Hi guys, first post here!

First some background information: I am doing a study that examines whether patents and trademarks (2 independent variables) influence gross margin (dependent variable). Now I speculate that both relationships are moderated by firm size, measured as number of employees (2 moderating variables).

To create the moderating variables, I centralized number of employees, amount of trademarks and amount of patents by subtracting the mean from all the corresponding data. I multiplied the centralized number of employees with centralized amount of trademarks and amount of patents, creating two moderating variables for my regression.

Aditionally, I control for 7 different industries (7 dummy variables), firm age, and whether a firm is state owned or not as these might impact the gross margin of a firm as well.

These are my regression results, where the first model excludes the moderator and the second model includes them, named firmsize_patents and firmsize_trademarks:

My questions are:

1) Are the steps I have taken to measure moderation done correctly?
2) When I leave one of the moderators out of the model, it leads to a very high statistical insignificance for the remaining other moderator, is this normal?
3) Apparently, when using multiple dummies for the same construct (in my case industry) you need to leave one dummy out of the regression, is this true? I left one industry dummy out of the independent variables which thus forms the 'base-level'