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I have built a logistic regression model in R and though the result appears to be satisfactory to some degree, there is one question I have not be able to address. I am not sure if my approach is at all correct.

I know that the overall purpose of the logistic model is to predict the probability of success for a binary random variable. From the same logistic model is it possible to know the probability for a given proportion? Say for instance we are interested in working out the probability of being admitted to a school, and we use a logistic regression to estimate that probability, which will obviously depends on some independent variables. My question is with the same model, is it possible to estimate the proportion of student that will be admitted in that particular school?

I have tried to use the Binomial probability to answer that but for some reason it doesn't give me the right answer. How I went about it. If we know the probability of success, then we also know that the Dependent variable follows a Binomial Distribution with Parameter N and P, where N is the Number of trials and P is the probability of success which can be estimate from the logistic model. So if I want the probability that the proportion is less or equal to say p then I thought this is equivalent to the probability that in N trials there are less or equal N*p success with the probability of success being P .

PS I know that the probability of success is an overall rate/proportion but what I am interested in is to find out the probability for a certain group. The group characteristic could be included in the model but that would be limiting in my case. Actually I am more interested in finding the probability for a proportion from the logistic model rather than the success of a certain group.

Thanks

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    $\begingroup$ If I have understood this question, it asks how to use a logistic model to estimate the distribution of the number of admitted students out of a specific pool of applicants. Such a result can be obtained, but if you are interested in applying it, then it might help to consider some of the assumptions that might be violated. In particular, computing that result has to assume that the admission of one person will not affect the chances of admitting others. If the school has a quota for certain kinds of applicants, that will not be the case, for example. $\endgroup$ – whuber Nov 13 '13 at 21:38
  • $\begingroup$ @whuber, Partly I want to estimate the number of students admitted out of a specific pool of applicants. Also of more interest though I may not have phrased it correctly, is it possible to assign a probability on the average success rate estimate from the logistic model. For example if the estimate success for a case is 85%, is there any way to find out the probability that this could be say less than 60% instead? Does it make sense now? I thought maybe I could use the standard error on the prediction to answer that, would that be correct? $\endgroup$ – ThinkStatsme Nov 13 '13 at 21:53
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If I understand your question correctly, you have predicted the probability for each individual, but want to know the average probability of a segment of those individuals? For instance you have 1000 individuals with the average rate of 65% but only 300 have blue eyes, what is the average rate of those with blue eyes? Then you can simply average your estimated probabilities for those with blue eyes.

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