Two negative main effects yet positive interaction effect? I have two main effects, V1 and V2. The effects of V1 and V2 on the response variables are negative. However, for some reason I am getting positive coefficient for the interaction term V1*V2. How can I interpret this? is such situation possible?
 A: An alternative way of looking at the situation to @underminer's brilliant example is to note that under least squares regression, your fitted values satisfy "correlation constraints"
$$\sum_{ i=1}^nx_{ik}\hat{y}_i=\sum_{ i=1}^nx_{ik}y_i$$
Where $ x_{ik} $ is the value of the kth (independent/explanatory/predictor/etc) variable on the ith observation.  Note that the right hand side does not depend on what other variables are in the model.  So if "y" generally increases/decreases with the kth variable then the fitted values also will.  This is easy to see through the betas when only main effects are present, but confusing when interactions are present.
Note how interactions generally "ruin" the typical interpretation of betas as "effect on the response by increasing that variable by one unit with all other variables held constant ".  This is a useless interpretation when  interactions are present as we know that varying a single variable will alter the values for the interaction terms as well as the main effects.  In the most simple case given by  your example you have that changing $V1$ by one will alter the fitted value by 
$$\beta_1 + V2\beta_{1*2} $$
Clearly just looking at $\beta_1 $ won't give you the proper "effect" of $ V1 $ on the response.
