Let's suppose I just want to run two regressions:
Y = b0 + b1x1
Y = b0 + b1x1 + b2x2
The idea here is that I want to see what happens to b1 when I include x2 into the regression. The problem is, I know that there is a third factor (which I can easily measure) which affects both x2 and Y. Therefore, including x2 without x3 will lead to a bias.
The catch is, I do not want to include x3. I just want to know what happens to b1 after including x2. Is anybody aware of any method in which I can accomplish this? For example, I imagine there might be a way to condition my values of x2 on values of x3 and include that in the second regression. Thanks so much!