds Ratio as well?  
 A: In your model: 
$$ y \sim Binomial(n, p) $$
$$logit(p) = \beta_0 + \beta_1 x $$
you get: 
$$ log{p \over{1-p}} = \beta_0 + \beta_1 x $$
$$ log{~O_{y|x}} = \beta_0 + \beta_1 x $$
and solving for $\beta_1$ gives you:
$$ \beta_1 = (\beta_0 + \beta_1) - \beta_0  $$
$$ ~~~~~~~~~~~~~\beta_1 = log{~O_{y|x=1}} - log{~O_{y|x=0}}  $$
$$\beta_1 = log{~O_{y|x=1} \over ~O_{y|x=0} } $$
and finally:
$$exp(\beta_1) = {O_{treatment} \over O_{control}} $$
Since your OR is in fact $exp(-.64) = 0.53$, you can convert this to a percentage via $(exp(\beta_1)-1) \times 100 = -47$% and conclude that: 
The average probability of getting positive savings is 47% lower at level "treatment" than level "control". 
If independent variable $x$ were continuous you would say:
The average probability of getting positive savings gets 47% lower for every unit increase in $x$. 
A: The OR is exp(-0.64) ~ 0.53.  This is the ratio: odds(Y=1 | X=1) / odds(Y=1 | X=0), where odds(Y=1 | X=x) is P(Y=1 | X=x) / P(Y=0 | X=x).
If X is continuous, then you get the same odds for any one-unit difference in X, e.g. odds(Y=1 | X=2) / odds(Y=1 | X=1) is also ~ 0.53.
If you want the OR for a two-unit difference, just take exp(2 * -0.64).  
