How to reduce the final set of significant variables from logistic model? I have built a logistic model, which has 40 significant predictors, p value<0.0001.
I want to reduce them to say about 10 variables, so that it can be presented to business. How do i go about doing that?
 A: See Harrell (2001), Regression Modeling Strategies, Ch. 5.4, pp 99 – 101.
Fit a linear model to the predicted values (on the logit scale), & use a backward stepwise procedure, stopping when the coefficient of determination falls below say 95%, or when you've reduced the predictors by as many as you wanted to. You've then got a straightforward measure of how much predictive power you've lost in the selection. (And if you're doing penalized regression the shrinkage will automatically be passed on to the approximate model.) Rough & ready inference can be based on a covariance matrix for the coefficient estimates derived from that of the full model.
All the same I'd still usually prefer presenting the most salient features of the full model & ignoring details. Plotting the relation of the most important predictors to the response at typical values of the others usually gets the idea across.
A: The following approach is computationally intensive, but it's intuitive and will achieve the goal that you're after.
First step is to split your dataset into three partitions: Train, Test, and Validate.
For the Train partition, follow these steps:
(1) For each one of the 40 predictors, build a one-variable model. Select the best one-variable model based on a statistical criteria (e.g., AUC).
(2) For each of the remaining 39 variables, add it to the best one-variable model to create 39 two-variable models. Select the best two-variable model based on the same  statistical criteria.
(3) For each of the remaining 38 variables...
..
..
(40)
At the end of this process, you will have 40 models: best one-variable model, best two-variable model, and so on.
Using each one of these models, score the Test partition (i.e., apply the same algorithm on the Test partition) and calculate the same statistical measure that you chose to select the best models in steps 1 thru 40.
Now you have 40 pairs of a statistical measure. Plot them on a line chart and find the inflection point (elbow/bend) in the curve. You will notice that the metric improves as you add more features to the model, but the improvement rate will decrease/diminish as you keep adding more features. Also, the gap between your Train and Test measures would widen as more features are added. 
Your best (parsimonious) model is where you detect the bend in the curve.
