Regression against the mean

#1
Hi, the data behaves in a certain way. It has the tendency to regress to the mean as well as is correlated to another factor Y. Is it correct to do a multiple regression and regress the dependent variable against its own mean and factor Y?
 
#2
When you are saying "has the tendency to regress to the mean", do you mean "has the tendency to revert to the mean over time"? If yes and you can monitor the dependent variable over time, a time series model would be appropriate. Such a model would differ from the simple linear regression you described because it would contain

1] autoregressive terms,
2] moving average terms,
3] deterministic trends,

generally speaking. The model may also contain jumps, stochastic volatility components, other predictors, etc. The complexity of modeling depends on how much data you have and what you see in the data.