Hello again to this wonderful community!

Quick question - I have a mathematical background but relatively new to finance and struggling to get my head round one vital point: how do we use the outputs from our regression analyses to predict returns, for example, equity returns? This is referenced in the 'Fundamental Factor Models' lecture with this line "Modeling future returns is accomplished by offsetting the returns in the regression, so that rather than predict for current returns, you are predicting for future returns. Once you have a predictive model, the most canonical way to create a strategy is to attempt a long-short equity approach." however I confess I don't know what is meant by 'offsetting the returns' in order to predict future, instead of current.

I understand that I can breakdown the predicted return of an asset into its alpha and various betas, but how do I then use those betas to predict the return? Taking a simple single linear regression example - let's say I find the beta of a stock and the SPY, and test for statistical significance and normality, kurtosis, heteroskedasticity etc - yes I know how the stock will vary as a function of the SPY, but surely by the time the SPY rises/falls, then the equity price will have already risen/fallen by the predicted amount, by the time I buy or sell? Thus how is it a prediction, given it gives me no insight into the future performance, only the current performance?

That is to say - doesn't the beta describe the price of the respective stock after the fact, instead of predicting what it will be in the future?

Happy to be pointed at a journal article or research paper!

Thanks in advance you wonderful Quantopians!!!