Let y be a continuous random variable, x1 be a categorical variable that has 3 levels (L1, L2, L3), x2 be a categorical variable that has 2 levels ("yes" or "no"), x3 be a continuous variable.

Construct a multiple linear regression model such that we can study the effect of x3 on y and study whether the effect of x3 on y is equal across all levels of x1 and x2.