The Gaussian and the (log) Poisson regressions share a very interesting property,
i.e. the average predicted value is the empirical mean of our sample.
> mean(predict(lm(dist~speed,data=cars)))  42.98 > mean(cars$dist)  42.98
One can prove that it is also the prediction for the average individual in our sample
> predict(lm(dist~speed,data=cars), + newdata=data.frame(speed=mean(cars$speed))) 42.98
The geometric interpretation is that the regression line passes through the centroid,
> plot(cars) > abline(lm(dist~speed,data=cars),col="red") > abline(h=mean(cars$dist),col="blue") > abline(v=mean(cars$speed),col="blue") > points(mean(cars$speed),mean(cars$dist))
But in all other cases, it is no longer the case. Consider for instance the case of a logistic regression. And to ask for something even more complicated, consider the case where we have only categorical explanatory variables. In that context, it is more difficult to get a prediction for the “average individual”. Unless we consider some fuzzy interpretation of the regression.