Describe FAQ/suppress here.
A suppressor variable is a variable which reduces the value of a regression estimate (X1, Y) when it is added to the model. ie B(X1, Y) < B(X1, Y | X2).
Howell (1992, p.507) quotes Darlington (1990) saying that a variable (such as X2) will serve as a suppressor variable when it correlates more highly with Yr than with Y’ (where Yr represents the residual or part of Y which is unexplained by X1).
You can have, therefore, suppressor variables when all the variables (predictors and response) are positively correlated and below is an example where X2 is a suppressor variable of X1 in predicting Y. Y, X1 and X2 all have r > 0. The regression coefficient for X1 on its own with the response, Y, is 1.15 and this goes down to 1.01 when X2 is put in the regression.