I have a small theoretical question. Is it correct to use multivariate linear regression to control for confounders ?
for example, if I want to check the relation between X1 and Y, and I know, that Y is strongly influenced by X2 and X3 too, will putting all 3 X's in the model give me the "real" relation between X1 and Y ?
In other words, if I include all 3 X's, will the p-value of the coefficient of X1 tell me reliably if X1 and Y are correlated ?
If you model the multiple regression model correctly like: y= a + b1x1 + b2x2 + b3x3 and your b3-coefficient is significantly different from zero, x3 has a significant relation with y even when you control for the variation in x1 and x2 -which could be potential confounders.