Regression with averaged data

I have data that represents the average for a group, which I would like to use for my response variable. I have different variables that are collected about my groups, and would like to predict the average using a linear model. While the usual assumptions don't hold for the individual data (and I don't want to predict for the individuals anyway), the assumptions for a linear model for the averaged data seem to hold quite well. Are there any precautions doing things this way? Is it okay to go ahead and use my linear model to predict averages for a group? How would I interpret the prediction interval in this case? Thank you in advance.