This question has two parts. On for the linear case, and one for the logistic case. Say X is a continous variable and we want to see how x affects the response when looking between two different groups. Say G1=Group1, G2=Group2 In linear regression, we can plot the regression lines using the estimated coefficients to see if there is an interaction between two different groups. If they are parallel, then that suggests interaction, if they are not, then that suggests the opposite. Then I would check the p value of the coefficient to see if this is really the case. Is that true? If it is, then why even plot using the estimated coefficients? The p values should be enough. if p!= 0 for the wald test for the interaction term, then there is insufficient evidence for interaction. Is it because if p=0, we still want to see just how much interaction there is? But wouldn't the absolute value of the interaction coeff be a good hint. Or do we still need visualization? What about for logistic regression. So I look at the probability curve, P[Y=1|X,G1] and P[Y=1|X,G2]. If the difference . delta =P[Y=1|X,G1] - P[Y=1|X,G2] is a constant at each X, then does that mean there is no interaction? Is this like the linear case?