Forecasting using regression coefficients I have a regression-based model that is trained on market-level data that I'd like to use to make predictions on submarket level observations.
For example, I fit the following model on market level data:
  s ~ pop + income + home_val + employment

where, s = consumer spend. Now, I'd like to use this model and it's coefficient to make predictions for submarket level data. I'd substitute the value of the variables in the equation with that of the submarket data.
For context, market level is city or MSA, example: Greater Los Angeles. Sub-market is Beverly Hills or even zip code level. We have the exact same data for submarket - income, population, employment etc but do not have the Dependent variable - consumer spend at that level. Therefore, need to run a model on market-level data.
My questions are,

*

*Is this a valid approach?

*Do I need to consider any nuances or potential issues with the predictions?


Your first question:
Yes, this is a valid approach. If you only want to do prediction and you think a linear dependency is appropriate, this is a valid approach.
Your second question:
Of course, you could think about whether your model is sufficiently sophisticated. Maybe it would improve predictions if you considered some interaction terms. Also, selection bias could be an issue, but there is not much you can do about it (one possibility is to follow this paper, but that is probably overkill). I also don't think that Simpson's paradox is a problem as long as you only want to do prediction.
All in all, I think your approach is a decent first step. Of course, there are myriads of possible other model- or data-driven methods, but I think this is an appropriate ansatz. Just fit this simple model, then look at the residuals and some predictions and continue from there.
