# Interpretation of interaction term between 2 continuous variables

I'm running a multiple linear regression of revenue (rev) on identity (ID), an index which measures a customers identity towards a company, and firm age (Age). These two input variables are expected to depend on each other, so that the effect of identity on revenue depends on how many years a company is already established in the market. To test this, I've included an interaction term of ID*Age.

rev = b1*ID + b2*Age + b3(ID*Age) + ui


This gives me following estimated coefficients:

rev = 0.7*ID + 0.1*Age + -0.003(ID*Age) + ui


The coefficient of ID and the interaction term are statistically significant. I'm not sure about how to interpret the negative interaction term. Is it correct to interpret it as follow:

The effect of ID on revenue depends negatively on age. So that the effect on an increase in identity will be weaker (lesser) if the company is older (Age is bigger).

Is that equal to the following interpretation: Identity is weaker for older firms.

Therefore, I could conclude that identity does play a (slightly) more important role for younger companies.