Can I use linear regression analysis in order to remove estimated effect of an independent variable so that I can find the effect of another variable? I have a dependent variable (DV) that is influenced by an independent variable (IV). However, I know that it is also influnced by another factor (F), for which I don't have any values. My hypothesis is that DV is influenced only by these two factors, IV and F.
What I want is to remove the estimated effect of IV on DV and find a new DV with only the effect of F remaining.
I tried the following steps:

*

*I did linear regression analysis of IV on DV

*I derived the estimated values of DV based only on the effect of IV, using the estimated equation y_iv=a+b*x, where y_iv are the estimated values of DV based only on the effect of IV and x is the IV.

*Ι subtracted y_iv from DV in order to find the estimated values of DV based only on the effect of F: y_f = DV-y_iv

*At the end, I want to use the mean value of y_f.

Does all this makes sense?
There must be (at least) one mistake because mean(y_f) is always zero! That means that mean(DV) equals mean(y_iv).

What you have done is removed the linear association between the outcome DV and predictor IV, leaving only the residual values not explained by that simple regression. Those residuals necessarily sum to 0, as you have found. It's not that the mean of DV is 0, it's that the mean difference between actual DV values and what's predicted by the regression is necessarily 0.
On the average, as a result, there is nothing left for F to explain. That doesn't mean that F is unimportant, but without data on F you can't estimate it. If you had data on F you might find that it explains a good deal of the variation in residual values; that's actually one way that multiple regression is sometimes explained.
