I'm trying to forecast next month's sales using linear regression for a company with ten products, with 24 months of data. Will I get the same results if I aggregate all the revenues of all the products or would I get a different total revenue number if I forecast each product individually and then sum the forecasts?Thanks

A quick answer, although I may be mistaken and would appreciate it if corrected:Since the regression that you're applying and the aggregation of the revenues are both linear processes, then it shouldn't matter. This, of course, implicitly assumes that the revenues of the different products are not correlated with each other over time, which is a requirement for the regression to be valid.

I think its a good thing to start with the multivariate regression (all 10 products) and then take care of any multicollinearity (or correlations as mentioned by rcohen below) once you have the model.I tried doing something similar though, and it failed miserably not because i didnt do the regression right, but i could not identify all the variables that affect my Y in the regression. It will be interesting to see what fit you get from the model. If you dont get a great fit, one of the reasons might be exogeneous factors (like increased marketing effort this quarter more than previous quarters) that are typically not measurable.(although you can try and create proxy variables)

It depends on the objective. If the objective is to get overall company revenue. Then adding all the values at once would be better - Occam's Razor - simpler is better.However if your objective is to understand the individual product revenue dynamics - especially if you believe that the true relationship for some prdocut lines may not necessarily be linear (perhaps log or quadratic) then you should forecast seperately. Forecast seperately only if you want to understand individual product line estimates. Else just do it all at once. Multicollinearity is less serious an issue for prediction. Besides for 24 months - your sample size is small so you are bound to have so low T-stats. Remember multicollinearity is also a small sample (which results in low T-stats) issue.

I'm not sure exactly what you mean. Are you regressing S_t on S_t-1? It is not likely that would be linear fit. However, if you do that, you will get different answers by aggregating, as rcohen says, due to the correlation between products.Suppose you had only two products and, for simplicity, both have mean zero and standard deviation 1. Then the formula for Beta is just the sum of XY. If you add products your Beta will be the sum of (X + X')(Y + Y') which is the sum of Beta and Beta' plus the cross Betas from estimating next month's sales of product B based on this month's sales of product A.