In my model I want to include two dummies ($d_1$,$d_2$) and also the interaction effects of these two dummies with another independent variable, $x_1$. The interaction terms are $x_1\cdot d_1$,$x_1 \cdot d_2$. The model also includes six other independent variables.
I run the model with all variables. Could I consider the interaction terms ($x_1 \cdot d_1$ and $x_1 \cdot d_2$) reliable if I find each of $x_1$, $d_1$, $d_2$ variables statistically significant but their interaction terms $x_1 \cdot d_1$, $x_1 \cdot d_2$ not statistically significant? In addition, if I find these results should I remove the interaction terms from the model? Since there is no reason to use them.