# Predicted probability from logistic regression higher than actual distribution

I am running logistic models with data where I typically have proportions for the dependent variable that looks like the following:

      0    1
Grp1  0.18 0.82
Grp2  0.24 0.76


Now I run a logistic regression with independent variables Grp (0 if Grp1 and 1 if Grp2) and control variables A, B and C (including a number of interactions) that gives me an estimate of 0.5 for Grp. I then calculate the predicted values for both groups where A, B and C are taken at their mean values, which gives me a probability of 0.82 for Grp2 and 0.88 for Grp1.

I am not sure I understand why it is possible for both groups to have a predicted probability above the actual proportions. Assuming that the calculations are correct (admittedly an ambitious assumption, although I have tried to verify with different ways of calculating the predicted values), is it theoretically possible to have higher predictions for both groups?

• Perhaps this Q&A stats.stackexchange.com/questions/25389/… will help you. – mdewey Feb 23 '17 at 12:06
• Thanks for the link, but that questions seems more concerned with turning predicted probabilities into integers. I'm more interested in whether it is theoretically possible to have predicted probabilities that are higher than the conditional probabilities calculated before running the model... – avriis Mar 3 '17 at 10:32