I'm trying to predict a distribution of a continuous variable, that looks like the real distributions I see in my training data. As an example, say I'm trying to predict people's wages, and I know various characteristics about each person e.g. age, gender, job type.
I have a large training set, and I have tried to build a model using multiple regression.
Using this model I try to predict wages for new people (i.e. people not in my training data) - from my understanding I am predicting the average wage for a person with those characteristics. So if I plot the distribution of my predictions it does not look my distribution of real wages, as these are averages. How do I go about making my predictions that look more 'real'? It seems to me I have to add in the 'error term', but how do I do this without making assumptions about the errors?
On looking at the errors, they are not normally distributed, so I tried some non-parametric prediction alogorithms e.g. random forest, and decision trees. But the predictions from these models had a similar distribution to the ones from my regression model.
So how do I go about making a realistic distribution from my predictions, without making assumptions about the distribution of the errors?
Sorry if this is a simple question, or I'm misunderstanding - I'm new to machine learning and predictive models. This seems like it should be a common issue, but I can't find any guides that talk about it.