A regression model with a dummy variable

d, a quantitative variable x , and an interaction variable xd is specified b y y = β 0 + β1x + β 2d + β 3xd + ε . We estimate this model to make predictions as ŷ = (b0 + b2) + (b1 + b3)x for d = 1, and as ŷ = b0 + b1x for d = 0. In addition, we can perform the t test to determine the significance of d or xd. Similarly, we can implement the partial F test to determine the joint significance of d and xd.