#1
I have a question about multiple regression. May I kindly ask how should I interpret the conditional main effect when the interaction is 0 and the coefficients have opposite signs, more specifically if one of the interaction term contains zero such as angle or time. Please see an example representing my problem below,

z= b0+b1*X+b2*Y-b3*X*Y
Y (time) and X are continues variables

If I am not mistaken, we cannot interpret an isolated main effect, when there is a significant interaction; however, we can conditionally interpret in a whole model . If we check the effect of X on z when the time is different than 0 and and equals to zero, the equations then becomes as follow,

z1= b0+b1*X+b2*Time-b3*X*Time
z1=b0+b1*X+b2-b3*X -> y1=b0+(b1-b3*Time)*X+b2*Time

The effect of X, while increasing by one unit, on z1 is b1-b3*Time. So as time increases the effect is moving to more negative side.

z2= b0+b1*X+b2*Time(0)-b3*X*Time (0)
z2=b0-b1*X

The effect of X, while increasing by one unit, on z2 is positive b1 and it actually increase the z2. What does this practically mean? Or, should we conclude that as the Time increases the effect of X on Z1 is decreasing b1-b3*Time and you cannot individually check each time point but treat it as continues ?

Last question, is it important if main effects here X and Time are significant or not if interaction is significant.

Can someone please help me to understand this kind of equation?