Trading Strategies and Portfolio Constructions based on Cross Sectional Regression?

Hi all,

I often see trading strategies and portfolio construction that are based on cross-sectional regression.

For example, I often see regressing some numbers against some factors.

I was wondering how cross-sectional regression is used in these scenarios?

And how does a cross-sectional regression have forecasting power?

And how is the goodness-of-fit of the regression related to the forecasting power?

I have been reading some portfolio management books but couldn't find the application of cross-sectional regression and the relation between the regression and the forecasting power...

Could anybody please shed some lights on me?

Thanks a lot!